%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET618+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 : n014.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 15:25:39 EDT 2023 % Result : Theorem 5.30s 1.49s % Output : Proof 6.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET618+3 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.35 % Computer : n014.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Sat Aug 26 11:03:02 EDT 2023 % 0.17/0.35 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.65 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 % 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.98/1.01 Prover 4: Preprocessing ... % 1.98/1.01 Prover 1: Preprocessing ... % 2.42/1.05 Prover 5: Preprocessing ... % 2.42/1.05 Prover 2: Preprocessing ... % 2.42/1.05 Prover 3: Preprocessing ... % 2.42/1.05 Prover 0: Preprocessing ... % 2.42/1.05 Prover 6: Preprocessing ... % 3.96/1.31 Prover 1: Warning: ignoring some quantifiers % 3.96/1.33 Prover 5: Proving ... % 3.96/1.33 Prover 1: Constructing countermodel ... % 3.96/1.33 Prover 6: Proving ... % 4.41/1.33 Prover 3: Warning: ignoring some quantifiers % 4.41/1.34 Prover 2: Proving ... % 4.41/1.34 Prover 3: Constructing countermodel ... % 4.41/1.35 Prover 4: Warning: ignoring some quantifiers % 4.41/1.35 Prover 0: Proving ... % 4.41/1.36 Prover 4: Constructing countermodel ... % 5.30/1.48 Prover 3: gave up % 5.30/1.48 Prover 1: gave up % 5.30/1.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.30/1.48 Prover 0: proved (831ms) % 5.30/1.48 % 5.30/1.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.30/1.49 % 5.30/1.49 Prover 2: proved (826ms) % 5.30/1.49 % 5.30/1.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.30/1.49 % 5.30/1.49 Prover 5: proved (820ms) % 5.30/1.49 % 5.30/1.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.30/1.49 % 5.30/1.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.30/1.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.30/1.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.30/1.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.30/1.49 Prover 6: stopped % 5.30/1.49 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 5.30/1.50 Prover 4: Found proof (size 19) % 5.30/1.50 Prover 4: proved (839ms) % 5.30/1.53 Prover 10: Preprocessing ... % 5.30/1.53 Prover 11: Preprocessing ... % 5.30/1.53 Prover 13: Preprocessing ... % 5.30/1.53 Prover 8: Preprocessing ... % 5.30/1.54 Prover 7: Preprocessing ... % 5.30/1.54 Prover 16: Preprocessing ... % 5.76/1.55 Prover 10: stopped % 5.76/1.56 Prover 13: stopped % 5.76/1.56 Prover 7: stopped % 5.76/1.57 Prover 16: stopped % 5.76/1.57 Prover 11: stopped % 5.98/1.63 Prover 8: Warning: ignoring some quantifiers % 6.19/1.64 Prover 8: Constructing countermodel ... % 6.19/1.65 Prover 8: stopped % 6.19/1.65 % 6.19/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.19/1.65 % 6.19/1.65 % SZS output start Proof for theBenchmark % 6.25/1.66 Assumptions after simplification: % 6.25/1.66 --------------------------------- % 6.25/1.66 % 6.25/1.66 (idempotency_of_union) % 6.25/1.68 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (union(v0, v0) = v1) | ~ $i(v0)) % 6.25/1.68 % 6.25/1.68 (prove_th93) % 6.25/1.69 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = empty_set) & % 6.25/1.69 symmetric_difference(v0, v0) = v1 & $i(v1) & $i(v0)) % 6.25/1.69 % 6.25/1.69 (self_difference_is_empty_set) % 6.25/1.69 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 6.25/1.69 (difference(v0, v0) = v1) | ~ $i(v0)) % 6.25/1.69 % 6.25/1.69 (symmetric_difference_defn) % 6.25/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0, v1) = % 6.25/1.69 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (difference(v1, % 6.25/1.69 v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2 & $i(v4) & % 6.25/1.69 $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 6.25/1.69 (difference(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 6.25/1.69 $i] : (symmetric_difference(v0, v1) = v3 & difference(v0, v1) = v4 & % 6.25/1.69 union(v4, v2) = v3 & $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 6.25/1.69 [v2: $i] : ( ~ (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] % 6.25/1.69 : ? [v4: $i] : (symmetric_difference(v0, v1) = v3 & difference(v1, v0) = v4 % 6.25/1.69 & union(v2, v4) = v3 & $i(v4) & $i(v3))) % 6.25/1.69 % 6.25/1.70 (function-axioms) % 6.25/1.70 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 6.25/1.70 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 6.25/1.70 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 