%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU148+3 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n007.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 17:42:47 EDT 2023 % Result : Theorem 4.57s 1.42s % Output : Proof 6.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU148+3 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n007.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Wed Aug 23 16:25:54 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.66 ________ _____ % 0.20/0.66 ___ __ \_________(_)________________________________ % 0.20/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.66 % 0.20/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.66 (2023-06-19) % 0.20/0.66 % 0.20/0.66 (c) Philipp Rümmer, 2009-2023 % 0.20/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.66 Amanda Stjerna. % 0.20/0.66 Free software under BSD-3-Clause. % 0.20/0.66 % 0.20/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.66 % 0.20/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.67 Running up to 7 provers in parallel. % 0.20/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.82/1.00 Prover 4: Preprocessing ... % 1.82/1.00 Prover 1: Preprocessing ... % 1.82/1.05 Prover 3: Preprocessing ... % 1.82/1.05 Prover 2: Preprocessing ... % 1.82/1.05 Prover 6: Preprocessing ... % 1.82/1.05 Prover 0: Preprocessing ... % 1.82/1.05 Prover 5: Preprocessing ... % 3.50/1.20 Prover 1: Warning: ignoring some quantifiers % 3.50/1.22 Prover 4: Warning: ignoring some quantifiers % 3.50/1.22 Prover 5: Proving ... % 3.50/1.22 Prover 6: Proving ... % 3.50/1.22 Prover 0: Proving ... % 3.50/1.22 Prover 3: Warning: ignoring some quantifiers % 3.50/1.23 Prover 2: Proving ... % 3.50/1.23 Prover 4: Constructing countermodel ... % 3.50/1.23 Prover 3: Constructing countermodel ... % 3.50/1.23 Prover 1: Constructing countermodel ... % 4.57/1.42 Prover 5: proved (730ms) % 4.57/1.42 Prover 2: proved (738ms) % 4.57/1.42 % 4.57/1.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.57/1.42 % 4.57/1.42 % 4.57/1.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.57/1.42 % 4.57/1.42 Prover 3: stopped % 4.57/1.42 Prover 6: stopped % 4.57/1.42 Prover 0: stopped % 4.57/1.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.57/1.43 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.57/1.43 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.57/1.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.57/1.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.57/1.45 Prover 1: gave up % 4.57/1.46 Prover 8: Preprocessing ... % 4.57/1.46 Prover 11: Preprocessing ... % 4.57/1.46 Prover 13: Preprocessing ... % 4.57/1.46 Prover 7: Preprocessing ... % 4.57/1.46 Prover 10: Preprocessing ... % 4.57/1.46 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 4.57/1.49 Prover 13: Warning: ignoring some quantifiers % 4.57/1.49 Prover 13: Constructing countermodel ... % 4.57/1.50 Prover 16: Preprocessing ... % 4.57/1.50 Prover 10: Warning: ignoring some quantifiers % 4.57/1.50 Prover 10: Constructing countermodel ... % 5.04/1.51 Prover 7: Warning: ignoring some quantifiers % 5.04/1.51 Prover 7: Constructing countermodel ... % 5.04/1.53 Prover 11: Warning: ignoring some quantifiers % 5.04/1.53 Prover 4: gave up % 5.04/1.53 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 5.04/1.53 Prover 8: Warning: ignoring some quantifiers % 5.04/1.53 Prover 11: Constructing countermodel ... % 5.04/1.54 Prover 19: Preprocessing ... % 5.04/1.55 Prover 8: Constructing countermodel ... % 6.02/1.57 Prover 16: Warning: ignoring some quantifiers % 6.02/1.57 Prover 16: Constructing countermodel ... % 6.02/1.58 Prover 10: Found proof (size 17) % 6.02/1.58 Prover 10: proved (150ms) % 6.02/1.58 Prover 16: stopped % 6.02/1.58 Prover 8: stopped % 6.02/1.58 Prover 7: stopped % 6.02/1.58 Prover 11: stopped % 6.02/1.58 Prover 13: stopped % 6.31/1.60 Prover 19: Warning: ignoring some quantifiers % 6.31/1.61 Prover 19: Constructing countermodel ... % 6.31/1.61 Prover 19: stopped % 6.31/1.61 % 6.31/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.31/1.61 % 6.31/1.62 % SZS output start Proof for theBenchmark % 6.31/1.62 Assumptions after simplification: % 6.31/1.62 --------------------------------- % 6.31/1.62 % 6.31/1.62 (d1_tarski) % 6.52/1.