%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG080+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 : n004.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 13:57:44 EDT 2023 % Result : Theorem 12.99s 2.53s % Output : Proof 21.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : RNG080+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n004.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Sun Aug 27 02:38:37 EDT 2023 % 0.14/0.35 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.62 % 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.62 (2023-06-19) % 0.19/0.62 % 0.19/0.62 (c) Philipp Rümmer, 2009-2023 % 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.62 Amanda Stjerna. % 0.19/0.62 Free software under BSD-3-Clause. % 0.19/0.62 % 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.62 % 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.68/1.23 Prover 1: Preprocessing ... % 3.68/1.23 Prover 4: Preprocessing ... % 3.95/1.28 Prover 5: Preprocessing ... % 3.95/1.28 Prover 6: Preprocessing ... % 3.95/1.28 Prover 2: Preprocessing ... % 3.95/1.28 Prover 0: Preprocessing ... % 3.95/1.28 Prover 3: Preprocessing ... % 9.13/2.11 Prover 1: Constructing countermodel ... % 10.23/2.16 Prover 3: Constructing countermodel ... % 10.23/2.18 Prover 6: Proving ... % 11.77/2.35 Prover 5: Constructing countermodel ... % 12.55/2.49 Prover 2: Proving ... % 12.55/2.49 Prover 4: Constructing countermodel ... % 12.99/2.53 Prover 3: proved (1885ms) % 12.99/2.53 % 12.99/2.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.99/2.53 % 12.99/2.53 Prover 6: stopped % 12.99/2.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.99/2.54 Prover 2: stopped % 13.41/2.55 Prover 5: stopped % 13.42/2.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.42/2.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.42/2.58 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.42/2.63 Prover 7: Preprocessing ... % 13.42/2.64 Prover 0: Proving ... % 13.42/2.64 Prover 0: stopped % 13.42/2.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.42/2.73 Prover 10: Preprocessing ... % 14.17/2.75 Prover 8: Preprocessing ... % 14.17/2.77 Prover 11: Preprocessing ... % 14.17/2.77 Prover 13: Preprocessing ... % 15.95/2.93 Prover 8: Warning: ignoring some quantifiers % 15.95/2.94 Prover 8: Constructing countermodel ... % 15.95/2.97 Prover 10: Constructing countermodel ... % 16.59/3.01 Prover 7: Constructing countermodel ... % 16.59/3.03 Prover 13: Constructing countermodel ... % 18.57/3.33 Prover 11: Constructing countermodel ... % 20.25/3.53 Prover 10: Found proof (size 72) % 20.25/3.53 Prover 10: proved (974ms) % 20.25/3.53 Prover 7: stopped % 20.25/3.53 Prover 13: stopped % 20.25/3.53 Prover 4: stopped % 20.25/3.53 Prover 8: stopped % 20.25/3.53 Prover 1: stopped % 20.25/3.53 Prover 11: stopped % 20.25/3.53 % 20.25/3.