%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET921+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 : n011.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 15:27:03 EDT 2023 % Result : Theorem 5.29s 1.46s % Output : Proof 7.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET921+1 : TPTP v8.1.2. Released v3.2.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n011.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 13:54:54 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 1.84/0.97 Prover 1: Preprocessing ... % 1.84/0.98 Prover 4: Preprocessing ... % 2.13/1.02 Prover 6: Preprocessing ... % 2.13/1.02 Prover 5: Preprocessing ... % 2.13/1.02 Prover 2: Preprocessing ... % 2.13/1.02 Prover 0: Preprocessing ... % 2.13/1.02 Prover 3: Preprocessing ... % 3.37/1.22 Prover 3: Warning: ignoring some quantifiers % 3.37/1.23 Prover 1: Warning: ignoring some quantifiers % 3.37/1.23 Prover 6: Proving ... % 3.37/1.23 Prover 5: Proving ... % 3.37/1.23 Prover 3: Constructing countermodel ... % 4.01/1.24 Prover 4: Warning: ignoring some quantifiers % 4.01/1.24 Prover 1: Constructing countermodel ... % 4.01/1.25 Prover 4: Constructing countermodel ... % 4.01/1.28 Prover 2: Proving ... % 4.01/1.30 Prover 0: Proving ... % 5.29/1.46 Prover 3: proved (793ms) % 5.29/1.46 % 5.29/1.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.29/1.46 % 5.29/1.46 Prover 0: stopped % 5.29/1.46 Prover 6: stopped % 5.29/1.47 Prover 2: stopped % 5.29/1.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.29/1.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.29/1.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.29/1.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.29/1.48 Prover 5: proved (819ms) % 5.29/1.48 % 5.29/1.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.29/1.48 % 5.29/1.48 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.29/1.48 Prover 10: Preprocessing ... % 5.29/1.48 Prover 7: Preprocessing ... % 5.29/1.49 Prover 8: Preprocessing ... % 5.29/1.49 Prover 11: Preprocessing ... % 5.29/1.49 Prover 13: Preprocessing ... % 6.01/1.54 Prover 7: Warning: ignoring some quantifiers % 6.01/1.54 Prover 7: Constructing countermodel ... % 6.01/1.54 Prover 8: Warning: ignoring some quantifiers % 6.01/1.55 Prover 10: Warning: ignoring some quantifiers % 6.01/1.55 Prover 8: Constructing countermodel ... % 6.01/1.56 Prover 10: Constructing countermodel ... % 6.01/1.57 Prover 13: Warning: ignoring some quantifiers % 6.01/1.58 Prover 13: Constructing countermodel ... % 6.01/1.59 Prover 11: Warning: ignoring some quantifiers % 6.56/1.60 Prover 11: Constructing countermodel ... % 6.56/1.63 Prover 7: Found proof (size 21) % 6.56/1.64 Prover 7: proved (171ms) % 6.56/1.64 Prover 8: stopped % 6.56/1.64 Prover 1: stopped % 6.56/1.64 Prover 4: stopped % 6.56/1.64 Prover 13: stopped % 6.56/1.64 Prover 11: stopped % 6.56/1.64 Prover 10: Found proof (size 20) % 6.56/1.64 Prover 10: proved (172ms) % 6.56/1.64 % 6.56/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.56/1.64 % 6.56/1.64 % SZS output start Proof for theBenchmark % 6.56/1.65 Assumptions after simplification: % 6.56/1.65 --------------------------------- % 6.56/1.65 % 6.56/1.65 (d1_tarski) % 7.11/1.