%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET893+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 : n026.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 15:26:56 EDT 2023 % Result : Theorem 5.86s 1.54s % Output : Proof 7.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET893+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n026.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sat Aug 26 15:22:49 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.60 % 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.60 % 0.21/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.61 Running up to 7 provers in parallel. % 0.21/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.31/1.01 Prover 4: Preprocessing ... % 2.31/1.01 Prover 1: Preprocessing ... % 2.39/1.05 Prover 3: Preprocessing ... % 2.39/1.05 Prover 2: Preprocessing ... % 2.39/1.05 Prover 0: Preprocessing ... % 2.39/1.05 Prover 5: Preprocessing ... % 2.39/1.05 Prover 6: Preprocessing ... % 4.08/1.28 Prover 5: Proving ... % 4.08/1.28 Prover 1: Warning: ignoring some quantifiers % 4.18/1.29 Prover 1: Constructing countermodel ... % 4.18/1.29 Prover 6: Proving ... % 4.18/1.30 Prover 4: Warning: ignoring some quantifiers % 4.18/1.30 Prover 3: Warning: ignoring some quantifiers % 4.18/1.30 Prover 0: Proving ... % 4.18/1.32 Prover 2: Proving ... % 4.18/1.32 Prover 4: Constructing countermodel ... % 4.18/1.32 Prover 3: Constructing countermodel ... % 5.86/1.54 Prover 3: proved (922ms) % 5.86/1.54 % 5.86/1.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.86/1.54 % 5.86/1.54 Prover 0: stopped % 5.86/1.54 Prover 5: stopped % 5.86/1.54 Prover 2: stopped % 5.86/1.55 Prover 6: stopped % 5.86/1.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.86/1.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.86/1.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.86/1.55 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.86/1.56 Prover 7: Preprocessing ... % 5.86/1.57 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.86/1.57 Prover 10: Preprocessing ... % 5.86/1.58 Prover 8: Preprocessing ... % 5.86/1.58 Prover 11: Preprocessing ... % 6.23/1.59 Prover 13: Preprocessing ... % 6.23/1.61 Prover 10: Warning: ignoring some quantifiers % 6.23/1.62 Prover 7: Warning: ignoring some quantifiers % 6.23/1.62 Prover 10: Constructing countermodel ... % 6.23/1.63 Prover 7: Constructing countermodel ... % 6.23/1.64 Prover 13: Warning: ignoring some quantifiers % 6.23/1.64 Prover 8: Warning: ignoring some quantifiers % 6.23/1.65 Prover 13: Constructing countermodel ... % 6.71/1.65 Prover 11: Warning: ignoring some quantifiers % 6.71/1.66 Prover 11: Constructing countermodel ... % 6.82/1.67 Prover 8: Constructing countermodel ... % 7.19/1.72 Prover 10: Found proof (size 24) % 7.19/1.72 Prover 10: proved (173ms) % 7.19/1.72 Prover 11: stopped % 7.19/1.72 Prover 4: stopped % 7.19/1.72 Prover 8: stopped % 7.19/1.72 Prover 7: stopped % 7.19/1.72 Prover 1: stopped % 7.19/1.72 Prover 13: stopped % 7.19/1.72 % 7.19/1.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.19/1.72 % 7.19/1.72 % SZS output start Proof for theBenchmark % 7.19/1.73 Assumptions after simplification: % 7.19/1.73 --------------------------------- % 7.19/1.73 % 7.19/1.73 (d1_tarski) % 7.39/1.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) | % 7.39/1.76 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1: % 7.39/1.76 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ % 7.39/1.76 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | % 7.39/1.76 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | % 7.39/1.76 ~ $i(v1) | ~ $i(v0) | in(v0, v1)) % 7.39/1.76 % 7.39/1.76 (l55_zfmisc_1) % 7.39/1.