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.25/3.53 % 20.25/3.55 % SZS output start Proof for theBenchmark % 20.25/3.55 Assumptions after simplification: % 20.25/3.55 --------------------------------- % 20.25/3.55 % 20.25/3.55 (mDefSPN) % 20.81/3.58 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 20.81/3.58 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v2 = % 20.81/3.58 sz00 | ~ (sdtasasdt0(v3, v4) = v5) | ~ (sziznziztdt0(v1) = v4) | ~ % 20.81/3.58 (sziznziztdt0(v0) = v3) | ~ (sdtlbdtrb0(v1, v2) = v7) | ~ (sdtlbdtrb0(v0, % 20.81/3.58 v2) = v6) | ~ (aDimensionOf0(v1) = v2) | ~ (aDimensionOf0(v0) = v2) | % 20.81/3.58 ~ (sdtasdt0(v6, v7) = v8) | ~ (sdtpldt0(v5, v8) = v9) | ~ $i(v1) | ~ % 20.81/3.58 $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | (sdtasasdt0(v0, v1) = v9 & % 20.81/3.58 $i(v9))) % 20.81/3.58 % 20.81/3.58 (m__) % 20.81/3.58 $i(xt) & $i(xs) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 20.81/3.58 [v4: $i] : (sdtasasdt0(xt, xt) = v3 & sdtasasdt0(xs, xt) = v0 & sdtasasdt0(xs, % 20.81/3.58 xs) = v2 & sdtasdt0(v2, v3) = v4 & sdtasdt0(v0, v0) = v1 & $i(v4) & $i(v3) % 20.81/3.58 & $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, v4)) % 20.81/3.58 % 20.81/3.58 (m__1652) % 20.81/3.58 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! % 20.81/3.58 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2) % 20.81/3.58 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~ % 20.81/3.58 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ? % 20.81/3.58 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 & % 20.81/3.58 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) | % 20.81/3.58 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) & % 20.81/3.58 aDimensionOf0(v2) = v7 & $i(v7))))))) % 20.81/3.58 % 20.81/3.58 (m__1678) % 20.81/3.58 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs) % 20.81/3.58 % 20.81/3.58 (m__1678_01) % 20.81/3.59 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = % 20.81/3.59 v0 & $i(v0)) % 20.81/3.59 % 20.81/3.59 (m__1692) % 20.81/3.59 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & % 20.81/3.59 $i(v0)) % 20.81/3.59 % 20.81/3.59 (m__1709) % 20.87/3.59 sziznziztdt0(xs) = xp & $i(xp) & $i(xs) & aVector0(xp) % 20.87/3.59 % 20.87/3.59 (m__1726) % 20.87/3.59 sziznziztdt0(xt) = xq & $i(xq) & $i(xt) & aVector0(xq) % 20.87/3.59 % 20.87/3.59 (m__1746) % 20.87/3.59 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = % 20.87/3.59 v0 & $i(v0) & aScalar0(xA)) % 20.87/3.59 % 20.87/3.59 (m__1766) % 20.87/3.59 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = % 20.87/3.59 v0 & $i(v0) & aScalar0(xB)) % 20.87/3.59 % 20.87/3.59 (m__1783) % 20.87/3.59 sdtasasdt0(xp, xp) = xC & $i(xC) & $i(xp) & aScalar0(xC) % 20.87/3.59 % 20.87/3.59 (m__1800) % 20.87/3.59 sdtasasdt0(xq, xq) = xD & $i(xD) & $i(xq) & aScalar0(xD) % 20.87/3.59 % 20.87/3.59 (m__1820) % 20.87/3.59 sdtasasdt0(xp, xq) = xE & $i(xE) & $i(xq) & $i(xp) & aScalar0(xE) % 20.87/3.59 % 20.87/3.59 (m__1837) % 20.87/3.59 sdtasdt0(xA, xA) = xF & $i(xF) & $i(xA) & aScalar0(xF) % 20.87/3.59 % 20.87/3.59 (m__1854) % 20.87/3.59 sdtasdt0(xB, xB) = xG & $i(xG) & $i(xB) & aScalar0(xG) % 20.87/3.59 % 20.87/3.59 (m__1873) % 20.87/3.59 sdtasdt0(xA, xB) = xH & $i(xH) & $i(xB) & $i(xA) & aScalar0(xH) % 20.87/3.59 % 20.87/3.59 (m__2733) % 20.87/3.59 $i(xH) & $i(xG) & $i(xF) & $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: % 20.87/3.59 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtasdt0(v2, v3) = v4 & % 20.87/3.59 sdtasdt0(v0, v0) = v1 & sdtpldt0(xE, xH) = v0 & sdtpldt0(xD, xG) = v3 & % 20.87/3.59 sdtpldt0(xC, xF) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 20.87/3.59 sdtlseqdt0(v1, v4)) % 20.87/3.59 % 20.87/3.59 (function-axioms) % 20.87/3.