%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG047+2 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n026.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 13:57:32 EDT 2023 % Result : Theorem 10.30s 2.22s % Output : Proof 14.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : RNG047+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n026.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sun Aug 27 03:07:34 EDT 2023 % 0.14/0.35 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.34/1.19 Prover 1: Preprocessing ... % 3.34/1.21 Prover 4: Preprocessing ... % 3.84/1.26 Prover 5: Preprocessing ... % 3.84/1.26 Prover 6: Preprocessing ... % 3.84/1.26 Prover 2: Preprocessing ... % 3.84/1.26 Prover 3: Preprocessing ... % 3.84/1.26 Prover 0: Preprocessing ... % 8.62/1.94 Prover 1: Constructing countermodel ... % 8.76/1.95 Prover 3: Constructing countermodel ... % 8.76/2.00 Prover 6: Proving ... % 9.66/2.17 Prover 5: Constructing countermodel ... % 10.30/2.22 Prover 3: proved (1577ms) % 10.30/2.22 % 10.30/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.30/2.22 % 10.30/2.22 Prover 5: stopped % 10.30/2.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.30/2.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.30/2.23 Prover 6: stopped % 10.30/2.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.95/2.31 Prover 7: Preprocessing ... % 11.18/2.32 Prover 8: Preprocessing ... % 11.31/2.35 Prover 10: Preprocessing ... % 11.31/2.36 Prover 4: Constructing countermodel ... % 11.31/2.41 Prover 2: Proving ... % 11.31/2.41 Prover 2: stopped % 11.93/2.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.47/2.48 Prover 11: Preprocessing ... % 12.47/2.50 Prover 10: Constructing countermodel ... % 12.47/2.52 Prover 0: Proving ... % 12.47/2.53 Prover 0: stopped % 12.47/2.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.47/2.55 Prover 7: Constructing countermodel ... % 13.10/2.57 Prover 8: Warning: ignoring some quantifiers % 13.21/2.58 Prover 8: Constructing countermodel ... % 13.39/2.62 Prover 13: Preprocessing ... % 13.39/2.63 Prover 1: Found proof (size 68) % 13.39/2.63 Prover 1: proved (1987ms) % 13.39/2.63 Prover 4: stopped % 13.39/2.63 Prover 8: stopped % 13.39/2.63 Prover 10: stopped % 13.39/2.63 Prover 7: stopped % 13.39/2.66 Prover 13: stopped % 13.95/2.78 Prover 11: Constructing countermodel ... % 13.95/2.79 Prover 11: stopped % 13.95/2.79 % 13.95/2.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.95/2.80 % 13.95/2.82 % SZS output start Proof for theBenchmark % 13.95/2.82 Assumptions after simplification: % 13.95/2.82 --------------------------------- % 13.95/2.83 % 13.95/2.83 (mDefInit) % 14.55/2.87 $i(sz00) & ! [v0: $i] : ( ~ (aVector0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 14.55/2.87 [v2: $i] : (sziznziztdt0(v0) = v2 & aDimensionOf0(v0) = v1 & $i(v2) & $i(v1) % 14.55/2.87 & (v1 = sz00 | ( ! [v3: $i] : (v3 = v2 | ~ (aVector0(v3) = 0) | ~ $i(v3) % 14.55/2.87 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & % 14.55/2.87 sdtlbdtrb0(v3, v4) = v5 & sdtlbdtrb0(v0, v4) = v6 & % 14.55/2.87 aNaturalNumber0(v4) = 0 & $i(v6) & $i(v5) & $i(v4)) | ? [v4: $i] % 14.55/2.87 : ? [v5: $i] : ( ~ (v5 = v1) & aDimensionOf0(v3) = v4 & % 14.55/2.87 szszuzczcdt0(v4) = v5 & $i(v5) & $i(v4))) & ! [v3: any] : ( ~ % 14.55/2.87 (aVector0(v2) = v3) | (v3 = 0 & ! [v4: $i] : ! [v5: $i] : ( ~ % 14.55/2.87 (sdtlbdtrb0(v0, v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: % 14.55/2.87 $i] : (sdtlbdtrb0(v2, v4) = v7 & aNaturalNumber0(v4) = v6 & % 14.55/2.87 $i(v7) & ( ~ (v6 = 0) | v7 = v5))) & ? [v4: $i] : % 14.55/2.87 (aDimensionOf0(v2) = v4 & szszuzczcdt0(v4) = v1 & $i(v4)))))))) % 14.55/2.87 % 14.55/2.87 (mDimNat) % 14.55/2.87 ! [v0: $i] : ( ~ (aVector0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 14.55/2.87 (aDimensionOf0(v0) = v1 & aNaturalNumber0(v1) = 0 & $i(v1))) % 14.55/2.87 % 14.55/2.87 (mSuccEqu) % 14.55/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v1) = % 14.55/2.87 v2) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 14.55/2.87 ? [v4: any] : (aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v4 % 14.55/2.87 = 0) | ~ (v3 = 0)))) % 14.55/2.87 % 14.55/2.87 (mSuccNat) % 14.55/2.88 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) % 14.55/2.88 | ? [v2: any] : ? [v3: any] : (aNaturalNumber0(v1) = v3 & % 14.55/2.88 aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = 0 & ~ (v1 = sz00))))) % 14.55/2.88 % 14.55/2.88 (m__) % 14.55/2.88 $i(xt) & $i(xs) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 14.55/2.88 [v4: $i] : ? [v5: $i] : ( ~ (v4 = v1) & sziznziztdt0(xt) = v3 & % 14.55/2.88 sziznziztdt0(xs) = v0 & aVector0(v3) = 0 & aVector0(v0) = 0 & % 14.55/2.88 aDimensionOf0(v3) = v4 & aDimensionOf0(v0) = v1 & aDimensionOf0(xt) = v5 & % 14.55/2.88 aDimensionOf0(xs) = v2 & szszuzczcdt0(v4) = v5 & szszuzczcdt0(v1) = v2 & % 14.55/2.88 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v6: $i] : ! [v7: % 14.55/2.88 $i] : ( ~ (sdtlbdtrb0(v3, v6) = v7) | ~ $i(v6) | ? [v8: any] : ? [v9: % 14.55/2.88 $i] : (sdtlbdtrb0(xt, v6) = v9 & aNaturalNumber0(v6) = v8 & $i(v9) & ( ~ % 14.55/2.88 (v8 = 0) | v9 = v7))) & ! [v6: $i] : ! [v7: $i] : ( ~ % 14.55/2.88 (sdtlbdtrb0(v0, v6) = v7) | ~ $i(v6) | ? [v8: any] : ? [v9: $i] : % 14.55/2.88 (sdtlbdtrb0(xs, v6) = v9 & aNaturalNumber0(v6) = v8 & $i(v9) & ( ~ (v8 = % 14.55/2.88 0) | v9 = v7)))) % 14.55/2.88 % 14.55/2.88 (m__1329_01) % 14.55/2.88 $i(xt) & $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xt) % 14.55/2.88 = v0 & aDimensionOf0(xs) = v0 & $i(v0)) % 14.55/2.88 % 14.55/2.88 (function-axioms) % 14.55/2.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.55/2.88 (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: % 14.55/2.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.55/2.88 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 14.55/2.88 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.55/2.88 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 14.55/2.88 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 14.55/2.88 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.55/2.88 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (iLess0(v3, % 14.55/2.88 v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 14.55/2.88 [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ (sziznziztdt0(v2) = v0)) % 14.55/2.88 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 14.55/2.88 = v0 | ~ (aVector0(v2) = v1) | ~ (aVector0(v2) = v0)) & ! [v0: $i] : ! % 14.55/2.88 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (aDimensionOf0(v2) = v1) | ~ % 14.55/2.88 (aDimensionOf0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 14.55/2.88 v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: % 14.55/2.