%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET366+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 : n012.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 15:24:46 EDT 2023 % Result : Theorem 5.37s 1.53s % Output : Proof 7.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET366+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n012.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Sat Aug 26 14:50:10 EDT 2023 % 0.13/0.33 % CPUTime : % 0.18/0.60 ________ _____ % 0.18/0.60 ___ __ \_________(_)________________________________ % 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.60 % 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.60 (2023-06-19) % 0.18/0.60 % 0.18/0.60 (c) Philipp Rümmer, 2009-2023 % 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.60 Amanda Stjerna. % 0.18/0.60 Free software under BSD-3-Clause. % 0.18/0.60 % 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.60 % 0.18/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.61 Running up to 7 provers in parallel. % 0.18/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.93/0.97 Prover 1: Preprocessing ... % 1.93/0.99 Prover 4: Preprocessing ... % 2.58/1.02 Prover 6: Preprocessing ... % 2.58/1.02 Prover 2: Preprocessing ... % 2.58/1.02 Prover 0: Preprocessing ... % 2.58/1.02 Prover 5: Preprocessing ... % 2.58/1.02 Prover 3: Preprocessing ... % 4.63/1.39 Prover 5: Proving ... % 4.63/1.40 Prover 6: Proving ... % 4.63/1.41 Prover 1: Constructing countermodel ... % 4.63/1.41 Prover 2: Proving ... % 4.63/1.42 Prover 3: Constructing countermodel ... % 4.63/1.42 Prover 4: Constructing countermodel ... % 4.63/1.48 Prover 0: Proving ... % 5.37/1.53 Prover 3: proved (910ms) % 5.37/1.53 % 5.37/1.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.37/1.53 % 5.37/1.53 Prover 6: stopped % 5.37/1.53 Prover 5: stopped % 5.37/1.53 Prover 2: stopped % 5.37/1.53 Prover 0: stopped % 5.37/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.37/1.54 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.37/1.54 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.37/1.54 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.37/1.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.37/1.57 Prover 1: Found proof (size 20) % 5.37/1.57 Prover 1: proved (950ms) % 5.37/1.57 Prover 11: Preprocessing ... % 5.37/1.57 Prover 4: stopped % 5.37/1.57 Prover 10: Preprocessing ... % 5.37/1.58 Prover 8: Preprocessing ... % 5.37/1.58 Prover 13: Preprocessing ... % 5.37/1.59 Prover 7: Preprocessing ... % 6.72/1.60 Prover 10: stopped % 6.72/1.61 Prover 7: stopped % 6.77/1.61 Prover 11: stopped % 6.77/1.61 Prover 13: stopped % 6.77/1.67 Prover 8: Warning: ignoring some quantifiers % 6.77/1.68 Prover 8: Constructing countermodel ... % 6.77/1.69 Prover 8: stopped % 6.77/1.69 % 6.77/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.77/1.69 % 6.77/1.69 % SZS output start Proof for theBenchmark % 6.77/1.69 Assumptions after simplification: % 6.77/1.69 --------------------------------- % 6.77/1.69 % 6.77/1.69 (empty_set) % 7.26/1.72 $i(empty_set) & ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0)) % 7.26/1.72 % 7.26/1.72 (power_set) % 7.26/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 7.26/1.73 (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 7.26/1.73 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] % 7.26/1.73 : ! [v2: $i] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) % 7.26/1.73 | ~ $i(v0) | subset(v0, v1) = 0) % 7.26/1.73 % 7.26/1.73 (subset) % 7.26/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 7.26/1.73 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 7.26/1.73 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 7.26/1.73 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 7.26/1.73 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 7.26/1.73 % 7.26/1.73 (thI47) % 7.26/1.73 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 7.26/1.73 power_set(v0) = v1 & member(empty_set, v1) = v2 & $i(v1) & $i(v0)) % 7.26/1.73 % 7.26/1.73 Further assumptions not needed in the proof: % 7.26/1.73 -------------------------------------------- % 7.26/1.73 difference, equal_set, intersection, product, singleton, sum, union, % 7.26/1.73 unordered_pair % 7.26/1.73 % 