%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET704+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 : n002.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 15:26:03 EDT 2023 % Result : Theorem 7.05s 1.65s % Output : Proof 8.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.11 % Problem : SET704+4 : TPTP v8.1.2. Released v2.2.0. % 0.08/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.08/0.30 % Computer : n002.cluster.edu % 0.08/0.30 % Model : x86_64 x86_64 % 0.08/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.30 % Memory : 8042.1875MB % 0.08/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.30 % CPULimit : 300 % 0.08/0.30 % WCLimit : 300 % 0.08/0.30 % DateTime : Sat Aug 26 12:51:33 EDT 2023 % 0.08/0.30 % CPUTime : % 0.13/0.52 ________ _____ % 0.13/0.52 ___ __ \_________(_)________________________________ % 0.13/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.13/0.52 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.13/0.52 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.13/0.52 % 0.13/0.52 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.13/0.52 (2023-06-19) % 0.13/0.52 % 0.13/0.52 (c) Philipp Rümmer, 2009-2023 % 0.13/0.52 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.13/0.52 Amanda Stjerna. % 0.13/0.52 Free software under BSD-3-Clause. % 0.13/0.52 % 0.13/0.52 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.13/0.52 % 0.13/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.13/0.54 Running up to 7 provers in parallel. % 0.13/0.55 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.13/0.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.13/0.55 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.13/0.55 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.13/0.55 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.13/0.55 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.13/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.31/0.98 Prover 4: Preprocessing ... % 2.31/0.98 Prover 1: Preprocessing ... % 2.31/1.02 Prover 6: Preprocessing ... % 2.31/1.02 Prover 3: Preprocessing ... % 2.31/1.03 Prover 5: Preprocessing ... % 2.31/1.03 Prover 2: Preprocessing ... % 2.31/1.03 Prover 0: Preprocessing ... % 5.78/1.49 Prover 3: Constructing countermodel ... % 5.78/1.49 Prover 6: Proving ... % 5.78/1.50 Prover 1: Constructing countermodel ... % 5.78/1.50 Prover 5: Proving ... % 5.78/1.52 Prover 2: Proving ... % 6.31/1.55 Prover 4: Constructing countermodel ... % 6.55/1.58 Prover 0: Proving ... % 6.94/1.65 Prover 3: proved (1099ms) % 7.05/1.65 % 7.05/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.05/1.65 % 7.05/1.65 Prover 2: stopped % 7.05/1.66 Prover 5: stopped % 7.05/1.66 Prover 0: stopped % 7.05/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.05/1.67 Prover 6: stopped % 7.05/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.05/1.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.05/1.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.05/1.68 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.05/1.69 Prover 8: Preprocessing ... % 7.05/1.69 Prover 7: Preprocessing ... % 7.49/1.73 Prover 10: Preprocessing ... % 7.49/1.73 Prover 11: Preprocessing ... % 7.49/1.73 Prover 13: Preprocessing ... % 7.49/1.75 Prover 1: Found proof (size 21) % 7.49/1.75 Prover 1: proved (1201ms) % 7.49/1.75 Prover 4: stopped % 7.49/1.76 Prover 10: stopped % 7.83/1.77 Prover 11: stopped % 7.83/1.79 Prover 7: Warning: ignoring some quantifiers % 7.83/1.79 Prover 13: stopped % 7.83/1.80 Prover 7: Constructing countermodel ... % 7.83/1.82 Prover 7: stopped % 8.29/1.85 Prover 8: Warning: ignoring some quantifiers % 8.29/1.86 Prover 8: Constructing countermodel ... % 8.29/1.87 Prover 8: stopped % 8.29/1.87 % 8.29/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.29/1.87 % 8.29/1.88 % SZS