%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET694+4 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n008.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 : 300s % DateTime : Thu Aug 31 15:26:01 EDT 2023 % Result : Theorem 6.89s 1.70s % Output : Proof 8.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET694+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.34 % Computer : n008.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Sat Aug 26 11:38:47 EDT 2023 % 0.17/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.44/1.03 Prover 4: Preprocessing ... % 2.44/1.03 Prover 1: Preprocessing ... % 2.74/1.07 Prover 3: Preprocessing ... % 2.74/1.07 Prover 5: Preprocessing ... % 2.74/1.07 Prover 2: Preprocessing ... % 2.74/1.07 Prover 0: Preprocessing ... % 2.74/1.09 Prover 6: Preprocessing ... % 4.61/1.43 Prover 6: Proving ... % 4.61/1.44 Prover 5: Proving ... % 4.61/1.46 Prover 1: Constructing countermodel ... % 4.61/1.48 Prover 2: Proving ... % 4.61/1.49 Prover 0: Proving ... % 4.61/1.49 Prover 3: Constructing countermodel ... % 4.61/1.50 Prover 4: Constructing countermodel ... % 6.89/1.70 Prover 3: proved (1073ms) % 6.89/1.70 % 6.89/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.89/1.70 % 6.89/1.70 Prover 6: stopped % 6.89/1.70 Prover 5: stopped % 6.89/1.70 Prover 2: stopped % 6.89/1.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.89/1.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.89/1.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.89/1.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.89/1.71 Prover 0: stopped % 6.89/1.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.60/1.74 Prover 8: Preprocessing ... % 7.60/1.74 Prover 11: Preprocessing ... % 7.60/1.75 Prover 7: Preprocessing ... % 7.60/1.75 Prover 13: Preprocessing ... % 7.60/1.76 Prover 10: Preprocessing ... % 7.60/1.78 Prover 1: Found proof (size 60) % 7.60/1.78 Prover 1: proved (1157ms) % 7.60/1.78 Prover 4: stopped % 7.60/1.78 Prover 7: stopped % 7.60/1.79 Prover 10: stopped % 8.06/1.80 Prover 13: stopped % 8.06/1.80 Prover 11: stopped % 8.06/1.85 Prover 8: Warning: ignoring some quantifiers % 8.06/1.86 Prover 8: Constructing countermodel ... % 8.46/1.87 Prover 8: stopped % 8.46/1.87 % 8.46/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.46/1.87 % 8.46/1.88 % SZS output start Proof for theBenchmark % 8.46/1.88 Assumptions after simplification: % 8.46/1.88 --------------------------------- % 8.46/1.88 % 8.46/1.88 (power_set) % 8.64/1.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.64/1.91 (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 8.64/1.91 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] % 8.64/1.91 : ! [v2: $i] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) % 8.64/1.91 | ~ $i(v0) | subset(v0, v1) = 0) % 8.64/1.91 % 8.64/1.91 (subset) % 8.64/1.91 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 8.64/1.91 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 8.64/1.92 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 8.64/1.92 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 8.64/1.92 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 8.64/1.92 % 8.64/1.92 (thI22) % 8.64/1.92 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 8.64/1.92 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & union(v2, v3) = v4 & % 8.64/1.92 union(v0, v1) = v5 & power_set(v5) = v6 & power_set(v1) = v3 & power_set(v0) % 8.64/1.92 = v2 & subset(v4, v6) = v7 