7.26/1.73 Those formulas are unsatisfiable: % 7.26/1.73 --------------------------------- % 7.26/1.73 % 7.26/1.73 Begin of proof % 7.26/1.73 | % 7.26/1.73 | ALPHA: (subset) implies: % 7.26/1.73 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 7.26/1.74 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 7.26/1.74 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 7.26/1.74 | % 7.26/1.74 | ALPHA: (power_set) implies: % 7.26/1.74 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 7.26/1.74 | (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ % 7.26/1.74 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 7.26/1.74 | % 7.26/1.74 | ALPHA: (empty_set) implies: % 7.26/1.74 | (3) ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0)) % 7.26/1.74 | % 7.26/1.74 | ALPHA: (thI47) implies: % 7.26/1.74 | (4) $i(empty_set) % 7.26/1.74 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & power_set(v0) % 7.26/1.74 | = v1 & member(empty_set, v1) = v2 & $i(v1) & $i(v0)) % 7.26/1.74 | % 7.26/1.74 | DELTA: instantiating (5) with fresh symbols all_15_0, all_15_1, all_15_2 % 7.26/1.74 | gives: % 7.26/1.74 | (6) ~ (all_15_0 = 0) & power_set(all_15_2) = all_15_1 & member(empty_set, % 7.26/1.74 | all_15_1) = all_15_0 & $i(all_15_1) & $i(all_15_2) % 7.26/1.74 | % 7.26/1.74 | ALPHA: (6) implies: % 7.26/1.74 | (7) ~ (all_15_0 = 0) % 7.26/1.74 | (8) $i(all_15_2) % 7.26/1.74 | (9) member(empty_set, all_15_1) = all_15_0 % 7.26/1.74 | (10) power_set(all_15_2) = all_15_1 % 7.26/1.74 | % 7.26/1.74 | GROUND_INST: instantiating (2) with empty_set, all_15_2, all_15_1, all_15_0, % 7.26/1.74 | simplifying with (4), (8), (9), (10) gives: % 7.26/1.74 | (11) all_15_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(empty_set, % 7.26/1.74 | all_15_2) = v0) % 7.26/1.74 | % 7.26/1.74 | BETA: splitting (11) gives: % 7.26/1.75 | % 7.26/1.75 | Case 1: % 7.26/1.75 | | % 7.26/1.75 | | (12) all_15_0 = 0 % 7.26/1.75 | | % 7.26/1.75 | | REDUCE: (7), (12) imply: % 7.26/1.75 | | (13) $false % 7.26/1.75 | | % 7.26/1.75 | | CLOSE: (13) is inconsistent. % 7.26/1.75 | | % 7.26/1.75 | Case 2: % 7.26/1.75 | | % 7.26/1.75 | | (14) ? [v0: int] : ( ~ (v0 = 0) & subset(empty_set, all_15_2) = v0) % 7.26/1.75 | | % 7.26/1.75 | | DELTA: instantiating (14) with fresh symbol all_24_0 gives: % 7.26/1.75 | | (15) ~ (all_24_0 = 0) & subset(empty_set, all_15_2) = all_24_0 % 7.26/1.75 | | % 7.26/1.75 | | ALPHA: (15) implies: % 7.26/1.75 | | (16) ~ (all_24_0 = 0) % 7.26/1.75 | | (17) subset(empty_set, all_15_2) = all_24_0 % 7.26/1.75 | | % 7.26/1.75 | | GROUND_INST: instantiating (1) with empty_set, all_15_2, all_24_0, % 7.26/1.75 | | simplifying with (4), (8), (17) gives: % 7.26/1.75 | | (18) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 7.26/1.75 | | member(v0, all_15_2) = v1 & member(v0, empty_set) = 0 & $i(v0)) % 7.26/1.75 | | % 7.26/1.75 | | BETA: splitting (18) gives: % 7.26/1.75 | | % 7.26/1.75 | | Case 1: % 7.26/1.75 | | | % 7.26/1.75 | | | (19) all_24_0 = 0 % 7.26/1.75 | | | % 7.26/1.75 | | | REDUCE: (16), (19) imply: % 7.26/1.75 | | | (20) $false % 7.26/1.75 | | | % 7.26/1.75 | | | CLOSE: (20) is inconsistent. % 7.26/1.75 | | | % 7.26/1.75 | | Case 2: % 7.26/1.75 | | | % 7.26/1.75 | | | (21) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_2) = % 7.26/1.75 | | | v1 & member(v0, empty_set) = 0 & $i(v0)) % 7.26/1.75 | | | % 7.26/1.75 | | | DELTA: instantiating (21) with fresh symbols all_33_0, all_33_1 gives: % 7.26/1.75 | | | (22) ~ (all_33_0 = 0) & member(all_33_1, all_15_2) = all_33_0 & % 7.26/1.75 | | | member(all_33_1, empty_set) = 0 & $i(all_33_1) % 7.26/1.75 | | | % 7.26/1.75 | | | ALPHA: (22) implies: % 7.26/1.75 | | | (23) $i(all_33_1) % 7.26/1.75 | | | (24) member(all_33_1, empty_set) = 0 % 7.26/1.75 | | | % 7.26/1.75 | | | GROUND_INST: instantiating (3) with all_33_1, simplifying with (23), (24) % 7.26/1.75 | | | gives: % 7.26/1.75 | | | (25) $false % 7.26/1.75 | | | % 7.26/1.75 | | | CLOSE: (25) is inconsistent. % 7.26/1.75 | | | % 7.26/1.75 | | End of split % 7.26/1.75 | | % 7.26/1.75 | End of split % 7.26/1.75 | % 7.26/1.75 End of proof % 7.26/1.75 % SZS output end Proof for theBenchmark % 7.26/1.75 % 7.26/1.75 1154ms %------------------------------------------------------------------------------