output start Proof for theBenchmark % 8.29/1.88 Assumptions after simplification: % 8.29/1.88 --------------------------------- % 8.29/1.88 % 8.29/1.88 (product) % 8.29/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.29/1.92 (product(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 8.29/1.92 [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) % 8.29/1.92 = v5 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 8.29/1.92 (product(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ! % 8.29/1.92 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (member(v0, v3) = v4) | ~ $i(v3) | % 8.29/1.92 ? [v5: int] : ( ~ (v5 = 0) & member(v3, v1) = v5))) % 8.29/1.92 % 8.29/1.92 (subset) % 8.29/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 8.29/1.93 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 8.29/1.93 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 8.29/1.93 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 8.29/1.93 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 8.29/1.93 % 8.29/1.93 (thI42) % 8.29/1.93 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 8.29/1.93 product(v0) = v2 & subset(v2, v1) = v3 & member(v1, v0) = 0 & $i(v2) & % 8.29/1.93 $i(v1) & $i(v0)) % 8.29/1.93 % 8.29/1.93 (function-axioms) % 8.29/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.29/1.94 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 8.29/1.94 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.29/1.94 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 8.29/1.94 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 8.29/1.94 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.29/1.94 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 8.29/1.94 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.29/1.94 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 8.29/1.94 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.29/1.94 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 8.29/1.94 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 8.29/1.94 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.29/1.94 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 8.29/1.94 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 8.29/1.94 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 8.29/1.94 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 8.29/1.94 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 8.29/1.94 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 8.29/1.94 (power_set(v2) = v0)) % 8.29/1.94 % 8.29/1.94 Further assumptions not needed in the proof: % 8.29/1.94 -------------------------------------------- % 8.29/1.95 difference, empty_set, equal_set, intersection, power_set, singleton, sum, % 8.29/1.95 union, unordered_pair % 8.29/1.95 % 8.29/1.95 Those formulas are unsatisfiable: % 8.29/1.95 --------------------------------- % 8.29/1.95 % 8.29/1.95 Begin of proof % 8.29/1.95 | % 8.29/1.95 | ALPHA: (subset) implies: % 8.29/1.95 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 8.29/1.95 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 8.29/1.95 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 8.29/1.95 | % 8.29/1.95 | ALPHA: (product) implies: % 8.29/1.95 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (product(v1) = v2) | ~ % 8.29/1.96 | (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ! [v4: % 8.29/1.96 | int] : (v4 = 0 | ~ (member(v0, v3) = v4) | ~ $i(v3) | ? [v5: % 8.29/1.96 | int] : ( ~ (v5 = 0) & member(v3, v1) = v5))) % 8.29/1.96 | % 8.29/1.96 | ALPHA: (function-axioms) implies: % 8.29/1.96 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.29/1.96 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 8.29/1.96 | = v0)) % 8.29/1.96 | % 8.29/1.96 | DELTA: instantiating (thI42) with fresh symbols all_15_0, all_15_1, all_15_2, % 8.29/1.96 | all_15_3 gives: % 