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 14.55/2.88 ~ (aScalar0(v2) = v1) | ~ (aScalar0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 14.55/2.88 : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 14.55/2.88 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.55/2.88 $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = % 14.55/2.88 v0)) % 14.55/2.88 % 14.55/2.88 Further assumptions not needed in the proof: % 14.55/2.88 -------------------------------------------- % 14.55/2.88 mArith, mDistr, mDistr2, mElmSc, mIH, mIHOrd, mLEASm, mLEMon, mLEMonM, mLERef, % 14.55/2.88 mLETot, mLETrn, mLess, mMDNeg, mMNeg, mMulSc, mNatExtr, mNatSort, mNegSc, % 14.55/2.88 mPosMon, mSZeroSc, mScSort, mScZero, mSqPos, mSqrt, mSumSc, mVcSort, mZeroNat, % 14.55/2.88 m__1329 % 14.55/2.88 % 14.55/2.88 Those formulas are unsatisfiable: % 14.55/2.88 --------------------------------- % 14.55/2.88 % 14.55/2.88 Begin of proof % 14.55/2.89 | % 14.55/2.89 | ALPHA: (mSuccNat) implies: % 14.55/2.89 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | % 14.55/2.89 | ? [v2: any] : ? [v3: any] : (aNaturalNumber0(v1) = v3 & % 14.55/2.89 | aNaturalNumber0(v0) = v2 & ( ~ (v2 = 0) | (v3 = 0 & ~ (v1 = % 14.55/2.89 | sz00))))) % 14.55/2.89 | % 14.55/2.89 | ALPHA: (mDefInit) implies: % 14.55/2.89 | (2) ! [v0: $i] : ( ~ (aVector0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 14.55/2.89 | [v2: $i] : (sziznziztdt0(v0) = v2 & aDimensionOf0(v0) = v1 & $i(v2) & % 14.55/2.89 | $i(v1) & (v1 = sz00 | ( ! [v3: $i] : (v3 = v2 | ~ (aVector0(v3) = % 14.55/2.89 | 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 14.55/2.89 | ( ~ (v6 = v5) & sdtlbdtrb0(v3, v4) = v5 & sdtlbdtrb0(v0, v4) % 14.55/2.89 | = v6 & aNaturalNumber0(v4) = 0 & $i(v6) & $i(v5) & $i(v4)) % 14.55/2.89 | | ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v1) & % 14.55/2.89 | aDimensionOf0(v3) = v4 & szszuzczcdt0(v4) = v5 & $i(v5) & % 14.55/2.89 | $i(v4))) & ! [v3: any] : ( ~ (aVector0(v2) = v3) | (v3 = 0 % 14.55/2.89 | & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0, v4) = v5) % 14.55/2.89 | | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : % 14.55/2.89 | (sdtlbdtrb0(v2, v4) = v7 & aNaturalNumber0(v4) = v6 & % 14.55/2.89 | $i(v7) & ( ~ (v6 = 0) | v7 = v5))) & ? [v4: $i] : % 14.55/2.89 | (aDimensionOf0(v2) = v4 & szszuzczcdt0(v4) = v1 & % 14.55/2.89 | $i(v4)))))))) % 14.55/2.89 | % 14.55/2.89 | ALPHA: (m__1329_01) implies: % 14.55/2.89 | (3) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xt) = v0 & % 14.55/2.89 | aDimensionOf0(xs) = v0 & $i(v0)) % 14.55/2.89 | % 14.55/2.89 | ALPHA: (m__) implies: % 14.55/2.89 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 14.55/2.89 | ? [v5: $i] : ( ~ (v4 = v1) & sziznziztdt0(xt) = v3 & sziznziztdt0(xs) = % 14.55/2.89 | v0 & aVector0(v3) = 0 & aVector0(v0) = 0 & aDimensionOf0(v3) = v4 & % 14.55/2.89 | aDimensionOf0(v0) = v1 & aDimensionOf0(xt) = v5 & aDimensionOf0(xs) = % 14.55/2.89 | v2 & szszuzczcdt0(v4) = v5 & szszuzczcdt0(v1) = v2 & $i(v5) & $i(v4) % 14.55/2.89 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v6: $i] : ! [v7: $i] : ( ~ % 14.55/2.89 | (sdtlbdtrb0(v3, v6) = v7) | ~ $i(v6) | ? [v8: any] : ? [v9: $i] % 14.55/2.89 | : (sdtlbdtrb0(xt, v6) = v9 & aNaturalNumber0(v6) = v8 & $i(v9) & ( % 14.55/2.89 | ~ (v8 = 0) | v9 = v7))) & ! [v6: $i] : ! [v7: $i] : ( ~ % 14.55/2.89 | (sdtlbdtrb0(v0, v6) = v7) | ~ $i(v6) | ? [v8: any] : ? [v9: $i] % 14.55/2.89 | : (sdtlbdtrb0(xs, v6) = v9 & aNaturalNumber0(v6) = v8 & $i(v9) & ( % 14.55/2.89 | ~ (v8 = 0) | v9 = v7)))) % 14.55/2.89 | % 14.55/2.89 | ALPHA: (function-axioms) implies: % 14.55/2.89 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.55/2.89 | (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = % 14.55/2.89 | v0)) % 14.55/2.89 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.55/2.89 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) % 14.55/2.89 | % 14.55/2.90 | DELTA: instantiating (3) with fresh symbol all_28_0 gives: % 14.55/2.90 | (7) ~ (all_28_0 = sz00) & aDimensionOf0(xt) = all_28_0 & aDimensionOf0(xs) % 14.55/2.90 | = all_28_0 & $i(all_28_0) % 14.55/2.90 | % 14.55/2.90 | ALPHA: (7) implies: % 14.55/2.90 | (8) aDimensionOf0(xs) = all_28_0 % 14.55/2.90 | (9) aDimensionOf0(xt) = all_28_0 % 14.55/2.90 | % 14.55/2.90 | DELTA: instantiating (4) with fresh symbols all_33_0, all_33_1, all_33_2, % 14.55/2.90 | all_33_3, all_33_4, all_33_5 gives: % 14.55/2.90 | (10) ~ (all_33_1 = all_33_4) & sziznziztdt0(xt) = all_33_2 & % 14.55/2.90 | sziznziztdt0(xs) = all_33_5 & aVector0(all_33_2) = 0 & % 14.55/2.90 | aVector0(all_33_5) = 0 & aDimensionOf0(all_33_2) = all_33_1 & % 14.55/2.90 | aDimensionOf0(all_33_5) = all_33_4 & aDimensionOf0(xt) = all_33_0 & % 14.55/2.90 | aDimensionOf0(xs) = all_33_3 & szszuzczcdt0(all_33_1) = all_33_0 & % 14.55/2.90 | szszuzczcdt0(all_33_4) = all_33_3 & $i(all_33_0) & $i(all_33_1) & % 14.55/2.90 | $i(all_33_2) & $i(all_33_3) & $i(all_33_4) & $i(all_33_5) & ! [v0: % 14.55/2.90 | $i] : ! [v1: $i] : ( ~ (sdtlbdtrb0(all_33_2, v0) = v1) | ~ $i(v0) % 14.55/2.90 | | ? [v2: any] : ? [v3: $i] : (sdtlbdtrb0(xt, v0) = v3 & % 14.55/2.90 | aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = v1))) & ! % 14.55/2.90 | [v0: $i] : ! [v1: $i] : ( ~ (sdtlbdtrb0(all_33_5, v0) = v1) | ~ % 14.55/2.90 | $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtlbdtrb0(xs, v0) = v3 & % 14.55/2.90 | aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = v1))) % 14.55/2.90 | % 14.55/2.90 | ALPHA: (10) implies: % 14.55/2.90 | (11) ~ (all_33_1 = all_33_4) % 14.55/2.90 | (12) $i(all_33_5) % 14.55/2.90 | (13) $i(all_33_4) % 14.55/2.90 | (14) $i(all_33_2) % 14.55/2.90 | (15) $i(all_33_1) % 14.55/2.90 | (16) szszuzczcdt0(all_33_4) = all_33_3 % 14.55/2.90 | (17) szszuzczcdt0(all_33_1) = all_33_0 % 14.55/2.90 | (18) aDimensionOf0(xs) = all_33_3 % 14.55/2.90 | (19) aDimensionOf0(xt) = all_33_0 % 14.55/2.90 | (20) aDimensionOf0(all_33_5) = all_33_4 % 14.55/2.90 | (21) aDimensionOf0(all_33_2) = all_33_1 % 14.55/2.90 | (22) aVector0(all_33_5) = 0 % 14.55/2.90 | (23) aVector0(all_33_2) = 0 % 14.55/2.90 | % 14.55/2.90 | GROUND_INST: instantiating (6) with all_28_0, all_33_3, xs, simplifying with % 14.55/2.90 | (8), (18) gives: % 14.55/2.90 | (24) all_33_3 = all_28_0 % 14.55/2.90 | % 14.55/2.90 | GROUND_INST: instantiating (6) with all_28_0, all_33_0, xt, simplifying with % 14.55/2.90 | (9), (19) gives: % 14.55/2.90 | (25) all_33_0 = all_28_0 % 14.55/2.90 | % 14.55/2.90 | REDUCE: (17), (25) imply: % 14.55/2.90 | (26) szszuzczcdt0(all_33_1) = all_28_0 % 14.55/2.90 | % 14.55/2.90 | REDUCE: (16), (24) imply: % 14.55/2.90 | (27) szszuzczcdt0(all_33_4) = all_28_0 % 14.55/2.90 | % 14.89/2.90 | GROUND_INST: instantiating (1) with all_33_4, all_28_0, simplifying with (13), % 14.89/2.90 | (27) gives: % 14.89/2.90 | (28) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_33_4) = v0 & % 14.89/2.90 | aNaturalNumber0(all_28_0) = v1 & ( ~ (v0 = 0) | (v1 = 0 & ~ % 14.89/2.90 | (all_28_0 = sz00)))) % 14.89/2.90 | % 14.89/2.90 | GROUND_INST: instantiating (mSuccEqu) with all_33_4, all_33_1, all_28_0, % 14.89/2.90 | simplifying with (13), (15), (26), (27) gives: % 14.89/2.90 | (29) all_33_1 = all_33_4 | ? [v0: any] : ? [v1: any] : % 14.89/2.90 | (aNaturalNumber0(all_33_1) = v1 & aNaturalNumber0(all_33_4) = v0 & ( ~ % 14.89/2.90 | (v1 = 0) | ~ (v0 = 0))) % 14.89/2.90 | % 14.89/2.91 | GROUND_INST: instantiating (mSuccEqu) with all_33_1, all_33_4, all_28_0, % 14.89/2.91 | simplifying with (13), (15), (26), (27) gives: % 14.89/2.91 | (30) all_33_1 = all_33_4 | ? [v0: any] : ? [v1: any] : % 14.89/2.91 | (aNaturalNumber0(all_33_1) = v0 & aNaturalNumber0(all_33_4) = v1 & ( ~ % 14.89/2.91 | (v1 = 0) | ~ (v0 = 0))) % 14.89/2.91 | % 14.89/2.91 | GROUND_INST: instantiating (1) with all_33_1, all_28_0, simplifying with (15), % 14.89/2.91 | (26) gives: % 14.89/2.91 | (31) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_33_1) = v0 & % 14.89/2.91 | aNaturalNumber0(all_28_0) = v1 & ( ~ (v0 = 0) | (v1 = 0 & ~ % 14.89/2.91 | (all_28_0 = sz00)))) % 14.89/2.91 | % 14.89/2.91 | GROUND_INST: instantiating (2) with all_33_5, simplifying with (12), (22) % 14.89/2.91 | gives: % 14.89/2.91 | (32) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(all_33_5) = v1 & % 14.89/2.91 | aDimensionOf0(all_33_5) = v0 & $i(v1) & $i(v0) & (v0 = sz00 | ( ! % 14.89/2.91 | [v2: $i] : (v2 = v1 | ~ (aVector0(v2) = 0) | ~ $i(v2) | ? % 14.89/2.91 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v4) & % 14.89/2.91 | sdtlbdtrb0(v2, v3) = v4 & sdtlbdtrb0(all_33_5, v3) = v5 & % 14.89/2.91 | aNaturalNumber0(v3) = 0 & $i(v5) & $i(v4) & $i(v3)) | ? % 14.89/2.91 | [v3: $i] : ? [v4: $i] : ( ~ (v4 = v0) & aDimensionOf0(v2) = % 14.89/2.91 | v3 & szszuzczcdt0(v3) = v4 & $i(v4) & $i(v3))) & ! [v2: % 14.89/2.91 | any] : ( ~ (aVector0(v1) = v2) | (v2 = 0 & ! [v3: $i] : ! % 14.89/2.91 | [v4: $i] : ( ~ (sdtlbdtrb0(all_33_5, v3) = v4) | ~ $i(v3) | % 14.89/2.91 | ? [v5: any] : ? [v6: $i] : (sdtlbdtrb0(v1, v3) = v6 & % 14.89/2.91 | aNaturalNumber0(v3) = v5 & $i(v6) & ( ~ (v5 = 0) | v6 = % 14.89/2.91 | v4))) & ? [v3: $i] : (aDimensionOf0(v1) = v3 & % 14.89/2.91 | szszuzczcdt0(v3) = v0 & $i(v3))))))) % 14.89/2.91 | % 14.89/2.91 | GROUND_INST: instantiating (mDimNat) with all_33_5, simplifying with (12), % 14.89/2.91 | (22) gives: % 14.89/2.91 | (33) ? [v0: $i] : (aDimensionOf0(all_33_5) = v0 & aNaturalNumber0(v0) = 0 % 14.89/2.91 | & $i(v0)) % 14.89/2.91 | % 14.89/2.91 | GROUND_INST: instantiating (2) with all_33_2, simplifying with (14), (23) % 14.89/2.91 | gives: % 14.89/2.91 | (34) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(all_33_2) = v1 & % 14.89/2.91 | aDimensionOf0(all_33_2) = v0 & $i(v1) & $i(v0) & (v0 = sz00 | ( ! % 14.89/2.91 | [v2: $i] : (v2 = v1 | ~ (aVector0(v2) = 0) | ~ $i(v2) | ? % 14.89/2.91 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v4) & % 14.89/2.91 | sdtlbdtrb0(v2, v3) = v4 & sdtlbdtrb0(all_33_2, v3) = v5 & % 14.89/2.91 | aNaturalNumber0(v3) = 0 & $i(v5) & $i(v4) & $i(v3)) | ? % 14.89/2.91 | [v3: $i] : ? [v4: $i] : ( ~ (v4 = v0) & aDimensionOf0(v2) = % 14.89/2.91 | v3 & szszuzczcdt0(v3) = v4 & $i(v4) & $i(v3))) & ! [v2: % 14.89/2.91 | any] : ( ~ (aVector0(v1) = v2) | (v2 = 0 & ! [v3: $i] : ! % 14.89/2.91 | [v4: $i] : ( ~ (sdtlbdtrb0(all_33_2, v3) = v4) | ~ $i(v3) | % 14.89/2.91 | ? [v5: any] : ? [v6: $i] : (sdtlbdtrb0(v1, v3) = v6 & % 14.89/2.91 | aNaturalNumber0(v3) = v5 & $i(v6) & ( ~ (v5 = 0) | v6 = % 14.89/2.91 | v4))) & ? [v3: $i] : (aDimensionOf0(v1) = v3 & % 14.89/2.91 | szszuzczcdt0(v3) = v0 & $i(v3))))))) % 14.89/2.91 | % 14.89/2.91 | GROUND_INST: instantiating (mDimNat) with all_33_2, simplifying with (14), % 14.89/2.91 | (23) gives: % 14.89/2.91 | (35) ? [v0: $i] : (aDimensionOf0(all_33_2) = v0 & aNaturalNumber0(v0) = 0 % 14.89/2.91 | & $i(v0)) % 14.89/2.91 | % 14.89/2.91 | DELTA: instantiating (35) with fresh symbol all_45_0 gives: % 14.89/2.91 | (36) aDimensionOf0(all_33_2) = all_45_0 & aNaturalNumber0(all_45_0) = 0 & % 14.89/2.91 | $i(all_45_0) % 14.89/2.91 | % 14.89/2.91 | ALPHA: (36) implies: % 14.89/2.91 | (37) aNaturalNumber0(all_45_0) = 0 % 14.89/2.91 | (38) aDimensionOf0(all_33_2) = all_45_0 % 14.89/2.91 | % 14.89/2.91 | DELTA: instantiating (33) with fresh symbol all_49_0 gives: % 14.89/2.91 | (39) aDimensionOf0(all_33_5) = all_49_0 & aNaturalNumber0(all_49_0) = 0 & % 14.89/2.91 | $i(all_49_0) % 14.89/2.91 | % 14.89/2.91 | ALPHA: (39) implies: % 14.89/2.91 | (40) aNaturalNumber0(all_49_0) = 0 % 14.89/2.91 | (41) aDimensionOf0(all_33_5) = all_49_0 % 14.89/2.91 | % 14.89/2.91 | DELTA: instantiating (31) with fresh symbols all_55_0, all_55_1 gives: % 14.89/2.91 | (42) aNaturalNumber0(all_33_1) = all_55_1 & aNaturalNumber0(all_28_0) = % 14.89/2.91 | all_55_0 & ( ~ (all_55_1 = 0) | (all_55_0 = 0 & ~ (all_28_0 = sz00))) % 14.89/2.91 | % 14.89/2.91 | ALPHA: (42) implies: % 14.89/2.92 | (43) aNaturalNumber0(all_33_1) = all_55_1 % 14.89/2.92 | % 14.89/2.92 | DELTA: instantiating (28) with fresh symbols all_57_0, all_57_1 gives: % 14.89/2.92 | (44) aNaturalNumber0(all_33_4) = all_57_1 & aNaturalNumber0(all_28_0) = % 14.89/2.92 | all_57_0 & ( ~ (all_57_1 = 0) | (all_57_0 = 0 & ~ (all_28_0 = sz00))) % 14.89/2.92 | % 14.89/2.92 | ALPHA: (44) implies: % 14.89/2.92 | (45) aNaturalNumber0(all_33_4) = all_57_1 % 14.89/2.92 | % 14.89/2.92 | DELTA: instantiating (34) with fresh symbols all_59_0, all_59_1 gives: % 14.89/2.92 | (46) sziznziztdt0(all_33_2) = all_59_0 & aDimensionOf0(all_33_2) = all_59_1 % 14.89/2.92 | & $i(all_59_0) & $i(all_59_1) & (all_59_1 = sz00 | ( ! [v0: any] : (v0 % 14.89/2.92 | = all_59_0 | ~ (aVector0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 14.89/2.92 | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & sdtlbdtrb0(v0, v1) = % 14.89/2.92 | v2 & sdtlbdtrb0(all_33_2, v1) = v3 & aNaturalNumber0(v1) = 0 & % 14.89/2.92 | $i(v3) & $i(v2) & $i(v1)) | ? [v1: $i] : ? [v2: any] : ( ~ % 14.89/2.92 | (v2 = all_59_1) & aDimensionOf0(v0) = v1 & szszuzczcdt0(v1) = % 14.89/2.92 | v2 & $i(v2) & $i(v1))) & ! [v0: any] : ( ~ % 14.89/2.92 | (aVector0(all_59_0) = v0) | (v0 = 0 & ! [v1: $i] : ! [v2: $i] % 14.89/2.92 | : ( ~ (sdtlbdtrb0(all_33_2, v1) = v2) | ~ $i(v1) | ? [v3: % 14.89/2.92 | any] : ? [v4: $i] : (sdtlbdtrb0(all_59_0, v1) = v4 & % 14.89/2.92 | aNaturalNumber0(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = % 14.89/2.92 | v2))) & ? [v1: $i] : (aDimensionOf0(all_59_0) = v1 & % 14.89/2.92 | szszuzczcdt0(v1) = all_59_1 & $i(v1)))))) % 14.89/2.92 | % 14.89/2.92 | ALPHA: (46) implies: % 14.89/2.92 | (47) aDimensionOf0(all_33_2) = all_59_1 % 14.89/2.92 | % 14.89/2.92 | DELTA: instantiating (32) with fresh symbols all_63_0, all_63_1 gives: % 