%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG081+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 : n005.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 13:57:45 EDT 2023 % Result : Theorem 13.71s 2.78s % Output : Proof 24.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : RNG081+1 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.31 % Computer : n005.cluster.edu % 0.11/0.31 % Model : x86_64 x86_64 % 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.31 % Memory : 8042.1875MB % 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 300 % 0.11/0.31 % DateTime : Sun Aug 27 01:51:23 EDT 2023 % 0.11/0.32 % CPUTime : % 0.17/0.58 ________ _____ % 0.17/0.58 ___ __ \_________(_)________________________________ % 0.17/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.58 % 0.17/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.58 (2023-06-19) % 0.17/0.58 % 0.17/0.58 (c) Philipp Rümmer, 2009-2023 % 0.17/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.58 Amanda Stjerna. % 0.17/0.58 Free software under BSD-3-Clause. % 0.17/0.58 % 0.17/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.58 % 0.17/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.17/0.59 Running up to 7 provers in parallel. % 0.17/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.17/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 3.28/1.27 Prover 1: Preprocessing ... % 3.28/1.27 Prover 4: Preprocessing ... % 3.91/1.35 Prover 3: Preprocessing ... % 3.91/1.35 Prover 0: Preprocessing ... % 3.91/1.35 Prover 5: Preprocessing ... % 3.91/1.35 Prover 2: Preprocessing ... % 3.91/1.35 Prover 6: Preprocessing ... % 10.83/2.35 Prover 3: Constructing countermodel ... % 11.50/2.38 Prover 1: Constructing countermodel ... % 11.67/2.41 Prover 6: Proving ... % 13.71/2.77 Prover 3: proved (2160ms) % 13.71/2.77 % 13.71/2.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.71/2.78 % 13.71/2.80 Prover 6: proved (2177ms) % 13.71/2.80 % 13.71/2.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.71/2.80 % 13.71/2.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.02/2.81 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.94/2.87 Prover 5: Constructing countermodel ... % 14.94/2.90 Prover 4: Constructing countermodel ... % 15.46/2.91 Prover 2: Proving ... % 15.46/2.91 Prover 2: stopped % 15.46/2.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.46/2.92 Prover 7: Preprocessing ... % 15.46/2.92 Prover 5: stopped % 15.46/2.94 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.92/3.03 Prover 8: Preprocessing ... % 17.19/3.13 Prover 0: Proving ... % 17.24/3.14 Prover 0: stopped % 17.24/3.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 17.24/3.15 Prover 10: Preprocessing ... % 17.24/3.16 Prover 11: Preprocessing ... % 18.22/3.27 Prover 13: Preprocessing ... % 18.22/3.28 Prover 8: Warning: ignoring some quantifiers % 18.22/3.31 Prover 8: Constructing countermodel ... % 18.22/3.39 Prover 10: Constructing countermodel ... % 18.22/3.40 Prover 7: Constructing countermodel ... % 21.08/3.67 Prover 13: Constructing countermodel ... % 22.48/3.84 Prover 11: Constructing countermodel ... % 23.59/3.99 Prover 10: Found proof (size 90) % 23.59/4.03 Prover 10: proved (1112ms) % 23.59/4.03 Prover 11: stopped % 23.59/4.03 Prover 13: stopped % 23.59/4.03 Prover 8: stopped % 23.59/4.03 Prover 7: stopped % 23.59/4.03 Prover 4: stopped % 23.59/4.03 Prover 1: stopped % 23.59/4.03 % 23.59/4.