%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG089+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 : n003.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 13:57:47 EDT 2023 % Result : Theorem 10.88s 2.24s % Output : Proof 13.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG089+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n003.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 : Sun Aug 27 02:48:54 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 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 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 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.60/1.08 Prover 1: Preprocessing ... % 2.60/1.09 Prover 4: Preprocessing ... % 3.10/1.12 Prover 2: Preprocessing ... % 3.10/1.12 Prover 5: Preprocessing ... % 3.10/1.12 Prover 3: Preprocessing ... % 3.10/1.12 Prover 0: Preprocessing ... % 3.10/1.12 Prover 6: Preprocessing ... % 8.47/1.87 Prover 1: Constructing countermodel ... % 8.47/1.87 Prover 3: Constructing countermodel ... % 8.47/1.87 Prover 6: Proving ... % 8.47/1.94 Prover 5: Proving ... % 9.15/2.01 Prover 2: Proving ... % 9.15/2.02 Prover 4: Constructing countermodel ... % 10.25/2.14 Prover 0: Proving ... % 10.88/2.23 Prover 3: proved (1603ms) % 10.88/2.23 % 10.88/2.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.88/2.24 % 10.88/2.24 Prover 0: stopped % 10.88/2.24 Prover 6: stopped % 10.88/2.24 Prover 2: stopped % 10.88/2.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.88/2.25 Prover 5: stopped % 10.88/2.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.88/2.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.88/2.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.88/2.25 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.43/2.29 Prover 10: Preprocessing ... % 11.43/2.31 Prover 11: Preprocessing ... % 11.43/2.33 Prover 13: Preprocessing ... % 11.43/2.33 Prover 7: Preprocessing ... % 11.43/2.33 Prover 8: Preprocessing ... % 12.54/2.43 Prover 10: Constructing countermodel ... % 12.54/2.45 Prover 8: Warning: ignoring some quantifiers % 12.54/2.46 Prover 8: Constructing countermodel ... % 13.16/2.51 Prover 1: Found proof (size 63) % 13.16/2.51 Prover 1: proved (1874ms) % 13.16/2.51 Prover 8: stopped % 13.16/2.51 Prover 10: stopped % 13.16/2.52 Prover 4: stopped % 13.16/2.53 Prover 7: Constructing countermodel ... % 13.16/2.54 Prover 13: Warning: ignoring some quantifiers % 13.16/2.54 Prover 7: stopped % 13.16/2.55 Prover 13: Constructing countermodel ... % 13.16/2.56 Prover 13: stopped % 13.16/2.58 Prover 11: Constructing countermodel ... % 13.61/2.59 Prover 11: stopped % 13.61/2.59 % 13.61/2.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.61/2.59 % 13.61/2.62 % SZS output start Proof for theBenchmark % 13.61/2.63 Assumptions after simplification: % 13.61/2.63 --------------------------------- % 13.61/2.63 % 13.61/2.63 (mDefIdeal) % 13.61/2.67 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aIdeal0(v0) = v1) | ~ $i(v0) | ? % 13.61/2.67 [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2) | ? [v2: $i] : (aElementOf0(v2, % 13.61/2.67 v0) = 0 & $i(v2) & ( ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = % 13.61/2.67 0) & aElementOf0(v4, v0) = v5 & aElementOf0(v3, v0) = 0 & % 13.61/2.67 sdtpldt0(v2, v3) = v4 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] : % 13.61/2.67 ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v4, v0) = v5 & sdtasdt0(v3, % 13.61/2.67 v2) = v4 & aElement0(v3) = 0 & $i(v4) & $i(v3))))) & ! [v0: $i] : ( % 13.61/2.67 ~ (aIdeal0(v0) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i] : ( ~ % 13.61/2.67 (aElementOf0(v1, v0) = 0) | ~ $i(v1) | ( ! [v2: $i] : ! [v3: $i] : ! % 13.61/2.67 [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, v0) = v4) | ~ (sdtasdt0(v2, % 13.61/2.67 v1) = v3) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & % 13.61/2.67 aElement0(v2) = v5)) & ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 13.61/2.67 (v4 = 0 | ~ (aElementOf0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | % 13.61/2.67 ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v2, v0) = % 13.61/2.67 v5)))))) % 13.61/2.67 % 13.61/2.67 (mMulComm) % 13.61/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 13.61/2.67 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 13.61/2.67 (sdtasdt0(v1, v0) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & $i(v5) & % 13.61/2.67 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 13.61/2.67 % 13.61/2.67 (mSortsB_02) % 13.61/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 13.61/2.67 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 13.61/2.67 (aElement0(v2) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & ( ~ (v4 = 0) % 13.61/2.68 | ~ (v3 = 0) | v5 = 0))) % 13.61/2.68 % 13.61/2.68 (m__) % 13.61/2.68 $i(xl) & $i(xk) & $i(xz) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: any] : ? % 13.61/2.68 [v2: $i] : ? [v3: any] : (aElementOf0(v2, xJ) = v3 & aElementOf0(v0, xI) = v1 % 13.61/2.68 & sdtasdt0(xz, xl) = v2 & sdtasdt0(xz, xk) = v0 & $i(v2) & $i(v0) & ( ~ (v3 % 13.61/2.68 = 0) | ~ (v1 = 0))) % 13.61/2.68 % 13.61/2.68 (m__870) % 13.61/2.68 aIdeal0(xJ) = 0 & aIdeal0(xI) = 0 & $i(xJ) & $i(xI) % 13.61/2.68 % 13.61/2.68 (m__901) % 13.61/2.68 $i(xz) & $i(xy) & $i(xx) & $i(xJ) & $i(xI) & ? [v0: $i] : (sdtpldt1(xI, xJ) = % 13.61/2.68 v0 & aElementOf0(xy, v0) = 0 & aElementOf0(xx, v0) = 0 & aElement0(xz) = 0 & % 13.61/2.68 $i(v0)) % 13.61/2.68 % 13.61/2.68 (m__934) % 13.61/2.68 aElementOf0(xl, xJ) = 0 & aElementOf0(xk, xI) = 0 & sdtpldt0(xk, xl) = xx & % 13.61/2.68 $i(xl) & $i(xk) & $i(xx) & $i(xJ) & $i(xI) % 13.61/2.68 % 13.61/2.68 (function-axioms) % 13.61/2.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.61/2.69 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 13.61/2.69 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 13.61/2.69 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.61/2.