%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET872+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 : n012.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 15:26:51 EDT 2023 % Result : Theorem 5.38s 1.40s % Output : Proof 6.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET872+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.34 % Computer : n012.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Sat Aug 26 12:28:25 EDT 2023 % 0.17/0.34 % CPUTime : % 0.20/0.56 ________ _____ % 0.20/0.56 ___ __ \_________(_)________________________________ % 0.20/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.56 % 0.20/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.56 (2023-06-19) % 0.20/0.56 % 0.20/0.56 (c) Philipp Rümmer, 2009-2023 % 0.20/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.56 Amanda Stjerna. % 0.20/0.56 Free software under BSD-3-Clause. % 0.20/0.56 % 0.20/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.56 % 0.20/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.58 Running up to 7 provers in parallel. % 0.20/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.77/0.97 Prover 4: Preprocessing ... % 1.77/0.97 Prover 1: Preprocessing ... % 2.46/1.02 Prover 3: Preprocessing ... % 2.46/1.02 Prover 5: Preprocessing ... % 2.46/1.02 Prover 0: Preprocessing ... % 2.46/1.02 Prover 2: Preprocessing ... % 2.46/1.02 Prover 6: Preprocessing ... % 3.94/1.23 Prover 4: Warning: ignoring some quantifiers % 3.94/1.23 Prover 6: Proving ... % 3.94/1.23 Prover 5: Proving ... % 3.94/1.23 Prover 3: Warning: ignoring some quantifiers % 3.94/1.23 Prover 1: Warning: ignoring some quantifiers % 3.94/1.24 Prover 0: Proving ... % 3.94/1.24 Prover 3: Constructing countermodel ... % 3.94/1.25 Prover 4: Constructing countermodel ... % 3.94/1.25 Prover 1: Constructing countermodel ... % 3.94/1.27 Prover 2: Proving ... % 5.38/1.40 Prover 3: proved (813ms) % 5.38/1.40 % 5.38/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.38/1.40 % 5.38/1.40 Prover 5: stopped % 5.38/1.41 Prover 2: stopped % 5.38/1.42 Prover 0: stopped % 5.38/1.42 Prover 6: stopped % 5.38/1.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.38/1.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.38/1.42 Prover 7: Preprocessing ... % 5.38/1.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.38/1.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.38/1.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.38/1.42 Prover 8: Preprocessing ... % 5.38/1.44 Prover 11: Preprocessing ... % 5.38/1.44 Prover 13: Preprocessing ... % 5.38/1.44 Prover 10: Preprocessing ... % 5.38/1.48 Prover 7: Warning: ignoring some quantifiers % 5.38/1.48 Prover 4: Found proof (size 20) % 5.38/1.48 Prover 4: proved (897ms) % 5.38/1.48 Prover 1: stopped % 5.38/1.49 Prover 10: Warning: ignoring some quantifiers % 5.38/1.49 Prover 7: Constructing countermodel ... % 6.09/1.49 Prover 7: stopped % 6.09/1.49 Prover 13: Warning: ignoring some quantifiers % 6.09/1.49 Prover 10: Constructing countermodel ... % 6.09/1.50 Prover 10: stopped % 6.09/1.50 Prover 13: Constructing countermodel ... % 6.09/1.51 Prover 8: Warning: ignoring some quantifiers % 6.09/1.51 Prover 13: stopped % 6.09/1.51 Prover 8: Constructing countermodel ... % 6.09/1.51 Prover 11: Warning: ignoring some quantifiers % 6.09/1.52 Prover 8: stopped % 6.09/1.52 Prover 11: Constructing countermodel ... % 6.09/1.53 Prover 11: stopped % 6.09/1.53 % 6.09/1.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.09/1.53 % 6.09/1.54 % SZS output start Proof for theBenchmark % 6.09/1.54 Assumptions after simplification: % 6.09/1.54 --------------------------------- % 6.09/1.54 % 6.09/1.54 (commutativity_k2_tarski) % 6.09/1.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | % 6.09/1.57 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i] % 6.09/1.57 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | % 6.09/1.57 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 6.09/1.57 % 6.09/1.57 (d1_tarski) % 6.09/1.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) | % 6.09/1.57 ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! % 6.09/1.57 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = % 6.09/1.57 v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 6.09/1.57 (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 6.09/1.57 [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = % 6.09/1.57 0 | v3 = v1))) % 6.09/1.57 % 6.09/1.57 (d2_tarski) % 6.09/1.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | % 6.09/1.58 ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 6.09/1.58 $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 6.09/1.58 ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = % 6.09/1.58 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! % 6.09/1.58 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ % 6.09/1.58 (in(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! % 6.09/1.58 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) = % 6.09/1.58 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : % 6.09/1.58 (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & % 6.09/1.58 (v5 = 0 | v4 = v2 | v4 = v1))) % 6.09/1.58 % 6.09/1.58 (d3_tarski) % 6.09/1.