%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET975+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 15:27:15 EDT 2023 % Result : Theorem 5.70s 1.48s % Output : Proof 7.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET975+1 : TPTP v8.1.2. Released v3.2.0. % 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n009.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Aug 26 12:17:05 EDT 2023 % 0.13/0.34 % CPUTime : % 0.61/0.60 ________ _____ % 0.61/0.60 ___ __ \_________(_)________________________________ % 0.61/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.61/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.61/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.61/0.60 % 0.61/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.61/0.60 (2023-06-19) % 0.61/0.60 % 0.61/0.60 (c) Philipp Rümmer, 2009-2023 % 0.61/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.61/0.60 Amanda Stjerna. % 0.61/0.60 Free software under BSD-3-Clause. % 0.61/0.60 % 0.61/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.61/0.60 % 0.61/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.61/0.61 Running up to 7 provers in parallel. % 0.61/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.61/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.61/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.61/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.61/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.61/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.61/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.96/0.99 Prover 1: Preprocessing ... % 1.96/0.99 Prover 4: Preprocessing ... % 2.41/1.04 Prover 0: Preprocessing ... % 2.41/1.04 Prover 5: Preprocessing ... % 2.41/1.04 Prover 3: Preprocessing ... % 2.41/1.04 Prover 2: Preprocessing ... % 2.41/1.04 Prover 6: Preprocessing ... % 3.98/1.24 Prover 1: Warning: ignoring some quantifiers % 3.98/1.24 Prover 4: Warning: ignoring some quantifiers % 3.98/1.25 Prover 3: Warning: ignoring some quantifiers % 3.98/1.25 Prover 4: Constructing countermodel ... % 3.98/1.25 Prover 3: Constructing countermodel ... % 3.98/1.27 Prover 1: Constructing countermodel ... % 3.98/1.27 Prover 5: Proving ... % 3.98/1.27 Prover 6: Proving ... % 3.98/1.28 Prover 0: Proving ... % 3.98/1.30 Prover 2: Proving ... % 5.70/1.48 Prover 3: proved (860ms) % 5.70/1.48 % 5.70/1.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.70/1.48 % 5.70/1.48 Prover 2: stopped % 5.70/1.48 Prover 5: stopped % 5.70/1.48 Prover 0: stopped % 5.70/1.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.70/1.48 Prover 6: stopped % 5.70/1.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.70/1.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.70/1.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.70/1.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.98/1.50 Prover 7: Preprocessing ... % 5.98/1.51 Prover 10: Preprocessing ... % 5.98/1.51 Prover 13: Preprocessing ... % 5.98/1.51 Prover 11: Preprocessing ... % 5.98/1.52 Prover 8: Preprocessing ... % 6.27/1.56 Prover 7: Warning: ignoring some quantifiers % 6.27/1.57 Prover 7: Constructing countermodel ... % 6.27/1.57 Prover 8: Warning: ignoring some quantifiers % 6.27/1.58 Prover 8: Constructing countermodel ... % 6.27/1.59 Prover 10: Warning: ignoring some quantifiers % 6.27/1.61 Prover 10: Constructing countermodel ... % 6.84/1.63 Prover 11: Warning: ignoring some quantifiers % 6.84/1.63 Prover 11: Constructing countermodel ... % 6.84/1.64 Prover 13: Warning: ignoring some quantifiers % 6.84/1.64 Prover 13: Constructing countermodel ... % 7.33/1.68 Prover 10: Found proof (size 20) % 7.33/1.68 Prover 10: proved (193ms) % 7.33/1.68 Prover 11: stopped % 7.33/1.68 Prover 7: stopped % 7.33/1.68 Prover 1: stopped % 7.33/1.68 Prover 4: stopped % 7.33/1.68 Prover 13: stopped % 7.33/1.68 Prover 8: stopped % 7.33/1.68 % 7.33/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.33/1.68 % 7.33/1.69 % SZS output start Proof for theBenchmark % 7.33/1.69 Assumptions after simplification: % 7.33/1.69 --------------------------------- % 7.33/1.69 % 7.33/1.69 (d1_tarski) % 7.33/1.