LeanEuler Demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from PW_explorer.pwe_nb_helper import ASPRules\n",
    "from LeanEuler.lean_euler import LeanEuler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "IPython.CodeCell.options_default.highlight_modes['prolog'] = {'reg':[/^%%(clingo|dlv)/]};"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%load_ext PWE_NB_Extension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from nxpd import draw\n",
    "from nxpd import nxpdParams\n",
    "nxpdParams['show'] = 'ipynb'\n",
    "from IPython.display import Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Experiment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Taxonomy Alignment Problem Instance\n",
    "\n",
    "Below we have a simple TAP instance in the CleanTax format"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "taxonomy 1 Taxonomy1\n",
      "(A B C D E)\n",
      "\n",
      "taxonomy 2 Taxonomy2\n",
      "(A B D F G)\n",
      "\n",
      "articulation abs abstract\n",
      "[1.A {is_included_in equals} 2.A]\n",
      "[1.B equals 2.B]\n",
      "[1.C {is_included_in overlaps} 2.F]\n",
      "[1.D equals 2.D]\n",
      "[1.E {equals overlaps} 2.G]\n"
     ]
    }
   ],
   "source": [
    "with open('cleanTax_files/abstract4.txt', 'r') as f:\n",
    "    cleantax_sample_file = f.read().splitlines()\n",
    "print(\"\\n\".join(cleantax_sample_file))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use LeanEuler to parse it and create an internal representation of the problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "rel_desc_dfs, taxonomy_trees = LeanEuler.parse_cleantax(cleantax_sample_file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Node1</th>\n",
       "      <th>Relation</th>\n",
       "      <th>Node2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>\"1_A\"</td>\n",
       "      <td>parent</td>\n",
       "      <td>\"1_B\"</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>\"1_A\"</td>\n",
       "      <td>parent</td>\n",
       "      <td>\"1_C\"</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>\"1_A\"</td>\n",
       "      <td>parent</td>\n",
       "      <td>\"1_D\"</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>\"1_A\"</td>\n",
       "      <td>parent</td>\n",
       "      <td>\"1_E\"</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>\"2_A\"</td>\n",
       "      <td>parent</td>\n",
       "      <td>\"2_B\"</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>\"2_A\"</td>\n",
       "      <td>parent</td>\n",
       "      <td>\"2_D\"</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>\"2_A\"</td>\n",
       "      <td>parent</td>\n",
       "      <td>\"2_F\"</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>\"2_A\"</td>\n",
       "      <td>parent</td>\n",
       "      <td>\"2_G\"</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>\"1_A\"</td>\n",
       "      <td>&lt;,=</td>\n",
       "      <td>\"2_A\"</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>\"1_B\"</td>\n",
       "      <td>=</td>\n",
       "      <td>\"2_B\"</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>\"1_C\"</td>\n",
       "      <td>&lt;,o</td>\n",
       "      <td>\"2_F\"</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>\"1_D\"</td>\n",
       "      <td>=</td>\n",
       "      <td>\"2_D\"</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>\"1_E\"</td>\n",
       "      <td>=,o</td>\n",
       "      <td>\"2_G\"</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Node1 Relation  Node2\n",
       "0   \"1_A\"   parent  \"1_B\"\n",
       "1   \"1_A\"   parent  \"1_C\"\n",
       "2   \"1_A\"   parent  \"1_D\"\n",
       "3   \"1_A\"   parent  \"1_E\"\n",
       "4   \"2_A\"   parent  \"2_B\"\n",
       "5   \"2_A\"   parent  \"2_D\"\n",
       "6   \"2_A\"   parent  \"2_F\"\n",
       "7   \"2_A\"   parent  \"2_G\"\n",
       "8   \"1_A\"      <,=  \"2_A\"\n",
       "9   \"1_B\"        =  \"2_B\"\n",
       "10  \"1_C\"      <,o  \"2_F\"\n",
       "11  \"1_D\"        =  \"2_D\"\n",
       "12  \"1_E\"      =,o  \"2_G\""
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rel_desc_dfs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'1': {'1': Node('/1'),\n",
       "  'A': Node('/1/\"1_A\"'),\n",
       "  'B': Node('/1/\"1_A\"/\"1_B\"'),\n",
       "  'C': Node('/1/\"1_A\"/\"1_C\"'),\n",
       "  'D': Node('/1/\"1_A\"/\"1_D\"'),\n",
       "  'E': Node('/1/\"1_A\"/\"1_E\"')},\n",
       " '2': {'2': Node('/2'),\n",
       "  'A': Node('/2/\"2_A\"'),\n",
       "  'B': Node('/2/\"2_A\"/\"2_B\"'),\n",
       "  'D': Node('/2/\"2_A\"/\"2_D\"'),\n",
       "  'F': Node('/2/\"2_A\"/\"2_F\"'),\n",
       "  'G': Node('/2/\"2_A\"/\"2_G\"')}}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "taxonomy_trees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# from anytree.exporter import DotExporter\n",
    "# taxonomy_tree_images = []\n",
    "# for k in taxonomy_trees.keys():\n",
    "#     t = DotExporter(taxonomy_trees[k][k])\n",
    "#     t.to_picture('{}.png'.format(k))\n",
    "#     taxonomy_tree_images.append(Image('{}.png'.format(k)))\n",
    "# display(*taxonomy_tree_images)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using these internal representations, we can visualize the input TAP instance as shown below using a simple function call:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "input_constraints_g = LeanEuler.visualize_input(rel_desc_dfs, taxonomy_trees)\n",
    "draw(input_constraints_g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Directly from the file (skipping the intermediate step)\n",
    "input_constraints_g = LeanEuler.visualize_input_from_cleantax(cleantax_sample_file)\n",
    "draw(input_constraints_g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can encode this TAP instance in ASP using LeanEuler:"
   ]
  },
  {
   "cell_type": "code",
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       "<div class=\"highlight\"><pre><span></span><span class=\"lineno\"> 1 </span><span class=\"c1\">%RCC RULES:</span>\n",
       "<span class=\"lineno\"> 2 </span>\n",
       "<span class=\"lineno\"> 3 </span><span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 4 </span><span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 5 </span><span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 6 </span><span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 7 </span><span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 8 </span>\n",
       "<span class=\"lineno\"> 9 </span><span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">10 </span><span class=\"mi\">1</span> <span class=\"p\">{</span><span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)}</span> <span class=\"p\">:-</span> <span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">11 </span><span class=\"mi\">1</span> <span class=\"p\">{</span><span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)}</span> <span class=\"p\">:-</span> <span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">12 </span><span class=\"mi\">1</span> <span class=\"p\">{</span><span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)}</span> <span class=\"p\">:-</span> <span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">13 </span>\n",
       "<span class=\"lineno\">14 </span><span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">15 </span><span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">16 </span><span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">17 </span><span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">18 </span>\n",
