%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET695+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n028.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 00:21:28 EDT 2022 % Result : Theorem 152.01s 105.01s % Output : Proof 155.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET695+4 : TPTP v8.1.0. Released v2.2.0. % 0.13/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n028.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sun Jul 10 00:13:26 EDT 2022 % 0.13/0.33 % CPUTime : % 0.57/0.59 ____ _ % 0.57/0.59 ___ / __ \_____(_)___ ________ __________ % 0.57/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.57/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.57/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.57/0.59 % 0.57/0.59 A Theorem Prover for First-Order Logic % 0.57/0.59 (ePrincess v.1.0) % 0.57/0.59 % 0.57/0.59 (c) Philipp Rümmer, 2009-2015 % 0.57/0.59 (c) Peter Backeman, 2014-2015 % 0.57/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.57/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.57/0.59 Bug reports to peter@backeman.se % 0.57/0.59 % 0.57/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.57/0.59 % 0.57/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.78/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.55/0.92 Prover 0: Preprocessing ... % 2.04/1.12 Prover 0: Warning: ignoring some quantifiers % 2.04/1.14 Prover 0: Constructing countermodel ... % 3.06/1.39 Prover 0: gave up % 3.06/1.39 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.06/1.41 Prover 1: Preprocessing ... % 3.64/1.52 Prover 1: Constructing countermodel ... % 3.74/1.61 Prover 1: gave up % 3.74/1.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.13/1.63 Prover 2: Preprocessing ... % 4.48/1.72 Prover 2: Warning: ignoring some quantifiers % 4.48/1.72 Prover 2: Constructing countermodel ... % 13.60/3.88 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 13.60/3.90 Prover 3: Preprocessing ... % 13.60/3.94 Prover 3: Warning: ignoring some quantifiers % 13.60/3.95 Prover 3: Constructing countermodel ... % 14.19/4.03 Prover 3: gave up % 14.19/4.03 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 14.19/4.04 Prover 4: Preprocessing ... % 14.39/4.12 Prover 4: Warning: ignoring some quantifiers % 14.39/4.13 Prover 4: Constructing countermodel ... % 18.52/5.08 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 18.52/5.10 Prover 5: Preprocessing ... % 19.16/5.17 Prover 5: Constructing countermodel ... % 40.91/20.67 Prover 5: stopped % 41.30/20.87 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 41.30/20.89 Prover 6: Preprocessing ... % 41.51/20.94 Prover 6: Warning: ignoring some quantifiers % 41.51/20.94 Prover 6: Constructing countermodel ... % 124.15/92.86 Prover 2: stopped % 124.37/93.