%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM474+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 : n009.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 11:48:00 EDT 2023 % Result : Theorem 10.32s 2.14s % Output : Proof 16.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : NUM474+2 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n009.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Aug 25 14:28:05 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 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 % 0.21/0.65 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 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 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.43/1.23 Prover 1: Preprocessing ... % 3.43/1.23 Prover 4: Preprocessing ... % 3.43/1.28 Prover 0: Preprocessing ... % 3.43/1.28 Prover 2: Preprocessing ... % 3.43/1.28 Prover 5: Preprocessing ... % 3.43/1.28 Prover 6: Preprocessing ... % 3.43/1.28 Prover 3: Preprocessing ... % 7.97/1.82 Prover 1: Constructing countermodel ... % 7.97/1.84 Prover 3: Constructing countermodel ... % 8.44/1.92 Prover 6: Proving ... % 8.44/1.99 Prover 5: Constructing countermodel ... % 9.80/2.13 Prover 3: proved (1485ms) % 10.32/2.14 % 10.32/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.32/2.14 % 10.32/2.14 Prover 6: stopped % 10.32/2.14 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.32/2.14 Prover 5: stopped % 10.32/2.14 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.32/2.14 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.32/2.16 Prover 2: Proving ... % 10.32/2.16 Prover 2: stopped % 10.32/2.16 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.54/2.19 Prover 4: Constructing countermodel ... % 11.00/2.24 Prover 7: Preprocessing ... % 11.00/2.26 Prover 8: Preprocessing ... % 11.26/2.26 Prover 11: Preprocessing ... % 11.26/2.26 Prover 10: Preprocessing ... % 12.11/2.37 Prover 0: Proving ... % 12.11/2.37 Prover 0: stopped % 12.11/2.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.64/2.44 Prover 13: Preprocessing ... % 12.82/2.48 Prover 8: Warning: ignoring some quantifiers % 12.82/2.48 Prover 10: Constructing countermodel ... % 12.82/2.49 Prover 8: Constructing countermodel ... % 12.82/2.56 Prover 7: Constructing countermodel ... % 13.97/2.68 Prover 13: Constructing countermodel ... % 15.45/2.81 Prover 11: Constructing countermodel ... % 16.33/2.95 Prover 10: Found proof (size 76) % 16.33/2.95 Prover 10: proved (812ms) % 16.33/2.95 Prover 11: stopped % 16.33/2.95 Prover 4: stopped % 16.33/2.95 Prover 7: stopped % 16.33/2.95 Prover 8: stopped % 16.33/2.95 Prover 1: stopped % 16.33/2.95 Prover 13: stopped % 16.33/2.95 % 16.33/2.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.33/2.95 % 16.33/2.97 % SZS output start Proof for theBenchmark % 16.33/2.97 Assumptions after simplification: % 16.33/2.97 --------------------------------- % 16.33/2.97 % 16.33/2.97 (mAMDistr) % 16.79/3.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 16.79/3.00 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 16.79/3.00 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 16.79/3.00 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? % 16.79/3.00 [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v7 % 16.79/3.00 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & % 16.79/3.00 sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & % 16.79/3.00 $i(v6) & $i(v5))) % 16.79/3.00 % 16.79/3.00 (mAddComm) % 16.79/3.