%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM532+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 : n032.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 4.39s 1.28s % Output : Proof 6.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.08 % Problem : NUM532+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.09 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.28 % Computer : n032.cluster.edu % 0.09/0.28 % Model : x86_64 x86_64 % 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.28 % Memory : 8042.1875MB % 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.28 % CPULimit : 300 % 0.09/0.28 % WCLimit : 300 % 0.09/0.28 % DateTime : Fri Aug 25 08:36:57 EDT 2023 % 0.09/0.28 % CPUTime : % 0.13/0.47 ________ _____ % 0.13/0.47 ___ __ \_________(_)________________________________ % 0.13/0.47 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.13/0.47 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.13/0.47 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.13/0.47 % 0.13/0.47 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.13/0.47 (2023-06-19) % 0.13/0.47 % 0.13/0.47 (c) Philipp Rümmer, 2009-2023 % 0.13/0.47 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.13/0.47 Amanda Stjerna. % 0.13/0.47 Free software under BSD-3-Clause. % 0.13/0.47 % 0.13/0.47 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.13/0.47 % 0.13/0.47 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.13/0.48 Running up to 7 provers in parallel. % 0.13/0.50 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.13/0.50 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.13/0.50 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.13/0.50 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.13/0.50 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.13/0.50 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.13/0.50 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.13/0.83 Prover 4: Preprocessing ... % 0.13/0.84 Prover 1: Preprocessing ... % 2.28/0.88 Prover 5: Preprocessing ... % 2.28/0.88 Prover 6: Preprocessing ... % 2.28/0.88 Prover 0: Preprocessing ... % 2.28/0.88 Prover 3: Preprocessing ... % 2.28/0.88 Prover 2: Preprocessing ... % 3.12/1.07 Prover 5: Constructing countermodel ... % 3.12/1.07 Prover 2: Constructing countermodel ... % 3.66/1.15 Prover 1: Constructing countermodel ... % 3.66/1.15 Prover 6: Proving ... % 3.66/1.15 Prover 3: Constructing countermodel ... % 4.28/1.22 Prover 4: Constructing countermodel ... % 4.39/1.25 Prover 0: Proving ... % 4.39/1.28 Prover 2: proved (775ms) % 4.39/1.28 Prover 3: proved (788ms) % 4.39/1.28 % 4.39/1.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.39/1.28 % 4.39/1.28 % 4.39/1.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.39/1.28 % 4.39/1.28 Prover 6: stopped % 4.39/1.28 Prover 5: stopped % 4.39/1.28 Prover 0: stopped % 4.39/1.29 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.39/1.29 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.39/1.29 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.39/1.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.39/1.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.89/1.33 Prover 11: Preprocessing ... % 4.89/1.34 Prover 10: Preprocessing ... % 4.89/1.34 Prover 7: Preprocessing ... % 4.89/1.35 Prover 13: Preprocessing ... % 4.89/1.36 Prover 8: Preprocessing ... % 4.89/1.39 Prover 7: Constructing countermodel ... % 4.89/1.39 Prover 10: Constructing countermodel ... % 4.89/1.42 Prover 1: Found proof (size 22) % 4.89/1.42 Prover 1: proved (932ms) % 4.89/1.42 Prover 7: Found proof (size 6) % 4.89/1.42 Prover 7: proved (129ms) % 4.89/1.42 Prover 4: stopped % 4.89/1.42 Prover 10: Found proof (size 6) % 4.89/1.42 Prover 10: proved (134ms) % 4.89/1.43 Prover 