%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET194+3 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n031.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 15:24:15 EDT 2023 % Result : Theorem 3.94s 1.40s % Output : Proof 5.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET194+3 : TPTP v8.1.2. Released v2.2.0. % 0.12/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n031.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sat Aug 26 12:49:23 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.97/1.01 Prover 4: Preprocessing ... % 1.97/1.01 Prover 1: Preprocessing ... % 2.38/1.08 Prover 3: Preprocessing ... % 2.38/1.08 Prover 5: Preprocessing ... % 2.38/1.08 Prover 0: Preprocessing ... % 2.38/1.08 Prover 2: Preprocessing ... % 2.38/1.08 Prover 6: Preprocessing ... % 3.01/1.24 Prover 1: Warning: ignoring some quantifiers % 3.01/1.24 Prover 5: Proving ... % 3.01/1.25 Prover 3: Warning: ignoring some quantifiers % 3.01/1.25 Prover 1: Constructing countermodel ... % 3.01/1.25 Prover 6: Proving ... % 3.69/1.26 Prover 3: Constructing countermodel ... % 3.69/1.27 Prover 4: Warning: ignoring some quantifiers % 3.69/1.28 Prover 4: Constructing countermodel ... % 3.69/1.28 Prover 2: Proving ... % 3.94/1.29 Prover 0: Proving ... % 3.94/1.40 Prover 3: proved (749ms) % 3.94/1.40 % 3.94/1.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.94/1.40 % 3.94/1.40 Prover 5: stopped % 3.94/1.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.94/1.41 Prover 0: proved (767ms) % 3.94/1.41 Prover 6: proved (754ms) % 3.94/1.41 % 3.94/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.94/1.41 % 3.94/1.42 % 3.94/1.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.94/1.42 % 3.94/1.42 Prover 2: stopped % 3.94/1.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.94/1.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.94/1.42 Prover 8: Preprocessing ... % 3.94/1.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.43/1.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.81/1.44 Prover 7: Preprocessing ... % 4.81/1.45 Prover 10: Preprocessing ... % 4.81/1.45 Prover 13: Preprocessing ... % 4.81/1.45 Prover 11: Preprocessing ... % 4.81/1.48 Prover 1: Found proof (size 23) % 4.81/1.48 Prover 10: Warning: ignoring some quantifiers % 4.81/1.48 Prover 1: proved (840ms) % 4.81/1.48 Prover 4: stopped % 4.81/1.48 Prover 10: Constructing countermodel ... % 4.81/1.48 Prover 11: stopped % 4.81/1.49 Prover 10: stopped % 4.81/1.49 Prover 13: Warning: ignoring some quantifiers % 4.81/1.49 Prover 13: Constructing countermodel ... % 4.81/1.49 Prover 13: stopped % 4.81/1.50 Prover 7: Warning: ignoring some quantifiers % 5.25/1.50 Prover 7: Constructing countermodel ... % 5.25/1.50 Prover 8: Warning: ignoring some quantifiers % 5.25/1.50 Prover 7: stopped % 5.25/1.51 Prover 8: Constructing countermodel ... % 5.25/1.51 Prover 8: stopped % 5.25/1.51 % 5.25/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.25/1.51 % 5.25/1.52 % SZS output start Proof for theBenchmark % 5.25/1.52 Assumptions after simplification: % 5.25/1.52 --------------------------------- % 5.25/1.52 % 5.25/1.52 (commutativity_of_union) % 5.52/1.