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 16.79/3.00 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 16.79/3.00 (sdtpldt0(v1, v0) = v2 & $i(v2))) % 16.79/3.00 % 16.79/3.00 (mDefDiff) % 16.79/3.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 16.79/3.01 (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ $i(v3) | ~ $i(v1) % 16.79/3.01 | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ % 16.79/3.01 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : % 16.79/3.01 ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ % 16.79/3.01 (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 16.79/3.01 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! % 16.79/3.01 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtmndt0(v1, v0) = % 16.79/3.01 v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 16.79/3.01 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 16.79/3.01 aNaturalNumber0(v2)) % 16.79/3.01 % 16.79/3.01 (mDefQuot) % 16.79/3.01 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | % 16.79/3.01 v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 16.79/3.01 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 16.79/3.01 aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! % 16.79/3.01 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v0 = sz00 | ~ % 16.79/3.01 (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 16.79/3.01 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ % 16.79/3.01 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 16.79/3.01 : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ % 16.79/3.01 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 16.79/3.01 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 16.79/3.01 % 16.79/3.01 (mMulComm) % 16.79/3.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 16.79/3.01 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 16.79/3.01 (sdtasdt0(v1, v0) = v2 & $i(v2))) % 16.79/3.01 % 16.79/3.01 (m__) % 16.79/3.01 $i(xr) & $i(xp) & $i(xn) & $i(xl) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 16.79/3.01 ? [v3: $i] : ( ~ (v3 = v2) & sdtasdt0(xl, xr) = v1 & sdtasdt0(xl, xp) = v0 & % 16.79/3.01 sdtpldt0(v0, v1) = v2 & sdtpldt0(v0, xn) = v3 & $i(v3) & $i(v2) & $i(v1) & % 16.79/3.01 $i(v0)) % 16.79/3.01 % 16.79/3.01 (m__1324) % 16.79/3.01 $i(xn) & $i(xm) & $i(xl) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & % 16.79/3.01 aNaturalNumber0(xl) % 16.79/3.01 % 16.79/3.01 (m__1324_04) % 16.79/3.01 $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 16.79/3.01 (sdtasdt0(xl, v2) = xm & sdtasdt0(xl, v1) = v0 & sdtpldt0(xm, xn) = v0 & % 16.79/3.01 $i(v2) & $i(v1) & $i(v0) & doDivides0(xl, v0) & doDivides0(xl, xm) & % 16.79/3.01 aNaturalNumber0(v2) & aNaturalNumber0(v1)) % 16.79/3.01 % 16.79/3.01 (m__1347) % 16.79/3.01 ~ (xl = sz00) & $i(xl) & $i(sz00) % 16.79/3.01 % 16.79/3.01 (m__1360) % 16.79/3.01 sdtsldt0(xm, xl) = xp & sdtasdt0(xl, xp) = xm & $i(xp) & $i(xm) & $i(xl) & % 16.79/3.01 