%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET196+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 : n023.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 3.57s 1.70s % Output : Proof 4.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.11 % Problem : SET196+3 : TPTP v8.1.2. Released v2.2.0. % 0.05/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.36 % Computer : n023.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8042.1875MB % 0.10/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Sat Aug 26 15:47:26 EDT 2023 % 0.10/0.36 % CPUTime : % 0.44/0.63 ________ _____ % 0.44/0.63 ___ __ \_________(_)________________________________ % 0.44/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.44/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.44/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.44/0.63 % 0.44/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.44/0.63 (2023-06-19) % 0.44/0.63 % 0.44/0.63 (c) Philipp Rümmer, 2009-2023 % 0.44/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.44/0.63 Amanda Stjerna. % 0.44/0.64 Free software under BSD-3-Clause. % 0.44/0.64 % 0.44/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.44/0.64 % 0.44/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.44/0.65 Running up to 7 provers in parallel. % 0.44/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.44/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.44/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.44/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.44/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.44/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.44/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 1.14/0.99 Prover 4: Preprocessing ... % 1.44/1.05 Prover 1: Preprocessing ... % 1.68/1.08 Prover 5: Preprocessing ... % 1.68/1.08 Prover 0: Preprocessing ... % 1.68/1.08 Prover 6: Preprocessing ... % 1.68/1.08 Prover 2: Preprocessing ... % 1.68/1.08 Prover 3: Preprocessing ... % 2.67/1.39 Prover 1: Warning: ignoring some quantifiers % 2.67/1.40 Prover 5: Proving ... % 2.67/1.42 Prover 1: Constructing countermodel ... % 2.67/1.42 Prover 2: Proving ... % 2.67/1.43 Prover 4: Warning: ignoring some quantifiers % 2.67/1.44 Prover 6: Proving ... % 2.95/1.51 Prover 3: Warning: ignoring some quantifiers % 2.95/1.51 Prover 4: Constructing countermodel ... % 2.95/1.52 Prover 0: Proving ... % 2.95/1.53 Prover 3: Constructing countermodel ... % 3.57/1.70 Prover 3: proved (1022ms) % 3.57/1.70 % 3.57/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.57/1.70 % 3.57/1.72 Prover 2: stopped % 3.57/1.74 Prover 6: proved (1022ms) % 3.57/1.74 % 3.57/1.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.57/1.74 % 3.76/1.78 Prover 0: proved (1054ms) % 3.76/1.78 % 3.76/1.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.76/1.78 % 3.81/1.79 Prover 5: stopped % 3.81/1.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.81/1.80 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.81/1.80 Prover 7: Preprocessing ... % 3.81/1.80 Prover 8: Preprocessing ... % 3.81/1.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.81/1.80 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.81/1.80 Prover 10: Preprocessing ... % 3.81/1.80 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.81/1.81 Prover 4: Found proof (size 19) % 3.81/1.81 Prover 4: proved (1137ms) % 3.81/1.81 Prover 11: Preprocessing ... % 3.81/1.81 Prover 1: stopped % 3.81/1.81 Prover 13: Preprocessing ... % 3.81/1.81 Prover 10: stopped % 4.00/1.84 Prover 7: Warning: ignoring some quantifiers % 4.00/1.84 Prover 13: stopped % 4.00/1.84 Prover 11: stopped % 4.00/1.87 Prover 7: Constructing countermodel ... % 4.00/1.87 Prover 7: stopped % 4.00/1.88 Prover 8: Warning: ignoring some quantifiers % 4.00/1.91 Prover 8: Constructing countermodel ... % 4.23/1.93 Prover 8: stopped % 4.23/1.93 % 4.23/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.23/1.93 % 4.23/1.93 % SZS output start Proof for theBenchmark % 4.23/1.94 Assumptions after simplification: % 4.23/1.94 --------------------------------- % 4.23/1.94 % 4.23/1.94 (commutativity_of_intersection) % 4.23/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) = v2) | ~ % 4.23/1.97 $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : % 4.23/1.97 ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ $i(v1) | ~ % 4.23/1.97 $i(v0) | (intersection(v1, v0) = v2 & $i(v2))) % 4.23/1.97 % 4.23/1.97 (intersection_defn) % 4.23/1.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 4.23/1.98 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ % 4.23/1.98 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 & % 4.23/1.98 member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 4.23/1.98 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v0, v1) = v3) | ~ % 4.23/1.98 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = % 4.23/1.98 0 & member(v2, v0) = 0)) % 4.23/1.98 % 4.23/1.98 (prove_intersection_is_subset) % 4.41/1.98 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 4.41/1.98 subset(v2, v0) = v3 & intersection(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0)) % 4.41/1.98 % 4.41/1.98 (subset_defn) % 4.41/1.