13: Constructing countermodel ... % 4.89/1.43 Prover 13: stopped % 4.89/1.46 Prover 8: Warning: ignoring some quantifiers % 4.89/1.46 Prover 8: Constructing countermodel ... % 4.89/1.47 Prover 8: stopped % 4.89/1.50 Prover 11: Constructing countermodel ... % 4.89/1.51 Prover 11: stopped % 4.89/1.51 % 4.89/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.89/1.51 % 4.89/1.51 % SZS output start Proof for theBenchmark % 4.89/1.52 Assumptions after simplification: % 4.89/1.52 --------------------------------- % 4.89/1.52 % 4.89/1.52 (mDefSub) % 6.10/1.56 ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: int] : % 6.10/1.56 (v2 = 0 | ~ (aSubsetOf0(v1, v0) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: % 6.10/1.56 int] : ( ~ (v4 = 0) & aElementOf0(v3, v1) = 0 & aElementOf0(v3, v0) = % 6.10/1.56 v4 & $i(v3)) | ? [v3: int] : ( ~ (v3 = 0) & aSet0(v1) = v3)) & ! % 6.10/1.56 [v1: $i] : ( ~ (aSubsetOf0(v1, v0) = 0) | ~ $i(v1) | (aSet0(v1) = 0 & ! % 6.10/1.56 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, v0) = v3) | ~ % 6.10/1.56 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v2, v1) = % 6.10/1.56 v4)))))) % 6.10/1.56 % 6.10/1.57 (m__) % 6.10/1.57 $i(xA) & ? [v0: int] : ( ~ (v0 = 0) & aSubsetOf0(xA, xA) = v0) % 6.10/1.57 % 6.10/1.57 (m__467) % 6.10/1.57 aSet0(xA) = 0 & $i(xA) % 6.10/1.57 % 6.10/1.57 (function-axioms) % 6.10/1.57 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 6.10/1.57 [v3: $i] : (v1 = v0 | ~ (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = % 6.10/1.57 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 6.10/1.57 $i] : ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ % 6.10/1.57 (aElementOf0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 6.10/1.57 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | % 6.10/1.57 ~ (isCountable0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 6.10/1.57 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isFinite0(v2) = v1) | ~ % 6.10/1.57 (isFinite0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 6.10/1.57 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~ % 6.10/1.57 (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 6.10/1.57 : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0)) % 6.10/1.57 % 6.10/1.57 Further assumptions not needed in the proof: % 6.10/1.57 -------------------------------------------- % 6.10/1.57 mCntRel, mCountNFin, mCountNFin_01, mDefEmp, mEOfElem, mElmSort, mEmpFin, % 6.10/1.57 mFinRel, mSetSort, mSubFSet % 6.10/1.57 % 6.10/1.57 Those formulas are unsatisfiable: % 6.10/1.57 --------------------------------- % 6.10/1.57 % 6.10/1.57 Begin of proof % 6.10/1.57 | % 6.10/1.58 | ALPHA: (m__467) implies: % 6.10/1.58 | (1) aSet0(xA) = 0 % 6.10/1.58 | % 6.10/1.58 | ALPHA: (m__) implies: % 6.10/1.58 | (2) $i(xA) % 6.10/1.58 | (3) ? [v0: int] : ( ~ (v0 = 0) & aSubsetOf0(xA, xA) = v0) % 6.10/1.58 | % 6.10/1.58 | ALPHA: (function-axioms) implies: % 6.10/1.58 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 6.10/1.58 | (v1 = v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) % 6.10/1.58 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 6.10/1.58 | ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ % 6.10/1.58 | (aElementOf0(v3, v2) = v0)) % 6.10/1.58 | % 6.10/1.58 | DELTA: instantiating (3) with fresh symbol all_9_0 gives: % 6.10/1.58 | (6) ~ (all_9_0 = 0) & aSubsetOf0(xA, xA) = all_9_0 % 6.10/1.58 | % 6.10/1.58 | ALPHA: (6) implies: % 6.10/1.58 | (7) ~ (all_9_0 = 0) % 6.10/1.58 | (8) aSubsetOf0(xA, xA) = all_9_0 % 6.10/1.58 | % 6.10/1.58 | GROUND_INST: instantiating (mDefSub) with xA, simplifying with (1), (2) gives: % 6.10/1.59 | (9) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xA) = v1) | % 6.10/1.59 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 