%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG080+2 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n032.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 11.75s 2.24s % Output : Proof 18.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.07 % Problem : RNG080+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.07 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.06/0.26 % Computer : n032.cluster.edu % 0.06/0.26 % Model : x86_64 x86_64 % 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.26 % Memory : 8042.1875MB % 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.06/0.26 % CPULimit : 300 % 0.06/0.26 % WCLimit : 300 % 0.06/0.26 % DateTime : Sun Aug 27 02:56:44 EDT 2023 % 0.06/0.26 % CPUTime : % 0.11/0.47 ________ _____ % 0.11/0.47 ___ __ \_________(_)________________________________ % 0.11/0.47 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.11/0.47 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.11/0.47 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.11/0.47 % 0.11/0.47 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.11/0.47 (2023-06-19) % 0.11/0.47 % 0.11/0.47 (c) Philipp Rümmer, 2009-2023 % 0.11/0.47 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.11/0.47 Amanda Stjerna. % 0.11/0.47 Free software under BSD-3-Clause. % 0.11/0.47 % 0.11/0.47 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.11/0.47 % 0.11/0.47 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.11/0.48 Running up to 7 provers in parallel. % 0.11/0.49 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.11/0.49 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.11/0.49 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.11/0.49 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.11/0.49 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.11/0.49 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.11/0.49 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.74/1.02 Prover 1: Preprocessing ... % 2.74/1.02 Prover 4: Preprocessing ... % 3.30/1.05 Prover 0: Preprocessing ... % 3.30/1.05 Prover 5: Preprocessing ... % 3.30/1.06 Prover 2: Preprocessing ... % 3.30/1.06 Prover 6: Preprocessing ... % 3.30/1.06 Prover 3: Preprocessing ... % 8.34/1.80 Prover 3: Constructing countermodel ... % 8.80/1.81 Prover 6: Proving ... % 8.80/1.81 Prover 1: Constructing countermodel ... % 9.90/1.97 Prover 5: Constructing countermodel ... % 10.18/2.11 Prover 2: Proving ... % 10.18/2.13 Prover 4: Constructing countermodel ... % 10.18/2.14 Prover 0: Proving ... % 11.75/2.24 Prover 3: proved (1754ms) % 11.75/2.24 % 11.75/2.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.75/2.24 % 11.75/2.25 Prover 5: stopped % 11.75/2.26 Prover 2: stopped % 12.23/2.28 Prover 0: stopped % 12.23/2.28 Prover 6: stopped % 12.23/2.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.23/2.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.23/2.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.23/2.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.23/2.