aNaturalNumber0(xp) % 16.79/3.01 % 16.79/3.01 (m__1379) % 16.79/3.02 $i(xq) & $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : (sdtsldt0(v0, xl) = xq & % 16.79/3.02 sdtasdt0(xl, xq) = v0 & sdtpldt0(xm, xn) = v0 & $i(v0) & % 16.79/3.02 aNaturalNumber0(xq)) % 16.79/3.02 % 16.79/3.02 (m__1395) % 16.79/3.02 $i(xq) & $i(xp) & ? [v0: $i] : (sdtpldt0(xp, v0) = xq & $i(v0) & % 16.79/3.02 sdtlseqdt0(xp, xq) & aNaturalNumber0(v0)) % 16.79/3.02 % 16.79/3.02 (m__1422) % 16.79/3.02 sdtmndt0(xq, xp) = xr & sdtpldt0(xp, xr) = xq & $i(xr) & $i(xq) & $i(xp) & % 16.79/3.02 aNaturalNumber0(xr) % 16.79/3.02 % 16.79/3.02 (function-axioms) % 16.79/3.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.79/3.02 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 16.79/3.02 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 16.79/3.02 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.79/3.02 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 16.79/3.02 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.79/3.02 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 16.79/3.02 % 16.79/3.02 Further assumptions not needed in the proof: % 16.79/3.02 -------------------------------------------- % 16.79/3.02 mAddAsso, mAddCanc, mDefDiv, mDefLE, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, % 16.79/3.02 mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, % 16.79/3.02 mMulCanc, mNatSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, mZeroAdd, % 16.79/3.02 mZeroMul, m_AddZero, m_MulUnit, m_MulZero % 16.79/3.02 % 16.79/3.02 Those formulas are unsatisfiable: % 16.79/3.02 --------------------------------- % 16.79/3.02 % 16.79/3.02 Begin of proof % 16.79/3.02 | % 16.79/3.02 | ALPHA: (mDefDiff) implies: % 16.79/3.02 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 16.79/3.02 | (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ $i(v3) | ~ % 16.79/3.02 | $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | % 16.79/3.02 | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 16.79/3.02 | % 16.79/3.02 | ALPHA: (mDefQuot) implies: % 16.79/3.02 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v0 = % 16.79/3.02 | sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 16.79/3.02 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 16.79/3.02 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ % 16.79/3.02 | aNaturalNumber0(v0)) % 16.79/3.02 | % 16.79/3.02 | ALPHA: (m__1324) implies: % 16.79/3.02 | (3) aNaturalNumber0(xl) % 16.79/3.02 | (4) aNaturalNumber0(xm) % 16.79/3.02 | % 16.79/3.02 | ALPHA: (m__1324_04) implies: % 16.79/3.02 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xl, v2) = xm & % 16.79/3.02 | sdtasdt0(xl, v1) = v0 & sdtpldt0(xm, xn) = v0 & $i(v2) & $i(v1) & % 16.79/3.02 | $i(v0) & doDivides0(xl, v0) & doDivides0(xl, xm) & % 16.79/3.02 | aNaturalNumber0(v2) & aNaturalNumber0(v1)) % 16.79/3.02 | % 16.79/3.02 | ALPHA: (m__1347) implies: % 16.79/3.02 | (6) ~ (xl = sz00) % 16.79/3.02 | % 16.79/3.02 | ALPHA: (m__1360) implies: % 16.79/3.02 | (7) aNaturalNumber0(xp) % 16.79/3.03 | (8) sdtasdt0(xl, xp) = xm % 16.79/3.03 | (9) sdtsldt0(xm, xl) = xp % 16.79/3.03 | % 16.79/3.03 | ALPHA: (m__1379) implies: % 16.79/3.03 | (10) ? [v0: $i] : (sdtsldt0(v0, xl) = xq & sdtasdt0(xl, xq) = v0 & % 16.79/3.03 | sdtpldt0(xm, xn) = v0 & $i(v0) & aNaturalNumber0(xq)) % 16.79/3.03 | % 16.79/3.03 | ALPHA: (m__1395) implies: % 16.79/3.03 | (11) ? [v0: $i] : (sdtpldt0(xp, v0) = xq & $i(v0) & sdtlseqdt0(xp, xq) & % 16.79/3.03 | aNaturalNumber0(v0)) % 16.79/3.03 | % 16.79/3.03 | ALPHA: (m__1422) implies: % 16.79/3.03 | (12) aNaturalNumber0(xr) % 16.79/3.03 | (13) sdtmndt0(xq, xp) = xr % 16.79/3.03 | % 16.79/3.03 | ALPHA: (m__) implies: % 16.79/3.03 | (14) $i(xl) % 16.79/3.03 | (15) $i(xp) % 16.79/3.03 | (16) $i(xr) % 16.79/3.03 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) % 16.79/3.03 | & sdtasdt0(xl, xr) = v1 & sdtasdt0(xl, xp) = v0 & sdtpldt0(v0, v1) = % 16.79/3.03 | v2 & sdtpldt0(v0, xn) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 16.79/3.03 | % 16.79/3.03 | ALPHA: (function-axioms) implies: % 16.79/3.03 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.79/3.03 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 16.79/3.03 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.79/3.03 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 16.79/3.03 | % 16.79/3.03 | DELTA: instantiating (11) with fresh symbol all_33_0 gives: % 16.79/3.03 | (20) sdtpldt0(xp, all_33_0) = xq & $i(all_33_0) & sdtlseqdt0(xp, xq) & % 16.79/3.03 | aNaturalNumber0(all_33_0) % 16.79/3.03 | % 16.79/3.03 | ALPHA: (20) implies: % 16.79/3.03 | (21) aNaturalNumber0(all_33_0) % 16.79/3.03 | (22) sdtlseqdt0(xp, xq) % 16.79/3.03 | (23) $i(all_33_0) % 16.79/3.03 | (24) sdtpldt0(xp, all_33_0) = xq % 16.79/3.03 | % 16.79/3.03 | DELTA: instantiating (10) with fresh symbol all_35_0 gives: % 16.79/3.03 | (25) sdtsldt0(all_35_0, xl) = xq & sdtasdt0(xl, xq) = all_35_0 & % 16.79/3.03 | sdtpldt0(xm, xn) = all_35_0 & $i(all_35_0) & aNaturalNumber0(xq) % 16.79/3.03 | % 16.79/3.03 | ALPHA: (25) implies: % 16.79/3.03 | (26) aNaturalNumber0(xq) % 16.79/3.03 | (27) sdtpldt0(xm, xn) = all_35_0 % 16.79/3.03 | (28) sdtasdt0(xl, xq) = all_35_0 % 16.79/3.03 | % 16.79/3.03 | DELTA: instantiating (17) with fresh symbols all_37_0, all_37_1, all_37_2, % 16.79/3.03 | all_37_3 gives: % 16.79/3.03 | (29) ~ (all_37_0 = all_37_1) & sdtasdt0(xl, xr) = all_37_2 & sdtasdt0(xl, % 16.79/3.03 | xp) = all_37_3 & sdtpldt0(all_37_3, all_37_2) = all_37_1 & % 16.79/3.03 | sdtpldt0(all_37_3, xn) = all_37_0 & $i(all_37_0) & $i(all_37_1) & % 16.79/3.03 | $i(all_37_2) & $i(all_37_3) % 16.79/3.03 | % 16.79/3.03 | ALPHA: (29) implies: % 16.79/3.03 | (30) ~ (all_37_0 = all_37_1) % 16.79/3.03 | (31) sdtpldt0(all_37_3, xn) = all_37_0 % 16.79/3.03 | (32) sdtpldt0(all_37_3, all_37_2) = all_37_1 % 16.79/3.03 | (33) sdtasdt0(xl, xp) = all_37_3 % 16.79/3.03 | (34) sdtasdt0(xl, xr) = all_37_2 % 16.79/3.03 | % 16.79/3.03 | DELTA: instantiating (5) with fresh symbols all_39_0, all_39_1, all_39_2 % 16.79/3.03 | gives: % 16.79/3.04 | (35) sdtasdt0(xl, all_39_0) = xm & sdtasdt0(xl, all_39_1) = all_39_2 & % 16.79/3.04 | sdtpldt0(xm, xn) = all_39_2 & $i(all_39_0) & $i(all_39_1) & % 16.79/3.04 | $i(all_39_2) & doDivides0(xl, all_39_2) & doDivides0(xl, xm) & % 16.79/3.04 | aNaturalNumber0(all_39_0) & aNaturalNumber0(all_39_1) % 16.79/3.04 | % 16.79/3.04 | ALPHA: (35) implies: % 16.79/3.04 | (36) aNaturalNumber0(all_39_0) % 16.79/3.04 | (37) doDivides0(xl, xm) % 16.79/3.04 | (38) $i(all_39_0) % 16.79/3.04 | (39) sdtpldt0(xm, xn) = all_39_2 % 16.79/3.04 | (40) sdtasdt0(xl, all_39_0) = xm % 16.79/3.04 | % 16.79/3.04 | GROUND_INST: instantiating (18) with all_35_0, all_39_2, xn, xm, simplifying % 16.79/3.04 | with (27), (39) gives: % 16.79/3.04 | (41) all_39_2 = all_35_0 % 16.79/3.04 | % 16.79/3.04 | GROUND_INST: instantiating (19) with xm, all_37_3, xp, xl, simplifying with % 16.79/3.04 | (8), (33) gives: % 16.79/3.04 | (42) all_37_3 = xm % 16.79/3.04 | % 16.79/3.04 | REDUCE: (32), (42) imply: % 16.79/3.04 | (43) sdtpldt0(xm, all_37_2) = all_37_1 % 16.79/3.04 | % 16.79/3.04 | REDUCE: (31), (42) imply: % 16.79/3.04 | (44) sdtpldt0(xm, xn) = all_37_0 % 16.79/3.04 | % 16.79/3.04 | GROUND_INST: instantiating (18) with all_35_0, all_37_0, xn, xm, simplifying % 16.79/3.04 | with (27), (44) gives: % 16.79/3.04 | (45) all_37_0 = all_35_0 % 16.79/3.04 | % 16.79/3.04 | REDUCE: (30), (45) imply: % 16.79/3.04 | (46) ~ (all_37_1 = all_35_0) % 16.79/3.04 | % 16.79/3.04 | SIMP: (46) implies: % 16.79/3.04 | (47) ~ (all_37_1 = all_35_0) % 16.79/3.04 | % 16.79/3.04 | GROUND_INST: instantiating (mAddComm) with xp, all_33_0, xq, simplifying with % 16.79/3.04 | (7), (15), (21), (23), (24) gives: % 16.79/3.04 | (48) sdtpldt0(all_33_0, xp) = xq & $i(xq) % 16.79/3.04 | % 16.79/3.04 | ALPHA: (48) implies: % 16.79/3.04 | (49) $i(xq) % 16.79/3.04 | % 16.79/3.04 | GROUND_INST: instantiating (mMulComm) with xl, xq, all_35_0, simplifying with % 16.79/3.04 | (3), (14), (26), (28), (49) gives: % 16.79/3.04 | (50) sdtasdt0(xq, xl) = all_35_0 & $i(all_35_0) % 16.79/3.04 | % 16.79/3.04 | ALPHA: (50) implies: % 16.79/3.04 | (51) sdtasdt0(xq, xl) = all_35_0 % 16.79/3.04 | % 16.79/3.04 | GROUND_INST: instantiating (mAMDistr) with xl, xp, xr, xm, all_37_2, all_37_1, % 16.79/3.04 | simplifying with (3), (7), (8), (12), (14), (15), (16), (34), % 16.79/3.04 | (43) gives: % 16.79/3.04 | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0, % 16.79/3.04 | xl) = v1 & sdtasdt0(xr, xl) = v3 & sdtasdt0(xp, xl) = v2 & % 16.79/3.04 | sdtasdt0(xl, v0) = all_37_1 & sdtpldt0(v2, v3) = v1 & sdtpldt0(xp, % 16.79/3.04 | xr) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_37_1)) % 16.79/3.04 | % 16.79/3.04 | GROUND_INST: instantiating (mMulComm) with xl, xr, all_37_2, simplifying with % 16.79/3.04 | (3), (12), (14), (16), (34) gives: % 16.79/3.04 | (53) sdtasdt0(xr, xl) = all_37_2 & $i(all_37_2) % 16.79/3.04 | % 16.79/3.04 | ALPHA: (53) implies: % 16.79/3.04 | (54) sdtasdt0(xr, xl) = all_37_2 % 16.79/3.04 | % 16.79/3.05 | GROUND_INST: instantiating (mAMDistr) with xl, all_39_0, xr, xm, all_37_2, % 16.79/3.05 | all_37_1, simplifying with (3), (12), (14), (16), (34), (36), % 16.79/3.05 | (38), (40), (43) gives: % 16.79/3.05 | (55) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0, % 16.79/3.05 | xl) = v1 & sdtasdt0(all_39_0, xl) = v2 & sdtasdt0(xr, xl) = v3 & % 16.79/3.05 | sdtasdt0(xl, v0) = all_37_1 & sdtpldt0(v2, v3) = v1 & % 16.79/3.05 | sdtpldt0(all_39_0, xr) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 16.79/3.05 | $i(all_37_1)) % 16.79/3.05 | % 16.79/3.05 | GROUND_INST: instantiating (mMulComm) with