       "<span class=\"lineno\">19 </span><span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">20 </span><span class=\"mi\">1</span> <span class=\"p\">{</span><span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)}</span> <span class=\"p\">:-</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">21 </span><span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">22 </span><span class=\"mi\">1</span> <span class=\"p\">{</span><span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)}</span> <span class=\"p\">:-</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">23 </span>\n",
       "<span class=\"lineno\">24 </span><span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">25 </span><span class=\"mi\">1</span> <span class=\"p\">{</span><span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)}</span> <span class=\"p\">:-</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">26 </span><span class=\"mi\">1</span> <span class=\"p\">{</span><span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)}</span> <span class=\"p\">:-</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">27 </span><span class=\"mi\">1</span> <span class=\"p\">{</span><span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)}</span> <span class=\"p\">:-</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">Z</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">28 </span>\n",
       "<span class=\"lineno\">29 </span><span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">30 </span><span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"k\">_</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">31 </span><span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">32 </span><span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"k\">_</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">33 </span><span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">34 </span><span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"k\">_</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">35 </span><span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">36 </span><span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"k\">_</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">37 </span><span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">38 </span><span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"k\">_</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">39 </span><span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"k\">_</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">40 </span><span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">41 </span>\n",
       "<span class=\"lineno\">42 </span><span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">43 </span><span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">44 </span><span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">45 </span><span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">46 </span><span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">47 </span><span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">48 </span><span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">),</span> <span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Z</span><span class=\"p\">),</span> <span class=\"nv\">Y</span> <span class=\"p\">!</span><span class=\"o\">=</span> <span class=\"nv\">Z</span><span class=\"p\">.</span>\n",
       "<span class=\"lineno\">49 </span><span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">50 </span>\n",
       "<span class=\"lineno\">51 </span><span class=\"mi\">1</span> <span class=\"p\">{</span><span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)}</span> <span class=\"p\">:-</span> <span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">),</span> <span class=\"nv\">X</span> <span class=\"p\">!</span><span class=\"o\">=</span> <span class=\"nv\">Y</span><span class=\"p\">.</span>\n",
       "<span class=\"lineno\">52 </span>\n",
       "<span class=\"lineno\">53 </span><span class=\"p\">:-</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">),</span> <span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">54 </span><span class=\"p\">:-</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">),</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">55 </span><span class=\"p\">:-</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">),</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">56 </span><span class=\"p\">:-</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">),</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">57 </span><span class=\"p\">:-</span> <span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">),</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">58 </span><span class=\"p\">:-</span> <span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">),</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">59 </span><span class=\"p\">:-</span> <span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">),</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">60 </span><span class=\"p\">:-</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">),</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">61 </span><span class=\"p\">:-</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">),</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">62 </span><span class=\"p\">:-</span> <span class=\"nf\">pi</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">),</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">63 </span>\n",
       "<span class=\"lineno\">64 </span><span class=\"c1\">%TAXONOMY DESC RULES</span>\n",
       "<span class=\"lineno\">65 </span>\n",
       "<span class=\"lineno\">66 </span><span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">67 </span><span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">68 </span><span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">69 </span><span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">70 </span><span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">71 </span><span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">72 </span><span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">73 </span><span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">74 </span><span class=\"mi\">1</span> <span class=\"p\">{</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">)</span> <span class=\"p\">}.</span>\n",
       "<span class=\"lineno\">75 </span><span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">76 </span><span class=\"mi\">1</span> <span class=\"p\">{</span> <span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">)</span> <span class=\"p\">}.</span>\n",
       "<span class=\"lineno\">77 </span><span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">78 </span><span class=\"mi\">1</span> <span class=\"p\">{</span> <span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">)</span> <span class=\"p\">}.</span>\n",
       "</pre></div>\n"
      ],
      "text/plain": [
