%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG060+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 : n010.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 13:57:36 EDT 2023 % Result : Theorem 12.36s 2.47s % Output : Proof 22.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG060+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n010.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sun Aug 27 01:23:49 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.67/1.20 Prover 4: Preprocessing ... % 3.67/1.20 Prover 1: Preprocessing ... % 3.67/1.25 Prover 2: Preprocessing ... % 3.67/1.25 Prover 5: Preprocessing ... % 3.67/1.25 Prover 3: Preprocessing ... % 3.67/1.25 Prover 0: Preprocessing ... % 3.67/1.25 Prover 6: Preprocessing ... % 9.28/2.00 Prover 1: Constructing countermodel ... % 9.28/2.01 Prover 3: Constructing countermodel ... % 9.28/2.02 Prover 6: Proving ... % 11.62/2.31 Prover 5: Constructing countermodel ... % 11.62/2.34 Prover 4: Constructing countermodel ... % 12.36/2.46 Prover 2: Proving ... % 12.36/2.46 Prover 3: proved (1842ms) % 12.36/2.47 % 12.36/2.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.36/2.47 % 12.36/2.48 Prover 5: stopped % 12.36/2.48 Prover 6: stopped % 12.36/2.48 Prover 2: stopped % 13.05/2.49 Prover 0: Proving ... % 13.05/2.49 Prover 0: stopped % 13.05/2.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.05/2.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.05/2.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.05/2.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.05/2.51 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.90/2.66 Prover 8: Preprocessing ... % 13.90/2.67 Prover 10: Preprocessing ... % 13.90/2.67 Prover 13: Preprocessing ... % 13.90/2.67 Prover 7: Preprocessing ... % 13.90/2.72 Prover 11: Preprocessing ... % 15.00/2.89 Prover 10: Constructing countermodel ... % 15.00/2.91 Prover 8: Warning: ignoring some quantifiers % 16.23/2.93 Prover 8: Constructing countermodel ... % 16.96/3.04 Prover 7: Constructing countermodel ... % 16.96/3.06 Prover 13: Constructing countermodel ... % 18.51/3.30 Prover 11: Constructing countermodel ... % 21.66/3.72 Prover 1: Found proof (size 158) % 21.66/3.72 Prover 1: proved (3099ms) % 22.14/3.72 Prover 11: stopped % 22.14/3.72 Prover 13: stopped % 22.14/3.72 Prover 8: stopped % 22.14/3.72 Prover 7: stopped % 22.14/3.72 Prover 4: stopped % 22.14/3.72 Prover 10: stopped % 22.14/3.72 % 22.14/3.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.14/3.72 % 22.31/3.77 % SZS output start Proof for theBenchmark % 22.31/3.77 Assumptions after simplification: % 22.31/3.77 --------------------------------- % 22.31/3.77 % 22.31/3.77 (mDistr) % 22.31/3.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 22.31/3.80 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 22.31/3.80 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : % 22.31/3.80 ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? % 22.31/3.80 [v12: $i] : ? [v13: $i] : ? [v14: $i] : (sdtasdt0(v11, v2) = v12 & % 22.31/3.80 sdtasdt0(v1, v2) = v13 & sdtasdt0(v0, v9) = v10 & sdtpldt0(v4, v13) = v14 % 22.31/3.80 & sdtpldt0(v1, v2) = v9 & sdtpldt0(v0, v1) = v11 & aScalar0(v2) = v8 & % 22.31/3.80 aScalar0(v1) = v7 & aScalar0(v0) = v6 & $i(v14) & $i(v13) & $i(v12) & % 22.31/3.80 $i(v11) & $i(v10) & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | % 22.31/3.80 (v14 = v12 & v10 = v5)))) % 22.31/3.80 % 22.31/3.80 (mDistr2) % 22.31/3.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 22.31/3.81 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 22.31/3.81 ( ~ (sdtasdt0(v1, v3) = v8) | ~ (sdtasdt0(v1, v2) = v7) | ~ (sdtasdt0(v0, % 22.31/3.81 v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtpldt0(v7, v8) = v9) | ~ % 22.31/3.81 (sdtpldt0(v6, v9) = v10) | ~ (sdtpldt0(v4, v5) = v6) | ~ $i(v3) | ~ % 22.31/3.81 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v11: any] : ? [v12: any] : ? [v13: % 22.31/3.81 any] : ? [v14: any] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : % 22.31/3.81 (sdtasdt0(v15, v16) = v17 & sdtpldt0(v2, v3) = v16 & sdtpldt0(v0, v1) = v15 % 22.31/3.81 & aScalar0(v3) = v14 & aScalar0(v2) = v13 & aScalar0(v1) = v12 & % 22.31/3.81 aScalar0(v0) = v11 & $i(v17) & $i(v16) & $i(v15) & ( ~ (v14 = 0) | ~ (v13 % 22.31/3.81 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | v17 = v10))) % 22.31/3.81 % 22.31/3.81 (mMNeg) % 22.31/3.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (smndt0(v0) = v2) % 22.31/3.81 | ~ (sdtasdt0(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 22.31/3.81 [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 22.31/3.81 (smndt0(v8) = v9 & smndt0(v1) = v6 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, % 22.31/3.81 v1) = v8 & aScalar0(v1) = v5 & aScalar0(v0) = v4 & $i(v9) & $i(v8) & % 22.31/3.81 $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | (v9 = v3 & v7 = v3)))) % 22.31/3.81 % 22.31/3.81 (mMulSc) % 22.31/3.