%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET958+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 : n024.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 15:27:12 EDT 2023 % Result : Theorem 4.36s 1.33s % Output : Proof 5.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET958+1 : TPTP v8.1.2. Released v3.2.0. % 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n024.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 16:05:23 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.26/0.97 Prover 4: Preprocessing ... % 2.26/0.97 Prover 1: Preprocessing ... % 2.38/1.01 Prover 0: Preprocessing ... % 2.38/1.01 Prover 2: Preprocessing ... % 2.38/1.01 Prover 5: Preprocessing ... % 2.38/1.01 Prover 6: Preprocessing ... % 2.38/1.01 Prover 3: Preprocessing ... % 3.13/1.17 Prover 3: Warning: ignoring some quantifiers % 3.66/1.18 Prover 1: Warning: ignoring some quantifiers % 3.66/1.19 Prover 2: Proving ... % 3.66/1.19 Prover 6: Proving ... % 3.66/1.20 Prover 3: Constructing countermodel ... % 3.66/1.20 Prover 5: Proving ... % 3.66/1.20 Prover 1: Constructing countermodel ... % 3.66/1.21 Prover 0: Proving ... % 3.66/1.21 Prover 4: Constructing countermodel ... % 4.36/1.32 Prover 0: proved (688ms) % 4.36/1.32 % 4.36/1.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.36/1.33 % 4.36/1.33 Prover 3: stopped % 4.36/1.33 Prover 2: stopped % 4.36/1.33 Prover 6: stopped % 4.36/1.33 Prover 5: stopped % 4.36/1.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.36/1.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.36/1.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.36/1.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.36/1.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.36/1.35 Prover 7: Preprocessing ... % 4.36/1.35 Prover 8: Preprocessing ... % 4.92/1.37 Prover 10: Preprocessing ... % 4.92/1.37 Prover 13: Preprocessing ... % 4.92/1.37 Prover 11: Preprocessing ... % 5.27/1.40 Prover 1: Found proof (size 17) % 5.27/1.40 Prover 7: Warning: ignoring some quantifiers % 5.27/1.40 Prover 1: proved (766ms) % 5.27/1.40 Prover 4: stopped % 5.27/1.40 Prover 11: stopped % 5.27/1.41 Prover 10: Warning: ignoring some quantifiers % 5.27/1.41 Prover 7: Constructing countermodel ... % 5.33/1.41 Prover 10: Constructing countermodel ... % 5.33/1.41 Prover 7: stopped % 5.33/1.41 Prover 10: stopped % 5.33/1.42 Prover 13: Warning: ignoring some quantifiers % 5.33/1.43 Prover 8: Warning: ignoring some quantifiers % 5.33/1.43 Prover 13: Constructing countermodel ... % 5.33/1.43 Prover 8: Constructing countermodel ... % 5.33/1.43 Prover 13: stopped % 5.33/1.44 Prover 8: stopped % 5.33/1.44 % 5.33/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.33/1.44 % 5.33/1.44 % SZS output start Proof for theBenchmark % 5.33/1.44 Assumptions after simplification: % 5.33/1.44 --------------------------------- % 5.33/1.44 % 5.33/1.44 (d3_tarski) % 5.33/1.47 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 5.33/1.47 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 5.33/1.47 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 5.33/1.47 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 5.33/1.47 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 5.33/1.47 % 5.33/1.47 (t111_zfmisc_1) % 5.33/1.47 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) = v2 % 5.33/1.47 & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 5.33/1.47 (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4) | ~ $i(v3) % 5.33/1.47 | in(v5, v1) = 0) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) | ~ $i(v3) | ? % 5.33/1.47 [v4: $i] : ? [v5: $i] : (ordered_pair(v4, v5) = v3 & $i(v5) & $i(v4)))) % 5.33/1.47 % 5.33/1.47 (function-axioms) % 5.33/1.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.33/1.48 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: % 5.33/1.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 5.33/1.48 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 5.33/1.48 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.33/1.48 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 5.33/1.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 5.33/1.48 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 5.33/1.