%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG088+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 : n016.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 9.34s 2.05s % Output : Proof 12.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG088+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 : n016.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 03:39:27 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/sandbox/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 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 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 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 % 2.74/1.09 Prover 1: Preprocessing ... % 2.74/1.10 Prover 4: Preprocessing ... % 2.74/1.13 Prover 5: Preprocessing ... % 2.74/1.13 Prover 6: Preprocessing ... % 2.74/1.13 Prover 2: Preprocessing ... % 2.74/1.13 Prover 3: Preprocessing ... % 2.74/1.13 Prover 0: Preprocessing ... % 6.61/1.70 Prover 1: Constructing countermodel ... % 7.16/1.73 Prover 3: Constructing countermodel ... % 7.16/1.73 Prover 6: Proving ... % 7.68/1.79 Prover 5: Proving ... % 7.68/1.84 Prover 4: Constructing countermodel ... % 8.73/1.95 Prover 2: Proving ... % 8.73/2.00 Prover 0: Proving ... % 9.34/2.05 Prover 3: proved (1412ms) % 9.34/2.05 % 9.34/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.34/2.05 % 9.34/2.05 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.34/2.05 Prover 5: stopped % 9.34/2.07 Prover 0: stopped % 9.34/2.07 Prover 6: stopped % 9.34/2.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.34/2.07 Prover 2: stopped % 9.34/2.08 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.34/2.08 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.34/2.09 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.34/2.14 Prover 13: Preprocessing ... % 9.34/2.15 Prover 10: Preprocessing ... % 9.34/2.15 Prover 8: Preprocessing ... % 9.34/2.16 Prover 7: Preprocessing ... % 9.34/2.17 Prover 11: Preprocessing ... % 10.07/2.27 Prover 10: Constructing countermodel ... % 11.76/2.36 Prover 13: Warning: ignoring some quantifiers % 11.76/2.37 Prover 1: Found proof (size 37) % 11.76/2.37 Prover 1: proved (1742ms) % 11.76/2.37 Prover 8: Warning: ignoring some quantifiers % 11.76/2.37 Prover 4: stopped % 11.76/2.37 Prover 10: stopped % 11.76/2.37 Prover 8: Constructing countermodel ... % 11.76/2.38 Prover 13: Constructing countermodel ... % 11.76/2.38 Prover 8: stopped % 11.76/2.39 Prover 7: Constructing countermodel ... % 11.76/2.39 Prover 13: stopped % 11.76/2.41 Prover 7: stopped % 12.24/2.46 Prover 11: Constructing countermodel ... % 12.47/2.47 Prover 11: stopped % 12.47/2.47 % 12.47/2.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.47/2.47 % 12.47/2.48 % SZS output start Proof for theBenchmark % 12.47/2.48 Assumptions after simplification: % 12.47/2.48 --------------------------------- % 12.47/2.48 % 12.47/2.48 (mDefIdeal) % 12.47/2.51 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aIdeal0(v0) = v1) | ~ $i(v0) | ? % 12.47/2.51 [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2) | ? [v2: $i] : (aElementOf0(v2, % 12.47/2.51 v0) = 0 & $i(v2) & ( ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = % 12.47/2.51 0) & aElementOf0(v4, v0) = v5 & aElementOf0(v3, v0) = 0 & % 12.47/2.51 sdtpldt0(v2, v3) = v4 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] : % 