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.87/3.59 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 20.87/3.59 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) % 20.87/3.59 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 20.87/3.59 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = % 20.87/3.59 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 20.87/3.59 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 20.87/3.59 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ % 20.87/3.59 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 20.87/3.59 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0: % 20.87/3.59 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 20.87/3.59 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 20.87/3.60 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 20.87/3.60 % 20.87/3.60 Further assumptions not needed in the proof: % 20.87/3.60 -------------------------------------------- % 20.87/3.60 mArith, mDefInit, mDefSPZ, mDimNat, mDistr, mDistr2, mElmSc, mEqInit, mIH, % 20.87/3.60 mIHOrd, mLEASm, mLEMon, mLEMonM, mLERef, mLETot, mLETrn, mLess, mMDNeg, mMNeg, % 20.87/3.60 mMulSc, mNatExtr, mNatSort, mNegSc, mPosMon, mSZeroSc, mScPr, mScSort, mScSqPos, % 20.87/3.60 mScZero, mSqPos, mSqrt, mSuccEqu, mSuccNat, mSumSc, mVcSort, mZeroNat, m__1892, % 20.87/3.60 m__1911, m__1930, m__1949, m__1967, m__1983 % 20.87/3.60 % 20.87/3.60 Those formulas are unsatisfiable: % 20.87/3.60 --------------------------------- % 20.87/3.60 % 20.87/3.60 Begin of proof % 20.87/3.60 | % 20.87/3.60 | ALPHA: (mDefSPN) implies: % 20.87/3.60 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 20.87/3.60 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : % 20.87/3.60 | (v2 = sz00 | ~ (sdtasasdt0(v3, v4) = v5) | ~ (sziznziztdt0(v1) = v4) % 20.87/3.60 | | ~ (sziznziztdt0(v0) = v3) | ~ (sdtlbdtrb0(v1, v2) = v7) | ~ % 20.87/3.60 | (sdtlbdtrb0(v0, v2) = v6) | ~ (aDimensionOf0(v1) = v2) | ~ % 20.87/3.60 | (aDimensionOf0(v0) = v2) | ~ (sdtasdt0(v6, v7) = v8) | ~ % 20.87/3.60 | (sdtpldt0(v5, v8) = v9) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | % 20.87/3.60 | ~ aVector0(v0) | (sdtasasdt0(v0, v1) = v9 & $i(v9))) % 20.87/3.60 | % 20.87/3.60 | ALPHA: (m__1678) implies: % 20.87/3.60 | (2) aVector0(xs) % 20.87/3.60 | (3) aVector0(xt) % 20.87/3.60 | % 20.87/3.60 | ALPHA: (m__1652) implies: % 20.87/3.60 | (4) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 20.87/3.60 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, % 20.87/3.60 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) % 20.87/3.60 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) % 20.87/3.60 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 20.87/3.60 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) % 20.87/3.60 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ % 20.87/3.60 