%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG057+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 : n023.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 13:57:35 EDT 2023 % Result : Theorem 15.12s 2.83s % Output : Proof 24.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : RNG057+1 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n023.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 02:41:41 EDT 2023 % 0.14/0.35 % CPUTime : % 0.64/0.62 ________ _____ % 0.64/0.62 ___ __ \_________(_)________________________________ % 0.64/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.64/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.64/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.64/0.62 % 0.64/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.64/0.62 (2023-06-19) % 0.64/0.62 % 0.64/0.62 (c) Philipp Rümmer, 2009-2023 % 0.64/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.64/0.62 Amanda Stjerna. % 0.64/0.62 Free software under BSD-3-Clause. % 0.64/0.62 % 0.64/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.64/0.62 % 0.64/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.67/0.64 Running up to 7 provers in parallel. % 0.67/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.67/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.67/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.67/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.67/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.67/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.67/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.49/1.26 Prover 1: Preprocessing ... % 3.49/1.26 Prover 4: Preprocessing ... % 3.49/1.30 Prover 6: Preprocessing ... % 3.49/1.30 Prover 2: Preprocessing ... % 3.49/1.30 Prover 0: Preprocessing ... % 3.49/1.30 Prover 3: Preprocessing ... % 3.96/1.31 Prover 5: Preprocessing ... % 8.92/2.05 Prover 1: Constructing countermodel ... % 8.92/2.07 Prover 3: Constructing countermodel ... % 9.60/2.08 Prover 6: Proving ... % 10.68/2.22 Prover 5: Constructing countermodel ... % 11.25/2.38 Prover 4: Constructing countermodel ... % 12.05/2.43 Prover 2: Proving ... % 12.05/2.46 Prover 0: Proving ... % 15.12/2.82 Prover 3: proved (2171ms) % 15.12/2.83 % 15.12/2.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.12/2.83 % 15.12/2.83 Prover 6: stopped % 15.12/2.83 Prover 2: stopped % 15.12/2.83 Prover 5: stopped % 15.12/2.83 Prover 0: stopped % 15.12/2.84 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.12/2.84 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.12/2.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.12/2.84 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.12/2.84 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.77/2.98 Prover 8: Preprocessing ... % 15.77/2.98 Prover 10: Preprocessing ... % 15.77/2.98 Prover 7: Preprocessing ... % 15.77/2.99 Prover 13: Preprocessing ... % 15.77/2.99 Prover 11: Preprocessing ... % 17.32/3.18 Prover 8: Warning: ignoring some quantifiers % 17.32/3.19 Prover 10: Constructing countermodel ... % 17.32/3.20 Prover 8: Constructing countermodel ... % 18.10/3.28 Prover 13: Constructing countermodel ... % 18.10/3.29 Prover 7: Constructing countermodel ... % 21.09/3.60 Prover 11: Constructing countermodel ... % 23.47/3.93 Prover 10: Found proof (size 96) % 23.47/3.93 Prover 10: proved (1097ms) % 23.47/3.93 Prover 4: stopped % 23.47/3.93 Prover 7: stopped % 23.47/3.93 Prover 11: stopped % 23.47/3.93 Prover 13: stopped % 23.47/3.93 Prover 8: stopped % 23.47/3.95 Prover 1: stopped % 23.47/3.95 % 23.47/3.