%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG049+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 : n001.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 13:57:33 EDT 2023 % Result : Theorem 11.91s 2.44s % Output : Proof 18.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : RNG049+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n001.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 03:02:17 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.20/1.21 Prover 1: Preprocessing ... % 3.20/1.21 Prover 4: Preprocessing ... % 3.67/1.25 Prover 0: Preprocessing ... % 3.67/1.25 Prover 2: Preprocessing ... % 3.67/1.25 Prover 6: Preprocessing ... % 3.67/1.25 Prover 5: Preprocessing ... % 3.67/1.27 Prover 3: Preprocessing ... % 8.50/1.97 Prover 1: Constructing countermodel ... % 8.50/2.03 Prover 3: Constructing countermodel ... % 8.50/2.04 Prover 6: Proving ... % 11.02/2.29 Prover 5: Constructing countermodel ... % 11.91/2.42 Prover 3: proved (1768ms) % 11.91/2.44 % 11.91/2.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.91/2.44 % 11.91/2.44 Prover 5: stopped % 11.91/2.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.91/2.46 Prover 6: stopped % 11.91/2.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.91/2.47 Prover 4: Constructing countermodel ... % 11.91/2.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.58/2.53 Prover 10: Preprocessing ... % 12.58/2.54 Prover 7: Preprocessing ... % 12.58/2.54 Prover 8: Preprocessing ... % 12.58/2.57 Prover 2: Proving ... % 12.58/2.57 Prover 2: stopped % 12.58/2.57 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.30/2.66 Prover 11: Preprocessing ... % 13.30/2.67 Prover 0: Proving ... % 13.30/2.67 Prover 0: stopped % 13.30/2.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.30/2.76 Prover 13: Preprocessing ... % 15.05/2.87 Prover 10: Constructing countermodel ... % 15.05/2.88 Prover 8: Warning: ignoring some quantifiers % 15.05/2.89 Prover 8: Constructing countermodel ... % 15.05/2.91 Prover 7: Constructing countermodel ... % 16.45/3.05 Prover 13: Constructing countermodel ... % 18.32/3.32 Prover 11: Constructing countermodel ... % 18.63/3.35 Prover 10: Found proof (size 104) % 18.63/3.35 Prover 10: proved (879ms) % 18.63/3.35 Prover 4: stopped % 18.63/3.35 Prover 13: stopped % 18.63/3.35 Prover 7: stopped % 18.63/3.35 Prover 1: stopped % 18.63/3.35 Prover 8: stopped % 18.63/3.35 Prover 11: stopped % 18.63/3.35 % 18.63/3.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.63/3.35 % 18.63/3.38 % SZS output start Proof for theBenchmark % 18.63/3.38 Assumptions after simplification: % 18.63/3.38 --------------------------------- % 18.63/3.38 % 18.63/3.38 (mDefInit) % 18.63/3.41 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) % 18.63/3.41 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 = % 18.63/3.41 sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0, % 18.63/3.41 v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ $i(v4) | ~ $i(v1) % 18.63/3.41 | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, v4) = v5 & $i(v5))) & ! % 18.63/3.41 [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~ % 18.63/3.41 $i(v3) | ~ aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 18.63/3.41 ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 & % 18.63/3.41 sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) & % 18.63/3.41 aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5 & % 18.63/3.41 $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ % 18.63/3.41 $i(v1) | szszuzczcdt0(v3) = v2) & ! [v3: $i] : ( ~ % 18.63/3.41 (aDimensionOf0(v1) = v3) | ~ $i(v1) | aVector0(v1)))))) % 18.63/3.41 % 18.63/3.41 (mDimNat) % 18.63/3.41 ! [v0: $i] : ! [v1: $i] : ( ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ % 18.63/3.41 aVector0(v0) | aNaturalNumber0(v1)) % 18.63/3.41 % 18.63/3.41 (mElmSc) % 18.63/3.