6.25/1.70 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! % 6.25/1.70 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 6.25/1.70 (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = % 6.25/1.70 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 6.25/1.70 ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : % 6.25/1.70 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | % 6.25/1.70 ~ (union(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 6.25/1.70 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 6.25/1.70 (empty(v2) = v0)) % 6.25/1.70 % 6.25/1.70 Further assumptions not needed in the proof: % 6.25/1.70 -------------------------------------------- % 6.25/1.70 commutativity_of_symmetric_difference, commutativity_of_union, empty_defn, % 6.25/1.70 empty_set_defn, equal_defn, equal_member_defn, reflexivity_of_subset, % 6.25/1.70 subset_defn % 6.25/1.70 % 6.25/1.70 Those formulas are unsatisfiable: % 6.25/1.70 --------------------------------- % 6.25/1.70 % 6.25/1.70 Begin of proof % 6.25/1.70 | % 6.25/1.70 | ALPHA: (symmetric_difference_defn) implies: % 6.25/1.71 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0, % 6.25/1.71 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 6.25/1.71 | (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = % 6.25/1.71 | v2 & $i(v4) & $i(v3) & $i(v2))) % 6.25/1.71 | % 6.25/1.71 | ALPHA: (self_difference_is_empty_set) implies: % 6.25/1.71 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ (difference(v0, v0) = % 6.25/1.71 | v1) | ~ $i(v0)) % 6.25/1.71 | % 6.25/1.71 | ALPHA: (prove_th93) implies: % 6.25/1.71 | (3) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = empty_set) & % 6.25/1.71 | symmetric_difference(v0, v0) = v1 & $i(v1) & $i(v0)) % 6.25/1.71 | % 6.25/1.71 | ALPHA: (function-axioms) implies: % 6.25/1.71 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 6.25/1.71 | (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 6.25/1.71 | % 6.25/1.71 | DELTA: instantiating (3) with fresh symbols all_14_0, all_14_1 gives: % 6.25/1.71 | (5) ~ (all_14_0 = empty_set) & symmetric_difference(all_14_1, all_14_1) = % 6.25/1.71 | all_14_0 & $i(all_14_0) & $i(all_14_1) % 6.25/1.71 | % 6.25/1.71 | ALPHA: (5) implies: % 6.25/1.71 | (6) ~ (all_14_0 = empty_set) % 6.25/1.71 | (7) $i(all_14_1) % 6.25/1.71 | (8) symmetric_difference(all_14_1, all_14_1) = all_14_0 % 6.25/1.71 | % 6.25/1.71 | GROUND_INST: instantiating (1) with all_14_1, all_14_1, all_14_0, simplifying % 6.25/1.71 | with (7), (8) gives: % 6.25/1.71 | (9) ? [v0: $i] : ? [v1: $i] : (difference(all_14_1, all_14_1) = v1 & % 6.25/1.71 | difference(all_14_1, all_14_1) = v0 & union(v0, v1) = all_14_0 & % 6.25/1.71 | $i(v1) & $i(v0) & $i(all_14_0)) % 6.25/1.71 | % 6.25/1.72 | DELTA: instantiating (9) with fresh symbols all_22_0, all_22_1 gives: % 6.25/1.72 | (10) difference(all_14_1, all_14_1) = all_22_0 & difference(all_14_1, % 6.25/1.72 | all_14_1) = all_22_1 & union(all_22_1, all_22_0) = all_14_0 & % 6.25/1.72 | $i(all_22_0) & $i(all_22_1) & $i(all_14_0) % 6.25/1.72 | % 6.25/1.72 | ALPHA: (10) implies: % 6.25/1.72 | (11) $i(all_22_0) % 6.25/1.72 | (12) union(all_22_1, all_22_0) = all_14_0 % 6.25/1.72 | (13) difference(all_14_1, all_14_1) = all_22_1 % 6.25/1.72 | (14) difference(all_14_1, all_14_1) = all_22_0 % 6.25/1.72 | % 6.25/1.72 | GROUND_INST: instantiating (4) with all_22_1, all_22_0, all_14_1, all_14_1, % 6.25/1.72 | simplifying with (13), (14) gives: % 6.25/1.72 | (15) all_22_0 = all_22_1 % 6.25/1.72 | % 6.25/1.72 | REDUCE: (12), (15) imply: % 6.25/1.72 | (16) union(all_22_1, all_22_1) = all_14_0 % 6.25/1.72 | % 6.25/1.72 | REDUCE: (11), (15) imply: % 6.56/1.72 | (17) $i(all_22_1) % 6.56/1.72 | % 6.56/1.72 | GROUND_INST: instantiating (idempotency_of_union) with all_22_1, all_14_0, % 6.56/1.72 | simplifying with (16), (17) gives: % 6.56/1.72 | (18) all_22_1 = all_14_0 % 6.56/1.72 | % 6.56/1.72 | GROUND_INST: instantiating (2) with all_14_1, all_22_1, simplifying with (7), % 6.56/1.72 | (13) gives: % 6.56/1.72 | (19) all_22_1 = empty_set % 6.56/1.72 | % 6.56/1.72 | COMBINE_EQS: (18), (19) imply: % 6.56/1.72 | (20) all_14_0 = empty_set % 6.56/1.72 | % 6.56/1.72 | SIMP: (20) implies: % 6.56/1.72 | (21) all_14_0 = empty_set % 6.56/1.72 | % 6.56/1.72 | REDUCE: (6), (21) imply: % 6.56/1.72 | (22) $false % 6.56/1.72 | % 6.56/1.72 | CLOSE: (22) is inconsistent. % 6.56/1.72 | % 6.56/1.72 End of proof % 6.56/1.72 % SZS output end Proof for theBenchmark % 6.56/1.72 % 6.56/1.72 1087ms %------------------------------------------------------------------------------