Resolution Experiment 1 Unsatisfiable E2 = or [ "A", "B" ] , or "A", "C", "D" , or "C", "D" , or "B", "C" , or "A", "B", "C" , or "A", "B", "C", "D" Resolution Block [{ $RecursionLimit = 5000 } , isSatisfiable [ E2, show → { proof, statistics }]] Proof 14 steps level pairs s.ancest- resoluti- failed resolven- true prezent f.subsum- clauses b.subsum- ors ons ts ed ed 1 15 0 15 1 14 1 0 0 13 0 2 156 26 130 26 104 25 53 0 26 0 3 819 52 767 303 464 102 342 0 20 0 4 425 14 411 135 276 82 193 0 1 0 total 1415 92 1323 465 858 210 588 0 60 0 Proof 14 steps: 9 { 3, 6 } or A, B, C { 3, 6 } {} 11 { 1, 5 } or B, C { 1, 5 } {} 13 { 3, 5 } or A, B, D { 3, 5 } {} 14 { 4, 5 } or A, C { 4, 5 } {} 15 { 1, 4 } or A, C { 1, 4 } {} 18 { 2, 3 } or A, C { 2, 3 } {} 19 { 1, 2 } or [ B, C, D ] { 1, 2 } {} 22 { 11, 19 } or [ B, D ] { 1, 2, 5 } { 1 } 27 { 9, 18 } or B, C { 2, 3, 6 } { 3 } 42 { 14, 15 } or [ C ] { 1, 4, 5 } { 4 } 43 { 1, 13 } or B, D { 1, 3, 5 } {} 56 { 22, 43 } or [ B ] { 1, 2, 3, 5 } { 1, 5 } 59 { 27, 42 } or [ B ] { 1, 2, 3, 4, 5, 6 } {} 66 { 56, 59 } { 1, 2, 3, 4, 5, 6 } { 1, 2, 3, 5 } Resolution with forward subsumption In[ ]:= Block [{ $RecursionLimit = 5000 } , isSatisfiable [ E2, use → { forwardSubsumption } , show → { proof, statistics }]]
2 Resolution-Experiments-presentation.nb Proof 14 steps level pairs s.ancest- resoluti- failed resolven- true prezent f.subsum- clauses b.subsum- ors ons ts ed ed 1 15 0 15 1 14 1 0 0 13 0 2 156 26 130 26 104 25 43 21 15 0 3 390 30 360 172 188 30 124 28 6 0 4 38 2 36 25 11 0 8 2 1 0 total 599 58 541 224 317 56 175 51 35 0 Proof 14 steps: 9 { 3, 6 } or A, B, C 11 { 1, 5 } or B, C 13 { 3, 5 } or A, B, D 14 { 4, 5 } or A, C 15 { 1, 4 } or A, C 18 { 2, 3 } or A, C 19 { 1, 2 } or [ B, C, D ] 22 { 11, 19 } or [ B, D ] 25 { 9, 18 } or B, C 32 { 14, 15 } or [ C ] 33 { 1, 13 } or B, D 38 { 22, 33 } or [ B ] 40 { 25, 32 } or [ B ] 41 { 38, 40 } Resolution with backward subsumption In[ ]:= Block [{ $RecursionLimit = 5000 } , isSatisfiable [ E2, use → { subsumption } , show → { proof, statistics }]] Proof 11 steps level pairs s.ancest- resoluti- failed resolven- true prezent f.subsum- clauses b.subsum- ors ons ts ed ed 1 9 0 9 1 8 0 0 0 8 3 2 11 3 8 3 5 0 0 0 5 7 3 12 2 10 6 4 0 0 0 4 7 4 8 3 5 3 2 0 0 0 2 2 5 1 0 1 0 1 0 0 0 1 0 total 41 8 33 13 20 0 0 0 20 19 Proof 11 steps: 7 { 1, 6 } or [ A, C, D ] 10 { 4, 5 } or A, C 11 { 1, 4 } or A, C 14 { 2, 3 } or A, C 17 { 7, 14 } or [ C, D ] 18 { 10, 14 } or [ A ] 19 { 3, 11 } or A, D 20 { 17, 19 } or [ A, C ] 23 { 11, 18 } or [ C ] 25 { 20, 23 } or [ A ] 26 { 18, 25 }
Resolution-Experiments-presentation.nb 3 Resolution Experiment 2 Unsatisfiable F1 = or "A", "B", "C" , or "A", "C", "D" , or [ "B", "C" ] , or "B", "C", "D" , In[ ]:= or "A", "D" , or "A", "C", "D" , or "B", "C" , or "A", "B", "C", "D" , or "A", "B", "C" Resolution Block [{ $RecursionLimit = 5000 } , isSatisfiable [ F1, show → { initialSet, levels, clauses, proof, statistics }]] 1 {} or A, B, C 2 {} or A, C, D 3 {} or [ B, C ] 4 {} or B, C, D 5 {} or A, D Set 0 : 6 {} or A, C, D 7 {} or B, C 8 {} or A, B, C, D 9 {} or A, B, C Resolution with forward subsumption Block [{ $RecursionLimit = 5000 } , isSatisfiable [ F1, use → { forwardSubsumption } , show → { subsumed, initialSet, levels, clauses, proof, statistics }]] Set initial: 1 {} or A, B, C 2 {} or A, C, D 3 {} or [ B, C ] 4 {} or B, C, D 5 {} or A, D 6 {} or A, C, D 7 {} or B, C 8 {} or A, B, C, D 9 {} or A, B, C Level 1 resolution 2 { 2, 9 } resolvent or B, C, D added as clause 10 resolution 3 { 3, 9 } resolvent or [ A, C ] added as clause 11 resolution 5 { 5, 9 } resolvent or B, C, D added as clause 12