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 23.59/4.03 % 23.59/4.05 % SZS output start Proof for theBenchmark % 23.59/4.06 Assumptions after simplification: % 23.59/4.06 --------------------------------- % 23.59/4.06 % 23.59/4.06 (mDefSPZ) % 23.59/4.09 $i(sz0z00) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz0z00 % 23.59/4.09 | ~ (sdtasasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | % 23.59/4.09 ~ aVector0(v0) | ? [v3: $i] : ? [v4: $i] : (aDimensionOf0(v1) = v4 & % 23.59/4.09 $i(v4) & ( ~ (v4 = sz00) | ( ~ (v3 = sz00) & aDimensionOf0(v0) = v3 & % 23.59/4.09 $i(v3))))) % 23.59/4.09 % 23.59/4.09 (mLEMonM) % 23.59/4.10 $i(sz0z00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 23.59/4.10 $i] : ! [v5: $i] : ( ~ (sdtasdt0(v1, v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) % 23.59/4.10 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v2, v3) | ~ % 23.59/4.10 sdtlseqdt0(v0, v1) | ~ sdtlseqdt0(sz0z00, v2) | ~ aScalar0(v3) | ~ % 23.59/4.10 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(v4, v5)) % 23.59/4.10 % 23.59/4.10 (mScPr) % 23.59/4.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ % 23.59/4.10 $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | aScalar0(v2) | ? % 23.59/4.10 [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) & aDimensionOf0(v1) = v4 & % 23.59/4.10 aDimensionOf0(v0) = v3 & $i(v4) & $i(v3))) % 23.59/4.10 % 23.59/4.10 (mScSqPos) % 23.59/4.10 $i(sz0z00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasasdt0(v0, v0) = v1) | ~ % 23.59/4.10 $i(v0) | ~ aVector0(v0) | sdtlseqdt0(sz0z00, v1)) % 23.59/4.10 % 23.59/4.10 (m__) % 23.59/4.11 $i(xt) & $i(xs) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 23.59/4.11 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 23.59/4.11 ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? % 23.59/4.11 [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : % 23.59/4.11 (sdtasasdt0(xt, xt) = v3 & sdtasasdt0(xs, xt) = v0 & sdtasasdt0(xs, xs) = v2 & % 23.59/4.11 aDimensionOf0(xs) = sz00 & sdtasdt0(v2, v3) = v4 & sdtasdt0(v0, v0) = v1 & % 23.59/4.11 $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 23.59/4.11 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 23.59/4.11 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, v4)) % 23.59/4.11 % 23.59/4.11 (m__1652) % 23.59/4.11 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! % 23.59/4.11 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2) % 23.59/4.11 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~ % 23.59/4.11 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ? % 23.59/4.11 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 & % 23.59/4.11 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) | % 23.59/4.11 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) & % 23.59/4.11 aDimensionOf0(v2) = v7 & $i(v7))))))) % 23.59/4.11 % 23.59/4.11 (m__1678) % 23.59/4.11 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs) % 23.59/4.11 % 23.59/4.11 (m__1678_01) % 23.59/4.11 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = % 23.59/4.11 v0 & $i(v0)) % 23.59/4.11 % 23.59/4.11 (function-axioms) % 23.59/4.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.59/4.12 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 23.59/4.