%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET873+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 : n009.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 5.98s 1.61s % Output : Proof 6.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET873+1 : TPTP v8.1.2. Released v3.2.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n009.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 08:57:35 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.64/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.64/0.62 Running up to 7 provers in parallel. % 0.73/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.73/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.73/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.73/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.73/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.73/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.73/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.14/1.01 Prover 1: Preprocessing ... % 2.14/1.01 Prover 4: Preprocessing ... % 2.14/1.06 Prover 3: Preprocessing ... % 2.14/1.06 Prover 5: Preprocessing ... % 2.14/1.06 Prover 6: Preprocessing ... % 2.14/1.06 Prover 2: Preprocessing ... % 2.14/1.06 Prover 0: Preprocessing ... % 3.78/1.25 Prover 1: Warning: ignoring some quantifiers % 3.78/1.25 Prover 4: Warning: ignoring some quantifiers % 3.78/1.26 Prover 3: Warning: ignoring some quantifiers % 3.78/1.27 Prover 1: Constructing countermodel ... % 3.78/1.27 Prover 4: Constructing countermodel ... % 3.78/1.27 Prover 2: Proving ... % 3.78/1.27 Prover 6: Proving ... % 3.78/1.27 Prover 5: Proving ... % 3.78/1.28 Prover 3: Constructing countermodel ... % 3.78/1.28 Prover 0: Proving ... % 5.71/1.53 Prover 3: gave up % 5.71/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.98/1.56 Prover 7: Preprocessing ... % 5.98/1.58 Prover 4: Found proof (size 17) % 5.98/1.58 Prover 4: proved (948ms) % 5.98/1.58 Prover 1: stopped % 5.98/1.58 Prover 5: stopped % 5.98/1.58 Prover 0: stopped % 5.98/1.58 Prover 2: stopped % 5.98/1.58 Prover 6: stopped % 5.98/1.60 Prover 7: Warning: ignoring some quantifiers % 5.98/1.61 Prover 7: Constructing countermodel ... % 5.98/1.61 Prover 7: stopped % 5.98/1.61 % 5.98/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.98/1.61 % 5.98/1.62 % SZS output start Proof for theBenchmark % 5.98/1.62 Assumptions after simplification: % 5.98/1.62 --------------------------------- % 5.98/1.62 % 5.98/1.62 (commutativity_k2_xboole_0) % 6.56/1.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 6.56/1.65 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 6.56/1.65 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 6.56/1.65 | (set_union2(v1, v0) = v2 & $i(v2))) % 6.56/1.65 % 6.56/1.65 (d1_tarski) % 6.56/1.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) | % 6.56/1.66 ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! % 6.56/1.66 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = % 6.56/1.66 v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 6.56/1.66 (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 6.56/1.66 [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = % 6.56/1.66 0 | v3 = v1))) % 6.56/1.66 % 6.56/1.66 (l21_zfmisc_1) % 6.56/1.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (singleton(v0) = % 6.56/1.66 v2) | ~ (set_union2(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] % 6.56/1.66 : ? [v5: any] : (subset(v3, v1) = v4 & in(v0, v1) = v5 & ( ~ (v4 = 0) | v5 % 6.56/1.66 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, % 6.56/1.66 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 6.56/1.66 int] : ( ~ (v5 = 0) & subset(v4, v1) = v5 & singleton(v0) = v3 & % 6.56/1.66 set_union2(v3, v1) = v4 & $i(v4) & $i(v3))) % 6.56/1.66 % 6.56/1.66 (reflexivity_r1_tarski) % 6.56/1.67 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0)) % 6.56/1.67 % 6.56/1.67 (t13_zfmisc_1) % 6.56/1.67 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v1 = v0) & % 6.56/1.67 singleton(v1) = v3 & singleton(v0) = v2 & set_union2(v2, v3) = v2 & $i(v3) & % 6.56/1.67 $i(v2) & $i(v1) & $i(v0)) % 6.56/1.67 % 6.56/1.67 