%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET899+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 : n015.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 3.62s 1.27s % Output : Proof 4.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET899+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n015.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 10:01:07 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.62 % 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.62 (2023-06-19) % 0.19/0.62 % 0.19/0.62 (c) Philipp Rümmer, 2009-2023 % 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.62 Amanda Stjerna. % 0.19/0.62 Free software under BSD-3-Clause. % 0.19/0.62 % 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.62 % 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.16/1.00 Prover 1: Preprocessing ... % 2.16/1.00 Prover 4: Preprocessing ... % 2.16/1.05 Prover 5: Preprocessing ... % 2.16/1.05 Prover 2: Preprocessing ... % 2.16/1.05 Prover 0: Preprocessing ... % 2.16/1.05 Prover 3: Preprocessing ... % 2.16/1.05 Prover 6: Preprocessing ... % 2.70/1.15 Prover 2: Proving ... % 2.70/1.15 Prover 5: Proving ... % 2.70/1.15 Prover 1: Warning: ignoring some quantifiers % 2.70/1.15 Prover 3: Warning: ignoring some quantifiers % 2.70/1.16 Prover 1: Constructing countermodel ... % 2.70/1.16 Prover 4: Constructing countermodel ... % 2.70/1.16 Prover 3: Constructing countermodel ... % 2.70/1.17 Prover 6: Proving ... % 2.70/1.18 Prover 0: Proving ... % 3.62/1.26 Prover 3: proved (622ms) % 3.62/1.26 % 3.62/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.62/1.27 % 3.62/1.27 Prover 0: proved (624ms) % 3.62/1.27 % 3.62/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.62/1.27 % 3.62/1.27 Prover 5: proved (623ms) % 3.62/1.27 % 3.62/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.62/1.27 % 3.62/1.27 Prover 6: proved (622ms) % 3.62/1.27 % 3.62/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.62/1.27 % 3.62/1.27 Prover 2: proved (627ms) % 3.62/1.27 % 3.62/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.62/1.27 % 3.62/1.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.62/1.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.62/1.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.62/1.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.62/1.28 Prover 7: Preprocessing ... % 3.62/1.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.62/1.28 Prover 8: Preprocessing ... % 3.62/1.29 Prover 11: Preprocessing ... % 3.62/1.30 Prover 10: Preprocessing ... % 4.25/1.30 Prover 13: Preprocessing ... % 4.25/1.31 Prover 7: Warning: ignoring some quantifiers % 4.25/1.31 Prover 7: Constructing countermodel ... % 4.25/1.32 Prover 4: Found proof (size 17) % 4.25/1.32 Prover 1: Found proof (size 17) % 4.25/1.32 Prover 4: proved (683ms) % 4.25/1.32 Prover 1: proved (684ms) % 4.25/1.32 Prover 7: stopped % 4.25/1.33 Prover 10: Warning: ignoring some quantifiers % 4.25/1.33 Prover 10: Constructing countermodel ... % 4.25/1.33 Prover 13: Warning: ignoring some quantifiers % 4.25/1.33 Prover 10: stopped % 4.25/1.34 Prover 13: Constructing countermodel ... % 4.25/1.34 Prover 8: Warning: ignoring some quantifiers % 4.25/1.34 Prover 13: stopped % 4.25/1.34 Prover 8: Constructing countermodel ... % 4.25/1.34 Prover 11: Constructing countermodel ... % 4.25/1.35 Prover 11: stopped % 4.25/1.35 Prover 8: stopped % 4.25/1.35 % 4.25/1.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.25/1.35 % 4.25/1.35 % SZS output start Proof for theBenchmark % 4.25/1.36 Assumptions after simplification: % 4.25/1.36 --------------------------------- % 4.25/1.36 % 4.25/1.36 (l3_zfmisc_1) % 4.25/1.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 4.25/1.39 int] : (v5 = 0 | ~ (singleton(v2) = v3) | ~ (set_difference(v1, v3) = v4) % 4.25/1.39 | ~ (subset(v0, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 4.25/1.39 any] : ? [v7: any] : (in(v2, v0) = v7 & subset(v0, v1) = v6 & ( ~ (v6 = % 4.25/1.39 0) | v7 = 0))) % 4.25/1.39 % 4.25/1.39 (t40_zfmisc_1) % 4.25/1.39 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: $i] : ? [v5: % 4.25/1.39 $i] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v3 = 0) & singleton(v2) = v4 & % 4.25/1.39 set_difference(v1, v4) = v5 & in(v2, v0) = v3 & subset(v0, v5) = v6 & % 4.25/1.39 subset(v0, v1) = 0 & $i(v5) & $i(v4) & $i(v2) & $i(v1) & $i(v0)) % 4.25/1.39 % 4.25/1.39 (function-axioms) % 4.25/1.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 4.25/1.40 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 4.25/1.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 4.25/1.40 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 4.25/1.