14.89/2.92 | (48) sziznziztdt0(all_33_5) = all_63_0 & aDimensionOf0(all_33_5) = all_63_1 % 14.89/2.92 | & $i(all_63_0) & $i(all_63_1) & (all_63_1 = sz00 | ( ! [v0: any] : (v0 % 14.89/2.92 | = all_63_0 | ~ (aVector0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 14.89/2.92 | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & sdtlbdtrb0(v0, v1) = % 14.89/2.92 | v2 & sdtlbdtrb0(all_33_5, v1) = v3 & aNaturalNumber0(v1) = 0 & % 14.89/2.92 | $i(v3) & $i(v2) & $i(v1)) | ? [v1: $i] : ? [v2: any] : ( ~ % 14.89/2.92 | (v2 = all_63_1) & aDimensionOf0(v0) = v1 & szszuzczcdt0(v1) = % 14.89/2.92 | v2 & $i(v2) & $i(v1))) & ! [v0: any] : ( ~ % 14.89/2.92 | (aVector0(all_63_0) = v0) | (v0 = 0 & ! [v1: $i] : ! [v2: $i] % 14.89/2.92 | : ( ~ (sdtlbdtrb0(all_33_5, v1) = v2) | ~ $i(v1) | ? [v3: % 14.89/2.92 | any] : ? [v4: $i] : (sdtlbdtrb0(all_63_0, v1) = v4 & % 14.89/2.92 | aNaturalNumber0(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = % 14.89/2.92 | v2))) & ? [v1: $i] : (aDimensionOf0(all_63_0) = v1 & % 14.89/2.92 | szszuzczcdt0(v1) = all_63_1 & $i(v1)))))) % 14.89/2.92 | % 14.89/2.92 | ALPHA: (48) implies: % 14.89/2.92 | (49) aDimensionOf0(all_33_5) = all_63_1 % 14.89/2.92 | % 14.89/2.92 | GROUND_INST: instantiating (6) with all_33_4, all_63_1, all_33_5, simplifying % 14.89/2.92 | with (20), (49) gives: % 14.89/2.92 | (50) all_63_1 = all_33_4 % 14.89/2.92 | % 14.89/2.92 | GROUND_INST: instantiating (6) with all_49_0, all_63_1, all_33_5, simplifying % 14.89/2.92 | with (41), (49) gives: % 14.89/2.92 | (51) all_63_1 = all_49_0 % 14.89/2.92 | % 14.89/2.92 | GROUND_INST: instantiating (6) with all_33_1, all_59_1, all_33_2, simplifying % 14.89/2.92 | with (21), (47) gives: % 14.89/2.92 | (52) all_59_1 = all_33_1 % 14.89/2.92 | % 14.89/2.92 | GROUND_INST: instantiating (6) with all_45_0, all_59_1, all_33_2, simplifying % 14.89/2.92 | with (38), (47) gives: % 14.89/2.92 | (53) all_59_1 = all_45_0 % 14.89/2.92 | % 14.89/2.92 | COMBINE_EQS: (50), (51) imply: % 14.89/2.92 | (54) all_49_0 = all_33_4 % 14.89/2.92 | % 14.89/2.92 | COMBINE_EQS: (52), (53) imply: % 14.89/2.92 | (55) all_45_0 = all_33_1 % 14.89/2.92 | % 14.89/2.92 | SIMP: (55) implies: % 14.89/2.92 | (56) all_45_0 = all_33_1 % 14.89/2.92 | % 14.89/2.92 | REDUCE: (40), (54) imply: % 14.89/2.92 | (57) aNaturalNumber0(all_33_4) = 0 % 14.89/2.92 | % 14.89/2.92 | REDUCE: (37), (56) imply: % 14.89/2.92 | (58) aNaturalNumber0(all_33_1) = 0 % 14.89/2.92 | % 14.89/2.92 | GROUND_INST: instantiating (5) with all_57_1, 0, all_33_4, simplifying with % 14.89/2.92 | (45), (57) gives: % 14.89/2.92 | (59) all_57_1 = 0 % 14.89/2.92 | % 14.89/2.93 | GROUND_INST: instantiating (5) with all_55_1, 0, all_33_1, simplifying with % 14.89/2.93 | (43), (58) gives: % 14.89/2.93 | (60) all_55_1 = 0 % 14.89/2.93 | % 14.89/2.93 | BETA: splitting (29) gives: % 14.89/2.93 | % 14.89/2.93 | Case 1: % 14.89/2.93 | | % 14.89/2.93 | | (61) all_33_1 = all_33_4 % 14.89/2.93 | | % 14.89/2.93 | | REDUCE: (11), (61) imply: % 14.89/2.93 | | (62) $false % 14.89/2.93 | | % 14.89/2.93 | | CLOSE: (62) is inconsistent. % 14.89/2.93 | | % 14.89/2.93 | Case 2: % 14.89/2.93 | | % 14.89/2.93 | | (63) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_33_1) = v1 & % 14.89/2.93 | | aNaturalNumber0(all_33_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 14.89/2.93 | | % 14.89/2.93 | | DELTA: instantiating (63) with fresh symbols all_92_0, all_92_1 