%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET705+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 : n032.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 15:26:04 EDT 2023 % Result : Theorem 5.02s 1.50s % Output : Proof 7.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SET705+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.30 % Computer : n032.cluster.edu % 0.11/0.30 % Model : x86_64 x86_64 % 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.30 % Memory : 8042.1875MB % 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.30 % CPULimit : 300 % 0.11/0.30 % WCLimit : 300 % 0.11/0.30 % DateTime : Sat Aug 26 09:40:43 EDT 2023 % 0.11/0.30 % CPUTime : % 0.15/0.54 ________ _____ % 0.15/0.54 ___ __ \_________(_)________________________________ % 0.15/0.54 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.15/0.54 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.15/0.54 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.15/0.54 % 0.15/0.54 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.15/0.54 (2023-06-19) % 0.15/0.54 % 0.15/0.54 (c) Philipp Rümmer, 2009-2023 % 0.15/0.54 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.15/0.54 Amanda Stjerna. % 0.15/0.54 Free software under BSD-3-Clause. % 0.15/0.54 % 0.15/0.54 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.15/0.54 % 0.15/0.54 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.15/0.55 Running up to 7 provers in parallel. % 0.15/0.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.15/0.56 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.15/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.15/0.56 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.15/0.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.15/0.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.15/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.10/0.92 Prover 1: Preprocessing ... % 2.10/0.92 Prover 4: Preprocessing ... % 2.10/0.96 Prover 2: Preprocessing ... % 2.10/0.96 Prover 3: Preprocessing ... % 2.10/0.97 Prover 6: Preprocessing ... % 2.10/0.97 Prover 5: Preprocessing ... % 2.10/0.97 Prover 0: Preprocessing ... % 5.02/1.35 Prover 6: Proving ... % 5.02/1.36 Prover 5: Proving ... % 5.02/1.36 Prover 1: Constructing countermodel ... % 5.02/1.37 Prover 3: Constructing countermodel ... % 5.02/1.38 Prover 2: Proving ... % 5.02/1.41 Prover 4: Constructing countermodel ... % 5.02/1.42 Prover 0: Proving ... % 5.02/1.50 Prover 3: proved (942ms) % 5.02/1.50 % 5.02/1.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.02/1.50 % 5.02/1.51 Prover 5: stopped % 5.02/1.52 Prover 2: stopped % 5.02/1.52 Prover 0: stopped % 5.02/1.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.02/1.52 Prover 6: proved (955ms) % 5.02/1.52 % 5.02/1.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.02/1.52 % 6.34/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.34/1.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.34/1.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.34/1.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.34/1.54 Prover 1: Found proof (size 20) % 6.34/1.55 Prover 1: proved (988ms) % 6.34/1.55 Prover 4: stopped % 6.34/1.56 Prover 7: Preprocessing ... % 6.34/1.56 Prover 11: Preprocessing ... % 6.34/1.56 Prover 8: Preprocessing ... % 6.34/1.57 Prover 10: Preprocessing ... % 6.34/1.58 Prover 13: Preprocessing ... % 6.34/1.59 Prover 10: stopped % 6.34/1.60 Prover 7: stopped % 6.34/1.60 Prover 11: stopped % 6.34/1.61 Prover 13: stopped % 7.16/1.66 Prover 8: Warning: ignoring some quantifiers % 7.16/1.67 Prover 8: Constructing countermodel ... % 7.16/1.68 Prover 8: stopped % 7.16/1.68 % 7.16/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.16/1.68 % 7.16/1.68 % SZS output start Proof for theBenchmark % 7.16/1.69 Assumptions after simplification: % 7.16/1.69 --------------------------------- % 7.16/1.69 % 7.16/1.69 (power_set) % 7.54/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 7.54/1.73 (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 7.54/1.73 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] % 7.54/1.73 : ! [v2: $i] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) % 7.54/1.73 | ~ $i(v0) | subset(v0, v1) = 0) % 7.54/1.73 % 7.54/1.73 (subset) % 7.54/1.74 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 7.54/1.74 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 7.54/1.74 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 7.54/1.74 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 7.54/1.74 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 7.54/1.74 % 7.54/1.74 (thI48) % 7.54/1.74 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & power_set(v0) = v1 & % 7.54/1.74 member(v0, v1) = v2 & $i(v1) & $i(v0)) % 7.54/1.74 % 7.54/1.74 (function-axioms) % 7.54/1.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.54/1.75 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 7.54/1.75 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.54/1.75 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 7.54/1.75 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 7.54/1.75 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 7.54/1.75 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 7.54/1.75 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 7.54/1.75 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 7.54/1.75 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 7.54/1.