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 124.37/93.08 Prover 7: Preprocessing ... % 124.55/93.12 Prover 7: Proving ... % 152.01/105.01 Prover 7: proved (7225ms) % 152.01/105.01 Prover 6: stopped % 152.01/105.01 Prover 4: stopped % 152.01/105.01 % 152.01/105.01 % SZS status Theorem for theBenchmark % 152.01/105.01 % 152.01/105.01 Generating proof ... found it (size 86) % 155.48/106.38 % 155.48/106.38 % SZS output start Proof for theBenchmark % 155.48/106.38 Assumed formulas after preprocessing and simplification: % 155.48/106.38 | (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] : (difference(v3, v2) = v4 & difference(v3, v1) = v5 & subset(v2, v3) & subset(v1, v3) & ((subset(v4, v5) & ~ subset(v1, v2)) | (subset(v1, v2) & ~ subset(v4, v5))))) % 155.76/106.40 | Instantiating (0) with all_0_0_0 yields: % 155.76/106.40 | (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] : (difference(v2, v1) = v3 & difference(v2, v0) = v4 & subset(v1, v2) & subset(v0, v2) & ((subset(v3, v4) & ~ subset(v0, v1)) | (subset(v0, v1) & ~ subset(v3, v4)))) % 155.76/106.41 | % 155.76/106.41 | Applying alpha-rule on (1) yields: % 155.76/106.41 | (2) ! [v0] : ~ member(v0, all_0_0_0) % 155.76/106.41 | (3) ! [v0] : ! [v1] : ( ~ (product(v0) = v1) | ! [v2] : (member(v2, v1) | ? [v3] : (member(v3, v0) & ~ member(v2, v3)))) % 155.76/106.41 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (product(v1) = v2) | ~ member(v0, v2) | ! [v3] : ( ~ member(v3, v1) | member(v0, v3))) % 155.76/106.41 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v2) | member(v0, v3) | member(v0, v1)) % 155.76/106.42 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 155.76/106.42 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3)) % 155.76/106.42 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ! [v3] : (member(v3, v2) | ( ~ (v3 = v1) & ~ (v3 = v0)))) % 155.76/106.42 | (9) ! [v0] : ! [v1] : ( ~ subset(v1, v0) | ~ subset(v0, v1) | equal_set(v0, v1)) % 155.76/106.42 | (10) ! [v0] : ! [v1] : ( ~ (sum(v0) = v1) | ! [v2] : (member(v2, v1) | ! [v3] : ( ~ member(v3, v0) | ~ member(v2, v3)))) % 155.76/106.42 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v3) | (member(v0, v2) & ~ member(v0, v1))) % 155.76/106.42 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ subset(v0, v1) | member(v0, v2)) % 155.76/106.42 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ member(v0, v2) | subset(v0, v1)) % 155.76/106.42 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 155.76/106.42 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v2) | member(v0, v1)) % 155.76/106.42 | (16) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 155.76/106.42 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | ! [v3] : (member(v3, v2) | ( ~ member(v3, v1) & ~ member(v3, v0)))) % 155.76/106.42 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ member(v0, v2) | ? [v3] : (member(v3, v1) & member(v0, v3))) % 155.76/106.42 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 155.76/106.42 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 155.76/106.42 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 155.76/106.42 | (22) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | member(v0, v1)) % 155.76/106.42 | (23) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ member(v2, v0) | member(v2, v1))) % 155.76/106.42 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 