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 4.25/1.40 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 4.25/1.40 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 4.25/1.40 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 4.25/1.40 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 4.25/1.40 (empty(v2) = v0)) % 4.25/1.40 % 4.25/1.40 Further assumptions not needed in the proof: % 4.25/1.40 -------------------------------------------- % 4.25/1.40 antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski % 4.25/1.40 % 4.25/1.40 Those formulas are unsatisfiable: % 4.25/1.40 --------------------------------- % 4.25/1.40 % 4.25/1.40 Begin of proof % 4.25/1.40 | % 4.25/1.40 | ALPHA: (function-axioms) implies: % 4.25/1.40 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.25/1.40 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) % 4.25/1.40 | = v0)) % 4.25/1.40 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.25/1.40 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 4.25/1.40 | % 4.25/1.40 | DELTA: instantiating (t40_zfmisc_1) with fresh symbols all_11_0, all_11_1, % 4.25/1.40 | all_11_2, all_11_3, all_11_4, all_11_5, all_11_6 gives: % 4.25/1.41 | (3) ~ (all_11_0 = 0) & ~ (all_11_3 = 0) & singleton(all_11_4) = all_11_2 % 4.25/1.41 | & set_difference(all_11_5, all_11_2) = all_11_1 & in(all_11_4, % 4.25/1.41 | all_11_6) = all_11_3 & subset(all_11_6, all_11_1) = all_11_0 & % 4.25/1.41 | subset(all_11_6, all_11_5) = 0 & $i(all_11_1) & $i(all_11_2) & % 4.25/1.41 | $i(all_11_4) & $i(all_11_5) & $i(all_11_6) % 4.25/1.41 | % 4.25/1.41 | ALPHA: (3) implies: % 4.25/1.41 | (4) ~ (all_11_3 = 0) % 4.25/1.41 | (5) ~ (all_11_0 = 0) % 4.25/1.41 | (6) $i(all_11_6) % 4.25/1.41 | (7) $i(all_11_5) % 4.25/1.41 | (8) $i(all_11_4) % 4.25/1.41 | (9) subset(all_11_6, all_11_5) = 0 % 4.25/1.41 | (10) subset(all_11_6, all_11_1) = all_11_0 % 4.25/1.41 | (11) in(all_11_4, all_11_6) = all_11_3 % 4.25/1.41 | (12) set_difference(all_11_5, all_11_2) = all_11_1 % 4.25/1.41 | (13) singleton(all_11_4) = all_11_2 % 4.25/1.41 | % 4.25/1.41 | GROUND_INST: instantiating (l3_zfmisc_1) with all_11_6, all_11_5, all_11_4, % 4.25/1.41 | all_11_2, all_11_1, all_11_0, simplifying with (6), (7), (8), % 4.25/1.41 | (10), (12), (13) gives: % 4.25/1.41 | (14) all_11_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_11_4, all_11_6) = % 4.25/1.41 | v1 & subset(all_11_6, all_11_5) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 4.25/1.41 | % 4.25/1.41 | BETA: splitting (14) gives: % 4.25/1.41 | % 4.25/1.41 | Case 1: % 4.25/1.41 | | % 4.25/1.41 | | (15) all_11_0 = 0 % 4.25/1.41 | | % 4.25/1.41 | | REDUCE: (5), (15) imply: % 4.25/1.41 | | (16) $false % 4.25/1.41 | | % 4.25/1.41 | | CLOSE: (16) is inconsistent. % 4.25/1.41 | | % 4.25/1.41 | Case 2: % 4.25/1.41 | | % 4.25/1.41 | | (17) ? [v0: any] : ? [v1: any] : (in(all_11_4, all_11_6) = v1 & % 4.25/1.41 | | subset(all_11_6, all_11_5) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 4.25/1.41 | | % 4.25/1.41 | | DELTA: instantiating (17) with fresh symbols all_20_0, all_20_1 gives: % 4.25/1.42 | | (18) in(all_11_4, all_11_6) = all_20_0 & subset(all_11_6, all_11_5) = % 4.25/1.42 | | all_20_1 & ( ~ (all_20_1 = 0) | all_20_0 = 0) % 4.25/1.42 | | % 4.25/1.42 | | ALPHA: (18) implies: % 4.25/1.42 | | (19) subset(all_11_6, all_11_5) = all_20_1 % 4.25/1.42 | | (20) in(all_11_4, all_11_6) = all_20_0 % 4.25/1.42 | | (21) ~ (all_20_1 = 0) | all_20_0 = 0 % 4.25/1.42 | | % 4.25/1.42 | | GROUND_INST: instantiating (1) with 0, all_20_1, all_11_5, all_11_6, % 4.25/1.42 | | simplifying with (9), (19) gives: % 4.25/1.42 | | (22) all_20_1 = 0 % 4.25/1.42 | | % 4.25/1.42 | | GROUND_INST: instantiating (2) with all_11_3, all_20_0, all_11_6, all_11_4, % 4.25/1.42 | | simplifying with (11), (20) gives: % 4.25/1.42 | | (23) all_20_0 = all_11_3 % 4.25/1.42 | | % 4.25/1.42 | | BETA: splitting (21) gives: % 4.25/1.42 | | % 4.25/1.42 | | Case 1: % 4.25/1.42 | | | % 4.25/1.42 | | | (24) ~ (all_20_1 = 0) % 4.25/1.42 | | | % 4.25/1.42 | | | REDUCE: (22), (24) imply: % 4.25/1.42 | | | (25) $false % 4.25/1.42 | | | % 4.25/1.42 | | | CLOSE: (25) is inconsistent. % 4.25/1.42 | | | % 4.25/1.42 | | Case 2: % 4.25/1.42 | | | % 4.25/1.42 | | | (26) all_20_0 = 0 % 4.25/1.42 | | | % 4.25/1.42 | | | COMBINE_EQS: (23), (26) imply: % 4.25/1.42 | | | (27) all_11_3 = 0 % 4.25/1.42 | | | % 4.25/1.42 | | | REDUCE: (4), (27) imply: % 4.25/1.42 | | | (28) $false % 4.25/1.42 | | | % 4.25/1.42 | | | CLOSE: (28) is inconsistent. % 4.25/1.42 | | | % 4.25/1.42 | | End of split % 4.25/1.42 | | % 4.25/1.42 | End of split % 4.25/1.42 | % 4.25/1.42 End of proof % 4.25/1.42 % SZS output end Proof for theBenchmark % 4.25/1.42 % 4.25/1.42 799ms %------------------------------------------------------------------------------