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 8.64/1.92 $i(v1) & $i(v0)) % 8.64/1.92 % 8.64/1.92 (union) % 8.64/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 8.64/1.92 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 8.64/1.92 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 8.64/1.92 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 8.64/1.92 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) % 8.64/1.92 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 8.64/1.92 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 8.64/1.92 % 8.64/1.92 (function-axioms) % 8.64/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.64/1.93 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 8.64/1.93 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.64/1.93 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 8.64/1.93 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 8.64/1.93 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.64/1.93 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 8.64/1.93 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.64/1.93 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 8.64/1.93 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.64/1.93 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 8.64/1.93 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 8.64/1.93 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.64/1.93 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 8.64/1.93 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 8.64/1.93 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 8.64/1.93 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 8.64/1.93 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 8.64/1.93 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 8.64/1.93 (power_set(v2) = v0)) % 8.64/1.93 % 8.64/1.93 Further assumptions not needed in the proof: % 8.64/1.93 -------------------------------------------- % 8.64/1.93 difference, empty_set, equal_set, intersection, product, singleton, sum, % 8.64/1.93 unordered_pair % 8.64/1.93 % 8.64/1.93 Those formulas are unsatisfiable: % 8.64/1.93 --------------------------------- % 8.64/1.93 % 8.64/1.93 Begin of proof % 8.64/1.93 | % 8.80/1.94 | ALPHA: (subset) implies: % 8.80/1.94 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 8.80/1.94 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 8.80/1.94 | member(v2, v1) = 0)) % 8.80/1.94 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 8.80/1.94 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 8.80/1.94 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 8.80/1.94 | % 8.80/1.94 | ALPHA: (power_set) implies: % 8.80/1.94 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (power_set(v1) = v2) | ~ % 8.80/1.94 | (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | subset(v0, v1) = 0) % 8.80/1.94 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.80/1.94 | (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ % 8.80/1.94 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 8.80/1.94 | % 8.80/1.94 | ALPHA: (union) implies: % 8.80/1.94 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, % 8.80/1.94 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 8.80/1.94 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 & % 8.80/1.94 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 8.80/1.94 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 8.80/1.94 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ % 8.80/1.94 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 8.80/1.94 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = % 8.80/1.94 | v5)) % 8.80/1.94 | % 8.80/1.94 | ALPHA: (function-axioms) implies: % 8.80/1.94 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.80/1.94 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 8.80/1.94 | = v0)) % 8.80/1.94 | % 8.80/1.95 | DELTA: instantiating (thI22) with fresh symbols all_15_0, all_15_1, all_15_2, % 8.80/1.95 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7 gives: % 8.80/1.95 | (8) ~ (all_15_0 = 0) & union(all_15_5, all_15_4) = all_15_3 & % 8.80/1.95 | union(all_15_7, all_15_6) = all_15_2 & power_set(all_15_2) = all_15_1 & % 8.80/1.95 | power_set(all_15_6) = all_15_4 & power_set(all_15_7) = all_15_5 & % 8.80/1.95 | subset(all_15_3, all_15_1) = all_15_0 & $i(all_15_1) & $i(all_15_2) & % 8.80/1.95 | $i(all_15_3) & $i(all_15_4) & $i(all_15_5) & $i(all_15_6) & % 8.80/1.95 | $i(all_15_7) % 8.80/1.95 | % 8.80/1.95 | ALPHA: (8) implies: % 8.80/1.95 | (9) ~ (all_15_0 = 0) % 8.80/1.95 | (10) $i(all_15_7) % 8.80/1.95 | (11) $i(all_15_6) % 8.80/1.95 | (12) $i(all_15_5) % 8.80/1.95 | (13) $i(all_15_4) % 8.80/1.95 | (14) $i(all_15_3) % 8.80/1.95 | (15) $i(all_15_2) % 8.80/1.95 | (16) $i(all_15_1) % 8.80/1.95 | (17) subset(all_15_3, all_15_1) = all_15_0 % 8.80/1.95 | (18) power_set(all_15_7) = all_15_5 % 8.80/1.95 | (19) power_set(all_15_6) = all_15_4 % 8.80/1.95 | (20) power_set(all_15_2) = all_15_1 % 8.80/1.95 | (21) union(all_15_7, all_15_6) = all_15_2 % 8.80/1.95 | (22) union(all_15_5, all_15_4) = all_15_3 % 8.80/1.95 | % 8.80/1.95 | GROUND_INST: instantiating (2) with all_15_3, all_15_1, all_15_0, simplifying % 8.80/1.95 | with (14), (16), (17) gives: % 8.80/1.95 | (23) all_15_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 8.80/1.95 | all_15_1) = v1 & member(v0, all_15_3) = 0 & $i(v0)) % 8.80/1.95 | % 8.80/1.95 | BETA: splitting (23) gives: % 8.80/1.95 | % 8.80/1.95 | Case 1: % 8.80/1.95 | | % 8.80/1.95 | | (24) all_15_0 = 0 % 8.80/1.95 | | % 8.80/1.95 | | REDUCE: (9), (24) imply: % 8.80/1.95 | | (25) $false % 8.80/1.95 | | % 8.80/1.95 | | CLOSE: (25) is inconsistent. % 8.80/1.95 | | % 8.80/1.95 | Case 2: % 8.80/1.95 | | % 8.80/1.95 | | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) = % 8.80/1.95 | | v1 & member(v0, all_15_3) = 0 & $i(v0)) % 8.80/1.95 | | % 8.80/1.95 | | DELTA: instantiating (26) with fresh symbols all_24_0, all_24_1 gives: % 8.80/1.95 | | (27) ~ (all_24_0 = 0) & member(all_24_1, all_15_1) = all_24_0 & % 8.80/1.95 | | member(all_24_1, all_15_3) = 0 & $i(all_24_1) % 8.80/1.95 | | % 8.80/1.95 | | ALPHA: (27) implies: % 8.80/1.96 | | (28) ~ (all_24_0 = 0) % 8.80/1.96 | | (29) $i(all_24_1) % 8.80/1.96 | | (30) member(all_24_1, all_15_3) = 0 % 8.80/1.96 | | (31) member(all_24_1, all_15_1) = all_24_0 % 8.80/1.96 | | % 8.80/1.96 | | GROUND_INST: instantiating (5) with all_24_1, all_15_5, all_15_4, all_15_3, % 8.80/1.96 | | simplifying with (12), (13), (22), (29), (30) gives: % 8.80/1.96 | | (32) ? [v0: any] : ? [v1: any] : (member(all_24_1, all_15_4) = v1 & % 8.80/1.96 | | member(all_24_1, all_15_5) = v0 & (v1 = 0 | v0 = 0)) % 8.80/1.96 | | % 8.80/1.96 | | GROUND_INST: instantiating (4) with all_24_1, all_15_2, all_15_1, all_24_0, % 8.80/1.96 | | simplifying with (15), (20), (29), (31) gives: % 8.80/1.96 | | (33) all_24_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_24_1, % 8.80/1.96 | | all_15_2) = v0) % 