%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET925+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 : n023.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 3.92s 1.21s % Output : Proof 4.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SET925+1 : TPTP v8.1.2. Released v3.2.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n023.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sat Aug 26 15:37:56 EDT 2023 % 0.12/0.33 % CPUTime : % 0.18/0.60 ________ _____ % 0.18/0.60 ___ __ \_________(_)________________________________ % 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.60 % 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.60 (2023-06-19) % 0.18/0.60 % 0.18/0.60 (c) Philipp Rümmer, 2009-2023 % 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.60 Amanda Stjerna. % 0.18/0.60 Free software under BSD-3-Clause. % 0.18/0.60 % 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.60 % 0.18/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.63/0.61 Running up to 7 provers in parallel. % 0.71/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.71/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.71/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.71/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.71/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.71/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.71/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.01/0.93 Prover 4: Preprocessing ... % 2.01/0.93 Prover 1: Preprocessing ... % 2.01/0.97 Prover 6: Preprocessing ... % 2.01/0.97 Prover 5: Preprocessing ... % 2.01/0.97 Prover 3: Preprocessing ... % 2.01/0.97 Prover 2: Preprocessing ... % 2.01/0.97 Prover 0: Preprocessing ... % 3.05/1.09 Prover 6: Constructing countermodel ... % 3.05/1.10 Prover 2: Proving ... % 3.05/1.10 Prover 5: Proving ... % 3.05/1.10 Prover 3: Constructing countermodel ... % 3.05/1.10 Prover 1: Constructing countermodel ... % 3.05/1.11 Prover 4: Constructing countermodel ... % 3.05/1.11 Prover 0: Proving ... % 3.92/1.21 Prover 3: proved (586ms) % 3.92/1.21 % 3.92/1.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.92/1.21 % 3.92/1.22 Prover 6: stopped % 3.92/1.22 Prover 5: stopped % 3.92/1.22 Prover 2: proved (591ms) % 3.92/1.22 % 3.92/1.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.92/1.22 % 3.92/1.22 Prover 0: proved (596ms) % 3.92/1.22 % 3.92/1.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.92/1.22 % 3.92/1.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.92/1.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.92/1.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.92/1.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.92/1.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.10/1.23 Prover 7: Preprocessing ... % 4.10/1.24 Prover 11: Preprocessing ... % 4.10/1.24 Prover 8: Preprocessing ... % 4.10/1.24 Prover 13: Preprocessing ... % 4.10/1.25 Prover 10: Preprocessing ... % 4.10/1.26 Prover 7: Constructing countermodel ... % 4.10/1.27 Prover 8: Warning: ignoring some quantifiers % 4.10/1.28 Prover 13: Warning: ignoring some quantifiers % 4.10/1.28 Prover 1: Found proof (size 23) % 4.10/1.28 Prover 1: proved (662ms) % 4.10/1.28 Prover 10: Constructing countermodel ... % 4.10/1.28 Prover 7: stopped % 4.10/1.28 Prover 4: stopped % 4.10/1.28 Prover 8: Constructing countermodel ... % 4.10/1.28 Prover 13: Constructing countermodel ... % 4.10/1.29 Prover 10: stopped % 4.10/1.29 Prover 8: stopped % 4.10/1.29 Prover 13: stopped % 4.10/1.29 Prover 11: Constructing countermodel ... % 4.10/1.30 Prover 11: stopped % 4.10/1.30 % 4.10/1.