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 22.31/3.81 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 22.31/3.81 (aScalar0(v2) = v5 & aScalar0(v1) = v4 & aScalar0(v0) = v3 & ( ~ (v4 = 0) | % 22.31/3.81 ~ (v3 = 0) | v5 = 0))) % 22.31/3.81 % 22.31/3.81 (mNegSc) % 22.31/3.81 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ? [v2: any] : % 22.31/3.81 ? [v3: any] : (aScalar0(v1) = v3 & aScalar0(v0) = v2 & ( ~ (v2 = 0) | v3 = % 22.31/3.81 0))) % 22.31/3.81 % 22.31/3.81 (mSqPos) % 22.31/3.81 $i(sz0z00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v0) = v1) | ~ % 22.31/3.81 $i(v0) | ? [v2: any] : ? [v3: any] : (sdtlseqdt0(sz0z00, v1) = v3 & % 22.31/3.81 aScalar0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 22.31/3.81 % 22.31/3.81 (mSumSc) % 22.31/3.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 22.31/3.81 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 22.31/3.81 (aScalar0(v2) = v5 & aScalar0(v1) = v4 & aScalar0(v0) = v3 & ( ~ (v4 = 0) | % 22.31/3.81 ~ (v3 = 0) | v5 = 0))) % 22.31/3.81 % 22.31/3.81 (m__) % 22.31/3.81 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 22.31/3.81 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 22.31/3.81 ( ~ (v8 = v2) & smndt0(xN) = v4 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & % 22.31/3.81 sdtasdt0(xS, xS) = v6 & sdtasdt0(xR, xR) = v3 & sdtpldt0(v5, v7) = v8 & % 22.31/3.81 sdtpldt0(v4, v6) = v7 & sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & % 22.31/3.81 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 22.31/3.81 $i(v0)) % 22.31/3.81 % 22.31/3.81 (m__1892) % 22.31/3.81 sdtasdt0(xC, xG) = xR & aScalar0(xR) = 0 & $i(xR) & $i(xG) & $i(xC) % 22.31/3.81 % 22.31/3.81 (m__1930) % 22.31/3.82 sdtasdt0(xF, xD) = xS & aScalar0(xS) = 0 & $i(xS) & $i(xF) & $i(xD) % 22.31/3.82 % 22.31/3.82 (m__2144) % 22.31/3.82 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 22.31/3.82 (smndt0(xN) = v1 & smndt0(xS) = v0 & sdtasdt0(v0, v0) = v2 & sdtasdt0(v0, xR) % 22.31/3.82 = v1 & sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, v0) = v1 & $i(v2) & $i(v1) & % 22.31/3.82 $i(v0)) % 22.31/3.82 % 22.31/3.82 (function-axioms) % 22.31/3.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.31/3.82 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 22.31/3.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) % 22.31/3.82 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 22.31/3.82 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.31/3.82 (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 22.31/3.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | % 22.31/3.82 ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 22.31/3.82 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 22.31/3.82 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 22.31/3.82 [v3: $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & % 22.31/3.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) % 22.31/3.82 | ~ (sziznziztdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 22.31/3.82 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aVector0(v2) = v1) | ~ % 22.31/3.82 (aVector0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 22.31/3.82 ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0: $i] : ! % 22.31/3.82 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = % 22.31/3.82 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 22.31/3.82 $i] : (v1 = v0 | ~ (aScalar0(v2) = v1) | ~ (aScalar0(v2) = v0)) & ! [v0: % 22.31/3.82 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ % 22.31/3.82 (szszuzczcdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 22.31/3.82 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) % 22.31/3.82 | ~ (aNaturalNumber0(v2) = v0)) % 22.31/3.82 % 22.31/3.82 Further assumptions not needed in the proof: % 22.31/3.82 -------------------------------------------- % 22.31/3.82 mArith, mDefInit, mDefSPN, mDefSPZ, mDimNat, mElmSc, mEqInit, mIH, mIHOrd, % 22.31/3.82 mLEASm, mLEMon, mLEMonM, mLERef, mLETot, mLETrn, mLess, mMDNeg, mNatExtr, % 22.31/3.82 mNatSort, mPosMon, mSZeroSc, mScPr, mScSort, mScSqPos, mScZero, mSqrt, mSuccEqu, % 22.31/3.82 mSuccNat, mVcSort, mZeroNat, m__1652, m__1678, m__1678_01, m__1692, m__1709, % 22.31/3.82 m__1726, m__1746, m__1766, m__1783, m__1800, m__1820, m__1837, m__1854, m__1873, % 22.31/3.82 m__1911, m__1949, m__1967, m__2004 % 22.31/3.82 % 22.31/3.82 Those formulas are unsatisfiable: % 22.31/3.82 --------------------------------- % 22.31/3.82 % 22.31/3.82 Begin of proof % 22.31/3.82 | % 22.31/3.82 | ALPHA: (mSqPos) implies: % 22.31/3.82 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v0) = v1) | ~ $i(v0) | % 22.31/3.82 | ? [v2: any] : ? [v3: any] : (sdtlseqdt0(sz0z00, v1) = v3 & % 22.31/3.82 | aScalar0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 22.31/3.82 | % 22.31/3.82 | ALPHA: (m__1892) implies: % 22.31/3.82 | (2) aScalar0(xR) = 0 % 22.31/3.82 | % 22.31/3.82 | ALPHA: (m__1930) implies: % 22.31/3.82 | (3) aScalar0(xS) = 0 % 22.31/3.82 | % 22.31/3.82 | ALPHA: (m__2144) implies: % 22.31/3.82 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (smndt0(xN) = v1 & smndt0(xS) % 22.31/3.82 | = v0 & sdtasdt0(v0, v0) = v2 & sdtasdt0(v0, xR) = v1 & sdtasdt0(xS, % 22.31/3.82 | xS) = v2 & sdtasdt0(xR, v0) = v1 & $i(v2) & $i(v1) & $i(v0)) % 22.31/3.82 | % 22.31/3.82 | ALPHA: (m__) implies: % 22.31/3.83 | (5) $i(xR) % 22.31/3.83 | (6) $i(xS) % 22.31/3.83 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 22.31/3.83 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v2) & % 22.31/3.83 | smndt0(xN) = v4 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & % 22.31/3.83 | sdtasdt0(xS, xS) = v6 & sdtasdt0(xR, xR) = v3 & sdtpldt0(v5, v7) = v8 % 22.31/3.83 | & sdtpldt0(v4, v6) = v7 & sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = % 22.31/3.83 | v1 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 22.31/3.83 | $i(v1) & $i(v0)) % 22.31/3.83 | % 22.31/3.83 | ALPHA: (function-axioms) implies: % 22.31/3.83 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 22.31/3.83 | (v1 = v0 | ~ (aScalar0(v2) = v1) | ~ (aScalar0(v2) = v0)) % 22.31/3.83 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 22.31/3.83 | v1) | ~ (smndt0(v2) = v0)) % 22.31/3.83 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.31/3.83 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 22.31/3.83 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.31/3.83 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 22.31/3.83 | % 22.31/3.83 | DELTA: instantiating (4) with fresh symbols all_45_0, all_45_1, all_45_2 % 22.31/3.83 | gives: % 22.31/3.83 | (12) smndt0(xN) = all_45_1 & smndt0(xS) = all_45_2 & sdtasdt0(all_45_2, % 22.31/3.83 | all_45_2) = all_45_0 & sdtasdt0(all_45_2, xR) = all_45_1 & % 22.31/3.83 | sdtasdt0(xS, xS) = all_45_0 & sdtasdt0(xR, all_45_2) = all_45_1 & % 22.31/3.83 | $i(all_45_0) & $i(all_45_1) & $i(all_45_2) % 22.31/3.83 | % 22.31/3.83 | ALPHA: (12) implies: % 22.31/3.83 | (13) sdtasdt0(xR, all_45_2) = all_45_1 % 22.31/3.83 | (14) sdtasdt0(xS, xS) = all_45_0 % 22.31/3.83 | (15) sdtasdt0(all_45_2, xR) = all_45_1 % 22.31/3.83 | (16) sdtasdt0(all_45_2, all_45_2) = all_45_0 % 22.31/3.83 | (17) smndt0(xS) = all_45_2 % 22.31/3.83 | (18) smndt0(xN) = all_45_1 % 22.31/3.83 | % 22.31/3.83 | DELTA: instantiating (7) with fresh symbols all_53_0, all_53_1, all_53_2, % 22.31/3.83 | all_53_3, all_53_4, all_53_5, all_53_6, all_53_7, all_53_8 gives: % 22.31/3.83 | (19) ~ (all_53_0 = all_53_6) & smndt0(xN) = all_53_4 & smndt0(xS) = % 22.31/3.83 | all_53_8 & sdtasdt0(all_53_7, all_53_7) = all_53_6 & sdtasdt0(xS, xS) % 22.31/3.83 | = all_53_2 & sdtasdt0(xR, xR) = all_53_5 & sdtpldt0(all_53_3, % 22.31/3.83 | all_53_1) = all_53_0 & sdtpldt0(all_53_4, all_53_2) = all_53_1 & % 22.31/3.83 | sdtpldt0(all_53_5, all_53_4) = all_53_3 & sdtpldt0(xR, all_53_8) = % 22.31/3.83 | all_53_7 & $i(all_53_0) & $i(all_53_1) & $i(all_53_2) & $i(all_53_3) & % 22.31/3.83 | $i(all_53_4) & $i(all_53_5) & $i(all_53_6) & $i(all_53_7) & % 22.31/3.83 | $i(all_53_8) % 22.31/3.83 | % 22.31/3.83 | ALPHA: (19) implies: % 22.31/3.83 | (20) ~ (all_53_0 = all_53_6) % 22.31/3.83 | (21) $i(all_53_8) % 22.31/3.83 | (22) sdtpldt0(xR, all_53_8) = all_53_7 % 22.31/3.83 | (23) sdtpldt0(all_53_5, all_53_4) = all_53_3 % 22.31/3.83 | (24) sdtpldt0(all_53_4, all_53_2) = all_53_1 % 22.31/3.83 | (25) sdtpldt0(all_53_3, all_53_1) = all_53_0 % 22.31/3.83 | (26) sdtasdt0(xR, xR) = all_53_5 % 22.31/3.83 | (27) sdtasdt0(xS, xS) = all_53_2 % 22.31/3.83 | (28) sdtasdt0(all_53_7, all_53_7) = all_53_6 % 22.31/3.83 | (29) smndt0(xS) = all_53_8 % 22.31/3.83 | (30) smndt0(xN) = all_53_4 % 22.31/3.83 | % 22.31/3.84 | GROUND_INST: instantiating (11) with all_45_0, all_53_2, xS, xS, simplifying % 22.31/3.84 | with (14), (27) gives: % 22.31/3.84 | (31) all_53_2 = all_45_0 % 22.31/3.84 | % 22.31/3.84 | GROUND_INST: instantiating (9) with all_45_2, all_53_8, xS, simplifying with % 22.31/3.84 | (17), (29) gives: % 22.68/3.84 | (32) all_53_8 = all_45_2 % 22.68/3.84 | % 22.68/3.84 | GROUND_INST: instantiating (9) with all_45_1, all_53_4, xN, simplifying with % 22.68/3.84 | (18), (30) gives: % 22.68/3.84 | (33) all_53_4 = all_45_1 % 22.68/3.84 | % 22.68/3.84 | REDUCE: (24), (31), (33) imply: % 22.68/3.84 | (34) sdtpldt0(all_45_1, all_45_0) = all_53_1 % 22.68/3.84 | % 22.68/3.84 | REDUCE: (23), (33) imply: % 22.68/3.84 | (35) sdtpldt0(all_53_5, all_45_1) = all_53_3 % 22.68/3.84 | % 22.68/3.84 | REDUCE: (22), (32) imply: % 22.68/3.84 | (36) sdtpldt0(xR, all_45_2) = all_53_7 % 22.68/3.84 | % 22.68/3.84 | REDUCE: (21), (32) imply: % 22.68/3.84 | (37) $i(all_45_2) % 22.68/3.84 | % 22.68/3.84 | GROUND_INST: instantiating (mSumSc) with xR, all_45_2, all_53_7, simplifying % 22.68/3.84 | with (5), (36), (37) gives: % 22.68/3.84 | (38) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aScalar0(all_53_7) = v2 % 22.68/3.84 | & aScalar0(all_45_2) = v1 & aScalar0(xR) = v0 & ( ~ (v1 = 0) | ~ % 22.68/3.84 | (v0 = 0) | v2 = 0)) % 22.68/3.84 | % 22.68/3.84 | GROUND_INST: instantiating (mDistr) with xR, xR, all_45_2, all_53_5, all_45_1, % 22.68/3.84 | all_53_3, simplifying with (5), (13), (26), (35), (37) gives: % 22.68/3.84 | (39) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 22.68/3.84 | : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 22.68/3.84 | (sdtasdt0(v5, all_45_2) = v6 & sdtasdt0(xR, v3) = v4 & sdtasdt0(xR, % 22.68/3.84 | all_45_2) = v7 & sdtpldt0(all_45_1, v7) = v8 & sdtpldt0(xR, % 22.68/3.84 | all_45_2) = v3 & sdtpldt0(xR, xR) = v5 & aScalar0(all_45_2) = v2 & % 22.68/3.84 | aScalar0(xR) = v1 & aScalar0(xR) = v0 & $i(v8) & $i(v7) & $i(v6) & % 22.68/3.84 | $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) % 22.68/3.84 | | (v8 = v6 & v4 = all_53_3))) % 22.68/3.84 | % 22.68/3.84 | GROUND_INST: instantiating (mMulSc) with xR, all_45_2, all_45_1, simplifying % 22.68/3.84 | with (5), (13), (37) gives: % 22.68/3.84 | (40) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aScalar0(all_45_1) = v2 % 22.68/3.84 | & aScalar0(all_45_2) = v1 & aScalar0(xR) = v0 & ( ~ (v1 = 0) | ~ % 22.68/3.84 | (v0 = 0) | v2 = 0)) % 22.68/3.84 | % 22.68/3.84 | GROUND_INST: instantiating (mMulSc) with xS, xS, all_45_0, simplifying with % 22.68/3.84 | (6), (14) gives: % 22.68/3.84 | (41) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aScalar0(all_45_0) = v2 % 22.68/3.84 | & aScalar0(xS) = v1 & aScalar0(xS) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) % 22.68/3.84 | | v2 = 0)) % 22.68/3.84 | % 22.68/3.84 | GROUND_INST: instantiating (mMulSc) with all_45_2, xR, all_45_1, simplifying % 22.68/3.84 | with (5), (15), (37) gives: % 22.68/3.84 | (42) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aScalar0(all_45_1) = v2 % 22.68/3.84 | & aScalar0(all_45_2) = v0 & aScalar0(xR) = v1 & ( ~ (v1 = 0) | ~ % 22.68/3.84 | (v0 = 0) | v2 = 0)) % 22.68/3.84 | % 22.68/3.85 | GROUND_INST: instantiating (mDistr2) with xR, all_45_2, xR, all_45_2, % 22.68/3.85 | all_53_5, all_45_1, all_53_3, all_45_1, all_45_0, all_53_1, % 22.68/3.85 | all_53_0, simplifying with (5), (13), (15), (16), (25), (26), % 22.68/3.85 | (34), (35), (37) gives: % 22.68/3.85 | (43) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 22.68/3.85 | $i] : ? [v5: $i] : ? [v6: $i] : (sdtasdt0(v4, v5) = v6 & % 22.68/3.85 | sdtpldt0(xR, all_45_2) = v5 & sdtpldt0(xR, all_45_2) = v4 & % 22.68/3.85 | aScalar0(all_45_2) = v3 & aScalar0(all_45_2) = v1 & aScalar0(xR) = % 22.68/3.85 | v2 & aScalar0(xR) = v0 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | % 22.68/3.85 | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v6 = all_53_0)) % 22.68/3.85 | % 22.68/3.85 | GROUND_INST: instantiating (mDistr) with all_45_2, xR, all_45_2, all_45_1, % 22.68/3.85 | all_45_0, all_53_1, simplifying with (5), (15), (16), (34), (37) % 22.68/3.85 | gives: % 22.68/3.85 | (44) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 22.68/3.85 | : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 22.68/3.85 | (sdtasdt0(v5, all_45_2) = v6 & sdtasdt0(all_45_2, v3) = v4 & % 22.68/3.85 | sdtasdt0(xR, all_45_2) = v7 & sdtpldt0(all_45_0, v7) = v8 & % 22.68/3.85 | sdtpldt0(all_45_2, xR) = v5 & sdtpldt0(xR, all_45_2) = v3 & % 22.68/3.85 | aScalar0(all_45_2) = v2 & aScalar0(all_45_2) = v0 & aScalar0(xR) = % 22.68/3.85 | v1 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = % 22.68/3.85 | 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v8 = v6 & v4 = all_53_1))) % 22.68/3.85 | % 22.68/3.85 | GROUND_INST: instantiating (1) with all_45_2, all_45_0, simplifying with (16), % 22.68/3.85 | (37) gives: % 22.68/3.85 | (45) ? [v0: any] : ? [v1: any] : (sdtlseqdt0(sz0z00, all_45_0) = v1 & % 22.68/3.85 | aScalar0(all_45_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 22.68/3.85 | % 22.68/3.85 | GROUND_INST: instantiating (mMulSc) with all_45_2, all_45_2, all_45_0, % 22.68/3.85 | simplifying with (16), (37) gives: % 22.68/3.85 | (46) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aScalar0(all_45_0) = v2 % 22.68/3.85 | & aScalar0(all_45_2) = v1 & aScalar0(all_45_2) = v0 & ( ~ (v1 = 0) | % 22.68/3.85 | ~ (v0 = 0) | v2 = 0)) % 22.68/3.85 | % 22.68/3.85 | GROUND_INST: instantiating (mMNeg) with xS, all_45_2, all_45_2, all_45_0, % 22.68/3.85 | simplifying with (6), (16), (17), (37) gives: % 22.68/3.85 | (47) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 22.68/3.85 | : ? [v5: $i] : (smndt0(v4) = v5 & smndt0(all_45_2) = v2 & % 22.68/3.85 | sdtasdt0(xS, v2) = v3 & sdtasdt0(xS, all_45_2) = v4 & % 22.68/3.85 | aScalar0(all_45_2) = v1 & aScalar0(xS) = v0 & $i(v5) & $i(v4) & % 22.68/3.85 | $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v5 = all_45_0 & v3 = % 22.68/3.85 | all_45_0))) % 22.68/3.85 | % 22.68/3.85 | GROUND_INST: instantiating (mMNeg) with xS, xR, all_45_2, all_45_1, % 22.68/3.85 | simplifying with (5), (6), (15), (17) gives: % 22.68/3.85 | (48) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 22.68/3.85 | : ? [v5: $i] : (smndt0(v4) = v5 & smndt0(xR) = v2 & sdtasdt0(xS, v2) % 22.68/3.85 | = v3 & sdtasdt0(xS, xR) = v4 & aScalar0(xS) = v0 & aScalar0(xR) = v1 % 22.68/3.85 | & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | % 22.68/3.85 | (v5 = all_45_1 & v3 = all_45_1))) % 22.68/3.85 | % 22.68/3.85 | GROUND_INST: instantiating (mNegSc) with xS, all_45_2, simplifying with (6), % 22.68/3.85 | (17) gives: % 22.68/3.85 | (49) ? [v0: any] : ? [v1: any] : (aScalar0(all_45_2) = v1 & aScalar0(xS) % 22.68/3.85 | = v0 & ( ~ (v0 = 0) | v1 = 0)) % 22.68/3.85 | % 22.68/3.85 | DELTA: instantiating (45) with fresh symbols all_86_0, all_86_1 gives: % 22.68/3.85 | (50) sdtlseqdt0(sz0z00, all_45_0) = all_86_0 & aScalar0(all_45_2) = % 22.68/3.85 | all_86_1 & ( ~ (all_86_1 = 0) | all_86_0 = 0) % 22.68/3.85 | % 22.68/3.85 | ALPHA: (50) implies: % 22.68/3.85 | (51) aScalar0(all_45_2) = all_86_1 % 22.68/3.85 | % 22.68/3.85 | DELTA: instantiating (49) with fresh symbols all_102_0, all_102_1 gives: % 22.68/3.85 | (52) aScalar0(all_45_2) = all_102_0 & aScalar0(xS) = all_102_1 & ( ~ % 22.68/3.85 | (all_102_1 = 0) | all_102_0 = 0) % 22.68/3.85 | % 22.68/3.85 | ALPHA: (52) implies: % 22.68/3.86 | (53) aScalar0(xS) = all_102_1 % 22.68/3.86 | (54) aScalar0(all_45_2) = all_102_0 % 22.68/3.86 | (55) ~ (all_102_1 = 0) | all_102_0 = 0 % 22.68/3.86 | % 22.68/3.86 | DELTA: instantiating (41) with fresh symbols all_110_0, all_110_1, all_110_2 % 22.68/3.86 | gives: % 22.68/3.86 | (56) aScalar0(all_45_0) = all_110_0 & aScalar0(xS) = all_110_1 & % 22.68/3.86 | aScalar0(xS) = all_110_2 & ( ~ (all_110_1 = 0) | ~ (all_110_2 = 0) | % 22.68/3.86 | all_110_0 = 0) % 22.68/3.86 | % 22.68/3.86 | ALPHA: (56) implies: % 22.68/3.86 | (57) aScalar0(xS) = all_110_2 % 22.68/3.86 | (58) aScalar0(xS) = all_110_1 % 22.68/3.86 | % 22.68/3.86 | DELTA: instantiating (46) with fresh symbols all_132_0, all_132_1, all_132_2 % 22.68/3.86 | gives: % 22.68/3.86 | (59) aScalar0(all_45_0) = all_132_0 & aScalar0(all_45_2) = all_132_1 & % 22.68/3.86 | aScalar0(all_45_2) = all_132_2 & ( ~ (all_132_1 = 0) | ~ (all_132_2 = % 22.68/3.86 | 0) | all_132_0 = 0) % 22.68/3.86 | % 22.68/3.86 | ALPHA: (59) implies: % 22.68/3.86 | (60) aScalar0(all_45_2) = all_132_2 % 22.68/3.86 | (61) aScalar0(all_45_2) = all_132_1 % 22.68/3.86 | % 22.68/3.86 | DELTA: instantiating (42) with fresh symbols all_134_0, all_134_1, all_134_2 % 22.68/3.86 | gives: % 22.68/3.86 | (62) aScalar0(all_45_1) = all_134_0 & aScalar0(all_45_2) = all_134_2 & % 22.68/3.86 | aScalar0(xR) = all_134_1 & ( ~ (all_134_1 = 0) | ~ (all_134_2 = 0) | % 22.68/3.86 | all_134_0 = 0) % 22.68/3.86 | % 22.68/3.86 | ALPHA: (62) implies: % 22.68/3.86 | (63) aScalar0(all_45_2) = all_134_2 % 22.68/3.86 | % 22.68/3.86 | DELTA: instantiating (40) with fresh symbols all_136_0, all_136_1, all_136_2 % 22.68/3.86 | gives: % 22.68/3.86 | (64) aScalar0(all_45_1) = all_136_0 & aScalar0(all_45_2) = all_136_1 & % 22.68/3.86 | aScalar0(xR) = all_136_2 & ( ~ (all_136_1 = 0) | ~ (all_136_2 = 0) | % 22.68/3.86 | all_136_0 = 0) % 22.68/3.86 | % 22.68/3.86 | ALPHA: (64) implies: % 22.68/3.86 | (65) aScalar0(all_45_2) = all_136_1 % 22.68/3.86 | % 22.68/3.86 | DELTA: instantiating (38) with fresh symbols all_138_0, all_138_1, all_138_2 % 22.68/3.86 | gives: % 22.68/3.86 | (66) aScalar0(all_53_7) = all_138_0 & aScalar0(all_45_2) = all_138_1 & % 22.68/3.86 | aScalar0(xR) = all_138_2 & ( ~ (all_138_1 = 0) | ~ (all_138_2 = 0) | % 22.68/3.86 | all_138_0 = 0) % 22.68/3.86 | % 22.68/3.86 | ALPHA: (66) implies: % 22.68/3.86 | (67) aScalar0(all_45_2) = all_138_1 % 22.68/3.86 | % 22.68/3.86 | DELTA: instantiating (48) with fresh symbols all_140_0, all_140_1, all_140_2, % 22.68/3.86 | all_140_3, all_140_4, all_140_5 gives: % 22.68/3.86 | (68) smndt0(all_140_1) = all_140_0 & smndt0(xR) = all_140_3 & sdtasdt0(xS, % 22.68/3.86 | all_140_3) = all_140_2 & sdtasdt0(xS, xR) = all_140_1 & aScalar0(xS) % 22.68/3.86 | = all_140_5 & aScalar0(xR) = all_140_4 & $i(all_140_0) & $i(all_140_1) % 22.68/3.86 | & $i(all_140_2) & $i(all_140_3) & ( ~ (all_140_4 = 0) | ~ (all_140_5 % 22.68/3.86 | = 0) | (all_140_0 = all_45_1 & all_140_2 = all_45_1)) % 22.68/3.86 | % 22.68/3.86 | ALPHA: (68) implies: % 22.68/3.86 | (69) aScalar0(xS) = all_140_5 % 22.68/3.86 | % 22.68/3.86 | DELTA: instantiating (47) with fresh symbols all_142_0, all_142_1, all_142_2, % 22.68/3.86 | all_142_3, all_142_4, all_142_5 gives: % 22.68/3.86 | (70) smndt0(all_142_1) = all_142_0 & smndt0(all_45_2) = all_142_3 & % 22.68/3.86 | sdtasdt0(xS, all_142_3) = all_142_2 & sdtasdt0(xS, all_45_2) = % 22.68/3.86 | all_142_1 & aScalar0(all_45_2) = all_142_4 & aScalar0(xS) = all_142_5 % 22.68/3.86 | & $i(all_142_0) & $i(all_142_1) & $i(all_142_2) & $i(all_142_3) & ( ~ % 22.68/3.86 | (all_142_4 = 0) | ~ (all_142_5 = 0) | (all_142_0 = all_45_0 & % 22.68/3.86 | all_142_2 = all_45_0)) % 22.68/3.86 | % 22.68/3.86 | ALPHA: (70) implies: % 22.68/3.86 | (71) aScalar0(xS) = all_142_5 % 22.68/3.86 | (72) aScalar0(all_45_2) = all_142_4 % 22.68/3.86 | % 22.68/3.86 | DELTA: instantiating (43) with fresh symbols all_144_0, all_144_1, all_144_2, % 22.68/3.86 | all_144_3, all_144_4, all_144_5, all_144_6 gives: % 22.68/3.86 | (73) sdtasdt0(all_144_2, all_144_1) = all_144_0 & sdtpldt0(xR, all_45_2) = % 22.68/3.86 | all_144_1 & sdtpldt0(xR, all_45_2) = all_144_2 & aScalar0(all_45_2) = % 22.68/3.86 | all_144_3 & aScalar0(all_45_2) = all_144_5 & aScalar0(xR) = all_144_4 % 22.68/3.86 | & aScalar0(xR) = all_144_6 & $i(all_144_0) & $i(all_144_1) & % 22.68/3.86 | $i(all_144_2) & ( ~ (all_144_3 = 0) | ~ (all_144_4 = 0) | ~ % 22.68/3.86 | (all_144_5 = 0) | ~ (all_144_6 = 0) | all_144_0 = all_53_0) % 22.68/3.86 | % 22.68/3.86 | ALPHA: (73) implies: % 22.68/3.86 | (74) aScalar0(xR) = all_144_6 % 22.68/3.86 | (75) aScalar0(xR) = all_144_4 % 22.68/3.86 | (76) aScalar0(all_45_2) = all_144_5 % 22.68/3.86 | (77) aScalar0(all_45_2) = all_144_3 % 22.68/3.86 | (78) sdtpldt0(xR, all_45_2) = all_144_2 % 22.68/3.86 | (79) sdtpldt0(xR, all_45_2) = all_144_1 % 22.68/3.86 | (80) sdtasdt0(all_144_2, all_144_1) = all_144_0 % 22.68/3.86 | (81) ~ (all_144_3 = 0) | ~ (all_144_4 = 0) | ~ (all_144_5 = 0) | ~ % 22.68/3.86 | (all_144_6 = 0) | all_144_0 = all_53_0 % 22.68/3.86 | % 22.68/3.86 | DELTA: instantiating (39) with fresh symbols all_150_0, all_150_1, all_150_2, % 22.68/3.86 | all_150_3, all_150_4, all_150_5, all_150_6, all_150_7, all_150_8 