8.80/1.96 | | % 8.80/1.96 | | DELTA: instantiating (32) with fresh symbols all_31_0, all_31_1 gives: % 8.80/1.96 | | (34) member(all_24_1, all_15_4) = all_31_0 & member(all_24_1, all_15_5) = % 8.80/1.96 | | all_31_1 & (all_31_0 = 0 | all_31_1 = 0) % 8.80/1.96 | | % 8.80/1.96 | | ALPHA: (34) implies: % 8.80/1.96 | | (35) member(all_24_1, all_15_5) = all_31_1 % 8.80/1.96 | | (36) member(all_24_1, all_15_4) = all_31_0 % 8.80/1.96 | | (37) all_31_0 = 0 | all_31_1 = 0 % 8.80/1.96 | | % 8.80/1.96 | | BETA: splitting (33) gives: % 8.80/1.96 | | % 8.80/1.96 | | Case 1: % 8.80/1.96 | | | % 8.80/1.96 | | | (38) all_24_0 = 0 % 8.80/1.96 | | | % 8.80/1.96 | | | REDUCE: (28), (38) imply: % 8.80/1.96 | | | (39) $false % 8.80/1.96 | | | % 8.80/1.96 | | | CLOSE: (39) is inconsistent. % 8.80/1.96 | | | % 8.80/1.96 | | Case 2: % 8.80/1.96 | | | % 8.80/1.96 | | | (40) ? [v0: int] : ( ~ (v0 = 0) & subset(all_24_1, all_15_2) = v0) % 8.80/1.96 | | | % 8.80/1.96 | | | DELTA: instantiating (40) with fresh symbol all_37_0 gives: % 8.80/1.96 | | | (41) ~ (all_37_0 = 0) & subset(all_24_1, all_15_2) = all_37_0 % 8.80/1.96 | | | % 8.80/1.96 | | | ALPHA: (41) implies: % 8.80/1.96 | | | (42) ~ (all_37_0 = 0) % 8.80/1.96 | | | (43) subset(all_24_1, all_15_2) = all_37_0 % 8.80/1.96 | | | % 8.80/1.96 | | | GROUND_INST: instantiating (2) with all_24_1, all_15_2, all_37_0, % 8.80/1.96 | | | simplifying with (15), (29), (43) gives: % 8.80/1.96 | | | (44) all_37_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 8.80/1.96 | | | member(v0, all_24_1) = 0 & member(v0, all_15_2) = v1 & $i(v0)) % 8.80/1.96 | | | % 8.80/1.96 | | | BETA: splitting (37) gives: % 8.80/1.96 | | | % 8.80/1.96 | | | Case 1: % 8.80/1.96 | | | | % 8.80/1.96 | | | | (45) all_31_0 = 0 % 8.80/1.96 | | | | % 8.80/1.96 | | | | REDUCE: (36), (45) imply: % 8.80/1.96 | | | | (46) member(all_24_1, all_15_4) = 0 % 8.80/1.96 | | | | % 8.80/1.96 | | | | BETA: splitting (44) gives: % 8.80/1.96 | | | | % 8.80/1.96 | | | | Case 1: % 8.80/1.96 | | | | | % 8.80/1.96 | | | | | (47) all_37_0 = 0 % 8.80/1.96 | | | | | % 8.80/1.96 | | | | | REDUCE: (42), (47) imply: % 8.80/1.96 | | | | | (48) $false % 8.80/1.96 | | | | | % 8.80/1.96 | | | | | CLOSE: (48) is inconsistent. % 8.80/1.96 | | | | | % 8.80/1.96 | | | | Case 2: % 8.80/1.96 | | | | | % 8.80/1.96 | | | | | (49) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 8.80/1.96 | | | | | all_24_1) = 0 & member(v0, all_15_2) = v1 & $i(v0)) % 8.80/1.96 | | | | | % 8.80/1.96 | | | | | DELTA: instantiating (49) with fresh symbols all_50_0, all_50_1 gives: % 8.80/1.96 | | | | | (50) ~ (all_50_0 = 0) & member(all_50_1, all_24_1) = 0 & % 8.80/1.96 | | | | | member(all_50_1, all_15_2) = all_50_0 & $i(all_50_1) % 8.80/1.96 | | | | | % 8.80/1.96 | | | | | ALPHA: (50) implies: % 8.80/1.97 | | | | | (51) ~ (all_50_0 = 0) % 8.80/1.97 | | | | | (52) $i(all_50_1) % 8.80/1.97 | | | | | (53) member(all_50_1, all_15_2) = all_50_0 % 8.80/1.97 | | | | | (54) member(all_50_1, all_24_1) = 0 % 8.80/1.97 | | | | | % 8.80/1.97 | | | | | GROUND_INST: instantiating (3) with all_24_1, all_15_6, all_15_4, % 8.80/1.97 | | | | | simplifying with (11), (19), (29), (46) gives: % 8.80/1.97 | | | | | (55) subset(all_24_1, all_15_6) = 0 % 8.80/1.97 | | | | | % 8.80/1.97 | | | | | GROUND_INST: instantiating (6) with all_50_1, all_15_7, all_15_6, % 8.80/1.97 | | | | | all_15_2, all_50_0, simplifying with (10), (11), (21), % 8.80/1.97 | | | | | (52), (53) gives: % 8.80/1.97 | | | | | (56) all_50_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ % 8.80/1.97 | | | | | (v0 = 0) & member(all_50_1, all_15_6) = v1 & % 8.80/1.97 | | | | | member(all_50_1, all_15_7) = v0) % 8.80/1.97 | | | | | % 8.80/1.97 | | | | | BETA: splitting (56) gives: % 8.80/1.97 | | | | | % 8.80/1.97 | | | | | Case 1: % 8.80/1.97 | | | | | | % 8.80/1.97 | | | | | | (57) all_50_0 = 0 % 8.80/1.97 | | | | | | % 8.80/1.97 | | | | | | REDUCE: (51), (57) imply: % 8.80/1.97 | | | | | | (58) $false % 8.80/1.97 | | | | | | % 8.80/1.97 | | | | | | CLOSE: (58) is inconsistent. % 8.80/1.97 | | | | | | % 8.80/1.97 | | | | | Case 2: % 8.80/1.97 | | | | | | % 8.80/1.97 | | | | | | (59) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 8.80/1.97 | | | | | | member(all_50_1, all_15_6) = v1 & member(all_50_1, % 8.80/1.97 | | | | | | all_15_7) = v0) % 8.80/1.97 | | | | | | % 8.80/1.97 | | | | | | DELTA: instantiating (59) with fresh symbols all_62_0, all_62_1 % 8.80/1.97 | | | | | | gives: % 8.80/1.97 | | | | | | (60) ~ (all_62_0 = 0) & ~ (all_62_1 = 0) & member(all_50_1, % 8.80/1.97 | | | | | | all_15_6) = all_62_0 & member(all_50_1, all_15_7) = % 8.80/1.97 | | | | | | all_62_1 % 8.80/1.97 | | | | | | % 8.80/1.97 | | | | | | ALPHA: (60) implies: % 8.80/1.97 | | | | | | (61) ~ (all_62_0 = 0) % 8.80/1.97 | | | | | | (62) member(all_50_1, all_15_6) = all_62_0 % 8.80/1.97 | | | | | | % 8.80/1.97 | | | | | | GROUND_INST: instantiating (1) with all_24_1, all_15_6, simplifying % 8.80/1.97 | | | | | | with (11), (29), (55) gives: % 8.80/1.97 | | | | | | (63) ! [v0: $i] : ( ~ (member(v0, all_24_1) = 0) | ~ $i(v0) | % 8.80/1.97 | | | | | | member(v0, all_15_6) = 0) % 8.80/1.97 | | | | | | % 8.80/1.97 | | | | | | GROUND_INST: instantiating (63) with all_50_1, simplifying with % 8.80/1.97 | | | | | | (52), (54) gives: % 8.80/1.97 | | | | | | (64) member(all_50_1, all_15_6) = 0 % 8.80/1.97 | | | | | | % 8.80/1.97 | | | | | | GROUND_INST: instantiating (7) with all_62_0, 0, all_15_6, all_50_1, % 8.80/1.97 | | | | | | simplifying with (62), (64) gives: % 8.80/1.97 | | | | | | (65) all_62_0 = 0 % 8.80/1.97 | | | | | | % 8.80/1.97 | | | | | | REDUCE: (61), (65) imply: % 8.80/1.97 | | | | | | (66) $false % 8.80/1.97 | | | | | | % 8.80/1.97 | | | | | | CLOSE: (66) is inconsistent. % 8.80/1.97 | | | | | | % 8.80/1.97 | | | | | End of split % 8.80/1.97 | | | | | % 8.80/1.97 | | | | End of split % 8.80/1.97 | | | | % 8.80/1.97 | | | Case 2: % 8.80/1.97 | | | | % 8.80/1.97 | | | | (67) all_31_1 = 0 % 8.80/1.97 | | | | % 8.80/1.97 | | | | REDUCE: (35), (67) imply: % 8.80/1.97 | | | | (68) member(all_24_1, all_15_5) = 0 % 8.80/1.97 | | | | % 8.80/1.97 | | | | BETA: splitting (44) gives: % 8.80/1.97 | | | | % 8.80/1.97 | | | | Case 1: % 8.80/1.97 | | | | | % 8.80/1.97 | | | | | (69) all_37_0 = 0 % 8.80/1.97 | | | | | % 8.80/1.97 | | | | | REDUCE: (42), (69) imply: % 8.80/1.97 | | | | | (70) $false % 8.80/1.97 | | | | | % 8.80/1.97 | | | | | CLOSE: (70) is inconsistent. % 8.80/1.97 | | | | | % 8.80/1.97 | | | | Case 2: % 8.80/1.97 | | | | | % 8.80/1.97 | | | | | (71) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 8.80/1.97 | | | | | all_24_1) = 0 & member(v0, all_15_2) = v1 & $i(v0)) % 8.80/1.97 | | | | | % 8.80/1.97 | | | | | DELTA: instantiating (71) with fresh symbols all_50_0, all_50_1 gives: % 8.80/1.98 | | | | | (72) ~ (all_50_0 = 0) & member(all_50_1, all_24_1) = 0 & % 8.80/1.98 | | | | | member(all_50_1, all_15_2) = all_50_0 & $i(all_50_1) % 8.80/1.98 | | | | | % 8.80/1.98 | | | | | ALPHA: (72) implies: % 8.80/1.98 | | | | | (73) ~ (all_50_0 = 0) % 8.80/1.98 | | | | | (74) $i(all_50_1) % 8.80/1.98 | | | | | (75) member(all_50_1, all_15_2) = all_50_0 % 8.80/1.98 | | | | | (76) member(all_50_1, all_24_1) = 0 % 8.80/1.98 | | | | | % 8.80/1.98 | | | | | GROUND_INST: instantiating (3) with all_24_1, all_15_7, all_15_5, % 8.80/1.98 | | | | | simplifying with (10), (18), (29), (68) gives: % 8.80/1.98 | | | | | (77) subset(all_24_1, all_15_7) = 0 % 8.80/1.98 | | | | | % 8.80/1.98 | | | | | GROUND_INST: instantiating (6) with all_50_1, all_15_7, all_15_6, % 8.80/1.98 | | | | | all_15_2, all_50_0, simplifying with (10), (11), (21), % 8.80/1.98 | | | | | (74), (75) gives: % 8.80/1.98 | | | | | (78) all_50_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ % 8.80/1.98 | | | | | (v0 = 0) & member(all_50_1, all_15_6) = v1 & % 8.80/1.98 | | | | | member(all_50_1, all_15_7) = v0) % 8.80/1.98 | | | | | % 8.80/1.98 | | | | | BETA: splitting (78) gives: % 8.80/1.98 | | | | | % 8.80/1.98 | | | | | Case 1: % 8.80/1.98 | | | | | | % 8.80/1.98 | | | | | | (79) all_50_0 = 0 % 8.80/1.98 | | | | | | % 8.80/1.98 | | | | | | REDUCE: (73), (79) imply: % 8.80/1.98 | | | | | | (80) $false % 8.80/1.98 | | | | | | % 8.80/1.98 | | | | | | CLOSE: (80) is inconsistent. % 8.80/1.98 | | | | | | % 8.80/1.98 | | | | | Case 2: % 8.80/1.98 | | | | | | % 8.80/1.98 | | | | | | (81) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 8.80/1.98 | | | | | | member(all_50_1, all_15_6) = v1 & member(all_50_1, % 8.80/1.98 | | | | | | all_15_7) = v0) % 8.80/1.98 | | | | | | % 8.80/1.98 | | | | | | DELTA: instantiating (81) with fresh symbols all_72_0, all_72_1 % 8.80/1.98 | | | | | | gives: % 8.80/1.98 | | | | | | (82) ~ (all_72_0 = 0) & ~ (all_72_1 = 0) & member(all_50_1, % 8.80/1.98 | | | | | | all_15_6) = all_72_0 & member(all_50_1, all_15_7) = % 8.80/1.98 | | | | | | all_72_1 % 8.80/1.98 | | | | | | % 8.80/1.98 | | | | | | ALPHA: (82) implies: % 8.80/1.98 | | | | | | (83) ~ (all_72_1 = 0) % 8.80/1.98 | | | | | | (84) member(all_50_1, all_15_7) = all_72_1 % 8.80/1.98 | | | | | | % 8.80/1.98 | | | | | | GROUND_INST: instantiating (1) with all_24_1, all_15_7, simplifying % 8.80/1.98 | | | | | | with (10), (29), (77) gives: % 8.80/1.98 | | | | | | (85) ! [v0: $i] : ( ~ (member(v0, all_24_1) = 0) | ~ $i(v0) | % 8.80/1.98 | | | | | | member(v0, all_15_7) = 0) % 8.80/1.98 | | | | | | % 8.80/1.98 | | | | | | GROUND_INST: instantiating (85) with all_50_1, simplifying with % 8.80/1.98 | | | | | | (74), (76) gives: % 8.80/1.98 | | | | | | (86) member(all_50_1, all_15_7) = 0 % 8.80/1.98 | | | | | | % 8.80/1.98 | | | | | | GROUND_INST: instantiating (7) with all_72_1, 0, all_15_7, all_50_1, % 8.80/1.98 | | | | | | simplifying with (84), (86) gives: % 8.80/1.98 | | | | | | (87) all_72_1 = 0 % 8.80/1.98 | | | | | | % 8.80/1.98 | | | | | | REDUCE: (83), (87) imply: % 8.80/1.98 | | | | | | (88) $false % 8.80/1.98 | | | | | | % 8.80/1.98 | | | | | | CLOSE: (88) is inconsistent. % 8.80/1.98 | | | | | | % 8.80/1.98 | | | | | End of split % 8.80/1.98 | | | | | % 8.80/1.98 | | | | End of split % 8.80/1.98 | | | | % 8.80/1.98 | | | End of split % 8.80/1.98 | | | % 8.80/1.98 | | End of split % 8.80/1.98 | | % 8.80/1.99 | End of split % 8.80/1.99 | % 8.80/1.99 End of proof % 8.80/1.99 % SZS output end Proof for theBenchmark % 8.80/1.99 % 8.80/1.99 1380ms %------------------------------------------------------------------------------