5-3-tableau.dot.svg (8311B)
1 <?xml version="1.0" encoding="UTF-8" standalone="no"?> 2 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" 3 "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"> 4 <!-- Generated by graphviz version 2.50.0 (20211204.2007) 5 --> 6 <!-- Title: g Pages: 1 --> 7 <svg width="462pt" height="524pt" 8 viewBox="0.00 0.00 462.29 524.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> 9 <g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 520)"> 10 <title>g</title> 11 <polygon fill="white" stroke="transparent" points="-4,4 -4,-520 458.29,-520 458.29,4 -4,4"/> 12 <!-- a --> 13 <g id="node1" class="node"> 14 <title>a</title> 15 <ellipse fill="none" stroke="black" cx="237.29" cy="-483" rx="134.58" ry="18"/> 16 <text text-anchor="middle" x="237.29" y="-479.3" font-family="Times,serif" font-size="14.00">* (¬ ◇ ¬ p ∧ ◇ ¬ q), ¬ ◇ (p ∧ ¬ q)</text> 17 <text text-anchor="middle" x="99.25" y="-504.8" font-family="Times,serif" font-size="14.00">1</text> 18 </g> 19 <!-- b --> 20 <g id="node2" class="node"> 21 <title>b</title> 22 <ellipse fill="none" stroke="black" cx="125.29" cy="-411" rx="118.08" ry="18"/> 23 <text text-anchor="middle" x="125.29" y="-407.3" font-family="Times,serif" font-size="14.00">◇ (p ∧ ¬ q) * ¬ ◇ ¬ p ∧ ◇ ¬ q</text> 24 <text text-anchor="middle" x="3.5" y="-432.8" font-family="Times,serif" font-size="14.00">1</text> 25 </g> 26 <!-- a--b --> 27 <g id="edge1" class="edge"> 28 <title>a--b</title> 29 <path fill="none" stroke="black" d="M210.46,-465.23C192.73,-454.15 169.58,-439.68 151.9,-428.63"/> 30 </g> 31 <!-- la --> 32 <g id="node3" class="node"> 33 <title>la</title> 34 <ellipse fill="none" stroke="black" cx="350.29" cy="-411" rx="88.28" ry="18"/> 35 <text text-anchor="middle" x="350.29" y="-407.3" font-family="Times,serif" font-size="14.00">◇ (p ∧ ¬ q) * ¬ ◇ ¬ p</text> 36 <text text-anchor="middle" x="258.4" y="-432.8" font-family="Times,serif" font-size="14.00">1</text> 37 </g> 38 <!-- a--la --> 39 <g id="edge2" class="edge"> 40 <title>a--la</title> 41 <path fill="none" stroke="black" d="M264.36,-465.23C282.38,-454.07 305.94,-439.47 323.83,-428.39"/> 42 </g> 43 <!-- ra --> 44 <g id="node9" class="node"> 45 <title>ra</title> 46 <ellipse fill="none" stroke="black" cx="125.29" cy="-339" rx="80.69" ry="18"/> 47 <text text-anchor="middle" x="125.29" y="-335.3" font-family="Times,serif" font-size="14.00">◇ (p ∧ ¬ q) * ◇ ¬ q</text> 48 <text text-anchor="middle" x="41.2" y="-360.8" font-family="Times,serif" font-size="14.00">1</text> 49 </g> 50 <!-- b--ra --> 51 <g id="edge8" class="edge"> 52 <title>b--ra</title> 53 <path fill="none" stroke="black" d="M125.29,-392.7C125.29,-381.85 125.29,-367.92 125.29,-357.1"/> 54 </g> 55 <!-- lb --> 56 <g id="node4" class="node"> 57 <title>lb</title> 58 <ellipse fill="none" stroke="black" cx="350.29" cy="-339" rx="83.39" ry="18"/> 59 <text text-anchor="middle" x="350.29" y="-335.3" font-family="Times,serif" font-size="14.00">◇ (p ∧ ¬ q), ◇ ¬ p *</text> 60 <text text-anchor="middle" x="263.6" y="-360.8" font-family="Times,serif" font-size="14.00">1</text> 61 </g> 62 <!-- la--lb --> 63 <g id="edge3" class="edge"> 64 <title>la--lb</title> 65 <path fill="none" stroke="black" d="M350.29,-392.7C350.29,-381.85 350.29,-367.92 350.29,-357.1"/> 66 </g> 67 <!-- lla --> 68 <g id="node5" class="node"> 69 <title>lla</title> 70 <ellipse fill="none" stroke="black" cx="298.29" cy="-261.5" rx="44.39" ry="18"/> 71 <text text-anchor="middle" x="298.29" y="-257.8" font-family="Times,serif" font-size="14.00">p ∧ ¬ q *</text> 72 <text text-anchor="middle" x="250.59" y="-283.3" font-family="Times,serif" font-size="14.00">2</text> 73 </g> 74 <!-- lb--lla --> 75 <g id="edge4" class="edge"> 76 <title>lb--lla</title> 77 <path fill="none" stroke="black" stroke-dasharray="5,2" d="M338.49,-320.87C329.86,-308.34 318.22,-291.44 309.69,-279.05"/> 78 </g> 79 <!-- lra --> 80 <g id="node8" class="node"> 81 <title>lra</title> 82 <polygon fill="none" stroke="black" points="360.29,-238.5 360.29,-284.5 454.29,-284.5 454.29,-238.5 360.29,-238.5"/> 83 <text text-anchor="middle" x="407.29" y="-269.3" font-family="Times,serif" font-size="14.00">¬ p *</text> 84 <polyline fill="none" stroke="black" points="360.29,-261.5 454.29,-261.5 "/> 85 <text text-anchor="middle" x="407.29" y="-246.3" font-family="Times,serif" font-size="14.00">does not close</text> 86 <text text-anchor="middle" x="356.79" y="-288.8" font-family="Times,serif" font-size="14.00">3</text> 87 </g> 88 <!