gives: % 22.68/3.87 | (82) sdtasdt0(all_150_3, all_45_2) = all_150_2 & sdtasdt0(xR, all_150_5) = % 22.68/3.87 | all_150_4 & sdtasdt0(xR, all_45_2) = all_150_1 & sdtpldt0(all_45_1, % 22.68/3.87 | all_150_1) = all_150_0 & sdtpldt0(xR, all_45_2) = all_150_5 & % 22.68/3.87 | sdtpldt0(xR, xR) = all_150_3 & aScalar0(all_45_2) = all_150_6 & % 22.68/3.87 | aScalar0(xR) = all_150_7 & aScalar0(xR) = all_150_8 & $i(all_150_0) & % 22.68/3.87 | $i(all_150_1) & $i(all_150_2) & $i(all_150_3) & $i(all_150_4) & % 22.68/3.87 | $i(all_150_5) & ( ~ (all_150_6 = 0) | ~ (all_150_7 = 0) | ~ % 22.68/3.87 | (all_150_8 = 0) | (all_150_0 = all_150_2 & all_150_4 = all_53_3)) % 22.68/3.87 | % 22.68/3.87 | ALPHA: (82) implies: % 22.68/3.87 | (83) aScalar0(xR) = all_150_8 % 22.68/3.87 | (84) aScalar0(xR) = all_150_7 % 22.68/3.87 | (85) aScalar0(all_45_2) = all_150_6 % 22.68/3.87 | (86) sdtpldt0(xR, all_45_2) = all_150_5 % 22.68/3.87 | % 22.68/3.87 | DELTA: instantiating (44) with fresh symbols all_152_0, all_152_1, all_152_2, % 22.68/3.87 | all_152_3, all_152_4, all_152_5, all_152_6, all_152_7, all_152_8 gives: % 22.68/3.87 | (87) sdtasdt0(all_152_3, all_45_2) = all_152_2 & sdtasdt0(all_45_2, % 22.68/3.87 | all_152_5) = all_152_4 & sdtasdt0(xR, all_45_2) = all_152_1 & % 22.68/3.87 | sdtpldt0(all_45_0, all_152_1) = all_152_0 & sdtpldt0(all_45_2, xR) = % 22.68/3.87 | all_152_3 & sdtpldt0(xR, all_45_2) = all_152_5 & aScalar0(all_45_2) = % 22.68/3.87 | all_152_6 & aScalar0(all_45_2) = all_152_8 & aScalar0(xR) = all_152_7 % 22.68/3.87 | & $i(all_152_0) & $i(all_152_1) & $i(all_152_2) & $i(all_152_3) & % 22.68/3.87 | $i(all_152_4) & $i(all_152_5) & ( ~ (all_152_6 = 0) | ~ (all_152_7 = % 22.68/3.87 | 0) | ~ (all_152_8 = 0) | (all_152_0 = all_152_2 & all_152_4 = % 22.68/3.87 | all_53_1)) % 22.68/3.87 | % 22.68/3.87 | ALPHA: (87) implies: % 22.68/3.87 | (88) aScalar0(xR) = all_152_7 % 22.68/3.87 | (89) aScalar0(all_45_2) = all_152_8 % 22.68/3.87 | (90) aScalar0(all_45_2) = all_152_6 % 22.68/3.87 | (91) sdtpldt0(xR, all_45_2) = all_152_5 % 22.68/3.87 | % 22.68/3.87 | GROUND_INST: instantiating (8) with 0, all_144_4, xR, simplifying with (2), % 22.68/3.87 | (75) gives: % 22.68/3.87 | (92) all_144_4 = 0 % 22.68/3.87 | % 22.68/3.87 | GROUND_INST: instantiating (8) with all_144_4, all_150_8, xR, simplifying with % 22.68/3.87 | (75), (83) gives: % 22.68/3.87 | (93) all_150_8 = all_144_4 % 22.68/3.87 | % 22.68/3.87 | GROUND_INST: instantiating (8) with all_150_8, all_150_7, xR, simplifying with % 22.68/3.87 | (83), (84) gives: % 22.68/3.87 | (94) all_150_7 = all_150_8 % 22.68/3.87 | % 22.68/3.87 | GROUND_INST: instantiating (8) with all_150_7, all_152_7, xR, simplifying with % 22.68/3.87 | (84), (88) gives: % 22.68/3.87 | (95) all_152_7 = all_150_7 % 22.68/3.87 | % 22.68/3.87 | GROUND_INST: instantiating (8) with all_144_6, all_152_7, xR, simplifying with % 22.68/3.87 | (74), (88) gives: % 22.68/3.87 | (96) all_152_7 = all_144_6 % 22.68/3.87 | % 22.68/3.87 | GROUND_INST: instantiating (8) with 0, all_140_5, xS, simplifying with (3), % 22.68/3.87 | (69) gives: % 22.68/3.87 | (97) all_140_5 = 0 % 22.68/3.87 | % 22.68/3.87 | GROUND_INST: instantiating (8) with all_110_1, all_140_5, xS, simplifying with % 22.68/3.87 | (58), (69) gives: % 22.68/3.87 | (98) all_140_5 = all_110_1 % 22.68/3.87 | % 22.68/3.87 | GROUND_INST: instantiating (8) with all_110_1, all_142_5, xS, simplifying with % 22.68/3.87 | (58), (71) gives: % 22.68/3.87 | (99) all_142_5 = all_110_1 % 22.68/3.87 | % 22.68/3.87 | GROUND_INST: instantiating (8) with all_110_2, all_142_5, xS, simplifying with % 22.68/3.87 | (57), (71) gives: % 22.68/3.87 | (100) all_142_5 = all_110_2 % 22.68/3.87 | % 22.68/3.87 | GROUND_INST: instantiating (8) with all_102_1, all_142_5, xS, simplifying with % 22.68/3.87 | (53), (71) gives: % 22.68/3.87 | (101) all_142_5 = all_102_1 % 22.68/3.87 | % 22.85/3.87 | GROUND_INST: instantiating (8) with all_132_2, all_132_1, all_45_2, % 22.85/3.87 | simplifying with (60), (61) gives: % 22.85/3.87 | (102) all_132_1 = all_132_2 % 22.85/3.87 | % 22.85/3.87 | GROUND_INST: instantiating (8) with all_132_1, all_134_2, all_45_2, % 22.85/3.87 | simplifying with (61), (63) gives: % 22.85/3.87 | (103) all_134_2 = all_132_1 % 22.85/3.87 | % 22.85/3.87 | GROUND_INST: instantiating (8) with all_134_2, all_138_1, all_45_2, % 22.85/3.87 | simplifying with (63), (67) gives: % 22.85/3.87 | (104) all_138_1 = all_134_2 % 22.85/3.87 | % 22.85/3.87 | GROUND_INST: instantiating (8) with all_132_2, all_142_4, all_45_2, % 22.85/3.87 | simplifying with (60), (72) gives: % 22.85/3.87 | (105) all_142_4 = all_132_2 % 22.85/3.87 | % 22.85/3.87 | GROUND_INST: instantiating (8) with all_86_1, all_142_4, all_45_2, simplifying % 22.85/3.87 | with (51), (72) gives: % 22.85/3.87 | (106) all_142_4 = all_86_1 % 22.85/3.87 | % 22.85/3.87 | GROUND_INST: instantiating (8) with all_138_1, all_144_5, all_45_2, % 22.85/3.87 | simplifying with (67), (76) gives: % 22.85/3.87 | (107) all_144_5 = all_138_1 % 22.85/3.87 | % 22.85/3.87 | GROUND_INST: instantiating (8) with all_138_1, all_150_6, all_45_2, % 22.85/3.87 | simplifying with (67), (85) gives: % 22.85/3.87 | (108) all_150_6 = all_138_1 % 22.85/3.87 | % 22.85/3.87 | GROUND_INST: instantiating (8) with