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 23.47/3.95 % 23.89/3.98 % SZS output start Proof for theBenchmark % 23.89/3.99 Assumptions after simplification: % 23.89/3.99 --------------------------------- % 23.89/3.99 % 23.89/3.99 (mDefInit) % 23.89/4.02 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) % 23.89/4.02 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 = % 23.89/4.02 sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0, % 23.89/4.02 v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ $i(v4) | ~ $i(v1) % 23.89/4.02 | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, v4) = v5 & $i(v5))) & ! % 23.89/4.02 [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~ % 23.89/4.02 $i(v3) | ~ aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 23.89/4.02 ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 & % 23.89/4.02 sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) & % 23.89/4.02 aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5 & % 23.89/4.02 $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ % 23.89/4.02 $i(v1) | szszuzczcdt0(v3) = v2) & ! [v3: $i] : ( ~ % 23.89/4.02 (aDimensionOf0(v1) = v3) | ~ $i(v1) | aVector0(v1)))))) % 23.89/4.02 % 23.89/4.02 (mEqInit) % 23.89/4.02 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 23.89/4.02 (sziznziztdt0(v1) = v3) | ~ (sziznziztdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) % 23.89/4.02 | ~ aVector0(v1) | ~ aVector0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: % 23.89/4.02 $i] : ? [v7: $i] : ((v7 = v6 & aDimensionOf0(v3) = v6 & aDimensionOf0(v2) % 23.89/4.02 = v6 & $i(v6)) | (aDimensionOf0(v1) = v5 & $i(v5) & (v5 = sz00 | ( ~ (v5 % 23.89/4.02 = v4) & aDimensionOf0(v0) = v4 & $i(v4)))))) % 23.89/4.02 % 23.89/4.02 (mLEMonM) % 23.89/4.03 $i(sz0z00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 23.89/4.03 $i] : ! [v5: $i] : ( ~ (sdtasdt0(v1, v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) % 23.89/4.03 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v2, v3) | ~ % 23.89/4.03 sdtlseqdt0(v0, v1) | ~ sdtlseqdt0(sz0z00, v2) | ~ aScalar0(v3) | ~ % 23.89/4.03 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(v4, v5)) % 23.89/4.03 % 23.89/4.03 (mLETot) % 23.89/4.03 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ % 23.89/4.03 aScalar0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) % 23.89/4.03 % 23.89/4.03 (mMulSc) % 23.89/4.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 23.89/4.03 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2)) % 23.89/4.03 % 23.89/4.03 (mSqPos) % 23.89/4.03 $i(sz0z00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v0) = v1) | ~ % 23.89/4.03 $i(v0) | ~ aScalar0(v0) | sdtlseqdt0(sz0z00, v1)) % 23.89/4.03 % 23.89/4.03 (m__) % 23.89/4.03 $i(xN) & $i(xP) & ? [v0: $i] : (sdtasdt0(xP, xP) = v0 & $i(v0) & ~ % 23.89/4.03 sdtlseqdt0(v0, xN)) % 23.89/4.03 % 23.89/4.03 (m__1652) % 23.89/4.03 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! % 23.89/4.03 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2) % 23.89/4.03 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~ % 23.89/4.03 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ? % 23.89/4.03 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 & % 23.89/4.03 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) | % 23.89/4.03 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) & % 23.89/4.03 aDimensionOf0(v2) = v7 & $i(v7))))))) % 23.89/4.03 % 23.89/4.03 (m__1678) % 23.89/4.03 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs) % 23.89/4.03 % 23.89/4.03 (m__1678_01) % 23.89/4.03 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = % 23.89/4.03 v0 & $i(v0)) % 23.89/4.03 % 23.89/4.03 (m__1692) % 23.89/4.03 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & % 23.89/4.03 $i(v0)) % 23.89/4.03 % 23.89/4.03 (m__1709) % 23.89/4.03 sziznziztdt0(xs) = xp & $i(xp) & $i(xs) & aVector0(xp) % 23.89/4.03 % 23.89/4.03 (m__1726) % 23.89/4.03 sziznziztdt0(xt) = xq & $i(xq) & $i(xt) & aVector0(xq) % 23.89/4.03 % 23.89/4.03 (m__1746) % 23.89/4.03 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = % 23.89/4.03 v0 & $i(v0) & aScalar0(xA)) % 23.89/4.03 % 23.89/4.03 (m__1766) % 23.89/4.03 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = % 23.89/4.03 v0 & $i(v0) & aScalar0(xB)) % 23.89/4.04 % 23.89/4.04 (m__1783) % 23.89/4.04 sdtasasdt0(xp, xp) = xC & $i(xC) & $i(xp) & aScalar0(xC) % 23.89/4.04 % 23.89/4.04 (m__1800) % 23.89/4.04 sdtasasdt0(xq, xq) = xD & $i(xD) & $i(xq) & aScalar0(xD) % 23.89/4.04 % 23.89/4.04 (m__1820) % 23.89/4.04 sdtasasdt0(xp, xq) = xE & $i(xE) & $i(xq) & $i(xp) & aScalar0(xE) % 23.89/4.04 % 23.89/4.04 (m__1873) % 23.89/4.04 sdtasdt0(xA, xB) = xH & $i(xH) & $i(xB) & $i(xA) & aScalar0(xH) % 23.89/4.04 % 23.89/4.04 (m__1967) % 23.89/4.04 $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xE, xE) = v0 % 23.89/4.04 & sdtasdt0(xC, xD) = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1)) % 23.89/4.04 % 23.89/4.04 (m__2027) % 23.89/4.04 $i(xP) & $i(xH) & $i(xE) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 23.89/4.04 (sdtasdt0(v1, v2) = v0 & sdtasdt0(xP, xP) = v0 & sdtasdt0(xH, xH) = v1 & % 23.89/4.04 sdtasdt0(xE, xE) = v2 & $i(v2) & $i(v1) & $i(v0)) % 23.89/4.04 % 23.89/4.04 (m__2052) % 23.89/4.04 $i(xN) & $i(xH) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(v0, % 23.89/4.04 v1) = xN & sdtasdt0(xH, xH) = v0 & sdtasdt0(xC, xD) = v1 & $i(v1) & % 23.89/4.04 $i(v0)) % 23.89/4.04 % 23.89/4.04 (function-axioms) % 23.89/4.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.89/4.04 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 23.89/4.04 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) % 23.89/4.04 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.89/4.04 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = % 23.89/4.04 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 23.89/4.04 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 23.89/4.04 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ % 23.89/4.04 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 23.89/4.04 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0: % 23.89/4.04 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 23.89/4.04 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.89/4.04 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 23.89/4.04 % 23.89/4.04 Further assumptions not needed in the proof: % 23.89/4.04 -------------------------------------------- % 23.89/4.04 mArith, mDefSPN, mDefSPZ, mDimNat, mDistr, mDistr2, mElmSc, mIH, mIHOrd, mLEASm, % 23.89/4.04 mLEMon, mLERef, mLETrn, mLess, mMDNeg, mMNeg, mNatExtr, mNatSort, mNegSc, % 23.89/4.04 mPosMon, mSZeroSc, mScPr, mScSort, mScSqPos, mScZero, mSqrt, mSuccEqu, mSuccNat, % 23.89/4.04 mSumSc, mVcSort, mZeroNat, m__1837, m__1854, m__1892, m__1911, m__1930, m__1949 % 23.89/4.04 % 23.89/4.04 Those formulas are unsatisfiable: % 23.89/4.04 --------------------------------- % 23.89/4.04 % 23.89/4.04 Begin of proof % 23.89/4.04 | % 23.89/4.04 | ALPHA: (mLEMonM) implies: % 23.89/4.04 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.89/4.04 | ! [v5: $i] : ( ~ (sdtasdt0(v1, v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) | % 23.89/4.04 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v2, v3) % 23.89/4.04 | | ~ sdtlseqdt0(v0, v1) | ~ sdtlseqdt0(sz0z00, v2) | ~ aScalar0(v3) % 23.89/4.04 | | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | % 23.89/4.04 | sdtlseqdt0(v4, v5)) % 23.89/4.04 | % 23.89/4.04 | ALPHA: (mSqPos) implies: % 23.89/4.04 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v0) = v1) | ~ $i(v0) | % 23.89/4.05 | ~ aScalar0(v0) | sdtlseqdt0(sz0z00, v1)) % 23.89/4.05 | % 23.89/4.05 | ALPHA: (mDefInit) implies: % 23.89/4.05 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) | % 23.89/4.05 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 % 23.89/4.05 | = sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 23.89/4.05 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ % 23.89/4.05 | $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, % 23.89/4.05 | v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 = % 23.89/4.05 | v1 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~ % 23.89/4.05 | aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? % 23.89/4.05 | [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 % 23.89/4.05 | & sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) & % 23.89/4.05 | aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) % 23.89/4.05 | = v5 & $i(v5))))) & ! [v3: $i] : ( ~ % 23.89/4.05 | (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2) % 23.89/4.05 | & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) | % 23.89/4.05 | aVector0(v1)))))) % 23.89/4.05 | % 23.89/4.05 | ALPHA: (mEqInit) implies: % 23.89/4.05 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 23.89/4.05 | (sziznziztdt0(v1) = v3) | ~ (sziznziztdt0(v0) = v2) | ~ $i(v1) | ~ % 23.89/4.05 | $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v4: $i] : ? [v5: % 23.89/4.05 | $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v6 & aDimensionOf0(v3) = % 23.89/4.05 | v6 & aDimensionOf0(v2) = v6 & $i(v6)) | (aDimensionOf0(v1) = v5 & % 23.89/4.05 | $i(v5) & (v5 = sz00 | ( ~ (v5 = v4) & aDimensionOf0(v0) = v4 & % 23.89/4.05 | $i(v4)))))) % 23.89/4.05 | % 23.89/4.05 | ALPHA: (m__1678) implies: % 23.89/4.05 | (5) aVector0(xs) % 23.89/4.05 | (6) aVector0(xt) % 23.89/4.05 | % 23.89/4.05 | ALPHA: (m__1652) implies: % 23.89/4.05 | (7) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 23.89/4.05 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, % 23.89/4.05 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) % 23.89/4.05 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) % 23.89/4.05 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 23.89/4.05 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) % 23.89/4.05 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ % 23.89/4.05 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 & % 23.89/4.05 | $i(v7))))))) % 23.89/4.05 | % 23.89/4.05 | ALPHA: (m__1678_01) implies: % 23.89/4.05 | (8) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 & % 23.89/4.05 | $i(v0)) % 23.89/4.05 | % 23.89/4.05 | ALPHA: (m__1692) implies: % 23.89/4.05 | (9) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0)) % 23.89/4.05 | % 23.89/4.05 | ALPHA: (m__1709) implies: % 23.89/4.05 | (10) sziznziztdt0(xs) = xp % 23.89/4.05 | % 23.89/4.05 | ALPHA: (m__1726) implies: % 23.89/4.05 | (11) sziznziztdt0(xt) = xq % 23.89/4.05 | % 23.89/4.05 | ALPHA: (m__1746) implies: % 23.89/4.05 | (12) $i(xs) % 23.89/4.05 | (13) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 & % 23.89/4.05 | $i(v0) & aScalar0(xA)) % 23.89/4.05 | % 23.89/4.05 | ALPHA: (m__1766) implies: % 23.89/4.05 | (14) $i(xt) % 23.89/4.05 | (15) ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = v0 & % 23.89/4.05 | $i(v0) & aScalar0(xB)) % 23.89/4.05 | % 23.89/4.05 | ALPHA: (m__1783) implies: % 23.89/4.05 | (16) aScalar0(xC) % 23.89/4.05 | % 23.89/4.05 | ALPHA: (m__1800) implies: % 23.89/4.05 | (17) aScalar0(xD) % 23.89/4.05 | % 23.89/4.05 | ALPHA: (m__1820) implies: % 23.89/4.05 | (18) aScalar0(xE) % 23.89/4.06 | % 23.89/4.06 | ALPHA: (m__1873) implies: % 23.89/4.06 | (19) aScalar0(xH) % 23.89/4.06 | % 23.89/4.06 | ALPHA: (m__1967) implies: % 23.89/4.06 | (20) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xE, xE) = v0 & sdtasdt0(xC, xD) % 23.89/4.06 | = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1)) % 23.89/4.06 | % 23.89/4.06 | ALPHA: (m__2027) implies: % 23.89/4.06 | (21) $i(xE) % 23.89/4.06 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(v1, v2) = v0 & % 23.89/4.06 | sdtasdt0(xP, xP) = v0 & sdtasdt0(xH, xH) = v1 & sdtasdt0(xE, xE) = % 23.89/4.06 | v2 & $i(v2) & $i(v1) & $i(v0)) % 23.89/4.06 | % 23.89/4.06 | ALPHA: (m__2052) implies: % 23.89/4.06 | (23) $i(xC) % 23.89/4.06 | (24) $i(xD) % 23.89/4.06 | (25) $i(xH) % 23.89/4.06 | (26) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(v0, v1) = xN & sdtasdt0(xH, xH) % 23.89/4.06 | = v0 & sdtasdt0(xC, xD) = v1 & $i(v1) & $i(v0)) % 23.89/4.06 | % 23.89/4.06 | ALPHA: (m__) implies: % 23.89/4.06 | (27) ? [v0: $i] : (sdtasdt0(xP, xP) = v0 & $i(v0) & ~ sdtlseqdt0(v0, xN)) % 23.89/4.06 | % 23.89/4.06 | ALPHA: (function-axioms) implies: % 23.89/4.06 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.89/4.06 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) % 23.89/4.06 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.89/4.06 