%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM531+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n013.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 11:48:25 EDT 2023 % Result : Theorem 3.78s 1.21s % Output : Proof 4.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM531+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n013.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 : Fri Aug 25 15:16:47 EDT 2023 % 0.13/0.34 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.83/0.97 Prover 1: Preprocessing ... % 1.83/0.97 Prover 4: Preprocessing ... % 1.83/1.02 Prover 3: Preprocessing ... % 1.83/1.02 Prover 2: Preprocessing ... % 1.83/1.02 Prover 0: Preprocessing ... % 1.83/1.02 Prover 5: Preprocessing ... % 1.83/1.02 Prover 6: Preprocessing ... % 3.00/1.12 Prover 5: Constructing countermodel ... % 3.00/1.12 Prover 2: Constructing countermodel ... % 3.00/1.13 Prover 1: Constructing countermodel ... % 3.00/1.14 Prover 3: Constructing countermodel ... % 3.00/1.15 Prover 4: Constructing countermodel ... % 3.57/1.17 Prover 6: Proving ... % 3.60/1.18 Prover 0: Proving ... % 3.78/1.21 Prover 2: proved (572ms) % 3.78/1.21 % 3.78/1.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.78/1.21 % 3.78/1.21 Prover 5: stopped % 3.90/1.22 Prover 0: stopped % 3.90/1.22 Prover 6: stopped % 3.90/1.23 Prover 3: stopped % 3.90/1.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.90/1.23 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.90/1.23 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.90/1.23 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.90/1.23 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.90/1.24 Prover 7: Preprocessing ... % 3.90/1.26 Prover 11: Preprocessing ... % 3.90/1.26 Prover 13: Preprocessing ... % 3.90/1.26 Prover 10: Preprocessing ... % 3.90/1.27 Prover 1: Found proof (size 13) % 3.90/1.27 Prover 8: Preprocessing ... % 3.90/1.27 Prover 1: proved (639ms) % 3.90/1.27 Prover 4: stopped % 3.90/1.27 Prover 7: Constructing countermodel ... % 3.90/1.27 Prover 7: stopped % 3.90/1.28 Prover 11: stopped % 3.90/1.29 Prover 10: Constructing countermodel ... % 3.90/1.29 Prover 10: stopped % 3.90/1.29 Prover 13: Constructing countermodel ... % 3.90/1.30 Prover 13: stopped % 3.90/1.31 Prover 8: Warning: ignoring some quantifiers % 3.90/1.31 Prover 8: Constructing countermodel ... % 4.52/1.32 Prover 8: stopped % 4.52/1.32 % 4.52/1.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.52/1.32 % 4.52/1.32 % SZS output start Proof for theBenchmark % 4.52/1.33 Assumptions after simplification: % 4.52/1.33 --------------------------------- % 4.52/1.33 % 4.52/1.33 (mCountNFin) % 4.52/1.36 ! [v0: $i] : ( ~ (isFinite0(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 4.52/1.36 any] : (isCountable0(v0) = v2 & aSet0(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = % 4.52/1.36 0)))) % 4.52/1.36 % 4.52/1.36 (mEmpFin) % 4.52/1.36 isFinite0(slcrc0) = 0 & $i(slcrc0) % 4.52/1.36 % 4.52/1.36 (m__) % 4.52/1.36 isCountable0(slcrc0) = 0 & aSet0(slcrc0) = 0 & $i(slcrc0) % 4.52/1.36 % 4.52/1.36 (function-axioms) % 4.52/1.36 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 4.52/1.36 [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) % 