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 7.39/1.77 $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) % 7.39/1.77 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v4, v5) | in(v1, % 7.39/1.77 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 7.39/1.77 : ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, % 7.39/1.77 v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v4, % 7.39/1.77 v5) | in(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 7.39/1.77 : ! [v4: $i] : ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ % 7.39/1.77 (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 7.39/1.77 | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) % 7.39/1.77 % 7.39/1.77 (t34_zfmisc_1) % 7.39/1.77 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 7.39/1.77 $i] : ? [v6: $i] : ? [v7: $i] : (cartesian_product2(v5, v6) = v7 & % 7.39/1.77 ordered_pair(v0, v1) = v4 & singleton(v3) = v6 & singleton(v2) = v5 & $i(v7) % 7.39/1.77 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v3 = v1 & % 7.39/1.77 v2 = v0 & ~ in(v4, v7)) | (in(v4, v7) & ( ~ (v3 = v1) | ~ (v2 = % 7.39/1.77 v0))))) % 7.39/1.77 % 7.39/1.77 Further assumptions not needed in the proof: % 7.39/1.77 -------------------------------------------- % 7.39/1.77 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, fc1_zfmisc_1, % 7.39/1.77 rc1_xboole_0, rc2_xboole_0 % 7.39/1.77 % 7.39/1.77 Those formulas are unsatisfiable: % 7.39/1.77 --------------------------------- % 7.39/1.77 % 7.39/1.77 Begin of proof % 7.39/1.77 | % 7.39/1.77 | ALPHA: (d1_tarski) implies: % 7.39/1.78 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ % 7.39/1.78 | $i(v0) | in(v0, v1)) % 7.39/1.78 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) % 7.39/1.78 | = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) % 7.39/1.78 | % 7.39/1.78 | ALPHA: (l55_zfmisc_1) implies: % 7.39/1.78 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 7.39/1.78 | ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ % 7.39/1.78 | (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 7.39/1.78 | $i(v0) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) % 7.39/1.78 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 7.39/1.78 | ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ % 7.39/1.78 | (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 7.39/1.78 | $i(v0) | ~ in(v4, v5) | in(v0, v2)) % 7.39/1.78 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 7.39/1.78 | ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ % 7.39/1.79 | (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 7.39/1.79 | $i(v0) | ~ in(v4, v5) | in(v1, v3)) % 7.39/1.79 | % 7.39/1.79 | DELTA: instantiating (t34_zfmisc_1) with fresh symbols all_15_0, all_15_1, % 7.39/1.79 | all_15_2, all_15_3, all_15_4, all_15_5, all_15_6, all_15_7 gives: % 7.39/1.79 | (6) cartesian_product2(all_15_2, all_15_1) = all_15_0 & % 7.39/1.79 | ordered_pair(all_15_7, all_15_6) = all_15_3 & singleton(all_15_4) = % 7.39/1.79 | all_15_1 & singleton(all_15_5) = all_15_2 & $i(all_15_0) & $i(all_15_1) % 7.39/1.79 | & $i(all_15_2) & $i(all_15_3) & $i(all_15_4) & $i(all_15_5) & % 7.39/1.79 | $i(all_15_6) & $i(all_15_7) & ((all_15_4 = all_15_6 & all_15_5 = % 7.39/1.79 | all_15_7 & ~ in(all_15_3, all_15_0)) | (in(all_15_3, all_15_0) & ( % 7.39/1.79 | ~ (all_15_4 = all_15_6) | ~ (all_15_5 = all_15_7)))) % 7.39/1.79 | % 7.39/1.79 | ALPHA: (6) implies: % 7.39/1.79 | (7) $i(all_15_7) % 7.39/1.79 | (8) $i(all_15_6) % 7.39/1.79 | (9) $i(all_15_5) % 7.39/1.79 | (10) $i(all_15_4) % 7.39/1.79 | (11) $i(all_15_2) % 7.39/1.79 | (12) $i(all_15_1) % 7.39/1.79 | (13) singleton(all_15_5) = all_15_2 % 7.39/1.79 | (14) singleton(all_15_4) = all_15_1 % 7.39/1.79 | (15) ordered_pair(all_15_7, all_15_6) = all_15_3 % 7.39/1.79 | (16) cartesian_product2(all_15_2, all_15_1) = all_15_0 % 7.39/1.79 | (17) (all_15_4 = all_15_6 & all_15_5 = all_15_7 & ~ in(all_15_3, % 7.39/1.79 | all_15_0)) | (in(all_15_3, all_15_0) & ( ~ (all_15_4 = all_15_6) | % 7.39/1.79 | ~ (all_15_5 = all_15_7))) % 7.39/1.79 | % 7.39/1.79 | GROUND_INST: instantiating (1) with all_15_5, all_15_2, simplifying with (9), % 7.39/1.79 | (11), (13) gives: % 7.39/1.79 | (18) in(all_15_5, all_15_2) % 7.39/1.79 | % 7.39/1.80 | GROUND_INST: instantiating (1) with all_15_4, all_15_1, simplifying with (10), % 7.39/1.80 | (12), (14) gives: % 7.39/1.80 | (19) in(all_15_4, all_15_1) % 7.39/1.80 | % 7.39/1.80 | BETA: splitting (17) gives: % 7.39/1.80 | % 7.39/1.80 | Case 1: % 7.39/1.80 | | % 7.39/1.80 | | (20) all_15_4 = all_15_6 & all_15_5 = all_15_7 & ~ in(all_15_3, % 7.39/1.80 | | all_15_0) % 7.39/1.80 | | % 7.39/1.80 | | ALPHA: (20) implies: % 7.39/1.80 | | (21) all_15_5 = all_15_7 % 7.39/1.80 | | (22) all_15_4 = all_15_6 % 7.39/1.80 | | (23) ~ in(all_15_3, all_15_0) % 7.39/1.80 | | % 7.39/1.80 | | REDUCE: (19), (22) imply: % 7.39/1.80 | | (24) in(all_15_6, all_15_1) % 7.39/1.80 | | % 7.39/1.80 | | REDUCE: (18), (21) imply: % 7.39/1.80 | | (25) in(all_15_7, all_15_2) % 7.39/1.80 | | % 7.39/1.80 | | GROUND_INST: instantiating (3) with all_15_7, all_15_6, all_15_2, all_15_1, % 7.39/1.80 | | all_15_3, all_15_0, simplifying with (7), (8), (11), (12), % 7.39/1.80 | | (15), (16), (23), (24), (25) gives: % 7.39/1.80 | | (26) $false % 7.39/1.80 | | % 7.39/1.80 | | CLOSE: (26) is inconsistent. % 7.39/1.80 | | % 7.39/1.80 | Case 2: % 7.39/1.80 | | % 7.39/1.80 | | (27) in(all_15_3, all_15_0) & ( ~ (all_15_4 = all_15_6) | ~ (all_15_5 = % 7.39/1.80 | | all_15_7)) % 7.39/1.80 | | % 7.39/1.80 | | ALPHA: (27) implies: % 7.39/1.80 | | (28) in(all_15_3, all_15_0) % 7.39/1.80 | | (29) ~ (all_15_4 = all_15_6) | ~ (all_15_5 = all_15_7) % 7.39/1.80 | | % 7.39/1.80 | | GROUND_INST: instantiating (5) with all_15_7, all_15_6, all_15_2, all_15_1, % 7.39/1.80 | | all_15_3, all_15_0, simplifying with (7), (8), (11), (12), % 7.39/1.80 | | (15), (16), (28) gives: % 7.39/1.80 | | (30) in(all_15_6, all_15_1) % 7.39/1.80 | | % 7.39/1.80 | | GROUND_INST: instantiating (4) with all_15_7, all_15_6, all_15_2, all_15_1, % 7.39/1.80 | | all_15_3, all_15_0, simplifying with (7), (8), (11), (12), % 7.39/1.80 | | (15), (16), (28) gives: % 7.39/1.81 | | (31) in(all_15_7, all_15_2) % 7.39/1.81 | | % 7.39/1.81 | | GROUND_INST: instantiating (2) with all_15_5, all_15_2, all_15_7, % 7.39/1.81 | | simplifying with (7), (9), (11), (13), (31) gives: % 7.39/1.81 | | (32) all_15_5 = all_15_7 % 7.39/1.81 | | % 7.39/1.81 | | GROUND_INST: instantiating (2) with all_15_4, all_15_1, all_15_6, % 7.39/1.81 | | simplifying with (8), (10), (12), (14), (30) gives: % 7.39/1.81 | | (33) all_15_4 = all_15_6 % 7.39/1.81 | | % 7.39/1.81 | | BETA: splitting (29) gives: % 7.39/1.81 | | % 7.39/1.81 | | Case 1: % 7.39/1.81 | | | % 7.39/1.81 | | | (34) ~ (all_15_4 = all_15_6) % 7.39/1.81 | | | % 7.39/1.81 | | | REDUCE: (33), (34) imply: % 7.39/1.81 | | | (35) $false % 7.39/1.81 | | | % 7.39/1.81 | | | CLOSE: (35) is inconsistent. % 7.39/1.81 | | | % 7.39/1.81 | | Case 2: % 7.39/1.81 | | | % 7.39/1.81 | | | (36) ~ (all_15_5 = all_15_7) % 7.39/1.81 | | | % 7.39/1.81 | | | REDUCE: (32), (36) imply: % 7.39/1.81 | | | (37) $false % 7.39/1.81 | | | % 7.39/1.81 | | | CLOSE: (37) is inconsistent. % 7.39/1.81 | | | % 7.39/1.81 | | End of split % 7.39/1.81 | | % 7.39/1.81 | End of split % 7.39/1.81 | % 7.39/1.81 End of proof % 7.39/1.81 % SZS output end Proof for theBenchmark % 7.39/1.81 % 7.39/1.81 1211ms 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