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 & % 20.87/3.60 | $i(v7))))))) % 20.87/3.60 | % 20.87/3.60 | ALPHA: (m__1678_01) implies: % 20.87/3.60 | (5) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 & % 20.87/3.60 | $i(v0)) % 20.87/3.60 | % 20.87/3.60 | ALPHA: (m__1692) implies: % 20.87/3.60 | (6) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0)) % 20.87/3.60 | % 20.87/3.60 | ALPHA: (m__1709) implies: % 20.87/3.60 | (7) sziznziztdt0(xs) = xp % 20.87/3.60 | % 20.87/3.60 | ALPHA: (m__1726) implies: % 20.87/3.60 | (8) sziznziztdt0(xt) = xq % 20.87/3.60 | % 20.87/3.60 | ALPHA: (m__1746) implies: % 20.87/3.60 | (9) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 & % 20.87/3.60 | $i(v0) & aScalar0(xA)) % 20.87/3.60 | % 20.87/3.60 | ALPHA: (m__1766) implies: % 20.87/3.60 | (10) ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = v0 & % 20.87/3.60 | $i(v0) & aScalar0(xB)) % 20.87/3.60 | % 20.87/3.60 | ALPHA: (m__1783) implies: % 20.87/3.60 | (11) sdtasasdt0(xp, xp) = xC % 20.87/3.60 | % 20.87/3.60 | ALPHA: (m__1800) implies: % 20.87/3.60 | (12) sdtasasdt0(xq, xq) = xD % 20.87/3.60 | % 20.87/3.60 | ALPHA: (m__1820) implies: % 20.87/3.60 | (13) sdtasasdt0(xp, xq) = xE % 20.87/3.60 | % 20.87/3.60 | ALPHA: (m__1837) implies: % 20.87/3.60 | (14) sdtasdt0(xA, xA) = xF % 20.87/3.60 | % 20.87/3.60 | ALPHA: (m__1854) implies: % 20.87/3.60 | (15) sdtasdt0(xB, xB) = xG % 20.87/3.60 | % 20.87/3.60 | ALPHA: (m__1873) implies: % 20.87/3.60 | (16) sdtasdt0(xA, xB) = xH % 20.87/3.60 | % 20.87/3.60 | ALPHA: (m__2733) implies: % 20.87/3.61 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 20.87/3.61 | (sdtasdt0(v2, v3) = v4 & sdtasdt0(v0, v0) = v1 & sdtpldt0(xE, xH) = v0 % 20.87/3.61 | & sdtpldt0(xD, xG) = v3 & sdtpldt0(xC, xF) = v2 & $i(v4) & $i(v3) & % 20.87/3.61 | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v1, v4)) % 20.87/3.61 | % 20.87/3.61 | ALPHA: (m__) implies: % 20.87/3.61 | (18) $i(xs) % 20.87/3.61 | (19) $i(xt) % 20.96/3.61 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 20.96/3.61 | (sdtasasdt0(xt, xt) = v3 & sdtasasdt0(xs, xt) = v0 & sdtasasdt0(xs, % 20.96/3.61 | xs) = v2 & sdtasdt0(v2, v3) = v4 & sdtasdt0(v0, v0) = v1 & $i(v4) % 20.96/3.61 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, v4)) % 20.96/3.61 | % 20.96/3.61 | ALPHA: (function-axioms) implies: % 20.96/3.61 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 20.96/3.61 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) % 20.96/3.61 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.96/3.61 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 20.96/3.61 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.96/3.61 | (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) % 20.96/3.61 | % 20.96/3.61 | DELTA: instantiating (5) with fresh symbol all_33_0 gives: % 20.96/3.61 | (24) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 & % 20.96/3.61 | $i(all_33_0) % 20.96/3.61 | % 20.96/3.61 | ALPHA: (24) implies: % 20.96/3.61 | (25) aDimensionOf0(xs) = all_33_0 % 20.96/3.61 | (26) aDimensionOf0(xt) = all_33_0 % 20.96/3.61 | % 20.96/3.61 | DELTA: instantiating (6) with fresh symbol all_35_0 gives: % 20.96/3.61 | (27) ~ (all_35_0 = sz00) & aDimensionOf0(xs) = all_35_0 & $i(all_35_0) % 20.96/3.61 | % 20.96/3.61 | ALPHA: (27) implies: % 20.96/3.61 | (28) ~ (all_35_0 = sz00) % 20.96/3.61 | (29) aDimensionOf0(xs) = all_35_0 % 20.96/3.61 | % 20.96/3.61 | DELTA: instantiating (10) with fresh symbol all_37_0 gives: % 20.96/3.61 | (30) sdtlbdtrb0(xt, all_37_0) = xB & aDimensionOf0(xt) = all_37_0 & % 20.96/3.61 | $i(all_37_0) & aScalar0(xB) % 20.96/3.61 | % 20.96/3.61 | ALPHA: (30) implies: % 20.96/3.61 | (31) aDimensionOf0(xt) = all_37_0 % 20.96/3.61 | (32) sdtlbdtrb0(xt, all_37_0) = xB % 20.96/3.61 | % 20.96/3.61 | DELTA: instantiating (9) with fresh symbol all_39_0 gives: % 20.96/3.61 | (33) sdtlbdtrb0(xs, all_39_0) = xA & aDimensionOf0(xs) = all_39_0 & % 20.96/3.61 | $i(all_39_0) & aScalar0(xA) % 20.96/3.61 | % 20.96/3.61 | ALPHA: (33) implies: % 20.96/3.61 | (34) aDimensionOf0(xs) = all_39_0 % 20.96/3.61 | (35) sdtlbdtrb0(xs, all_39_0) = xA % 20.96/3.61 | % 20.96/3.61 | DELTA: instantiating (20) with fresh symbols all_45_0, all_45_1, all_45_2, % 20.96/3.61 | all_45_3, all_45_4 gives: % 20.96/3.61 | (36) sdtasasdt0(xt, xt) = all_45_1 & sdtasasdt0(xs, xt) = all_45_4 & % 20.96/3.61 | sdtasasdt0(xs, xs) = all_45_2 & sdtasdt0(all_45_2, all_45_1) = % 20.96/3.61 | all_45_0 & sdtasdt0(all_45_4, all_45_4) = all_45_3 & $i(all_45_0) & % 20.96/3.61 | $i(all_45_1) & $i(all_45_2) & $i(all_45_3) & $i(all_45_4) & ~ % 20.96/3.61 | sdtlseqdt0(all_45_3, all_45_0) % 20.96/3.61 | % 20.96/3.61 | ALPHA: (36) implies: % 20.96/3.61 | (37) ~ sdtlseqdt0(all_45_3, all_45_0) % 20.96/3.61 | (38) sdtasdt0(all_45_4, all_45_4) = all_45_3 % 20.96/3.61 | (39) sdtasdt0(all_45_2, all_45_1) = all_45_0 % 20.96/3.61 | (40) sdtasasdt0(xs, xs) = all_45_2 % 20.96/3.61 | (41) sdtasasdt0(xs, xt) = all_45_4 % 20.96/3.61 | (42) sdtasasdt0(xt, xt) = all_45_1 % 20.96/3.61 | % 20.96/3.61 | DELTA: instantiating (17) with fresh symbols all_47_0, all_47_1, all_47_2, % 20.96/3.61 | all_47_3, all_47_4 gives: % 20.96/3.61 | (43) sdtasdt0(all_47_2, all_47_1) = all_47_0 & sdtasdt0(all_47_4, all_47_4) % 20.96/3.61 | = all_47_3 & sdtpldt0(xE, xH) = all_47_4 & sdtpldt0(xD, xG) = all_47_1 % 20.96/3.61 | & sdtpldt0(xC, xF) = all_47_2 & $i(all_47_0) & $i(all_47_1) & % 20.96/3.61 | $i(all_47_2) & $i(all_47_3) & $i(all_47_4) & sdtlseqdt0(all_47_3, % 20.96/3.61 | all_47_0) % 20.96/3.61 | % 20.96/3.61 | ALPHA: (43) implies: % 20.96/3.61 | (44) sdtlseqdt0(all_47_3, all_47_0) % 20.96/3.62 | (45) sdtpldt0(xC, xF) = all_47_2 % 20.96/3.62 | (46) sdtpldt0(xD, xG) = all_47_1 % 20.96/3.62 | (47) sdtpldt0(xE, xH) = all_47_4 % 20.96/3.62 | (48) sdtasdt0(all_47_4, all_47_4) = all_47_3 % 20.96/3.62 | (49) sdtasdt0(all_47_2, all_47_1) = all_47_0 % 20.96/3.62 | % 20.96/3.62 | DELTA: instantiating (4) with fresh symbol all_49_0 gives: % 21.01/3.62 | (50) aDimensionOf0(xs) = all_49_0 & $i(all_49_0) & ! [v0: $i] : ! [v1: % 21.01/3.62 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1, % 21.01/3.62 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3) % 21.01/3.62 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) % 21.01/3.62 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 