       "'%RCC RULES:\\n\\neq(X,Y) :- eq(X,Z), eq(Z,Y).\\ndr(X,Y) :- eq(X,Z), dr(Z,Y).\\npp(X,Y) :- eq(X,Z), pp(Z,Y).\\npi(X,Y) :- eq(X,Z), pi(Z,Y).\\npo(X,Y) :- eq(X,Z), po(Z,Y).\\n\\ndr(X,Y) :- dr(X,Z), eq(Z,Y).\\n1 {dr(X,Y) ; pp(X,Y) ; po(X,Y)} :- dr(X,Z), pp(Z,Y).\\n1 {dr(X,Y) ; pi(X,Y) ; po(X,Y)} :- dr(X,Z), pi(Z,Y).\\n1 {dr(X,Y) ; pp(X,Y) ; po(X,Y)} :- dr(X,Z), po(Z,Y).\\n\\npp(X,Y) :- pp(X,Z), eq(Z,Y).\\ndr(X,Y) :- pp(X,Z), dr(Z,Y).\\npp(X,Y) :- pp(X,Z), pp(Z,Y).\\ndr(X,Y) ; pp(X,Y) ; po(X,Y) :- pp(X,Z), po(Z,Y).\\n\\npi(X,Y) :- pi(X,Z), eq(Z,Y).\\n1 {dr(X,Y) ; pi(X,Y) ; po(X,Y)} :- pi(X,Z), dr(Z,Y).\\npi(X,Y) :- pi(X,Z), pi(Z,Y).\\n1 {pi(X,Y) ; po(X,Y)} :- pi(X,Z), po(Z,Y).\\n\\npo(X,Y) :- po(X,Z), eq(Z,Y).\\n1 {dr(X,Y) ; pi(X,Y) ; po(X,Y)} :- po(X,Z), dr(Z,Y).\\n1 {pp(X,Y) ; po(X,Y)} :- po(X,Z), pp(Z,Y).\\n1 {dr(X,Y) ; pi(X,Y) ; po(X,Y)} :- po(X,Z), pi(Z,Y).\\n\\nu(X) :- dr(X,_).\\nu(X) :- dr(_,X).\\nu(X) :- eq(X,_).\\nu(X) :- eq(_,X).\\nu(X) :- po(X,_).\\nu(X) :- po(_,X).\\nu(X) :- pp(X,_).\\nu(X) :- pp(_,X).\\nu(X) :- pi(X,_).\\nu(X) :- pi(_,X).\\nu(X) :- bl(_,X).\\nu(X) :- bl(X,_).\\n\\neq(X,X) :- u(X).\\npi(X,Y) :- pp(Y,X).\\npp(X,Y) :- pi(Y,X).\\neq(X,Y) :- eq(Y,X).\\npo(X,Y) :- po(Y,X).\\ndr(X,Y) :- dr(Y,X).\\ndr(Y,Z) :- bl(X,Y), bl(X,Z), Y != Z.\\npp(Y,X) :- bl(X,Y).\\n\\n1 {eq(X,Y) ; dr(X,Y) ; pp(X,Y) ; pi(X,Y) ; po(X,Y)} :- u(X), u(Y), X != Y.\\n\\n:- eq(X,Y), dr(X,Y).\\n:- eq(X,Y), pp(X,Y).\\n:- eq(X,Y), pi(X,Y).\\n:- eq(X,Y), po(X,Y).\\n:- dr(X,Y), pp(X,Y).\\n:- dr(X,Y), pi(X,Y).\\n:- dr(X,Y), po(X,Y).\\n:- pp(X,Y), pi(X,Y).\\n:- pp(X,Y), po(X,Y).\\n:- pi(X,Y), po(X,Y).\\n\\n%TAXONOMY DESC RULES\\n\\nbl(\"1_A\",\"1_B\").\\nbl(\"1_A\",\"1_C\").\\nbl(\"1_A\",\"1_D\").\\nbl(\"1_A\",\"1_E\").\\nbl(\"2_A\",\"2_B\").\\nbl(\"2_A\",\"2_D\").\\nbl(\"2_A\",\"2_F\").\\nbl(\"2_A\",\"2_G\").\\n1 { pp(\"1_A\",\"2_A\") ; eq(\"1_A\",\"2_A\") }.\\neq(\"1_B\",\"2_B\").\\n1 { pp(\"1_C\",\"2_F\") ; po(\"1_C\",\"2_F\") }.\\neq(\"1_D\",\"2_D\").\\n1 { eq(\"1_E\",\"2_G\") ; po(\"1_E\",\"2_G\") }.'"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "euler_asp_alignment_rules = LeanEuler.gen_asp_rules(rel_desc_dfs, taxonomy_trees, encoding='rcc')\n",
    "ASPRules(\"\\n\".join(euler_asp_alignment_rules))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <style>\n",
       "        .highlight .hll { background-color: #ffffcc }\n",
       ".highlight  { background: #f8f8f8; }\n",
       ".highlight .c { color: #408080; font-style: italic } /* Comment */\n",
       ".highlight .err { border: 1px solid #FF0000 } /* Error */\n",
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       "<div class=\"highlight\"><pre><span></span><span class=\"lineno\">  1 </span><span class=\"nf\">r</span><span class=\"p\">(</span><span class=\"mf\">1..24</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">  2 </span>\n",
       "<span class=\"lineno\">  3 </span><span class=\"c1\">% Region Meanings</span>\n",
       "<span class=\"lineno\">  4 </span><span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">M</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">r</span><span class=\"p\">(</span><span class=\"nv\">M</span><span class=\"p\">),</span> <span class=\"nf\">concept</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">T</span><span class=\"p\">,</span> <span class=\"nv\">N</span><span class=\"p\">),</span> <span class=\"nv\">N1</span><span class=\"o\">=</span><span class=\"nv\">N</span><span class=\"o\">+</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"nf\">bit</span><span class=\"p\">(</span><span class=\"nv\">M</span><span class=\"p\">,</span> <span class=\"nv\">T</span><span class=\"p\">,</span> <span class=\"nv\">N1</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">  5 </span><span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">M</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">r</span><span class=\"p\">(</span><span class=\"nv\">M</span><span class=\"p\">),</span> <span class=\"nf\">concept</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">T</span><span class=\"p\">,</span> <span class=\"nv\">N</span><span class=\"p\">),</span> <span class=\"nv\">N1</span><span class=\"o\">=</span><span class=\"nv\">N</span><span class=\"o\">+</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"o\">not</span> <span class=\"nf\">bit</span><span class=\"p\">(</span><span class=\"nv\">M</span><span class=\"p\">,</span> <span class=\"nv\">T</span><span class=\"p\">,</span> <span class=\"nv\">N1</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">  6 </span><span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">M</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">r</span><span class=\"p\">(</span><span class=\"nv\">M</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"k\">_</span><span class=\"p\">),</span> <span class=\"o\">not</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">M</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">  7 </span><span class=\"nf\">irs</span><span class=\"p\">(</span><span class=\"nv\">M</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">M</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">M</span><span class=\"p\">),</span> <span class=\"nf\">r</span><span class=\"p\">(</span><span class=\"nv\">M</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">  8 </span>\n",
       "<span class=\"lineno\">  9 </span><span class=\"c1\">% Region Constraints</span>\n",
       "<span class=\"lineno\"> 10 </span><span class=\"nf\">irs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 11 </span><span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">vr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 12 </span><span class=\"nf\">vr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"o\">not</span> <span class=\"nf\">irs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">r</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 13 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"o\">not</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">r</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 14 </span><span class=\"p\">:-</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">irs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 15 </span>\n",
       "<span class=\"lineno\"> 16 </span><span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">concept</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">,</span><span class=\"nv\">B</span><span class=\"p\">,</span><span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 17 </span>\n",
       "<span class=\"lineno\"> 18 </span><span class=\"c1\">% Taxonomy Description</span>\n",
       "<span class=\"lineno\"> 19 </span>\n",
       "<span class=\"lineno\"> 20 </span><span class=\"c1\">%  Euler Bit</span>\n",
       "<span class=\"lineno\"> 21 </span><span class=\"nf\">bit</span><span class=\"p\">(</span><span class=\"nv\">M</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"nv\">V</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">r</span><span class=\"p\">(</span><span class=\"nv\">M</span><span class=\"p\">),</span> <span class=\"nv\">M1</span><span class=\"o\">=</span><span class=\"nv\">M</span><span class=\"o\">/</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"nv\">V</span> <span class=\"o\">=</span> <span class=\"nv\">M1</span> <span class=\"s s-Atom\">\\</span> <span class=\"mf\">5.</span>\n",
       "<span class=\"lineno\"> 22 </span>\n",
       "<span class=\"lineno\"> 23 </span><span class=\"c1\">%  Euler Bit</span>\n",
       "<span class=\"lineno\"> 24 </span><span class=\"nf\">bit</span><span class=\"p\">(</span><span class=\"nv\">M</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"nv\">V</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">r</span><span class=\"p\">(</span><span class=\"nv\">M</span><span class=\"p\">),</span> <span class=\"nv\">M1</span><span class=\"o\">=</span><span class=\"nv\">M</span><span class=\"o\">/</span><span class=\"mi\">5</span><span class=\"p\">,</span> <span class=\"nv\">V</span> <span class=\"o\">=</span> <span class=\"nv\">M1</span> <span class=\"s s-Atom\">\\</span> <span class=\"mf\">5.</span>\n",
       "<span class=\"lineno\"> 25 </span>\n",
       "<span class=\"lineno\"> 26 </span><span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 27 </span><span class=\"nf\">concept</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 28 </span><span class=\"nf\">concept</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 29 </span><span class=\"nf\">concept</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 30 </span><span class=\"nf\">concept</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">3</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 31 </span><span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 32 </span><span class=\"nf\">concept</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 33 </span><span class=\"nf\">concept</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 34 </span><span class=\"nf\">concept</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 35 </span><span class=\"nf\">concept</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">3</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 36 </span>\n",