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.61/2.69 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: $i] : % 13.61/2.69 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) % 13.61/2.69 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 13.61/2.69 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 13.61/2.69 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 13.61/2.69 = v0 | ~ (aIdeal0(v2) = v1) | ~ (aIdeal0(v2) = v0)) & ! [v0: % 13.61/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 13.61/2.69 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 13.61/2.69 [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: % 13.61/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 13.61/2.69 ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0)) % 13.61/2.69 % 13.61/2.69 Further assumptions not needed in the proof: % 13.61/2.69 -------------------------------------------- % 13.61/2.69 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mDefSInt, mDefSSum, % 13.61/2.69 mEOfElem, mElmSort, mMulAsso, mMulMnOne, mMulUnit, mMulZero, mSetEq, mSetSort, % 13.61/2.69 mSortsB, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__967, m__994 % 13.61/2.69 % 13.61/2.69 Those formulas are unsatisfiable: % 13.61/2.69 --------------------------------- % 13.61/2.69 % 13.61/2.69 Begin of proof % 13.61/2.69 | % 13.61/2.69 | ALPHA: (mDefIdeal) implies: % 13.61/2.69 | (1) ! [v0: $i] : ( ~ (aIdeal0(v0) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! % 13.61/2.69 | [v1: $i] : ( ~ (aElementOf0(v1, v0) = 0) | ~ $i(v1) | ( ! [v2: $i] % 13.61/2.69 | : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, % 13.61/2.69 | v0) = v4) | ~ (sdtasdt0(v2, v1) = v3) | ~ $i(v2) | ? % 13.61/2.69 | [v5: int] : ( ~ (v5 = 0) & aElement0(v2) = v5)) & ! [v2: $i] % 13.61/2.69 | : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, % 13.61/2.69 | v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ? % 13.61/2.69 | [v5: int] : ( ~ (v5 = 0) & aElementOf0(v2, v0) = v5)))))) % 13.61/2.69 | % 13.61/2.69 | ALPHA: (m__870) implies: % 13.61/2.70 | (2) aIdeal0(xI) = 0 % 13.61/2.70 | (3) aIdeal0(xJ) = 0 % 13.61/2.70 | % 13.61/2.70 | ALPHA: (m__901) implies: % 13.61/2.70 | (4) ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & aElementOf0(xy, v0) = 0 & % 13.61/2.70 | aElementOf0(xx, v0) = 0 & aElement0(xz) = 0 & $i(v0)) % 13.61/2.70 | % 13.61/2.70 | ALPHA: (m__934) implies: % 13.61/2.70 | (5) aElementOf0(xk, xI) = 0 % 13.61/2.70 | (6) aElementOf0(xl, xJ) = 0 % 13.61/2.70 | % 13.61/2.70 | ALPHA: (m__) implies: % 13.61/2.70 | (7) $i(xI) % 13.61/2.70 | (8) $i(xJ) % 13.61/2.70 | (9) $i(xz) % 13.61/2.70 | (10) $i(xk) % 13.61/2.70 | (11) $i(xl) % 13.61/2.70 | (12) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 13.61/2.70 | (aElementOf0(v2, xJ) = v3 & aElementOf0(v0, xI) = v1 & sdtasdt0(xz, % 13.61/2.70 | xl) = v2 & sdtasdt0(xz, xk) = v0 & $i(v2) & $i(v0) & ( ~ (v3 = 0) % 13.61/2.70 | | ~ (v1 = 0))) % 13.61/2.70 | % 13.61/2.70 | ALPHA: (function-axioms) implies: % 13.61/2.70 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 13.61/2.70 | : (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0)) % 13.61/2.70 | % 13.61/2.70 | DELTA: instantiating (4) with fresh symbol all_22_0 gives: % 13.61/2.70 | (14) sdtpldt1(xI, xJ) = all_22_0 & aElementOf0(xy, all_22_0) = 0 & % 13.61/2.70 | aElementOf0(xx, all_22_0) = 0 & aElement0(xz) = 0 & $i(all_22_0) % 13.61/2.70 | % 13.61/2.70 | ALPHA: (14) implies: % 13.61/2.70 | (15) aElement0(xz) = 0 % 13.61/2.70 | % 13.61/2.70 | DELTA: instantiating (12) with fresh symbols all_26_0, all_26_1, all_26_2, % 13.61/2.70 | all_26_3 gives: % 13.61/2.70 | (16) aElementOf0(all_26_1, xJ) = all_26_0 & aElementOf0(all_26_3, xI) = % 13.61/2.70 | all_26_2 & sdtasdt0(xz, xl) = all_26_1 & sdtasdt0(xz, xk) = all_26_3 & % 13.61/2.70 | $i(all_26_1) & $i(all_26_3) & ( ~ (all_26_0 = 0) | ~ (all_26_2 = 0)) % 13.61/2.70 | % 13.61/2.70 | ALPHA: (16) implies: % 13.61/2.70 | (17) sdtasdt0(xz, xk) = all_26_3 % 13.61/2.70 | (18) sdtasdt0(xz, xl) = all_26_1 % 13.61/2.70 | (19) aElementOf0(all_26_3, xI) = all_26_2 % 13.61/2.70 | (20) aElementOf0(all_26_1, xJ) = all_26_0 % 13.61/2.70 | (21) ~ (all_26_0 = 0) | ~ (all_26_2 = 0) % 13.61/2.70 | % 13.61/2.71 | GROUND_INST: instantiating (mMulComm) with xz, xk, all_26_3, simplifying with % 13.61/2.71 | (9), (10), (17) gives: % 13.61/2.71 | (22) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xk, xz) = v2 & % 13.61/2.71 | aElement0(xk) = v1 & aElement0(xz) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ % 13.61/2.71 | (v0 = 0) | v2 = all_26_3)) % 13.61/2.71 | % 13.61/2.71 | GROUND_INST: instantiating (mSortsB_02) with xz, xk, all_26_3, simplifying % 13.61/2.71 | with (9), (10), (17) gives: % 13.61/2.71 | (23) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_26_3) = v2 % 13.61/2.71 | & aElement0(xk) = v1 & aElement0(xz) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 13.61/2.71 | 0) | v2 = 0)) % 13.61/2.71 | % 13.61/2.71 | GROUND_INST: instantiating (mMulComm) with xz, xl, all_26_1, simplifying with % 13.61/2.71 | (9), (11), (18) gives: % 13.61/2.71 | (24) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xl, xz) = v2 & % 13.61/2.71 | aElement0(xl) = v1 & aElement0(xz) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ % 13.61/2.71 | (v0 = 0) | v2 = all_26_1)) % 13.61/2.71 | % 13.61/2.71 | GROUND_INST: instantiating (mSortsB_02) with xz, xl, all_26_1, simplifying % 13.61/2.71 | with (9), (11), (18) gives: % 13.61/2.71 | (25) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_26_1) = v2 % 13.61/2.71 | & aElement0(xl) = v1 & aElement0(xz) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 13.61/2.71 | 0) | v2 = 0)) % 13.61/2.71 | % 13.61/2.71 | GROUND_INST: instantiating (1) with xI, simplifying with (2), (7) gives: % 13.61/2.71 | (26) aSet0(xI) = 0 & ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~ % 13.61/2.71 | $i(v0) | ( ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 13.61/2.71 | (aElementOf0(v2, xI) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ~ % 13.61/2.71 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aElement0(v1) = v4)) & ! % 13.61/2.71 | [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 13.61/2.71 | (aElementOf0(v2, xI) = v3) | ~ (sdtpldt0(v0, v1) = v2) | ~ % 13.61/2.71 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v1, xI) = % 13.61/2.71 | v4)))) % 13.61/2.71 | % 13.61/2.71 | ALPHA: (26) implies: % 13.61/2.71 | (27) ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ( ! [v1: $i] % 13.61/2.71 | : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xI) = % 13.61/2.71 | v3) | ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v4: int] : % 13.61/2.71 | ( ~ (v4 = 0) & aElement0(v1) = v4)) & ! [v1: $i] : ! [v2: $i] % 13.61/2.71 | : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xI) = v3) | ~ % 13.61/2.71 | (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = % 13.61/2.71 | 0) & aElementOf0(v1, xI) = v4)))) % 13.61/2.71 | % 13.61/2.71 | GROUND_INST: instantiating (1) with xJ, simplifying with (3), (8) gives: % 13.61/2.72 | (28) aSet0(xJ) = 0 & ! [v0: $i] : ( ~ (aElementOf0(v0, xJ) = 0) | ~ % 13.61/2.72 | $i(v0) | ( ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 13.61/2.72 | (aElementOf0(v2, xJ) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ~ % 13.61/2.72 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aElement0(v1) = v4)) & ! % 13.61/2.72 | [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 13.61/2.72 | (aElementOf0(v2, xJ) = v3) | ~ (sdtpldt0(v0, v1) = v2) | ~ % 13.61/2.72 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v1, xJ) = % 13.61/2.72 | v4)))) % 13.61/2.72 | % 13.61/2.72 | ALPHA: (28) implies: % 13.61/2.72 | (29) ! [v0: $i] : ( ~ (aElementOf0(v0, xJ) = 0) | ~ $i(v0) | ( ! [v1: $i] % 13.61/2.72 | : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xJ) = % 13.61/2.72 | v3) | ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v4: int] : % 13.61/2.72 | ( ~ (v4 = 0) & aElement0(v1) = v4)) & ! [v1: $i] : ! [v2: $i] % 13.61/2.72 | : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xJ) = v3) | ~ % 13.61/2.72 | (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = % 13.61/2.72 | 0) & aElementOf0(v1, xJ) = v4)))) % 13.61/2.72 | % 13.61/2.72 | GROUND_INST: instantiating (27) with xk, simplifying with (5), (10) gives: % 13.61/2.72 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 13.61/2.72 | (aElementOf0(v1, xI) = v2) | ~ (sdtasdt0(v0, xk) = v1) | ~ $i(v0) % 13.61/2.72 | | ? [v3: int] : ( ~ (v3 = 0) & aElement0(v0) = v3)) & ! [v0: $i] : % 13.61/2.72 | ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xI) = v2) | % 13.61/2.72 | ~ (sdtpldt0(xk, v0) = v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) % 13.61/2.72 | & aElementOf0(v0, xI) = v3)) % 13.61/2.72 | % 13.61/2.72 | ALPHA: (30) implies: % 13.61/2.72 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 13.61/2.72 | (aElementOf0(v1, xI) = v2) | ~ (sdtasdt0(v0, xk) = v1) | ~ $i(v0) % 13.61/2.72 | | ? [v3: int] : ( ~ (v3 = 0) & aElement0(v0) = v3)) % 13.61/2.72 | % 13.61/2.72 | GROUND_INST: instantiating (29) with xl, simplifying with (6), (11) gives: % 13.61/2.72 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 13.61/2.72 | (aElementOf0(v1, xJ) = v2) | ~ (sdtasdt0(v0, xl) = v1) | ~ $i(v0) % 13.61/2.72 | | ? [v3: int] : ( ~ (v3 = 0) & aElement0(v0) = v3)) & ! [v0: $i] : % 13.61/2.72 | ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xJ) = v2) | % 13.61/2.72 | ~ (sdtpldt0(xl, v0) = v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) % 13.61/2.72 | & aElementOf0(v0, xJ) = v3)) % 13.61/2.72 | % 13.61/2.72 | ALPHA: (32) implies: % 13.61/2.72 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 13.61/2.72 | (aElementOf0(v1, xJ) = v2) | ~ (sdtasdt0(v0, xl) = v1) | ~ $i(v0) % 13.61/2.72 | | ? [v3: int] : ( ~ (v3 = 0) & aElement0(v0) = v3)) % 