%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET949+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 : n017.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 15:27:10 EDT 2023 % Result : Theorem 5.09s 1.48s % Output : Proof 5.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET949+1 : TPTP v8.1.2. Released v3.2.0. % 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n017.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 : Sat Aug 26 11:53:25 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.02/0.99 Prover 4: Preprocessing ... % 2.02/0.99 Prover 1: Preprocessing ... % 2.02/1.03 Prover 3: Preprocessing ... % 2.02/1.03 Prover 5: Preprocessing ... % 2.02/1.03 Prover 2: Preprocessing ... % 2.02/1.03 Prover 6: Preprocessing ... % 2.02/1.03 Prover 0: Preprocessing ... % 3.62/1.25 Prover 1: Warning: ignoring some quantifiers % 3.62/1.27 Prover 4: Warning: ignoring some quantifiers % 3.62/1.27 Prover 1: Constructing countermodel ... % 3.62/1.28 Prover 3: Warning: ignoring some quantifiers % 3.62/1.28 Prover 6: Proving ... % 3.62/1.28 Prover 4: Constructing countermodel ... % 3.62/1.29 Prover 3: Constructing countermodel ... % 3.62/1.30 Prover 5: Proving ... % 3.62/1.33 Prover 0: Proving ... % 3.62/1.34 Prover 2: Proving ... % 5.09/1.48 Prover 4: Found proof (size 8) % 5.09/1.48 Prover 1: Found proof (size 10) % 5.09/1.48 Prover 4: proved (830ms) % 5.09/1.48 Prover 3: proved (831ms) % 5.09/1.48 Prover 1: proved (834ms) % 5.09/1.48 % 5.09/1.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.09/1.48 % 5.09/1.48 Prover 6: stopped % 5.09/1.48 Prover 2: stopped % 5.09/1.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.09/1.48 Prover 5: stopped % 5.09/1.48 Prover 0: stopped % 5.09/1.49 Prover 7: Preprocessing ... % 5.09/1.51 Prover 7: stopped % 5.53/1.51 % 5.53/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.53/1.51 % 5.53/1.51 % SZS output start Proof for theBenchmark % 5.53/1.52 Assumptions after simplification: % 5.53/1.52 --------------------------------- % 5.53/1.52 % 5.53/1.52 (d2_zfmisc_1) % 5.53/1.56 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 5.53/1.56 (cartesian_product2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 5.53/1.56 [v4: $i] : ? [v5: any] : (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ! [v6: % 5.53/1.56 $i] : ! [v7: $i] : ( ~ (ordered_pair(v6, v7) = v4) | ~ $i(v7) | ~ % 5.53/1.56 $i(v6) | ? [v8: any] : ? [v9: any] : (in(v7, v2) = v9 & in(v6, v1) = % 5.53/1.56 v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & (v5 = 0 | ? [v6: $i] : ? % 5.53/1.56 [v7: $i] : (ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0 % 5.53/1.56 & $i(v7) & $i(v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 5.53/1.56 (cartesian_product2(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! % 5.53/1.56 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ! % 5.53/1.56 [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v6) = v3) | ~ $i(v6) | % 5.53/1.56 ~ $i(v5) | ? [v7: any] : ? [v8: any] : (in(v6, v1) = v8 & in(v5, v0) % 5.53/1.56 = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))) & ! [v3: $i] : ( ~ (in(v3, % 5.53/1.56 v2) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: $i] : (ordered_pair(v4, % 5.53/1.56 v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0 & $i(v5) & $i(v4))))) % 5.53/1.56 % 5.53/1.56 (t102_zfmisc_1) % 5.53/1.56 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 5.53/1.56 (cartesian_product2(v1, v2) = v3 & in(v0, v3) = 0 & $i(v3) & $i(v2) & $i(v1) & % 5.53/1.56 $i(v0) & ! [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v4, v5) = v0) | ~ % 5.53/1.56 $i(v5) | ~ $i(v4))) % 5.53/1.56 % 5.53/1.56 Further assumptions not needed in the proof: % 5.53/1.56 -------------------------------------------- % 5.53/1.56 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, fc1_zfmisc_1, % 