155.76/106.42 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v2) | ~ member(v0, v1) | member(v0, v3)) % 155.76/106.42 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 155.76/106.42 | (27) ! [v0] : ! [v1] : ( ~ equal_set(v0, v1) | (subset(v1, v0) & subset(v0, v1))) % 155.76/106.42 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v3) | (member(v0, v2) & member(v0, v1))) % 155.76/106.42 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ member(v0, v2)) % 155.76/106.42 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 155.76/106.42 | (31) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (difference(v2, v1) = v3 & difference(v2, v0) = v4 & subset(v1, v2) & subset(v0, v2) & ((subset(v3, v4) & ~ subset(v0, v1)) | (subset(v0, v1) & ~ subset(v3, v4)))) % 155.76/106.42 | % 155.76/106.42 | Instantiating (31) with all_2_0_1, all_2_1_2, all_2_2_3, all_2_3_4, all_2_4_5 yields: % 155.76/106.42 | (32) difference(all_2_2_3, all_2_3_4) = all_2_1_2 & difference(all_2_2_3, all_2_4_5) = all_2_0_1 & subset(all_2_3_4, all_2_2_3) & subset(all_2_4_5, all_2_2_3) & ((subset(all_2_1_2, all_2_0_1) & ~ subset(all_2_4_5, all_2_3_4)) | (subset(all_2_4_5, all_2_3_4) & ~ subset(all_2_1_2, all_2_0_1))) % 155.76/106.42 | % 155.76/106.42 | Applying alpha-rule on (32) yields: % 155.76/106.42 | (33) difference(all_2_2_3, all_2_3_4) = all_2_1_2 % 155.76/106.42 | (34) difference(all_2_2_3, all_2_4_5) = all_2_0_1 % 155.76/106.42 | (35) subset(all_2_3_4, all_2_2_3) % 155.76/106.42 | (36) subset(all_2_4_5, all_2_2_3) % 155.76/106.42 | (37) (subset(all_2_1_2, all_2_0_1) & ~ subset(all_2_4_5, all_2_3_4)) | (subset(all_2_4_5, all_2_3_4) & ~ subset(all_2_1_2, all_2_0_1)) % 155.76/106.42 | % 155.76/106.42 | Instantiating formula (23) with all_2_2_3, all_2_3_4 and discharging atoms subset(all_2_3_4, all_2_2_3), yields: % 155.76/106.42 | (38) ! [v0] : ( ~ member(v0, all_2_3_4) | member(v0, all_2_2_3)) % 155.76/106.43 | % 155.76/106.43 | Instantiating formula (23) with all_2_2_3, all_2_4_5 and discharging atoms subset(all_2_4_5, all_2_2_3), yields: % 155.76/106.43 | (39) ! [v0] : ( ~ member(v0, all_2_4_5) | member(v0, all_2_2_3)) % 155.76/106.43 | % 155.76/106.43 +-Applying beta-rule and splitting (37), into two cases. % 155.76/106.43 |-Branch one: % 155.76/106.43 | (40) subset(all_2_1_2, all_2_0_1) & ~ subset(all_2_4_5, all_2_3_4) % 155.76/106.43 | % 155.76/106.43 | Applying alpha-rule on (40) yields: % 155.76/106.43 | (41) subset(all_2_1_2, all_2_0_1) % 155.76/106.43 | (42) ~ subset(all_2_4_5, all_2_3_4) % 155.76/106.43 | % 155.76/106.43 | Instantiating formula (23) with all_2_0_1, all_2_1_2 and discharging atoms subset(all_2_1_2, all_2_0_1), yields: % 155.76/106.43 | (43) ! [v0] : ( ~ member(v0, all_2_1_2) | member(v0, all_2_0_1)) % 155.76/106.43 | % 155.76/106.43 | Introducing new symbol ex_24_1_7 defined by: % 155.76/106.43 | (44) ex_24_1_7 = all_2_4_5 % 155.76/106.43 | % 155.76/106.43 | Introducing new symbol ex_24_0_6 defined by: % 155.76/106.43 | (45) ex_24_0_6 = all_2_3_4 % 155.76/106.43 | % 155.76/106.43 | Instantiating formula (16) with ex_24_0_6, ex_24_1_7 yields: % 155.76/106.43 | (46) subset(ex_24_1_7, ex_24_0_6) | ? [v0] : (member(v0, ex_24_1_7) & ~ member(v0, ex_24_0_6)) % 155.76/106.43 | % 155.76/106.43 +-Applying beta-rule and splitting (46), into two cases. % 155.76/106.43 |-Branch one: % 155.76/106.43 | (47) subset(ex_24_1_7, ex_24_0_6) % 155.76/106.43 | % 155.76/106.43 | From (44)(45) and (47) follows: % 155.76/106.43 | (48) subset(all_2_4_5, all_2_3_4) % 155.76/106.43 | % 155.76/106.43 | Using (48) and (42) yields: % 155.76/106.43 | (49) $false % 155.76/106.43 | % 155.76/106.43 |-The branch is then unsatisfiable % 155.76/106.43 |-Branch two: % 155.76/106.43 | (50) ? [v0] : (member(v0, ex_24_1_7) & ~ member(v0, ex_24_0_6)) % 155.76/106.43 | % 155.76/106.43 | Instantiating (50) with all_26_0_8 yields: % 155.76/106.43 | (51) member(all_26_0_8, ex_24_1_7) & ~ member(all_26_0_8, ex_24_0_6) % 155.76/106.43 | % 155.76/106.43 | Applying alpha-rule on (51) yields: % 155.76/106.43 | (52) member(all_26_0_8, ex_24_1_7) % 155.76/106.43 | (53) ~ member(all_26_0_8, ex_24_0_6) % 155.76/106.43 | % 155.76/106.43 | Instantiating formula (5) with all_2_1_2, all_2_2_3, all_2_3_4, all_26_0_8 and discharging atoms difference(all_2_2_3, all_2_3_4) = all_2_1_2, yields: % 155.76/106.43 | (54) ~ member(all_26_0_8, all_2_2_3) | member(all_26_0_8, all_2_1_2) | member(all_26_0_8, all_2_3_4) % 155.76/106.43 | % 155.76/106.43 | Instantiating formula (11) with all_2_0_1, all_2_2_3, all_2_4_5, all_26_0_8 and discharging atoms difference(all_2_2_3, all_2_4_5) = all_2_0_1, yields: % 155.76/106.43 | (55) ~ member(all_26_0_8, all_2_0_1) | (member(all_26_0_8, all_2_2_3) & ~ member(all_26_0_8, all_2_4_5)) % 155.76/106.43 | % 155.76/106.43 | Instantiating formula (43) with all_26_0_8 yields: % 155.76/106.43 | (56) ~ member(all_26_0_8, all_2_1_2) | member(all_26_0_8, all_2_0_1) % 155.76/106.43 | % 155.76/106.43 | Instantiating formula (39) with all_26_0_8 yields: % 155.76/106.43 | (57) ~ member(all_26_0_8, all_2_4_5) | member(all_26_0_8, all_2_2_3) % 155.76/106.43 | % 155.76/106.43 +-Applying beta-rule and splitting (57), into two cases. % 155.76/106.43 |-Branch one: % 155.76/106.43 | (58) ~ member(all_26_0_8, all_2_4_5) % 155.76/106.43 | % 155.76/106.43 | From (44) and (52) follows: % 155.76/106.43 | (59) member(all_26_0_8, all_2_4_5) % 155.76/106.43 | % 155.76/106.43 | Using (59) and (58) yields: % 155.76/106.43 | (49) $false % 155.76/106.43 | % 155.76/106.43 |-The branch is then unsatisfiable % 155.76/106.43 |-Branch two: % 155.76/106.43 | (59) member(all_26_0_8, all_2_4_5) % 155.76/106.43 | (62) member(all_26_0_8, all_2_2_3) % 155.76/106.43 | % 155.76/106.43 +-Applying beta-rule and splitting (56), into two cases. % 155.76/106.43 |-Branch one: % 155.76/106.43 | (63) ~ member(all_26_0_8, all_2_1_2) % 155.76/106.43 | % 155.76/106.43 +-Applying beta-rule and splitting (54), into two cases. % 155.76/106.43 |-Branch one: % 155.76/106.43 | (64) ~ member(all_26_0_8, all_2_2_3) % 155.76/106.43 | % 155.76/106.43 | Using (62) and (64) yields: % 155.76/106.43 | (49) $false % 155.76/106.43 | % 