-- lb--lra --> 89 <g id="edge7" class="edge"> 90 <title>lb--lra</title> 91 <path fill="none" stroke="black" stroke-dasharray="5,2" d="M363.22,-320.87C371.3,-310.17 381.79,-296.27 390.51,-284.73"/> 92 </g> 93 <!-- llb --> 94 <g id="node6" class="node"> 95 <title>llb</title> 96 <ellipse fill="none" stroke="black" cx="298.29" cy="-184" rx="38.99" ry="18"/> 97 <text text-anchor="middle" x="298.29" y="-180.3" font-family="Times,serif" font-size="14.00">p, ¬ q *</text> 98 <text text-anchor="middle" x="255.79" y="-205.8" font-family="Times,serif" font-size="14.00">2</text> 99 </g> 100 <!-- lla--llb --> 101 <g id="edge5" class="edge"> 102 <title>lla--llb</title> 103 <path fill="none" stroke="black" d="M298.29,-243.37C298.29,-231.01 298.29,-214.4 298.29,-202.06"/> 104 </g> 105 <!-- llc --> 106 <g id="node7" class="node"> 107 <title>llc</title> 108 <polygon fill="none" stroke="black" points="251.29,-83.5 251.29,-129.5 345.29,-129.5 345.29,-83.5 251.29,-83.5"/> 109 <text text-anchor="middle" x="298.29" y="-114.3" font-family="Times,serif" font-size="14.00">p * q</text> 110 <polyline fill="none" stroke="black" points="251.29,-106.5 345.29,-106.5 "/> 111 <text text-anchor="middle" x="298.29" y="-91.3" font-family="Times,serif" font-size="14.00">does not close</text> 112 <text text-anchor="middle" x="247.79" y="-133.8" font-family="Times,serif" font-size="14.00">2</text> 113 </g> 114 <!-- llb--llc --> 115 <g id="edge6" class="edge"> 116 <title>llb--llc</title> 117 <path fill="none" stroke="black" d="M298.29,-165.87C298.29,-155.17 298.29,-141.27 298.29,-129.73"/> 118 </g> 119 <!-- rb --> 120 <g id="node10" class="node"> 121 <title>rb</title> 122 <ellipse fill="none" stroke="black" cx="125.29" cy="-261.5" rx="59.29" ry="18"/> 123 <text text-anchor="middle" x="125.29" y="-257.8" font-family="Times,serif" font-size="14.00">p ∧ ¬ q * ¬ q</text> 124 <text text-anchor="middle" x="62.64" y="-283.3" font-family="Times,serif" font-size="14.00">4</text> 125 </g> 126 <!-- ra--rb --> 127 <g id="edge9" class="edge"> 128 <title>ra--rb</title> 129 <path fill="none" stroke="black" stroke-dasharray="5,2" d="M125.29,-320.87C125.29,-308.51 125.29,-291.9 125.29,-279.56"/> 130 </g> 131 <!-- rc --> 132 <g id="node11" class="node"> 133 <title>rc</title> 134 <ellipse fill="none" stroke="black" cx="125.29" cy="-184" rx="53.89" ry="18"/> 135 <text text-anchor="middle" x="125.29" y="-180.3" font-family="Times,serif" font-size="14.00">p ∧ ¬ q, q *</text> 136 <text text-anchor="middle" x="67.84" y="-205.8" font-family="Times,serif" font-size="14.00">4</text> 137 </g> 138 <!-- rb--rc --> 139 <g id="edge10" class="edge"> 140 <title>rb--rc</title> 141 <path fill="none" stroke="black" d="M125.29,-243.37C125.29,-231.01 125.29,-214.4 125.29,-202.06"/> 142 </g> 143 <!-- rd --> 144 <g id="node12" class="node"> 145 <title>rd</title> 146 <ellipse fill="none" stroke="black" cx="125.29" cy="-106.5" rx="48.19" ry="18"/> 147 <text text-anchor="middle" x="125.29" y="-102.8" font-family="Times,serif" font-size="14.00">p, ¬ q, q *</text> 148 <text text-anchor="middle" x="73.69" y="-128.3" font-family="Times,serif" font-size="14.00">4</text> 149 </g> 150 <!-- rc--rd --> 151 <g id="edge11" class="edge"> 152 <title>rc--rd</title> 153 <path fill="none" stroke="black" d="M125.29,-165.87C125.29,-153.51 125.29,-136.9 125.29,-124.56"/> 154 </g> 155 <!-- re --> 156 <g id="node13" class="node"> 157 <title>re</title> 158 <polygon fill="none" stroke="black" points="95.79,-0.5 95.79,-46.5 154.79,-46.5 154.79,-0.5 95.79,-0.5"/> 159 <text text-anchor="middle" x="125.29" y="-31.3" font-family="Times,serif" font-size="14.00">p, q * q</text> 160 <polyline fill="none" stroke="black" points="95.79,-23.5 154.79,-23.5 "/> 161 <text text-anchor="middle" x="125.29" y="-8.3" font-family="Times,serif" font-size="14.00">closes</text> 162 <text text-anchor="middle" x="92.29" y="-50.8" font-family="Times,serif" font-size="14.00">4</text> 163 </g> 164 <!-- rd--re --> 165 <g id="edge12" class="edge"> 166 <title>rd--re</title> 167 <path fill="none" stroke="black" d="M125.29,-88.32C125.29,-76.15 125.29,-59.73 125.29,-46.59"/> 168 </g> 169 </g> 170 </svg>