5.53/1.56 rc1_xboole_0, rc2_xboole_0 % 5.53/1.56 % 5.53/1.56 Those formulas are unsatisfiable: % 5.53/1.56 --------------------------------- % 5.53/1.56 % 5.53/1.56 Begin of proof % 5.53/1.56 | % 5.53/1.56 | ALPHA: (d2_zfmisc_1) implies: % 5.53/1.57 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0, % 5.83/1.57 | v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! % 5.83/1.57 | [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ! [v5: % 5.83/1.57 | $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v6) = v3) | ~ $i(v6) % 5.83/1.57 | | ~ $i(v5) | ? [v7: any] : ? [v8: any] : (in(v6, v1) = v8 & % 5.83/1.57 | in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))) & ! [v3: % 5.83/1.57 | $i] : ( ~ (in(v3, v2) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: % 5.83/1.57 | $i] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) % 5.83/1.57 | = 0 & $i(v5) & $i(v4))))) % 5.83/1.57 | % 5.83/1.57 | DELTA: instantiating (t102_zfmisc_1) with fresh symbols all_12_0, all_12_1, % 5.83/1.57 | all_12_2, all_12_3 gives: % 5.83/1.57 | (2) cartesian_product2(all_12_2, all_12_1) = all_12_0 & in(all_12_3, % 5.83/1.57 | all_12_0) = 0 & $i(all_12_0) & $i(all_12_1) & $i(all_12_2) & % 5.83/1.57 | $i(all_12_3) & ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) = % 5.83/1.57 | all_12_3) | ~ $i(v1) | ~ $i(v0)) % 5.83/1.57 | % 5.83/1.57 | ALPHA: (2) implies: % 5.83/1.57 | (3) $i(all_12_3) % 5.83/1.57 | (4) $i(all_12_2) % 5.83/1.58 | (5) $i(all_12_1) % 5.83/1.58 | (6) $i(all_12_0) % 5.83/1.58 | (7) in(all_12_3, all_12_0) = 0 % 5.83/1.58 | (8) cartesian_product2(all_12_2, all_12_1) = all_12_0 % 5.83/1.58 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) = all_12_3) | ~ % 5.83/1.58 | $i(v1) | ~ $i(v0)) % 5.83/1.58 | % 5.83/1.58 | GROUND_INST: instantiating (1) with all_12_2, all_12_1, all_12_0, simplifying % 5.83/1.58 | with (4), (5), (6), (8) gives: % 5.83/1.58 | (10) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_12_0) = v1) | ~ % 5.83/1.58 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) = v0) % 5.83/1.58 | | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : (in(v3, % 5.83/1.58 | all_12_1) = v5 & in(v2, all_12_2) = v4 & ( ~ (v5 = 0) | ~ (v4 % 5.83/1.58 | = 0))))) & ! [v0: $i] : ( ~ (in(v0, all_12_0) = 0) | ~ % 5.83/1.58 | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v2) = v0 & % 5.83/1.58 | in(v2, all_12_1) = 0 & in(v1, all_12_2) = 0 & $i(v2) & $i(v1))) % 5.83/1.58 | % 5.83/1.58 | ALPHA: (10) implies: % 5.83/1.58 | (11) ! [v0: $i] : ( ~ (in(v0, all_12_0) = 0) | ~ $i(v0) | ? [v1: $i] : % 5.83/1.58 | ? [v2: $i] : (ordered_pair(v1, v2) = v0 & in(v2, all_12_1) = 0 & % 5.83/1.58 | in(v1, all_12_2) = 0 & $i(v2) & $i(v1))) % 5.83/1.58 | % 5.83/1.58 | GROUND_INST: instantiating (11) with all_12_3, simplifying with (3), (7) % 5.83/1.58 | gives: % 5.83/1.59 | (12) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_12_3 & in(v1, % 5.83/1.59 | all_12_1) = 0 & in(v0, all_12_2) = 0 & $i(v1) & $i(v0)) % 5.83/1.59 | % 5.83/1.59 | DELTA: instantiating (12) with fresh symbols all_25_0, all_25_1 gives: % 5.83/1.59 | (13) ordered_pair(all_25_1, all_25_0) = all_12_3 & in(all_25_0, all_12_1) = % 5.83/1.59 | 0 & in(all_25_1, all_12_2) = 0 & $i(all_25_0) & $i(all_25_1) % 5.83/1.59 | % 5.83/1.59 | ALPHA: (13) implies: % 5.83/1.59 | (14) $i(all_25_1) % 5.83/1.59 | (15) $i(all_25_0) % 5.83/1.59 | (16) ordered_pair(all_25_1, all_25_0) = all_12_3 % 5.83/1.59 | % 5.83/1.59 | GROUND_INST: instantiating (9) with all_25_1, all_25_0, simplifying with (14), % 5.83/1.59 | (15), (16) gives: % 5.83/1.59 | (17) $false % 5.83/1.59 | % 5.83/1.59 | CLOSE: (17) is inconsistent. % 5.83/1.59 | % 5.83/1.59 End of proof % 5.83/1.59 % SZS output end Proof for theBenchmark % 5.83/1.59 % 5.83/1.59 965ms %------------------------------------------------------------------------------