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) % 23.59/4.12 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.59/4.12 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = % 23.59/4.12 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 23.59/4.12 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 23.59/4.12 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ % 23.59/4.12 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 23.59/4.12 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0: % 23.59/4.12 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 23.59/4.12 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.59/4.12 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 23.59/4.12 % 23.59/4.12 Further assumptions not needed in the proof: % 23.59/4.12 -------------------------------------------- % 23.59/4.12 mArith, mDefInit, mDefSPN, mDimNat, mDistr, mDistr2, mElmSc, mEqInit, mIH, % 23.59/4.12 mIHOrd, mLEASm, mLEMon, mLERef, mLETot, mLETrn, mLess, mMDNeg, mMNeg, mMulSc, % 23.59/4.12 mNatExtr, mNatSort, mNegSc, mPosMon, mSZeroSc, mScSort, mScZero, mSqPos, mSqrt, % 23.59/4.12 mSuccEqu, mSuccNat, mSumSc, mVcSort, mZeroNat % 23.59/4.12 % 23.59/4.12 Those formulas are unsatisfiable: % 23.59/4.12 --------------------------------- % 23.59/4.12 % 23.59/4.12 Begin of proof % 23.59/4.12 | % 23.59/4.12 | ALPHA: (mLEMonM) implies: % 23.59/4.12 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.59/4.12 | ! [v5: $i] : ( ~ (sdtasdt0(v1, v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) | % 23.59/4.12 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v2, v3) % 23.59/4.12 | | ~ sdtlseqdt0(v0, v1) | ~ sdtlseqdt0(sz0z00, v2) | ~ aScalar0(v3) % 23.59/4.12 | | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | % 23.59/4.12 | sdtlseqdt0(v4, v5)) % 23.59/4.12 | % 23.59/4.12 | ALPHA: (mDefSPZ) implies: % 23.59/4.13 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz0z00 | ~ % 23.59/4.13 | (sdtasasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | % 23.59/4.13 | ~ aVector0(v0) | ? [v3: $i] : ? [v4: $i] : (aDimensionOf0(v1) = v4 % 23.59/4.13 | & $i(v4) & ( ~ (v4 = sz00) | ( ~ (v3 = sz00) & aDimensionOf0(v0) = % 23.59/4.13 | v3 & $i(v3))))) % 23.59/4.13 | % 23.59/4.13 | ALPHA: (mScSqPos) implies: % 23.59/4.13 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasasdt0(v0, v0) = v1) | ~ $i(v0) | % 23.59/4.13 | ~ aVector0(v0) | sdtlseqdt0(sz0z00, v1)) % 23.59/4.13 | % 23.59/4.13 | ALPHA: (m__1678) implies: % 23.59/4.13 | (4) aVector0(xs) % 23.59/4.13 | (5) aVector0(xt) % 23.59/4.13 | % 23.59/4.13 | ALPHA: (m__1652) implies: % 23.59/4.13 | (6) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 23.59/4.13 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, % 23.59/4.13 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) % 23.59/4.13 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) % 23.59/4.13 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 23.59/4.13 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) % 23.59/4.13 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ % 23.59/4.13 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 & % 23.59/4.13 | $i(v7))))))) % 23.59/4.13 | % 23.59/4.13 | ALPHA: (m__1678_01) implies: % 23.59/4.13 | (7) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 & % 23.59/4.13 | $i(v0)) % 23.59/4.13 | % 23.59/4.13 | ALPHA: (m__) implies: % 23.59/4.13 | (8) $i(xs) % 23.59/4.13 | (9) $i(xt) % 23.59/4.13 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 23.59/4.13 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 23.59/4.13 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 23.59/4.13 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : % 23.59/4.13 | (sdtasasdt0(xt, xt) = v3 & sdtasasdt0(xs, xt) = v0 & sdtasasdt0(xs, % 23.59/4.14 | xs) = v2 & aDimensionOf0(xs) = sz00 & sdtasdt0(v2, v3) = v4 & % 23.59/4.14 | sdtasdt0(v0, v0) = v1 & $i(v18) & $i(v17) & $i(v16) & $i(v15) & % 23.59/4.14 | $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & % 23.59/4.14 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 23.59/4.14 | $i(v0) & ~ sdtlseqdt0(v1, v4)) % 23.59/4.14 | % 23.59/4.14 | ALPHA: (function-axioms) implies: % 23.59/4.14 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.59/4.14 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) % 23.59/4.14 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.59/4.14 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 23.59/4.14 | % 23.59/4.14 | DELTA: instantiating (7) with fresh symbol all_33_0 gives: % 23.59/4.14 | (13) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 & % 23.59/4.14 | $i(all_33_0) % 23.59/4.14 | % 23.59/4.14 | ALPHA: (13) implies: % 23.59/4.14 | (14) aDimensionOf0(xs) = all_33_0 % 23.59/4.14 | (15) aDimensionOf0(xt) = all_33_0 % 23.59/4.14 | % 23.59/4.14 | DELTA: instantiating (6) with fresh symbol all_35_0 gives: % 23.59/4.14 | (16) aDimensionOf0(xs) = all_35_0 & $i(all_35_0) & ! [v0: $i] : ! [v1: % 23.59/4.14 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1, % 23.59/4.14 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3) % 23.59/4.14 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) % 23.59/4.14 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 23.59/4.14 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7) % 23.59/4.14 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~ % 23.59/4.14 | iLess0(v5, all_35_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6 % 23.59/4.14 | & $i(v6)))))) % 23.59/4.14 | % 23.59/4.14 | ALPHA: (16) implies: % 23.59/4.14 | (17) aDimensionOf0(xs) = all_35_0 % 23.59/4.14 | % 23.59/4.14 | DELTA: instantiating (10) with fresh symbols all_41_0, all_41_1, all_41_2, % 23.59/4.14 | all_41_3, all_41_4, all_41_5, all_41_6, all_41_7, all_41_8, all_41_9, % 23.59/4.14 | all_41_10, all_41_11, all_41_12, all_41_13, all_41_14, all_41_15, % 23.59/4.14 | all_41_16, all_41_17, all_41_18 gives: % 23.59/4.14 | (18) sdtasasdt0(xt, xt) = all_41_15 & sdtasasdt0(xs, xt) = all_41_18 & % 23.59/4.14 | sdtasasdt0(xs, xs) = all_41_16 & aDimensionOf0(xs) = sz00 & % 23.59/4.14 | sdtasdt0(all_41_16, all_41_15) = all_41_14 & sdtasdt0(all_41_18, % 23.59/4.14 | all_41_18) = all_41_17 & $i(all_41_0) & $i(all_41_1) & $i(all_41_2) % 23.59/4.14 | & $i(all_41_3) & $i(all_41_4) & $i(all_41_5) & $i(all_41_6) & % 23.59/4.14 | $i(all_41_7) & $i(all_41_8) & $i(all_41_9) & $i(all_41_10) & % 23.59/4.14 | $i(all_41_11) & $i(all_41_12) & $i(all_41_13) & $i(all_41_14) & % 23.59/4.14 | $i(all_41_15) & $i(all_41_16) & $i(all_41_17) & $i(all_41_18) & ~ % 23.59/4.14 | sdtlseqdt0(all_41_17, all_41_14) % 23.59/4.14 | % 23.59/4.14 | ALPHA: (18) implies: % 23.59/4.15 | (19) ~ sdtlseqdt0(all_41_17, all_41_14) % 23.59/4.15 | (20) $i(all_41_16) % 23.59/4.15 | (21) sdtasdt0(all_41_18, all_41_18) = all_41_17 % 23.59/4.15 | (22) sdtasdt0(all_41_16, all_41_15) = all_41_14 % 23.59/4.15 | (23) aDimensionOf0(xs) = sz00 % 23.59/4.15 | (24) sdtasasdt0(xs, xs) = all_41_16 % 23.59/4.15 | (25) sdtasasdt0(xs, xt) = all_41_18 % 23.59/4.15 | (26) sdtasasdt0(xt, xt) = all_41_15 % 23.59/4.15 | % 23.59/4.15 | GROUND_INST: instantiating (11) with all_33_0, all_35_0, xs, simplifying with % 23.59/4.15 | (14), (17) gives: % 23.59/4.15 | (27) all_35_0 = all_33_0 % 23.59/4.15 | % 23.59/4.15 | GROUND_INST: instantiating (11) with sz00, all_35_0, xs, simplifying with % 23.59/4.15 | (17), (23) gives: % 23.59/4.15 | (28) all_35_0 = sz00 % 23.59/4.15 | % 23.59/4.15 | COMBINE_EQS: (27), (28) imply: % 23.59/4.15 | (29) all_33_0 = sz00 % 23.59/4.15 | % 23.59/4.15 | SIMP: (29) implies: % 23.59/4.15 | (30) all_33_0 = sz00 % 23.59/4.15 | % 23.59/4.15 | REDUCE: (15), (30) imply: % 24.02/4.15 | (31) aDimensionOf0(xt) = sz00 % 24.02/4.15 | % 24.02/4.15 | GROUND_INST: instantiating (2) with xs, xs, all_41_16, simplifying with (4), % 24.02/4.15 | (8), (24) gives: % 24.02/4.15 | (32) all_41_16 = sz0z00 | ? [v0: $i] : ? [v1: $i] : (aDimensionOf0(xs) = % 24.02/4.15 | v1 & $i(v1) & ( ~ (v1 = sz00) | ( ~ (v0 = sz00) & aDimensionOf0(xs) % 24.02/4.15 | = v0 & $i(v0)))) % 24.02/4.15 | % 24.02/4.15 | GROUND_INST: instantiating (mScPr) with xs, xs, all_41_16, simplifying with % 24.02/4.15 | (4), (8), (24) gives: % 24.02/4.15 | (33) aScalar0(all_41_16) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 24.02/4.15 | aDimensionOf0(xs) = v1 & aDimensionOf0(xs) = v0 & $i(v1) & $i(v0)) % 24.02/4.15 | % 24.02/4.15 | GROUND_INST: instantiating (3) with xs, all_41_16, simplifying with (4), (8), % 24.02/4.15 | (24) gives: % 24.02/4.15 | (34) sdtlseqdt0(sz0z00, all_41_16) % 24.02/4.15 | % 24.02/4.15 | GROUND_INST: instantiating (2) with xs, xt, all_41_18, simplifying with (4), % 24.02/4.15 | (5), (8), (9), (25) gives: % 24.02/4.16 | (35) all_41_18 = sz0z00 | ? [v0: $i] : ? [v1: $i] : (aDimensionOf0(xt) = % 24.02/4.16 | v1 & $i(v1) & ( ~ (v1 = sz00) | ( ~ (v0 = sz00) & aDimensionOf0(xs) % 24.02/4.16 | = v0 & $i(v0)))) % 24.02/4.16 | % 24.02/4.16 | GROUND_INST: instantiating (2) with xt, xt, all_41_15, simplifying with (5), % 24.02/4.16 | (9), (26) gives: % 24.02/4.16 | (36) all_41_15 = sz0z00 | ? [v0: $i] : ? [v1: $i] : (aDimensionOf0(xt) = % 24.02/4.16 | v1 & $i(v1) & ( ~ (v1 = sz00) | ( ~ (v0 = sz00) & aDimensionOf0(xt) % 24.02/4.16 | = v0 & $i(v0)))) % 24.02/4.16 | % 24.02/4.16 | BETA: splitting (33) gives: % 24.02/4.16 | % 24.02/4.16 | Case 1: % 24.02/4.16 | | % 24.02/4.16 | | (37) aScalar0(all_41_16) % 24.02/4.16 | | % 24.02/4.16 | | BETA: splitting (36) gives: % 24.02/4.16 | | % 24.02/4.16 | | Case 1: % 24.02/4.16 | | | % 24.02/4.16 | | | (38) all_41_15 = sz0z00 % 24.02/4.16 | | | % 24.02/4.16 | | | REDUCE: (22), (38) imply: % 24.02/4.16 | | | (39) sdtasdt0(all_41_16, sz0z00) = all_41_14 % 24.02/4.16 | | | % 24.02/4.16 | | | BETA: splitting (35) gives: % 24.02/4.16 | | | % 24.02/4.16 | | | Case 1: % 24.02/4.16 | | | | % 24.02/4.16 | | | | (40) all_41_18 = sz0z00 % 24.02/4.16 | | | | % 24.02/4.16 | | | | REDUCE: (21), (40) imply: % 