13.61/2.72 | % 13.61/2.72 | GROUND_INST: instantiating (31) with xz, all_26_3, all_26_2, simplifying with % 13.61/2.72 | (9), (17), (19) gives: % 13.61/2.72 | (34) all_26_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) & aElement0(xz) = v0) % 13.61/2.72 | % 13.61/2.73 | GROUND_INST: instantiating (33) with xz, all_26_1, all_26_0, simplifying with % 13.61/2.73 | (9), (18), (20) gives: % 13.61/2.73 | (35) all_26_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & aElement0(xz) = v0) % 13.61/2.73 | % 13.61/2.73 | DELTA: instantiating (25) with fresh symbols all_51_0, all_51_1, all_51_2 % 13.61/2.73 | gives: % 13.61/2.73 | (36) aElement0(all_26_1) = all_51_0 & aElement0(xl) = all_51_1 & % 13.61/2.73 | aElement0(xz) = all_51_2 & ( ~ (all_51_1 = 0) | ~ (all_51_2 = 0) | % 13.61/2.73 | all_51_0 = 0) % 13.61/2.73 | % 13.61/2.73 | ALPHA: (36) implies: % 13.61/2.73 | (37) aElement0(xz) = all_51_2 % 13.61/2.73 | % 13.61/2.73 | DELTA: instantiating (23) with fresh symbols all_53_0, all_53_1, all_53_2 % 13.61/2.73 | gives: % 13.61/2.73 | (38) aElement0(all_26_3) = all_53_0 & aElement0(xk) = all_53_1 & % 13.61/2.73 | aElement0(xz) = all_53_2 & ( ~ (all_53_1 = 0) | ~ (all_53_2 = 0) | % 13.61/2.73 | all_53_0 = 0) % 13.61/2.73 | % 13.61/2.73 | ALPHA: (38) implies: % 13.61/2.73 | (39) aElement0(xz) = all_53_2 % 13.61/2.73 | % 13.61/2.73 | DELTA: instantiating (24) with fresh symbols all_59_0, all_59_1, all_59_2 % 13.61/2.73 | gives: % 13.61/2.73 | (40) sdtasdt0(xl, xz) = all_59_0 & aElement0(xl) = all_59_1 & aElement0(xz) % 13.61/2.73 | = all_59_2 & $i(all_59_0) & ( ~ (all_59_1 = 0) | ~ (all_59_2 = 0) | % 13.61/2.73 | all_59_0 = all_26_1) % 13.61/2.73 | % 13.61/2.73 | ALPHA: (40) implies: % 13.61/2.73 | (41) aElement0(xz) = all_59_2 % 13.61/2.73 | % 13.61/2.73 | DELTA: instantiating (22) with fresh symbols all_63_0, all_63_1, all_63_2 % 13.61/2.73 | gives: % 13.61/2.73 | (42) sdtasdt0(xk, xz) = all_63_0 & aElement0(xk) = all_63_1 & aElement0(xz) % 13.61/2.73 | = all_63_2 & $i(all_63_0) & ( ~ (all_63_1 = 0) | ~ (all_63_2 = 0) | % 13.61/2.73 | all_63_0 = all_26_3) % 13.61/2.73 | % 13.61/2.73 | ALPHA: (42) implies: % 13.61/2.73 | (43) aElement0(xz) = all_63_2 % 13.61/2.73 | % 13.61/2.73 | GROUND_INST: instantiating (13) with all_51_2, all_53_2, xz, simplifying with % 13.61/2.73 | (37), (39) gives: % 13.61/2.73 | (44) all_53_2 = all_51_2 % 13.61/2.73 | % 13.61/2.73 | GROUND_INST: instantiating (13) with 0, all_63_2, xz, simplifying with (15), % 13.61/2.73 | (43) gives: % 13.61/2.73 | (45) all_63_2 = 0 % 13.61/2.73 | % 13.61/2.73 | GROUND_INST: instantiating (13) with all_59_2, all_63_2, xz, simplifying with % 13.61/2.73 | (41), (43) gives: % 13.61/2.73 | (46) all_63_2 = all_59_2 % 13.61/2.73 | % 13.61/2.73 | GROUND_INST: instantiating (13) with all_53_2, all_63_2, xz, simplifying with % 13.61/2.73 | (39), (43) gives: % 13.61/2.73 | (47) all_63_2 = all_53_2 % 13.61/2.73 | % 13.61/2.73 | COMBINE_EQS: (46), (47) imply: % 13.61/2.73 | (48) all_59_2 = all_53_2 % 13.61/2.73 | % 13.61/2.73 | COMBINE_EQS: (45), (46) imply: % 13.61/2.73 | (49) all_59_2 = 0 % 13.61/2.73 | % 13.61/2.73 | COMBINE_EQS: (48), (49) imply: % 