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~ % 18.63/3.41 $i(v1) | ~ $i(v0) | ~ aVector0(v0) | ~ aNaturalNumber0(v1) | % 18.63/3.41 aScalar0(v2)) % 18.63/3.41 % 18.63/3.41 (mEqInit) % 18.63/3.41 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 18.63/3.41 (sziznziztdt0(v1) = v3) | ~ (sziznziztdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) % 18.63/3.41 | ~ aVector0(v1) | ~ aVector0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: % 18.63/3.41 $i] : ? [v7: $i] : ((v7 = v6 & aDimensionOf0(v3) = v6 & aDimensionOf0(v2) % 18.63/3.41 = v6 & $i(v6)) | (aDimensionOf0(v1) = v5 & $i(v5) & (v5 = sz00 | ( ~ (v5 % 18.63/3.42 = v4) & aDimensionOf0(v0) = v4 & $i(v4)))))) % 18.63/3.42 % 18.63/3.42 (mMulSc) % 18.63/3.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 18.63/3.42 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2)) % 18.63/3.42 % 18.63/3.42 (mPosMon) % 18.63/3.42 $i(sz0z00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = % 18.63/3.42 v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(sz0z00, v1) | ~ % 18.63/3.42 sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | % 18.63/3.42 sdtlseqdt0(sz0z00, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 18.63/3.42 (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(sz0z00, v1) % 18.63/3.42 | ~ sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v3: % 18.63/3.42 $i] : (sdtasdt0(v0, v1) = v3 & $i(v3) & sdtlseqdt0(sz0z00, v3))) % 18.63/3.42 % 18.63/3.42 (mScPr) % 18.63/3.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ % 18.63/3.42 $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | aScalar0(v2) | ? % 18.63/3.42 [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) & aDimensionOf0(v1) = v4 & % 18.63/3.42 aDimensionOf0(v0) = v3 & $i(v4) & $i(v3))) % 18.63/3.42 % 18.63/3.42 (m__) % 18.63/3.42 $i(xs) & $i(sz0z00) & ? [v0: $i] : (sdtasasdt0(xs, xs) = v0 & $i(v0) & ~ % 18.63/3.42 sdtlseqdt0(sz0z00, v0)) % 18.63/3.42 % 18.63/3.42 (m__1516) % 18.63/3.42 $i(xs) & $i(sz0z00) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: % 18.63/3.42 $i] : ! [v2: $i] : ( ~ (sdtasasdt0(v1, v1) = v2) | ~ $i(v1) | ~ % 18.63/3.42 aVector0(v1) | sdtlseqdt0(sz0z00, v2) | ? [v3: $i] : (aDimensionOf0(v1) = % 18.63/3.42 v3 & $i(v3) & ~ iLess0(v3, v0)))) % 18.63/3.42 % 18.63/3.42 (m__1542) % 18.63/3.42 $i(xs) & aVector0(xs) % 18.63/3.42 % 18.63/3.42 (m__1542_01) % 18.63/3.42 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & % 18.63/3.42 $i(v0)) % 18.63/3.42 % 18.63/3.42 (m__1568) % 18.63/3.42 $i(xs) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 18.63/3.42 ? [v5: $i] : (sdtasasdt0(v1, v1) = v2 & sdtasasdt0(xs, xs) = v0 & % 18.63/3.42 sziznziztdt0(xs) = v1 & sdtlbdtrb0(xs, v3) = v4 & aDimensionOf0(xs) = v3 & % 18.63/3.42 sdtasdt0(v4, v4) = v5 & sdtpldt0(v2, v5) = v0 & $i(v5) & $i(v4) & $i(v3) & % 18.63/3.42 $i(v2) & $i(v1) & $i(v0)) % 18.63/3.42 % 18.63/3.42 (m__1590) % 18.63/3.42 $i(xs) & $i(sz0z00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 18.63/3.42 ? [v4: $i] : (sdtasasdt0(v0, v0) = v1 & sziznziztdt0(xs) = v0 & sdtlbdtrb0(xs, % 18.63/3.43 v2) = v3 & aDimensionOf0(xs) = v2 & sdtasdt0(v3, v3) = v4 & $i(v4) & % 18.63/3.43 $i(v3) & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(sz0z00, v4) & % 18.63/3.43 sdtlseqdt0(sz0z00, v1)) % 18.63/3.43 % 18.63/3.43 (function-axioms) % 18.63/3.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.63/3.43 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 18.63/3.43 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) % 18.63/3.43 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 18.63/3.43 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = % 18.63/3.43 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 18.63/3.43 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 18.63/3.43 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ % 18.63/3.43 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 18.63/3.43 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0: % 18.63/3.43 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 18.63/3.43 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 18.63/3.43 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 18.63/3.43 % 18.63/3.43 Further assumptions not needed in the proof: % 18.63/3.43 -------------------------------------------- % 18.63/3.43 mArith, mDefSPN, mDefSPZ, mDistr, mDistr2, mIH, mIHOrd, mLEASm, mLEMon, mLEMonM, % 18.63/3.43 mLERef, mLETot, mLETrn, mLess, mMDNeg, mMNeg, mNatExtr, mNatSort, mNegSc, % 