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 23.89/4.06 | % 23.89/4.06 | DELTA: instantiating (8) with fresh symbol all_33_0 gives: % 23.89/4.06 | (30) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 & % 23.89/4.06 | $i(all_33_0) % 23.89/4.06 | % 23.89/4.06 | ALPHA: (30) implies: % 23.89/4.06 | (31) aDimensionOf0(xs) = all_33_0 % 23.89/4.06 | (32) aDimensionOf0(xt) = all_33_0 % 23.89/4.06 | % 23.89/4.06 | DELTA: instantiating (27) with fresh symbol all_35_0 gives: % 23.89/4.06 | (33) sdtasdt0(xP, xP) = all_35_0 & $i(all_35_0) & ~ sdtlseqdt0(all_35_0, % 23.89/4.06 | xN) % 23.89/4.06 | % 23.89/4.06 | ALPHA: (33) implies: % 23.89/4.06 | (34) ~ sdtlseqdt0(all_35_0, xN) % 23.89/4.06 | (35) sdtasdt0(xP, xP) = all_35_0 % 23.89/4.06 | % 23.89/4.06 | DELTA: instantiating (9) with fresh symbol all_37_0 gives: % 23.89/4.06 | (36) ~ (all_37_0 = sz00) & aDimensionOf0(xs) = all_37_0 & $i(all_37_0) % 23.89/4.06 | % 23.89/4.06 | ALPHA: (36) implies: % 23.89/4.06 | (37) ~ (all_37_0 = sz00) % 23.89/4.06 | (38) aDimensionOf0(xs) = all_37_0 % 23.89/4.06 | % 23.89/4.06 | DELTA: instantiating (15) with fresh symbol all_39_0 gives: % 23.89/4.06 | (39) sdtlbdtrb0(xt, all_39_0) = xB & aDimensionOf0(xt) = all_39_0 & % 23.89/4.06 | $i(all_39_0) & aScalar0(xB) % 23.89/4.06 | % 23.89/4.06 | ALPHA: (39) implies: % 23.89/4.06 | (40) aDimensionOf0(xt) = all_39_0 % 23.89/4.06 | % 23.89/4.06 | DELTA: instantiating (13) with fresh symbol all_41_0 gives: % 23.89/4.06 | (41) sdtlbdtrb0(xs, all_41_0) = xA & aDimensionOf0(xs) = all_41_0 & % 23.89/4.06 | $i(all_41_0) & aScalar0(xA) % 23.89/4.06 | % 23.89/4.06 | ALPHA: (41) implies: % 23.89/4.06 | (42) aDimensionOf0(xs) = all_41_0 % 23.89/4.06 | % 23.89/4.06 | DELTA: instantiating (26) with fresh symbols all_43_0, all_43_1 gives: % 23.89/4.06 | (43) sdtasdt0(all_43_1, all_43_0) = xN & sdtasdt0(xH, xH) = all_43_1 & % 23.89/4.06 | sdtasdt0(xC, xD) = all_43_0 & $i(all_43_0) & $i(all_43_1) % 23.89/4.06 | % 23.89/4.06 | ALPHA: (43) implies: % 23.89/4.06 | (44) sdtasdt0(xC, xD) = all_43_0 % 23.89/4.06 | (45) sdtasdt0(xH, xH) = all_43_1 % 23.89/4.06 | (46) sdtasdt0(all_43_1, all_43_0) = xN % 23.89/4.06 | % 23.89/4.06 | DELTA: instantiating (20) with fresh symbols all_45_0, all_45_1 gives: % 23.89/4.06 | (47) sdtasdt0(xE, xE) = all_45_1 & sdtasdt0(xC, xD) = all_45_0 & % 23.89/4.06 | $i(all_45_0) & $i(all_45_1) & sdtlseqdt0(all_45_1, all_45_0) % 23.89/4.06 | % 23.89/4.06 | ALPHA: (47) implies: % 23.89/4.06 | (48) sdtlseqdt0(all_45_1, all_45_0) % 23.89/4.06 | (49) $i(all_45_0) % 23.89/4.07 | (50) sdtasdt0(xC, xD) = all_45_0 % 23.89/4.07 | (51) sdtasdt0(xE, xE) = all_45_1 % 23.89/4.07 | % 23.89/4.07 | DELTA: instantiating (22) with fresh symbols all_47_0, all_47_1, all_47_2 % 23.89/4.07 | gives: % 23.89/4.07 | (52) sdtasdt0(all_47_1, all_47_0) = all_47_2 & sdtasdt0(xP, xP) = all_47_2 % 23.89/4.07 | & sdtasdt0(xH, xH) = all_47_1 & sdtasdt0(xE, xE) = all_47_0 & % 23.89/4.07 | $i(all_47_0) & $i(all_47_1) & $i(all_47_2) % 23.89/4.07 | % 23.89/4.07 | ALPHA: (52) implies: % 23.89/4.07 | (53) $i(all_47_1) % 23.89/4.07 | (54) $i(all_47_0) % 23.89/4.07 | (55) sdtasdt0(xE, xE) = all_47_0 % 23.89/4.07 | (56) sdtasdt0(xH, xH) = all_47_1 % 23.89/4.07 | (57) sdtasdt0(xP, xP) = all_47_2 % 23.89/4.07 | (58) sdtasdt0(all_47_1, all_47_0) = all_47_2 % 23.89/4.07 | % 23.89/4.07 | DELTA: instantiating (7) with fresh symbol all_49_0 gives: % 23.89/4.07 | (59) aDimensionOf0(xs) = all_49_0 & $i(all_49_0) & ! [v0: $i] : ! [v1: % 23.89/4.07 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1, % 23.89/4.07 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3) % 23.89/4.07 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) % 23.89/4.07 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 23.89/4.07 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7) % 23.89/4.07 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~ % 23.89/4.07 | iLess0(v5, all_49_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6 % 23.89/4.07 | & $i(v6)))))) % 23.89/4.07 | % 23.89/4.07 | ALPHA: (59) implies: % 23.89/4.07 | (60) aDimensionOf0(xs) = all_49_0 % 23.89/4.07 | % 23.89/4.07 | GROUND_INST: instantiating (29) with all_43_0, all_45_0, xD, xC, simplifying % 23.89/4.07 | with (44), (50) gives: % 23.89/4.07 | (61) all_45_0 = all_43_0 % 23.89/4.07 | % 23.89/4.07 | GROUND_INST: instantiating (29) with all_45_1, all_47_0, xE, xE, simplifying % 23.89/4.07 | with (51), (55) gives: % 23.89/4.07 | (62) all_47_0 = all_45_1 % 23.89/4.07 | % 23.89/4.07 | GROUND_INST: instantiating (29) with all_43_1, all_47_1, xH, xH, simplifying % 23.89/4.07 | with (45), (56) gives: % 23.89/4.07 | (63) all_47_1 = all_43_1 % 23.89/4.07 | % 23.89/4.07 | GROUND_INST: instantiating (29) with all_35_0, all_47_2, xP, xP, simplifying % 23.89/4.07 | with (35), (57) gives: % 23.89/4.07 | (64) all_47_2 = all_35_0 % 23.89/4.07 | % 23.89/4.07 | GROUND_INST: instantiating (28) with all_37_0, all_41_0, xs, simplifying with % 23.89/4.07 | (38), (42) gives: % 23.89/4.07 | (65) all_41_0 = all_37_0 % 23.89/4.07 | % 23.89/4.07 | GROUND_INST: instantiating (28) with all_41_0, all_49_0, xs, simplifying with % 23.89/4.07 | (42), (60) gives: % 23.89/4.07 | (66) all_49_0 = all_41_0 % 23.89/4.07 | % 23.89/4.07 | GROUND_INST: instantiating (28) with all_33_0, all_49_0, xs, simplifying with % 23.89/4.07 | (31), (60) gives: % 23.89/4.07 | (67) all_49_0 = all_33_0 % 23.89/4.07 | % 23.89/4.07 | GROUND_INST: instantiating (28) with all_33_0, all_39_0, xt, simplifying with % 23.89/4.07 | (32), (40) gives: % 23.89/4.07 | (68) all_39_0 = all_33_0 % 23.89/4.07 | % 23.89/4.07 | COMBINE_EQS: (66), (67) imply: % 23.89/4.07 | (69) all_41_0 = all_33_0 % 23.89/4.07 | % 23.89/4.07 | SIMP: (69) implies: % 23.89/4.07 | (70) all_41_0 = all_33_0 % 23.89/4.07 | % 23.89/4.07 | COMBINE_EQS: (65), (70) imply: % 23.89/4.07 | (71) all_37_0 = all_33_0 % 23.89/4.07 | % 23.89/4.07 | REDUCE: (37), (71) imply: % 23.89/4.07 | (72) ~ (all_33_0 = sz00) % 23.89/4.07 | % 23.89/4.07 | REDUCE: (58), (62), (63), (64) imply: % 23.89/4.07 | (73) sdtasdt0(all_43_1, all_45_1) = all_35_0 % 23.89/4.07 | % 23.89/4.07 | REDUCE: (54), (62) imply: % 23.89/4.07 | (74) $i(all_45_1) % 23.89/4.07 | % 23.89/4.07 | REDUCE: (53), (63) imply: % 23.89/4.07 | (75) $i(all_43_1) % 23.89/4.07 | % 23.89/4.07 | REDUCE: (49), (61) imply: % 23.89/4.07 | (76) $i(all_43_0) % 23.89/4.07 | % 23.89/4.07 | REDUCE: (48), (61) imply: % 23.89/4.07 | (77) sdtlseqdt0(all_45_1, all_43_0) % 23.89/4.07 | % 23.89/4.08 | GROUND_INST: instantiating (mMulSc) with xC, xD, all_43_0, simplifying with % 23.89/4.08 | (16), (17), (23), (24), (44) gives: % 23.89/4.08 | (78) aScalar0(all_43_0) % 23.89/4.08 | % 23.89/4.08 | GROUND_INST: instantiating (mMulSc) with xE, xE, all_45_1, simplifying with % 23.89/4.08 | (18), (21), (51) gives: % 23.89/4.08 | (79) aScalar0(all_45_1) % 23.89/4.08 | % 23.89/4.08 | GROUND_INST: instantiating (2) with xE, all_45_1, simplifying with (18), (21), % 23.89/4.08 | (51) gives: % 23.89/4.08 | (80) sdtlseqdt0(sz0z00, all_45_1) % 23.89/4.08 | % 23.89/4.08 | GROUND_INST: instantiating (mMulSc) with xH, xH, all_43_1, simplifying with % 24.37/4.08 | (19), (25), (45) gives: % 24.37/4.08 | (81) aScalar0(all_43_1) % 24.37/4.08 | % 24.37/4.08 | GROUND_INST: instantiating (3) with xs, xp, simplifying with (5), (10), (12) % 24.37/4.08 | gives: % 24.37/4.08 | (82) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & (v0 = sz00 | ( ! [v1: % 24.37/4.08 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xs, v2) = % 24.37/4.08 | v3) | ~ (aDimensionOf0(xp) = v1) | ~ $i(v2) | ~ $i(xp) | % 24.37/4.08 | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xp, v2) = v3 & $i(v3))) & % 24.37/4.08 | ! [v1: $i] : ! [v2: $i] : (v1 = xp | ~ (aDimensionOf0(v1) = % 24.37/4.08 | v2) | ~ $i(v1) | ~ aVector0(v1) | ? [v3: $i] : ? [v4: % 24.37/4.08 | $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4) & (( ~ (v6 = v5) & % 24.37/4.08 | sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xs, v4) = v6 & % 24.37/4.08 | $i(v6) & $i(v5) & aNaturalNumber0(v4)) | ( ~ (v3 = v0) & % 24.37/4.08 | szszuzczcdt0(v2) = v3 & $i(v3))))) & ! [v1: $i] : ( ~ % 24.37/4.08 | (aDimensionOf0(xp) = v1) | ~ $i(xp) | szszuzczcdt0(v1) = v0) % 24.37/4.08 | & ! [v1: $i] : ( ~ (aDimensionOf0(xp) = v1) | ~ $i(xp) | % 24.37/4.08 | aVector0(xp))))) % 24.37/4.08 | % 24.37/4.08 | GROUND_INST: instantiating (4) with xt, xs, xq, xp, simplifying with (5), (6), % 24.37/4.08 | (10), (11), (12), (14) gives: % 24.37/4.08 | (83) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 & % 24.37/4.08 | aDimensionOf0(xq) = v2 & aDimensionOf0(xp) = v2 & $i(v2)) | % 24.37/4.08 | (aDimensionOf0(xs) = v1 & $i(v1) & (v1 = sz00 | ( ~ (v1 = v0) & % 24.37/4.08 | aDimensionOf0(xt) = v0 & $i(v0))))) % 24.37/4.08 | % 24.37/4.08 | GROUND_INST: instantiating (3) with xt, xq, simplifying with (6), (11), (14) % 24.37/4.08 | gives: % 24.37/4.08 | (84) ? [v0: $i] : (aDimensionOf0(xt) = v0 & $i(v0) & (v0 = sz00 | ( ! [v1: % 24.37/4.08 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xt, v2) = % 24.37/4.08 | v3) | ~ (aDimensionOf0(xq) = v1) | ~ $i(v2) | ~ $i(xq) | % 24.37/4.08 | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xq, v2) = v3 & $i(v3))) & % 24.37/4.08 | ! [v1: $i] : ! [v2: $i] : (v1 = xq | ~ (aDimensionOf0(v1) = % 24.37/4.08 | v2) | ~ $i(v1) | ~ aVector0(v1) | ? [v3: $i] : ? [v4: % 24.37/4.08 | $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4) & (( ~ (v6 = v5) & % 24.37/4.08 | sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xt, v4) = v6 & % 24.37/4.08 | $i(v6) & $i(v5) & aNaturalNumber0(v4)) | ( ~ (v3 = v0) & % 24.37/4.08 | szszuzczcdt0(v2) = v3 & $i(v3))))) & ! [v1: $i] : ( ~ % 24.37/4.08 | (aDimensionOf0(xq) = v1) | ~ $i(xq) | szszuzczcdt0(v1) = v0) % 24.37/4.08 | & ! [v1: $i] : ( ~ (aDimensionOf0(xq) = v1) | ~ $i(xq) | % 24.37/4.08 | aVector0(xq))))) % 24.37/4.08 | % 24.37/4.08 | DELTA: instantiating (83) with fresh symbols all_67_0, all_67_1, all_67_2, % 24.37/4.08 | all_67_3 gives: % 24.37/4.08 | (85) (all_67_0 = all_67_1 & aDimensionOf0(xq) = all_67_1 & % 24.37/4.08 | aDimensionOf0(xp) = all_67_1 & $i(all_67_1)) | (aDimensionOf0(xs) = % 24.37/4.08 | all_67_2 & $i(all_67_2) & (all_67_2 = sz00 | ( ~ (all_67_2 = % 24.37/4.08 | all_67_3) & aDimensionOf0(xt) = all_67_3 & $i(all_67_3)))) % 24.37/4.08 | % 24.37/4.08 | DELTA: instantiating (84) with fresh symbol all_70_0 gives: % 24.37/4.09 | (86) aDimensionOf0(xt) = all_70_0 & $i(all_70_0) & (all_70_0 = sz00 | ( ! % 24.37/4.09 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xt, v1) = % 24.37/4.09 | v2) | ~ (aDimensionOf0(xq) = v0) | ~ $i(v1) | ~ $i(xq) | ~ % 24.37/4.09 | aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1) = v2 & $i(v2))) & ! % 24.37/4.09 | [v0: $i] : ! [v1: $i] : (v0 = xq | ~ (aDimensionOf0(v0) = v1) | % 24.37/4.09 | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ? % 24.37/4.09 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) & % 24.37/4.09 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) = v5 & $i(v5) % 24.37/4.09 | & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 = all_70_0) & % 24.37/4.09 | szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: $i] : ( ~ % 24.37/4.09 | (aDimensionOf0(xq) = v0) | ~ $i(xq) | szszuzczcdt0(v0) = % 24.37/4.09 | all_70_0) & ! [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ % 24.37/4.09 | $i(xq) | aVector0(xq)))) % 24.37/4.09 | % 24.37/4.09 | ALPHA: (86) implies: % 24.37/4.09 | (87) aDimensionOf0(xt) = all_70_0 % 24.37/4.09 | % 24.37/4.09 | DELTA: instantiating (82) with fresh symbol all_72_0 gives: % 24.37/4.09 | (88) aDimensionOf0(xs) = all_72_0 & $i(all_72_0) & (all_72_0 = sz00 | ( ! % 24.37/4.09 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xs, v1) = % 24.37/4.09 | v2) | ~ (aDimensionOf0(xp) = v0) | ~ $i(v1) | ~ $i(xp) | ~ % 24.37/4.09 | aNaturalNumber0(v1) | (sdtlbdtrb0(xp, v1) = v2 & $i(v2))) & ! % 24.37/4.09 | [v0: $i] : ! [v1: $i] : (v0 = xp | ~ (aDimensionOf0(v0) = v1) | % 24.37/4.09 | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ? % 24.37/4.09 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) & % 