%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET879+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 : n006.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 15:26:53 EDT 2023 % Result : Theorem 4.20s 1.41s % Output : Proof 6.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET879+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.18/0.34 % Computer : n006.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Sat Aug 26 13:10:22 EDT 2023 % 0.18/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 2.09/0.98 Prover 4: Preprocessing ... % 2.09/0.99 Prover 1: Preprocessing ... % 2.09/1.03 Prover 6: Preprocessing ... % 2.09/1.03 Prover 0: Preprocessing ... % 2.09/1.03 Prover 5: Preprocessing ... % 2.09/1.03 Prover 2: Preprocessing ... % 2.09/1.03 Prover 3: Preprocessing ... % 3.39/1.17 Prover 1: Warning: ignoring some quantifiers % 3.39/1.17 Prover 3: Warning: ignoring some quantifiers % 3.39/1.18 Prover 1: Constructing countermodel ... % 3.39/1.19 Prover 4: Warning: ignoring some quantifiers % 3.39/1.19 Prover 6: Proving ... % 3.39/1.19 Prover 5: Proving ... % 3.39/1.19 Prover 2: Proving ... % 3.39/1.19 Prover 3: Constructing countermodel ... % 3.39/1.19 Prover 4: Constructing countermodel ... % 3.39/1.21 Prover 0: Proving ... % 4.20/1.40 Prover 0: proved (788ms) % 4.20/1.40 % 4.20/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.20/1.41 % 4.20/1.41 Prover 2: proved (788ms) % 4.20/1.41 % 4.20/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.20/1.41 % 4.20/1.41 Prover 3: stopped % 4.20/1.41 Prover 6: stopped % 4.20/1.41 Prover 5: stopped % 4.20/1.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.20/1.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.20/1.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.20/1.42 Prover 4: Found proof (size 28) % 4.20/1.42 Prover 4: proved (792ms) % 4.20/1.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.20/1.42 Prover 7: Preprocessing ... % 4.20/1.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.20/1.42 Prover 8: Preprocessing ... % 4.20/1.43 Prover 11: Preprocessing ... % 4.20/1.43 Prover 1: Found proof (size 32) % 4.20/1.43 Prover 1: proved (815ms) % 4.20/1.43 Prover 10: Preprocessing ... % 4.20/1.45 Prover 11: stopped % 4.20/1.45 Prover 13: Preprocessing ... % 5.45/1.46 Prover 7: Warning: ignoring some quantifiers % 5.45/1.46 Prover 10: Warning: ignoring some quantifiers % 5.45/1.47 Prover 13: stopped % 5.45/1.47 Prover 10: Constructing countermodel ... % 5.45/1.47 Prover 7: Constructing countermodel ... % 5.45/1.47 Prover 8: Warning: ignoring some quantifiers % 5.45/1.47 Prover 7: stopped % 5.45/1.47 Prover 10: stopped % 5.45/1.47 Prover 8: Constructing countermodel ... % 5.45/1.48 Prover 8: stopped % 5.45/1.48 % 5.45/1.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.45/1.48 % 5.66/1.48 % SZS output start Proof for theBenchmark % 5.66/1.48 Assumptions after simplification: % 5.66/1.48 --------------------------------- % 5.66/1.49 % 5.66/1.49 (d1_tarski) % 5.66/1.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) | % 5.66/1.52 ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! % 5.66/1.52 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = % 5.66/1.52 v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 5.66/1.52 (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 5.66/1.52 [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = % 5.66/1.52 0 | v3 = v1))) % 5.66/1.52 % 5.66/1.52 (l34_zfmisc_1) % 5.66/1.