%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET027+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 : n011.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 15:23:16 EDT 2023 % Result : Theorem 6.13s 1.63s % Output : Proof 7.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET027+4 : TPTP v8.1.2. Released v2.2.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n011.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Aug 26 11:35:24 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.67 ________ _____ % 0.19/0.67 ___ __ \_________(_)________________________________ % 0.19/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.67 % 0.19/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.67 (2023-06-19) % 0.19/0.67 % 0.19/0.67 (c) Philipp Rümmer, 2009-2023 % 0.19/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.67 Amanda Stjerna. % 0.19/0.67 Free software under BSD-3-Clause. % 0.19/0.67 % 0.19/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.67 % 0.19/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.68 Running up to 7 provers in parallel. % 0.19/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.49/1.06 Prover 1: Preprocessing ... % 2.49/1.06 Prover 4: Preprocessing ... % 2.81/1.10 Prover 0: Preprocessing ... % 2.81/1.10 Prover 2: Preprocessing ... % 2.81/1.10 Prover 3: Preprocessing ... % 2.81/1.10 Prover 5: Preprocessing ... % 2.81/1.10 Prover 6: Preprocessing ... % 5.14/1.49 Prover 6: Proving ... % 5.14/1.49 Prover 5: Proving ... % 5.65/1.51 Prover 1: Constructing countermodel ... % 5.65/1.51 Prover 3: Constructing countermodel ... % 5.65/1.51 Prover 2: Proving ... % 5.65/1.52 Prover 4: Constructing countermodel ... % 5.65/1.53 Prover 0: Proving ... % 6.13/1.63 Prover 3: proved (937ms) % 6.13/1.63 % 6.13/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.13/1.63 % 6.13/1.63 Prover 5: stopped % 6.13/1.63 Prover 2: stopped % 6.13/1.64 Prover 6: stopped % 6.13/1.64 Prover 0: stopped % 6.13/1.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.13/1.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.13/1.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.13/1.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.13/1.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.87/1.68 Prover 7: Preprocessing ... % 6.87/1.68 Prover 13: Preprocessing ... % 6.87/1.68 Prover 8: Preprocessing ... % 6.87/1.68 Prover 10: Preprocessing ... % 6.87/1.68 Prover 11: Preprocessing ... % 6.87/1.69 Prover 1: Found proof (size 17) % 6.87/1.69 Prover 1: proved (1000ms) % 6.87/1.69 Prover 4: stopped % 7.09/1.70 Prover 10: stopped % 7.09/1.70 Prover 7: stopped % 7.09/1.73 Prover 13: stopped % 7.33/1.73 Prover 11: stopped % 7.33/1.77 Prover 8: Warning: ignoring some quantifiers % 7.33/1.78 Prover 8: Constructing countermodel ... % 7.33/1.79 Prover 8: stopped % 7.33/1.79 % 7.33/1.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.33/1.79 % 7.33/1.80 % SZS output start Proof for theBenchmark % 7.33/1.80 Assumptions after simplification: % 7.33/1.80 --------------------------------- % 7.66/1.80 % 7.66/1.80 (subset) % 7.66/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 7.66/1.83 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 7.66/1.83 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 7.66/1.83 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 7.66/1.83 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 7.66/1.83 % 7.66/1.83 (thI03) % 7.66/1.83 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 7.66/1.83 subset(v1, v2) = 0 & subset(v0, v2) = v3 & subset(v0, v1) = 0 & $i(v2) & % 7.66/1.83 $i(v1) & $i(v0)) % 7.66/1.83 % 7.66/1.83 (function-axioms) % 7.66/1.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.66/1.84 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 7.66/1.84 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.66/1.84 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 7.66/1.84 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 7.66/1.84 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 7.66/1.84 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 7.66/1.84 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 7.66/1.