24.02/4.16 | | | | (41) sdtasdt0(sz0z00, sz0z00) = all_41_17 % 24.02/4.16 | | | | % 24.02/4.16 | | | | BETA: splitting (32) gives: % 24.02/4.16 | | | | % 24.02/4.16 | | | | Case 1: % 24.02/4.16 | | | | | % 24.02/4.16 | | | | | (42) all_41_16 = sz0z00 % 24.02/4.16 | | | | | % 24.02/4.16 | | | | | REDUCE: (39), (42) imply: % 24.02/4.16 | | | | | (43) sdtasdt0(sz0z00, sz0z00) = all_41_14 % 24.02/4.16 | | | | | % 24.02/4.16 | | | | | REDUCE: (20), (42) imply: % 24.02/4.16 | | | | | (44) $i(sz0z00) % 24.02/4.16 | | | | | % 24.02/4.16 | | | | | REDUCE: (34), (42) imply: % 24.02/4.16 | | | | | (45) sdtlseqdt0(sz0z00, sz0z00) % 24.02/4.16 | | | | | % 24.02/4.16 | | | | | REDUCE: (37), (42) imply: % 24.02/4.16 | | | | | (46) aScalar0(sz0z00) % 24.02/4.16 | | | | | % 24.02/4.16 | | | | | GROUND_INST: instantiating (12) with all_41_17, all_41_14, sz0z00, % 24.02/4.16 | | | | | sz0z00, simplifying with (41), (43) gives: % 24.02/4.16 | | | | | (47) all_41_14 = all_41_17 % 24.02/4.16 | | | | | % 24.02/4.16 | | | | | REDUCE: (19), (47) imply: % 24.02/4.16 | | | | | (48) ~ sdtlseqdt0(all_41_17, all_41_17) % 24.02/4.16 | | | | | % 24.02/4.16 | | | | | GROUND_INST: instantiating (1) with sz0z00, sz0z00, sz0z00, sz0z00, % 24.02/4.16 | | | | | all_41_17, all_41_17, simplifying with (41), (44), (45), % 24.02/4.16 | | | | | (46), (48) gives: % 24.02/4.16 | | | | | (49) $false % 24.02/4.16 | | | | | % 24.02/4.16 | | | | | CLOSE: (49) is inconsistent. % 24.02/4.16 | | | | | % 24.02/4.17 | | | | Case 2: % 24.02/4.17 | | | | | % 24.02/4.17 | | | | | (50) ? [v0: $i] : ? [v1: $i] : (aDimensionOf0(xs) = v1 & $i(v1) & % 24.02/4.17 | | | | | ( ~ (v1 = sz00) | ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & % 24.02/4.17 | | | | | $i(v0)))) % 24.02/4.17 | | | | | % 24.02/4.17 | | | | | DELTA: instantiating (50) with fresh symbols all_78_0, all_78_1 gives: % 24.02/4.17 | | | | | (51) aDimensionOf0(xs) = all_78_0 & $i(all_78_0) & ( ~ (all_78_0 = % 24.02/4.17 | | | | | sz00) | ( ~ (all_78_1 = sz00) & aDimensionOf0(xs) = % 24.02/4.17 | | | | | all_78_1 & $i(all_78_1))) % 24.02/4.17 | | | | | % 24.02/4.17 | | | | | ALPHA: (51) implies: % 24.02/4.17 | | | | | (52) aDimensionOf0(xs) = all_78_0 % 24.02/4.17 | | | | | (53) ~ (all_78_0 = sz00) | ( ~ (all_78_1 = sz00) & % 24.02/4.17 | | | | | aDimensionOf0(xs) = all_78_1 & $i(all_78_1)) % 24.02/4.17 | | | | | % 24.02/4.17 | | | | | BETA: splitting (53) gives: % 24.02/4.17 | | | | | % 24.02/4.17 | | | | | Case 1: % 24.02/4.17 | | | | | | % 24.02/4.17 | | | | | | (54) ~ (all_78_0 = sz00) % 24.02/4.17 | | | | | | % 24.02/4.17 | | | | | | GROUND_INST: instantiating (11) with sz00, all_78_0, xs, simplifying % 24.02/4.17 | | | | | | with (23), (52) gives: % 24.02/4.17 | | | | | | (55) all_78_0 = sz00 % 24.02/4.17 | | | | | | % 24.02/4.17 | | | | | | REDUCE: (54), (55) imply: % 24.02/4.17 | | | | | | (56) $false % 24.02/4.17 | | | | | | % 24.02/4.17 | | | | | | CLOSE: (56) is inconsistent. % 24.02/4.17 | | | | | | % 24.02/4.17 | | | | | Case 2: % 24.02/4.17 | | | | | | % 24.02/4.17 | | | | | | (57) all_78_0 = sz00 % 24.02/4.17 | | | | | | (58) ~ (all_78_1 = sz00) & aDimensionOf0(xs) = all_78_1 & % 24.02/4.17 | | | | | | $i(all_78_1) % 24.02/4.17 | | | | | | % 24.02/4.17 | | | | | | ALPHA: (58) implies: % 24.02/4.17 | | | | | | (59) ~ (all_78_1 = sz00) % 24.02/4.17 | | | | | | (60) aDimensionOf0(xs) = all_78_1 % 24.02/4.17 | | | | | | % 24.58/4.17 | | | | | | GROUND_INST: instantiating (11) with sz00, all_78_1, xs, simplifying % 24.58/4.17 | | | | | | with (23), (60) gives: % 24.58/4.17 | | | | | | (61) all_78_1 = sz00 % 24.58/4.17 | | | | | | % 24.58/4.17 | | | | | | REDUCE: (59), (61) imply: % 24.58/4.17 | | | | | | (62) $false % 24.58/4.17 | | | | | | % 24.58/4.17 | | | | | | CLOSE: (62) is inconsistent. % 24.58/4.17 | | | | | | % 24.58/4.17 | | | | | End of split % 24.58/4.17 | | | | | % 24.58/4.17 | | | | End of split % 24.58/4.17 | | | | % 24.58/4.17 | | | Case 2: % 24.58/4.17 | | | | % 24.58/4.17 | | | | (63) ? [v0: $i] : ? [v1: $i] : (aDimensionOf0(xt) = v1 & $i(v1) & ( % 24.58/4.17 | | | | ~ (v1 = sz00) | ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & % 24.58/4.17 | | | | $i(v0)))) % 24.58/4.17 | | | | % 24.58/4.17 | | | | DELTA: instantiating (63) with fresh symbols all_74_0, all_74_1 gives: % 24.58/4.17 | | | | (64) aDimensionOf0(xt) = all_74_0 & $i(all_74_0) & ( ~ (all_74_0 = % 24.58/4.17 | | | | sz00) | ( ~ (all_74_1 = sz00) & aDimensionOf0(xs) = all_74_1 % 24.58/4.17 | | | | & $i(all_74_1))) % 24.58/4.17 | | | | % 24.58/4.17 | | | | ALPHA: (64) implies: % 24.58/4.17 | | | | (65) aDimensionOf0(xt) = all_74_0 % 24.58/4.18 | | | | (66) ~ (all_74_0 = sz00) | ( ~ (all_74_1 = sz00) & aDimensionOf0(xs) % 24.58/4.18 | | | | = all_74_1 & $i(all_74_1)) % 24.58/4.18 | | | | % 24.58/4.18 | | | | BETA: splitting (66) gives: % 24.58/4.18 | | | | % 24.58/4.18 | | | | Case 1: % 24.58/4.18 | | | | | % 24.58/4.18 | | | | | (67) ~ (all_74_0 = sz00) % 24.58/4.18 | | | | | % 24.58/4.18 | | | | | GROUND_INST: instantiating (11) with sz00, all_74_0, xt, simplifying % 24.58/4.18 | | | | | with (31), (65) gives: % 24.58/4.18 | | | | | (68) all_74_0 = sz00 % 24.58/4.18 | | | | | % 24.58/4.18 | | | | | REDUCE: (67), (68) imply: % 24.58/4.18 | | | | | (69) $false % 24.58/4.18 | | | | | % 24.58/4.18 | | | | | CLOSE: (69) is inconsistent. % 24.58/4.18 | | | | | % 24.58/4.18 | | | | Case 2: % 24.58/4.18 | | | | | % 24.58/4.18 | | | | | (70) ~ (all_74_1 = sz00) & aDimensionOf0(xs) = all_74_1 & % 24.58/4.18 | | | | | $i(all_74_1) % 24.58/4.18 | | | | | % 24.58/4.18 | | | | | ALPHA: (70) implies: % 24.58/4.18 | | | | | (71) ~ (all_74_1 = sz00) % 24.58/4.18 | | | | | (72) aDimensionOf0(xs) = all_74_1 % 24.58/4.18 | | | | | % 24.58/4.18 | | | | | GROUND_INST: instantiating (11) with sz00, all_74_1, xs, simplifying % 24.58/4.18 | | | | | with (23), (72) gives: % 24.58/4.18 | | | | | (73) all_74_1 = sz00 % 24.58/4.18 | | | | | % 24.58/4.18 | | | | | REDUCE: (71), (73) imply: % 24.58/4.18 | | | | | (74) $false % 24.58/4.18 | | | | | % 24.58/4.18 | | | | | CLOSE: (74) is inconsistent. % 24.58/4.18 | | | | | % 24.58/4.18 | | | | End of split % 24.58/4.18 | | | | % 24.58/4.18 | | | End of split % 24.58/4.18 | | | % 24.58/4.18 | | Case 2: % 24.58/4.18 | | | % 24.58/4.18 | | | (75) ? [v0: $i] : ? [v1: $i] : (aDimensionOf0(xt) = v1 & $i(v1) & ( ~ % 24.58/4.18 | | | (v1 = sz00) | ( ~ (v0 = sz00) & aDimensionOf0(xt) = v0 & % 24.58/4.18 | | | $i(v0)))) % 24.58/4.18 | | | % 24.58/4.18 | | | DELTA: instantiating (75) with fresh symbols all_70_0, all_70_1 gives: % 24.58/4.18 | | | (76) aDimensionOf0(xt) = all_70_0 & $i(all_70_0) & ( ~ (all_70_0 = % 