12.47/2.51 ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v4, v0) = v5 & sdtasdt0(v3, % 12.47/2.51 v2) = v4 & aElement0(v3) = 0 & $i(v4) & $i(v3))))) & ! [v0: $i] : ( % 12.47/2.51 ~ (aIdeal0(v0) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i] : ( ~ % 12.47/2.51 (aElementOf0(v1, v0) = 0) | ~ $i(v1) | ( ! [v2: $i] : ! [v3: $i] : ! % 12.47/2.51 [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, v0) = v4) | ~ (sdtasdt0(v2, % 12.47/2.51 v1) = v3) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & % 12.47/2.51 aElement0(v2) = v5)) & ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 12.47/2.51 (v4 = 0 | ~ (aElementOf0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | % 12.47/2.51 ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v2, v0) = % 12.47/2.51 v5)))))) % 12.47/2.51 % 12.47/2.51 (m__) % 12.47/2.51 $i(xn) & $i(xm) & $i(xl) & $i(xk) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: % 12.47/2.51 any] : ? [v2: $i] : ? [v3: any] : (aElementOf0(v2, xJ) = v3 & % 12.47/2.51 aElementOf0(v0, xI) = v1 & sdtpldt0(xl, xn) = v2 & sdtpldt0(xk, xm) = v0 & % 12.47/2.51 $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0))) % 12.47/2.51 % 12.47/2.51 (m__870) % 12.47/2.51 aIdeal0(xJ) = 0 & aIdeal0(xI) = 0 & $i(xJ) & $i(xI) % 12.47/2.51 % 12.47/2.51 (m__934) % 12.47/2.52 aElementOf0(xl, xJ) = 0 & aElementOf0(xk, xI) = 0 & sdtpldt0(xk, xl) = xx & % 12.47/2.52 $i(xl) & $i(xk) & $i(xx) & $i(xJ) & $i(xI) % 12.47/2.52 % 12.47/2.52 (m__967) % 12.47/2.52 aElementOf0(xn, xJ) = 0 & aElementOf0(xm, xI) = 0 & sdtpldt0(xm, xn) = xy & % 12.47/2.52 $i(xn) & $i(xm) & $i(xy) & $i(xJ) & $i(xI) % 12.47/2.52 % 12.47/2.52 (function-axioms) % 12.47/2.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.47/2.52 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 12.47/2.52 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 12.47/2.52 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.47/2.52 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.47/2.52 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: $i] : % 12.47/2.52 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) % 12.47/2.52 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 12.47/2.52 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 12.47/2.52 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 12.47/2.52 = v0 | ~ (aIdeal0(v2) = v1) | ~ (aIdeal0(v2) = v0)) & ! [v0: % 12.47/2.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 12.47/2.52 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 12.47/2.52 [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: % 12.47/2.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 12.47/2.52 ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0)) % 12.47/2.52 % 12.47/2.52 Further assumptions not needed in the proof: % 12.47/2.52 -------------------------------------------- % 12.47/2.52 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mDefSInt, mDefSSum, % 12.47/2.52 mEOfElem, mElmSort, mMulAsso, mMulComm, mMulMnOne, mMulUnit, mMulZero, mSetEq, % 12.47/2.52 mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__901 % 12.47/2.52 % 12.47/2.52 Those formulas are unsatisfiable: % 12.47/2.52 --------------------------------- % 12.47/2.52 % 12.47/2.52 Begin of proof % 12.47/2.53 | % 12.47/2.53 | ALPHA: (mDefIdeal) implies: % 12.47/2.53 | (1) ! [v0: $i] : ( ~ (aIdeal0(v0) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! % 12.47/2.53 | [v1: $i] : ( ~ (aElementOf0(v1, v0) = 0) | ~ $i(v1) | ( ! [v2: $i] % 12.47/2.53 | : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, % 12.47/2.53 | v0) = v4) | ~ (sdtasdt0(v2, v1) = v3) | ~ $i(v2) | ? % 12.47/2.53 | [v5: int] : ( ~ (v5 = 0) & aElement0(v2) = v5)) & ! [v2: $i] % 12.47/2.53 | : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, % 12.47/2.53 | v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ? % 12.47/2.53 | [v5: int] : ( ~ (v5 = 0) & aElementOf0(v2, v0) = v5)))))) % 12.47/2.53 | % 12.47/2.53 | ALPHA: (m__870) implies: % 12.47/2.53 | (2) aIdeal0(xI) = 0 % 12.47/2.53 | (3) aIdeal0(xJ) = 0 % 12.47/2.53 | % 12.47/2.53 | ALPHA: (m__934) implies: % 12.47/2.53 | (4) aElementOf0(xk, xI) = 0 % 12.47/2.53 | (5) aElementOf0(xl, xJ) = 0 % 12.47/2.53 | % 12.47/2.53 | ALPHA: (m__967) implies: % 12.47/2.53 | (6) aElementOf0(xm, xI) = 0 % 12.47/2.53 | (7) aElementOf0(xn, xJ) = 0 % 12.47/2.53 | % 12.47/2.53 | ALPHA: (m__) implies: % 12.47/2.53 | (8) $i(xI) % 12.47/2.53 | (9) $i(xJ) % 12.47/2.53 | (10) $i(xk) % 12.47/2.53 | (11) $i(xl) % 12.47/2.53 | (12) $i(xm) % 12.47/2.53 | (13) $i(xn) % 12.47/2.53 | (14) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 12.47/2.53 | (aElementOf0(v2, xJ) = v3 & aElementOf0(v0, xI) = v1 & sdtpldt0(xl, % 12.47/2.53 | xn) = v2 & sdtpldt0(xk, xm) = v0 & $i(v2) & $i(v0) & ( ~ (v3 = 0) % 12.47/2.53 | | ~ (v1 = 0))) % 12.47/2.53 | % 12.47/2.53 | ALPHA: (function-axioms) implies: % 12.47/2.54 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 12.47/2.54 | : ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ % 12.47/2.54 | (aElementOf0(v3, v2) = v0)) % 12.47/2.54 | % 12.47/2.54 | DELTA: instantiating (14) with fresh symbols all_24_0, all_24_1, all_24_2, % 12.47/2.54 | all_24_3 gives: % 12.47/2.54 | (16) aElementOf0(all_24_1, xJ) = all_24_0 & aElementOf0(all_24_3, xI) = % 12.47/2.54 | all_24_2 & sdtpldt0(xl, xn) = all_24_1 & sdtpldt0(xk, xm) = all_24_3 & % 12.47/2.54 | $i(all_24_1) & $i(all_24_3) & ( ~ (all_24_0 = 0) | ~ (all_24_2 = 0)) % 12.47/2.54 | % 12.47/2.54 | ALPHA: (16) implies: % 12.47/2.54 | (17) sdtpldt0(xk, xm) = all_24_3 % 12.47/2.54 | (18) sdtpldt0(xl, xn) = all_24_1 % 12.47/2.54 | (19) aElementOf0(all_24_3, xI) = all_24_2 % 12.47/2.54 | (20) aElementOf0(all_24_1, xJ) = all_24_0 % 12.47/2.54 | (21) ~ (all_24_0 = 0) | ~ (all_24_2 = 0) % 12.47/2.54 | % 12.47/2.54 | GROUND_INST: instantiating (1) with xI, simplifying with (2), (8) gives: % 12.47/2.54 | (22) aSet0(xI) = 0 & ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~ % 12.47/2.54 | $i(v0) | ( ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.47/2.54 | (aElementOf0(v2, xI) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ~ % 12.47/2.54 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aElement0(v1) = v4)) & ! % 12.47/2.54 | [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.47/2.54 | (aElementOf0(v2, xI) = v3) | ~ (sdtpldt0(v0, v1) = v2) | ~ % 12.47/2.54 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v1, xI) = % 12.47/2.54 | v4)))) % 12.47/2.54 | % 12.47/2.54 | ALPHA: (22) implies: % 12.47/2.54 | (23) ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ( ! [v1: $i] % 12.47/2.54 | : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xI) = % 12.47/2.54 | v3) | ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v4: int] : % 12.47/2.54 | ( ~ (v4 = 0) & aElement0(v1) = v4)) & ! [v1: $i] : ! [v2: $i] % 12.47/2.54 | : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xI) = v3) | ~ % 12.47/2.54 | (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = % 12.47/2.54 | 0) & aElementOf0(v1, xI) = v4)))) % 12.47/2.54 | % 12.47/2.54 | GROUND_INST: instantiating (1) with xJ, simplifying with (3), (9) gives: % 12.85/2.54 | (24) aSet0(xJ) = 0 & ! [v0: $i] : ( ~ (aElementOf0(v0, xJ) = 0) | ~ % 12.85/2.54 | $i(v0) | ( ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.85/2.54 | (aElementOf0(v2, xJ) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ~ % 12.85/2.54 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aElement0(v1) = v4)) & ! % 12.85/2.54 | [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.85/2.54 | (aElementOf0(v2, xJ) = v3) | ~ (sdtpldt0(v0, v1) = v2) | ~ % 12.85/2.54 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v1, xJ) = % 12.85/2.54 | v4)))) % 12.85/2.54 | % 12.85/2.54 | ALPHA: (24) implies: % 12.85/2.54 | (25) ! [v0: $i] : ( ~ (aElementOf0(v0, xJ) = 0) | ~ $i(v0) | ( ! [v1: $i] % 12.85/2.55 | : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xJ) = % 12.85/2.55 | v3) | ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v4: int] : % 12.85/2.55 | ( ~ (v4 = 0) & aElement0(v1) = v4)) & ! [v1: $i] : ! [v2: $i] % 12.85/2.55 | : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xJ) = v3) | ~ % 12.85/2.55 | (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = % 12.85/2.55 | 0) & aElementOf0(v1, xJ) = v4)))) % 12.85/2.55 | % 12.85/2.55 | GROUND_INST: instantiating (25) with xl, simplifying with (5), (11) gives: % 12.85/2.55 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 12.85/2.55 | (aElementOf0(v1, xJ) = v2) | ~ (sdtasdt0(v0, xl) = v1) | ~ $i(v0) % 12.85/2.55 | | ? [v3: int] : ( ~ (v3 = 0) & aElement0(v0) = v3)) & ! [v0: $i] : % 12.85/2.55 | ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xJ) = v2) | % 12.85/2.55 | ~ (sdtpldt0(xl, v0) = v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) % 12.85/2.55 | & aElementOf0(v0, xJ) = v3)) % 12.85/2.55 | % 12.85/2.55 | ALPHA: (26) implies: % 12.85/2.55 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 12.85/2.55 | (aElementOf0(v1, xJ) = v2) | ~ (sdtpldt0(xl, v0) = v1) | ~ $i(v0) % 12.85/2.55 | | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v0, xJ) = v3)) % 12.85/2.55 | % 12.85/2.55 | GROUND_INST: instantiating (23) with xk, simplifying with (4), (10) gives: % 12.85/2.55 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 12.85/2.55 | (aElementOf0(v1, xI) = v2) | ~ (sdtasdt0(v0, xk) = v1) | ~ $i(v0) % 12.85/2.55 | | ? [v3: int] : ( ~ (v3 = 0) & aElement0(v0) = v3)) & ! [v0: $i] : % 12.85/2.55 | ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xI) = v2) | % 12.85/2.55 | ~ (sdtpldt0(xk, v0) = v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) % 12.85/2.55 | & aElementOf0(v0, xI) = v3)) % 12.85/2.55 | % 12.85/2.55 | ALPHA: (28) implies: % 12.85/2.55 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 12.85/2.55 | (aElementOf0(v1, xI) = v2) | ~ (sdtpldt0(xk, v0) = v1) | ~ $i(v0) % 12.85/2.55 | | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v0, xI) = v3)) % 12.85/2.55 | % 12.85/2.55 | GROUND_INST: instantiating (27) with