21.01/3.62 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7) % 21.01/3.62 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~ % 21.01/3.62 | iLess0(v5, all_49_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6 % 21.01/3.62 | & $i(v6)))))) % 21.01/3.62 | % 21.01/3.62 | ALPHA: (50) implies: % 21.01/3.62 | (51) aDimensionOf0(xs) = all_49_0 % 21.01/3.62 | % 21.01/3.62 | GROUND_INST: instantiating (21) with all_35_0, all_39_0, xs, simplifying with % 21.01/3.62 | (29), (34) gives: % 21.01/3.62 | (52) all_39_0 = all_35_0 % 21.01/3.62 | % 21.01/3.62 | GROUND_INST: instantiating (21) with all_39_0, all_49_0, xs, simplifying with % 21.01/3.62 | (34), (51) gives: % 21.01/3.62 | (53) all_49_0 = all_39_0 % 21.01/3.62 | % 21.01/3.62 | GROUND_INST: instantiating (21) with all_33_0, all_49_0, xs, simplifying with % 21.01/3.62 | (25), (51) gives: % 21.01/3.62 | (54) all_49_0 = all_33_0 % 21.01/3.62 | % 21.01/3.62 | GROUND_INST: instantiating (21) with all_33_0, all_37_0, xt, simplifying with % 21.01/3.62 | (26), (31) gives: % 21.01/3.62 | (55) all_37_0 = all_33_0 % 21.01/3.62 | % 21.01/3.62 | COMBINE_EQS: (53), (54) imply: % 21.01/3.62 | (56) all_39_0 = all_33_0 % 21.01/3.62 | % 21.01/3.62 | SIMP: (56) implies: % 21.01/3.62 | (57) all_39_0 = all_33_0 % 21.01/3.62 | % 21.01/3.62 | COMBINE_EQS: (52), (57) imply: % 21.01/3.62 | (58) all_35_0 = all_33_0 % 21.01/3.62 | % 21.01/3.62 | REDUCE: (28), (58) imply: % 21.01/3.62 | (59) ~ (all_33_0 = sz00) % 21.01/3.62 | % 21.01/3.62 | REDUCE: (32), (55) imply: % 21.01/3.62 | (60) sdtlbdtrb0(xt, all_33_0) = xB % 21.01/3.62 | % 21.01/3.62 | REDUCE: (35), (57) imply: % 21.01/3.62 | (61) sdtlbdtrb0(xs, all_33_0) = xA % 21.01/3.62 | % 21.01/3.62 | GROUND_INST: instantiating (1) with xs, xs, all_33_0, xp, xp, xC, xA, xA, xF, % 21.01/3.62 | all_47_2, simplifying with (2), (7), (11), (14), (18), (25), % 21.01/3.62 | (45), (61) gives: % 21.01/3.62 | (62) all_33_0 = sz00 | (sdtasasdt0(xs, xs) = all_47_2 & $i(all_47_2)) % 21.01/3.62 | % 21.01/3.62 | GROUND_INST: instantiating (1) with xs, xt, all_33_0, xp, xq, xE, xA, xB, xH, % 21.01/3.62 | all_47_4, simplifying with (2), (3), (7), (8), (13), (16), (18), % 21.01/3.62 | (19), (25), (26), (47), (60), (61) gives: % 21.01/3.63 | (63) all_33_0 = sz00 | (sdtasasdt0(xs, xt) = all_47_4 & $i(all_47_4)) % 21.01/3.63 | % 21.01/3.63 | GROUND_INST: instantiating (1) with xt, xt, all_33_0, xq, xq, xD, xB, xB, xG, % 21.01/3.63 | all_47_1, simplifying with (3), (8), (12), (15), (19), (26), % 21.01/3.63 | (46), (60) gives: % 21.01/3.63 | (64) all_33_0 = sz00 | (sdtasasdt0(xt, xt) = all_47_1 & $i(all_47_1)) % 21.01/3.63 | % 21.01/3.63 | BETA: splitting (62) gives: % 21.01/3.63 | % 21.01/3.63 | Case 1: % 21.01/3.63 | | % 21.01/3.63 | | (65) all_33_0 = sz00 % 21.01/3.63 | | % 21.01/3.63 | | REDUCE: (59), (65) imply: % 21.01/3.63 | | (66) $false % 21.01/3.63 | | % 21.01/3.63 | | CLOSE: (66) is inconsistent. % 21.01/3.63 | | % 21.01/3.63 | Case 2: % 21.01/3.63 | | % 21.01/3.63 | | (67) sdtasasdt0(xs, xs) = all_47_2 & $i(all_47_2) % 21.01/3.63 | | % 21.01/3.63 | | ALPHA: (67) implies: % 21.01/3.63 | | (68) sdtasasdt0(xs, xs) = all_47_2 % 21.01/3.63 | | % 