xl, all_39_0, xm, simplifying with % 16.79/3.05 | (3), (14), (36), (38), (40) gives: % 16.79/3.05 | (56) sdtasdt0(all_39_0, xl) = xm & $i(xm) % 16.79/3.05 | % 16.79/3.05 | ALPHA: (56) implies: % 16.79/3.05 | (57) $i(xm) % 16.79/3.05 | (58) sdtasdt0(all_39_0, xl) = xm % 16.79/3.05 | % 16.79/3.05 | GROUND_INST: instantiating (1) with xp, xq, xr, all_33_0, simplifying with % 16.79/3.05 | (7), (13), (15), (21), (22), (23), (24), (26), (49) gives: % 16.79/3.05 | (59) all_33_0 = xr % 16.79/3.05 | % 16.79/3.05 | GROUND_INST: instantiating (2) with xl, xm, xp, all_39_0, simplifying with % 16.79/3.05 | (3), (4), (9), (14), (36), (37), (38), (40), (57) gives: % 16.79/3.05 | (60) all_39_0 = xp | xl = sz00 % 16.79/3.05 | % 16.79/3.05 | DELTA: instantiating (52) with fresh symbols all_59_0, all_59_1, all_59_2, % 16.79/3.05 | all_59_3 gives: % 16.79/3.05 | (61) sdtasdt0(all_59_3, xl) = all_59_2 & sdtasdt0(xr, xl) = all_59_0 & % 16.79/3.05 | sdtasdt0(xp, xl) = all_59_1 & sdtasdt0(xl, all_59_3) = all_37_1 & % 16.79/3.05 | sdtpldt0(all_59_1, all_59_0) = all_59_2 & sdtpldt0(xp, xr) = all_59_3 % 16.79/3.05 | & $i(all_59_0) & $i(all_59_1) & $i(all_59_2) & $i(all_59_3) & % 16.79/3.05 | $i(all_37_1) % 16.79/3.05 | % 16.79/3.05 | ALPHA: (61) implies: % 16.79/3.05 | (62) sdtpldt0(xp, xr) = all_59_3 % 16.79/3.05 | (63) sdtpldt0(all_59_1, all_59_0) = all_59_2 % 16.79/3.05 | (64) sdtasdt0(xp, xl) = all_59_1 % 16.79/3.05 | (65) sdtasdt0(xr, xl) = all_59_0 % 16.79/3.05 | (66) sdtasdt0(all_59_3, xl) = all_59_2 % 16.79/3.05 | % 16.79/3.05 | DELTA: instantiating (55) with fresh symbols all_61_0, all_61_1, all_61_2, % 16.79/3.05 | all_61_3 gives: % 16.79/3.05 | (67) sdtasdt0(all_61_3, xl) = all_61_2 & sdtasdt0(all_39_0, xl) = all_61_1 % 16.79/3.05 | & sdtasdt0(xr, xl) = all_61_0 & sdtasdt0(xl, all_61_3) = all_37_1 & % 16.79/3.05 | sdtpldt0(all_61_1, all_61_0) = all_61_2 & sdtpldt0(all_39_0, xr) = % 16.79/3.05 | all_61_3 & $i(all_61_0) & $i(all_61_1) & $i(all_61_2) & $i(all_61_3) & % 16.79/3.05 | $i(all_37_1) % 16.79/3.05 | % 16.79/3.05 | ALPHA: (67) implies: % 16.79/3.05 | (68) sdtpldt0(all_39_0, xr) = all_61_3 % 16.79/3.05 | (69) sdtasdt0(xr, xl) = all_61_0 % 16.79/3.05 | (70) sdtasdt0(all_39_0, xl) = all_61_1 % 16.79/3.05 | (71) sdtasdt0(all_61_3, xl) = all_61_2 % 16.79/3.05 | % 16.79/3.05 | REDUCE: (24), (59) imply: % 16.79/3.05 | (72) sdtpldt0(xp, xr) = xq % 16.79/3.05 | % 16.79/3.05 | BETA: splitting (60) gives: % 16.79/3.05 | % 16.79/3.05 | Case 1: % 16.79/3.05 | | % 16.79/3.05 | | (73) xl = sz00 % 16.79/3.05 | | % 16.79/3.05 | | REDUCE: (6), (73) imply: % 16.79/3.05 | | (74) $false % 16.79/3.06 | | % 16.79/3.06 | | CLOSE: (74) is inconsistent. % 16.79/3.06 | | % 16.79/3.06 | Case 2: % 16.79/3.06 | | % 16.79/3.06 | | (75) all_39_0 = xp % 16.79/3.06 | | % 16.79/3.06 | | REDUCE: (70), (75) imply: % 16.79/3.06 | | (76) sdtasdt0(xp, xl) = all_61_1 % 16.79/3.06 | | % 16.79/3.06 | | REDUCE: (58), (75) imply: % 16.79/3.06 | | (77) sdtasdt0(xp, xl) = xm % 16.79/3.06 | | % 16.79/3.06 | | REDUCE: (68), (75) imply: % 16.79/3.06 | | (78) sdtpldt0(xp, xr) = all_61_3 % 16.79/3.06 | | % 16.79/3.06 | | GROUND_INST: instantiating (18) with xq, all_61_3, xr, xp, simplifying with % 16.79/3.06 | | (72), (78) gives: % 16.79/3.06 | | (79) all_61_3 = xq % 16.79/3.06 | | % 16.79/3.06 | | GROUND_INST: instantiating (18) with all_59_3, all_61_3, xr, xp, simplifying % 16.79/3.06 | | with (62), (78) gives: % 16.79/3.06 | | (80) all_61_3 = all_59_3 % 16.79/3.06 | | % 16.79/3.06 | | GROUND_INST: instantiating (19) with all_59_1, all_61_1, xl, xp, simplifying % 16.79/3.06 | | with (64), (76) gives: % 16.79/3.06 | | (81) all_61_1 = all_59_1 % 16.79/3.06 | | % 16.79/3.06 | | GROUND_INST: instantiating (19) with xm, all_61_1, xl, xp, simplifying with % 16.79/3.06 | | (76), (77) gives: % 16.79/3.06 | | (82) all_61_1 = xm % 16.79/3.06 | | % 16.79/3.06 | | GROUND_INST: instantiating (19) with all_59_0, all_61_0, xl, xr, simplifying % 16.79/3.06 | | with (65), (69) gives: % 16.79/3.06 | | (83) all_61_0 = all_59_0 % 16.79/3.06 | | % 16.79/3.06 | | GROUND_INST: instantiating (19) with all_37_2, all_61_0, xl, xr, simplifying % 16.79/3.06 | | with (54), (69) gives: % 16.79/3.06 | | (84) all_61_0 = all_37_2 % 16.79/3.06 | | % 16.79/3.06 | | COMBINE_EQS: (83), (84) imply: % 16.79/3.06 | | (85) all_59_0 = all_37_2 % 16.79/3.06 | | % 16.79/3.06 | | SIMP: (85) implies: % 16.79/3.06 | | (86) all_59_0 = all_37_2 % 16.79/3.06 | | % 16.79/3.06 | | COMBINE_EQS: (81), (82) imply: % 16.79/3.06 | | (87) all_59_1 = xm % 16.79/3.06 | | % 16.79/3.06 | | SIMP: (87) implies: % 16.79/3.06 | | (88) all_59_1 = xm % 16.79/3.06 | | % 16.79/3.06 | | COMBINE_EQS: (79), (80) imply: % 16.79/3.06 | | (89) all_59_3 = xq % 16.79/3.06 | | % 16.79/3.06 | | REDUCE: (71), (79) imply: % 16.79/3.06 | | (90) sdtasdt0(xq, xl) = all_61_2 % 16.79/3.06 | | % 16.79/3.06 | | REDUCE: (66), (89) imply: % 16.79/3.06 | | (91) sdtasdt0(xq, xl) = all_59_2 % 16.79/3.06 | | % 16.79/3.06 | | REDUCE: (63), (86), (88) imply: % 16.79/3.06 | | (92) sdtpldt0(xm, all_37_2) = all_59_2 % 16.79/3.06 | | % 16.79/3.06 | | GROUND_INST: instantiating (18) with all_37_1, all_59_2, all_37_2, xm, % 16.79/3.06 | | simplifying with (43), (92) gives: % 16.79/3.06 | | (93) all_59_2 = all_37_1 % 16.79/3.06 | | % 16.79/3.06 | | GROUND_INST: instantiating (19) with all_35_0, all_61_2, xl, xq, simplifying % 16.79/3.06 | | with (51), (90) gives: % 16.79/3.06 | | (94) all_61_2 = all_35_0 % 16.79/3.06 | | % 16.79/3.06 | | GROUND_INST: instantiating (19) with all_59_2, all_61_2, xl, xq, simplifying % 16.79/3.06 | | with (90), (91) gives: % 16.79/3.06 | | (95) all_61_2 = all_59_2 % 16.79/3.06 | | % 16.79/3.06 | | COMBINE_EQS: (94), (95) imply: % 16.79/3.06 | | (96) all_59_2 = all_35_0 % 16.79/3.06 | | % 16.79/3.06 | | SIMP: (96) implies: % 16.79/3.06 | | (97) all_59_2 = all_35_0 % 16.79/3.06 | | % 16.79/3.06 | | COMBINE_EQS: (93), (97) imply: % 16.79/3.06 | | (98) all_37_1 = all_35_0 % 16.79/3.06 | | % 16.79/3.06 | | SIMP: (98) implies: % 16.79/3.06 | | (99) all_37_1 = all_35_0 % 16.79/3.06 | | % 16.79/3.06 | | REDUCE: (47), (99) imply: % 16.79/3.06 | | (100) $false % 16.79/3.06 | | % 16.79/3.06 | | CLOSE: (100) is inconsistent. % 16.79/3.06 | | % 16.79/3.06 | End of split % 16.79/3.06 | % 16.79/3.06 End of proof % 16.79/3.06 % SZS output end Proof for theBenchmark % 16.79/3.06 % 16.79/3.06 2434ms %------------------------------------------------------------------------------