%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET885+1 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n021.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 15:26:54 EDT 2023 % Result : Theorem 5.62s 1.56s % Output : Proof 7.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET885+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n021.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 13:13:42 EDT 2023 % 0.20/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.82/0.98 Prover 4: Preprocessing ... % 1.82/0.98 Prover 1: Preprocessing ... % 2.24/1.03 Prover 5: Preprocessing ... % 2.24/1.03 Prover 3: Preprocessing ... % 2.24/1.03 Prover 2: Preprocessing ... % 2.24/1.03 Prover 0: Preprocessing ... % 2.24/1.04 Prover 6: Preprocessing ... % 3.91/1.25 Prover 1: Warning: ignoring some quantifiers % 3.91/1.25 Prover 4: Warning: ignoring some quantifiers % 3.91/1.25 Prover 3: Warning: ignoring some quantifiers % 3.91/1.26 Prover 6: Proving ... % 3.91/1.26 Prover 5: Proving ... % 3.91/1.27 Prover 2: Proving ... % 3.91/1.28 Prover 4: Constructing countermodel ... % 3.91/1.28 Prover 1: Constructing countermodel ... % 3.91/1.28 Prover 3: Constructing countermodel ... % 4.34/1.30 Prover 0: Proving ... % 4.84/1.52 Prover 3: gave up % 4.84/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.62/1.56 Prover 2: proved (928ms) % 5.62/1.56 % 5.62/1.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.62/1.56 % 5.62/1.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.62/1.56 Prover 0: stopped % 5.62/1.56 Prover 6: stopped % 6.18/1.58 Prover 5: stopped % 6.18/1.59 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.18/1.59 Prover 1: gave up % 6.18/1.59 Prover 10: Preprocessing ... % 6.18/1.59 Prover 7: Preprocessing ... % 6.18/1.59 Prover 8: Preprocessing ... % 6.18/1.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.18/1.59 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.18/1.60 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.18/1.60 Prover 4: gave up % 6.18/1.61 Prover 16: Preprocessing ... % 6.18/1.61 Prover 11: Preprocessing ... % 6.18/1.61 Prover 13: Preprocessing ... % 6.18/1.62 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 6.18/1.63 Prover 19: Preprocessing ... % 6.18/1.65 Prover 16: Warning: ignoring some quantifiers % 6.18/1.65 Prover 10: Warning: ignoring some quantifiers % 6.18/1.65 Prover 8: Warning: ignoring some quantifiers % 6.18/1.66 Prover 16: Constructing countermodel ... % 6.18/1.66 Prover 10: Constructing countermodel ... % 6.84/1.66 Prover 7: Warning: ignoring some quantifiers % 6.84/1.66 Prover 8: Constructing countermodel ... % 6.84/1.67 Prover 13: Warning: ignoring some quantifiers % 6.84/1.67 Prover 7: Constructing countermodel ... % 6.84/1.67 Prover 13: Constructing countermodel ... % 7.03/1.72 Prover 11: Warning: ignoring some quantifiers % 7.34/1.74 Prover 11: Constructing countermodel ... % 7.34/1.74 Prover 19: Warning: ignoring some quantifiers % 7.34/1.74 Prover 19: Constructing countermodel ... % 7.34/1.76 Prover 10: Found proof (size 17) % 7.34/1.76 Prover 10: proved (194ms) % 7.34/1.76 Prover 13: stopped % 7.34/1.76 Prover 8: stopped % 7.34/1.76 Prover 11: stopped % 7.34/1.76 Prover 16: stopped % 7.34/1.76 Prover 7: stopped % 7.34/1.76 Prover 19: stopped % 7.34/1.76 % 7.34/1.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.34/1.76 % 7.34/1.76 % SZS output start Proof for theBenchmark % 7.34/1.77 Assumptions after simplification: % 7.34/1.77 --------------------------------- % 7.34/1.77 % 7.34/1.77 (commutativity_k2_tarski) % 7.34/1.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | % 7.34/1.79 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 7.34/1.79 % 7.34/1.79 (d1_tarski) % 7.34/1.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) | % 7.34/1.80 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1: % 7.34/1.80 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ % 7.34/1.80 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | % 7.34/1.80 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | % 7.34/1.80 ~ $i(v1) | ~ $i(v0) | in(v0, v1)) % 7.34/1.80 % 7.34/1.80 (d2_tarski) % 7.34/1.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | % 7.34/1.80 ~ (unordered_pair(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 7.34/1.80 $i(v0) | ~ in(v3, v2)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 7.34/1.80 $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 7.34/1.80 ~ $i(v0) | ? [v4: $i] : ($i(v4) & (v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ % 7.34/1.80 in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0: $i] : ! [v1: % 7.34/1.80 $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ % 7.34/1.80 $i(v1) | ~ $i(v0) | in(v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 7.34/1.80 ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0, % 7.34/1.80 v2)) % 7.34/1.80 % 7.34/1.80 (d3_tarski) % 7.78/1.