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 7.54/1.75 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 7.54/1.75 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.54/1.75 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 7.54/1.75 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 7.54/1.75 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 7.54/1.75 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 7.54/1.75 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 7.54/1.75 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 7.54/1.75 (power_set(v2) = v0)) % 7.54/1.75 % 7.54/1.75 Further assumptions not needed in the proof: % 7.54/1.75 -------------------------------------------- % 7.54/1.75 difference, empty_set, equal_set, intersection, product, singleton, sum, union, % 7.54/1.75 unordered_pair % 7.54/1.75 % 7.54/1.75 Those formulas are unsatisfiable: % 7.54/1.75 --------------------------------- % 7.54/1.75 % 7.54/1.75 Begin of proof % 7.54/1.75 | % 7.54/1.75 | ALPHA: (subset) implies: % 7.54/1.76 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 7.54/1.76 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 7.54/1.76 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 7.54/1.76 | % 7.54/1.76 | ALPHA: (power_set) implies: % 7.54/1.76 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 7.54/1.76 | (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ % 7.54/1.76 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 7.54/1.76 | % 7.54/1.76 | ALPHA: (function-axioms) implies: % 7.54/1.76 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 7.54/1.76 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 7.54/1.76 | = v0)) % 7.54/1.76 | % 7.54/1.76 | DELTA: instantiating (thI48) with fresh symbols all_15_0, all_15_1, all_15_2 % 7.54/1.76 | gives: % 7.54/1.76 | (4) ~ (all_15_0 = 0) & power_set(all_15_2) = all_15_1 & member(all_15_2, % 7.54/1.76 | all_15_1) = all_15_0 & $i(all_15_1) & $i(all_15_2) % 7.54/1.76 | % 7.54/1.76 | ALPHA: (4) implies: % 7.54/1.76 | (5) ~ (all_15_0 = 0) % 7.54/1.76 | (6) $i(all_15_2) % 7.54/1.76 | (7) member(all_15_2, all_15_1) = all_15_0 % 7.54/1.76 | (8) power_set(all_15_2) = all_15_1 % 7.54/1.76 | % 7.54/1.76 | GROUND_INST: instantiating (2) with all_15_2, all_15_2, all_15_1, all_15_0, % 7.54/1.76 | simplifying with (6), (7), (8) gives: % 7.54/1.76 | (9) all_15_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_15_2, all_15_2) % 7.54/1.76 | = v0) % 7.54/1.76 | % 7.54/1.76 | BETA: splitting (9) gives: % 7.54/1.76 | % 7.54/1.77 | Case 1: % 7.54/1.77 | | % 7.54/1.77 | | (10) all_15_0 = 0 % 7.54/1.77 | | % 7.54/1.77 | | REDUCE: (5), (10) imply: % 7.54/1.77 | | (11) $false % 7.54/1.77 | | % 7.54/1.77 | | CLOSE: (11) is inconsistent. % 7.54/1.77 | | % 7.54/1.77 | Case 2: % 7.54/1.77 | | % 7.54/1.77 | | (12) ? [v0: int] : ( ~ (v0 = 0) & subset(all_15_2, all_15_2) = v0) % 7.54/1.77 | | % 7.54/1.77 | | DELTA: instantiating (12) with fresh symbol all_24_0 gives: % 7.54/1.77 | | (13) ~ (all_24_0 = 0) & subset(all_15_2, all_15_2) = all_24_0 % 7.54/1.77 | | % 7.54/1.77 | | ALPHA: (13) implies: % 7.54/1.77 | | (14) ~ (all_24_0 = 0) % 7.54/1.77 | | (15) subset(all_15_2, all_15_2) = all_24_0 % 7.54/1.77 | | % 7.54/1.77 | | GROUND_INST: instantiating (1) with all_15_2, all_15_2, all_24_0, % 7.54/1.77 | | simplifying with (6), (15) gives: % 7.54/1.77 | | (16) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 7.54/1.77 | | member(v0, all_15_2) = v1 & member(v0, all_15_2) = 0 & $i(v0)) % 7.54/1.77 | | % 7.54/1.77 | | BETA: splitting (16) gives: % 7.54/1.77 | | % 7.54/1.77 | | Case 1: % 7.54/1.77 | | | % 7.54/1.77 | | | (17) all_24_0 = 0 % 7.54/1.77 | | | % 7.54/1.77 | | | REDUCE: (14), (17) imply: % 7.54/1.77 | | | (18) $false % 7.54/1.77 | | | % 7.54/1.77 | | | CLOSE: (18) is inconsistent. % 7.54/1.77 | | | % 7.54/1.77 | | Case 2: % 7.54/1.77 | | | % 7.54/1.77 | | | (19) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_2) = % 7.54/1.77 | | | v1 & member(v0, all_15_2) = 0 & $i(v0)) % 7.54/1.77 | | | % 7.54/1.77 | | | DELTA: instantiating (19) with fresh symbols all_33_0, all_33_1 gives: % 7.54/1.77 | | | (20) ~ (all_33_0 = 0) & member(all_33_1, all_15_2) = all_33_0 & % 7.54/1.77 | | | member(all_33_1, all_15_2) = 0 & $i(all_33_1) % 7.54/1.77 | | | % 7.54/1.77 | | | ALPHA: (20) implies: % 7.54/1.77 | | | (21) ~ (all_33_0 = 0) % 7.54/1.77 | | | (22) member(all_33_1, all_15_2) = 0 % 7.54/1.77 | | | (23) member(all_33_1, all_15_2) = all_33_0 % 7.54/1.77 | | | % 7.54/1.77 | | | GROUND_INST: instantiating (3) with 0, all_33_0, all_15_2, all_33_1, % 7.54/1.77 | | | simplifying with (22), (23) gives: % 7.54/1.77 | | | (24) all_33_0 = 0 % 7.54/1.77 | | | % 7.54/1.77 | | | REDUCE: (21), (24) imply: % 7.54/1.77 | | | (25) $false % 7.54/1.77 | | | % 7.54/1.77 | | | CLOSE: (25) is inconsistent. % 7.54/1.77 | | | % 7.54/1.77 | | End of split % 7.54/1.77 | | % 7.54/1.77 | End of split % 7.54/1.77 | % 7.54/1.77 End of proof % 7.54/1.77 % SZS output end Proof for theBenchmark % 7.54/1.77 % 7.54/1.77 1233ms %------------------------------------------------------------------------------