       "<span class=\"lineno\"> 37 </span><span class=\"c1\">% &quot;1_B&quot; isa &quot;1_A&quot;</span>\n",
       "<span class=\"lineno\"> 38 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r6</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 39 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 40 </span>\n",
       "<span class=\"lineno\"> 41 </span><span class=\"c1\">% &quot;1_C&quot; isa &quot;1_A&quot;</span>\n",
       "<span class=\"lineno\"> 42 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r7</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 43 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 44 </span>\n",
       "<span class=\"lineno\"> 45 </span><span class=\"c1\">% &quot;1_D&quot; isa &quot;1_A&quot;</span>\n",
       "<span class=\"lineno\"> 46 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r8</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 47 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 48 </span>\n",
       "<span class=\"lineno\"> 49 </span><span class=\"c1\">% &quot;1_E&quot; isa &quot;1_A&quot;</span>\n",
       "<span class=\"lineno\"> 50 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r9</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 51 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 52 </span>\n",
       "<span class=\"lineno\"> 53 </span><span class=\"c1\">% &quot;2_B&quot; isa &quot;2_A&quot;</span>\n",
       "<span class=\"lineno\"> 54 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r16</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 55 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 56 </span>\n",
       "<span class=\"lineno\"> 57 </span><span class=\"c1\">% &quot;2_D&quot; isa &quot;2_A&quot;</span>\n",
       "<span class=\"lineno\"> 58 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r17</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 59 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 60 </span>\n",
       "<span class=\"lineno\"> 61 </span><span class=\"c1\">% &quot;2_F&quot; isa &quot;2_A&quot;</span>\n",
       "<span class=\"lineno\"> 62 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r18</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 63 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 64 </span>\n",
       "<span class=\"lineno\"> 65 </span><span class=\"c1\">% &quot;2_G&quot; isa &quot;2_A&quot;</span>\n",
       "<span class=\"lineno\"> 66 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r19</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 67 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 68 </span>\n",
       "<span class=\"lineno\"> 69 </span><span class=\"c1\">% Coverage for &quot;1_A&quot;</span>\n",
       "<span class=\"lineno\"> 70 </span><span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 71 </span>\n",
       "<span class=\"lineno\"> 72 </span><span class=\"c1\">% Coverage for &quot;2_A&quot;</span>\n",
       "<span class=\"lineno\"> 73 </span><span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 74 </span>\n",
       "<span class=\"lineno\"> 75 </span><span class=\"c1\">% &quot;1_B&quot; ! &quot;1_C&quot;</span>\n",
       "<span class=\"lineno\"> 76 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r0</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 77 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 78 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 79 </span>\n",
       "<span class=\"lineno\"> 80 </span><span class=\"c1\">% &quot;1_B&quot; ! &quot;1_D&quot;</span>\n",
       "<span class=\"lineno\"> 81 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r1</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 82 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 83 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 84 </span>\n",
       "<span class=\"lineno\"> 85 </span><span class=\"c1\">% &quot;1_B&quot; ! &quot;1_E&quot;</span>\n",
       "<span class=\"lineno\"> 86 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r2</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 87 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 88 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 89 </span>\n",
       "<span class=\"lineno\"> 90 </span><span class=\"c1\">% &quot;1_C&quot; ! &quot;1_D&quot;</span>\n",
       "<span class=\"lineno\"> 91 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r3</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 92 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 93 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 94 </span>\n",
       "<span class=\"lineno\"> 95 </span><span class=\"c1\">% &quot;1_C&quot; ! &quot;1_E&quot;</span>\n",
       "<span class=\"lineno\"> 96 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r4</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 97 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 98 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\"> 99 </span>\n",
       "<span class=\"lineno\">100 </span><span class=\"c1\">% &quot;1_D&quot; ! &quot;1_E&quot;</span>\n",
       "<span class=\"lineno\">101 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r5</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">102 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">103 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">104 </span>\n",
       "<span class=\"lineno\">105 </span><span class=\"c1\">% &quot;2_B&quot; ! &quot;2_D&quot;</span>\n",
       "<span class=\"lineno\">106 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r10</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">107 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">108 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">109 </span>\n",
       "<span class=\"lineno\">110 </span><span class=\"c1\">% &quot;2_B&quot; ! &quot;2_F&quot;</span>\n",
       "<span class=\"lineno\">111 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r11</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">112 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">113 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">114 </span>\n",
       "<span class=\"lineno\">115 </span><span class=\"c1\">% &quot;2_B&quot; ! &quot;2_G&quot;</span>\n",
       "<span class=\"lineno\">116 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r12</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">117 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">118 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">119 </span>\n",
       "<span class=\"lineno\">120 </span><span class=\"c1\">% &quot;2_D&quot; ! &quot;2_F&quot;</span>\n",
       "<span class=\"lineno\">121 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r13</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">122 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">123 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">124 </span>\n",
       "<span class=\"lineno\">125 </span><span class=\"c1\">% &quot;2_D&quot; ! &quot;2_G&quot;</span>\n",
       "<span class=\"lineno\">126 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r14</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">127 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">128 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">129 </span>\n",
       "<span class=\"lineno\">130 </span><span class=\"c1\">% &quot;2_F&quot; ! &quot;2_G&quot;</span>\n",
       "<span class=\"lineno\">131 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r15</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">132 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">133 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">134 </span>\n",