155.76/106.43 |-The branch is then unsatisfiable % 155.76/106.43 |-Branch two: % 155.76/106.43 | (66) member(all_26_0_8, all_2_1_2) | member(all_26_0_8, all_2_3_4) % 155.76/106.43 | % 155.76/106.43 +-Applying beta-rule and splitting (66), into two cases. % 155.76/106.43 |-Branch one: % 155.76/106.43 | (67) member(all_26_0_8, all_2_1_2) % 155.76/106.43 | % 155.76/106.43 | Using (67) and (63) yields: % 155.76/106.43 | (49) $false % 155.76/106.43 | % 155.76/106.43 |-The branch is then unsatisfiable % 155.76/106.43 |-Branch two: % 155.76/106.43 | (69) member(all_26_0_8, all_2_3_4) % 155.76/106.43 | % 155.76/106.43 | From (45) and (53) follows: % 155.76/106.43 | (70) ~ member(all_26_0_8, all_2_3_4) % 155.76/106.43 | % 155.76/106.43 | Using (69) and (70) yields: % 155.76/106.43 | (49) $false % 155.76/106.43 | % 155.76/106.43 |-The branch is then unsatisfiable % 155.76/106.43 |-Branch two: % 155.76/106.43 | (72) member(all_26_0_8, all_2_0_1) % 155.76/106.43 | % 155.76/106.43 +-Applying beta-rule and splitting (55), into two cases. % 155.76/106.43 |-Branch one: % 155.76/106.43 | (73) ~ member(all_26_0_8, all_2_0_1) % 155.76/106.43 | % 155.76/106.43 | Using (72) and (73) yields: % 155.76/106.43 | (49) $false % 155.76/106.43 | % 155.76/106.43 |-The branch is then unsatisfiable % 155.76/106.43 |-Branch two: % 155.76/106.43 | (75) member(all_26_0_8, all_2_2_3) & ~ member(all_26_0_8, all_2_4_5) % 155.76/106.43 | % 155.76/106.43 | Applying alpha-rule on (75) yields: % 155.76/106.43 | (62) member(all_26_0_8, all_2_2_3) % 155.76/106.43 | (58) ~ member(all_26_0_8, all_2_4_5) % 155.76/106.43 | % 155.76/106.43 | Using (59) and (58) yields: % 155.76/106.43 | (49) $false % 155.76/106.43 | % 155.76/106.43 |-The branch is then unsatisfiable % 155.76/106.43 |-Branch two: % 155.76/106.43 | (79) subset(all_2_4_5, all_2_3_4) & ~ subset(all_2_1_2, all_2_0_1) % 155.76/106.43 | % 155.76/106.43 | Applying alpha-rule on (79) yields: % 155.76/106.43 | (48) subset(all_2_4_5, all_2_3_4) % 155.76/106.43 | (81) ~ subset(all_2_1_2, all_2_0_1) % 155.76/106.43 | % 155.76/106.43 | Instantiating formula (23) with all_2_3_4, all_2_4_5 and discharging atoms subset(all_2_4_5, all_2_3_4), yields: % 155.76/106.43 | (82) ! [v0] : ( ~ member(v0, all_2_4_5) | member(v0, all_2_3_4)) % 155.76/106.43 | % 155.76/106.43 | Introducing new symbol ex_32_1_10 defined by: % 155.76/106.43 | (83) ex_32_1_10 = all_2_1_2 % 155.76/106.43 | % 155.76/106.43 | Introducing new symbol ex_32_0_9 defined by: % 155.76/106.43 | (84) ex_32_0_9 = all_2_0_1 % 155.76/106.43 | % 155.76/106.43 | Instantiating formula (16) with ex_32_0_9, ex_32_1_10 yields: % 155.76/106.43 | (85) subset(ex_32_1_10, ex_32_0_9) | ? [v0] : (member(v0, ex_32_1_10) & ~ member(v0, ex_32_0_9)) % 155.76/106.43 | % 155.76/106.43 +-Applying beta-rule and splitting (85), into two cases. % 155.76/106.43 |-Branch one: % 155.76/106.43 | (86) subset(ex_32_1_10, ex_32_0_9) % 155.76/106.43 | % 155.76/106.43 | From (83)(84) and (86) follows: % 155.76/106.43 | (41) subset(all_2_1_2, all_2_0_1) % 155.76/106.43 | % 155.76/106.43 | Using (41) and (81) yields: % 155.76/106.43 | (49) $false % 155.76/106.43 | % 155.76/106.43 |-The branch is then unsatisfiable % 155.76/106.43 |-Branch two: % 155.76/106.43 | (89) ? [v0] : (member(v0, ex_32_1_10) & ~ member(v0, ex_32_0_9)) % 155.76/106.43 | % 155.76/106.44 | Instantiating (89) with all_34_0_11 yields: % 155.76/106.44 | (90) member(all_34_0_11, ex_32_1_10) & ~ member(all_34_0_11, ex_32_0_9) % 155.76/106.44 | % 155.76/106.44 | Applying alpha-rule on (90) yields: % 155.76/106.44 | (91) member(all_34_0_11, ex_32_1_10) % 155.76/106.44 | (92) ~ member(all_34_0_11, ex_32_0_9) % 155.76/106.44 | % 155.76/106.44 | Instantiating formula (11) with all_2_1_2, all_2_2_3, all_2_3_4, all_34_0_11 and discharging atoms difference(all_2_2_3, all_2_3_4) = all_2_1_2, yields: % 155.76/106.44 | (93) ~ member(all_34_0_11, all_2_1_2) | (member(all_34_0_11, all_2_2_3) & ~ member(all_34_0_11, all_2_3_4)) % 155.76/106.44 | % 155.76/106.44 | Instantiating formula (11) with all_2_0_1, all_2_2_3, all_2_4_5, all_34_0_11 and discharging atoms difference(all_2_2_3, all_2_4_5) = all_2_0_1, yields: % 155.76/106.44 | (94) ~ member(all_34_0_11, all_2_0_1) | (member(all_34_0_11, all_2_2_3) & ~ member(all_34_0_11, all_2_4_5)) % 155.76/106.44 | % 155.76/106.44 | Instantiating formula (5) with all_2_0_1, all_2_2_3, all_2_4_5, all_34_0_11 and discharging atoms difference(all_2_2_3, all_2_4_5) = all_2_0_1, yields: % 155.76/106.44 | (95) ~ member(all_34_0_11, all_2_2_3) | member(all_34_0_11, all_2_0_1) | member(all_34_0_11, all_2_4_5) % 155.76/106.44 | % 155.76/106.44 | Instantiating formula (82) with all_34_0_11 yields: % 155.76/106.44 | (96) ~ member(all_34_0_11, all_2_4_5) | member(all_34_0_11, all_2_3_4) % 155.76/106.44 | % 155.76/106.44 | Instantiating formula (38) with all_34_0_11 yields: % 155.76/106.44 | (97) ~ member(all_34_0_11, all_2_3_4) | member(all_34_0_11, all_2_2_3) % 155.76/106.44 | % 155.76/106.44 +-Applying beta-rule and splitting (97), into two cases. % 155.76/106.44 |-Branch one: % 155.76/106.44 | (98) ~ member(all_34_0_11, all_2_3_4) % 155.76/106.44 | % 155.76/106.44 +-Applying beta-rule and splitting (96), into two cases. % 155.76/106.44 |-Branch one: % 155.76/106.44 | (99) ~ member(all_34_0_11, all_2_4_5) % 155.76/106.44 | % 155.76/106.44 +-Applying beta-rule and splitting (95), into two cases. % 155.76/106.44 |-Branch one: % 155.76/106.44 | (100) ~ member(all_34_0_11, all_2_2_3) % 155.76/106.44 | % 155.76/106.44 +-Applying beta-rule and splitting (93), into two cases. % 155.76/106.44 |-Branch one: % 155.76/106.44 | (101) ~ member(all_34_0_11, all_2_1_2) % 155.76/106.44 | % 155.76/106.44 | From (83) and (91) follows: % 155.76/106.44 | (102) member(all_34_0_11, all_2_1_2) % 155.76/106.44 | % 155.76/106.44 | Using (102) and (101) yields: % 155.76/106.44 | (49) $false % 155.76/106.44 | % 155.76/106.44 |-The branch is then unsatisfiable % 155.76/106.44 |-Branch two: % 155.76/106.44 | (104) member(all_34_0_11, all_2_2_3) & ~ member(all_34_0_11, all_2_3_4) % 155.76/106.44 | % 155.76/106.44 | Applying alpha-rule on (104) yields: % 155.76/106.44 | (105) member(all_34_0_11, all_2_2_3) % 155.76/106.44 | (98) ~ member(all_34_0_11, all_2_3_4) % 155.76/106.44 | % 155.76/106.44 | Using (105) and (100) yields: % 155.76/106.44 | (49) $false % 155.76/106.44 | % 155.76/106.44 |-The branch is then unsatisfiable % 155.76/106.44 |-Branch two: % 155.76/106.44 | (108) member(all_34_0_11, all_2_0_1) | member(all_34_0_11, all_2_4_5) % 155.76/106.44 | % 155.76/106.44 +-Applying beta-rule and splitting (94), into two cases. % 155.76/106.44 |-Branch one: % 155.76/106.44 | (109) ~ member(all_34_0_11, all_2_0_1) % 155.76/106.44 | % 155.76/106.44 +-Applying beta-rule and splitting (108), into two cases. % 155.76/106.44 |-Branch one: % 155.76/106.44 | (110) member(all_34_0_11, all_2_0_1) % 155.76/106.44 | % 155.76/106.44 | Using (110) and (109) yields: % 155.76/106.44 | (49) $false % 155.76/106.44 | % 155.76/106.44 |-The branch is then unsatisfiable % 155.76/106.44 |-Branch two: % 155.76/106.44 | (112) member(all_34_0_11, all_2_4_5) % 155.76/106.44 | % 155.76/106.44 | Using (112) and (99) yields: % 155.76/106.44 | (49) $false % 155.76/106.44 | % 155.76/106.44 |-The branch is then unsatisfiable % 155.76/106.44 |-Branch two: % 155.76/106.44 | (110) member(all_34_0_11, all_2_0_1) % 155.76/106.44 | (115) member(all_34_0_11, all_2_2_3) & ~ member(all_34_0_11, all_2_4_5) % 155.76/106.44 | % 155.76/106.44 | From (84) and (92) follows: % 155.76/106.44 | (109) ~ member(all_34_0_11, all_2_0_1) % 155.76/106.44 | % 155.76/106.44 | Using (110) and (109) yields: % 155.76/106.44 | (49) $false % 155.76/106.44 | % 155.76/106.44 |-The branch is then unsatisfiable % 155.76/106.44 |-Branch two: % 155.76/106.44 | (118) member(all_34_0_11, all_2_3_4) % 155.76/106.44 | % 155.76/106.44 | Using (118) and (98) yields: % 155.76/106.44 | (49) $false % 155.76/106.44 | % 155.76/106.44 |-The branch is then unsatisfiable % 155.76/106.44 |-Branch two: % 155.76/106.44 | (118) member(all_34_0_11, all_2_3_4) % 155.76/106.44 | (105) member(all_34_0_11, all_2_2_3) % 155.76/106.44 | % 155.76/106.44 +-Applying beta-rule and splitting (93), into two cases. % 155.76/106.44 |-Branch one: % 155.76/106.44 | (101) ~ member(all_34_0_11, all_2_1_2) % 155.76/106.44 | % 155.76/106.44 | From (83) and (91) follows: % 155.76/106.44 | (102) member(all_34_0_11, all_2_1_2) % 155.76/106.44 | % 155.76/106.44 | Using (102) and (101) yields: % 155.76/106.44 | (49) $false % 155.76/106.44 | % 155.76/106.44 |-The branch is then unsatisfiable % 155.76/106.44 |-Branch two: % 155.76/106.44 | (104) member(all_34_0_11, all_2_2_3) & ~ member(all_34_0_11, all_2_3_4) % 155.76/106.44 | % 155.76/106.44 | Applying alpha-rule on (104) yields: % 155.76/106.44 | (105) member(all_34_0_11, all_2_2_3) % 155.76/106.44 | (98) ~ member(all_34_0_11, all_2_3_4) % 155.76/106.44 | % 155.76/106.44 | Using (118) and (98) yields: % 155.76/106.44 | (49) $false % 155.76/106.44 | % 155.76/106.44 |-The branch is then unsatisfiable % 155.76/106.44 % SZS output end Proof for theBenchmark % 155.76/106.44 % 155.76/106.44 105841ms %------------------------------------------------------------------------------