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) | % 7.11/1.68 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1: % 7.11/1.68 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ % 7.11/1.68 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | % 7.11/1.68 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | % 7.11/1.68 ~ $i(v1) | ~ $i(v0) | in(v0, v1)) % 7.11/1.68 % 7.11/1.68 (d4_xboole_0) % 7.15/1.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 7.15/1.68 (set_difference(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 7.15/1.68 $i(v0) | ~ in(v3, v2) | ~ in(v3, v1)) & ! [v0: $i] : ! [v1: $i] : ! % 7.15/1.68 [v2: $i] : ! [v3: $i] : ( ~ (set_difference(v0, v1) = v2) | ~ $i(v3) | ~ % 7.15/1.68 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v2) | in(v3, v0)) & ! [v0: $i] : % 7.15/1.68 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_difference(v0, v1) = v2) | % 7.15/1.68 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v0) | in(v3, v2) | % 7.15/1.68 in(v3, v1)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = % 7.15/1.68 v0 | ~ (set_difference(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 7.15/1.68 ? [v4: $i] : ($i(v4) & ( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & % 7.15/1.68 (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2))))) % 7.15/1.68 % 7.15/1.68 (t64_zfmisc_1) % 7.15/1.69 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 7.15/1.69 (set_difference(v1, v3) = v4 & singleton(v2) = v3 & $i(v4) & $i(v3) & $i(v2) & % 7.15/1.69 $i(v1) & $i(v0) & (( ~ (v2 = v0) & in(v0, v1) & ~ in(v0, v4)) | (in(v0, v4) % 7.15/1.69 & (v2 = v0 | ~ in(v0, v1))))) % 7.15/1.69 % 7.15/1.69 Further assumptions not needed in the proof: % 7.15/1.69 -------------------------------------------- % 7.15/1.69 antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0 % 7.15/1.69 % 7.15/1.69 Those formulas are unsatisfiable: % 7.15/1.69 --------------------------------- % 7.15/1.69 % 7.15/1.69 Begin of proof % 7.15/1.69 | % 7.15/1.69 | ALPHA: (d1_tarski) implies: % 7.15/1.69 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ % 7.15/1.69 | $i(v0) | in(v0, v1)) % 7.15/1.69 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) % 7.15/1.69 | = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) % 7.15/1.69 | % 7.15/1.69 | ALPHA: (d4_xboole_0) implies: % 7.15/1.69 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 7.15/1.69 | (set_difference(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 7.15/1.69 | ~ $i(v0) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) % 7.15/1.70 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 7.15/1.70 | (set_difference(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 7.15/1.70 | ~ $i(v0) | ~ in(v3, v2) | in(v3, v0)) % 7.15/1.70 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 7.15/1.70 | (set_difference(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 7.15/1.70 | ~ $i(v0) | ~ in(v3, v2) | ~ in(v3, v1)) % 7.15/1.70 | % 7.15/1.70 | DELTA: instantiating (t64_zfmisc_1) with fresh symbols all_14_0, all_14_1, % 7.15/1.70 | all_14_2, all_14_3, all_14_4 gives: % 7.15/1.70 | (6) set_difference(all_14_3, all_14_1) = all_14_0 & singleton(all_14_2) = % 7.15/1.70 | all_14_1 & $i(all_14_0) & $i(all_14_1) & $i(all_14_2) & $i(all_14_3) & % 7.15/1.70 | $i(all_14_4) & (( ~ (all_14_2 = all_14_4) & in(all_14_4, all_14_3) & ~ % 7.15/1.70 | in(all_14_4, all_14_0)) | (in(all_14_4, all_14_0) & (all_14_2 = % 7.15/1.70 | all_14_4 | ~ in(all_14_4, all_14_3)))) % 7.15/1.70 | % 7.15/1.70 | ALPHA: (6) implies: % 7.26/1.70 | (7) $i(all_14_4) % 