8.29/1.96 | (4) ~ (all_15_0 = 0) & product(all_15_3) = all_15_1 & subset(all_15_1, % 8.29/1.96 | all_15_2) = all_15_0 & member(all_15_2, all_15_3) = 0 & $i(all_15_1) % 8.29/1.96 | & $i(all_15_2) & $i(all_15_3) % 8.29/1.96 | % 8.29/1.96 | ALPHA: (4) implies: % 8.81/1.96 | (5) ~ (all_15_0 = 0) % 8.81/1.96 | (6) $i(all_15_3) % 8.81/1.96 | (7) $i(all_15_2) % 8.81/1.96 | (8) $i(all_15_1) % 8.81/1.96 | (9) member(all_15_2, all_15_3) = 0 % 8.81/1.96 | (10) subset(all_15_1, all_15_2) = all_15_0 % 8.81/1.96 | (11) product(all_15_3) = all_15_1 % 8.81/1.96 | % 8.81/1.96 | GROUND_INST: instantiating (1) with all_15_1, all_15_2, all_15_0, simplifying % 8.81/1.96 | with (7), (8), (10) gives: % 8.81/1.97 | (12) all_15_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 8.81/1.97 | all_15_1) = 0 & member(v0, all_15_2) = v1 & $i(v0)) % 8.81/1.97 | % 8.81/1.97 | BETA: splitting (12) gives: % 8.81/1.97 | % 8.81/1.97 | Case 1: % 8.81/1.97 | | % 8.81/1.97 | | (13) all_15_0 = 0 % 8.81/1.97 | | % 8.81/1.97 | | REDUCE: (5), (13) imply: % 8.81/1.97 | | (14) $false % 8.81/1.97 | | % 8.81/1.97 | | CLOSE: (14) is inconsistent. % 8.81/1.97 | | % 8.81/1.97 | Case 2: % 8.81/1.97 | | % 8.81/1.97 | | (15) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) = 0 % 8.81/1.97 | | & member(v0, all_15_2) = v1 & $i(v0)) % 8.81/1.97 | | % 8.81/1.97 | | DELTA: instantiating (15) with fresh symbols all_24_0, all_24_1 gives: % 8.81/1.97 | | (16) ~ (all_24_0 = 0) & member(all_24_1, all_15_1) = 0 & % 8.81/1.97 | | member(all_24_1, all_15_2) = all_24_0 & $i(all_24_1) % 8.81/1.97 | | % 8.81/1.97 | | ALPHA: (16) implies: % 8.81/1.97 | | (17) ~ (all_24_0 = 0) % 8.81/1.97 | | (18) $i(all_24_1) % 8.81/1.97 | | (19) member(all_24_1, all_15_2) = all_24_0 % 8.81/1.97 | | (20) member(all_24_1, all_15_1) = 0 % 8.81/1.97 | | % 8.81/1.97 | | GROUND_INST: instantiating (2) with all_24_1, all_15_3, all_15_1, % 8.81/1.97 | | simplifying with (6), (11), (18), (20) gives: % 8.81/1.97 | | (21) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (member(all_24_1, v0) = % 8.81/1.97 | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0, % 8.81/1.97 | | all_15_3) = v2)) % 8.81/1.97 | | % 8.81/1.97 | | GROUND_INST: instantiating (21) with all_15_2, all_24_0, simplifying with % 8.81/1.97 | | (7), (19) gives: % 8.81/1.97 | | (22) all_24_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_15_2, % 8.81/1.97 | | all_15_3) = v0) % 8.81/1.97 | | % 8.81/1.97 | | BETA: splitting (22) gives: % 8.81/1.97 | | % 8.81/1.97 | | Case 1: % 8.81/1.97 | | | % 8.81/1.97 | | | (23) all_24_0 = 0 % 8.81/1.98 | | | % 8.81/1.98 | | | REDUCE: (17), (23) imply: % 8.81/1.98 | | | (24) $false % 8.81/1.98 | | | % 8.81/1.98 | | | CLOSE: (24) is inconsistent. % 8.81/1.98 | | | % 8.81/1.98 | | Case 2: % 8.81/1.98 | | | % 8.81/1.98 | | | (25) ? [v0: int] : ( ~ (v0 = 0) & member(all_15_2, all_15_3) = v0) % 8.81/1.98 | | | % 8.81/1.98 | | | DELTA: instantiating (25) with fresh symbol all_36_0 gives: % 8.81/1.98 | | | (26) ~ (all_36_0 = 0) & member(all_15_2, all_15_3) = all_36_0 % 8.81/1.98 | | | % 8.81/1.98 | | | ALPHA: (26) implies: % 8.81/1.98 | | | (27) ~ (all_36_0 = 0) % 8.81/1.98 | | | (28) member(all_15_2, all_15_3) = all_36_0 % 8.81/1.98 | | | % 8.81/1.98 | | | GROUND_INST: instantiating (3) with 0, all_36_0, all_15_3, all_15_2, % 8.81/1.98 | | | simplifying with (9), (28) gives: % 8.81/1.98 | | | (29) all_36_0 = 0 % 8.81/1.98 | | | % 8.81/1.98 | | | REDUCE: (27), (29) imply: % 8.81/1.98 | | | (30) $false % 8.81/1.98 | | | % 8.81/1.98 | | | CLOSE: (30) is inconsistent. % 8.81/1.98 | | | % 8.81/1.98 | | End of split % 8.81/1.98 | | % 8.81/1.98 | End of split % 8.81/1.98 | % 8.81/1.98 End of proof % 8.81/1.98 % SZS output end Proof for theBenchmark % 8.81/1.98 % 8.81/1.98 1454ms %------------------------------------------------------------------------------