18.63/3.43 mSZeroSc, mScSort, mScZero, mSqPos, mSqrt, mSuccEqu, mSuccNat, mSumSc, mVcSort, % 18.63/3.43 mZeroNat % 18.63/3.43 % 18.63/3.43 Those formulas are unsatisfiable: % 18.63/3.43 --------------------------------- % 18.63/3.43 % 18.63/3.43 Begin of proof % 18.63/3.43 | % 18.63/3.43 | ALPHA: (mPosMon) implies: % 18.63/3.43 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | % 18.63/3.43 | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(sz0z00, v1) | ~ % 18.63/3.43 | sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | % 18.63/3.43 | sdtlseqdt0(sz0z00, v2)) % 18.63/3.43 | % 18.63/3.43 | ALPHA: (mDefInit) implies: % 18.63/3.43 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) | % 18.63/3.43 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 % 18.63/3.43 | = sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 18.63/3.43 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ % 18.63/3.43 | $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, % 18.63/3.43 | v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 = % 18.63/3.44 | v1 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~ % 18.63/3.44 | aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? % 18.63/3.44 | [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 % 18.63/3.44 | & sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) & % 18.63/3.44 | aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) % 18.63/3.44 | = v5 & $i(v5))))) & ! [v3: $i] : ( ~ % 18.63/3.44 | (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2) % 18.63/3.44 | & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) | % 18.63/3.44 | aVector0(v1)))))) % 18.63/3.44 | % 18.63/3.44 | ALPHA: (mEqInit) implies: % 18.63/3.44 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 18.63/3.44 | (sziznziztdt0(v1) = v3) | ~ (sziznziztdt0(v0) = v2) | ~ $i(v1) | ~ % 18.63/3.44 | $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v4: $i] : ? [v5: % 18.63/3.44 | $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v6 & aDimensionOf0(v3) = % 18.63/3.44 | v6 & aDimensionOf0(v2) = v6 & $i(v6)) | (aDimensionOf0(v1) = v5 & % 18.63/3.44 | $i(v5) & (v5 = sz00 | ( ~ (v5 = v4) & aDimensionOf0(v0) = v4 & % 18.63/3.44 | $i(v4)))))) % 18.63/3.44 | % 18.63/3.44 | ALPHA: (m__1542) implies: % 18.63/3.44 | (4) aVector0(xs) % 18.63/3.44 | % 18.63/3.44 | ALPHA: (m__1516) implies: % 18.63/3.44 | (5) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 18.63/3.44 | $i] : ( ~ (sdtasasdt0(v1, v1) = v2) | ~ $i(v1) | ~ aVector0(v1) | % 18.63/3.44 | sdtlseqdt0(sz0z00, v2) | ? [v3: $i] : (aDimensionOf0(v1) = v3 & % 18.63/3.44 | $i(v3) & ~ iLess0(v3, v0)))) % 18.63/3.44 | % 18.63/3.44 | ALPHA: (m__1542_01) implies: % 18.63/3.44 | (6) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0)) % 18.63/3.44 | % 18.63/3.44 | ALPHA: (m__1568) implies: % 18.63/3.44 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 18.63/3.44 | ? [v5: $i] : (sdtasasdt0(v1, v1) = v2 & sdtasasdt0(xs, xs) = v0 & % 18.63/3.44 | sziznziztdt0(xs) = v1 & sdtlbdtrb0(xs, v3) = v4 & aDimensionOf0(xs) = % 18.63/3.44 | v3 & sdtasdt0(v4, v4) = v5 & sdtpldt0(v2, v5) = v0 & $i(v5) & $i(v4) % 18.63/3.44 | & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 18.63/3.44 | % 18.63/3.44 | ALPHA: (m__1590) implies: % 18.63/3.44 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 18.63/3.44 | (sdtasasdt0(v0, v0) = v1 & sziznziztdt0(xs) = v0 & sdtlbdtrb0(xs, v2) = % 18.63/3.44 | v3 & aDimensionOf0(xs) = v2 & sdtasdt0(v3, v3) = v4 & $i(v4) & $i(v3) % 18.63/3.44 | & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(sz0z00, v4) & % 18.63/3.44 | sdtlseqdt0(sz0z00, v1)) % 18.63/3.44 | % 18.63/3.44 | ALPHA: (m__) implies: % 18.63/3.44 | (9) $i(xs) % 18.63/3.44 | (10) ? [v0: $i] : (sdtasasdt0(xs, xs) = v0 & $i(v0) & ~ % 18.63/3.44 | sdtlseqdt0(sz0z00, v0)) % 18.63/3.44 | % 18.63/3.44 | ALPHA: (function-axioms) implies: % 18.63/3.44 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 18.63/3.44 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) % 18.63/3.44 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 18.63/3.44 | (sziznziztdt0(v2) = v1) | ~ (sziznziztdt0(v2) = v0)) % 