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 5.33/1.48 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 5.33/1.48 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 5.33/1.48 % 5.33/1.48 Further assumptions not needed in the proof: % 5.33/1.48 -------------------------------------------- % 5.33/1.48 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, fc1_zfmisc_1, % 5.33/1.48 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski % 5.33/1.48 % 5.33/1.48 Those formulas are unsatisfiable: % 5.33/1.48 --------------------------------- % 5.33/1.48 % 5.33/1.48 Begin of proof % 5.33/1.48 | % 5.33/1.48 | ALPHA: (d3_tarski) implies: % 5.33/1.48 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 5.33/1.48 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 5.33/1.48 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 5.33/1.48 | % 5.33/1.48 | ALPHA: (function-axioms) implies: % 5.33/1.49 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 5.33/1.49 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 5.33/1.49 | % 5.33/1.49 | DELTA: instantiating (t111_zfmisc_1) with fresh symbols all_14_0, all_14_1, % 5.33/1.49 | all_14_2 gives: % 5.33/1.49 | (3) ~ (all_14_0 = 0) & subset(all_14_2, all_14_1) = all_14_0 & % 5.33/1.49 | $i(all_14_1) & $i(all_14_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 5.33/1.49 | ( ~ (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_14_2) = 0) | ~ $i(v1) % 5.33/1.49 | | ~ $i(v0) | in(v2, all_14_1) = 0) & ! [v0: $i] : ( ~ (in(v0, % 5.33/1.49 | all_14_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 5.33/1.49 | (ordered_pair(v1, v2) = v0 & $i(v2) & $i(v1))) % 5.33/1.49 | % 5.33/1.49 | ALPHA: (3) implies: % 5.33/1.49 | (4) ~ (all_14_0 = 0) % 5.33/1.49 | (5) $i(all_14_2) % 5.33/1.49 | (6) $i(all_14_1) % 5.33/1.49 | (7) subset(all_14_2, all_14_1) = all_14_0 % 5.33/1.49 | (8) ! [v0: $i] : ( ~ (in(v0, all_14_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 5.33/1.49 | [v2: $i] : (ordered_pair(v1, v2) = v0 & $i(v2) & $i(v1))) % 5.33/1.50 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = % 5.33/1.50 | v2) | ~ (in(v2, all_14_2) = 0) | ~ $i(v1) | ~ $i(v0) | in(v2, % 5.33/1.50 | all_14_1) = 0) % 5.33/1.50 | % 5.33/1.50 | GROUND_INST: instantiating (1) with all_14_2, all_14_1, all_14_0, simplifying % 5.33/1.50 | with (5), (6), (7) gives: % 5.33/1.50 | (10) all_14_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 5.33/1.50 | all_14_1) = v1 & in(v0, all_14_2) = 0 & $i(v0)) % 5.33/1.50 | % 5.33/1.50 | BETA: splitting (10) gives: % 5.33/1.50 | % 5.33/1.50 | Case 1: % 5.33/1.50 | | % 5.33/1.50 | | (11) all_14_0 = 0 % 5.33/1.50 | | % 5.33/1.50 | | REDUCE: (4), (11) imply: % 5.33/1.50 | | (12) $false % 5.33/1.50 | | % 5.33/1.50 | | CLOSE: (12) is inconsistent. % 5.33/1.50 | | % 5.33/1.50 | Case 2: % 5.33/1.50 | | % 5.33/1.50 | | (13) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_14_1) = v1 & % 5.33/1.50 | | in(v0, all_14_2) = 0 & $i(v0)) % 5.33/1.50 | | % 5.33/1.50 | | DELTA: instantiating (13) with fresh symbols all_24_0, all_24_1 gives: % 5.33/1.50 | | (14) ~ (all_24_0 = 0) & in(all_24_1, all_14_1) = all_24_0 & in(all_24_1, % 5.33/1.50 | | all_14_2) = 0 & $i(all_24_1) % 5.33/1.50 | | % 5.33/1.50 | | ALPHA: (14) implies: % 5.33/1.50 | | (15) ~ (all_24_0 = 0) % 5.33/1.50 | | (16) $i(all_24_1) % 5.33/1.50 | | (17) in(all_24_1, all_14_2) = 0 % 5.33/1.50 | | (18) in(all_24_1, all_14_1) = all_24_0 % 5.33/1.50 | | % 5.33/1.50 | | GROUND_INST: instantiating (8) with all_24_1, simplifying with (16), (17) % 5.33/1.50 | | gives: % 5.33/1.50 | | (19) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_24_1 & % 5.33/1.50 | | $i(v1) & $i(v0)) % 5.33/1.50 | | % 5.33/1.50 | | DELTA: instantiating (19) with fresh symbols all_33_0, all_33_1 gives: % 5.33/1.50 | | (20) ordered_pair(all_33_1, all_33_0) = all_24_1 & $i(all_33_0) & % 5.33/1.50 | | $i(all_33_1) % 5.33/1.50 | | % 5.33/1.50 | | ALPHA: (20) implies: % 5.33/1.50 | | (21) $i(all_33_1) % 5.33/1.50 | | (22) $i(all_33_0) % 5.33/1.50 | | (23) ordered_pair(all_33_1, all_33_0) = all_24_1 % 5.33/1.50 | | % 5.33/1.51 | | GROUND_INST: instantiating (9) with all_33_1, all_33_0, all_24_1, % 5.33/1.51 | | simplifying with (17), (21), (22), (23) gives: % 5.33/1.51 | | (24) in(all_24_1, all_14_1) = 0 % 5.33/1.51 | | % 5.33/1.51 | | GROUND_INST: instantiating (2) with all_24_0, 0, all_14_1, all_24_1, % 5.33/1.51 | | simplifying with (18), (24) gives: % 5.33/1.51 | | (25) all_24_0 = 0 % 5.33/1.51 | | % 5.84/1.51 | | REDUCE: (15), (25) imply: % 5.84/1.51 | | (26) $false % 5.84/1.51 | | % 5.84/1.51 | | CLOSE: (26) is inconsistent. % 5.84/1.51 | | % 5.84/1.51 | End of split % 5.84/1.51 | % 5.84/1.51 End of proof % 5.84/1.51 % SZS output end Proof for theBenchmark % 5.84/1.51 % 5.84/1.51 890ms %------------------------------------------------------------------------------