       "<span class=\"lineno\">135 </span><span class=\"c1\">% Articulations</span>\n",
       "<span class=\"lineno\">136 </span>\n",
       "<span class=\"lineno\">137 </span><span class=\"c1\">% &quot;1_A&quot; [&#39;&lt;&#39;, &#39;=&#39;] &quot;2_A&quot;</span>\n",
       "<span class=\"lineno\">138 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">139 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">140 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">141 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">142 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">143 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">144 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">145 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">146 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">147 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r20</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">148 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">149 </span><span class=\"nf\">vr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r20</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r20</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">150 </span>\n",
       "<span class=\"lineno\">151 </span><span class=\"c1\">% &quot;1_B&quot; [&#39;=&#39;] &quot;2_B&quot;</span>\n",
       "<span class=\"lineno\">152 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">153 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">154 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">155 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">156 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">157 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">158 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">159 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">160 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">161 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">162 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">163 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">164 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r21</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">165 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">166 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r21</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">167 </span>\n",
       "<span class=\"lineno\">168 </span><span class=\"c1\">% &quot;1_C&quot; [&#39;&lt;&#39;, &#39;o&#39;] &quot;2_F&quot;</span>\n",
       "<span class=\"lineno\">169 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">170 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">171 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">172 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">173 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">174 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">175 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">176 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">177 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">178 </span><span class=\"nf\">vr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r22</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r22</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">179 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">180 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">181 </span>\n",
       "<span class=\"lineno\">182 </span><span class=\"c1\">% &quot;1_D&quot; [&#39;=&#39;] &quot;2_D&quot;</span>\n",
       "<span class=\"lineno\">183 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">184 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">185 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">186 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">187 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">188 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">189 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">190 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">191 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">192 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">193 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">194 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">195 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r23</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">196 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">197 </span><span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r23</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">198 </span>\n",
       "<span class=\"lineno\">199 </span><span class=\"c1\">% &quot;1_E&quot; [&#39;=&#39;, &#39;o&#39;] &quot;2_G&quot;</span>\n",
       "<span class=\"lineno\">200 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">201 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">202 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">203 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">204 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">205 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">206 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">A</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">207 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">B</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mi\">0</span><span class=\"p\">,</span>\n",
       "<span class=\"lineno\">208 </span>   <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">C</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">C</span><span class=\"p\">)}</span> <span class=\"o\">&gt;</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">209 </span><span class=\"nf\">vr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r24</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r24</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">210 </span><span class=\"p\">:-</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span> <span class=\"s s-Atom\">:</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">)}</span> <span class=\"o\">=</span> <span class=\"mf\">0.</span>\n",
       "<span class=\"lineno\">211 </span><span class=\"nf\">vr</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r24</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"nf\">ir</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"s s-Atom\">r24</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">,</span> <span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">212 </span>\n",
       "<span class=\"lineno\">213 </span><span class=\"c1\">% Decoding Rules</span>\n",