18.63/3.45 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.63/3.45 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 18.63/3.45 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.63/3.45 | (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0)) % 18.63/3.45 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.63/3.45 | (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) % 18.63/3.45 | % 18.63/3.45 | DELTA: instantiating (10) with fresh symbol all_32_0 gives: % 18.63/3.45 | (16) sdtasasdt0(xs, xs) = all_32_0 & $i(all_32_0) & ~ sdtlseqdt0(sz0z00, % 18.63/3.45 | all_32_0) % 18.63/3.45 | % 18.63/3.45 | ALPHA: (16) implies: % 18.63/3.45 | (17) ~ sdtlseqdt0(sz0z00, all_32_0) % 18.63/3.45 | (18) sdtasasdt0(xs, xs) = all_32_0 % 18.63/3.45 | % 18.63/3.45 | DELTA: instantiating (6) with fresh symbol all_34_0 gives: % 18.63/3.45 | (19) ~ (all_34_0 = sz00) & aDimensionOf0(xs) = all_34_0 & $i(all_34_0) % 18.63/3.45 | % 18.63/3.45 | ALPHA: (19) implies: % 18.63/3.45 | (20) ~ (all_34_0 = sz00) % 18.63/3.45 | (21) aDimensionOf0(xs) = all_34_0 % 18.63/3.45 | % 18.63/3.45 | DELTA: instantiating (5) with fresh symbol all_36_0 gives: % 18.63/3.45 | (22) aDimensionOf0(xs) = all_36_0 & $i(all_36_0) & ! [v0: $i] : ! [v1: % 18.63/3.45 | $i] : ( ~ (sdtasasdt0(v0, v0) = v1) | ~ $i(v0) | ~ aVector0(v0) | % 18.63/3.45 | sdtlseqdt0(sz0z00, v1) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & % 18.63/3.45 | $i(v2) & ~ iLess0(v2, all_36_0))) % 18.63/3.45 | % 18.63/3.45 | ALPHA: (22) implies: % 18.63/3.45 | (23) aDimensionOf0(xs) = all_36_0 % 18.63/3.45 | (24) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasasdt0(v0, v0) = v1) | ~ $i(v0) % 18.63/3.45 | | ~ aVector0(v0) | sdtlseqdt0(sz0z00, v1) | ? [v2: $i] : % 18.63/3.45 | (aDimensionOf0(v0) = v2 & $i(v2) & ~ iLess0(v2, all_36_0))) % 18.63/3.45 | % 18.63/3.45 | DELTA: instantiating (8) with fresh symbols all_39_0, all_39_1, all_39_2, % 18.63/3.45 | all_39_3, all_39_4 gives: % 18.63/3.45 | (25) sdtasasdt0(all_39_4, all_39_4) = all_39_3 & sziznziztdt0(xs) = % 18.63/3.45 | all_39_4 & sdtlbdtrb0(xs, all_39_2) = all_39_1 & aDimensionOf0(xs) = % 18.63/3.45 | all_39_2 & sdtasdt0(all_39_1, all_39_1) = all_39_0 & $i(all_39_0) & % 18.63/3.45 | $i(all_39_1) & $i(all_39_2) & $i(all_39_3) & $i(all_39_4) & % 18.63/3.45 | sdtlseqdt0(sz0z00, all_39_0) & sdtlseqdt0(sz0z00, all_39_3) % 18.63/3.45 | % 18.63/3.45 | ALPHA: (25) implies: % 18.63/3.45 | (26) sdtlseqdt0(sz0z00, all_39_3) % 18.63/3.45 | (27) sdtlseqdt0(sz0z00, all_39_0) % 18.63/3.45 | (28) sdtasdt0(all_39_1, all_39_1) = all_39_0 % 18.63/3.45 | (29) aDimensionOf0(xs) = all_39_2 % 18.63/3.45 | (30) sdtlbdtrb0(xs, all_39_2) = all_39_1 % 18.63/3.45 | (31) sziznziztdt0(xs) = all_39_4 % 18.63/3.45 | (32) sdtasasdt0(all_39_4, all_39_4) = all_39_3 % 18.63/3.45 | % 18.63/3.45 | DELTA: instantiating (7) with fresh symbols all_41_0, all_41_1, all_41_2, % 18.63/3.45 | all_41_3, all_41_4, all_41_5 gives: % 18.63/3.45 | (33) sdtasasdt0(all_41_4, all_41_4) = all_41_3 & sdtasasdt0(xs, xs) = % 18.63/3.45 | all_41_5 & sziznziztdt0(xs) = all_41_4 & sdtlbdtrb0(xs, all_41_2) = % 18.63/3.45 | all_41_1 & aDimensionOf0(xs) = all_41_2 & sdtasdt0(all_41_1, all_41_1) % 18.63/3.45 | = all_41_0 & sdtpldt0(all_41_3, all_41_0) = all_41_5 & $i(all_41_0) & % 18.63/3.45 | $i(all_41_1) & $i(all_41_2) & $i(all_41_3) & $i(all_41_4) & % 18.63/3.45 | $i(all_41_5) % 18.63/3.45 | % 18.63/3.45 | ALPHA: (33) implies: % 18.63/3.46 | (34) $i(all_41_4) % 18.63/3.46 | (35) $i(all_41_3) % 18.63/3.46 | (36) $i(all_41_0) % 18.63/3.46 | (37) sdtpldt0(all_41_3, all_41_0) = all_41_5 % 18.63/3.46 | (38) sdtasdt0(all_41_1, all_41_1) = all_41_0 % 18.63/3.46 | (39) aDimensionOf0(xs) = all_41_2 % 18.63/3.46 | (40) sdtlbdtrb0(xs, all_41_2) = all_41_1 % 18.63/3.46 | (41) sziznziztdt0(xs) = all_41_4 % 18.63/3.46 | (42) sdtasasdt0(xs, xs) = all_41_5 % 18.63/3.46 | (43) sdtasasdt0(all_41_4, all_41_4) = all_41_3 % 18.63/3.46 | % 18.63/3.46 | GROUND_INST: instantiating (11) with all_36_0, all_39_2, xs, simplifying with % 18.63/3.46 | (23), (29) gives: % 18.63/3.46 | (44) all_39_2 = all_36_0 % 18.63/3.46 | % 18.63/3.46 | GROUND_INST: instantiating (11) with