21.01/3.63 | | BETA: splitting (63) gives: % 21.01/3.63 | | % 21.01/3.63 | | Case 1: % 21.01/3.63 | | | % 21.01/3.63 | | | (69) all_33_0 = sz00 % 21.01/3.63 | | | % 21.01/3.63 | | | REDUCE: (59), (69) imply: % 21.01/3.63 | | | (70) $false % 21.01/3.63 | | | % 21.01/3.63 | | | CLOSE: (70) is inconsistent. % 21.01/3.63 | | | % 21.01/3.63 | | Case 2: % 21.01/3.63 | | | % 21.01/3.63 | | | (71) sdtasasdt0(xs, xt) = all_47_4 & $i(all_47_4) % 21.01/3.63 | | | % 21.01/3.63 | | | ALPHA: (71) implies: % 21.01/3.63 | | | (72) sdtasasdt0(xs, xt) = all_47_4 % 21.01/3.63 | | | % 21.01/3.63 | | | BETA: splitting (64) gives: % 21.01/3.63 | | | % 21.01/3.63 | | | Case 1: % 21.01/3.63 | | | | % 21.01/3.63 | | | | (73) all_33_0 = sz00 % 21.01/3.63 | | | | % 21.01/3.63 | | | | REDUCE: (59), (73) imply: % 21.01/3.63 | | | | (74) $false % 21.01/3.63 | | | | % 21.01/3.63 | | | | CLOSE: (74) is inconsistent. % 21.01/3.63 | | | | % 21.01/3.63 | | | Case 2: % 21.01/3.63 | | | | % 21.01/3.63 | | | | (75) sdtasasdt0(xt, xt) = all_47_1 & $i(all_47_1) % 21.01/3.63 | | | | % 21.01/3.63 | | | | ALPHA: (75) implies: % 21.01/3.63 | | | | (76) sdtasasdt0(xt, xt) = all_47_1 % 21.01/3.63 | | | | % 21.01/3.63 | | | | GROUND_INST: instantiating (23) with all_45_2, all_47_2, xs, xs, % 21.01/3.63 | | | | simplifying with (40), (68) gives: % 21.01/3.63 | | | | (77) all_47_2 = all_45_2 % 21.01/3.63 | | | | % 21.01/3.63 | | | | GROUND_INST: instantiating (23) with all_45_4, all_47_4, xt, xs, % 21.01/3.63 | | | | simplifying with (41), (72) gives: % 21.01/3.63 | | | | (78) all_47_4 = all_45_4 % 21.01/3.63 | | | | % 21.01/3.63 | | | | GROUND_INST: instantiating (23) with all_45_1, all_47_1, xt, xt, % 21.01/3.63 | | | | simplifying with (42), (76) gives: % 21.01/3.63 | | | | (79) all_47_1 = all_45_1 % 21.01/3.63 | | | | % 21.01/3.63 | | | | REDUCE: (49), (77), (79) imply: % 21.01/3.63 | | | | (80) sdtasdt0(all_45_2, all_45_1) = all_47_0 % 21.01/3.63 | | | | % 21.01/3.63 | | | | REDUCE: (48), (78) imply: % 21.01/3.63 | | | | (81) sdtasdt0(all_45_4, all_45_4) = all_47_3 % 21.01/3.63 | | | | % 21.01/3.63 | | | | GROUND_INST: instantiating (22) with all_45_3, all_47_3, all_45_4, % 21.01/3.63 | | | | all_45_4, simplifying with (38), (81) gives: % 21.01/3.63 | | | | (82) all_47_3 = all_45_3 % 21.01/3.63 | | | | % 21.01/3.63 | | | | GROUND_INST: instantiating (22) with all_45_0, all_47_0, all_45_1, % 21.01/3.63 | | | | all_45_2, simplifying with (39), (80) gives: % 21.01/3.63 | | | | (83) all_47_0 = all_45_0 % 21.01/3.63 | | | | % 21.01/3.63 | | | | REDUCE: (44), (82), (83) imply: % 21.01/3.63 | | | | (84) sdtlseqdt0(all_45_3, all_45_0) % 21.01/3.63 | | | | % 21.01/3.63 | | | | PRED_UNIFY: (37), (84) imply: % 21.01/3.63 | | | | (85) $false % 21.01/3.63 | | | | % 21.01/3.63 | | | | CLOSE: (85) is inconsistent. % 21.01/3.63 | | | | % 21.01/3.63 | | | End of split % 21.01/3.63 | | | % 21.01/3.63 | | End of split % 21.01/3.63 | | % 21.01/3.63 | End of split % 21.01/3.63 | % 21.01/3.63 End of proof % 21.01/3.64 % SZS output end Proof for theBenchmark % 21.01/3.64 % 21.01/3.64 3016ms %------------------------------------------------------------------------------