       "<span class=\"lineno\">214 </span><span class=\"p\">:-</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;o&quot;</span><span class=\"p\">),</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;!&quot;</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">N1</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">N2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">215 </span><span class=\"p\">:-</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;o&quot;</span><span class=\"p\">),</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;=&quot;</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">N1</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">N2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">216 </span><span class=\"p\">:-</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;o&quot;</span><span class=\"p\">),</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;&lt;&quot;</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">N1</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">N2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">217 </span><span class=\"p\">:-</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;o&quot;</span><span class=\"p\">),</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;&gt;&quot;</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">N1</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">N2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">218 </span><span class=\"p\">:-</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;!&quot;</span><span class=\"p\">),</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;=&quot;</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">N1</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">N2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">219 </span><span class=\"p\">:-</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;!&quot;</span><span class=\"p\">),</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;&lt;&quot;</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">N1</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">N2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">220 </span><span class=\"p\">:-</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;!&quot;</span><span class=\"p\">),</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;&gt;&quot;</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">N1</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">N2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">221 </span><span class=\"p\">:-</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;=&quot;</span><span class=\"p\">),</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;&lt;&quot;</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">N1</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">N2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">222 </span><span class=\"p\">:-</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;=&quot;</span><span class=\"p\">),</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;&gt;&quot;</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">N1</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">N2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">223 </span><span class=\"p\">:-</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;&lt;&quot;</span><span class=\"p\">),</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;&gt;&quot;</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">N1</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">N2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">224 </span>\n",
       "<span class=\"lineno\">225 </span><span class=\"p\">:-</span> <span class=\"o\">not</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;o&quot;</span><span class=\"p\">),</span> <span class=\"o\">not</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;!&quot;</span><span class=\"p\">),</span> <span class=\"o\">not</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;=&quot;</span><span class=\"p\">),</span> <span class=\"o\">not</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;&lt;&quot;</span><span class=\"p\">),</span> <span class=\"o\">not</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;&gt;&quot;</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">N1</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">N2</span><span class=\"p\">),</span> <span class=\"nv\">N1</span> <span class=\"o\">&lt;</span> <span class=\"nv\">N2</span><span class=\"p\">.</span>\n",
       "<span class=\"lineno\">226 </span>\n",
       "<span class=\"lineno\">227 </span><span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;o&quot;</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">),</span> <span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">),</span> <span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">228 </span><span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;!&quot;</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">),</span> <span class=\"o\">not</span> <span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">),</span> <span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">229 </span><span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;=&quot;</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"o\">not</span> <span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">),</span> <span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">),</span> <span class=\"o\">not</span> <span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">230 </span><span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;&lt;&quot;</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"o\">not</span> <span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">),</span> <span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">),</span> <span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">231 </span><span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"s2\">&quot;&gt;&quot;</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">),</span> <span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">),</span> <span class=\"o\">not</span> <span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">232 </span>\n",
       "<span class=\"lineno\">233 </span><span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">N1</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">N2</span><span class=\"p\">),</span> <span class=\"nv\">N1</span> <span class=\"o\">&lt;</span> <span class=\"nv\">N2</span><span class=\"p\">,</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">R</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">R</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">R</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">234 </span><span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">N1</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">N2</span><span class=\"p\">),</span> <span class=\"nv\">N1</span> <span class=\"o\">&lt;</span> <span class=\"nv\">N2</span><span class=\"p\">,</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">R</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">R</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">R</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">235 </span><span class=\"nf\">hint</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">N1</span><span class=\"p\">),</span> <span class=\"nf\">concept2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">N2</span><span class=\"p\">),</span> <span class=\"nv\">N1</span> <span class=\"o\">&lt;</span> <span class=\"nv\">N2</span><span class=\"p\">,</span> <span class=\"nf\">vrs</span><span class=\"p\">(</span><span class=\"nv\">R</span><span class=\"p\">),</span> <span class=\"nf\">out</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span> <span class=\"nv\">R</span><span class=\"p\">),</span> <span class=\"nf\">in</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span> <span class=\"nv\">R</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">236 </span>\n",
       "<span class=\"lineno\">237 </span>\n",
       "<span class=\"lineno\">238 </span><span class=\"c1\">% Child Parent Rules for Viz</span>\n",
       "<span class=\"lineno\">239 </span>\n",
       "<span class=\"lineno\">240 </span><span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"s2\">&quot;1_B&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">241 </span><span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"s2\">&quot;1_C&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">242 </span><span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"s2\">&quot;1_D&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">243 </span><span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"s2\">&quot;1_A&quot;</span><span class=\"p\">,</span> <span class=\"s2\">&quot;1_E&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">244 </span><span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"s2\">&quot;2_B&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">245 </span><span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"s2\">&quot;2_D&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">246 </span><span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"s2\">&quot;2_F&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">247 </span><span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"s2\">&quot;2_A&quot;</span><span class=\"p\">,</span> <span class=\"s2\">&quot;2_G&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">248 </span>\n",
