%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET019+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 : n006.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 15:23:11 EDT 2023 % Result : Theorem 7.47s 1.78s % Output : Proof 8.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SET019+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.32 % Computer : n006.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Sat Aug 26 16:05:22 EDT 2023 % 0.11/0.32 % CPUTime : % 0.16/0.57 ________ _____ % 0.16/0.57 ___ __ \_________(_)________________________________ % 0.16/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.57 % 0.16/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.57 (2023-06-19) % 0.16/0.57 % 0.16/0.57 (c) Philipp Rümmer, 2009-2023 % 0.16/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.57 Amanda Stjerna. % 0.16/0.57 Free software under BSD-3-Clause. % 0.16/0.57 % 0.16/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.57 % 0.16/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.16/0.58 Running up to 7 provers in parallel. % 0.16/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.88/1.04 Prover 1: Preprocessing ... % 2.44/1.05 Prover 4: Preprocessing ... % 2.68/1.10 Prover 5: Preprocessing ... % 2.68/1.10 Prover 0: Preprocessing ... % 2.68/1.10 Prover 2: Preprocessing ... % 2.68/1.10 Prover 6: Preprocessing ... % 2.68/1.10 Prover 3: Preprocessing ... % 6.13/1.61 Prover 3: Constructing countermodel ... % 6.44/1.62 Prover 6: Proving ... % 6.44/1.62 Prover 1: Constructing countermodel ... % 6.44/1.62 Prover 5: Proving ... % 6.44/1.63 Prover 4: Constructing countermodel ... % 6.60/1.65 Prover 2: Proving ... % 6.60/1.68 Prover 0: Proving ... % 7.47/1.78 Prover 2: proved (1181ms) % 7.47/1.78 % 7.47/1.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.47/1.78 % 7.47/1.79 Prover 6: proved (1180ms) % 7.47/1.79 % 7.47/1.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.47/1.79 % 7.47/1.80 Prover 0: stopped % 7.47/1.80 Prover 3: stopped % 7.47/1.80 Prover 5: stopped % 7.47/1.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.47/1.80 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.47/1.81 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.47/1.81 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.47/1.81 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.47/1.84 Prover 7: Preprocessing ... % 7.47/1.85 Prover 13: Preprocessing ... % 7.47/1.85 Prover 10: Preprocessing ... % 7.47/1.85 Prover 11: Preprocessing ... % 7.98/1.87 Prover 8: Preprocessing ... % 8.08/1.89 Prover 1: Found proof (size 17) % 8.08/1.89 Prover 1: proved (1297ms) % 8.08/1.89 Prover 4: stopped % 8.08/1.91 Prover 13: stopped % 8.40/1.92 Prover 11: stopped % 8.40/1.93 Prover 7: Warning: ignoring some quantifiers % 8.40/1.93 Prover 10: Warning: ignoring some quantifiers % 8.58/1.94 Prover 7: Constructing countermodel ... % 8.58/1.95 Prover 10: Constructing countermodel ... % 8.58/1.95 Prover 7: stopped % 8.58/1.96 Prover 10: stopped % 8.58/1.99 Prover 8: Warning: ignoring some quantifiers % 8.58/2.00 Prover 8: Constructing countermodel ... % 8.58/2.01 Prover 8: stopped % 8.58/2.01 % 8.58/2.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.58/2.01 % 8.58/2.02 % SZS output start Proof for theBenchmark % 8.58/2.02 Assumptions after simplification: % 8.58/2.02 --------------------------------- % 8.58/2.02 % 8.58/2.02 (equal_set) % 8.58/2.07 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 8.58/2.07 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 8.58/2.07 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 8.58/2.07 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 8.58/2.07 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 8.58/2.07 % 8.58/2.07 (thI02) % 8.58/2.07 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & equal_set(v0, v1) = % 8.58/2.07 v2 & subset(v1, v0) = 0 & subset(v0, v1) = 0 & $i(v1) & $i(v0)) % 8.58/2.07 % 8.58/2.07 (function-axioms) % 8.58/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.58/2.08 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 8.58/2.08 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.58/2.08 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 8.58/2.08 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 8.58/2.08 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.58/2.08 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 8.58/2.08 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.58/2.08 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 8.58/2.08 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.58/2.08 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 