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 5.66/1.52 (set_difference(v2, v1) = v3) | ~ (singleton(v0) = v2) | ~ $i(v1) | ~ % 5.66/1.52 $i(v0) | in(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = % 5.66/1.52 0 | ~ (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 5.66/1.52 (set_difference(v3, v1) = v3 & singleton(v0) = v3 & $i(v3))) & ! [v0: $i] : % 5.66/1.52 ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v2, v1) = v2) | ~ % 5.66/1.52 (singleton(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 5.66/1.52 in(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ % 5.66/1.52 $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & % 5.66/1.52 set_difference(v2, v1) = v3 & singleton(v0) = v2 & $i(v3) & $i(v2))) % 5.66/1.52 % 5.66/1.53 (t20_zfmisc_1) % 5.66/1.53 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 5.66/1.53 (set_difference(v2, v3) = v4 & singleton(v1) = v3 & singleton(v0) = v2 & % 5.66/1.53 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v4 = v2 & v1 = v0) | ( ~ (v4 % 5.66/1.53 = v2) & ~ (v1 = v0)))) % 5.66/1.53 % 5.66/1.53 (function-axioms) % 5.66/1.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.66/1.53 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 5.66/1.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 5.66/1.53 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 5.66/1.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 5.66/1.53 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 5.66/1.53 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 5.66/1.53 % 5.66/1.53 Further assumptions not needed in the proof: % 5.66/1.53 -------------------------------------------- % 5.66/1.53 antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0 % 5.66/1.53 % 5.66/1.53 Those formulas are unsatisfiable: % 5.66/1.53 --------------------------------- % 5.66/1.53 % 5.66/1.53 Begin of proof % 5.66/1.53 | % 5.66/1.53 | ALPHA: (d1_tarski) implies: % 5.66/1.54 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) % 5.66/1.54 | = v1) | ~ (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 5.66/1.54 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) % 5.66/1.54 | = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 5.66/1.54 | % 5.66/1.54 | ALPHA: (l34_zfmisc_1) implies: % 5.66/1.54 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v2, v1) = % 5.66/1.54 | v2) | ~ (singleton(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 5.66/1.54 | int] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 5.95/1.54 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 5.95/1.54 | (set_difference(v2, v1) = v3) | ~ (singleton(v0) = v2) | ~ $i(v1) | % 5.95/1.54 | ~ $i(v0) | in(v0, v1) = 0) % 5.95/1.54 | % 5.95/1.54 | ALPHA: (function-axioms) implies: % 5.95/1.54 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) % 5.95/1.54 | = v1) | ~ (singleton(v2) = v0)) % 5.95/1.54 | % 5.95/1.54 | DELTA: instantiating (t20_zfmisc_1) with fresh symbols all_12_0, all_12_1, % 5.95/1.54 | all_12_2, all_12_3, all_12_4 gives: % 5.95/1.55 | (6) set_difference(all_12_2, all_12_1) = all_12_0 & singleton(all_12_3) = % 5.95/1.55 | all_12_1 & singleton(all_12_4) = all_12_2 & $i(all_12_0) & $i(all_12_1) % 5.95/1.55 | & $i(all_12_2) & $i(all_12_3) & $i(all_12_4) & ((all_12_0 = all_12_2 & % 5.95/1.55 | all_12_3 = all_12_4) | ( ~ (all_12_0 = all_12_2) & ~ (all_12_3 = % 5.95/1.55 | all_12_4))) % 5.95/1.55 | % 5.95/1.55 | ALPHA: (6) implies: % 5.95/1.55 | (7) $i(all_12_4) % 5.95/1.55 | (8) $i(all_12_3) % 5.95/1.55 | (9) $i(all_12_1) % 5.95/1.55 | (10) singleton(all_12_4) = all_12_2 % 5.95/1.55 | (11) singleton(all_12_3) = all_12_1 % 5.95/1.55 | (12) set_difference(all_12_2, all_12_1) = all_12_0 % 5.95/1.55 | (13) (all_12_0 = all_12_2 & all_12_3 = all_12_4) | ( ~ (all_12_0 = % 5.95/1.55 | all_12_2) & ~ (all_12_3 = all_12_4)) % 5.95/1.55 | % 5.95/1.55 | GROUND_INST: instantiating (4) with all_12_4, all_12_1, all_12_2, all_12_0, % 5.95/1.55 | simplifying with (7), (9), (10), (12) gives: % 5.95/1.55 | (14) all_12_0 = all_12_2 | in(all_12_4, all_12_1) = 0 % 5.95/1.55 | % 5.95/1.55 | BETA: splitting (13) gives: % 5.95/1.55 | % 5.95/1.55 | Case 1: % 5.95/1.55 | | % 5.95/1.55 | | (15) all_12_0 = all_12_2 & all_12_3 = all_12_4 % 5.95/1.55 | | % 5.95/1.55 | | ALPHA: (15) implies: % 5.95/1.55 | | (16) all_12_3 = all_12_4 % 5.95/1.55 | | (17) all_12_0 = all_12_2 % 5.95/1.55 | | % 5.95/1.55 | | REDUCE: (12), (17) imply: % 5.95/1.56 | | (18) set_difference(all_12_2, all_12_1) = all_12_2 % 5.95/1.56 | | % 5.95/1.56 | | REDUCE: (11), (16) imply: % 5.95/1.56 | | (19) singleton(all_12_4) = all_12_1 % 5.95/1.56 | | % 5.95/1.56 | | GROUND_INST: instantiating (5) with all_12_2, all_12_1, all_12_4, % 5.95/1.56 | | simplifying with (10), (19) gives: % 5.95/1.56 | | (20) all_12_1 = all_12_2 % 5.95/1.56 | | % 5.95/1.56 | | REDUCE: (18), (20) imply: % 5.95/1.56 | | (21) set_difference(all_12_2, all_12_2) = all_12_2 % 5.95/1.56 | | % 5.95/1.56 | | REDUCE: (9), (20) imply: % 6.03/1.56 | | (22) $i(all_12_2) % 6.03/1.56 | | % 6.03/1.56 | | GROUND_INST: instantiating (3) with all_12_4, all_12_2, all_12_2, % 6.03/1.56 | | simplifying with (7), (10), (21), (22) gives: % 6.03/1.56 | | (23) ? [v0: int] : ( ~ (v0 = 0) & in(all_12_4, all_12_2) = v0) % 6.03/1.56 | | % 6.03/1.56 | | DELTA: instantiating (23) with fresh symbol all_30_0 gives: % 6.03/1.56 | | (24) ~ (all_30_0 = 0) & in(all_12_4, all_12_2) = all_30_0 % 6.03/1.56 | | % 6.03/1.56 | | ALPHA: (24) implies: % 6.03/1.56 | | (25) ~ (all_30_0 = 0) % 6.03/1.56 | | (26) in(all_12_4, all_12_2) = all_30_0 % 6.03/1.56 | | % 6.03/1.56 | | GROUND_INST: instantiating (1) with all_12_4, all_12_2, all_30_0, % 6.03/1.56 | | simplifying with (7), (10), (22), (26) gives: % 6.03/1.56 | | (27) all_30_0 = 0 % 6.03/1.56 | | % 6.03/1.56 | | REDUCE: (25), (27) imply: % 6.03/1.56 | | (28) $false % 6.03/1.56 | | % 6.03/1.56 | | CLOSE: (28) is inconsistent. % 6.03/1.56 | | % 6.03/1.56 | Case 2: % 6.03/1.56 | | % 6.03/1.56 | | (29) ~ (all_12_0 = all_12_2) & ~ (all_12_3 = all_12_4) % 6.03/1.56 | | % 6.03/1.56 | | ALPHA: (29) implies: % 6.03/1.56 | | (30) ~ (all_12_3 = all_12_4) % 6.03/1.56 | | (31) ~ (all_12_0 = all_12_2) % 6.03/1.56 | | % 6.03/1.56 | | BETA: splitting (14) gives: % 6.03/1.56 | | % 6.03/1.56 | | Case 1: % 6.03/1.56 | | | % 6.03/1.56 | | | (32) in(all_12_4, all_12_1) = 0 % 6.03/1.56 | | | % 6.03/1.56 | | | GROUND_INST: instantiating (2) with all_12_3, all_12_1, all_12_4, % 6.03/1.56 | | | simplifying with (7), (8), (9), (11), (32) gives: % 6.03/1.56 | | | (33) all_12_3 = all_12_4 % 6.03/1.56 | | | % 6.03/1.56 | | | REDUCE: (30), (33) imply: % 6.03/1.56 | | | (34) $false % 6.03/1.56 | | | % 6.03/1.56 | | | CLOSE: (34) is inconsistent. % 6.03/1.56 | | | % 6.03/1.56 | | Case 2: % 6.03/1.56 | | | % 6.03/1.56 | | | (35) all_12_0 = all_12_2 % 6.03/1.56 | | | % 6.03/1.56 | | | REDUCE: (31), (35) imply: % 6.03/1.56 | | | (36) $false % 6.03/1.56 | | | % 6.03/1.56 | | | CLOSE: (36) is inconsistent. % 6.03/1.56 | | | % 6.03/1.56 | | End of split % 6.03/1.56 | | % 6.03/1.57 | End of split % 6.03/1.57 | % 6.03/1.57 End of proof % 6.03/1.57 % SZS output end Proof for theBenchmark % 6.03/1.57 % 6.03/1.57 966ms %------------------------------------------------------------------------------