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.23/2.35 Prover 7: Preprocessing ... % 13.10/2.39 Prover 8: Preprocessing ... % 13.10/2.41 Prover 10: Preprocessing ... % 13.38/2.43 Prover 11: Preprocessing ... % 13.44/2.45 Prover 13: Preprocessing ... % 14.04/2.53 Prover 10: Constructing countermodel ... % 14.04/2.54 Prover 8: Warning: ignoring some quantifiers % 14.04/2.56 Prover 8: Constructing countermodel ... % 14.53/2.59 Prover 7: Constructing countermodel ... % 14.53/2.63 Prover 13: Constructing countermodel ... % 15.47/2.81 Prover 11: Constructing countermodel ... % 17.97/3.06 Prover 10: Found proof (size 82) % 17.97/3.06 Prover 10: proved (779ms) % 17.97/3.06 Prover 7: stopped % 17.97/3.06 Prover 13: stopped % 17.97/3.06 Prover 8: stopped % 17.97/3.06 Prover 4: stopped % 17.97/3.06 Prover 11: stopped % 17.97/3.06 Prover 1: stopped % 17.97/3.06 % 17.97/3.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.97/3.06 % 17.97/3.08 % SZS output start Proof for theBenchmark % 17.97/3.08 Assumptions after simplification: % 17.97/3.08 --------------------------------- % 17.97/3.08 % 17.97/3.09 (mDefSPN) % 17.97/3.11 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 17.97/3.11 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v2 = % 17.97/3.11 sz00 | ~ (sdtasasdt0(v3, v4) = v5) | ~ (sziznziztdt0(v1) = v4) | ~ % 17.97/3.11 (sziznziztdt0(v0) = v3) | ~ (sdtlbdtrb0(v1, v2) = v7) | ~ (sdtlbdtrb0(v0, % 17.97/3.11 v2) = v6) | ~ (aDimensionOf0(v1) = v2) | ~ (aDimensionOf0(v0) = v2) | % 17.97/3.11 ~ (sdtasdt0(v6, v7) = v8) | ~ (sdtpldt0(v5, v8) = v9) | ~ $i(v1) | ~ % 17.97/3.11 $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | (sdtasasdt0(v0, v1) = v9 & % 17.97/3.11 $i(v9))) % 17.97/3.11 % 17.97/3.11 (m__) % 17.97/3.11 $i(xt) & $i(xs) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 17.97/3.11 [v4: $i] : (sdtasasdt0(xt, xt) = v3 & sdtasasdt0(xs, xt) = v0 & sdtasasdt0(xs, % 17.97/3.11 xs) = v2 & sdtasdt0(v2, v3) = v4 & sdtasdt0(v0, v0) = v1 & $i(v4) & $i(v3) % 17.97/3.11 & $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, v4)) % 17.97/3.11 % 17.97/3.11 (m__1652) % 17.97/3.11 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! % 17.97/3.11 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2) % 17.97/3.11 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~ % 17.97/3.11 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ? % 17.97/3.11 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 & % 17.97/3.11 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) | % 17.97/3.11 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) & % 17.97/3.11 aDimensionOf0(v2) = v7 & $i(v7))))))) % 17.97/3.11 % 17.97/3.11 (m__1678) % 17.97/3.11 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs) % 17.97/3.11 % 17.97/3.11 (m__1678_01) % 17.97/3.12 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = % 17.97/3.12 v0 & $i(v0)) % 17.97/3.12 % 17.97/3.12 (m__1692) % 17.97/3.12 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & % 17.97/3.12 $i(v0)) % 17.97/3.12 % 17.97/3.12 (m__1709) % 17.97/3.12 $i(xp) & $i(xs) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp & % 17.97/3.12 aDimensionOf0(xp) = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 & % 17.97/3.12 $i(v1) & $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~ % 17.97/3.12 (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 17.97/3.12 (sdtlbdtrb0(xs, v2) = v3 & $i(v3)))) % 17.97/3.12 % 17.97/3.12 (m__1726) % 17.97/3.12 $i(xq) & $i(xt) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq & % 17.97/3.12 aDimensionOf0(xq) = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 & % 17.97/3.12 $i(v1) & $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~ % 17.97/3.12 (sdtlbdtrb0(xq, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 17.97/3.12 (sdtlbdtrb0(xt, v2) = v3 & $i(v3)))) % 17.97/3.12 % 17.97/3.12 (m__1746) % 17.97/3.12 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = % 17.97/3.12 v0 & $i(v0) & aScalar0(xA)) % 17.97/3.12 % 17.97/3.12 (m__1766) % 17.97/3.12 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = % 17.97/3.12 v0 & $i(v0) & aScalar0(xB)) % 17.97/3.12 % 17.97/3.12 (m__1783) % 17.97/3.12 sdtasasdt0(xp, xp) = xC & $i(xC) & $i(xp) & aScalar0(xC) % 17.97/3.12 % 17.97/3.12 (m__1800) % 17.97/3.12 sdtasasdt0(xq, xq) = xD & $i(xD) & $i(xq) & aScalar0(xD) % 17.97/3.12 % 17.97/3.12 (m__1820) % 17.97/3.12 sdtasasdt0(xp, xq) = xE & $i(xE) & $i(xq) & $i(xp) & aScalar0(xE) % 17.97/3.12 % 17.97/3.12 (m__1837) % 17.97/3.12 sdtasdt0(xA, xA) = xF & $i(xF) & $i(xA) & aScalar0(xF) % 17.97/3.12 % 17.97/3.12 (m__1854) % 18.54/3.12 sdtasdt0(xB, xB) = xG & $i(xG) & $i(xB) & aScalar0(xG) % 18.54/3.12 % 18.54/3.12 (m__1873) % 18.54/3.12 sdtasdt0(xA, xB) = xH & $i(xH) & $i(xB) & $i(xA) & aScalar0(xH) % 18.54/3.12 % 18.54/3.12 (m__2733) % 18.54/3.13 $i(xH) & $i(xG) & $i(xF) & $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: % 18.54/3.13 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtasdt0(v2, v3) = v4 & % 18.54/3.13 sdtasdt0(v0, v0) = v1 & sdtpldt0(xE, xH) = v0 & sdtpldt0(xD, xG) = v3 & % 18.54/3.13 sdtpldt0(xC, xF) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 18.54/3.13 sdtlseqdt0(v1, v4)) % 18.54/3.13 % 18.54/3.13 (function-axioms) % 18.54/3.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.54/3.13 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 18.54/3.13 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) % 18.54/3.13 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 18.54/3.13 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = % 18.54/3.13 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 18.54/3.13 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 18.54/3.13 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~ % 18.54/3.13 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 18.54/3.13 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0: % 18.54/3.13 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ % 18.54/3.13 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 18.54/3.13 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 18.54/3.13 % 18.54/3.13 Further assumptions not needed in the proof: % 18.54/3.13 -------------------------------------------- % 18.54/3.13 mArith, mDefInit, mDefSPZ, mDimNat, mDistr, mDistr2, mElmSc, mEqInit, mIH, % 18.54/3.13 mIHOrd, mLEASm, mLEMon, mLEMonM, mLERef, mLETot, mLETrn, mLess, mMDNeg, mMNeg, % 18.54/3.13 mMulSc, mNatExtr, mNatSort, mNegSc, mPosMon, mSZeroSc, mScPr, mScSort, mScSqPos, % 18.54/3.13 mScZero, mSqPos, mSqrt, mSuccEqu, mSuccNat, mSumSc, mVcSort, mZeroNat, m__1892, % 18.54/3.13 m__1911, m__1930, m__1949, m__1967, m__1983 % 18.54/3.13 % 18.54/3.13 Those formulas are unsatisfiable: % 18.54/3.13 --------------------------------- % 18.54/3.13 % 18.54/3.13 Begin of proof % 18.54/3.13 | % 18.54/3.13 | ALPHA: (mDefSPN) implies: % 18.54/3.13 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 