8.58/2.08 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 8.58/2.08 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.58/2.08 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 8.58/2.08 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 8.58/2.08 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 8.58/2.08 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 8.58/2.08 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 8.58/2.08 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 8.58/2.08 (power_set(v2) = v0)) % 8.58/2.08 % 8.58/2.08 Further assumptions not needed in the proof: % 8.58/2.08 -------------------------------------------- % 8.58/2.09 difference, empty_set, intersection, power_set, product, singleton, subset, sum, % 8.58/2.09 union, unordered_pair % 8.58/2.09 % 8.58/2.09 Those formulas are unsatisfiable: % 8.58/2.09 --------------------------------- % 8.58/2.09 % 8.58/2.09 Begin of proof % 8.58/2.09 | % 8.58/2.09 | ALPHA: (equal_set) implies: % 8.58/2.09 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 8.58/2.09 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 8.58/2.09 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 8.58/2.09 | 0)))) % 8.58/2.09 | % 8.58/2.09 | ALPHA: (function-axioms) implies: % 8.58/2.09 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.58/2.09 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) % 8.58/2.09 | = v0)) % 8.58/2.09 | % 8.58/2.09 | DELTA: instantiating (thI02) with fresh symbols all_15_0, all_15_1, all_15_2 % 8.58/2.09 | gives: % 8.58/2.10 | (3) ~ (all_15_0 = 0) & equal_set(all_15_2, all_15_1) = all_15_0 & % 8.58/2.10 | subset(all_15_1, all_15_2) = 0 & subset(all_15_2, all_15_1) = 0 & % 8.58/2.10 | $i(all_15_1) & $i(all_15_2) % 8.58/2.10 | % 8.58/2.10 | ALPHA: (3) implies: % 8.58/2.10 | (4) ~ (all_15_0 = 0) % 8.58/2.10 | (5) $i(all_15_2) % 8.58/2.10 | (6) $i(all_15_1) % 8.58/2.10 | (7) subset(all_15_2, all_15_1) = 0 % 8.58/2.10 | (8) subset(all_15_1, all_15_2) = 0 % 8.58/2.10 | (9) equal_set(all_15_2, all_15_1) = all_15_0 % 8.58/2.10 | % 8.58/2.10 | GROUND_INST: instantiating (1) with all_15_2, all_15_1, all_15_0, simplifying % 8.58/2.10 | with (5), (6), (9) gives: % 8.58/2.10 | (10) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1, % 8.58/2.10 | all_15_2) = v1 & subset(all_15_2, all_15_1) = v0 & ( ~ (v1 = 0) | % 8.58/2.10 | ~ (v0 = 0))) % 8.58/2.10 | % 8.58/2.10 | BETA: splitting (10) gives: % 8.58/2.10 | % 8.58/2.10 | Case 1: % 8.58/2.10 | | % 8.58/2.10 | | (11) all_15_0 = 0 % 8.58/2.10 | | % 8.58/2.11 | | REDUCE: (4), (11) imply: % 8.58/2.11 | | (12) $false % 8.58/2.11 | | % 8.58/2.11 | | CLOSE: (12) is inconsistent. % 8.58/2.11 | | % 8.58/2.11 | Case 2: % 8.58/2.11 | | % 8.58/2.11 | | (13) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_2) = v1 & % 8.58/2.11 | | subset(all_15_2, all_15_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.58/2.11 | | % 8.58/2.11 | | DELTA: instantiating (13) with fresh symbols all_27_0, all_27_1 gives: % 8.58/2.11 | | (14) subset(all_15_1, all_15_2) = all_27_0 & subset(all_15_2, all_15_1) = % 8.58/2.11 | | all_27_1 & ( ~ (all_27_0 = 0) | ~ (all_27_1 = 0)) % 8.58/2.11 | | % 8.58/2.11 | | ALPHA: (14) implies: % 8.58/2.11 | | (15) subset(all_15_2, all_15_1) = all_27_1 % 8.58/2.11 | | (16) subset(all_15_1, all_15_2) = all_27_0 % 8.58/2.11 | | (17) ~ (all_27_0 = 0) | ~ (all_27_1 = 0) % 8.58/2.11 | | % 8.58/2.11 | | GROUND_INST: instantiating (2) with 0, all_27_1, all_15_1, all_15_2, % 8.58/2.11 | | simplifying with (7), (15) gives: % 8.58/2.11 | | (18) all_27_1 = 0 % 8.58/2.11 | | % 8.58/2.11 | | GROUND_INST: instantiating (2) with 0, all_27_0, all_15_2, all_15_1, % 8.58/2.11 | | simplifying with (8), (16) gives: % 8.58/2.11 | | (19) all_27_0 = 0 % 8.58/2.11 | | % 8.58/2.11 | | BETA: splitting (17) gives: % 8.58/2.11 | | % 8.58/2.11 | | Case 1: % 8.58/2.11 | | | % 8.58/2.11 | | | (20) ~ (all_27_0 = 0) % 8.58/2.11 | | | % 8.58/2.11 | | | REDUCE: (19), (20) imply: % 8.58/2.11 | | | (21) $false % 8.58/2.11 | | | % 8.58/2.11 | | | CLOSE: (21) is inconsistent. % 8.58/2.11 | | | % 8.58/2.11 | | Case 2: % 8.58/2.11 | | | % 8.58/2.11 | | | (22) ~ (all_27_1 = 0) % 8.58/2.11 | | | % 8.58/2.11 | | | REDUCE: (18), (22) imply: % 8.58/2.12 | | | (23) $false % 8.58/2.12 | | | % 8.58/2.12 | | | CLOSE: (23) is inconsistent. % 8.58/2.12 | | | % 8.58/2.12 | | End of split % 8.58/2.12 | | % 8.58/2.12 | End of split % 8.58/2.12 | % 8.58/2.12 End of proof % 8.58/2.12 % SZS output end Proof for theBenchmark % 8.58/2.12 % 8.58/2.12 1547ms %------------------------------------------------------------------------------