4 Resolution-Experiments-presentation.nb resolution 6 { 6, 9 } resolvent or A, B, D added as clause 13 resolution 7 { 7, 9 } resolvent or A, B added as clause 14 resolution 11 { 3, 8 } resolvent or A, B, D added as clause 15 resolution 16 { 1, 7 } resolvent or A, C added as clause 16 resolution 17 { 2, 7 } resolvent or A, B, D added as clause 17 resolution 19 { 4, 7 } resolvent or C, D added as clause 18 resolution 27 { 1, 5 } resolvent or B, C, D added as clause 19 resolution 28 { 2, 5 } resolvent or A, C added as clause 20 resolution 30 { 4, 5 } resolvent or A, B, C added as clause 21 resolution 32 { 2, 4 } resolvent or A, B, D added as clause 22 resolution 33 { 3, 4 } resolvent or B, D added as clause 23 resolution 34 { 1, 3 } resolvent or [ A, B ] added as clause 24 Level 2 resolution 37 { 2, 24 } resolvent or B, C, D subsumed by 3 resolution 39 { 5, 24 } resolvent or [ B, D ] added as clause 25 resolution 44 { 10, 24 } resolvent or A, C, D subsumed by 11 resolution 46 { 12, 24 } resolvent or [ A, C, D ] subsumed by 11 resolution 47 { 13, 24 } resolvent or A, D added as clause 26 resolution 48 { 14, 24 } resolvent or [ A ] added as clause 27 resolution 55 { 21, 24 } resolvent or B, C added as clause 28 resolution 60 { 5, 23 } resolvent or A, B added as clause 29 resolution 64 { 9, 23 } resolvent or A, C, D subsumed by 11 resolution 65 { 10, 23 } resolvent or C, D added as clause 30 resolution 72 { 17, 23 } resolvent or A, D added as clause 31 resolution 82 { 7, 22 } resolvent or A, C, D subsumed by 18 resolution 86 { 11, 22 } resolvent or B, C, D subsumed by 3 resolution 101 { 7, 21 } resolvent or A, C added as clause 32 resolution 111 { 17, 21 } resolvent or A, C, D subsumed by 18 resolution 119 { 7, 20 } resolvent or A, B added as clause 33 resolution 121 { 9, 20 } resolvent or B, C added as clause 34 resolution 123 { 11, 20 } resolvent or [ C ] added as clause 35 resolution 127 { 15, 20 } resolvent or B, C, D subsumed by 3 resolution 131 { 19, 20 } resolvent or A, B, D subsumed by 5 resolution 136 { 7, 19 } resolvent or C, D added as clause 36 resolution 140 { 11, 19 } resolvent or [ A, B, D ] subsumed by 24 resolution 143 { 14, 19 } resolvent or A, C, D subsumed by 16
Resolution-Experiments-presentation.nb 5 resolution 155 { 10, 18 } resolvent or B, D added as clause 37 resolution 165 { 4, 17 } resolvent or A, C, D subsumed by 18 resolution 167 { 6, 17 } resolvent or B, C, D subsumed by 7 resolution 172 { 12, 17 } resolvent or A, B, C subsumed by 20 resolution 176 { 16, 17 } resolvent or B, C, D subsumed by 7 resolution 186 { 12, 16 } resolvent or A, B, D subsumed by 14 resolution 191 { 2, 15 } resolvent or B, C, D subsumed by 3 resolution 196 { 9, 15 } resolvent or A, C, D subsumed by 11 resolution 197 { 10, 15 } resolvent or A, C, D subsumed by 11 resolution 206 { 5, 14 } resolvent or B, D added as clause 38 resolution 215 { 3, 13 } resolvent or A, C, D subsumed by 11 resolution 224 { 2, 12 } resolvent or A, B, C subsumed by 20 resolution 225 { 3, 12 } resolvent or [ C, D ] subsumed by 35 resolution 235 { 5, 11 } resolvent or [ C, D ] subsumed by 35 resolution 243 { 5, 10 } resolvent or A, B, C subsumed by 20 Level 3 resolution 247 { 1, 38 } resolvent or A, C, D subsumed by 16 resolution 248 { 2, 38 } resolvent or A, B, C subsumed by 20 resolution 249 { 3, 38 } resolvent or [ C, D ] subsumed by 35 resolution 251 { 6, 38 } resolvent or A, B, C subsumed by 7 resolution 265 { 21, 38 } resolvent or A, C, D subsumed by 5 resolution 268 { 24, 38 } resolvent or [ A, D ] subsumed by 27 resolution 269 { 25, 38 } resolvent or [ D ] added as clause 39 resolution 281 { 37, 38 } resolvent or [ B ] added as clause 40 resolution 300 { 21, 37 } resolvent or A, C, D subsumed by 18 resolution 302 { 23, 37 } resolvent or [ D ] added as clause 41 resolution 323 { 9, 36 } resolvent or A, B, D subsumed by 14 resolution 325 { 11, 36 } resolvent or [ A, D ] subsumed by 27 resolution 327 { 13, 36 } resolvent or A, B, C subsumed by 7 resolution 331 { 17, 36 } resolvent or A, B, C subsumed by 7 resolution 332 { 18, 36 } resolvent or [ C ] added as clause 42 resolution 374 { 28, 35 } resolvent or [ B ] added as clause 43 resolution 378 { 32, 35 } resolvent or [ A ] added as clause 44 resolution 394 { 15, 34 } resolvent or A, C, D subsumed by 11 resolution 403 { 25, 34 } resolvent or [ C, D ] subsumed by 35 resolution 415 { 4, 33 } resolvent or A, C, D subsumed by 18
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