24.58/4.18 | | | sz00) | ( ~ (all_70_1 = sz00) & aDimensionOf0(xt) = all_70_1 & % 24.58/4.18 | | | $i(all_70_1))) % 24.58/4.18 | | | % 24.58/4.18 | | | ALPHA: (76) implies: % 24.58/4.18 | | | (77) aDimensionOf0(xt) = all_70_0 % 24.58/4.18 | | | (78) ~ (all_70_0 = sz00) | ( ~ (all_70_1 = sz00) & aDimensionOf0(xt) = % 24.58/4.18 | | | all_70_1 & $i(all_70_1)) % 24.58/4.18 | | | % 24.58/4.18 | | | BETA: splitting (78) gives: % 24.58/4.18 | | | % 24.58/4.18 | | | Case 1: % 24.58/4.18 | | | | % 24.58/4.18 | | | | (79) ~ (all_70_0 = sz00) % 24.58/4.18 | | | | % 24.58/4.18 | | | | GROUND_INST: instantiating (11) with sz00, all_70_0, xt, simplifying % 24.58/4.18 | | | | with (31), (77) gives: % 24.58/4.18 | | | | (80) all_70_0 = sz00 % 24.58/4.18 | | | | % 24.58/4.18 | | | | REDUCE: (79), (80) imply: % 24.58/4.18 | | | | (81) $false % 24.58/4.18 | | | | % 24.58/4.18 | | | | CLOSE: (81) is inconsistent. % 24.58/4.18 | | | | % 24.58/4.18 | | | Case 2: % 24.58/4.18 | | | | % 24.58/4.18 | | | | (82) all_70_0 = sz00 % 24.58/4.18 | | | | (83) ~ (all_70_1 = sz00) & aDimensionOf0(xt) = all_70_1 & % 24.58/4.18 | | | | $i(all_70_1) % 24.58/4.18 | | | | % 24.58/4.18 | | | | ALPHA: (83) implies: % 24.58/4.19 | | | | (84) ~ (all_70_1 = sz00) % 24.58/4.19 | | | | (85) aDimensionOf0(xt) = all_70_1 % 24.58/4.19 | | | | % 24.58/4.19 | | | | GROUND_INST: instantiating (11) with sz00, all_70_1, xt, simplifying % 24.58/4.19 | | | | with (31), (85) gives: % 24.58/4.19 | | | | (86) all_70_1 = sz00 % 24.58/4.19 | | | | % 24.58/4.19 | | | | REDUCE: (84), (86) imply: % 24.58/4.19 | | | | (87) $false % 24.58/4.19 | | | | % 24.58/4.19 | | | | CLOSE: (87) is inconsistent. % 24.58/4.19 | | | | % 24.58/4.19 | | | End of split % 24.58/4.19 | | | % 24.58/4.19 | | End of split % 24.58/4.19 | | % 24.58/4.19 | Case 2: % 24.58/4.19 | | % 24.58/4.19 | | (88) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & aDimensionOf0(xs) = v1 & % 24.58/4.19 | | aDimensionOf0(xs) = v0 & $i(v1) & $i(v0)) % 24.58/4.19 | | % 24.58/4.19 | | DELTA: instantiating (88) with fresh symbols all_62_0, all_62_1 gives: % 24.58/4.19 | | (89) ~ (all_62_0 = all_62_1) & aDimensionOf0(xs) = all_62_0 & % 24.58/4.19 | | aDimensionOf0(xs) = all_62_1 & $i(all_62_0) & $i(all_62_1) % 24.58/4.19 | | % 24.58/4.19 | | ALPHA: (89) implies: % 24.58/4.19 | | (90) ~ (all_62_0 = all_62_1) % 24.58/4.19 | | (91) aDimensionOf0(xs) = all_62_1 % 24.58/4.19 | | (92) aDimensionOf0(xs) = all_62_0 % 24.58/4.19 | | % 24.58/4.19 | | GROUND_INST: instantiating (11) with sz00, all_62_0, xs, simplifying with % 24.58/4.19 | | (23), (92) gives: % 24.58/4.19 | | (93) all_62_0 = sz00 % 24.58/4.19 | | % 24.58/4.19 | | GROUND_INST: instantiating (11) with all_62_1, all_62_0, xs, simplifying % 24.58/4.19 | | with (91), (92) gives: % 24.58/4.19 | | (94) all_62_0 = all_62_1 % 24.58/4.19 | | % 24.58/4.19 | | COMBINE_EQS: (93), (94) imply: % 24.58/4.19 | | (95) all_62_1 = sz00 % 24.58/4.19 | | % 24.58/4.19 | | REDUCE: (90), (93), (95) imply: % 24.58/4.19 | | (96) $false % 24.58/4.19 | | % 24.58/4.19 | | CLOSE: (96) is inconsistent. % 24.58/4.19 | | % 24.58/4.19 | End of split % 24.58/4.19 | % 24.58/4.19 End of proof % 24.58/4.19 % SZS output end Proof for theBenchmark % 24.58/4.19 % 24.58/4.19 3609ms %------------------------------------------------------------------------------