       "<span class=\"lineno\">249 </span><span class=\"c1\">#show rel/3.</span>\n",
       "<span class=\"lineno\">250 </span><span class=\"nf\">eq</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">,</span> <span class=\"s2\">&quot;=&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">251 </span><span class=\"nf\">po</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">,</span> <span class=\"s2\">&quot;o&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">252 </span><span class=\"nf\">dr</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">,</span> <span class=\"s2\">&quot;!&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">253 </span><span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">,</span> <span class=\"s2\">&quot;&lt;&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">254 </span><span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">B</span><span class=\"p\">,</span> <span class=\"nv\">A</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">rel</span><span class=\"p\">(</span><span class=\"nv\">A</span><span class=\"p\">,</span> <span class=\"nv\">B</span><span class=\"p\">,</span> <span class=\"s2\">&quot;&gt;&quot;</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">255 </span><span class=\"nf\">pp</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">256 </span><span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"k\">_</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">257 </span><span class=\"nf\">u</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">bl</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">258 </span><span class=\"c1\">#show eq/2.</span>\n",
       "<span class=\"lineno\">259 </span><span class=\"c1\">#show po/2.</span>\n",
       "<span class=\"lineno\">260 </span><span class=\"c1\">#show pp/2.</span>\n",
       "<span class=\"lineno\">261 </span><span class=\"c1\">#show dr/2.</span>\n",
       "<span class=\"lineno\">262 </span><span class=\"c1\">#show bl/2.</span>\n",
       "<span class=\"lineno\">263 </span><span class=\"c1\">#show u/1.</span>\n",
       "</pre></div>\n"
      ],
      "text/plain": [
       "'r(1..24).\\n\\n% Region Meanings\\nin(X, M) :- r(M), concept(X, T, N), N1=N+1, bit(M, T, N1).\\nout(X, M) :- r(M), concept(X, T, N), N1=N+1, not bit(M, T, N1).\\nin(X, M) :- r(M), concept2(X, _), not out(X, M).\\nirs(M) :- in(X, M), out(X, M), r(M), concept2(X, _).\\n\\n% Region Constraints\\nirs(X) :- ir(X, _).\\nvrs(X) :- vr(X, _).\\nvr(X, X) :- not irs(X), r(X).\\nir(X, X) :- not vrs(X), r(X).\\n:- vrs(X), irs(X).\\n\\nconcept2(A, B) :- concept(A,B,_).\\n\\n% Taxonomy Description\\n\\n%  Euler Bit\\nbit(M, 0, V) :- r(M), M1=M/1, V = M1 \\\\ 5.\\n\\n%  Euler Bit\\nbit(M, 1, V) :- r(M), M1=M/5, V = M1 \\\\ 5.\\n\\nconcept2(\"1_A\", 0).\\nconcept(\"1_B\", 0, 0).\\nconcept(\"1_C\", 0, 1).\\nconcept(\"1_D\", 0, 2).\\nconcept(\"1_E\", 0, 3).\\nconcept2(\"2_A\", 1).\\nconcept(\"2_B\", 1, 0).\\nconcept(\"2_D\", 1, 1).\\nconcept(\"2_F\", 1, 2).\\nconcept(\"2_G\", 1, 3).\\n\\n% \"1_B\" isa \"1_A\"\\nir(X, r6) :- in(\"1_B\", X), out(\"1_A\", X).\\n:- #count {X : vrs(X), in(\"1_B\", X), in(\"1_A\", X)} = 0.\\n\\n% \"1_C\" isa \"1_A\"\\nir(X, r7) :- in(\"1_C\", X), out(\"1_A\", X).\\n:- #count {X : vrs(X), in(\"1_C\", X), in(\"1_A\", X)} = 0.\\n\\n% \"1_D\" isa \"1_A\"\\nir(X, r8) :- in(\"1_D\", X), out(\"1_A\", X).\\n:- #count {X : vrs(X), in(\"1_D\", X), in(\"1_A\", X)} = 0.\\n\\n% \"1_E\" isa \"1_A\"\\nir(X, r9) :- in(\"1_E\", X), out(\"1_A\", X).\\n:- #count {X : vrs(X), in(\"1_E\", X), in(\"1_A\", X)} = 0.\\n\\n% \"2_B\" isa \"2_A\"\\nir(X, r16) :- in(\"2_B\", X), out(\"2_A\", X).\\n:- #count {X : vrs(X), in(\"2_B\", X), in(\"2_A\", X)} = 0.\\n\\n% \"2_D\" isa \"2_A\"\\nir(X, r17) :- in(\"2_D\", X), out(\"2_A\", X).\\n:- #count {X : vrs(X), in(\"2_D\", X), in(\"2_A\", X)} = 0.\\n\\n% \"2_F\" isa \"2_A\"\\nir(X, r18) :- in(\"2_F\", X), out(\"2_A\", X).\\n:- #count {X : vrs(X), in(\"2_F\", X), in(\"2_A\", X)} = 0.\\n\\n% \"2_G\" isa \"2_A\"\\nir(X, r19) :- in(\"2_G\", X), out(\"2_A\", X).\\n:- #count {X : vrs(X), in(\"2_G\", X), in(\"2_A\", X)} = 0.\\n\\n% Coverage for \"1_A\"\\nout(\"1_A\", X) :- out(\"1_B\", X), out(\"1_C\", X), out(\"1_D\", X), out(\"1_E\", X).\\n\\n% Coverage for \"2_A\"\\nout(\"2_A\", X) :- out(\"2_B\", X), out(\"2_D\", X), out(\"2_F\", X), out(\"2_G\", X).\\n\\n% \"1_B\" ! \"1_C\"\\nir(X, r0) :- in(\"1_B\", X), in(\"1_C\", X).\\n:- #count {X : vrs(X), in(\"1_B\", X), out(\"1_C\", X)} = 0.\\n:- #count {X : vrs(X), in(\"1_C\", X), out(\"1_B\", X)} = 0.\\n\\n% \"1_B\" ! \"1_D\"\\nir(X, r1) :- in(\"1_B\", X), in(\"1_D\", X).\\n:- #count {X : vrs(X), in(\"1_B\", X), out(\"1_D\", X)} = 0.\\n:- #count {X : vrs(X), in(\"1_D\", X), out(\"1_B\", X)} = 0.\\n\\n% \"1_B\" ! \"1_E\"\\nir(X, r2) :- in(\"1_B\", X), in(\"1_E\", X).\\n:- #count {X : vrs(X), in(\"1_B\", X), out(\"1_E\", X)} = 0.\\n:- #count {X : vrs(X), in(\"1_E\", X), out(\"1_B\", X)} = 0.\\n\\n% \"1_C\" ! \"1_D\"\\nir(X, r3) :- in(\"1_C\", X), in(\"1_D\", X).\\n:- #count {X : vrs(X), in(\"1_C\", X), out(\"1_D\", X)} = 0.\\n:- #count {X : vrs(X), in(\"1_D\", X), out(\"1_C\", X)} = 0.\\n\\n% \"1_C\" ! \"1_E\"\\nir(X, r4) :- in(\"1_C\", X), in(\"1_E\", X).\\n:- #count {X : vrs(X), in(\"1_C\", X), out(\"1_E\", X)} = 0.\\n:- #count {X : vrs(X), in(\"1_E\", X), out(\"1_C\", X)} = 0.\\n\\n% \"1_D\" ! \"1_E\"\\nir(X, r5) :- in(\"1_D\", X), in(\"1_E\", X).\\n:- #count {X : vrs(X), in(\"1_D\", X), out(\"1_E\", X)} = 0.\\n:- #count {X : vrs(X), in(\"1_E\", X), out(\"1_D\", X)} = 0.\\n\\n% \"2_B\" ! \"2_D\"\\nir(X, r10) :- in(\"2_B\", X), in(\"2_D\", X).\\n:- #count {X : vrs(X), in(\"2_B\", X), out(\"2_D\", X)} = 0.\\n:- #count {X : vrs(X), in(\"2_D\", X), out(\"2_B\", X)} = 0.\\n\\n% \"2_B\" ! \"2_F\"\\nir(X, r11) :- in(\"2_B\", X), in(\"2_F\", X).\\n:- #count {X : vrs(X), in(\"2_B\", X), out(\"2_F\", X)} = 0.\\n:- #count {X : vrs(X), in(\"2_F\", X), out(\"2_B\", X)} = 0.\\n\\n% \"2_B\" ! \"2_G\"\\nir(X, r12) :- in(\"2_B\", X), in(\"2_G\", X).\\n:- #count {X : vrs(X), in(\"2_B\", X), out(\"2_G\", X)} = 0.\\n:- #count {X : vrs(X), in(\"2_G\", X), out(\"2_B\", X)} = 0.\\n\\n% \"2_D\" ! \"2_F\"\\nir(X, r13) :- in(\"2_D\", X), in(\"2_F\", X).\\n:- #count {X : vrs(X), in(\"2_D\", X), out(\"2_F\", X)} = 0.\\n:- #count {X : vrs(X), in(\"2_F\", X), out(\"2_D\", X)} = 0.\\n\\n% \"2_D\" ! \"2_G\"\\nir(X, r14) :- in(\"2_D\", X), in(\"2_G\", X).\\n:- #count {X : vrs(X), in(\"2_D\", X), out(\"2_G\", X)} = 0.\\n:- #count {X : vrs(X), in(\"2_G\", X), out(\"2_D\", X)} = 0.\\n\\n% \"2_F\" ! \"2_G\"\\nir(X, r15) :- in(\"2_F\", X), in(\"2_G\", X).\\n:- #count {X : vrs(X), in(\"2_F\", X), out(\"2_G\", X)} = 0.\\n:- #count {X : vrs(X), in(\"2_G\", X), out(\"2_F\", X)} = 0.\\n\\n% Articulations\\n\\n% \"1_A\" [\\'<\\', \\'=\\'] \"2_A\"\\n:- #count {A : vrs(A), in(\"1_A\", A), out(\"2_A\", A)} > 0,\\n   #count {B : vrs(B), in(\"1_A\", B), in(\"2_A\", B)} > 0,\\n   #count {C : vrs(C), out(\"1_A\", C), in(\"2_A\", C)} = 0.\\n:- #count {A : vrs(A), in(\"1_A\", A), out(\"2_A\", A)} > 0,\\n   #count {B : vrs(B), in(\"1_A\", B), in(\"2_A\", B)} = 0,\\n   #count {C : vrs(C), out(\"1_A\", C), in(\"2_A\", C)} > 0.\\n:- #count {A : vrs(A), in(\"1_A\", A), out(\"2_A\", A)} > 0,\\n   #count {B : vrs(B), in(\"1_A\", B), in(\"2_A\", B)} > 0,\\n   #count {C : vrs(C), out(\"1_A\", C), in(\"2_A\", C)} > 0.