gives: % 14.89/2.93 | | (64) aNaturalNumber0(all_33_1) = all_92_0 & aNaturalNumber0(all_33_4) = % 14.89/2.93 | | all_92_1 & ( ~ (all_92_0 = 0) | ~ (all_92_1 = 0)) % 14.89/2.93 | | % 14.89/2.93 | | ALPHA: (64) implies: % 14.89/2.93 | | (65) aNaturalNumber0(all_33_4) = all_92_1 % 14.89/2.93 | | (66) aNaturalNumber0(all_33_1) = all_92_0 % 14.89/2.93 | | (67) ~ (all_92_0 = 0) | ~ (all_92_1 = 0) % 14.89/2.93 | | % 14.89/2.93 | | BETA: splitting (30) gives: % 14.89/2.93 | | % 14.89/2.93 | | Case 1: % 14.89/2.93 | | | % 14.89/2.93 | | | (68) all_33_1 = all_33_4 % 14.89/2.93 | | | % 14.89/2.93 | | | REDUCE: (11), (68) imply: % 14.89/2.93 | | | (69) $false % 14.89/2.93 | | | % 14.89/2.93 | | | CLOSE: (69) is inconsistent. % 14.89/2.93 | | | % 14.89/2.93 | | Case 2: % 14.89/2.93 | | | % 14.89/2.93 | | | (70) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_33_1) = v0 & % 14.89/2.93 | | | aNaturalNumber0(all_33_4) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 14.89/2.93 | | | % 14.89/2.93 | | | DELTA: instantiating (70) with fresh symbols all_98_0, all_98_1 gives: % 14.89/2.93 | | | (71) aNaturalNumber0(all_33_1) = all_98_1 & aNaturalNumber0(all_33_4) = % 14.89/2.93 | | | all_98_0 & ( ~ (all_98_0 = 0) | ~ (all_98_1 = 0)) % 14.89/2.93 | | | % 14.89/2.93 | | | ALPHA: (71) implies: % 14.89/2.93 | | | (72) aNaturalNumber0(all_33_4) = all_98_0 % 14.89/2.93 | | | (73) aNaturalNumber0(all_33_1) = all_98_1 % 14.89/2.93 | | | % 14.89/2.93 | | | GROUND_INST: instantiating (5) with 0, all_98_0, all_33_4, simplifying % 14.89/2.93 | | | with (57), (72) gives: % 14.89/2.93 | | | (74) all_98_0 = 0 % 14.89/2.93 | | | % 14.89/2.93 | | | GROUND_INST: instantiating (5) with all_92_1, all_98_0, all_33_4, % 14.89/2.93 | | | simplifying with (65), (72) gives: % 14.89/2.93 | | | (75) all_98_0 = all_92_1 % 14.89/2.93 | | | % 14.89/2.93 | | | GROUND_INST: instantiating (5) with 0, all_98_1, all_33_1, simplifying % 14.89/2.93 | | | with (58), (73) gives: % 14.89/2.93 | | | (76) all_98_1 = 0 % 14.89/2.93 | | | % 14.89/2.93 | | | GROUND_INST: instantiating (5) with all_92_0, all_98_1, all_33_1, % 14.89/2.93 | | | simplifying with (66), (73) gives: % 14.89/2.93 | | | (77) all_98_1 = all_92_0 % 14.89/2.93 | | | % 14.89/2.93 | | | COMBINE_EQS: (74), (75) imply: % 14.89/2.93 | | | (78) all_92_1 = 0 % 14.89/2.93 | | | % 14.89/2.93 | | | COMBINE_EQS: (76), (77) imply: % 14.89/2.93 | | | (79) all_92_0 = 0 % 14.89/2.93 | | | % 14.89/2.93 | | | BETA: splitting (67) gives: % 14.89/2.93 | | | % 14.89/2.93 | | | Case 1: % 14.89/2.93 | | | | % 14.89/2.93 | | | | (80) ~ (all_92_0 = 0) % 14.89/2.93 | | | | % 14.89/2.93 | | | | REDUCE: (79), (80) imply: % 14.89/2.93 | | | | (81) $false % 14.89/2.93 | | | | % 14.89/2.93 | | | | CLOSE: (81) is inconsistent. % 14.89/2.93 | | | | % 14.89/2.93 | | | Case 2: % 14.89/2.93 | | | | % 14.89/2.93 | | | | (82) ~ (all_92_1 = 0) % 14.89/2.93 | | | | % 14.89/2.93 | | | | REDUCE: (78), (82) imply: % 14.89/2.93 | | | | (83) $false % 14.89/2.93 | | | | % 14.89/2.93 | | | | CLOSE: (83) is inconsistent. % 14.89/2.93 | | | | % 14.89/2.93 | | | End of split % 14.89/2.93 | | | % 14.89/2.93 | | End of split % 14.89/2.93 | | % 14.89/2.93 | End of split % 14.89/2.93 | % 14.89/2.93 End of proof % 14.89/2.93 % SZS output end Proof for theBenchmark % 14.89/2.93 % 14.89/2.93 2314ms %------------------------------------------------------------------------------