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) | % 7.33/1.72 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1: % 7.33/1.72 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ % 7.33/1.72 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | % 7.33/1.72 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | % 7.33/1.72 ~ $i(v1) | ~ $i(v0) | in(v0, v1)) % 7.33/1.72 % 7.33/1.72 (l55_zfmisc_1) % 7.33/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 7.33/1.73 $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) % 7.33/1.73 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v4, v5) | in(v1, % 7.33/1.73 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 7.33/1.73 : ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, % 7.33/1.73 v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v4, % 7.33/1.73 v5) | in(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 7.33/1.73 : ! [v4: $i] : ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ % 7.33/1.73 (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 7.33/1.73 | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) % 7.33/1.73 % 7.33/1.73 (t128_zfmisc_1) % 7.33/1.73 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 7.33/1.73 $i] : ? [v6: $i] : (cartesian_product2(v5, v3) = v6 & ordered_pair(v0, v1) % 7.33/1.73 = v4 & singleton(v2) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 7.33/1.73 $i(v1) & $i(v0) & ((v2 = v0 & in(v1, v3) & ~ in(v4, v6)) | (in(v4, v6) & ( % 7.33/1.73 ~ (v2 = v0) | ~ in(v1, v3))))) % 7.33/1.73 % 7.33/1.73 Further assumptions not needed in the proof: % 7.33/1.73 -------------------------------------------- % 7.33/1.73 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, fc1_zfmisc_1, % 7.33/1.73 rc1_xboole_0, rc2_xboole_0 % 7.33/1.73 % 7.33/1.73 Those formulas are unsatisfiable: % 7.33/1.73 --------------------------------- % 7.33/1.73 % 7.33/1.73 Begin of proof % 7.33/1.74 | % 7.33/1.74 | ALPHA: (d1_tarski) implies: % 7.33/1.74 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ % 7.33/1.74 | $i(v0) | in(v0, v1)) % 7.33/1.74 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) % 7.33/1.74 | = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) % 7.33/1.74 | % 7.33/1.74 | ALPHA: (l55_zfmisc_1) implies: % 7.33/1.74 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 7.33/1.74 | ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ % 7.33/1.74 | (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 7.33/1.74 | $i(v0) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) % 7.33/1.74 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 7.33/1.74 | ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ % 7.33/1.74 | (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 7.33/1.74 | $i(v0) | ~ in(v4, v5) | in(v0, v2)) % 7.33/1.75 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 7.33/1.75 | ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ % 7.33/1.75 | (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 7.33/1.75 | $i(v0) | ~ in(v4, v5) | in(v1, v3)) % 7.33/1.75 | % 7.33/1.75 | DELTA: instantiating (t128_zfmisc_1) with fresh symbols all_15_0, all_15_1, % 7.33/1.75 | all_15_2, all_15_3, all_15_4, all_15_5, all_15_6 gives: % 7.33/1.75 | (6) cartesian_product2(all_15_1, all_15_3) = all_15_0 & % 7.33/1.75 | ordered_pair(all_15_6, all_15_5) = all_15_2 & singleton(all_15_4) = % 7.33/1.75 | all_15_1 & $i(all_15_0) & $i(all_15_1) & $i(all_15_2) & $i(all_15_3) & % 7.33/1.75 | $i(all_15_4) & $i(all_15_5) & $i(all_15_6) & ((all_15_4 = all_15_6 & % 7.33/1.75 | in(all_15_5, all_15_3) & ~ in(all_15_2, all_15_0)) | (in(all_15_2, % 7.33/1.75 | all_15_0) & ( ~ (all_15_4 = all_15_6) | ~ in(all_15_5, % 7.33/1.75 | all_15_3)))) % 7.33/1.75 | % 7.33/1.75 | ALPHA: (6) implies: % 7.33/1.75 | (7) $i(all_15_6) % 7.33/1.75 | (8) $i(all_15_5) % 7.33/1.75 | (9) $i(all_15_4) % 7.33/1.75 | (10) $i(all_15_3) % 7.33/1.75 | (11) $i(all_15_1) % 7.33/1.75 | (12) singleton(all_15_4) = all_15_1 % 7.33/1.75 | (13) ordered_pair(all_15_6, all_15_5) = all_15_2 % 7.33/1.75 | (14) cartesian_product2(all_15_1, all_15_3) = all_15_0 % 7.33/1.75 | (15) (all_15_4 = all_15_6 & in(all_15_5, all_15_3) & ~ in(all_15_2, % 7.33/1.75 | all_15_0)) | (in(all_15_2, all_15_0) & ( ~ (all_15_4 = all_15_6) | % 7.33/1.75 | ~ in(all_15_5, all_15_3))) % 7.33/1.75 | % 7.33/1.75 | GROUND_INST: instantiating (1) with all_15_4, all_15_1, simplifying with (9), % 7.33/1.75 | (11), (12) gives: % 7.33/1.75 | (16) in(all_15_4, all_15_1) % 7.33/1.75 | % 7.33/1.75 | BETA: splitting (15) gives: % 7.33/1.75 | % 7.33/1.75 | Case 1: % 7.33/1.75 | | % 7.33/1.75 | | (17) all_15_4 = all_15_6 & in(all_15_5, all_15_3) & ~ in(all_15_2, % 7.33/1.75 | | all_15_0) % 7.33/1.76 | | % 7.33/1.76 | | ALPHA: (17) implies: % 7.33/1.76 | | (18) all_15_4 = all_15_6 % 7.33/1.76 | | (19) ~ in(all_15_2, all_15_0) % 7.33/1.76 | | (20) in(all_15_5, all_15_3) % 7.33/1.76 | | % 7.33/1.76 | | REDUCE: (16), (18) imply: % 7.33/1.76 | | (21) in(all_15_6, all_15_1) % 7.33/1.76 | | % 7.33/1.76 | | GROUND_INST: instantiating (3) with all_15_6, all_15_5, all_15_1, all_15_3, % 7.33/1.76 | | all_15_2, all_15_0, simplifying with (7), (8), (10), (11), % 7.33/1.76 | | (13), (14), (19), (20), (21) gives: % 7.33/1.76 | | (22) $false % 7.33/1.76 | | % 7.33/1.76 | | CLOSE: (22) is inconsistent. % 7.33/1.76 | | % 7.33/1.76 | Case 2: % 7.33/1.76 | | % 7.33/1.76 | | (23) in(all_15_2, all_15_0) & ( ~ (all_15_4 = all_15_6) | ~ in(all_15_5, % 7.33/1.76 | | all_15_3)) % 7.33/1.76 | | % 7.33/1.76 | | ALPHA: (23) implies: % 7.33/1.76 | | (24) in(all_15_2, all_15_0) % 7.33/1.76 | | (25) ~ (all_15_4 = all_15_6) | ~ in(all_15_5, all_15_3) % 7.33/1.76 | | % 7.33/1.76 | | GROUND_INST: instantiating (5) with all_15_6, all_15_5, all_15_1, all_15_3, % 7.33/1.76 | | all_15_2, all_15_0, simplifying with (7), (8), (10), (11), % 7.33/1.76 | | (13), (14), (24) gives: % 7.33/1.76 | | (26) in(all_15_5, all_15_3) % 7.33/1.76 | | % 7.33/1.76 | | GROUND_INST: instantiating (4) with all_15_6, all_15_5, all_15_1, all_15_3, % 7.33/1.76 | | all_15_2, all_15_0, simplifying with (7), (8), (10), (11), % 7.33/1.76 | | (13), (14), (24) gives: % 7.33/1.76 | | (27) in(all_15_6, all_15_1) % 7.33/1.76 | | % 7.33/1.76 | | BETA: splitting (25) gives: % 7.33/1.76 | | % 7.33/1.76 | | Case 1: % 7.33/1.76 | | | % 7.33/1.76 | | | (28) ~ in(all_15_5, all_15_3) % 7.33/1.76 | | | % 7.33/1.76 | | | PRED_UNIFY: (26), (28) imply: % 7.33/1.76 | | | (29) $false % 7.33/1.76 | | | % 7.33/1.76 | | | CLOSE: (29) is inconsistent. % 7.33/1.76 | | | % 7.33/1.76 | | Case 2: % 7.33/1.76 | | | % 7.33/1.76 | | | (30) ~ (all_15_4 = all_15_6) % 7.33/1.76 | | | % 7.33/1.76 | | | GROUND_INST: instantiating (2) with all_15_4, all_15_1, all_15_6, % 7.33/1.76 | | | simplifying with (7), (9), (11), (12), (27) gives: % 7.33/1.76 | | | (31) all_15_4 = all_15_6 % 7.33/1.76 | | | % 7.33/1.76 | | | REDUCE: (30), (31) imply: % 7.33/1.76 | | | (32) $false % 7.33/1.76 | | | % 7.33/1.76 | | | CLOSE: (32) is inconsistent. % 7.33/1.76 | | | % 7.33/1.76 | | End of split % 7.33/1.76 | | % 7.33/1.76 | End of split % 7.33/1.76 | % 7.33/1.76 End of proof % 7.33/1.76 % SZS output end Proof for theBenchmark % 7.33/1.77 % 7.33/1.77 1166ms %------------------------------------------------------------------------------