7.26/1.70 | (8) $i(all_14_3) % 7.26/1.70 | (9) $i(all_14_2) % 7.26/1.70 | (10) $i(all_14_1) % 7.26/1.70 | (11) $i(all_14_0) % 7.26/1.70 | (12) singleton(all_14_2) = all_14_1 % 7.26/1.70 | (13) set_difference(all_14_3, all_14_1) = all_14_0 % 7.26/1.70 | (14) ( ~ (all_14_2 = all_14_4) & in(all_14_4, all_14_3) & ~ in(all_14_4, % 7.26/1.70 | all_14_0)) | (in(all_14_4, all_14_0) & (all_14_2 = all_14_4 | ~ % 7.26/1.70 | in(all_14_4, all_14_3))) % 7.26/1.70 | % 7.26/1.71 | GROUND_INST: instantiating (1) with all_14_2, all_14_1, simplifying with (9), % 7.26/1.71 | (10), (12) gives: % 7.26/1.71 | (15) in(all_14_2, all_14_1) % 7.26/1.71 | % 7.26/1.71 | BETA: splitting (14) gives: % 7.26/1.71 | % 7.26/1.71 | Case 1: % 7.26/1.71 | | % 7.26/1.71 | | (16) ~ (all_14_2 = all_14_4) & in(all_14_4, all_14_3) & ~ in(all_14_4, % 7.26/1.71 | | all_14_0) % 7.26/1.71 | | % 7.26/1.71 | | ALPHA: (16) implies: % 7.26/1.71 | | (17) ~ (all_14_2 = all_14_4) % 7.26/1.71 | | (18) ~ in(all_14_4, all_14_0) % 7.26/1.71 | | (19) in(all_14_4, all_14_3) % 7.26/1.71 | | % 7.26/1.71 | | GROUND_INST: instantiating (3) with all_14_3, all_14_1, all_14_0, all_14_4, % 7.26/1.71 | | simplifying with (7), (8), (10), (11), (13), (18), (19) gives: % 7.26/1.71 | | (20) in(all_14_4, all_14_1) % 7.26/1.71 | | % 7.26/1.71 | | GROUND_INST: instantiating (2) with all_14_2, all_14_1, all_14_4, % 7.26/1.71 | | simplifying with (7), (9), (10), (12), (20) gives: % 7.26/1.71 | | (21) all_14_2 = all_14_4 % 7.26/1.71 | | % 7.26/1.71 | | REDUCE: (17), (21) imply: % 7.26/1.71 | | (22) $false % 7.26/1.71 | | % 7.26/1.71 | | CLOSE: (22) is inconsistent. % 7.26/1.71 | | % 7.26/1.71 | Case 2: % 7.26/1.71 | | % 7.26/1.71 | | (23) in(all_14_4, all_14_0) & (all_14_2 = all_14_4 | ~ in(all_14_4, % 7.26/1.71 | | all_14_3)) % 7.26/1.71 | | % 7.26/1.71 | | ALPHA: (23) implies: % 7.26/1.71 | | (24) in(all_14_4, all_14_0) % 7.26/1.71 | | (25) all_14_2 = all_14_4 | ~ in(all_14_4, all_14_3) % 7.26/1.71 | | % 7.26/1.71 | | GROUND_INST: instantiating (5) with all_14_3, all_14_1, all_14_0, all_14_4, % 7.26/1.71 | | simplifying with (7), (8), (10), (11), (13), (24) gives: % 7.26/1.71 | | (26) ~ in(all_14_4, all_14_1) % 7.26/1.71 | | % 7.26/1.71 | | GROUND_INST: instantiating (4) with all_14_3, all_14_1, all_14_0, all_14_4, % 7.26/1.71 | | simplifying with (7), (8), (10), (11), (13), (24) gives: % 7.26/1.71 | | (27) in(all_14_4, all_14_3) % 7.26/1.71 | | % 7.26/1.71 | | BETA: splitting (25) gives: % 7.26/1.71 | | % 7.26/1.71 | | Case 1: % 7.26/1.71 | | | % 7.26/1.71 | | | (28) ~ in(all_14_4, all_14_3) % 7.26/1.71 | | | % 7.26/1.72 | | | PRED_UNIFY: (27), (28) imply: % 7.26/1.72 | | | (29) $false % 7.26/1.72 | | | % 7.26/1.72 | | | CLOSE: (29) is inconsistent. % 7.26/1.72 | | | % 7.26/1.72 | | Case 2: % 7.26/1.72 | | | % 7.26/1.72 | | | (30) all_14_2 = all_14_4 % 7.26/1.72 | | | % 7.26/1.72 | | | REDUCE: (15), (30) imply: % 7.26/1.72 | | | (31) in(all_14_4, all_14_1) % 7.26/1.72 | | | % 7.26/1.72 | | | PRED_UNIFY: (26), (31) imply: % 7.26/1.72 | | | (32) $false % 7.26/1.72 | | | % 7.26/1.72 | | | CLOSE: (32) is inconsistent. % 7.26/1.72 | | | % 7.26/1.72 | | End of split % 7.26/1.72 | | % 7.26/1.72 | End of split % 7.26/1.72 | % 7.26/1.72 End of proof % 7.26/1.72 % SZS output end Proof for theBenchmark % 7.26/1.72 % 7.26/1.72 1084ms %------------------------------------------------------------------------------