all_39_2, all_41_2, xs, simplifying with % 18.63/3.46 | (29), (39) gives: % 18.63/3.46 | (45) all_41_2 = all_39_2 % 18.63/3.46 | % 18.63/3.46 | GROUND_INST: instantiating (11) with all_34_0, all_41_2, xs, simplifying with % 18.63/3.46 | (21), (39) gives: % 18.63/3.46 | (46) all_41_2 = all_34_0 % 18.63/3.46 | % 18.63/3.46 | GROUND_INST: instantiating (12) with all_39_4, all_41_4, xs, simplifying with % 18.63/3.46 | (31), (41) gives: % 18.63/3.46 | (47) all_41_4 = all_39_4 % 18.63/3.46 | % 18.63/3.46 | GROUND_INST: instantiating (15) with all_32_0, all_41_5, xs, xs, simplifying % 18.63/3.46 | with (18), (42) gives: % 18.63/3.46 | (48) all_41_5 = all_32_0 % 18.63/3.46 | % 18.63/3.46 | COMBINE_EQS: (45), (46) imply: % 18.63/3.46 | (49) all_39_2 = all_34_0 % 18.63/3.46 | % 18.63/3.46 | SIMP: (49) implies: % 18.63/3.46 | (50) all_39_2 = all_34_0 % 18.63/3.46 | % 18.63/3.46 | COMBINE_EQS: (44), (50) imply: % 18.63/3.46 | (51) all_36_0 = all_34_0 % 18.63/3.46 | % 18.63/3.46 | SIMP: (51) implies: % 18.63/3.46 | (52) all_36_0 = all_34_0 % 18.63/3.46 | % 18.63/3.46 | REDUCE: (43), (47) imply: % 18.63/3.46 | (53) sdtasasdt0(all_39_4, all_39_4) = all_41_3 % 18.63/3.46 | % 18.63/3.46 | REDUCE: (40), (46) imply: % 18.63/3.46 | (54) sdtlbdtrb0(xs, all_34_0) = all_41_1 % 18.63/3.46 | % 18.63/3.46 | REDUCE: (30), (50) imply: % 18.63/3.46 | (55) sdtlbdtrb0(xs, all_34_0) = all_39_1 % 18.63/3.46 | % 18.63/3.46 | REDUCE: (37), (48) imply: % 18.63/3.46 | (56) sdtpldt0(all_41_3, all_41_0) = all_32_0 % 18.63/3.46 | % 18.63/3.46 | REDUCE: (34), (47) imply: % 18.63/3.46 | (57) $i(all_39_4) % 18.63/3.46 | % 18.63/3.46 | GROUND_INST: instantiating (14) with all_39_1, all_41_1, all_34_0, xs, % 18.63/3.46 | simplifying with (54), (55) gives: % 18.63/3.46 | (58) all_41_1 = all_39_1 % 18.63/3.46 | % 18.63/3.46 | GROUND_INST: instantiating (15) with all_39_3, all_41_3, all_39_4, all_39_4, % 18.63/3.46 | simplifying with (32), (53) gives: % 18.63/3.46 | (59) all_41_3 = all_39_3 % 18.63/3.46 | % 18.63/3.46 | REDUCE: (38), (58) imply: % 18.63/3.46 | (60) sdtasdt0(all_39_1, all_39_1) = all_41_0 % 18.63/3.46 | % 18.63/3.46 | REDUCE: (56), (59) imply: % 18.63/3.47 | (61) sdtpldt0(all_39_3, all_41_0) = all_32_0 % 18.63/3.47 | % 18.63/3.47 | REDUCE: (35), (59) imply: % 18.63/3.47 | (62) $i(all_39_3) % 18.63/3.47 | % 18.63/3.47 | GROUND_INST: instantiating (13) with all_39_0, all_41_0, all_39_1, all_39_1, % 18.63/3.47 | simplifying with (28), (60) gives: % 18.63/3.47 | (63) all_41_0 = all_39_0 % 18.63/3.47 | % 18.63/3.47 | REDUCE: (61), (63) imply: % 18.63/3.47 | (64) sdtpldt0(all_39_3, all_39_0) = all_32_0 % 18.63/3.47 | % 18.63/3.47 | REDUCE: (36), (63) imply: % 18.63/3.47 | (65) $i(all_39_0) % 18.63/3.47 | % 18.63/3.47 | GROUND_INST: instantiating (mDimNat) with xs, all_34_0, simplifying with (4), % 18.63/3.47 | (9), (21) gives: % 18.63/3.47 | (66) aNaturalNumber0(all_34_0) % 18.63/3.47 | % 18.63/3.47 | GROUND_INST: instantiating (3) with xs, xs, all_39_4, all_39_4, simplifying % 18.63/3.47 | with (4), (9), (31) gives: % 18.63/3.47 | (67) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 & % 18.63/3.47 | aDimensionOf0(all_39_4) = v2 & $i(v2)) | (aDimensionOf0(xs) = v1 & % 18.63/3.47 | $i(v1) & (v1 = sz00 | ( ~ (v1 = v0) & aDimensionOf0(xs) = v0 & % 18.63/3.47 | $i(v0))))) % 18.63/3.47 | % 18.63/3.47 | GROUND_INST: instantiating (2) with xs, all_39_4, simplifying with (4), (9), % 18.63/3.47 | (31) gives: % 18.63/3.47 | (68) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & (v0 = sz00 | ( ! [v1: % 18.63/3.47 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xs, v2) = % 18.63/3.47 | v3) | ~ (aDimensionOf0(all_39_4) = v1) | ~ $i(v2) | ~ % 18.63/3.47 | $i(all_39_4) | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(all_39_4, % 18.63/3.47 | v2) = v3 & $i(v3))) & ! [v1: any] : ! [v2: $i] : (v1 = % 18.63/3.47 | all_39_4 | ~ (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ % 18.63/3.47 | aVector0(v1) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 18.63/3.47 | [v6: $i] : ($i(v4) & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5 % 18.63/3.47 | & sdtlbdtrb0(xs, v4) = v6 & $i(v6) & $i(v5) & % 18.63/3.47 | aNaturalNumber0(v4)) | ( ~ (v3 = v0) & szszuzczcdt0(v2) % 18.63/3.47 | = v3 & $i(v3))))) & ! [v1: $i] : ( ~ % 18.63/3.47 | (aDimensionOf0(all_39_4) = v1) | ~ $i(all_39_4) | % 18.63/3.47 | szszuzczcdt0(v1) = v0) & ! [v1: $i] : ( ~ % 18.63/3.47 | (aDimensionOf0(all_39_4) = v1) | ~ $i(all_39_4) | % 18.63/3.47 | aVector0(all_39_4))))) % 18.63/3.47 | % 18.63/3.47 | GROUND_INST: instantiating (24) with xs, all_32_0, simplifying with (4), (9), % 18.63/3.47 | (17), (18) gives: % 18.63/3.47 | (69) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ~ iLess0(v0, % 18.63/3.47 | all_36_0)) % 18.63/3.47 | % 18.63/3.47 | DELTA: instantiating (69) with fresh symbol all_64_0 gives: % 18.63/3.47 | (70) aDimensionOf0(xs) = all_64_0 & $i(all_64_0) & ~ iLess0(all_64_0, % 18.63/3.47 | all_36_0) % 18.63/3.47 | % 18.63/3.47 | ALPHA: (70) implies: % 18.63/3.47 | (71) $i(all_64_0) % 18.63/3.47 | (72) aDimensionOf0(xs) = all_64_0 % 18.63/3.47 | % 18.63/3.47 | DELTA: instantiating (67) with fresh symbols all_66_0, all_66_1, all_66_2, % 18.63/3.48 | all_66_3 gives: % 18.63/3.48 | (73) (all_66_0 = all_66_1 & aDimensionOf0(all_39_4) = all_66_1 & % 18.63/3.48 | $i(all_66_1)) | (aDimensionOf0(xs) = all_66_2 & $i(all_66_2) & % 18.63/3.48 | (all_66_2 = sz00 | ( ~ (all_66_2 = all_66_3) & aDimensionOf0(xs) = % 18.63/3.48 | all_66_3 & $i(all_66_3)))) % 18.63/3.48 | % 18.63/3.48 | DELTA: instantiating (68) with fresh symbol all_67_0 gives: % 18.63/3.48 | (74) aDimensionOf0(xs) = all_67_0 & $i(all_67_0) & (all_67_0 = sz00 | ( ! % 18.63/3.48 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xs, v1) = % 18.63/3.48 | v2) | ~ (aDimensionOf0(all_39_4) = v0) | ~ $i(v1) | ~ % 18.63/3.48 | $i(all_39_4) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(all_39_4, % 18.63/3.48 | v1) = v2 & $i(v2))) & ! [v0: any] : ! [v1: $i] : (v0 = % 18.63/3.48 | all_39_4 | ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ % 18.63/3.48 | aVector0(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? % 18.63/3.48 | [v5: $i] : ($i(v3) & (( ~ (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & % 18.63/3.48 | sdtlbdtrb0(xs, v3) = v5 & $i(v5) & $i(v4) & % 18.63/3.48 | aNaturalNumber0(v3)) | ( ~ (v2 = all_67_0) & % 18.63/3.48 | szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: $i] : ( ~ % 18.63/3.48 | (aDimensionOf0(all_39_4) = v0) | ~ $i(all_39_4) | % 18.63/3.48 | szszuzczcdt0(v0) = all_67_0) & ! [v0: $i] : ( ~ % 18.63/3.48 | (aDimensionOf0(all_39_4) = v0) | ~ $i(all_39_4) | % 18.63/3.48 | aVector0(all_39_4)))) % 18.63/3.48 | % 18.63/3.48 | ALPHA: (74) implies: % 18.63/3.48 | (75) aDimensionOf0(xs) = all_67_0 % 18.63/3.48 | (76) all_67_0 = sz00 | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 18.63/3.48 | (sdtlbdtrb0(xs, v1) = v2) | ~ (aDimensionOf0(all_39_4) = v0) | ~ % 18.63/3.48 | $i(v1) | ~ $i(all_39_4) | ~ aNaturalNumber0(v1) | % 18.63/3.48 | (sdtlbdtrb0(all_39_4, v1) = v2 & $i(v2))) & ! [v0: any] : ! [v1: % 18.63/3.48 | $i] : (v0 = all_39_4 | ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | % 18.63/3.48 | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? % 18.63/3.48 | [v5: $i] : ($i(v3) & (( ~ (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & % 18.63/3.48 | sdtlbdtrb0(xs, v3) = v5 & $i(v5) & $i(v4) & % 18.63/3.48 | aNaturalNumber0(v3)) | ( ~ (v2 = all_67_0) & % 18.63/3.48 | szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: $i] : ( ~ % 18.63/3.48 | (aDimensionOf0(all_39_4) = v0) | ~ $i(all_39_4) | % 18.63/3.48 | szszuzczcdt0(v0) = all_67_0) & ! [v0: $i] : ( ~ % 18.63/3.48 | (aDimensionOf0(all_39_4) = v0) | ~ $i(all_39_4) | % 18.63/3.48 | aVector0(all_39_4))) % 18.63/3.48 | % 18.63/3.48 | GROUND_INST: instantiating (11) with all_34_0, all_67_0, xs, simplifying with % 18.63/3.48 | (21), (75) gives: % 18.63/3.48 | (77) all_67_0 = all_34_0 % 18.63/3.48 | % 18.63/3.48 | GROUND_INST: instantiating (11) with all_64_0, all_67_0, xs, simplifying with % 18.63/3.48 | (72), (75) gives: % 18.63/3.48 | (78) all_67_0 = all_64_0 % 18.63/3.48 | % 18.63/3.48 | COMBINE_EQS: (77), (78) imply: % 18.63/3.48 | (79) all_64_0 = all_34_0 % 18.63/3.48 | % 18.63/3.48 | REDUCE: (71), (79) imply: % 18.63/3.48 | (80) $i(all_34_0) % 