Further assumptions not needed in the proof: % 6.56/1.67 -------------------------------------------- % 6.56/1.67 antisymmetry_r2_hidden, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, % 6.56/1.67 rc1_xboole_0, rc2_xboole_0 % 6.56/1.67 % 6.56/1.67 Those formulas are unsatisfiable: % 6.56/1.67 --------------------------------- % 6.56/1.67 % 6.56/1.67 Begin of proof % 6.56/1.67 | % 6.56/1.67 | ALPHA: (commutativity_k2_xboole_0) implies: % 6.56/1.67 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 6.56/1.67 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 6.56/1.67 | % 6.56/1.67 | ALPHA: (d1_tarski) implies: % 6.56/1.67 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) % 6.56/1.67 | = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 6.56/1.67 | % 6.56/1.67 | ALPHA: (l21_zfmisc_1) implies: % 6.56/1.68 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 6.56/1.68 | (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ $i(v1) | ~ % 6.56/1.68 | $i(v0) | ? [v4: any] : ? [v5: any] : (subset(v3, v1) = v4 & in(v0, % 6.56/1.68 | v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) % 6.56/1.68 | % 6.56/1.68 | DELTA: instantiating (t13_zfmisc_1) with fresh symbols all_15_0, all_15_1, % 6.56/1.68 | all_15_2, all_15_3 gives: % 6.56/1.68 | (4) ~ (all_15_2 = all_15_3) & singleton(all_15_2) = all_15_0 & % 6.56/1.68 | singleton(all_15_3) = all_15_1 & set_union2(all_15_1, all_15_0) = % 6.56/1.68 | all_15_1 & $i(all_15_0) & $i(all_15_1) & $i(all_15_2) & $i(all_15_3) % 6.56/1.68 | % 6.56/1.68 | ALPHA: (4) implies: % 6.56/1.68 | (5) ~ (all_15_2 = all_15_3) % 6.56/1.68 | (6) $i(all_15_3) % 6.56/1.68 | (7) $i(all_15_2) % 6.56/1.68 | (8) $i(all_15_1) % 6.56/1.68 | (9) $i(all_15_0) % 6.56/1.68 | (10) set_union2(all_15_1, all_15_0) = all_15_1 % 6.56/1.68 | (11) singleton(all_15_3) = all_15_1 % 6.56/1.68 | (12) singleton(all_15_2) = all_15_0 % 6.56/1.68 | % 6.56/1.68 | GROUND_INST: instantiating (1) with all_15_0, all_15_1, all_15_1, simplifying % 6.56/1.68 | with (8), (9), (10) gives: % 6.56/1.68 | (13) set_union2(all_15_0, all_15_1) = all_15_1 % 6.56/1.68 | % 6.56/1.69 | GROUND_INST: instantiating (3) with all_15_2, all_15_1, all_15_0, all_15_1, % 6.56/1.69 | simplifying with (7), (8), (12), (13) gives: % 6.56/1.69 | (14) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_1) = v0 & % 6.56/1.69 | in(all_15_2, all_15_1) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 6.56/1.69 | % 6.56/1.69 | DELTA: instantiating (14) with fresh symbols all_42_0, all_42_1 gives: % 6.56/1.69 | (15) subset(all_15_1, all_15_1) = all_42_1 & in(all_15_2, all_15_1) = % 6.56/1.69 | all_42_0 & ( ~ (all_42_1 = 0) | all_42_0 = 0) % 6.56/1.69 | % 6.56/1.69 | ALPHA: (15) implies: % 6.56/1.69 | (16) in(all_15_2, all_15_1) = all_42_0 % 6.56/1.69 | (17) subset(all_15_1, all_15_1) = all_42_1 % 6.56/1.69 | (18) ~ (all_42_1 = 0) | all_42_0 = 0 % 6.56/1.69 | % 6.83/1.69 | GROUND_INST: instantiating (reflexivity_r1_tarski) with all_15_1, all_42_1, % 6.83/1.69 | simplifying with (8), (17) gives: % 6.83/1.69 | (19) all_42_1 = 0 % 6.83/1.69 | % 6.83/1.69 | BETA: splitting (18) gives: % 6.83/1.69 | % 6.83/1.69 | Case 1: % 6.83/1.69 | | % 6.83/1.69 | | (20) ~ (all_42_1 = 0) % 6.83/1.69 | | % 6.83/1.69 | | REDUCE: (19), (20) imply: % 6.83/1.69 | | (21) $false % 6.83/1.69 | | % 6.83/1.69 | | CLOSE: (21) is inconsistent. % 6.83/1.69 | | % 6.83/1.69 | Case 2: % 6.83/1.69 | | % 6.83/1.69 | | (22) all_42_0 = 0 % 6.83/1.69 | | % 6.83/1.69 | | REDUCE: (16), (22) imply: % 6.83/1.69 | | (23) in(all_15_2, all_15_1) = 0 % 6.83/1.69 | | % 6.83/1.69 | | GROUND_INST: instantiating (2) with all_15_3, all_15_1, all_15_2, % 6.83/1.69 | | simplifying with (6), (7), (8), (11), (23) gives: % 6.83/1.69 | | (24) all_15_2 = all_15_3 % 6.83/1.69 | | % 6.83/1.69 | | REDUCE: (5), (24) imply: % 6.83/1.69 | | (25) $false % 6.83/1.69 | | % 6.83/1.69 | | CLOSE: (25) is inconsistent. % 6.83/1.69 | | % 6.83/1.69 | End of split % 6.83/1.69 | % 6.83/1.69 End of proof % 6.83/1.69 % SZS output end Proof for theBenchmark % 6.83/1.69 % 6.83/1.69 1084ms %------------------------------------------------------------------------------