\\nir(X, r20) :- in(\"1_A\", X), out(\"2_A\", X).\\n:- #count {X : vrs(X), in(\"1_A\", X), in(\"2_A\", X)} = 0.\\nvr(X, r20) ; ir(X, r20) :- out(\"1_A\", X), in(\"2_A\", X).\\n\\n% \"1_B\" [\\'=\\'] \"2_B\"\\n:- #count {A : vrs(A), in(\"1_B\", A), out(\"2_B\", A)} > 0,\\n   #count {B : vrs(B), in(\"1_B\", B), in(\"2_B\", B)} > 0,\\n   #count {C : vrs(C), out(\"1_B\", C), in(\"2_B\", C)} = 0.\\n:- #count {A : vrs(A), in(\"1_B\", A), out(\"2_B\", A)} > 0,\\n   #count {B : vrs(B), in(\"1_B\", B), in(\"2_B\", B)} = 0,\\n   #count {C : vrs(C), out(\"1_B\", C), in(\"2_B\", C)} > 0.\\n:- #count {A : vrs(A), in(\"1_B\", A), out(\"2_B\", A)} = 0,\\n   #count {B : vrs(B), in(\"1_B\", B), in(\"2_B\", B)} > 0,\\n   #count {C : vrs(C), out(\"1_B\", C), in(\"2_B\", C)} > 0.\\n:- #count {A : vrs(A), in(\"1_B\", A), out(\"2_B\", A)} > 0,\\n   #count {B : vrs(B), in(\"1_B\", B), in(\"2_B\", B)} > 0,\\n   #count {C : vrs(C), out(\"1_B\", C), in(\"2_B\", C)} > 0.\\nir(X, r21) :- in(\"1_B\", X), out(\"2_B\", X).\\n:- #count {X : vrs(X), in(\"1_B\", X), in(\"2_B\", X)} = 0.\\nir(X, r21) :- out(\"1_B\", X), in(\"2_B\", X).\\n\\n% \"1_C\" [\\'<\\', \\'o\\'] \"2_F\"\\n:- #count {A : vrs(A), in(\"1_C\", A), out(\"2_F\", A)} > 0,\\n   #count {B : vrs(B), in(\"1_C\", B), in(\"2_F\", B)} > 0,\\n   #count {C : vrs(C), out(\"1_C\", C), in(\"2_F\", C)} = 0.\\n:- #count {A : vrs(A), in(\"1_C\", A), out(\"2_F\", A)} > 0,\\n   #count {B : vrs(B), in(\"1_C\", B), in(\"2_F\", B)} = 0,\\n   #count {C : vrs(C), out(\"1_C\", C), in(\"2_F\", C)} > 0.\\n:- #count {A : vrs(A), in(\"1_C\", A), out(\"2_F\", A)} = 0,\\n   #count {B : vrs(B), in(\"1_C\", B), in(\"2_F\", B)} > 0,\\n   #count {C : vrs(C), out(\"1_C\", C), in(\"2_F\", C)} = 0.\\nvr(X, r22) ; ir(X, r22) :- in(\"1_C\", X), out(\"2_F\", X).\\n:- #count {X : vrs(X), in(\"1_C\", X), in(\"2_F\", X)} = 0.\\n:- #count {X : vrs(X), out(\"1_C\", X), in(\"2_F\", X)} = 0.\\n\\n% \"1_D\" [\\'=\\'] \"2_D\"\\n:- #count {A : vrs(A), in(\"1_D\", A), out(\"2_D\", A)} > 0,\\n   #count {B : vrs(B), in(\"1_D\", B), in(\"2_D\", B)} > 0,\\n   #count {C : vrs(C), out(\"1_D\", C), in(\"2_D\", C)} = 0.\\n:- #count {A : vrs(A), in(\"1_D\", A), out(\"2_D\", A)} > 0,\\n   #count {B : vrs(B), in(\"1_D\", B), in(\"2_D\", B)} = 0,\\n   #count {C : vrs(C), out(\"1_D\", C), in(\"2_D\", C)} > 0.\\n:- #count {A : vrs(A), in(\"1_D\", A), out(\"2_D\", A)} = 0,\\n   #count {B : vrs(B), in(\"1_D\", B), in(\"2_D\", B)} > 0,\\n   #count {C : vrs(C), out(\"1_D\", C), in(\"2_D\", C)} > 0.\\n:- #count {A : vrs(A), in(\"1_D\", A), out(\"2_D\", A)} > 0,\\n   #count {B : vrs(B), in(\"1_D\", B), in(\"2_D\", B)} > 0,\\n   #count {C : vrs(C), out(\"1_D\", C), in(\"2_D\", C)} > 0.\\nir(X, r23) :- in(\"1_D\", X), out(\"2_D\", X).\\n:- #count {X : vrs(X), in(\"1_D\", X), in(\"2_D\", X)} = 0.\\nir(X, r23) :- out(\"1_D\", X), in(\"2_D\", X).\\n\\n% \"1_E\" [\\'=\\', \\'o\\'] \"2_G\"\\n:- #count {A : vrs(A), in(\"1_E\", A), out(\"2_G\", A)} > 0,\\n   #count {B : vrs(B), in(\"1_E\", B), in(\"2_G\", B)} > 0,\\n   #count {C : vrs(C), out(\"1_E\", C), in(\"2_G\", C)} = 0.\\n:- #count {A : vrs(A), in(\"1_E\", A), out(\"2_G\", A)} > 0,\\n   #count {B : vrs(B), in(\"1_E\", B), in(\"2_G\", B)} = 0,\\n   #count {C : vrs(C), out(\"1_E\", C), in(\"2_G\", C)} > 0.\\n:- #count {A : vrs(A), in(\"1_E\", A), out(\"2_G\", A)} = 0,\\n   #count {B : vrs(B), in(\"1_E\", B), in(\"2_G\", B)} > 0,\\n   #count {C : vrs(C), out(\"1_E\", C), in(\"2_G\", C)} > 0.\\nvr(X, r24) ; ir(X, r24) :- in(\"1_E\", X), out(\"2_G\", X).\\n:- #count {X : vrs(X), in(\"1_E\", X), in(\"2_G\", X)} = 0.\\nvr(X, r24) ; ir(X, r24) :- out(\"1_E\", X), in(\"2_G\", X).\\n\\n% Decoding Rules\\n:- rel(X, Y, \"o\"), rel(X, Y, \"!\"), concept2(X, N1), concept2(Y, N2).\\n:- rel(X, Y, \"o\"), rel(X, Y, \"=\"), concept2(X, N1), concept2(Y, N2).\\n:- rel(X, Y, \"o\"), rel(X, Y, \"<\"), concept2(X, N1), concept2(Y, N2).\\n:- rel(X, Y, \"o\"), rel(X, Y, \">\"), concept2(X, N1), concept2(Y, N2).\\n:- rel(X, Y, \"!\"), rel(X, Y, \"=\"), concept2(X, N1), concept2(Y, N2).\\n:- rel(X, Y, \"!\"), rel(X, Y, \"<\"), concept2(X, N1), concept2(Y, N2).\\n:- rel(X, Y, \"!\"), rel(X, Y, \">\"), concept2(X, N1), concept2(Y, N2).\\n:- rel(X, Y, \"=\"), rel(X, Y, \"<\"), concept2(X, N1), concept2(Y, N2).\\n:- rel(X, Y, \"=\"), rel(X, Y, \">\"), concept2(X, N1), concept2(Y, N2).\\n:- rel(X, Y, \"<\"), rel(X, Y, \">\"), concept2(X, N1), concept2(Y, N2).\\n\\n:- not rel(X, Y, \"o\"), not rel(X, Y, \"!\"), not rel(X, Y, \"=\"), not rel(X, Y, \"<\"), not rel(X, Y, \">\"), concept2(X, N1), concept2(Y, N2), N1 < N2.\\n\\nrel(X, Y, \"o\") :- hint(X, Y, 0), hint(X, Y, 1), hint(X, Y, 2).\\nrel(X, Y, \"!\") :- hint(X, Y, 0), not hint(X, Y, 1), hint(X, Y, 2).\\nrel(X, Y, \"=\") :- not hint(X, Y, 0), hint(X, Y, 1), not hint(X, Y, 2).\\nrel(X, Y, \"<\") :- not hint(X, Y, 0), hint(X, Y, 1), hint(X, Y, 2).\\nrel(X, Y, \">\") :- hint(X, Y, 0), hint(X, Y, 1), not hint(X, Y, 2).\\n\\nhint(X, Y, 0) :- concept2(X, N1), concept2(Y, N2), N1 < N2, vrs(R), in(X, R), out(Y, R).\\nhint(X, Y, 1) :- concept2(X, N1), concept2(Y, N2), N1 < N2, vrs(R), in(X, R), in(Y, R).\\nhint(X, Y, 2) :- concept2(X, N1), concept2(Y, N2), N1 < N2, vrs(R), out(X, R), in(Y, R).\\n\\n\\n% Child Parent Rules for Viz\\n\\nbl(\"1_A\", \"1_B\").\\nbl(\"1_A\", \"1_C\").\\nbl(\"1_A\", \"1_D\").\\nbl(\"1_A\", \"1_E\").\\nbl(\"2_A\", \"2_B\").\\nbl(\"2_A\", \"2_D\").\\nbl(\"2_A\", \"2_F\").\\nbl(\"2_A\", \"2_G\").\\n\\n#show rel/3.\\neq(A, B) :- rel(A, B, \"=\").\\npo(A, B) :- rel(A, B, \"o\").\\ndr(A, B) :- rel(A, B, \"!\").\\npp(A, B) :- rel(A, B, \"<\").\\npp(B, A) :- rel(A, B, \">\").\\npp(Y,X) :- bl(X,Y).\\nu(X) :- bl(_,X).\\nu(X) :- bl(X,_).\\n#show eq/2.\\n#show po/2.\\n#show pp/2.\\n#show dr/2.\\n#show bl/2.\\n#show u/1.'"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Directly from the file (short-circuiting)\n",
    "euler_asp_alignment_rules = LeanEuler.gen_asp_rules(rel_desc_dfs, \n",
    "                                                    taxonomy_trees, \n",
    "                                                    encoding='mnpw')\n",
    "ASPRules(\"\\n\".join(euler_asp_alignment_rules))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Directly from the file (short-circuiting)\n",
    "\n",
    "# euler_asp_alignment_rules = LeanEuler.gen_asp_rules_from_cleantax(cleantax_sample_file, encoding='mnpw')\n",
    "# ASPRules(\"\\n\".join(euler_asp_alignment_rules))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once we have an ASP encoding for the TAP instance, we can use ASP reasoner (via LeanEuler/PWE) to find the possible alignments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Models: 7\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "dict_keys(['u_1', 'bl_2', 'pp_2', 'rel_3', 'dr_2', 'eq_2', 'po_2'])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pw_rels_dfs, rel_schemas, pw_objs = LeanEuler.generate_pws(euler_asp_alignment_rules)\n",
    "pw_rels_dfs.keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, in this case we have 7 possible alignments.\n",
    "\n",
    "We can visualize them using a simple function call to LeanEuler as shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Models: 1\n",
      "Number of Models: 1\n",
      "Number of Models: 1\n",
      "Number of Models: 1\n",
      "Number of Models: 1\n",
      "Number of Models: 1\n",
      "Number of Models: 1\n"
     ]
    }
   ],
   "source": [
    "pws_vizs = LeanEuler.visualize_output(pw_rels_dfs, project_name='Sample_Euler_Problem', \n",
    "                                      pws_to_visualize=pw_objs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "t=[draw(pws_vizs[i]) for i in pws_vizs.keys()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(*t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}