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 4.41/1.99 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 4.41/1.99 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] : % 4.41/1.99 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | % 4.41/1.99 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 & % 4.41/1.99 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 4.41/1.99 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | % 4.41/1.99 ~ $i(v0) | member(v2, v1) = 0) % 4.41/1.99 % 4.41/1.99 (function-axioms) % 4.41/2.00 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 4.41/2.00 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 4.41/2.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 4.41/2.00 (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0: % 4.41/2.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 4.41/2.00 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 4.41/2.00 % 4.41/2.00 Further assumptions not needed in the proof: % 4.41/2.00 -------------------------------------------- % 4.41/2.00 equal_member_defn, reflexivity_of_subset % 4.41/2.00 % 4.41/2.00 Those formulas are unsatisfiable: % 4.41/2.00 --------------------------------- % 4.41/2.00 % 4.41/2.00 Begin of proof % 4.41/2.00 | % 4.41/2.00 | ALPHA: (intersection_defn) implies: % 4.41/2.00 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 4.41/2.00 | (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | % 4.41/2.00 | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & member(v2, v0) = 0)) % 4.41/2.00 | % 4.41/2.00 | ALPHA: (subset_defn) implies: % 4.41/2.00 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 4.41/2.00 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 4.41/2.00 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 4.41/2.00 | % 4.41/2.01 | ALPHA: (commutativity_of_intersection) implies: % 4.41/2.01 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) = % 4.41/2.01 | v2) | ~ $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) % 4.41/2.01 | % 4.41/2.01 | ALPHA: (function-axioms) implies: % 4.41/2.01 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.41/2.01 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 4.41/2.01 | = v0)) % 4.41/2.01 | % 4.41/2.01 | DELTA: instantiating (prove_intersection_is_subset) with fresh symbols % 4.41/2.01 | all_7_0, all_7_1, all_7_2, all_7_3 gives: % 4.41/2.01 | (5) ~ (all_7_0 = 0) & subset(all_7_1, all_7_3) = all_7_0 & % 4.41/2.01 | intersection(all_7_3, all_7_2) = all_7_1 & $i(all_7_1) & $i(all_7_2) & % 4.41/2.01 | $i(all_7_3) % 4.41/2.01 | % 4.41/2.01 | ALPHA: (5) implies: % 4.41/2.02 | (6) ~ (all_7_0 = 0) % 4.41/2.02 | (7) $i(all_7_3) % 4.41/2.02 | (8) $i(all_7_2) % 4.41/2.02 | (9) intersection(all_7_3, all_7_2) = all_7_1 % 4.41/2.02 | (10) subset(all_7_1, all_7_3) = all_7_0 % 4.41/2.02 | % 4.41/2.02 | GROUND_INST: instantiating (3) with all_7_2, all_7_3, all_7_1, simplifying % 4.41/2.02 | with (7), (8), (9) gives: % 4.41/2.02 | (11) intersection(all_7_2, all_7_3) = all_7_1 & $i(all_7_1) % 4.41/2.02 | % 4.41/2.02 | ALPHA: (11) implies: % 4.41/2.02 | (12) $i(all_7_1) % 4.41/2.02 | (13) intersection(all_7_2, all_7_3) = all_7_1 % 4.41/2.02 | % 4.41/2.02 | GROUND_INST: instantiating (2) with all_7_1, all_7_3, all_7_0, simplifying % 4.41/2.02 | with (7), (10), (12) gives: % 4.41/2.02 | (14) all_7_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 4.41/2.02 | all_7_1) = 0 & member(v0, all_7_3) = v1 & $i(v0)) % 4.41/2.02 | % 4.41/2.02 | BETA: splitting (14) gives: % 4.41/2.02 | % 4.41/2.02 | Case 1: % 4.41/2.02 | | % 4.41/2.02 | | (15) all_7_0 = 0 % 4.41/2.02 | | % 4.41/2.02 | | REDUCE: (6), (15) imply: % 4.41/2.03 | | (16) $false % 4.41/2.03 | | % 4.41/2.03 | | CLOSE: (16) is inconsistent. % 4.41/2.03 | | % 4.41/2.03 | Case 2: % 4.41/2.03 | | % 4.41/2.04 | | (17) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_7_1) = 0 % 4.41/2.04 | | & member(v0, all_7_3) = v1 & $i(v0)) % 4.41/2.04 | | % 4.41/2.04 | | DELTA: instantiating (17) with fresh symbols all_20_0, all_20_1 gives: % 4.41/2.04 | | (18) ~ (all_20_0 = 0) & member(all_20_1, all_7_1) = 0 & member(all_20_1, % 4.41/2.04 | | all_7_3) = all_20_0 & $i(all_20_1) % 4.41/2.04 | | % 4.41/2.04 | | ALPHA: (18) implies: % 4.41/2.04 | | (19) ~ (all_20_0 = 0) % 4.41/2.04 | | (20) $i(all_20_1) % 4.41/2.04 | | (21) member(all_20_1, all_7_3) = all_20_0 % 4.41/2.04 | | (22) member(all_20_1, all_7_1) = 0 % 4.63/2.07 | | % 4.63/2.08 | | GROUND_INST: instantiating (1) with all_7_2, all_7_3, all_20_1, all_7_1, % 4.63/2.08 | | simplifying with (7), (8), (13), (20), (22) gives: % 4.65/2.08 | | (23) member(all_20_1, all_7_2) = 0 & member(all_20_1, all_7_3) = 0 % 4.65/2.08 | | % 4.65/2.08 | | ALPHA: (23) implies: % 4.65/2.08 | | (24) member(all_20_1, all_7_3) = 0 % 4.65/2.08 | | % 4.65/2.08 | | GROUND_INST: instantiating (4) with all_20_0, 0, all_7_3, all_20_1, % 4.65/2.08 | | simplifying with (21), (24) gives: % 4.65/2.08 | | (25) all_20_0 = 0 % 4.65/2.08 | | % 4.65/2.08 | | REDUCE: (19), (25) imply: % 4.65/2.08 | | (26) $false % 4.65/2.08 | | % 4.65/2.08 | | CLOSE: (26) is inconsistent. % 4.65/2.08 | | % 4.65/2.08 | End of split % 4.65/2.08 | % 4.65/2.08 End of proof % 4.65/2.11 % SZS output end Proof for theBenchmark % 4.65/2.11 % 4.65/2.11 1474ms %------------------------------------------------------------------------------