18.63/3.48 | % 18.63/3.48 | BETA: splitting (73) gives: % 18.63/3.48 | % 18.63/3.48 | Case 1: % 18.63/3.48 | | % 18.63/3.48 | | (81) all_66_0 = all_66_1 & aDimensionOf0(all_39_4) = all_66_1 & % 18.63/3.48 | | $i(all_66_1) % 18.63/3.48 | | % 18.63/3.48 | | ALPHA: (81) implies: % 18.63/3.49 | | (82) aDimensionOf0(all_39_4) = all_66_1 % 18.63/3.49 | | % 18.63/3.49 | | BETA: splitting (76) gives: % 18.63/3.49 | | % 18.63/3.49 | | Case 1: % 18.63/3.49 | | | % 18.63/3.49 | | | (83) all_67_0 = sz00 % 18.63/3.49 | | | % 18.63/3.49 | | | COMBINE_EQS: (77), (83) imply: % 18.63/3.49 | | | (84) all_34_0 = sz00 % 18.63/3.49 | | | % 18.63/3.49 | | | REDUCE: (20), (84) imply: % 18.63/3.49 | | | (85) $false % 18.63/3.49 | | | % 18.63/3.49 | | | CLOSE: (85) is inconsistent. % 18.63/3.49 | | | % 18.63/3.49 | | Case 2: % 18.63/3.49 | | | % 18.63/3.49 | | | (86) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xs, v1) % 18.63/3.49 | | | = v2) | ~ (aDimensionOf0(all_39_4) = v0) | ~ $i(v1) | ~ % 18.63/3.49 | | | $i(all_39_4) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(all_39_4, % 18.63/3.49 | | | v1) = v2 & $i(v2))) & ! [v0: any] : ! [v1: $i] : (v0 = % 18.63/3.49 | | | all_39_4 | ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ % 18.63/3.49 | | | aVector0(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? % 18.63/3.49 | | | [v5: $i] : ($i(v3) & (( ~ (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & % 18.63/3.49 | | | sdtlbdtrb0(xs, v3) = v5 & $i(v5) & $i(v4) & % 18.63/3.49 | | | aNaturalNumber0(v3)) | ( ~ (v2 = all_67_0) & % 18.63/3.49 | | | szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: $i] : ( ~ % 18.63/3.49 | | | (aDimensionOf0(all_39_4) = v0) | ~ $i(all_39_4) | % 18.63/3.49 | | | szszuzczcdt0(v0) = all_67_0) & ! [v0: $i] : ( ~ % 18.63/3.49 | | | (aDimensionOf0(all_39_4) = v0) | ~ $i(all_39_4) | % 18.63/3.49 | | | aVector0(all_39_4)) % 18.63/3.49 | | | % 18.63/3.49 | | | ALPHA: (86) implies: % 18.63/3.49 | | | (87) ! [v0: $i] : ( ~ (aDimensionOf0(all_39_4) = v0) | ~ $i(all_39_4) % 18.63/3.49 | | | | aVector0(all_39_4)) % 18.63/3.49 | | | (88) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xs, v1) % 18.63/3.49 | | | = v2) | ~ (aDimensionOf0(all_39_4) = v0) | ~ $i(v1) | ~ % 18.63/3.49 | | | $i(all_39_4) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(all_39_4, % 18.63/3.49 | | | v1) = v2 & $i(v2))) % 18.63/3.49 | | | % 18.63/3.49 | | | GROUND_INST: instantiating (mElmSc) with xs, all_34_0, all_39_1, % 18.63/3.49 | | | simplifying with (4), (9), (55), (66), (80) gives: % 18.63/3.49 | | | (89) aScalar0(all_39_1) % 18.63/3.49 | | | % 18.63/3.49 | | | GROUND_INST: instantiating (88) with all_66_1, all_34_0, all_39_1, % 18.63/3.49 | | | simplifying with (55), (57), (66), (80), (82) gives: % 18.63/3.49 | | | (90) sdtlbdtrb0(all_39_4, all_34_0) = all_39_1 & $i(all_39_1) % 18.63/3.49 | | | % 18.63/3.49 | | | ALPHA: (90) implies: % 18.63/3.49 | | | (91) $i(all_39_1) % 18.63/3.49 | | | % 18.63/3.49 | | | GROUND_INST: instantiating (87) with all_66_1, simplifying with (57), (82) % 18.63/3.49 | | | gives: % 18.63/3.49 | | | (92) aVector0(all_39_4) % 18.63/3.49 | | | % 18.63/3.49 | | | GROUND_INST: instantiating (mMulSc) with all_39_1, all_39_1, all_39_0, % 18.63/3.49 | | | simplifying with (28), (89), (91) gives: % 18.63/3.49 | | | (93) aScalar0(all_39_0) % 18.63/3.49 | | | % 18.63/3.50 | | | GROUND_INST: instantiating (mScPr) with all_39_4, all_39_4, all_39_3, % 18.63/3.50 | | | simplifying with (32), (57), (92) gives: % 18.63/3.50 | | | (94) aScalar0(all_39_3) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 18.63/3.50 | | | aDimensionOf0(all_39_4) = v1 & aDimensionOf0(all_39_4) = v0 & % 18.63/3.50 | | | $i(v1) & $i(v0)) % 18.63/3.50 | | | % 18.63/3.50 | | | BETA: splitting (94) gives: % 18.63/3.50 | | | % 18.63/3.50 | | | Case 1: % 18.63/3.50 | | | | % 18.63/3.50 | | | | (95) aScalar0(all_39_3) % 18.63/3.50 | | | | % 18.63/3.50 | | | | GROUND_INST: instantiating (1) with all_39_3, all_39_0, all_32_0, % 18.63/3.50 | | | | simplifying with (17), (26), (27), (62), (64), (65), (93), % 18.63/3.50 | | | | (95) gives: % 18.63/3.50 | | | | (96) $false % 18.63/3.50 | | | | % 