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) | % 6.52/1.65 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1: % 6.52/1.65 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ % 6.52/1.65 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | % 6.52/1.65 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | % 6.52/1.65 ~ $i(v1) | ~ $i(v0) | in(v0, v1)) % 6.52/1.65 % 6.52/1.65 (l1_zfmisc_1) % 6.52/1.65 $i(empty_set) & ! [v0: $i] : ( ~ (singleton(v0) = empty_set) | ~ $i(v0)) % 6.52/1.65 % 6.52/1.65 (l4_zfmisc_1) % 6.52/1.65 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | v0 = % 6.52/1.66 empty_set | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ subset(v0, % 6.52/1.66 v2)) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v1) = v0) | ~ $i(v1) | % 6.52/1.66 ~ $i(v0) | subset(v0, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) % 6.52/1.66 = v1) | ~ $i(v0) | subset(empty_set, v1)) % 6.52/1.66 % 6.52/1.66 (t6_zfmisc_1) % 6.52/1.66 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v1 = v0) & % 6.52/1.66 singleton(v1) = v3 & singleton(v0) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) % 6.52/1.66 & subset(v2, v3)) % 6.52/1.66 % 6.52/1.66 Further assumptions not needed in the proof: % 6.52/1.66 -------------------------------------------- % 6.52/1.66 antisymmetry_r2_hidden, fc1_xboole_0, rc1_xboole_0, rc2_xboole_0, % 6.52/1.66 reflexivity_r1_tarski % 6.52/1.66 % 6.52/1.66 Those formulas are unsatisfiable: % 6.52/1.66 --------------------------------- % 6.52/1.66 % 6.52/1.66 Begin of proof % 6.52/1.66 | % 6.52/1.66 | ALPHA: (d1_tarski) implies: % 6.52/1.66 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ % 6.52/1.66 | $i(v0) | in(v0, v1)) % 6.52/1.66 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) % 6.52/1.66 | = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) % 6.52/1.66 | % 6.52/1.66 | ALPHA: (l1_zfmisc_1) implies: % 6.52/1.66 | (3) ! [v0: $i] : ( ~ (singleton(v0) = empty_set) | ~ $i(v0)) % 6.52/1.66 | % 6.52/1.66 | ALPHA: (l4_zfmisc_1) implies: % 6.52/1.67 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | v0 = empty_set | % 6.52/1.67 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v2)) % 6.52/1.67 | % 6.52/1.67 | DELTA: instantiating (t6_zfmisc_1) with fresh symbols all_13_0, all_13_1, % 6.52/1.67 | all_13_2, all_13_3 gives: % 6.52/1.67 | (5) ~ (all_13_2 = all_13_3) & singleton(all_13_2) = all_13_0 & % 6.52/1.67 | singleton(all_13_3) = all_13_1 & $i(all_13_0) & $i(all_13_1) & % 6.52/1.67 | $i(all_13_2) & $i(all_13_3) & subset(all_13_1, all_13_0) % 6.52/1.67 | % 6.52/1.67 | ALPHA: (5) implies: % 6.52/1.67 | (6) ~ (all_13_2 = all_13_3) % 6.52/1.67 | (7) subset(all_13_1, all_13_0) % 6.52/1.67 | (8) $i(all_13_3) % 6.52/1.67 | (9) $i(all_13_2) % 6.52/1.67 | (10) $i(all_13_1) % 6.52/1.67 | (11) $i(all_13_0) % 6.52/1.67 | (12) singleton(all_13_3) = all_13_1 % 6.52/1.67 | (13) singleton(all_13_2) = all_13_0 % 6.52/1.67 | % 6.52/1.67 | GROUND_INST: instantiating (1) with all_13_3, all_13_1, simplifying with (8), % 6.52/1.67 | (10), (12) gives: % 6.52/1.67 | (14) in(all_13_3, all_13_1) % 6.52/1.67 | % 6.52/1.67 | GROUND_INST: instantiating (4) with all_13_1, all_13_2, all_13_0, simplifying % 6.52/1.67 | with (7), (9), (10), (13) gives: % 6.52/1.68 | (15) all_13_0 = all_13_1 | all_13_1 = empty_set % 6.52/1.68 | % 6.52/1.68 | BETA: splitting (15) gives: % 6.52/1.68 | % 6.52/1.68 | Case 1: % 6.52/1.68 | | % 6.52/1.68 | | (16) all_13_1 = empty_set % 6.52/1.68 | | % 6.52/1.68 | | REDUCE: (12), (16) imply: % 6.52/1.68 | | (17) singleton(all_13_3) = empty_set % 6.52/1.68 | | % 6.52/1.68 | | GROUND_INST: instantiating (3) with all_13_3, simplifying with (8), (17) % 6.52/1.68 | | gives: % 6.52/1.68 | | (18) $false % 6.52/1.68 | | % 6.52/1.68 | | CLOSE: (18) is inconsistent. % 6.52/1.68 | | % 6.52/1.68 | Case 2: % 6.52/1.68 | | % 6.52/1.68 | | (19) all_13_0 = all_13_1 % 6.52/1.68 | | % 6.52/1.68 | | REDUCE: (13), (19) imply: % 6.52/1.68 | | (20) singleton(all_13_2) = all_13_1 % 6.52/1.68 | | % 6.52/1.68 | | GROUND_INST: instantiating (2) with all_13_2, all_13_1, all_13_3, % 6.52/1.68 | | simplifying with (8), (9), (10), (14), (20) gives: % 6.52/1.68 | | (21) all_13_2 = all_13_3 % 6.52/1.68 | | % 6.52/1.68 | | REDUCE: (6), (21) imply: % 6.52/1.68 | | (22) $false % 6.52/1.68 | | % 6.52/1.68 | | CLOSE: (22) is inconsistent. % 6.52/1.68 | | % 6.52/1.68 | End of split % 6.52/1.68 | % 6.52/1.68 End of proof % 6.52/1.68 % SZS output end Proof for theBenchmark % 6.52/1.68 % 6.52/1.68 1018ms %------------------------------------------------------------------------------