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.10/1.30 % 4.10/1.30 % SZS output start Proof for theBenchmark % 4.10/1.31 Assumptions after simplification: % 4.10/1.31 --------------------------------- % 4.10/1.31 % 4.10/1.31 (l36_zfmisc_1) % 4.72/1.34 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = % 4.72/1.34 empty_set | ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | ~ % 4.72/1.34 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! % 4.72/1.34 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v0) = v2) | ~ % 4.72/1.34 (set_difference(v2, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) | in(v0, v1) = % 4.72/1.34 0) % 4.72/1.34 % 4.72/1.34 (t68_zfmisc_1) % 4.72/1.34 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 4.72/1.34 [v4: any] : (singleton(v0) = v2 & set_difference(v2, v1) = v3 & in(v0, v1) = % 4.72/1.34 v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v4 = 0 & ~ (v3 = empty_set)) | % 4.72/1.34 (v3 = empty_set & ~ (v4 = 0)))) % 4.72/1.34 % 4.72/1.34 (function-axioms) % 4.72/1.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 4.72/1.35 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 4.72/1.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 4.72/1.35 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 4.72/1.35 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 4.72/1.35 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 4.72/1.35 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 4.72/1.35 (empty(v2) = v0)) % 4.72/1.35 % 4.72/1.35 Further assumptions not needed in the proof: % 4.72/1.35 -------------------------------------------- % 4.72/1.35 antisymmetry_r2_hidden, fc1_xboole_0, rc1_xboole_0, rc2_xboole_0 % 4.72/1.35 % 4.72/1.35 Those formulas are unsatisfiable: % 4.72/1.35 --------------------------------- % 4.72/1.35 % 4.72/1.35 Begin of proof % 4.72/1.35 | % 4.72/1.35 | ALPHA: (l36_zfmisc_1) implies: % 4.72/1.35 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v0) = v2) | ~ % 4.72/1.35 | (set_difference(v2, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) | in(v0, % 4.72/1.35 | v1) = 0) % 4.72/1.35 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set % 4.72/1.35 | | ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | ~ % 4.72/1.35 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) % 4.72/1.35 | % 4.72/1.35 | ALPHA: (t68_zfmisc_1) implies: % 4.72/1.36 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : % 4.72/1.36 | (singleton(v0) = v2 & set_difference(v2, v1) = v3 & in(v0, v1) = v4 & % 4.72/1.36 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v4 = 0 & ~ (v3 = empty_set)) | % 4.72/1.36 | (v3 = empty_set & ~ (v4 = 0)))) % 4.72/1.36 | % 4.72/1.36 | ALPHA: (function-axioms) implies: % 4.72/1.36 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.72/1.36 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 4.72/1.36 | % 4.72/1.36 | DELTA: instantiating (3) with fresh symbols all_10_0, all_10_1, all_10_2, % 4.72/1.36 | all_10_3, all_10_4 gives: % 4.72/1.36 | (5) singleton(all_10_4) = all_10_2 & set_difference(all_10_2, all_10_3) = % 4.72/1.36 | all_10_1 & in(all_10_4, all_10_3) = all_10_0 & $i(all_10_1) & % 4.72/1.36 | $i(all_10_2) & $i(all_10_3) & $i(all_10_4) & ((all_10_0 = 0 & ~ % 4.72/1.36 | (all_10_1 = empty_set)) | (all_10_1 = empty_set & ~ (all_10_0 = % 4.72/1.36 | 0))) % 4.72/1.36 | % 4.72/1.36 | ALPHA: (5) implies: % 4.72/1.36 | (6) $i(all_10_4) % 4.72/1.36 | (7) $i(all_10_3) % 4.72/1.36 | (8) in(all_10_4, all_10_3) = all_10_0 % 4.72/1.36 | (9) set_difference(all_10_2, all_10_3) = all_10_1 % 4.72/1.36 | (10) singleton(all_10_4) = all_10_2 % 4.72/1.36 | (11) (all_10_0 = 0 & ~ (all_10_1 = empty_set)) | (all_10_1 = empty_set & % 4.72/1.36 | ~ (all_10_0 = 0)) % 4.72/1.36 | % 4.72/1.37 | GROUND_INST: instantiating (2) with all_10_4, all_10_3, all_10_2, all_10_1, % 4.72/1.37 | simplifying with (6), (7), (9), (10) gives: % 4.72/1.37 | (12) all_10_1 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & in(all_10_4, % 4.72/1.37 | all_10_3) = v0) % 4.72/1.37 | % 4.72/1.37 | BETA: splitting (11) gives: % 4.72/1.37 | % 4.72/1.37 | Case 1: % 4.72/1.37 | | % 4.72/1.37 | | (13) all_10_0 = 0 & ~ (all_10_1 = empty_set) % 4.72/1.37 | | % 4.72/1.37 | | ALPHA: (13) implies: % 4.72/1.37 | | (14) all_10_0 = 0 % 4.72/1.37 | | (15) ~ (all_10_1 = empty_set) % 4.72/1.37 | | % 4.72/1.37 | | REDUCE: (8), (14) imply: % 4.72/1.37 | | (16) in(all_10_4, all_10_3) = 0 % 4.72/1.37 | | % 4.72/1.37 | | BETA: splitting (12) gives: % 4.72/1.37 | | % 4.72/1.37 | | Case 1: % 4.72/1.37 | | | % 4.72/1.37 | | | (17) all_10_1 = empty_set % 4.72/1.37 | | | % 4.72/1.37 | | | REDUCE: (15), (17) imply: % 4.72/1.37 | | | (18) $false % 4.72/1.37 | | | % 4.72/1.37 | | | CLOSE: (18) is inconsistent. % 4.72/1.37 | | | % 4.72/1.37 | | Case 2: % 4.72/1.37 | | | % 4.72/1.37 | | | (19) ? [v0: int] : ( ~ (v0 = 0) & in(all_10_4, all_10_3) = v0) % 4.72/1.37 | | | % 4.72/1.37 | | | DELTA: instantiating (19) with fresh symbol all_23_0 gives: % 4.72/1.37 | | | (20) ~ (all_23_0 = 0) & in(all_10_4, all_10_3) = all_23_0 % 4.72/1.37 | | | % 4.72/1.37 | | | ALPHA: (20) implies: % 4.72/1.37 | | | (21) ~ (all_23_0 = 0) % 4.72/1.37 | | | (22) in(all_10_4, all_10_3) = all_23_0 % 4.72/1.37 | | | % 4.72/1.38 | | | GROUND_INST: instantiating (4) with 0, all_23_0, all_10_3, all_10_4, % 4.72/1.38 | | | simplifying with (16), (22) gives: % 4.72/1.38 | | | (23) all_23_0 = 0 % 4.72/1.38 | | | % 4.72/1.38 | | | REDUCE: (21), (23) imply: % 4.72/1.38 | | | (24) $false % 4.72/1.38 | | | % 4.72/1.38 | | | CLOSE: (24) is inconsistent. % 4.72/1.38 | | | % 4.72/1.38 | | End of split % 4.72/1.38 | | % 4.72/1.38 | Case 2: % 4.72/1.38 | | % 4.72/1.38 | | (25) all_10_1 = empty_set & ~ (all_10_0 = 0) % 4.72/1.38 | | % 4.72/1.38 | | ALPHA: (25) implies: % 4.72/1.38 | | (26) all_10_1 = empty_set % 4.72/1.38 | | (27) ~ (all_10_0 = 0) % 4.72/1.38 | | % 4.72/1.38 | | REDUCE: (9), (26) imply: % 4.72/1.38 | | (28) set_difference(all_10_2, all_10_3) = empty_set % 4.72/1.38 | | % 4.72/1.38 | | GROUND_INST: instantiating (1) with all_10_4, all_10_3, all_10_2, % 4.72/1.38 | | simplifying with (6), (7), (10), (28) gives: % 4.72/1.38 | | (29) in(all_10_4, all_10_3) = 0 % 4.72/1.38 | | % 4.72/1.38 | | GROUND_INST: instantiating (4) with all_10_0, 0, all_10_3, all_10_4, % 4.72/1.38 | | simplifying with (8), (29) gives: % 4.72/1.38 | | (30) all_10_0 = 0 % 4.72/1.38 | | % 4.72/1.38 | | REDUCE: (27), (30) imply: % 4.72/1.38 | | (31) $false % 4.72/1.38 | | % 4.72/1.38 | | CLOSE: (31) is inconsistent. % 4.72/1.38 | | % 4.72/1.38 | End of split % 4.72/1.38 | % 4.72/1.38 End of proof % 4.72/1.38 % SZS output end Proof for theBenchmark % 4.72/1.38 % 4.72/1.38 782ms %------------------------------------------------------------------------------