%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET631+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 : n010.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 15:25:45 EDT 2023 % Result : Theorem 3.84s 1.34s % Output : Proof 5.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET631+3 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n010.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Sat Aug 26 09:36:05 EDT 2023 % 0.14/0.34 % 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/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.86/1.01 Prover 1: Preprocessing ... % 1.86/1.01 Prover 4: Preprocessing ... % 2.26/1.05 Prover 0: Preprocessing ... % 2.26/1.05 Prover 5: Preprocessing ... % 2.26/1.05 Prover 3: Preprocessing ... % 2.26/1.05 Prover 2: Preprocessing ... % 2.26/1.05 Prover 6: Preprocessing ... % 3.17/1.19 Prover 2: Proving ... % 3.17/1.19 Prover 1: Constructing countermodel ... % 3.17/1.20 Prover 5: Proving ... % 3.17/1.20 Prover 6: Proving ... % 3.17/1.21 Prover 3: Constructing countermodel ... % 3.17/1.21 Prover 0: Proving ... % 3.17/1.21 Prover 4: Constructing countermodel ... % 3.84/1.34 Prover 3: proved (701ms) % 3.84/1.34 % 3.84/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.84/1.34 % 3.84/1.35 Prover 5: stopped % 3.84/1.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.84/1.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.84/1.35 Prover 0: proved (708ms) % 3.84/1.35 % 3.84/1.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.84/1.35 % 3.84/1.35 Prover 2: stopped % 3.84/1.35 Prover 6: stopped % 3.84/1.38 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.84/1.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.84/1.38 Prover 8: Preprocessing ... % 3.84/1.38 Prover 7: Preprocessing ... % 3.84/1.38 Prover 10: Preprocessing ... % 3.84/1.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.84/1.39 Prover 13: Preprocessing ... % 3.84/1.41 Prover 1: Found proof (size 21) % 3.84/1.41 Prover 1: proved (767ms) % 3.84/1.41 Prover 4: stopped % 3.84/1.42 Prover 7: Constructing countermodel ... % 3.84/1.42 Prover 11: Preprocessing ... % 3.84/1.42 Prover 8: Warning: ignoring some quantifiers % 3.84/1.42 Prover 7: stopped % 3.84/1.42 Prover 10: Constructing countermodel ... % 3.84/1.43 Prover 8: Constructing countermodel ... % 3.84/1.43 Prover 10: stopped % 4.75/1.43 Prover 8: stopped % 4.75/1.44 Prover 11: stopped % 4.75/1.44 Prover 13: Warning: ignoring some quantifiers % 4.75/1.45 Prover 13: Constructing countermodel ... % 4.75/1.45 Prover 13: stopped % 4.75/1.45 % 4.75/1.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.75/1.45 % 4.75/1.45 % SZS output start Proof for theBenchmark % 4.75/1.46 Assumptions after simplification: % 4.75/1.46 --------------------------------- % 4.75/1.46 % 4.75/1.46 (difference_defn) % 5.13/1.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 5.13/1.49 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ % 5.13/1.49 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 & % 5.13/1.49 member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] % 5.13/1.49 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v0, v1) = v3) | ~ (member(v2, % 5.13/1.49 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = % 5.13/1.49 0) & member(v2, v1) = v4 & member(v2, v0) = 0)) % 5.13/1.49 % 5.13/1.49 (intersect_defn) % 5.13/1.50 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0, v1) = % 5.13/1.50 v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (member(v3, v0) = 0) | ~ % 5.13/1.50 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4))) & ! [v0: % 5.13/1.50 $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 5.13/1.50 [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2))) % 5.13/1.50 % 5.13/1.50 (prove_th113) % 5.13/1.50 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 5.13/1.50 = 0) & intersect(v0, v3) = 0 & intersect(v0, v1) = v4 & difference(v1, v2) % 5.13/1.50 = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 5.13/1.50 % 5.13/1.50 (function-axioms) % 5.13/1.50 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 5.13/1.50 [v3: $i] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) = % 5.13/1.50 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 5.13/1.50 ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: % 5.13/1.50 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 5.13/1.50 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 5.13/1.50 % 5.13/1.50 Further assumptions not needed in the proof: % 5.13/1.50 -------------------------------------------- % 5.13/1.50 symmetry_of_intersect % 5.13/1.50 % 5.13/1.50 Those formulas are unsatisfiable: % 5.13/1.50 --------------------------------- % 5.13/1.50 % 5.13/1.50 Begin of proof % 5.13/1.50 | % 5.13/1.50 | ALPHA: (difference_defn) implies: % 5.13/1.51 