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 7.66/1.84 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 7.66/1.84 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 7.66/1.84 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 7.66/1.84 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.66/1.84 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 7.66/1.84 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 7.66/1.84 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 7.66/1.84 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 7.66/1.84 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 7.66/1.84 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 7.66/1.84 (power_set(v2) = v0)) % 7.66/1.84 % 7.66/1.84 Further assumptions not needed in the proof: % 7.66/1.84 -------------------------------------------- % 7.66/1.84 difference, empty_set, equal_set, intersection, power_set, product, singleton, % 7.66/1.84 sum, union, unordered_pair % 7.66/1.84 % 7.66/1.84 Those formulas are unsatisfiable: % 7.66/1.84 --------------------------------- % 7.66/1.84 % 7.66/1.84 Begin of proof % 7.66/1.84 | % 7.66/1.84 | ALPHA: (subset) implies: % 7.66/1.85 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 7.66/1.85 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 7.66/1.85 | member(v2, v1) = 0)) % 7.66/1.85 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 7.66/1.85 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 7.66/1.85 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 7.66/1.85 | % 7.66/1.85 | ALPHA: (function-axioms) implies: % 7.66/1.85 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 7.66/1.85 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 7.66/1.85 | = v0)) % 7.66/1.85 | % 7.66/1.85 | DELTA: instantiating (thI03) with fresh symbols all_15_0, all_15_1, all_15_2, % 7.66/1.85 | all_15_3 gives: % 7.66/1.85 | (4) ~ (all_15_0 = 0) & subset(all_15_2, all_15_1) = 0 & subset(all_15_3, % 7.66/1.85 | all_15_1) = all_15_0 & subset(all_15_3, all_15_2) = 0 & $i(all_15_1) % 7.66/1.85 | & $i(all_15_2) & $i(all_15_3) % 7.66/1.85 | % 7.66/1.85 | ALPHA: (4) implies: % 7.66/1.85 | (5) ~ (all_15_0 = 0) % 7.66/1.85 | (6) $i(all_15_3) % 7.66/1.85 | (7) $i(all_15_2) % 7.66/1.85 | (8) $i(all_15_1) % 7.66/1.85 | (9) subset(all_15_3, all_15_2) = 0 % 7.66/1.85 | (10) subset(all_15_3, all_15_1) = all_15_0 % 7.66/1.85 | (11) subset(all_15_2, all_15_1) = 0 % 7.66/1.85 | % 7.66/1.85 | GROUND_INST: instantiating (1) with all_15_3, all_15_2, simplifying with (6), % 7.66/1.85 | (7), (9) gives: % 7.66/1.85 | (12) ! [v0: $i] : ( ~ (member(v0, all_15_3) = 0) | ~ $i(v0) | member(v0, % 7.66/1.85 | all_15_2) = 0) % 7.66/1.85 | % 7.66/1.85 | GROUND_INST: instantiating (2) with all_15_3, all_15_1, all_15_0, simplifying % 7.66/1.85 | with (6), (8), (10) gives: % 7.66/1.85 | (13) all_15_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 7.66/1.85 | all_15_1) = v1 & member(v0, all_15_3) = 0 & $i(v0)) % 7.66/1.86 | % 7.66/1.86 | GROUND_INST: instantiating (1) with all_15_2, all_15_1, simplifying with (7), % 7.66/1.86 | (8), (11) gives: % 7.66/1.86 | (14) ! [v0: $i] : ( ~ (member(v0, all_15_2) = 0) | ~ $i(v0) | member(v0, % 7.66/1.86 | all_15_1) = 0) % 7.66/1.86 | % 7.66/1.86 | BETA: splitting (13) gives: % 7.66/1.86 | % 7.66/1.86 | Case 1: % 7.66/1.86 | | % 7.66/1.86 | | (15) all_15_0 = 0 % 7.66/1.86 | | % 7.66/1.86 | | REDUCE: (5), (15) imply: % 7.66/1.86 | | (16) $false % 7.66/1.86 | | % 7.66/1.86 | | CLOSE: (16) is inconsistent. % 7.66/1.86 | | % 7.66/1.86 | Case 2: % 7.66/1.86 | | % 7.66/1.86 | | (17) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) = % 7.66/1.86 | | v1 & member(v0, all_15_3) = 0 & $i(v0)) % 7.66/1.86 | | % 7.66/1.86 | | DELTA: instantiating (17) with fresh symbols all_27_0, all_27_1 gives: % 7.66/1.86 | | (18) ~ (all_27_0 = 0) & member(all_27_1, all_15_1) = all_27_0 & % 7.66/1.86 | | member(all_27_1, all_15_3) = 0 & $i(all_27_1) % 7.66/1.86 | | % 7.66/1.86 | | ALPHA: (18) implies: % 7.66/1.86 | | (19) ~ (all_27_0 = 0) % 7.66/1.86 | | (20) $i(all_27_1) % 7.66/1.86 | | (21) member(all_27_1, all_15_3) = 0 % 7.66/1.86 | | (22) member(all_27_1, all_15_1) = all_27_0 % 7.66/1.86 | | % 7.66/1.86 | | GROUND_INST: instantiating (12) with all_27_1, simplifying with (20), (21) % 7.66/1.86 | | gives: % 7.66/1.86 | | (23) member(all_27_1, all_15_2) = 0 % 7.66/1.86 | | % 7.66/1.86 | | GROUND_INST: instantiating (14) with all_27_1, simplifying with (20), (23) % 7.66/1.86 | | gives: % 7.66/1.86 | | (24) member(all_27_1, all_15_1) = 0 % 7.66/1.86 | | % 7.66/1.86 | | GROUND_INST: instantiating (3) with all_27_0, 0, all_15_1, all_27_1, % 7.66/1.86 | | simplifying with (22), (24) gives: % 7.66/1.86 | | (25) all_27_0 = 0 % 7.66/1.86 | | % 7.66/1.86 | | REDUCE: (19), (25) imply: % 7.66/1.86 | | (26) $false % 7.66/1.86 | | % 7.66/1.86 | | CLOSE: (26) is inconsistent. % 7.66/1.86 | | % 7.66/1.86 | End of split % 7.66/1.86 | % 7.66/1.86 End of proof % 7.66/1.86 % SZS output end Proof for theBenchmark % 7.66/1.86 % 7.66/1.86 1193ms %------------------------------------------------------------------------------