6.10/1.59 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xA) = v3 & $i(v2)) | ? % 6.10/1.59 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~ % 6.10/1.59 | (aSubsetOf0(v0, xA) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i] : % 6.10/1.59 | ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xA) = v2) | ~ $i(v1) % 6.10/1.59 | | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, v0) = v3)))) % 6.10/1.59 | % 6.10/1.59 | ALPHA: (9) implies: % 6.10/1.59 | (10) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xA) = v1) | % 6.10/1.59 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 6.10/1.59 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xA) = v3 & $i(v2)) | ? % 6.10/1.59 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) % 6.10/1.59 | % 6.10/1.59 | GROUND_INST: instantiating (10) with xA, all_9_0, simplifying with (2), (8) % 6.10/1.59 | gives: % 6.10/1.59 | (11) all_9_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 6.10/1.59 | aElementOf0(v0, xA) = v1 & aElementOf0(v0, xA) = 0 & $i(v0)) | ? % 6.10/1.59 | [v0: int] : ( ~ (v0 = 0) & aSet0(xA) = v0) % 6.10/1.59 | % 6.10/1.59 | BETA: splitting (11) gives: % 6.10/1.59 | % 6.10/1.59 | Case 1: % 6.10/1.59 | | % 6.10/1.59 | | (12) all_9_0 = 0 % 6.10/1.59 | | % 6.10/1.59 | | REDUCE: (7), (12) imply: % 6.10/1.59 | | (13) $false % 6.10/1.59 | | % 6.10/1.59 | | CLOSE: (13) is inconsistent. % 6.10/1.59 | | % 6.10/1.59 | Case 2: % 6.10/1.59 | | % 6.10/1.60 | | (14) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0, xA) = v1 % 6.10/1.60 | | & aElementOf0(v0, xA) = 0 & $i(v0)) | ? [v0: int] : ( ~ (v0 = 0) % 6.10/1.60 | | & aSet0(xA) = v0) % 6.10/1.60 | | % 6.10/1.60 | | BETA: splitting (14) gives: % 6.10/1.60 | | % 6.10/1.60 | | Case 1: % 6.10/1.60 | | | % 6.10/1.60 | | | (15) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0, xA) = % 6.10/1.60 | | | v1 & aElementOf0(v0, xA) = 0 & $i(v0)) % 6.10/1.60 | | | % 6.10/1.60 | | | DELTA: instantiating (15) with fresh symbols all_24_0, all_24_1 gives: % 6.10/1.60 | | | (16) ~ (all_24_0 = 0) & aElementOf0(all_24_1, xA) = all_24_0 & % 6.10/1.60 | | | aElementOf0(all_24_1, xA) = 0 & $i(all_24_1) % 6.10/1.60 | | | % 6.10/1.60 | | | ALPHA: (16) implies: % 6.10/1.60 | | | (17) ~ (all_24_0 = 0) % 6.10/1.60 | | | (18) aElementOf0(all_24_1, xA) = 0 % 6.10/1.60 | | | (19) aElementOf0(all_24_1, xA) = all_24_0 % 6.10/1.60 | | | % 6.10/1.60 | | | GROUND_INST: instantiating (5) with 0, all_24_0, xA, all_24_1, simplifying % 6.10/1.60 | | | with (18), (19) gives: % 6.10/1.60 | | | (20) all_24_0 = 0 % 6.10/1.60 | | | % 6.10/1.60 | | | REDUCE: (17), (20) imply: % 6.10/1.60 | | | (21) $false % 6.10/1.60 | | | % 6.10/1.60 | | | CLOSE: (21) is inconsistent. % 6.10/1.60 | | | % 6.10/1.60 | | Case 2: % 6.10/1.60 | | | % 6.10/1.60 | | | (22) ? [v0: int] : ( ~ (v0 = 0) & aSet0(xA) = v0) % 6.10/1.60 | | | % 6.10/1.60 | | | DELTA: instantiating (22) with fresh symbol all_24_0 gives: % 6.10/1.60 | | | (23) ~ (all_24_0 = 0) & aSet0(xA) = all_24_0 % 6.10/1.60 | | | % 6.10/1.60 | | | ALPHA: (23) implies: % 6.10/1.60 | | | (24) ~ (all_24_0 = 0) % 6.10/1.60 | | | (25) aSet0(xA) = all_24_0 % 6.10/1.60 | | | % 6.10/1.60 | | | GROUND_INST: instantiating (4) with 0, all_24_0, xA, simplifying with (1), % 6.10/1.60 | | | (25) gives: % 6.10/1.60 | | | (26) all_24_0 = 0 % 6.10/1.60 | | | % 6.10/1.60 | | | REDUCE: (24), (26) imply: % 6.10/1.60 | | | (27) $false % 6.10/1.60 | | | % 6.10/1.60 | | | CLOSE: (27) is inconsistent. % 6.10/1.60 | | | % 6.10/1.60 | | End of split % 6.10/1.60 | | % 6.10/1.60 | End of split % 6.10/1.60 | % 6.10/1.60 End of proof % 6.10/1.60 % SZS output end Proof for theBenchmark % 6.10/1.60 % 6.10/1.60 1129ms %------------------------------------------------------------------------------