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 5.13/1.51 | (difference(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ % 5.13/1.51 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = % 5.13/1.51 | v4 & member(v2, v0) = 0)) % 5.13/1.51 | % 5.13/1.51 | ALPHA: (intersect_defn) implies: % 5.13/1.51 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | % 5.13/1.51 | ~ $i(v0) | ? [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & % 5.13/1.51 | $i(v2))) % 5.13/1.51 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0, % 5.13/1.51 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (member(v3, % 5.13/1.51 | v0) = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, % 5.13/1.51 | v1) = v4))) % 5.13/1.51 | % 5.13/1.51 | ALPHA: (function-axioms) implies: % 5.13/1.51 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 5.13/1.51 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 5.13/1.51 | = v0)) % 5.13/1.51 | % 5.13/1.51 | DELTA: instantiating (prove_th113) with fresh symbols all_6_0, all_6_1, % 5.13/1.51 | all_6_2, all_6_3, all_6_4 gives: % 5.13/1.52 | (5) ~ (all_6_0 = 0) & intersect(all_6_4, all_6_1) = 0 & intersect(all_6_4, % 5.13/1.52 | all_6_3) = all_6_0 & difference(all_6_3, all_6_2) = all_6_1 & % 5.13/1.52 | $i(all_6_1) & $i(all_6_2) & $i(all_6_3) & $i(all_6_4) % 5.13/1.52 | % 5.13/1.52 | ALPHA: (5) implies: % 5.13/1.52 | (6) ~ (all_6_0 = 0) % 5.13/1.52 | (7) $i(all_6_4) % 5.13/1.52 | (8) $i(all_6_3) % 5.13/1.52 | (9) $i(all_6_2) % 5.13/1.52 | (10) $i(all_6_1) % 5.13/1.52 | (11) difference(all_6_3, all_6_2) = all_6_1 % 5.13/1.52 | (12) intersect(all_6_4, all_6_3) = all_6_0 % 5.13/1.52 | (13) intersect(all_6_4, all_6_1) = 0 % 5.13/1.52 | % 5.13/1.52 | GROUND_INST: instantiating (3) with all_6_4, all_6_3, all_6_0, simplifying % 5.13/1.52 | with (7), (8), (12) gives: % 5.13/1.52 | (14) all_6_0 = 0 | ! [v0: $i] : ( ~ (member(v0, all_6_4) = 0) | ~ $i(v0) % 5.13/1.52 | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_6_3) = v1)) % 5.13/1.52 | % 5.13/1.52 | GROUND_INST: instantiating (2) with all_6_4, all_6_1, simplifying with (7), % 5.13/1.52 | (10), (13) gives: % 5.13/1.52 | (15) ? [v0: $i] : (member(v0, all_6_1) = 0 & member(v0, all_6_4) = 0 & % 5.13/1.52 | $i(v0)) % 5.13/1.52 | % 5.13/1.52 | DELTA: instantiating (15) with fresh symbol all_14_0 gives: % 5.13/1.52 | (16) member(all_14_0, all_6_1) = 0 & member(all_14_0, all_6_4) = 0 & % 5.13/1.52 | $i(all_14_0) % 5.13/1.52 | % 5.13/1.52 | ALPHA: (16) implies: % 5.13/1.52 | (17) $i(all_14_0) % 5.13/1.52 | (18) member(all_14_0, all_6_4) = 0 % 5.13/1.52 | (19) member(all_14_0, all_6_1) = 0 % 5.13/1.52 | % 5.13/1.52 | BETA: splitting (14) gives: % 5.13/1.52 | % 5.13/1.52 | Case 1: % 5.13/1.52 | | % 5.13/1.53 | | (20) all_6_0 = 0 % 5.13/1.53 | | % 5.13/1.53 | | REDUCE: (6), (20) imply: % 5.13/1.53 | | (21) $false % 5.13/1.53 | | % 5.13/1.53 | | CLOSE: (21) is inconsistent. % 5.13/1.53 | | % 5.13/1.53 | Case 2: % 5.13/1.53 | | % 5.13/1.53 | | (22) ! [v0: $i] : ( ~ (member(v0, all_6_4) = 0) | ~ $i(v0) | ? [v1: % 5.13/1.53 | | int] : ( ~ (v1 = 0) & member(v0, all_6_3) = v1)) % 5.13/1.53 | | % 5.13/1.53 | | GROUND_INST: instantiating (22) with all_14_0, simplifying with (17), (18) % 5.13/1.53 | | gives: % 5.13/1.53 | | (23) ? [v0: int] : ( ~ (v0 = 0) & member(all_14_0, all_6_3) = v0) % 5.13/1.53 | | % 5.13/1.53 | | GROUND_INST: instantiating (1) with all_6_3, all_6_2, all_14_0, all_6_1, % 5.13/1.53 | | simplifying with (8), (9), (11), (17), (19) gives: % 5.13/1.53 | | (24) ? [v0: int] : ( ~ (v0 = 0) & member(all_14_0, all_6_2) = v0 & % 5.13/1.53 | | member(all_14_0, all_6_3) = 0) % 5.13/1.53 | | % 5.13/1.53 | | DELTA: instantiating (23) with fresh symbol all_26_0 gives: % 5.45/1.53 | | (25) ~ (all_26_0 = 0) & member(all_14_0, all_6_3) = all_26_0 % 5.45/1.53 | | % 5.45/1.53 | | ALPHA: (25) implies: % 5.45/1.53 | | (26) ~ (all_26_0 = 0) % 5.45/1.53 | | (27) member(all_14_0, all_6_3) = all_26_0 % 5.45/1.53 | | % 5.45/1.53 | | DELTA: instantiating (24) with fresh symbol all_30_0 gives: % 5.45/1.53 | | (28) ~ (all_30_0 = 0) & member(all_14_0, all_6_2) = all_30_0 & % 5.45/1.53 | | member(all_14_0, all_6_3) = 0 % 5.45/1.53 | | % 5.45/1.53 | | ALPHA: (28) implies: % 5.45/1.53 | | (29) member(all_14_0, all_6_3) = 0 % 5.45/1.53 | | % 5.45/1.53 | | GROUND_INST: instantiating (4) with 0, all_26_0, all_6_3, all_14_0, % 5.45/1.53 | | simplifying with (27), (29) gives: % 5.45/1.53 | | (30) all_26_0 = 0 % 5.45/1.53 | | % 5.45/1.53 | | REDUCE: (26), (30) imply: % 5.45/1.53 | | (31) $false % 5.45/1.53 | | % 5.45/1.53 | | CLOSE: (31) is inconsistent. % 5.45/1.53 | | % 5.45/1.53 | End of split % 5.45/1.53 | % 5.45/1.53 End of proof % 5.45/1.53 % SZS output end Proof for theBenchmark % 5.45/1.53 % 5.45/1.53 912ms %------------------------------------------------------------------------------