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1) % 5.52/1.56 | ~ $i(v0) | (union(v1, v0) = v2 & $i(v2))) % 5.52/1.56 % 5.52/1.56 (prove_subset_of_union) % 5.52/1.56 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 5.52/1.56 subset(v0, v2) = v3 & union(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0)) % 5.52/1.56 % 5.52/1.56 (subset_defn) % 5.52/1.57 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 5.52/1.57 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 5.52/1.57 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 5.52/1.57 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 5.52/1.57 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 5.52/1.57 % 5.52/1.57 (union_defn) % 5.52/1.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 5.52/1.57 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 5.52/1.57 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 5.52/1.57 member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0: $i] : ! [v1: $i] : % 5.52/1.57 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) % 5.52/1.57 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 5.52/1.57 (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0))) % 5.52/1.57 % 5.52/1.57 (function-axioms) % 5.52/1.58 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 5.52/1.58 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 5.52/1.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.52/1.58 (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 5.52/1.58 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.52/1.58 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 5.52/1.58 % 5.52/1.58 Further assumptions not needed in the proof: % 5.52/1.58 -------------------------------------------- % 5.52/1.58 equal_member_defn, reflexivity_of_subset % 5.52/1.58 % 5.52/1.58 Those formulas are unsatisfiable: % 5.52/1.58 --------------------------------- % 5.52/1.58 % 5.52/1.58 Begin of proof % 5.52/1.58 | % 5.52/1.58 | ALPHA: (union_defn) implies: % 5.52/1.58 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 5.52/1.58 | (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ % 5.52/1.58 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 5.52/1.58 | (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = % 5.52/1.58 | v5)) % 5.52/1.58 | % 5.52/1.58 | ALPHA: (subset_defn) implies: % 5.52/1.58 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 5.52/1.58 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 5.52/1.58 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 5.52/1.58 | % 5.52/1.58 | ALPHA: (function-axioms) implies: % 5.52/1.58 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 5.52/1.58 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 5.52/1.58 | = v0)) % 5.52/1.58 | % 5.52/1.58 | DELTA: instantiating (prove_subset_of_union) with fresh symbols all_7_0, % 5.52/1.58 | all_7_1, all_7_2, all_7_3 gives: % 5.52/1.59 | (4) ~ (all_7_0 = 0) & subset(all_7_3, all_7_1) = all_7_0 & union(all_7_3, % 5.52/1.59 | all_7_2) = all_7_1 & $i(all_7_1) & $i(all_7_2) & $i(all_7_3) % 5.52/1.59 | % 5.52/1.59 | ALPHA: (4) implies: % 5.52/1.59 | (5) ~ (all_7_0 = 0) % 5.52/1.59 | (6) $i(all_7_3) % 5.52/1.59 | (7) $i(all_7_2) % 5.52/1.59 | (8) union(all_7_3, all_7_2) = all_7_1 % 5.52/1.59 | (9) subset(all_7_3, all_7_1) = all_7_0 % 5.52/1.59 | % 5.52/1.59 | GROUND_INST: instantiating (commutativity_of_union) with all_7_3, all_7_2, % 5.52/1.59 | all_7_1, simplifying with (6), (7), (8) gives: % 5.52/1.59 | (10) union(all_7_2, all_7_3) = all_7_1 & $i(all_7_1) % 5.52/1.59 | % 5.52/1.59 | ALPHA: (10) implies: % 5.52/1.59 | (11) $i(all_7_1) % 5.52/1.59 | (12) union(all_7_2, all_7_3) = all_7_1 % 5.52/1.59 | % 5.52/1.59 | GROUND_INST: instantiating (2) with all_7_3, all_7_1, all_7_0, simplifying % 5.52/1.59 | with (6), (9), (11) gives: % 5.52/1.59 | (13) all_7_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 5.52/1.59 | all_7_1) = v1 & member(v0, all_7_3) = 0 & $i(v0)) % 5.52/1.59 | % 5.52/1.59 | BETA: splitting (13) gives: % 5.52/1.59 | % 5.52/1.59 | Case 1: % 5.52/1.59 | | % 5.52/1.59 | | (14) all_7_0 = 0 % 5.52/1.59 | | % 5.52/1.59 | | REDUCE: (5), (14) imply: % 5.52/1.59 | | (15) $false % 5.52/1.59 | | % 5.52/1.59 | | CLOSE: (15) is inconsistent. % 5.52/1.59 | | % 5.52/1.59 | Case 2: % 5.52/1.59 | | % 5.52/1.59 | | (16) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_7_1) = v1 % 5.52/1.59 | | & member(v0, all_7_3) = 0 & $i(v0)) % 5.52/1.59 | | % 5.52/1.59 | | DELTA: instantiating (16) with fresh symbols all_20_0, all_20_1 gives: % 5.52/1.60 | | (17) ~ (all_20_0 = 0) & member(all_20_1, all_7_1) = all_20_0 & % 5.52/1.60 | | member(all_20_1, all_7_3) = 0 & $i(all_20_1) % 5.52/1.60 | | % 5.52/1.60 | | ALPHA: (17) implies: % 5.52/1.60 | | (18) ~ (all_20_0 = 0) % 5.52/1.60 | | (19) $i(all_20_1) % 5.52/1.60 | | (20) member(all_20_1, all_7_3) = 0 % 5.52/1.60 | | (21) member(all_20_1, all_7_1) = all_20_0 % 5.52/1.60 | | % 5.52/1.60 | | GROUND_INST: instantiating (1) with all_7_2, all_7_3, all_20_1, all_7_1, % 5.52/1.60 | | all_20_0, simplifying with (6), (7), (12), (19), (21) gives: % 5.52/1.60 | | (22) all_20_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 5.52/1.60 | | 0) & member(all_20_1, all_7_2) = v0 & member(all_20_1, all_7_3) % 5.52/1.60 | | = v1) % 5.52/1.60 | | % 5.52/1.60 | | BETA: splitting (22) gives: % 5.52/1.60 | | % 5.52/1.60 | | Case 1: % 5.52/1.60 | | | % 5.52/1.60 | | | (23) all_20_0 = 0 % 5.52/1.60 | | | % 5.52/1.60 | | | REDUCE: (18), (23) imply: % 5.52/1.60 | | | (24) $false % 5.52/1.60 | | | % 5.52/1.60 | | | CLOSE: (24) is inconsistent. % 5.52/1.60 | | | % 5.52/1.60 | | Case 2: % 5.52/1.60 | | | % 5.52/1.60 | | | (25) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 5.52/1.60 | | | member(all_20_1, all_7_2) = v0 & member(all_20_1, all_7_3) = v1) % 5.52/1.60 | | | % 5.52/1.60 | | | DELTA: instantiating (25) with fresh symbols all_33_0, all_33_1 gives: % 5.52/1.60 | | | (26) ~ (all_33_0 = 0) & ~ (all_33_1 = 0) & member(all_20_1, all_7_2) % 5.52/1.60 | | | = all_33_1 & member(all_20_1, all_7_3) = all_33_0 % 5.52/1.60 | | | % 5.52/1.60 | | | ALPHA: (26) implies: % 5.52/1.60 | | | (27) ~ (all_33_0 = 0) % 5.52/1.60 | | | (28) member(all_20_1, all_7_3) = all_33_0 % 5.52/1.60 | | | % 5.52/1.60 | | | GROUND_INST: instantiating (3) with 0, all_33_0, all_7_3, all_20_1, % 5.52/1.60 | | | simplifying with (20), (28) gives: % 5.52/1.60 | | | (29) all_33_0 = 0 % 5.52/1.60 | | | % 5.52/1.60 | | | REDUCE: (27), (29) imply: % 5.52/1.60 | | | (30) $false % 5.52/1.60 | | | % 5.52/1.60 | | | CLOSE: (30) is inconsistent. % 5.52/1.60 | | | % 5.52/1.60 | | End of split % 5.52/1.60 | | % 5.52/1.60 | End of split % 5.52/1.60 | % 5.52/1.60 End of proof % 5.52/1.60 % SZS output end Proof for theBenchmark % 5.52/1.60 % 5.52/1.60 981ms %------------------------------------------------------------------------------