%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET629+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 : n005.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 15:25:44 EDT 2023 % Result : Theorem 5.45s 1.49s % Output : Proof 6.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET629+3 : TPTP v8.1.2. Released v2.2.0. % 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n005.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sat Aug 26 11:44:08 EDT 2023 % 0.12/0.33 % CPUTime : % 0.18/0.59 ________ _____ % 0.18/0.59 ___ __ \_________(_)________________________________ % 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.59 % 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.59 (2023-06-19) % 0.18/0.59 % 0.18/0.59 (c) Philipp Rümmer, 2009-2023 % 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.59 Amanda Stjerna. % 0.18/0.59 Free software under BSD-3-Clause. % 0.18/0.59 % 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.59 % 0.18/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.60 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 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 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 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 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 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 % 1.75/1.00 Prover 1: Preprocessing ... % 1.75/1.00 Prover 4: Preprocessing ... % 2.39/1.05 Prover 6: Preprocessing ... % 2.39/1.05 Prover 2: Preprocessing ... % 2.39/1.05 Prover 5: Preprocessing ... % 2.39/1.05 Prover 3: Preprocessing ... % 2.39/1.05 Prover 0: Preprocessing ... % 4.18/1.32 Prover 1: Warning: ignoring some quantifiers % 4.18/1.33 Prover 3: Warning: ignoring some quantifiers % 4.18/1.33 Prover 4: Warning: ignoring some quantifiers % 4.18/1.34 Prover 3: Constructing countermodel ... % 4.18/1.34 Prover 1: Constructing countermodel ... % 4.18/1.34 Prover 5: Proving ... % 4.18/1.34 Prover 0: Proving ... % 4.18/1.34 Prover 6: Proving ... % 4.18/1.34 Prover 2: Proving ... % 4.18/1.34 Prover 4: Constructing countermodel ... % 4.81/1.49 Prover 6: proved (874ms) % 5.45/1.49 % 5.45/1.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.45/1.49 % 5.45/1.50 Prover 5: stopped % 5.45/1.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.45/1.50 Prover 2: stopped % 5.45/1.50 Prover 3: proved (882ms) % 5.45/1.50 % 5.45/1.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.45/1.50 % 5.45/1.50 Prover 0: stopped % 5.45/1.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.45/1.51 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.45/1.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.45/1.51 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.45/1.52 Prover 7: Preprocessing ... % 5.45/1.53 Prover 8: Preprocessing ... % 5.45/1.53 Prover 11: Preprocessing ... % 5.45/1.53 Prover 1: Found proof (size 24) % 5.45/1.53 Prover 1: proved (920ms) % 5.45/1.53 Prover 4: stopped % 5.45/1.54 Prover 10: Preprocessing ... % 5.45/1.54 Prover 7: stopped % 5.45/1.54 Prover 13: Preprocessing ... % 5.45/1.55 Prover 10: stopped % 5.45/1.55 Prover 11: stopped % 5.45/1.56 Prover 13: stopped % 6.09/1.60 Prover 8: Warning: ignoring some quantifiers % 6.09/1.61 Prover 8: Constructing countermodel ... % 6.13/1.61 Prover 8: stopped % 6.13/1.61 % 6.13/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.13/1.61 % 6.13/1.62 % SZS output start Proof for theBenchmark % 6.13/1.62 Assumptions after simplification: % 6.13/1.62 --------------------------------- % 6.13/1.62 % 6.13/1.62 (commutativity_of_intersection) % 6.13/1.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ % 6.13/1.65 $i(v1) | ~ $i(v0) | (intersection(v1, v0) = v2 & $i(v2))) % 6.13/1.65 % 6.13/1.65 (difference_defn) % 6.13/1.