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 7.78/1.81 ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ? [v0: $i] : ? [v1: $i] % 7.78/1.81 : ( ~ $i(v1) | ~ $i(v0) | subset(v0, v1) | ? [v2: $i] : ($i(v2) & in(v2, v0) % 7.78/1.81 & ~ in(v2, v1))) % 7.78/1.81 % 7.78/1.81 (t26_zfmisc_1) % 7.78/1.81 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v2 % 7.78/1.81 = v0) & singleton(v2) = v4 & unordered_pair(v0, v1) = v3 & $i(v4) & $i(v3) % 7.78/1.81 & $i(v2) & $i(v1) & $i(v0) & subset(v3, v4)) % 7.78/1.81 % 7.78/1.81 Further assumptions not needed in the proof: % 7.78/1.81 -------------------------------------------- % 7.78/1.81 antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski % 7.78/1.81 % 7.78/1.81 Those formulas are unsatisfiable: % 7.78/1.81 --------------------------------- % 7.78/1.81 % 7.78/1.81 Begin of proof % 7.78/1.81 | % 7.78/1.81 | ALPHA: (d1_tarski) implies: % 7.78/1.81 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) % 7.78/1.81 | = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) % 7.78/1.81 | % 7.78/1.81 | ALPHA: (d2_tarski) implies: % 7.78/1.81 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 7.78/1.81 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0, v2)) % 7.78/1.81 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 7.78/1.81 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v1, v2)) % 7.78/1.81 | % 7.78/1.81 | ALPHA: (d3_tarski) implies: % 7.78/1.82 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 7.78/1.82 | $i(v0) | ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 7.78/1.82 | % 7.78/1.82 | DELTA: instantiating (t26_zfmisc_1) with fresh symbols all_14_0, all_14_1, % 7.78/1.82 | all_14_2, all_14_3, all_14_4 gives: % 7.78/1.82 | (5) ~ (all_14_2 = all_14_4) & singleton(all_14_2) = all_14_0 & % 7.78/1.82 | unordered_pair(all_14_4, all_14_3) = all_14_1 & $i(all_14_0) & % 7.78/1.82 | $i(all_14_1) & $i(all_14_2) & $i(all_14_3) & $i(all_14_4) & % 7.78/1.82 | subset(all_14_1, all_14_0) % 7.78/1.82 | % 7.78/1.82 | ALPHA: (5) implies: % 7.78/1.82 | (6) ~ (all_14_2 = all_14_4) % 7.78/1.82 | (7) subset(all_14_1, all_14_0) % 7.78/1.82 | (8) $i(all_14_4) % 7.78/1.82 | (9) $i(all_14_3) % 7.78/1.82 | (10) $i(all_14_2) % 7.78/1.82 | (11) $i(all_14_1) % 7.78/1.82 | (12) $i(all_14_0) % 7.78/1.82 | (13) unordered_pair(all_14_4, all_14_3) = all_14_1 % 7.78/1.82 | (14) singleton(all_14_2) = all_14_0 % 7.78/1.82 | % 7.78/1.82 | GROUND_INST: instantiating (3) with all_14_4, all_14_3, all_14_1, simplifying % 7.78/1.82 | with (8), (9), (11), (13) gives: % 7.78/1.82 | (15) in(all_14_3, all_14_1) % 7.78/1.82 | % 7.78/1.82 | GROUND_INST: instantiating (2) with all_14_4, all_14_3, all_14_1, simplifying % 7.78/1.82 | with (8), (9), (11), (13) gives: % 7.78/1.82 | (16) in(all_14_4, all_14_1) % 7.78/1.82 | % 7.78/1.82 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_14_4, all_14_3, % 7.78/1.82 | all_14_1, simplifying with (8), (9), (13) gives: % 7.78/1.82 | (17) unordered_pair(all_14_3, all_14_4) = all_14_1 & $i(all_14_1) % 7.78/1.82 | % 7.78/1.82 | GROUND_INST: instantiating (4) with all_14_1, all_14_0, all_14_4, simplifying % 7.78/1.82 | with (7), (8), (11), (12), (16) gives: % 7.78/1.83 | (18) in(all_14_4, all_14_0) % 7.78/1.83 | % 7.78/1.83 | GROUND_INST: instantiating (4) with all_14_1, all_14_0, all_14_3, simplifying % 7.78/1.83 | with (7), (9), (11), (12), (15) gives: % 7.78/1.83 | (19) in(all_14_3, all_14_0) % 7.78/1.83 | % 7.78/1.83 | GROUND_INST: instantiating (1) with all_14_2, all_14_0, all_14_4, simplifying % 7.78/1.83 | with (8), (10), (12), (14), (18) gives: % 7.78/1.83 | (20) all_14_2 = all_14_4 % 7.78/1.83 | % 7.78/1.83 | GROUND_INST: instantiating (1) with all_14_2, all_14_0, all_14_3, simplifying % 7.78/1.83 | with (9), (10), (12), (14), (19) gives: % 7.78/1.83 | (21) all_14_2 = all_14_3 % 7.78/1.83 | % 7.78/1.83 | COMBINE_EQS: (20), (21) imply: % 7.78/1.83 | (22) all_14_3 = all_14_4 % 7.78/1.83 | % 7.78/1.83 | REDUCE: (6), (20) imply: % 7.78/1.83 | (23) $false % 7.78/1.83 | % 7.78/1.83 | CLOSE: (23) is inconsistent. % 7.78/1.83 | % 7.78/1.83 End of proof % 7.78/1.83 % SZS output end Proof for theBenchmark % 7.78/1.83 % 7.78/1.83 1220ms %------------------------------------------------------------------------------