xn, all_24_1, all_24_0, simplifying with % 12.85/2.55 | (13), (18), (20) gives: % 12.85/2.55 | (30) all_24_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xn, xJ) = v0) % 12.85/2.55 | % 12.85/2.55 | GROUND_INST: instantiating (29) with xm, all_24_3, all_24_2, simplifying with % 12.85/2.55 | (12), (17), (19) gives: % 12.85/2.55 | (31) all_24_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xm, xI) = v0) % 12.85/2.55 | % 12.85/2.55 | BETA: splitting (31) gives: % 12.85/2.55 | % 12.85/2.55 | Case 1: % 12.85/2.55 | | % 12.85/2.55 | | (32) all_24_2 = 0 % 12.85/2.55 | | % 12.85/2.55 | | BETA: splitting (21) gives: % 12.85/2.55 | | % 12.85/2.55 | | Case 1: % 12.85/2.55 | | | % 12.85/2.55 | | | (33) ~ (all_24_0 = 0) % 12.85/2.55 | | | % 12.85/2.55 | | | BETA: splitting (30) gives: % 12.85/2.55 | | | % 12.85/2.55 | | | Case 1: % 12.85/2.55 | | | | % 12.85/2.55 | | | | (34) all_24_0 = 0 % 12.85/2.55 | | | | % 12.85/2.55 | | | | REDUCE: (33), (34) imply: % 12.85/2.55 | | | | (35) $false % 12.85/2.55 | | | | % 12.85/2.55 | | | | CLOSE: (35) is inconsistent. % 12.85/2.55 | | | | % 12.85/2.55 | | | Case 2: % 12.85/2.55 | | | | % 12.85/2.55 | | | | (36) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xn, xJ) = v0) % 12.85/2.55 | | | | % 12.85/2.55 | | | | DELTA: instantiating (36) with fresh symbol all_73_0 gives: % 12.85/2.55 | | | | (37) ~ (all_73_0 = 0) & aElementOf0(xn, xJ) = all_73_0 % 12.85/2.55 | | | | % 12.85/2.55 | | | | ALPHA: (37) implies: % 12.85/2.55 | | | | (38) ~ (all_73_0 = 0) % 12.85/2.55 | | | | (39) aElementOf0(xn, xJ) = all_73_0 % 12.85/2.55 | | | | % 12.85/2.55 | | | | GROUND_INST: instantiating (15) with 0, all_73_0, xJ, xn, simplifying % 12.85/2.55 | | | | with (7), (39) gives: % 12.85/2.55 | | | | (40) all_73_0 = 0 % 12.85/2.55 | | | | % 12.85/2.55 | | | | REDUCE: (38), (40) imply: % 12.85/2.55 | | | | (41) $false % 12.85/2.55 | | | | % 12.85/2.55 | | | | CLOSE: (41) is inconsistent. % 12.85/2.55 | | | | % 12.85/2.56 | | | End of split % 12.85/2.56 | | | % 12.85/2.56 | | Case 2: % 12.85/2.56 | | | % 12.85/2.56 | | | (42) ~ (all_24_2 = 0) % 12.85/2.56 | | | % 12.85/2.56 | | | REDUCE: (32), (42) imply: % 12.85/2.56 | | | (43) $false % 12.85/2.56 | | | % 12.85/2.56 | | | CLOSE: (43) is inconsistent. % 12.85/2.56 | | | % 12.85/2.56 | | End of split % 12.85/2.56 | | % 12.85/2.56 | Case 2: % 12.85/2.56 | | % 12.85/2.56 | | (44) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xm, xI) = v0) % 12.85/2.56 | | % 12.85/2.56 | | DELTA: instantiating (44) with fresh symbol all_65_0 gives: % 12.85/2.56 | | (45) ~ (all_65_0 = 0) & aElementOf0(xm, xI) = all_65_0 % 12.85/2.56 | | % 12.85/2.56 | | ALPHA: (45) implies: % 12.85/2.56 | | (46) ~ (all_65_0 = 0) % 12.85/2.56 | | (47) aElementOf0(xm, xI) = all_65_0 % 12.85/2.56 | | % 12.85/2.56 | | GROUND_INST: instantiating (15) with 0, all_65_0, xI, xm, simplifying with % 12.85/2.56 | | (6), (47) gives: % 12.85/2.56 | | (48) all_65_0 = 0 % 12.85/2.56 | | % 12.85/2.56 | | REDUCE: (46), (48) imply: % 12.85/2.56 | | (49) $false % 12.85/2.56 | | % 12.85/2.56 | | CLOSE: (49) is inconsistent. % 12.85/2.56 | | % 12.85/2.56 | End of split % 12.85/2.56 | % 12.85/2.56 End of proof % 12.85/2.56 % SZS output end Proof for theBenchmark % 12.85/2.56 % 12.85/2.56 1950ms %------------------------------------------------------------------------------