24.37/4.09 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xs, v3) = v5 & $i(v5) % 24.37/4.09 | & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 = all_72_0) & % 24.37/4.09 | szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: $i] : ( ~ % 24.37/4.09 | (aDimensionOf0(xp) = v0) | ~ $i(xp) | szszuzczcdt0(v0) = % 24.37/4.09 | all_72_0) & ! [v0: $i] : ( ~ (aDimensionOf0(xp) = v0) | ~ % 24.37/4.09 | $i(xp) | aVector0(xp)))) % 24.37/4.09 | % 24.37/4.09 | ALPHA: (88) implies: % 24.37/4.09 | (89) aDimensionOf0(xs) = all_72_0 % 24.37/4.09 | % 24.37/4.09 | GROUND_INST: instantiating (28) with all_33_0, all_72_0, xs, simplifying with % 24.37/4.09 | (31), (89) gives: % 24.37/4.09 | (90) all_72_0 = all_33_0 % 24.37/4.09 | % 24.37/4.09 | GROUND_INST: instantiating (28) with all_33_0, all_70_0, xt, simplifying with % 24.37/4.09 | (32), (87) gives: % 24.37/4.09 | (91) all_70_0 = all_33_0 % 24.37/4.09 | % 24.37/4.09 | BETA: splitting (85) gives: % 24.37/4.09 | % 24.37/4.09 | Case 1: % 24.37/4.09 | | % 24.37/4.09 | | % 24.37/4.09 | | GROUND_INST: instantiating (mLETot) with all_43_1, all_43_1, simplifying % 24.37/4.09 | | with (75), (81) gives: % 24.37/4.09 | | (92) sdtlseqdt0(all_43_1, all_43_1) % 24.37/4.09 | | % 24.37/4.09 | | GROUND_INST: instantiating (1) with all_43_1, all_43_1, all_45_1, all_43_0, % 24.37/4.09 | | all_35_0, xN, simplifying with (34), (46), (73), (74), (75), % 24.37/4.09 | | (76), (77), (78), (79), (80), (81), (92) gives: % 24.37/4.09 | | (93) $false % 24.37/4.09 | | % 24.37/4.09 | | CLOSE: (93) is inconsistent. % 24.37/4.09 | | % 24.37/4.09 | Case 2: % 24.37/4.09 | | % 24.37/4.10 | | (94) aDimensionOf0(xs) = all_67_2 & $i(all_67_2) & (all_67_2 = sz00 | ( ~ % 24.37/4.10 | | (all_67_2 = all_67_3) & aDimensionOf0(xt) = all_67_3 & % 24.37/4.10 | | $i(all_67_3))) % 24.37/4.10 | | % 24.37/4.10 | | ALPHA: (94) implies: % 24.37/4.10 | | (95) aDimensionOf0(xs) = all_67_2 % 24.37/4.10 | | (96) all_67_2 = sz00 | ( ~ (all_67_2 = all_67_3) & aDimensionOf0(xt) = % 24.37/4.10 | | all_67_3 & $i(all_67_3)) % 24.37/4.10 | | % 24.37/4.10 | | GROUND_INST: instantiating (28) with all_33_0, all_67_2, xs, simplifying % 24.37/4.10 | | with (31), (95) gives: % 24.37/4.10 | | (97) all_67_2 = all_33_0 % 24.37/4.10 | | % 24.37/4.10 | | BETA: splitting (96) gives: % 24.37/4.10 | | % 24.37/4.10 | | Case 1: % 24.37/4.10 | | | % 24.37/4.10 | | | (98) all_67_2 = sz00 % 24.37/4.10 | | | % 24.37/4.10 | | | COMBINE_EQS: (97), (98) imply: % 24.37/4.10 | | | (99) all_33_0 = sz00 % 24.37/4.10 | | | % 24.37/4.10 | | | SIMP: (99) implies: % 24.37/4.10 | | | (100) all_33_0 = sz00 % 24.37/4.10 | | | % 24.37/4.10 | | | REDUCE: (72), (100) imply: % 24.37/4.10 | | | (101) $false % 24.37/4.10 | | | % 24.37/4.10 | | | CLOSE: (101) is inconsistent. % 24.37/4.10 | | | % 24.37/4.10 | | Case 2: % 24.37/4.10 | | | % 24.37/4.10 | | | (102) ~ (all_67_2 = all_67_3) & aDimensionOf0(xt) = all_67_3 & % 24.37/4.10 | | | $i(all_67_3) % 24.48/4.10 | | | % 24.48/4.10 | | | ALPHA: (102) implies: % 24.48/4.10 | | | (103) ~ (all_67_2 = all_67_3) % 24.48/4.10 | | | (104) aDimensionOf0(xt) = all_67_3 % 24.48/4.10 | | | % 24.48/4.10 | | | REDUCE: (97), (103) imply: % 24.48/4.10 | | | (105) ~ (all_67_3 = all_33_0) % 24.48/4.10 | | | % 24.48/4.10 | | | SIMP: (105) implies: % 24.48/4.10 | | | (106) ~ (all_67_3 = all_33_0) % 24.48/4.10 | | | % 24.48/4.10 | | | GROUND_INST: instantiating (28) with all_33_0, all_67_3, xt, simplifying % 24.48/4.10 | | | with (32), (104) gives: % 24.48/4.10 | | | (107) all_67_3 = all_33_0 % 24.48/4.10 | | | % 24.48/4.10 | | | REDUCE: (106), (107) imply: % 24.48/4.10 | | | (108) $false % 24.48/4.10 | | | % 24.48/4.10 | | | CLOSE: (108) is inconsistent. % 24.48/4.10 | | | % 24.48/4.10 | | End of split % 24.48/4.10 | | % 24.48/4.10 | End of split % 24.48/4.10 | % 24.48/4.10 End of proof % 24.48/4.10 % SZS output end Proof for theBenchmark % 24.48/4.10 % 24.48/4.10 3473ms %------------------------------------------------------------------------------