%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET699+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n005.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 00:21:29 EDT 2022 % Result : Theorem 263.78s 201.42s % Output : Proof 266.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SET699+4 : TPTP v8.1.0. Released v2.2.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.32 % Computer : n005.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 600 % 0.12/0.32 % DateTime : Sun Jul 10 03:45:22 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.56 ____ _ % 0.18/0.56 ___ / __ \_____(_)___ ________ __________ % 0.18/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.56 % 0.18/0.56 A Theorem Prover for First-Order Logic % 0.18/0.57 (ePrincess v.1.0) % 0.18/0.57 % 0.18/0.57 (c) Philipp Rümmer, 2009-2015 % 0.18/0.57 (c) Peter Backeman, 2014-2015 % 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.57 Bug reports to peter@backeman.se % 0.18/0.57 % 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.57 % 0.18/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.71/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.58/0.90 Prover 0: Preprocessing ... % 2.07/1.11 Prover 0: Warning: ignoring some quantifiers % 2.07/1.13 Prover 0: Constructing countermodel ... % 3.15/1.39 Prover 0: gave up % 3.15/1.39 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.15/1.41 Prover 1: Preprocessing ... % 3.74/1.52 Prover 1: Constructing countermodel ... % 4.20/1.63 Prover 1: gave up % 4.20/1.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.20/1.65 Prover 2: Preprocessing ... % 4.61/1.73 Prover 2: Warning: ignoring some quantifiers % 4.61/1.74 Prover 2: Constructing countermodel ... % 13.71/3.89 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 13.71/3.92 Prover 3: Preprocessing ... % 13.71/3.96 Prover 3: Warning: ignoring some quantifiers % 13.71/3.97 Prover 3: Constructing countermodel ... % 14.36/4.04 Prover 3: gave up % 14.36/4.04 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 14.36/4.05 Prover 4: Preprocessing ... % 14.79/4.12 Prover 4: Warning: ignoring some quantifiers % 14.79/4.12 Prover 4: Constructing countermodel ... % 18.59/5.07 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 18.88/5.10 Prover 5: Preprocessing ... % 19.23/5.17 Prover 5: Constructing countermodel ... % 41.14/20.65 Prover 5: stopped % 41.55/20.85 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 41.55/20.88 Prover 6: Preprocessing ... % 41.89/20.93 Prover 6: Warning: ignoring some quantifiers % 41.89/20.93 Prover 6: Constructing countermodel ... % 124.39/92.94 Prover 2: stopped % 124.58/93.14 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 124.58/93.15 Prover 7: Preprocessing ... % 124.58/93.17 Prover 7: Proving ... % 185.31/133.98 Prover 4: stopped % 185.52/134.18 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 185.52/134.20 Prover 8: Preprocessing ... % 185.67/134.24 Prover 8: Constructing countermodel ... % 185.67/134.28 Prover 8: gave up % 185.67/134.28 Prover 9: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=completeFrugal % 186.04/134.30 Prover 9: Preprocessing ... % 186.04/134.33 Prover 9: Proving ... % 203.85/148.71 Prover 9: stopped % 204.15/148.91 Prover 10: Options: -triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 204.19/148.92 Prover 10: Preprocessing ... % 204.22/148.94 Prover 10: Warning: ignoring some quantifiers % 204.22/148.95 Prover 10: Constructing countermodel ... % 204.22/148.99 Prover 10: gave up % 204.22/148.99 Prover 11: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 204.41/149.01 Prover 11: Preprocessing ... % 204.41/149.03 Prover 11: Warning: ignoring some quantifiers % 204.41/149.03 Prover 11: Constructing countermodel ... % 204.41/149.08 Prover 11: gave up % 204.41/149.08 Prover 12: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 204.71/149.09 Prover 12: Preprocessing ... % 204.71/149.12 Prover 12: Constructing countermodel ... % 204.71/149.16 Prover 12: gave up % 204.71/149.16 Prover 13: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 204.71/149.17 Prover 13: Preprocessing ... % 205.14/149.20 Prover 13: Warning: ignoring some quantifiers % 205.14/149.20 Prover 13: Constructing countermodel ... % 255.87/195.93 Prover 6: stopped % 256.10/196.14 Prover 14: Options: -triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 256.10/196.15 Prover 14: Preprocessing ... % 256.10/196.17 Prover 14: Warning: ignoring some quantifiers % 256.10/196.17 Prover 14: Constructing countermodel ... % 256.29/196.22 Prover 14: gave up % 256.29/196.22 Prover 15: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 256.29/196.23 Prover 15: Preprocessing ... % 256.29/196.25 Prover 15: Constructing countermodel ... % 256.59/196.28 Prover 15: gave up % 256.59/196.28 Prover 16: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 256.63/196.29 Prover 16: Preprocessing ... % 256.75/196.31 Prover 16: Constructing countermodel ... % 256.81/196.33 Prover 16: gave up % 256.81/196.33 Prover 17: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 256.81/196.34 Prover 17: Preprocessing ... % 256.81/196.35 Prover 17: Warning: ignoring some quantifiers % 256.81/196.35 Prover 17: Constructing countermodel ... % 256.81/196.38 Prover 17: gave up % 256.81/196.38 Prover 18: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 256.81/196.39 Prover 18: Preprocessing ... % 256.81/196.40 Prover 18: Warning: ignoring some quantifiers % 256.81/196.40 Prover 18: Constructing countermodel ... % 257.16/196.43 Prover 18: gave up % 257.16/196.43 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 257.16/196.44 Prover 19: Preprocessing ... % 257.16/196.46 Prover 19: Constructing countermodel ... % 257.16/196.48 Prover 19: gave up % 261.03/199.30 Prover 13: stopped % 263.78/201.42 Prover 7: proved (22782ms) % 263.78/201.42 % 263.78/201.42 % SZS status Theorem for theBenchmark % 263.78/201.42 % 263.78/201.42 Generating proof ... found it (size 90) % 265.99/202.46 % 265.99/202.46 % SZS output start Proof for theBenchmark % 265.99/202.46 Assumed formulas after preprocessing and simplification: % 265.99/202.46 | (0) ? [v0] : ( ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | v2 = v1 | ~ (unordered_pair(v2, v3) = v4) | ~ member(v1, v4)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (unordered_pair(v4, v3) = v2) | ~ (unordered_pair(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (difference(v4, v3) = v2) | ~ (difference(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (union(v4, v3) = v2) | ~ (union(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (intersection(v4, v3) = v2) | ~ (intersection(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v3, v2) = v4) | ~ member(v1, v4) | (member(v1, v3) & ~ member(v1, v2))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v3, v2) = v4) | ~ member(v1, v3) | member(v1, v4) | member(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (union(v2, v3) = v4) | ~ member(v1, v4) | member(v1, v3) | member(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v2, v3) = v4) | ~ member(v1, v4) | (member(v1, v3) & member(v1, v2))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v2, v3) = v4) | ~ member(v1, v3) | ~ member(v1, v2) | member(v1, v4)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (product(v3) = v2) | ~ (product(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sum(v3) = v2) | ~ (sum(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v3) = v2) | ~ (singleton(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v2) = v3) | ~ member(v1, v3)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (power_set(v3) = v2) | ~ (power_set(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v2) = v3) | ~ member(v1, v3) | ! [v4] : ( ~ member(v4, v2) | member(v1, v4))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v2) = v3) | ~ member(v1, v3) | ? [v4] : (member(v4, v2) & member(v1, v4))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) | ! [v4] : (member(v4, v3) | ( ~ (v4 = v2) & ~ (v4 = v1)))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ! [v4] : (member(v4, v3) | ( ~ member(v4, v2) & ~ member(v4, v1)))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (power_set(v2) = v3) | ~ member(v1, v3) | subset(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (power_set(v2) = v3) | ~ subset(v1, v2) | member(v1, v3)) & ! [v1] : ! [v2] : ( ~ (product(v1) = v2) | ! [v3] : (member(v3, v2) | ? [v4] : (member(v4, v1) & ~ member(v3, v4)))) & ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ! [v3] : (member(v3, v2) | ! [v4] : ( ~ member(v4, v1) | ~ member(v3, v4)))) & ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | member(v1, v2)) & ! [v1] : ! [v2] : ( ~ equal_set(v1, v2) | (subset(v2, v1) & subset(v1, v2))) & ! [v1] : ! [v2] : ( ~ subset(v2, v1) | ~ subset(v1, v2) | equal_set(v1, v2)) & ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ! [v3] : ( ~ member(v3, v1) | member(v3, v2))) & ! [v1] : ! [v2] : (subset(v1, v2) | ? [v3] : (member(v3, v1) & ~ member(v3, v2))) & ! [v1] : ~ member(v1, v0) & ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (difference(v3, v2) = v4 & difference(v3, v1) = v6 & intersection(v1, v4) = v5 & subset(v2, v3) & subset(v1, v3) & ((subset(v5, v6) & ~ subset(v1, v2)) | (subset(v1, v2) & ~ subset(v5, v6))))) % 265.99/202.48 | Instantiating (0) with all_0_0_0 yields: % 265.99/202.48 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v3) | (member(v0, v2) & ~ member(v0, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v2) | member(v0, v3) | member(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v2) | member(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v3) | (member(v0, v2) & member(v0, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v2) | ~ member(v0, v1) | member(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (product(v1) = v2) | ~ member(v0, v2) | ! [v3] : ( ~ member(v3, v1) | member(v0, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ member(v0, v2) | ? [v3] : (member(v3, v1) & member(v0, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ! [v3] : (member(v3, v2) | ( ~ (v3 = v1) & ~ (v3 = v0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | ! [v3] : (member(v3, v2) | ( ~ member(v3, v1) & ~ member(v3, v0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ member(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ subset(v0, v1) | member(v0, v2)) & ! [v0] : ! [v1] : ( ~ (product(v0) = v1) | ! [v2] : (member(v2, v1) | ? [v3] : (member(v3, v0) & ~ member(v2, v3)))) & ! [v0] : ! [v1] : ( ~ (sum(v0) = v1) | ! [v2] : (member(v2, v1) | ! [v3] : ( ~ member(v3, v0) | ~ member(v2, v3)))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | member(v0, v1)) & ! [v0] : ! [v1] : ( ~ equal_set(v0, v1) | (subset(v1, v0) & subset(v0, v1))) & ! [v0] : ! [v1] : ( ~ subset(v1, v0) | ~ subset(v0, v1) | equal_set(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ member(v2, v0) | member(v2, v1))) & ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) & ! [v0] : ~ member(v0, all_0_0_0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (difference(v2, v1) = v3 & difference(v2, v0) = v5 & intersection(v0, v3) = v4 & subset(v1, v2) & subset(v0, v2) & ((subset(v4, v5) & ~ subset(v0, v1)) | (subset(v0, v1) & ~ subset(v4, v5)))) % 265.99/202.49 | % 265.99/202.49 | Applying alpha-rule on (1) yields: % 265.99/202.49 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ subset(v0, v1) | member(v0, v2)) % 265.99/202.49 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ member(v0, v2) | subset(v0, v1)) % 265.99/202.49 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | ! [v3] : (member(v3, v2) | ( ~ member(v3, v1) & ~ member(v3, v0)))) % 265.99/202.49 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 265.99/202.49 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 265.99/202.49 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v2) | member(v0, v1)) % 265.99/202.49 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 265.99/202.49 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v3) | (member(v0, v2) & member(v0, v1))) % 265.99/202.49 | (10) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ member(v2, v0) | member(v2, v1))) % 265.99/202.49 | (11) ! [v0] : ! [v1] : ( ~ (sum(v0) = v1) | ! [v2] : (member(v2, v1) | ! [v3] : ( ~ member(v3, v0) | ~ member(v2, v3)))) % 265.99/202.49 | (12) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | member(v0, v1)) % 265.99/202.49 | (13) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (difference(v2, v1) = v3 & difference(v2, v0) = v5 & intersection(v0, v3) = v4 & subset(v1, v2) & subset(v0, v2) & ((subset(v4, v5) & ~ subset(v0, v1)) | (subset(v0, v1) & ~ subset(v4, v5)))) % 265.99/202.49 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 265.99/202.49 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (product(v1) = v2) | ~ member(v0, v2) | ! [v3] : ( ~ member(v3, v1) | member(v0, v3))) % 265.99/202.49 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v2) | ~ member(v0, v1) | member(v0, v3)) % 265.99/202.49 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v2) | member(v0, v3) | member(v0, v1)) % 265.99/202.49 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ member(v0, v2)) % 265.99/202.49 | (19) ! [v0] : ~ member(v0, all_0_0_0) % 265.99/202.49 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 265.99/202.49 | (21) ! [v0] : ! [v1] : ( ~ equal_set(v0, v1) | (subset(v1, v0) & subset(v0, v1))) % 265.99/202.49 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v3) | (member(v0, v2) & ~ member(v0, v1))) % 265.99/202.49 | (23) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 265.99/202.49 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ member(v0, v2) | ? [v3] : (member(v3, v1) & member(v0, v3))) % 265.99/202.49 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 265.99/202.49 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3)) % 265.99/202.49 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 265.99/202.49 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 265.99/202.50 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ! [v3] : (member(v3, v2) | ( ~ (v3 = v1) & ~ (v3 = v0)))) % 265.99/202.50 | (30) ! [v0] : ! [v1] : ( ~ subset(v1, v0) | ~ subset(v0, v1) | equal_set(v0, v1)) % 265.99/202.50 | (31) ! [v0] : ! [v1] : ( ~ (product(v0) = v1) | ! [v2] : (member(v2, v1) | ? [v3] : (member(v3, v0) & ~ member(v2, v3)))) % 265.99/202.50 | % 265.99/202.50 | Instantiating (13) with all_2_0_1, all_2_1_2, all_2_2_3, all_2_3_4, all_2_4_5, all_2_5_6 yields: % 265.99/202.50 | (32) difference(all_2_3_4, all_2_4_5) = all_2_2_3 & difference(all_2_3_4, all_2_5_6) = all_2_0_1 & intersection(all_2_5_6, all_2_2_3) = all_2_1_2 & subset(all_2_4_5, all_2_3_4) & subset(all_2_5_6, all_2_3_4) & ((subset(all_2_1_2, all_2_0_1) & ~ subset(all_2_5_6, all_2_4_5)) | (subset(all_2_5_6, all_2_4_5) & ~ subset(all_2_1_2, all_2_0_1))) % 265.99/202.50 | % 265.99/202.50 | Applying alpha-rule on (32) yields: % 265.99/202.50 | (33) intersection(all_2_5_6, all_2_2_3) = all_2_1_2 % 265.99/202.50 | (34) subset(all_2_5_6, all_2_3_4) % 265.99/202.50 | (35) difference(all_2_3_4, all_2_5_6) = all_2_0_1 % 265.99/202.50 | (36) difference(all_2_3_4, all_2_4_5) = all_2_2_3 % 265.99/202.50 | (37) subset(all_2_4_5, all_2_3_4) % 265.99/202.50 | (38) (subset(all_2_1_2, all_2_0_1) & ~ subset(all_2_5_6, all_2_4_5)) | (subset(all_2_5_6, all_2_4_5) & ~ subset(all_2_1_2, all_2_0_1)) % 265.99/202.50 | % 265.99/202.50 | Instantiating formula (10) with all_2_3_4, all_2_4_5 and discharging atoms subset(all_2_4_5, all_2_3_4), yields: % 265.99/202.50 | (39) ! [v0] : ( ~ member(v0, all_2_4_5) | member(v0, all_2_3_4)) % 265.99/202.50 | % 265.99/202.50 | Instantiating formula (10) with all_2_3_4, all_2_5_6 and discharging atoms subset(all_2_5_6, all_2_3_4), yields: % 265.99/202.50 | (40) ! [v0] : ( ~ member(v0, all_2_5_6) | member(v0, all_2_3_4)) % 265.99/202.50 | % 265.99/202.50 +-Applying beta-rule and splitting (38), into two cases. % 265.99/202.50 |-Branch one: % 265.99/202.50 | (41) subset(all_2_1_2, all_2_0_1) & ~ subset(all_2_5_6, all_2_4_5) % 265.99/202.50 | % 265.99/202.50 | Applying alpha-rule on (41) yields: % 265.99/202.50 | (42) subset(all_2_1_2, all_2_0_1) % 265.99/202.50 | (43) ~ subset(all_2_5_6, all_2_4_5) % 265.99/202.50 | % 265.99/202.50 | Instantiating formula (10) with all_2_0_1, all_2_1_2 and discharging atoms subset(all_2_1_2, all_2_0_1), yields: % 265.99/202.50 | (44) ! [v0] : ( ~ member(v0, all_2_1_2) | member(v0, all_2_0_1)) % 265.99/202.50 | % 265.99/202.50 | Introducing new symbol ex_24_1_8 defined by: % 265.99/202.50 | (45) ex_24_1_8 = all_2_5_6 % 265.99/202.50 | % 265.99/202.50 | Introducing new symbol ex_24_0_7 defined by: % 265.99/202.50 | (46) ex_24_0_7 = all_2_4_5 % 265.99/202.50 | % 265.99/202.50 | Instantiating formula (23) with ex_24_0_7, ex_24_1_8 yields: % 265.99/202.50 | (47) subset(ex_24_1_8, ex_24_0_7) | ? [v0] : (member(v0, ex_24_1_8) & ~ member(v0, ex_24_0_7)) % 265.99/202.50 | % 265.99/202.50 +-Applying beta-rule and splitting (47), into two cases. % 265.99/202.50 |-Branch one: % 265.99/202.50 | (48) subset(ex_24_1_8, ex_24_0_7) % 265.99/202.50 | % 265.99/202.50 | From (45)(46) and (48) follows: % 265.99/202.50 | (49) subset(all_2_5_6, all_2_4_5) % 265.99/202.50 | % 265.99/202.50 | Using (49) and (43) yields: % 265.99/202.50 | (50) $false % 265.99/202.50 | % 265.99/202.50 |-The branch is then unsatisfiable % 265.99/202.50 |-Branch two: % 265.99/202.50 | (51) ? [v0] : (member(v0, ex_24_1_8) & ~ member(v0, ex_24_0_7)) % 265.99/202.50 | % 265.99/202.50 | Instantiating (51) with all_26_0_9 yields: % 265.99/202.50 | (52) member(all_26_0_9, ex_24_1_8) & ~ member(all_26_0_9, ex_24_0_7) % 265.99/202.50 | % 265.99/202.50 | Applying alpha-rule on (52) yields: % 265.99/202.50 | (53) member(all_26_0_9, ex_24_1_8) % 265.99/202.50 | (54) ~ member(all_26_0_9, ex_24_0_7) % 265.99/202.50 | % 265.99/202.50 | Instantiating formula (22) with all_2_2_3, all_2_3_4, all_2_4_5, all_26_0_9 and discharging atoms difference(all_2_3_4, all_2_4_5) = all_2_2_3, yields: % 265.99/202.50 | (55) ~ member(all_26_0_9, all_2_2_3) | (member(all_26_0_9, all_2_3_4) & ~ member(all_26_0_9, all_2_4_5)) % 265.99/202.50 | % 265.99/202.50 | Instantiating formula (17) with all_2_2_3, all_2_3_4, all_2_4_5, all_26_0_9 and discharging atoms difference(all_2_3_4, all_2_4_5) = all_2_2_3, yields: % 265.99/202.50 | (56) ~ member(all_26_0_9, all_2_3_4) | member(all_26_0_9, all_2_2_3) | member(all_26_0_9, all_2_4_5) % 265.99/202.50 | % 265.99/202.50 | Instantiating formula (22) with all_2_0_1, all_2_3_4, all_2_5_6, all_26_0_9 and discharging atoms difference(all_2_3_4, all_2_5_6) = all_2_0_1, yields: % 265.99/202.50 | (57) ~ member(all_26_0_9, all_2_0_1) | (member(all_26_0_9, all_2_3_4) & ~ member(all_26_0_9, all_2_5_6)) % 265.99/202.50 | % 265.99/202.50 | Instantiating formula (44) with all_26_0_9 yields: % 265.99/202.50 | (58) ~ member(all_26_0_9, all_2_1_2) | member(all_26_0_9, all_2_0_1) % 265.99/202.50 | % 265.99/202.50 | Instantiating formula (40) with all_26_0_9 yields: % 265.99/202.50 | (59) ~ member(all_26_0_9, all_2_5_6) | member(all_26_0_9, all_2_3_4) % 265.99/202.50 | % 265.99/202.50 +-Applying beta-rule and splitting (59), into two cases. % 265.99/202.50 |-Branch one: % 265.99/202.50 | (60) ~ member(all_26_0_9, all_2_5_6) % 265.99/202.50 | % 265.99/202.50 | From (45) and (53) follows: % 265.99/202.50 | (61) member(all_26_0_9, all_2_5_6) % 265.99/202.50 | % 265.99/202.50 | Using (61) and (60) yields: % 265.99/202.50 | (50) $false % 265.99/202.50 | % 265.99/202.50 |-The branch is then unsatisfiable % 265.99/202.50 |-Branch two: % 265.99/202.50 | (61) member(all_26_0_9, all_2_5_6) % 265.99/202.50 | (64) member(all_26_0_9, all_2_3_4) % 265.99/202.50 | % 265.99/202.50 | Instantiating formula (16) with all_2_1_2, all_2_2_3, all_2_5_6, all_26_0_9 and discharging atoms intersection(all_2_5_6, all_2_2_3) = all_2_1_2, yields: % 265.99/202.50 | (65) ~ member(all_26_0_9, all_2_2_3) | ~ member(all_26_0_9, all_2_5_6) | member(all_26_0_9, all_2_1_2) % 265.99/202.50 | % 265.99/202.50 +-Applying beta-rule and splitting (58), into two cases. % 265.99/202.50 |-Branch one: % 265.99/202.50 | (66) ~ member(all_26_0_9, all_2_1_2) % 265.99/202.50 | % 265.99/202.50 +-Applying beta-rule and splitting (56), into two cases. % 265.99/202.50 |-Branch one: % 265.99/202.50 | (67) ~ member(all_26_0_9, all_2_3_4) % 265.99/202.50 | % 265.99/202.50 | Using (64) and (67) yields: % 265.99/202.50 | (50) $false % 265.99/202.50 | % 265.99/202.50 |-The branch is then unsatisfiable % 265.99/202.50 |-Branch two: % 265.99/202.50 | (69) member(all_26_0_9, all_2_2_3) | member(all_26_0_9, all_2_4_5) % 265.99/202.51 | % 265.99/202.51 +-Applying beta-rule and splitting (55), into two cases. % 265.99/202.51 |-Branch one: % 265.99/202.51 | (70) ~ member(all_26_0_9, all_2_2_3) % 265.99/202.51 | % 265.99/202.51 +-Applying beta-rule and splitting (69), into two cases. % 265.99/202.51 |-Branch one: % 265.99/202.51 | (71) member(all_26_0_9, all_2_2_3) % 265.99/202.51 | % 265.99/202.51 | Using (71) and (70) yields: % 265.99/202.51 | (50) $false % 265.99/202.51 | % 265.99/202.51 |-The branch is then unsatisfiable % 265.99/202.51 |-Branch two: % 265.99/202.51 | (73) member(all_26_0_9, all_2_4_5) % 266.45/202.51 | % 266.45/202.51 | From (46) and (54) follows: % 266.45/202.51 | (74) ~ member(all_26_0_9, all_2_4_5) % 266.45/202.51 | % 266.45/202.51 | Using (73) and (74) yields: % 266.45/202.51 | (50) $false % 266.45/202.51 | % 266.45/202.51 |-The branch is then unsatisfiable % 266.45/202.51 |-Branch two: % 266.45/202.51 | (71) member(all_26_0_9, all_2_2_3) % 266.45/202.51 | (77) member(all_26_0_9, all_2_3_4) & ~ member(all_26_0_9, all_2_4_5) % 266.45/202.51 | % 266.45/202.51 +-Applying beta-rule and splitting (65), into two cases. % 266.45/202.51 |-Branch one: % 266.45/202.51 | (70) ~ member(all_26_0_9, all_2_2_3) % 266.45/202.51 | % 266.45/202.51 | Using (71) and (70) yields: % 266.45/202.51 | (50) $false % 266.45/202.51 | % 266.45/202.51 |-The branch is then unsatisfiable % 266.45/202.51 |-Branch two: % 266.45/202.51 | (80) ~ member(all_26_0_9, all_2_5_6) | member(all_26_0_9, all_2_1_2) % 266.45/202.51 | % 266.45/202.51 +-Applying beta-rule and splitting (80), into two cases. % 266.45/202.51 |-Branch one: % 266.45/202.51 | (60) ~ member(all_26_0_9, all_2_5_6) % 266.45/202.51 | % 266.45/202.51 | Using (61) and (60) yields: % 266.45/202.51 | (50) $false % 266.45/202.51 | % 266.45/202.51 |-The branch is then unsatisfiable % 266.45/202.51 |-Branch two: % 266.45/202.51 | (83) member(all_26_0_9, all_2_1_2) % 266.45/202.51 | % 266.45/202.51 | Using (83) and (66) yields: % 266.45/202.51 | (50) $false % 266.45/202.51 | % 266.45/202.51 |-The branch is then unsatisfiable % 266.45/202.51 |-Branch two: % 266.45/202.51 | (85) member(all_26_0_9, all_2_0_1) % 266.45/202.51 | % 266.45/202.51 +-Applying beta-rule and splitting (57), into two cases. % 266.45/202.51 |-Branch one: % 266.45/202.51 | (86) ~ member(all_26_0_9, all_2_0_1) % 266.45/202.51 | % 266.45/202.51 | Using (85) and (86) yields: % 266.45/202.51 | (50) $false % 266.45/202.51 | % 266.45/202.51 |-The branch is then unsatisfiable % 266.45/202.51 |-Branch two: % 266.45/202.51 | (88) member(all_26_0_9, all_2_3_4) & ~ member(all_26_0_9, all_2_5_6) % 266.45/202.51 | % 266.45/202.51 | Applying alpha-rule on (88) yields: % 266.45/202.51 | (64) member(all_26_0_9, all_2_3_4) % 266.45/202.51 | (60) ~ member(all_26_0_9, all_2_5_6) % 266.45/202.51 | % 266.45/202.51 | Using (61) and (60) yields: % 266.45/202.51 | (50) $false % 266.45/202.51 | % 266.45/202.51 |-The branch is then unsatisfiable % 266.45/202.51 |-Branch two: % 266.45/202.51 | (92) subset(all_2_5_6, all_2_4_5) & ~ subset(all_2_1_2, all_2_0_1) % 266.45/202.51 | % 266.45/202.51 | Applying alpha-rule on (92) yields: % 266.45/202.51 | (49) subset(all_2_5_6, all_2_4_5) % 266.45/202.51 | (94) ~ subset(all_2_1_2, all_2_0_1) % 266.45/202.51 | % 266.45/202.51 | Instantiating formula (10) with all_2_4_5, all_2_5_6 and discharging atoms subset(all_2_5_6, all_2_4_5), yields: % 266.45/202.51 | (95) ! [v0] : ( ~ member(v0, all_2_5_6) | member(v0, all_2_4_5)) % 266.45/202.51 | % 266.45/202.51 | Introducing new symbol ex_32_1_11 defined by: % 266.45/202.51 | (96) ex_32_1_11 = all_2_1_2 % 266.45/202.51 | % 266.45/202.51 | Introducing new symbol ex_32_0_10 defined by: % 266.45/202.51 | (97) ex_32_0_10 = all_2_0_1 % 266.45/202.51 | % 266.45/202.51 | Instantiating formula (23) with ex_32_0_10, ex_32_1_11 yields: % 266.45/202.51 | (98) subset(ex_32_1_11, ex_32_0_10) | ? [v0] : (member(v0, ex_32_1_11) & ~ member(v0, ex_32_0_10)) % 266.45/202.51 | % 266.45/202.51 +-Applying beta-rule and splitting (98), into two cases. % 266.45/202.51 |-Branch one: % 266.45/202.51 | (99) subset(ex_32_1_11, ex_32_0_10) % 266.45/202.51 | % 266.45/202.51 | From (96)(97) and (99) follows: % 266.45/202.51 | (42) subset(all_2_1_2, all_2_0_1) % 266.45/202.51 | % 266.45/202.51 | Using (42) and (94) yields: % 266.45/202.51 | (50) $false % 266.45/202.51 | % 266.45/202.51 |-The branch is then unsatisfiable % 266.45/202.51 |-Branch two: % 266.45/202.51 | (102) ? [v0] : (member(v0, ex_32_1_11) & ~ member(v0, ex_32_0_10)) % 266.45/202.51 | % 266.45/202.51 | Instantiating (102) with all_34_0_12 yields: % 266.45/202.51 | (103) member(all_34_0_12, ex_32_1_11) & ~ member(all_34_0_12, ex_32_0_10) % 266.45/202.51 | % 266.45/202.51 | Applying alpha-rule on (103) yields: % 266.45/202.51 | (104) member(all_34_0_12, ex_32_1_11) % 266.45/202.51 | (105) ~ member(all_34_0_12, ex_32_0_10) % 266.45/202.51 | % 266.45/202.51 | Instantiating formula (22) with all_2_2_3, all_2_3_4, all_2_4_5, all_34_0_12 and discharging atoms difference(all_2_3_4, all_2_4_5) = all_2_2_3, yields: % 266.45/202.51 | (106) ~ member(all_34_0_12, all_2_2_3) | (member(all_34_0_12, all_2_3_4) & ~ member(all_34_0_12, all_2_4_5)) % 266.45/202.51 | % 266.45/202.51 | Instantiating formula (9) with all_2_1_2, all_2_2_3, all_2_5_6, all_34_0_12 and discharging atoms intersection(all_2_5_6, all_2_2_3) = all_2_1_2, yields: % 266.45/202.51 | (107) ~ member(all_34_0_12, all_2_1_2) | (member(all_34_0_12, all_2_2_3) & member(all_34_0_12, all_2_5_6)) % 266.45/202.51 | % 266.45/202.51 | Instantiating formula (95) with all_34_0_12 yields: % 266.45/202.51 | (108) ~ member(all_34_0_12, all_2_5_6) | member(all_34_0_12, all_2_4_5) % 266.45/202.51 | % 266.45/202.51 | Instantiating formula (39) with all_34_0_12 yields: % 266.45/202.51 | (109) ~ member(all_34_0_12, all_2_4_5) | member(all_34_0_12, all_2_3_4) % 266.45/202.51 | % 266.45/202.51 +-Applying beta-rule and splitting (109), into two cases. % 266.45/202.51 |-Branch one: % 266.45/202.51 | (110) ~ member(all_34_0_12, all_2_4_5) % 266.45/202.51 | % 266.45/202.51 +-Applying beta-rule and splitting (108), into two cases. % 266.45/202.51 |-Branch one: % 266.45/202.51 | (111) ~ member(all_34_0_12, all_2_5_6) % 266.45/202.51 | % 266.45/202.51 +-Applying beta-rule and splitting (107), into two cases. % 266.45/202.51 |-Branch one: % 266.45/202.51 | (112) ~ member(all_34_0_12, all_2_1_2) % 266.45/202.51 | % 266.45/202.51 | From (96) and (104) follows: % 266.45/202.51 | (113) member(all_34_0_12, all_2_1_2) % 266.45/202.51 | % 266.45/202.51 | Using (113) and (112) yields: % 266.45/202.51 | (50) $false % 266.45/202.51 | % 266.45/202.51 |-The branch is then unsatisfiable % 266.45/202.51 |-Branch two: % 266.45/202.51 | (115) member(all_34_0_12, all_2_2_3) & member(all_34_0_12, all_2_5_6) % 266.45/202.51 | % 266.45/202.51 | Applying alpha-rule on (115) yields: % 266.45/202.51 | (116) member(all_34_0_12, all_2_2_3) % 266.45/202.51 | (117) member(all_34_0_12, all_2_5_6) % 266.45/202.51 | % 266.45/202.51 | Using (117) and (111) yields: % 266.45/202.51 | (50) $false % 266.45/202.51 | % 266.45/202.51 |-The branch is then unsatisfiable % 266.45/202.51 |-Branch two: % 266.45/202.51 | (119) member(all_34_0_12, all_2_4_5) % 266.45/202.51 | % 266.45/202.51 | Using (119) and (110) yields: % 266.45/202.51 | (50) $false % 266.45/202.51 | % 266.45/202.51 |-The branch is then unsatisfiable % 266.45/202.51 |-Branch two: % 266.45/202.51 | (119) member(all_34_0_12, all_2_4_5) % 266.45/202.51 | (122) member(all_34_0_12, all_2_3_4) % 266.45/202.51 | % 266.45/202.51 +-Applying beta-rule and splitting (106), into two cases. % 266.45/202.51 |-Branch one: % 266.45/202.51 | (123) ~ member(all_34_0_12, all_2_2_3) % 266.45/202.51 | % 266.45/202.51 +-Applying beta-rule and splitting (107), into two cases. % 266.45/202.51 |-Branch one: % 266.45/202.51 | (112) ~ member(all_34_0_12, all_2_1_2) % 266.45/202.51 | % 266.45/202.51 | From (96) and (104) follows: % 266.45/202.51 | (113) member(all_34_0_12, all_2_1_2) % 266.45/202.51 | % 266.45/202.51 | Using (113) and (112) yields: % 266.45/202.51 | (50) $false % 266.45/202.51 | % 266.45/202.51 |-The branch is then unsatisfiable % 266.45/202.51 |-Branch two: % 266.45/202.51 | (115) member(all_34_0_12, all_2_2_3) & member(all_34_0_12, all_2_5_6) % 266.45/202.51 | % 266.45/202.51 | Applying alpha-rule on (115) yields: % 266.45/202.51 | (116) member(all_34_0_12, all_2_2_3) % 266.45/202.51 | (117) member(all_34_0_12, all_2_5_6) % 266.45/202.51 | % 266.45/202.51 | Using (116) and (123) yields: % 266.45/202.51 | (50) $false % 266.45/202.51 | % 266.45/202.51 |-The branch is then unsatisfiable % 266.45/202.51 |-Branch two: % 266.45/202.51 | (131) member(all_34_0_12, all_2_3_4) & ~ member(all_34_0_12, all_2_4_5) % 266.45/202.52 | % 266.45/202.52 | Applying alpha-rule on (131) yields: % 266.45/202.52 | (122) member(all_34_0_12, all_2_3_4) % 266.45/202.52 | (110) ~ member(all_34_0_12, all_2_4_5) % 266.45/202.52 | % 266.45/202.52 | Using (119) and (110) yields: % 266.45/202.52 | (50) $false % 266.45/202.52 | % 266.45/202.52 |-The branch is then unsatisfiable % 266.45/202.52 % SZS output end Proof for theBenchmark % 266.45/202.52 % 266.45/202.52 201936ms %------------------------------------------------------------------------------