4.52/1.36 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 4.52/1.36 $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) & % 4.52/1.36 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 4.52/1.36 v0 | ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0: % 4.52/1.36 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 4.52/1.36 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 4.52/1.36 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | % 4.52/1.36 ~ (aElement0(v2) = v0)) % 4.52/1.36 % 4.52/1.36 Further assumptions not needed in the proof: % 4.52/1.36 -------------------------------------------- % 4.52/1.36 mCntRel, mDefEmp, mEOfElem, mElmSort, mFinRel, mSetSort % 4.52/1.36 % 4.52/1.36 Those formulas are unsatisfiable: % 4.52/1.36 --------------------------------- % 4.52/1.36 % 4.52/1.36 Begin of proof % 4.52/1.36 | % 4.52/1.37 | ALPHA: (mEmpFin) implies: % 4.52/1.37 | (1) isFinite0(slcrc0) = 0 % 4.52/1.37 | % 4.52/1.37 | ALPHA: (m__) implies: % 4.52/1.37 | (2) $i(slcrc0) % 4.52/1.37 | (3) aSet0(slcrc0) = 0 % 4.52/1.37 | (4) isCountable0(slcrc0) = 0 % 4.52/1.37 | % 4.52/1.37 | ALPHA: (function-axioms) implies: % 4.52/1.37 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.52/1.37 | (v1 = v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) % 4.52/1.37 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.52/1.37 | (v1 = v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) % 4.52/1.37 | % 4.52/1.37 | GROUND_INST: instantiating (mCountNFin) with slcrc0, simplifying with (1), (2) % 4.52/1.37 | gives: % 4.52/1.37 | (7) ? [v0: any] : ? [v1: any] : (isCountable0(slcrc0) = v1 & % 4.52/1.37 | aSet0(slcrc0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 4.52/1.37 | % 4.52/1.37 | DELTA: instantiating (7) with fresh symbols all_14_0, all_14_1 gives: % 4.52/1.37 | (8) isCountable0(slcrc0) = all_14_0 & aSet0(slcrc0) = all_14_1 & ( ~ % 4.52/1.37 | (all_14_0 = 0) | ~ (all_14_1 = 0)) % 4.52/1.37 | % 4.52/1.37 | ALPHA: (8) implies: % 4.52/1.38 | (9) aSet0(slcrc0) = all_14_1 % 4.52/1.38 | (10) isCountable0(slcrc0) = all_14_0 % 4.52/1.38 | (11) ~ (all_14_0 = 0) | ~ (all_14_1 = 0) % 4.52/1.38 | % 4.52/1.38 | GROUND_INST: instantiating (5) with 0, all_14_1, slcrc0, simplifying with (3), % 4.52/1.38 | (9) gives: % 4.52/1.38 | (12) all_14_1 = 0 % 4.52/1.38 | % 4.52/1.38 | GROUND_INST: instantiating (6) with 0, all_14_0, slcrc0, simplifying with (4), % 4.52/1.38 | (10) gives: % 4.52/1.38 | (13) all_14_0 = 0 % 4.52/1.38 | % 4.52/1.38 | BETA: splitting (11) gives: % 4.52/1.38 | % 4.52/1.38 | Case 1: % 4.52/1.38 | | % 4.52/1.38 | | (14) ~ (all_14_0 = 0) % 4.52/1.38 | | % 4.52/1.38 | | REDUCE: (13), (14) imply: % 4.52/1.38 | | (15) $false % 4.52/1.38 | | % 4.52/1.38 | | CLOSE: (15) is inconsistent. % 4.52/1.38 | | % 4.52/1.38 | Case 2: % 4.52/1.38 | | % 4.52/1.38 | | (16) ~ (all_14_1 = 0) % 4.52/1.38 | | % 4.52/1.38 | | REDUCE: (12), (16) imply: % 4.52/1.38 | | (17) $false % 4.52/1.38 | | % 4.52/1.38 | | CLOSE: (17) is inconsistent. % 4.52/1.38 | | % 4.52/1.38 | End of split % 4.52/1.38 | % 4.52/1.38 End of proof % 4.52/1.38 % SZS output end Proof for theBenchmark % 4.52/1.38 % 4.52/1.38 770ms %------------------------------------------------------------------------------