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 6.13/1.65 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ % 6.13/1.65 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 & % 6.13/1.65 member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] % 6.13/1.65 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v0, v1) = v3) | ~ (member(v2, % 6.13/1.65 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = % 6.13/1.66 0) & member(v2, v1) = v4 & member(v2, v0) = 0)) % 6.13/1.66 % 6.13/1.66 (disjoint_defn) % 6.13/1.66 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) = % 6.13/1.66 v2) | ~ $i(v1) | ~ $i(v0) | intersect(v0, v1) = 0) & ! [v0: $i] : ! % 6.13/1.66 [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : % 6.13/1.66 ( ~ (v2 = 0) & intersect(v0, v1) = v2)) % 6.13/1.66 % 6.13/1.66 (intersect_defn) % 6.13/1.66 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0, v1) = % 6.13/1.66 v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (member(v3, v0) = 0) | ~ % 6.13/1.66 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4))) & ! [v0: % 6.13/1.66 $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 6.13/1.66 [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2))) % 6.13/1.66 % 6.13/1.66 (intersection_defn) % 6.13/1.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 6.13/1.67 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ % 6.13/1.67 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 & % 6.13/1.67 member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 6.13/1.67 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v0, v1) = v3) | ~ % 6.13/1.67 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = % 6.13/1.67 0 & member(v2, v0) = 0)) % 6.13/1.67 % 6.13/1.67 (prove_intersection_and_difference_disjoint) % 6.13/1.67 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 6.13/1.67 = 0) & disjoint(v2, v3) = v4 & difference(v0, v1) = v3 & intersection(v0, % 6.13/1.67 v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 6.13/1.67 % 6.13/1.67 (function-axioms) % 6.13/1.67 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 6.13/1.67 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 6.13/1.67 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 6.13/1.67 [v3: $i] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) = % 6.13/1.67 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 6.13/1.67 ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : % 6.13/1.67 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = % 6.13/1.67 v1) | ~ (intersection(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 6.13/1.67 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 6.13/1.67 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 6.13/1.67 % 6.13/1.67 Further assumptions not needed in the proof: % 6.13/1.67 -------------------------------------------- % 6.13/1.67 equal_member_defn, symmetry_of_intersect % 6.13/1.67 % 6.13/1.67 Those formulas are unsatisfiable: % 6.13/1.67 --------------------------------- % 6.13/1.67 % 6.13/1.67 Begin of proof % 6.13/1.67 | % 6.13/1.68 | ALPHA: (intersection_defn) implies: % 6.13/1.68 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 6.13/1.68 | (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | % 6.13/1.68 | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & member(v2, v0) = 0)) % 6.13/1.68 | % 6.13/1.68 | ALPHA: (difference_defn) implies: % 6.13/1.68 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 6.13/1.68 | (difference(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ % 6.13/1.68 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = % 6.13/1.68 | v4 & member(v2, v0) = 0)) % 6.13/1.68 | % 6.13/1.68 | ALPHA: (intersect_defn) implies: % 6.13/1.68 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | % 6.13/1.68 | ~ $i(v0) | ? [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & % 6.13/1.68 | $i(v2))) % 6.13/1.68 | % 6.13/1.68 | ALPHA: (disjoint_defn) implies: % 6.13/1.68 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, % 6.13/1.68 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | intersect(v0, v1) = 0) % 6.13/1.68 | % 6.13/1.68 | ALPHA: (function-axioms) implies: % 6.13/1.68 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 6.13/1.68 