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 6.09/1.59 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 6.09/1.59 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 6.09/1.59 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 6.09/1.59 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 6.09/1.59 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 6.09/1.59 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 6.09/1.59 $i(v0) | in(v2, v1) = 0) % 6.09/1.59 % 6.09/1.59 (t12_zfmisc_1) % 6.09/1.59 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 6.09/1.59 = 0) & subset(v2, v3) = v4 & singleton(v0) = v2 & unordered_pair(v0, v1) = % 6.09/1.59 v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 6.09/1.59 % 6.09/1.59 Further assumptions not needed in the proof: % 6.09/1.59 -------------------------------------------- % 6.09/1.59 antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski % 6.09/1.59 % 6.09/1.59 Those formulas are unsatisfiable: % 6.09/1.59 --------------------------------- % 6.09/1.59 % 6.09/1.59 Begin of proof % 6.09/1.59 | % 6.09/1.59 | ALPHA: (commutativity_k2_tarski) implies: % 6.09/1.59 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = % 6.09/1.59 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & % 6.09/1.59 | $i(v2))) % 6.09/1.59 | % 6.09/1.59 | ALPHA: (d1_tarski) implies: % 6.09/1.60 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) % 6.09/1.60 | = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 6.09/1.60 | % 6.09/1.60 | ALPHA: (d2_tarski) implies: % 6.09/1.60 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 6.09/1.60 | (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3) | ~ $i(v2) | ~ % 6.09/1.60 | $i(v1) | ~ $i(v0)) % 6.09/1.60 | % 6.09/1.60 | ALPHA: (d3_tarski) implies: % 6.09/1.60 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 6.09/1.60 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 6.09/1.60 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 6.09/1.60 | % 6.09/1.60 | DELTA: instantiating (t12_zfmisc_1) with fresh symbols all_13_0, all_13_1, % 6.09/1.60 | all_13_2, all_13_3, all_13_4 gives: % 6.09/1.60 | (5) ~ (all_13_0 = 0) & subset(all_13_2, all_13_1) = all_13_0 & % 6.09/1.60 | singleton(all_13_4) = all_13_2 & unordered_pair(all_13_4, all_13_3) = % 6.09/1.60 | all_13_1 & $i(all_13_1) & $i(all_13_2) & $i(all_13_3) & $i(all_13_4) % 6.09/1.60 | % 6.09/1.60 | ALPHA: (5) implies: % 6.09/1.60 | (6) ~ (all_13_0 = 0) % 6.09/1.60 | (7) $i(all_13_4) % 6.09/1.60 | (8) $i(all_13_3) % 6.09/1.60 | (9) $i(all_13_2) % 6.09/1.60 | (10) unordered_pair(all_13_4, all_13_3) = all_13_1 % 6.09/1.60 | (11) singleton(all_13_4) = all_13_2 % 6.09/1.60 | (12) subset(all_13_2, all_13_1) = all_13_0 % 6.09/1.60 | % 6.09/1.60 | GROUND_INST: instantiating (1) with all_13_3, all_13_4, all_13_1, simplifying % 6.09/1.60 | with (7), (8), (10) gives: % 6.09/1.60 | (13) unordered_pair(all_13_3, all_13_4) = all_13_1 & $i(all_13_1) % 6.09/1.60 | % 6.09/1.60 | ALPHA: (13) implies: % 6.09/1.60 | (14) $i(all_13_1) % 6.09/1.60 | % 6.09/1.61 | GROUND_INST: instantiating (4) with all_13_2, all_13_1, all_13_0, simplifying % 6.09/1.61 | with (9), (12), (14) gives: % 6.09/1.61 | (15) all_13_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 6.09/1.61 | all_13_1) = v1 & in(v0, all_13_2) = 0 & $i(v0)) % 6.09/1.61 | % 6.09/1.61 | BETA: splitting (15) gives: % 6.09/1.61 | % 6.09/1.61 | Case 1: % 6.09/1.61 | | % 6.09/1.61 | | (16) all_13_0 = 0 % 6.09/1.61 | | % 6.09/1.61 | | REDUCE: (6), (16) imply: % 6.09/1.61 | | (17) $false % 6.09/1.61 | | % 6.09/1.61 | | CLOSE: (17) is inconsistent. % 6.09/1.61 | | % 6.09/1.61 | Case 2: % 6.09/1.61 | | % 6.09/1.61 | | (18) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_13_1) = v1 & % 6.09/1.61 | | in(v0, all_13_2) = 0 & $i(v0)) % 6.09/1.61 | | % 6.09/1.61 | | DELTA: instantiating (18) with fresh symbols all_29_0, all_29_1 gives: % 6.09/1.61 | | (19) ~ (all_29_0 = 0) & in(all_29_1, all_13_1) = all_29_0 & in(all_29_1, % 6.09/1.61 | | all_13_2) = 0 & $i(all_29_1) % 6.09/1.61 | | % 6.09/1.61 | | ALPHA: (19) implies: % 6.09/1.61 | | (20) ~ (all_29_0 = 0) % 6.09/1.61 | | (21) $i(all_29_1) % 6.09/1.61 | | (22) in(all_29_1, all_13_2) = 0 % 6.09/1.61 | | (23) in(all_29_1, all_13_1) = all_29_0 % 6.09/1.61 | | % 6.09/1.61 | | GROUND_INST: instantiating (2) with all_13_4, all_13_2, all_29_1, % 6.09/1.61 | | simplifying with (7), (9), (11), (21), (22) gives: % 6.09/1.61 | | (24) all_29_1 = all_13_4 % 6.09/1.61 | | % 6.09/1.61 | | REDUCE: (23), (24) imply: % 6.09/1.61 | | (25) in(all_13_4, all_13_1) = all_29_0 % 6.09/1.61 | | % 6.09/1.61 | | GROUND_INST: instantiating (3) with all_13_4, all_13_3, all_13_1, all_29_0, % 6.09/1.61 | | simplifying with (7), (8), (10), (14), (25) gives: % 6.09/1.61 | | (26) all_29_0 = 0 % 6.09/1.61 | | % 6.09/1.61 | | REDUCE: (20), (26) imply: % 6.09/1.61 | | (27) $false % 6.09/1.61 | | % 6.09/1.61 | | CLOSE: (27) is inconsistent. % 6.09/1.61 | | % 6.09/1.61 | End of split % 6.09/1.61 | % 6.09/1.61 End of proof % 6.09/1.61 % SZS output end Proof for theBenchmark % 6.09/1.61 % 6.09/1.61 1049ms %------------------------------------------------------------------------------