all_136_1, all_150_6, all_45_2, % 22.85/3.87 | simplifying with (65), (85) gives: % 22.85/3.87 | (109) all_150_6 = all_136_1 % 22.85/3.87 | % 22.85/3.87 | GROUND_INST: instantiating (8) with all_144_5, all_152_8, all_45_2, % 22.85/3.87 | simplifying with (76), (89) gives: % 22.85/3.87 | (110) all_152_8 = all_144_5 % 22.85/3.87 | % 22.85/3.87 | GROUND_INST: instantiating (8) with all_102_0, all_152_8, all_45_2, % 22.85/3.87 | simplifying with (54), (89) gives: % 22.85/3.87 | (111) all_152_8 = all_102_0 % 22.85/3.87 | % 22.85/3.87 | GROUND_INST: instantiating (8) with all_150_6, all_152_6, all_45_2, % 22.85/3.87 | simplifying with (85), (90) gives: % 22.85/3.87 | (112) all_152_6 = all_150_6 % 22.85/3.87 | % 22.85/3.87 | GROUND_INST: instantiating (8) with all_144_3, all_152_6, all_45_2, % 22.85/3.87 | simplifying with (77), (90) gives: % 22.85/3.87 | (113) all_152_6 = all_144_3 % 22.85/3.87 | % 22.85/3.87 | GROUND_INST: instantiating (10) with all_144_2, all_144_1, all_45_2, xR, % 22.85/3.87 | simplifying with (78), (79) gives: % 22.85/3.87 | (114) all_144_1 = all_144_2 % 22.85/3.87 | % 22.85/3.88 | GROUND_INST: instantiating (10) with all_144_1, all_150_5, all_45_2, xR, % 22.85/3.88 | simplifying with (79), (86) gives: % 22.85/3.88 | (115) all_150_5 = all_144_1 % 22.85/3.88 | % 22.85/3.88 | GROUND_INST: instantiating (10) with all_53_7, all_152_5, all_45_2, xR, % 22.85/3.88 | simplifying with (36), (91) gives: % 22.85/3.88 | (116) all_152_5 = all_53_7 % 22.85/3.88 | % 22.85/3.88 | GROUND_INST: instantiating (10) with all_150_5, all_152_5, all_45_2, xR, % 22.85/3.88 | simplifying with (86), (91) gives: % 22.85/3.88 | (117) all_152_5 = all_150_5 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (116), (117) imply: % 22.85/3.88 | (118) all_150_5 = all_53_7 % 22.85/3.88 | % 22.85/3.88 | SIMP: (118) implies: % 22.85/3.88 | (119) all_150_5 = all_53_7 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (112), (113) imply: % 22.85/3.88 | (120) all_150_6 = all_144_3 % 22.85/3.88 | % 22.85/3.88 | SIMP: (120) implies: % 22.85/3.88 | (121) all_150_6 = all_144_3 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (95), (96) imply: % 22.85/3.88 | (122) all_150_7 = all_144_6 % 22.85/3.88 | % 22.85/3.88 | SIMP: (122) implies: % 22.85/3.88 | (123) all_150_7 = all_144_6 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (110), (111) imply: % 22.85/3.88 | (124) all_144_5 = all_102_0 % 22.85/3.88 | % 22.85/3.88 | SIMP: (124) implies: % 22.85/3.88 | (125) all_144_5 = all_102_0 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (115), (119) imply: % 22.85/3.88 | (126) all_144_1 = all_53_7 % 22.85/3.88 | % 22.85/3.88 | SIMP: (126) implies: % 22.85/3.88 | (127) all_144_1 = all_53_7 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (108), (121) imply: % 22.85/3.88 | (128) all_144_3 = all_138_1 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (109), (121) imply: % 22.85/3.88 | (129) all_144_3 = all_136_1 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (94), (123) imply: % 22.85/3.88 | (130) all_150_8 = all_144_6 % 22.85/3.88 | % 22.85/3.88 | SIMP: (130) implies: % 22.85/3.88 | (131) all_150_8 = all_144_6 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (93), (131) imply: % 22.85/3.88 | (132) all_144_4 = all_144_6 % 22.85/3.88 | % 22.85/3.88 | SIMP: (132) implies: % 22.85/3.88 | (133) all_144_4 = all_144_6 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (114), (127) imply: % 22.85/3.88 | (134) all_144_2 = all_53_7 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (128), (129) imply: % 22.85/3.88 | (135) all_138_1 = all_136_1 % 22.85/3.88 | % 22.85/3.88 | SIMP: (135) implies: % 22.85/3.88 | (136) all_138_1 = all_136_1 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (92), (133) imply: % 22.85/3.88 | (137) all_144_6 = 0 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (107), (125) imply: % 22.85/3.88 | (138) all_138_1 = all_102_0 % 22.85/3.88 | % 22.85/3.88 | SIMP: (138) implies: % 22.85/3.88 | (139) all_138_1 = all_102_0 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (105), (106) imply: % 22.85/3.88 | (140) all_132_2 = all_86_1 % 22.85/3.88 | % 22.85/3.88 | SIMP: (140) implies: % 22.85/3.88 | (141) all_132_2 = all_86_1 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (99), (100) imply: % 22.85/3.88 | (142) all_110_1 = all_110_2 % 22.85/3.88 | % 22.85/3.88 | SIMP: (142) implies: % 22.85/3.88 | (143) all_110_1 = all_110_2 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (100), (101) imply: % 22.85/3.88 | (144) all_110_2 = all_102_1 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (97), (98) imply: % 22.85/3.88 | (145) all_110_1 = 0 % 22.85/3.88 | % 22.85/3.88 | SIMP: (145) implies: % 22.85/3.88 | (146) all_110_1 = 0 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (104), (136) imply: % 22.85/3.88 | (147) all_136_1 = all_134_2 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (136), (139) imply: % 22.85/3.88 | (148) all_136_1 = all_102_0 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (147), (148) imply: % 22.85/3.88 | (149) all_134_2 = all_102_0 % 22.85/3.88 | % 22.85/3.88 | SIMP: (149) implies: % 22.85/3.88 | (150) all_134_2 = all_102_0 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (103), (150) imply: % 22.85/3.88 | (151) all_132_1 = all_102_0 % 22.85/3.88 | % 22.85/3.88 | SIMP: (151) implies: % 22.85/3.88 | (152) all_132_1 = all_102_0 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (102), (152) imply: % 22.85/3.88 | (153) all_132_2 = all_102_0 % 22.85/3.88 | % 22.85/3.88 | SIMP: (153) implies: % 22.85/3.88 | (154) all_132_2 = all_102_0 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (141), (154) imply: % 22.85/3.88 | (155) all_102_0 = all_86_1 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (143), (146) imply: % 22.85/3.88 | (156) all_110_2 = 0 % 22.85/3.88 | % 22.85/3.88 | SIMP: (156) implies: % 22.85/3.88 | (157) all_110_2 = 0 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (144), (157) imply: % 22.85/3.88 | (158) all_102_1 = 0 % 22.85/3.88 | % 22.85/3.88 | SIMP: (158) implies: % 22.85/3.88 | (159) all_102_1 = 0 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (148), (155) imply: % 22.85/3.88 | (160) all_136_1 = all_86_1 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (125), (155) imply: % 22.85/3.88 | (161) all_144_5 = all_86_1 % 22.85/3.88 | % 22.85/3.88 | COMBINE_EQS: (129), (160) imply: % 22.85/3.88 | (162) all_144_3 = all_86_1 % 22.85/3.88 | % 22.85/3.88 | REDUCE: (80), (127), (134) imply: % 22.85/3.88 | (163) sdtasdt0(all_53_7, all_53_7) = all_144_0 % 22.85/3.88 | % 22.85/3.88 | BETA: splitting (55) gives: % 22.85/3.88 | % 22.85/3.88 | Case 1: % 22.85/3.88 | | % 22.85/3.88 | | (164) ~ (all_102_1 = 0) % 22.85/3.88 | | % 22.85/3.88 | | REDUCE: (159), (164) imply: % 22.85/3.88 | | (165) $false % 22.85/3.88 | | % 22.85/3.88 | | CLOSE: (165) is inconsistent. % 22.85/3.88 | | % 22.85/3.88 | Case 2: % 22.85/3.88 | | % 22.85/3.88 | | (166) all_102_0 = 0 % 22.85/3.88 | | % 22.85/3.88 | | COMBINE_EQS: (155), (166) imply: % 22.85/3.88 | | (167) all_86_1 = 0 % 22.85/3.88 | | % 22.85/3.88 | | SIMP: (167) implies: % 22.85/3.88 | | (168) all_86_1 = 0 % 22.85/3.88 | | % 22.85/3.88 | | COMBINE_EQS: (161), (168) imply: % 22.85/3.88 | | (169) all_144_5 = 0 % 22.85/3.88 | | % 22.85/3.88 | | COMBINE_EQS: (162), (168) imply: % 22.85/3.88 | | (170) all_144_3 = 0 % 22.85/3.88 | | % 22.85/3.88 | | BETA: splitting (81) gives: % 22.85/3.88 | | % 22.85/3.88 | | Case 1: % 22.85/3.88 | | | % 22.85/3.88 | | | (171) ~ (all_144_3 = 0) % 22.85/3.88 | | | % 22.85/3.88 | | | REDUCE: (170), (171) imply: % 22.85/3.89 | | | (172) $false % 22.85/3.89 | | | % 22.85/3.89 | | | CLOSE: (172) is inconsistent. % 22.85/3.89 | | | % 22.85/3.89 | | Case 2: % 22.85/3.89 | | | % 22.85/3.89 | | | (173) ~ (all_144_4 = 0) | ~ (all_144_5 = 0) | ~ (all_144_6 = 0) | % 22.85/3.89 | | | all_144_0 = all_53_0 % 22.85/3.89 | | | % 22.85/3.89 | | | BETA: splitting (173) gives: % 22.85/3.89 | | | % 22.85/3.89 | | | Case 1: % 22.85/3.89 | | | | % 22.85/3.89 | | | | (174) ~ (all_144_4 = 0) % 22.85/3.89 | | | | % 22.85/3.89 | | | | REDUCE: (92), (174) imply: % 22.85/3.89 | | | | (175) $false % 22.85/3.89 | | | | % 22.85/3.89 | | | | CLOSE: (175) is inconsistent. % 22.85/3.89 | | | | % 22.85/3.89 | | | Case 2: % 22.85/3.89 | | | | % 22.85/3.89 | | | | (176) ~ (all_144_5 = 0) | ~ (all_144_6 = 0) | all_144_0 = all_53_0 % 22.85/3.89 | | | | % 22.85/3.89 | | | | BETA: splitting (176) gives: % 22.85/3.89 | | | | % 22.85/3.89 | | | | Case 1: % 22.85/3.89 | | | | | % 22.85/3.89 | | | | | (177) ~ (all_144_5 = 0) % 22.85/3.89 | | | | | % 22.85/3.89 | | | | | REDUCE: (169), (177) imply: % 22.85/3.89 | | | | | (178) $false % 22.85/3.89 | | | | | % 22.85/3.89 | | | | | CLOSE: (178) is inconsistent. % 22.85/3.89 | | | | | % 22.85/3.89 | | | | Case 2: % 22.85/3.89 | | | | | % 22.85/3.89 | | | | | (179) ~ (all_144_6 = 0) | all_144_0 = all_53_0 % 22.85/3.89 | | | | | % 22.85/3.89 | | | | | BETA: splitting (179) gives: % 22.85/3.89 | | | | | % 22.85/3.89 | | | | | Case 1: % 22.85/3.89 | | | | | | % 22.85/3.89 | | | | | | (180) ~ (all_144_6 = 0) % 22.85/3.89 | | | | | | % 22.85/3.89 | | | | | | REDUCE: (137), (180) imply: % 22.85/3.89 | | | | | | (181) $false % 22.85/3.89 | | | | | | % 22.85/3.89 | | | | | | CLOSE: (181) is inconsistent. % 22.85/3.89 | | | | | | % 22.85/3.89 | | | | | Case 2: % 22.85/3.89 | | | | | | % 22.85/3.89 | | | | | | (182) all_144_0 = all_53_0 % 22.85/3.89 | | | | | | % 22.85/3.89 | | | | | | REDUCE: (163), (182) imply: % 22.85/3.89 | | | | | | (183) sdtasdt0(all_53_7, all_53_7) = all_53_0 % 22.85/3.89 | | | | | | % 22.85/3.89 | | | | | | GROUND_INST: instantiating (11) with all_53_6, all_53_0, all_53_7, % 22.85/3.89 | | | | | | all_53_7, simplifying with (28), (183) gives: % 22.85/3.89 | | | | | | (184) all_53_0 = all_53_6 % 22.85/3.89 | | | | | | % 22.85/3.89 | | | | | | REDUCE: (20), (184) imply: % 22.85/3.89 | | | | | | (185) $false % 22.85/3.89 | | | | | | % 22.85/3.89 | | | | | | CLOSE: (185) is inconsistent. % 22.85/3.89 | | | | | | % 22.85/3.89 | | | | | End of split % 22.85/3.89 | | | | | % 22.85/3.89 | | | | End of split % 22.85/3.89 | | | | % 22.85/3.89 | | | End of split % 22.85/3.89 | | | % 22.85/3.89 | | End of split % 22.85/3.89 | | % 22.85/3.89 | End of split % 22.85/3.89 | % 22.85/3.89 End of proof % 22.85/3.89 % SZS output end Proof for theBenchmark % 22.85/3.89 % 22.85/3.89 3285ms %------------------------------------------------------------------------------