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 6.13/1.68 | = v0)) % 6.13/1.68 | % 6.13/1.68 | DELTA: instantiating (prove_intersection_and_difference_disjoint) with fresh % 6.13/1.68 | symbols all_9_0, all_9_1, all_9_2, all_9_3, all_9_4 gives: % 6.13/1.68 | (6) ~ (all_9_0 = 0) & disjoint(all_9_2, all_9_1) = all_9_0 & % 6.13/1.68 | difference(all_9_4, all_9_3) = all_9_1 & intersection(all_9_4, all_9_3) % 6.13/1.68 | = all_9_2 & $i(all_9_1) & $i(all_9_2) & $i(all_9_3) & $i(all_9_4) % 6.13/1.68 | % 6.13/1.68 | ALPHA: (6) implies: % 6.13/1.68 | (7) ~ (all_9_0 = 0) % 6.13/1.68 | (8) $i(all_9_4) % 6.13/1.69 | (9) $i(all_9_3) % 6.13/1.69 | (10) $i(all_9_1) % 6.13/1.69 | (11) intersection(all_9_4, all_9_3) = all_9_2 % 6.13/1.69 | (12) difference(all_9_4, all_9_3) = all_9_1 % 6.13/1.69 | (13) disjoint(all_9_2, all_9_1) = all_9_0 % 6.13/1.69 | % 6.13/1.69 | GROUND_INST: instantiating (commutativity_of_intersection) with all_9_4, % 6.13/1.69 | all_9_3, all_9_2, simplifying with (8), (9), (11) gives: % 6.13/1.69 | (14) intersection(all_9_3, all_9_4) = all_9_2 & $i(all_9_2) % 6.13/1.69 | % 6.13/1.69 | ALPHA: (14) implies: % 6.13/1.69 | (15) $i(all_9_2) % 6.13/1.69 | % 6.13/1.69 | GROUND_INST: instantiating (4) with all_9_2, all_9_1, all_9_0, simplifying % 6.13/1.69 | with (10), (13), (15) gives: % 6.13/1.69 | (16) all_9_0 = 0 | intersect(all_9_2, all_9_1) = 0 % 6.13/1.69 | % 6.13/1.69 | BETA: splitting (16) gives: % 6.13/1.69 | % 6.13/1.69 | Case 1: % 6.13/1.69 | | % 6.13/1.69 | | (17) intersect(all_9_2, all_9_1) = 0 % 6.13/1.69 | | % 6.13/1.69 | | GROUND_INST: instantiating (3) with all_9_2, all_9_1, simplifying with (10), % 6.13/1.69 | | (15), (17) gives: % 6.13/1.69 | | (18) ? [v0: $i] : (member(v0, all_9_1) = 0 & member(v0, all_9_2) = 0 & % 6.13/1.69 | | $i(v0)) % 6.13/1.69 | | % 6.13/1.69 | | DELTA: instantiating (18) with fresh symbol all_28_0 gives: % 6.13/1.69 | | (19) member(all_28_0, all_9_1) = 0 & member(all_28_0, all_9_2) = 0 & % 6.13/1.69 | | $i(all_28_0) % 6.13/1.69 | | % 6.13/1.69 | | ALPHA: (19) implies: % 6.13/1.69 | | (20) $i(all_28_0) % 6.13/1.69 | | (21) member(all_28_0, all_9_2) = 0 % 6.13/1.69 | | (22) member(all_28_0, all_9_1) = 0 % 6.13/1.69 | | % 6.13/1.69 | | GROUND_INST: instantiating (1) with all_9_4, all_9_3, all_28_0, all_9_2, % 6.13/1.69 | | simplifying with (8), (9), (11), (20), (21) gives: % 6.13/1.69 | | (23) member(all_28_0, all_9_3) = 0 & member(all_28_0, all_9_4) = 0 % 6.13/1.69 | | % 6.13/1.69 | | ALPHA: (23) implies: % 6.13/1.69 | | (24) member(all_28_0, all_9_3) = 0 % 6.13/1.69 | | % 6.13/1.69 | | GROUND_INST: instantiating (2) with all_9_4, all_9_3, all_28_0, all_9_1, % 6.13/1.69 | | simplifying with (8), (9), (12), (20), (22) gives: % 6.13/1.70 | | (25) ? [v0: int] : ( ~ (v0 = 0) & member(all_28_0, all_9_3) = v0 & % 6.13/1.70 | | member(all_28_0, all_9_4) = 0) % 6.13/1.70 | | % 6.13/1.70 | | DELTA: instantiating (25) with fresh symbol all_38_0 gives: % 6.13/1.70 | | (26) ~ (all_38_0 = 0) & member(all_28_0, all_9_3) = all_38_0 & % 6.13/1.70 | | member(all_28_0, all_9_4) = 0 % 6.13/1.70 | | % 6.13/1.70 | | ALPHA: (26) implies: % 6.13/1.70 | | (27) ~ (all_38_0 = 0) % 6.13/1.70 | | (28) member(all_28_0, all_9_3) = all_38_0 % 6.13/1.70 | | % 6.13/1.70 | | GROUND_INST: instantiating (5) with 0, all_38_0, all_9_3, all_28_0, % 6.13/1.70 | | simplifying with (24), (28) gives: % 6.13/1.70 | | (29) all_38_0 = 0 % 6.13/1.70 | | % 6.13/1.70 | | REDUCE: (27), (29) imply: % 6.13/1.70 | | (30) $false % 6.13/1.70 | | % 6.13/1.70 | | CLOSE: (30) is inconsistent. % 6.13/1.70 | | % 6.13/1.70 | Case 2: % 6.13/1.70 | | % 6.13/1.70 | | (31) all_9_0 = 0 % 6.13/1.70 | | % 6.13/1.70 | | REDUCE: (7), (31) imply: % 6.13/1.70 | | (32) $false % 6.13/1.70 | | % 6.13/1.70 | | CLOSE: (32) is inconsistent. % 6.13/1.70 | | % 6.13/1.70 | End of split % 6.13/1.70 | % 6.13/1.70 End of proof % 6.13/1.70 % SZS output end Proof for theBenchmark % 6.13/1.70 % 6.13/1.70 1108ms %------------------------------------------------------------------------------