18.63/3.50 | | | | CLOSE: (96) is inconsistent. % 18.63/3.50 | | | | % 18.63/3.50 | | | Case 2: % 18.63/3.50 | | | | % 18.63/3.50 | | | | (97) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 18.63/3.50 | | | | aDimensionOf0(all_39_4) = v1 & aDimensionOf0(all_39_4) = v0 & % 18.63/3.50 | | | | $i(v1) & $i(v0)) % 18.63/3.50 | | | | % 18.63/3.50 | | | | DELTA: instantiating (97) with fresh symbols all_108_0, all_108_1 gives: % 18.63/3.50 | | | | (98) ~ (all_108_0 = all_108_1) & aDimensionOf0(all_39_4) = all_108_0 % 18.63/3.50 | | | | & aDimensionOf0(all_39_4) = all_108_1 & $i(all_108_0) & % 18.63/3.50 | | | | $i(all_108_1) % 18.63/3.50 | | | | % 18.63/3.50 | | | | ALPHA: (98) implies: % 18.63/3.50 | | | | (99) ~ (all_108_0 = all_108_1) % 18.63/3.50 | | | | (100) aDimensionOf0(all_39_4) = all_108_1 % 18.63/3.50 | | | | (101) aDimensionOf0(all_39_4) = all_108_0 % 18.63/3.50 | | | | % 18.63/3.50 | | | | GROUND_INST: instantiating (11) with all_66_1, all_108_0, all_39_4, % 18.63/3.50 | | | | simplifying with (82), (101) gives: % 18.63/3.50 | | | | (102) all_108_0 = all_66_1 % 18.63/3.50 | | | | % 18.63/3.50 | | | | GROUND_INST: instantiating (11) with all_108_1, all_108_0, all_39_4, % 18.63/3.50 | | | | simplifying with (100), (101) gives: % 18.63/3.50 | | | | (103) all_108_0 = all_108_1 % 18.63/3.50 | | | | % 18.63/3.50 | | | | COMBINE_EQS: (102), (103) imply: % 18.63/3.50 | | | | (104) all_108_1 = all_66_1 % 18.63/3.50 | | | | % 18.63/3.50 | | | | REDUCE: (99), (102), (104) imply: % 18.63/3.50 | | | | (105) $false % 18.63/3.50 | | | | % 18.63/3.50 | | | | CLOSE: (105) is inconsistent. % 18.63/3.50 | | | | % 18.63/3.50 | | | End of split % 18.63/3.50 | | | % 18.63/3.50 | | End of split % 18.63/3.50 | | % 18.63/3.50 | Case 2: % 18.63/3.50 | | % 18.63/3.50 | | (106) aDimensionOf0(xs) = all_66_2 & $i(all_66_2) & (all_66_2 = sz00 | ( % 18.63/3.50 | | ~ (all_66_2 = all_66_3) & aDimensionOf0(xs) = all_66_3 & % 18.63/3.50 | | $i(all_66_3))) % 18.63/3.50 | | % 18.63/3.50 | | ALPHA: (106) implies: % 18.63/3.50 | | (107) aDimensionOf0(xs) = all_66_2 % 18.63/3.50 | | (108) all_66_2 = sz00 | ( ~ (all_66_2 = all_66_3) & aDimensionOf0(xs) = % 18.63/3.50 | | all_66_3 & $i(all_66_3)) % 18.63/3.50 | | % 18.63/3.50 | | BETA: splitting (108) gives: % 18.63/3.50 | | % 18.63/3.50 | | Case 1: % 18.63/3.50 | | | % 18.63/3.50 | | | (109) all_66_2 = sz00 % 18.63/3.50 | | | % 18.63/3.50 | | | REDUCE: (107), (109) imply: % 18.63/3.50 | | | (110) aDimensionOf0(xs) = sz00 % 18.63/3.50 | | | % 18.63/3.50 | | | GROUND_INST: instantiating (11) with all_34_0, sz00, xs, simplifying with % 18.63/3.50 | | | (21), (110) gives: % 18.63/3.50 | | | (111) all_34_0 = sz00 % 18.63/3.50 | | | % 18.63/3.50 | | | REDUCE: (20), (111) imply: % 18.63/3.50 | | | (112) $false % 18.63/3.50 | | | % 18.63/3.50 | | | CLOSE: (112) is inconsistent. % 18.63/3.50 | | | % 18.63/3.50 | | Case 2: % 18.63/3.50 | | | % 18.63/3.50 | | | (113) ~ (all_66_2 = all_66_3) & aDimensionOf0(xs) = all_66_3 & % 18.63/3.50 | | | $i(all_66_3) % 18.63/3.50 | | | % 18.63/3.50 | | | ALPHA: (113) implies: % 18.63/3.50 | | | (114) ~ (all_66_2 = all_66_3) % 18.63/3.50 | | | (115) aDimensionOf0(xs) = all_66_3 % 18.63/3.50 | | | % 18.63/3.51 | | | GROUND_INST: instantiating (11) with all_34_0, all_66_2, xs, simplifying % 18.63/3.51 | | | with (21), (107) gives: % 18.63/3.51 | | | (116) all_66_2 = all_34_0 % 18.63/3.51 | | | % 18.63/3.51 | | | GROUND_INST: instantiating (11) with all_66_3, all_66_2, xs, simplifying % 18.63/3.51 | | | with (107), (115) gives: % 18.63/3.51 | | | (117) all_66_2 = all_66_3 % 18.63/3.51 | | | % 18.63/3.51 | | | COMBINE_EQS: (116), (117) imply: % 18.63/3.51 | | | (118) all_66_3 = all_34_0 % 18.63/3.51 | | | % 18.63/3.51 | | | REDUCE: (114), (116), (118) imply: % 18.63/3.51 | | | (119) $false % 18.63/3.51 | | | % 18.63/3.51 | | | CLOSE: (119) is inconsistent. % 18.63/3.51 | | | % 18.63/3.51 | | End of split % 18.63/3.51 | | % 18.63/3.51 | End of split % 18.63/3.51 | % 18.63/3.51 End of proof % 18.63/3.51 % SZS output end Proof for theBenchmark % 18.63/3.51 % 18.63/3.51 2884ms %------------------------------------------------------------------------------