18.54/3.13 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : % 18.54/3.13 | (v2 = sz00 | ~ (sdtasasdt0(v3, v4) = v5) | ~ (sziznziztdt0(v1) = v4) % 18.54/3.13 | | ~ (sziznziztdt0(v0) = v3) | ~ (sdtlbdtrb0(v1, v2) = v7) | ~ % 18.54/3.13 | (sdtlbdtrb0(v0, v2) = v6) | ~ (aDimensionOf0(v1) = v2) | ~ % 18.54/3.13 | (aDimensionOf0(v0) = v2) | ~ (sdtasdt0(v6, v7) = v8) | ~ % 18.54/3.13 | (sdtpldt0(v5, v8) = v9) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | % 18.54/3.13 | ~ aVector0(v0) | (sdtasasdt0(v0, v1) = v9 & $i(v9))) % 18.54/3.13 | % 18.54/3.13 | ALPHA: (m__1678) implies: % 18.54/3.13 | (2) aVector0(xs) % 18.54/3.13 | (3) aVector0(xt) % 18.54/3.13 | % 18.54/3.13 | ALPHA: (m__1652) implies: % 18.54/3.14 | (4) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 18.54/3.14 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, % 18.54/3.14 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) % 18.54/3.14 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) % 18.54/3.14 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 18.54/3.14 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) % 18.54/3.14 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ % 18.54/3.14 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 & % 18.54/3.14 | $i(v7))))))) % 18.54/3.14 | % 18.54/3.14 | ALPHA: (m__1678_01) implies: % 18.54/3.14 | (5) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 & % 18.54/3.14 | $i(v0)) % 18.54/3.14 | % 18.54/3.14 | ALPHA: (m__1692) implies: % 18.54/3.14 | (6) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0)) % 18.54/3.14 | % 18.54/3.14 | ALPHA: (m__1709) implies: % 18.54/3.14 | (7) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp & aDimensionOf0(xp) % 18.54/3.14 | = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) & % 18.54/3.14 | $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~ % 18.54/3.14 | (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 18.54/3.14 | (sdtlbdtrb0(xs, v2) = v3 & $i(v3)))) % 18.54/3.14 | % 18.54/3.14 | ALPHA: (m__1726) implies: % 18.54/3.14 | (8) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq & aDimensionOf0(xq) % 18.54/3.14 | = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) & % 18.54/3.14 | $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~ % 18.54/3.14 | (sdtlbdtrb0(xq, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) | % 18.54/3.14 | (sdtlbdtrb0(xt, v2) = v3 & $i(v3)))) % 18.54/3.14 | % 18.54/3.14 | ALPHA: (m__1746) implies: % 18.54/3.14 | (9) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 & % 18.54/3.14 | $i(v0) & aScalar0(xA)) % 18.54/3.14 | % 18.54/3.14 | ALPHA: (m__1766) implies: % 18.54/3.14 | (10) ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = v0 & % 18.54/3.14 | $i(v0) & aScalar0(xB)) % 18.54/3.14 | % 18.54/3.14 | ALPHA: (m__1783) implies: % 18.54/3.14 | (11) sdtasasdt0(xp, xp) = xC % 18.54/3.14 | % 18.54/3.14 | ALPHA: (m__1800) implies: % 18.54/3.14 | (12) sdtasasdt0(xq, xq) = xD % 18.54/3.14 | % 18.54/3.14 | ALPHA: (m__1820) implies: % 18.54/3.14 | (13) sdtasasdt0(xp, xq) = xE % 18.54/3.14 | % 18.54/3.14 | ALPHA: (m__1837) implies: % 18.54/3.14 | (14) sdtasdt0(xA, xA) = xF % 18.54/3.14 | % 18.54/3.14 | ALPHA: (m__1854) implies: % 18.54/3.14 | (15) sdtasdt0(xB, xB) = xG % 18.54/3.14 | % 18.54/3.14 | ALPHA: (m__1873) implies: % 18.54/3.14 | (16) sdtasdt0(xA, xB) = xH % 18.54/3.14 | % 18.54/3.14 | ALPHA: (m__2733) implies: % 18.54/3.14 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 18.54/3.14 | (sdtasdt0(v2, v3) = v4 & sdtasdt0(v0, v0) = v1 & sdtpldt0(xE, xH) = v0 % 18.54/3.14 | & sdtpldt0(xD, xG) = v3 & sdtpldt0(xC, xF) = v2 & $i(v4) & $i(v3) & % 18.54/3.14 | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v1, v4)) % 18.54/3.14 | % 18.54/3.14 | ALPHA: (m__) implies: % 18.54/3.14 | (18) $i(xs) % 18.54/3.14 | (19) $i(xt) % 18.54/3.14 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 18.54/3.14 | (sdtasasdt0(xt, xt) = v3 & sdtasasdt0(xs, xt) = v0 & sdtasasdt0(xs, % 18.54/3.14 | xs) = v2 & sdtasdt0(v2, v3) = v4 & sdtasdt0(v0, v0) = v1 & $i(v4) % 18.54/3.14 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, v4)) % 18.54/3.14 | % 18.54/3.14 | ALPHA: (function-axioms) implies: % 18.54/3.15 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 18.54/3.15 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) % 18.54/3.15 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.54/3.15 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 18.54/3.15 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.54/3.15 | (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) % 18.54/3.15 | % 18.54/3.15 | DELTA: instantiating (5) with fresh symbol all_33_0 gives: % 18.54/3.15 | (24) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 & % 18.54/3.15 | $i(all_33_0) % 18.54/3.15 | % 18.54/3.15 | ALPHA: (24) implies: % 18.54/3.15 | (25) aDimensionOf0(xs) = all_33_0 % 18.54/3.15 | (26) aDimensionOf0(xt) = all_33_0 % 18.54/3.15 | % 18.54/3.15 | DELTA: instantiating (6) with fresh symbol all_35_0 gives: % 18.54/3.15 | (27) ~ (all_35_0 = sz00) & aDimensionOf0(xs) = all_35_0 & $i(all_35_0) % 18.54/3.15 | % 18.54/3.15 | ALPHA: (27) implies: % 18.54/3.15 | (28) ~ (all_35_0 = sz00) % 18.54/3.15 | (29) aDimensionOf0(xs) = all_35_0 % 18.54/3.15 | % 18.54/3.15 | DELTA: instantiating (9) with fresh symbol all_37_0 gives: % 18.54/3.15 | (30) sdtlbdtrb0(xs, all_37_0) = xA & aDimensionOf0(xs) = all_37_0 & % 18.54/3.15 | $i(all_37_0) & aScalar0(xA) % 18.54/3.15 | % 18.54/3.15 | ALPHA: (30) implies: % 18.54/3.15 | (31) aDimensionOf0(xs) = all_37_0 % 18.54/3.15 | (32) sdtlbdtrb0(xs, all_37_0) = xA % 18.54/3.15 | % 18.54/3.15 | DELTA: instantiating (10) with fresh symbol all_39_0 gives: % 18.54/3.15 | (33) sdtlbdtrb0(xt, all_39_0) = xB & aDimensionOf0(xt) = all_39_0 & % 18.54/3.15 | $i(all_39_0) & aScalar0(xB) % 18.54/3.15 | % 18.54/3.15 | ALPHA: (33) implies: % 18.54/3.15 | (34) aDimensionOf0(xt) = all_39_0 % 18.54/3.15 | (35) sdtlbdtrb0(xt, all_39_0) = xB % 18.54/3.15 | % 18.54/3.15 | DELTA: instantiating (17) with fresh symbols all_45_0, all_45_1, all_45_2, % 18.54/3.15 | all_45_3, all_45_4 gives: % 18.54/3.15 | (36) sdtasdt0(all_45_2, all_45_1) = all_45_0 & sdtasdt0(all_45_4, all_45_4) % 18.54/3.15 | = all_45_3 & sdtpldt0(xE, xH) = all_45_4 & sdtpldt0(xD, xG) = all_45_1 % 18.54/3.15 | & sdtpldt0(xC, xF) = all_45_2 & $i(all_45_0) & $i(all_45_1) & % 18.54/3.15 | $i(all_45_2) & $i(all_45_3) & $i(all_45_4) & sdtlseqdt0(all_45_3, % 18.54/3.15 | all_45_0) % 18.54/3.15 | % 18.54/3.15 | ALPHA: (36) implies: % 18.54/3.15 | (37) sdtlseqdt0(all_45_3, all_45_0) % 18.54/3.15 | (38) sdtpldt0(xC, xF) = all_45_2 % 18.54/3.15 | (39) sdtpldt0(xD, xG) = all_45_1 % 18.54/3.15 | (40) sdtpldt0(xE, xH) = all_45_4 % 18.54/3.15 | (41) sdtasdt0(all_45_4, all_45_4) = all_45_3 % 18.54/3.15 | (42) sdtasdt0(all_45_2, all_45_1) = all_45_0 % 18.54/3.15 | % 18.54/3.15 | DELTA: instantiating (20) with fresh symbols all_47_0, all_47_1, all_47_2, % 18.54/3.15 | all_47_3, all_47_4 gives: % 18.54/3.15 | (43) sdtasasdt0(xt, xt) = all_47_1 & sdtasasdt0(xs, xt) = all_47_4 & % 18.54/3.15 | sdtasasdt0(xs, xs) = all_47_2 & sdtasdt0(all_47_2, all_47_1) = % 18.54/3.15 | all_47_0 & sdtasdt0(all_47_4, all_47_4) = all_47_3 & $i(all_47_0) & % 18.54/3.15 | $i(all_47_1) & $i(all_47_2) & $i(all_47_3) & $i(all_47_4) & ~ % 18.54/3.15 | sdtlseqdt0(all_47_3, all_47_0) % 18.54/3.15 | % 18.54/3.15 | ALPHA: (43) implies: % 18.54/3.15 | (44) ~ sdtlseqdt0(all_47_3, all_47_0) % 18.54/3.15 | (45) sdtasdt0(all_47_4, all_47_4) = all_47_3 % 18.54/3.15 | (46) sdtasdt0(all_47_2, all_47_1) = all_47_0 % 18.54/3.15 | (47) sdtasasdt0(xs, xs) = all_47_2 % 18.54/3.15 | (48) sdtasasdt0(xs, xt) = all_47_4 % 18.54/3.15 | (49) sdtasasdt0(xt, xt) = all_47_1 % 18.54/3.15 | % 18.54/3.15 | DELTA: instantiating (7) with fresh symbols all_49_0, all_49_1 gives: % 18.54/3.16 | (50) sziznziztdt0(xs) = xp & aDimensionOf0(xp) = all_49_1 & % 18.54/3.16 | aDimensionOf0(xs) = all_49_0 & szszuzczcdt0(all_49_1) = all_49_0 & % 18.54/3.16 | $i(all_49_0) & $i(all_49_1) & aVector0(xp) & ! [v0: $i] : ! [v1: $i] % 18.54/3.16 | : ( ~ (sdtlbdtrb0(xp, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | % 18.54/3.16 | (sdtlbdtrb0(xs, v0) = v1 & $i(v1))) % 18.54/3.16 | % 18.54/3.16 | ALPHA: (50) implies: % 18.54/3.16 | (51) aDimensionOf0(xs) = all_49_0 % 18.54/3.16 | (52) sziznziztdt0(xs) = xp % 18.54/3.16 | % 18.54/3.16 | DELTA: instantiating (8) with fresh symbols all_52_0, all_52_1 gives: % 18.54/3.16 | (53) sziznziztdt0(xt) = xq & aDimensionOf0(xq) = all_52_1 & % 18.54/3.16 | aDimensionOf0(xt) = all_52_0 & szszuzczcdt0(all_52_1) = all_52_0 & % 18.54/3.16 | $i(all_52_0) & $i(all_52_1) & aVector0(xq) & ! [v0: $i] : ! [v1: $i] % 18.54/3.16 | : ( ~ (sdtlbdtrb0(xq, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | % 18.54/3.16 | (sdtlbdtrb0(xt, v0) = v1 & $i(v1))) % 18.54/3.16 | % 18.54/3.16 | ALPHA: (53) implies: % 18.54/3.16 | (54) aDimensionOf0(xt) = all_52_0 % 18.54/3.16 | (55) sziznziztdt0(xt) = xq % 18.54/3.16 | % 18.54/3.16 | DELTA: instantiating (4) with fresh symbol all_55_0 gives: % 18.54/3.16 | (56) aDimensionOf0(xs) = all_55_0 & $i(all_55_0) & ! [v0: $i] : ! [v1: % 18.54/3.16 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1, % 18.54/3.16 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3) % 18.54/3.16 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) % 18.54/3.16 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 18.54/3.16 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7) % 18.54/3.16 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~ % 18.54/3.16 | iLess0(v5, all_55_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6 % 18.54/3.16 | & $i(v6)))))) % 18.54/3.16 | % 18.54/3.16 | ALPHA: (56) implies: % 18.54/3.16 | (57) aDimensionOf0(xs) = all_55_0 % 18.54/3.16 | % 18.54/3.16 | GROUND_INST: instantiating (21) with all_37_0, all_49_0, xs, simplifying with % 18.54/3.16 | (31), (51) gives: % 18.54/3.16 | (58) all_49_0 = all_37_0 % 18.54/3.16 | % 18.54/3.16 | GROUND_INST: instantiating (21) with all_35_0, all_49_0, xs, simplifying with % 18.54/3.16 | (29), (51) gives: % 18.54/3.16 | (59) all_49_0 = all_35_0 % 18.54/3.16 | % 18.54/3.16 | GROUND_INST: instantiating (21) with all_49_0, all_55_0, xs, simplifying with % 18.54/3.16 | (51), (57) gives: % 18.54/3.16 | (60) all_55_0 = all_49_0 % 18.54/3.16 | % 18.54/3.16 | GROUND_INST: instantiating (21) with all_33_0, all_55_0, xs, simplifying with % 18.54/3.16 | (25), (57) gives: % 18.54/3.16 | (61) all_55_0 = all_33_0 % 18.54/3.16 | % 18.54/3.16 | GROUND_INST: instantiating (21) with all_39_0, all_52_0, xt, simplifying with % 18.54/3.16 | (34), (54) gives: % 18.54/3.16 | (62) all_52_0 = all_39_0 % 18.54/3.16 | % 18.54/3.16 | GROUND_INST: instantiating (21) with all_33_0, all_52_0, xt, simplifying with % 18.54/3.16 | (26), (54) gives: % 18.54/3.16 | (63) all_52_0 = all_33_0 % 18.54/3.16 | % 18.54/3.16 | COMBINE_EQS: (60), (61) imply: % 18.54/3.16 | (64) all_49_0 = all_33_0 % 18.54/3.16 | % 18.54/3.16 | SIMP: (64) implies: % 18.54/3.16 | (65) all_49_0 = all_33_0 % 18.54/3.16 | % 18.54/3.16 | COMBINE_EQS: (62), (63) imply: % 18.54/3.16 | (66) all_39_0 = all_33_0 % 18.54/3.16 | % 18.54/3.16 | COMBINE_EQS: (58), (65) imply: % 18.54/3.16 | (67) all_37_0 = all_33_0 % 18.54/3.16 | % 18.54/3.16 | COMBINE_EQS: (58), (59) imply: % 18.54/3.16 | (68) all_37_0 = all_35_0 % 18.54/3.16 | % 18.54/3.16 | COMBINE_EQS: (67), (68) imply: % 18.54/3.16 | (69) all_35_0 = all_33_0 % 18.54/3.16 | % 18.54/3.16 | SIMP: (69) implies: % 18.54/3.16 | (70) all_35_0 = all_33_0 % 18.54/3.16 | % 18.54/3.16 | REDUCE: (28), (70) imply: % 18.54/3.16 | (71) ~ (all_33_0 = sz00) % 18.54/3.16 | % 18.54/3.16 | REDUCE: (35), (66) imply: % 18.54/3.17 | (72) sdtlbdtrb0(xt, all_33_0) = xB % 18.54/3.17 | % 18.54/3.17 | REDUCE: (32), (67) imply: % 18.54/3.17 | (73) sdtlbdtrb0(xs, all_33_0) = xA % 18.54/3.17 | % 18.54/3.17 | GROUND_INST: instantiating (1) with xs, xs, all_33_0, xp, xp, xC, xA, xA, xF, % 18.54/3.17 | all_45_2, simplifying with (2), (11), (14), (18), (25), (38), % 18.54/3.17 | (52), (73) gives: % 18.54/3.17 | (74) all_33_0 = sz00 | (sdtasasdt0(xs, xs) = all_45_2 & $i(all_45_2)) % 18.54/3.17 | % 18.54/3.17 | GROUND_INST: instantiating (1) with xs, xt, all_33_0, xp, xq, xE, xA, xB, xH, % 18.54/3.17 | all_45_4, simplifying with (2), (3), (13), (16), (18), (19), % 18.54/3.17 | (25), (26), (40), (52), (55), (72), (73) gives: % 18.54/3.17 | (75) all_33_0 = sz00 | (sdtasasdt0(xs, xt) = all_45_4 & $i(all_45_4)) % 18.54/3.17 | % 18.54/3.17 | GROUND_INST: instantiating (1) with xt, xt, all_33_0, xq, xq, xD, xB, xB, xG, % 18.54/3.17 | all_45_1, simplifying with (3), (12), (15), (19), (26), (39), % 18.54/3.17 | (55), (72) gives: % 18.54/3.17 | (76) all_33_0 = sz00 | (sdtasasdt0(xt, xt) = all_45_1 & $i(all_45_1)) % 18.54/3.17 | % 18.54/3.17 | BETA: splitting (76) gives: % 18.54/3.17 | % 18.54/3.17 | Case 1: % 18.54/3.17 | | % 18.54/3.17 | | (77) all_33_0 = sz00 % 18.54/3.17 | | % 18.54/3.17 | | REDUCE: (71), (77) imply: % 18.54/3.17 | | (78) $false % 18.54/3.17 | | % 18.54/3.17 | | CLOSE: (78) is inconsistent. % 18.54/3.17 | | % 18.54/3.17 | Case 2: % 18.54/3.17 | | % 18.54/3.17 | | (79) sdtasasdt0(xt, xt) = all_45_1 & $i(all_45_1) % 18.54/3.17 | | % 18.54/3.17 | | ALPHA: (79) implies: % 18.54/3.17 | | (80) sdtasasdt0(xt, xt) = all_45_1 % 18.54/3.17 | | % 18.54/3.17 | | BETA: splitting (74) gives: % 18.54/3.17 | | % 18.54/3.17 | | Case 1: % 18.54/3.17 | | | % 18.54/3.17 | | | (81) all_33_0 = sz00 % 18.54/3.17 | | | % 18.54/3.17 | | | REDUCE: (71), (81) imply: % 18.54/3.17 | | | (82) $false % 18.54/3.17 | | | % 18.54/3.17 | | | CLOSE: (82) is inconsistent. % 18.54/3.17 | | | % 18.54/3.17 | | Case 2: % 18.54/3.17 | | | % 18.54/3.17 | | | (83) sdtasasdt0(xs, xs) = all_45_2 & $i(all_45_2) % 18.54/3.17 | | | % 18.54/3.17 | | | ALPHA: (83) implies: % 18.54/3.17 | | | (84) sdtasasdt0(xs, xs) = all_45_2 % 18.54/3.17 | | | % 18.54/3.17 | | | BETA: splitting (75) gives: % 18.54/3.17 | | | % 18.54/3.17 | | | Case 1: % 18.54/3.17 | | | | % 18.54/3.17 | | | | (85) all_33_0 = sz00 % 18.54/3.17 | | | | % 18.54/3.17 | | | | REDUCE: (71), (85) imply: % 18.54/3.17 | | | | (86) $false % 18.54/3.17 | | | | % 18.54/3.17 | | | | CLOSE: (86) is inconsistent. % 18.54/3.17 | | | | % 18.54/3.17 | | | Case 2: % 18.54/3.17 | | | | % 18.54/3.17 | | | | (87) sdtasasdt0(xs, xt) = all_45_4 & $i(all_45_4) % 18.54/3.17 | | | | % 18.54/3.17 | | | | ALPHA: (87) implies: % 18.54/3.17 | | | | (88) sdtasasdt0(xs, xt) = all_45_4 % 18.54/3.17 | | | | % 18.54/3.17 | | | | GROUND_INST: instantiating (23) with all_47_2, all_45_2, xs, xs, % 18.54/3.17 | | | | simplifying with (47), (84) gives: % 18.54/3.17 | | | | (89) all_47_2 = all_45_2 % 18.54/3.17 | | | | % 18.54/3.17 | | | | GROUND_INST: instantiating (23) with all_47_4, all_45_4, xt, xs, % 18.54/3.17 | | | | simplifying with (48), (88) gives: % 18.54/3.17 | | | | (90) all_47_4 = all_45_4 % 18.54/3.17 | | | | % 18.54/3.17 | | | | GROUND_INST: instantiating (23) with all_47_1, all_45_1, xt, xt, % 18.54/3.17 | | | | simplifying with (49), (80) gives: % 18.54/3.17 | | | | (91) all_47_1 = all_45_1 % 18.54/3.17 | | | | % 18.54/3.17 | | | | REDUCE: (46), (89), (91) imply: % 18.54/3.17 | | | | (92) sdtasdt0(all_45_2, all_45_1) = all_47_0 % 18.54/3.17 | | | | % 18.54/3.17 | | | | REDUCE: (45), (90) imply: % 18.54/3.17 | | | | (93) sdtasdt0(all_45_4, all_45_4) = all_47_3 % 18.54/3.17 | | | | % 18.54/3.17 | | | | GROUND_INST: instantiating (22) with all_45_3, all_47_3, all_45_4, % 18.54/3.17 | | | | all_45_4, simplifying with (41), (93) gives: % 18.54/3.18 | | | | (94) all_47_3 = all_45_3 % 18.54/3.18 | | | | % 18.54/3.18 | | | | GROUND_INST: instantiating (22) with all_45_0, all_47_0, all_45_1, % 18.54/3.18 | | | | all_45_2, simplifying with (42), (92) gives: % 18.54/3.18 | | | | (95) all_47_0 = all_45_0 % 18.54/3.18 | | | | % 18.54/3.18 | | | | REDUCE: (44), (94), (95) imply: % 18.54/3.18 | | | | (96) ~ sdtlseqdt0(all_45_3, all_45_0) % 18.54/3.18 | | | | % 18.54/3.18 | | | | PRED_UNIFY: (37), (96) imply: % 18.54/3.18 | | | | (97) $false % 18.54/3.18 | | | | % 18.54/3.18 | | | | CLOSE: (97) is inconsistent. % 18.54/3.18 | | | | % 18.54/3.18 | | | End of split % 18.54/3.18 | | | % 18.54/3.18 | | End of split % 18.54/3.18 | | % 18.54/3.18 | End of split % 18.54/3.18 | % 18.54/3.18 End of proof % 18.54/3.18 % SZS output end Proof for theBenchmark % 18.54/3.18 % 18.54/3.18 2706ms %------------------------------------------------------------------------------