13.61/2.73 | (50) all_53_2 = 0 % 13.61/2.73 | % 13.61/2.73 | SIMP: (50) implies: % 13.61/2.73 | (51) all_53_2 = 0 % 13.61/2.73 | % 13.61/2.73 | COMBINE_EQS: (44), (51) imply: % 13.61/2.73 | (52) all_51_2 = 0 % 13.61/2.73 | % 13.61/2.73 | SIMP: (52) implies: % 13.61/2.73 | (53) all_51_2 = 0 % 13.61/2.73 | % 13.61/2.73 | BETA: splitting (35) gives: % 13.61/2.73 | % 13.61/2.73 | Case 1: % 13.61/2.73 | | % 13.61/2.73 | | (54) all_26_0 = 0 % 13.61/2.73 | | % 13.61/2.73 | | BETA: splitting (21) gives: % 13.61/2.73 | | % 13.61/2.73 | | Case 1: % 13.61/2.73 | | | % 13.61/2.73 | | | (55) ~ (all_26_0 = 0) % 13.61/2.73 | | | % 13.61/2.73 | | | REDUCE: (54), (55) imply: % 13.61/2.73 | | | (56) $false % 13.61/2.73 | | | % 13.61/2.73 | | | CLOSE: (56) is inconsistent. % 13.61/2.73 | | | % 13.61/2.73 | | Case 2: % 13.61/2.73 | | | % 13.61/2.74 | | | (57) ~ (all_26_2 = 0) % 13.61/2.74 | | | % 13.61/2.74 | | | BETA: splitting (34) gives: % 13.61/2.74 | | | % 13.61/2.74 | | | Case 1: % 13.61/2.74 | | | | % 13.61/2.74 | | | | (58) all_26_2 = 0 % 13.61/2.74 | | | | % 13.61/2.74 | | | | REDUCE: (57), (58) imply: % 13.61/2.74 | | | | (59) $false % 13.61/2.74 | | | | % 13.61/2.74 | | | | CLOSE: (59) is inconsistent. % 13.61/2.74 | | | | % 13.61/2.74 | | | Case 2: % 13.61/2.74 | | | | % 13.61/2.74 | | | | (60) ? [v0: int] : ( ~ (v0 = 0) & aElement0(xz) = v0) % 13.61/2.74 | | | | % 13.61/2.74 | | | | DELTA: instantiating (60) with fresh symbol all_90_0 gives: % 13.61/2.74 | | | | (61) ~ (all_90_0 = 0) & aElement0(xz) = all_90_0 % 13.61/2.74 | | | | % 13.61/2.74 | | | | ALPHA: (61) implies: % 13.61/2.74 | | | | (62) ~ (all_90_0 = 0) % 13.61/2.74 | | | | (63) aElement0(xz) = all_90_0 % 13.61/2.74 | | | | % 13.61/2.74 | | | | GROUND_INST: instantiating (13) with 0, all_90_0, xz, simplifying with % 13.61/2.74 | | | | (15), (63) gives: % 13.61/2.74 | | | | (64) all_90_0 = 0 % 13.61/2.74 | | | | % 13.61/2.74 | | | | REDUCE: (62), (64) imply: % 13.61/2.74 | | | | (65) $false % 13.61/2.74 | | | | % 13.61/2.74 | | | | CLOSE: (65) is inconsistent. % 13.61/2.74 | | | | % 13.61/2.74 | | | End of split % 13.61/2.74 | | | % 13.61/2.74 | | End of split % 13.61/2.74 | | % 13.61/2.74 | Case 2: % 13.61/2.74 | | % 13.61/2.74 | | (66) ? [v0: int] : ( ~ (v0 = 0) & aElement0(xz) = v0) % 13.61/2.74 | | % 13.61/2.74 | | DELTA: instantiating (66) with fresh symbol all_82_0 gives: % 13.61/2.74 | | (67) ~ (all_82_0 = 0) & aElement0(xz) = all_82_0 % 13.61/2.74 | | % 13.61/2.74 | | ALPHA: (67) implies: % 13.61/2.74 | | (68) ~ (all_82_0 = 0) % 13.61/2.74 | | (69) aElement0(xz) = all_82_0 % 13.61/2.74 | | % 13.61/2.74 | | GROUND_INST: instantiating (13) with 0, all_82_0, xz, simplifying with (15), % 13.61/2.74 | | (69) gives: % 13.61/2.74 | | (70) all_82_0 = 0 % 13.61/2.74 | | % 13.61/2.74 | | REDUCE: (68), (70) imply: % 13.61/2.74 | | (71) $false % 13.61/2.74 | | % 13.61/2.74 | | CLOSE: (71) is inconsistent. % 13.61/2.74 | | % 13.61/2.74 | End of split % 13.61/2.74 | % 13.61/2.74 End of proof % 13.61/2.74 % SZS output end Proof for theBenchmark % 13.61/2.74 % 13.61/2.74 2130ms %------------------------------------------------------------------------------