%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM496+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n017.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 11:48:10 EDT 2023 % Result : Theorem 22.81s 4.00s % Output : Proof 83.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : NUM496+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n017.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 07:52:55 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 4.07/1.37 Prover 4: Preprocessing ... % 4.07/1.38 Prover 1: Preprocessing ... % 4.76/1.44 Prover 5: Preprocessing ... % 4.76/1.44 Prover 0: Preprocessing ... % 4.76/1.44 Prover 6: Preprocessing ... % 4.76/1.44 Prover 3: Preprocessing ... % 4.76/1.44 Prover 2: Preprocessing ... % 12.54/2.55 Prover 3: Constructing countermodel ... % 12.54/2.57 Prover 1: Constructing countermodel ... % 12.54/2.57 Prover 6: Proving ... % 13.12/2.68 Prover 5: Constructing countermodel ... % 15.95/3.06 Prover 4: Constructing countermodel ... % 15.95/3.06 Prover 2: Proving ... % 16.89/3.14 Prover 0: Proving ... % 22.81/4.00 Prover 3: proved (3346ms) % 22.81/4.00 % 22.81/4.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 22.81/4.00 % 22.81/4.00 Prover 5: stopped % 22.81/4.00 Prover 0: stopped % 22.81/4.01 Prover 2: stopped % 22.81/4.02 Prover 6: stopped % 23.45/4.04 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 23.45/4.04 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 23.45/4.04 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 23.45/4.04 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 23.45/4.04 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 23.45/4.16 Prover 7: Preprocessing ... % 23.45/4.16 Prover 8: Preprocessing ... % 23.45/4.18 Prover 11: Preprocessing ... % 23.45/4.19 Prover 10: Preprocessing ... % 24.39/4.25 Prover 13: Preprocessing ... % 25.62/4.40 Prover 10: Constructing countermodel ... % 26.42/4.43 Prover 8: Warning: ignoring some quantifiers % 26.42/4.47 Prover 8: Constructing countermodel ... % 26.42/4.49 Prover 7: Constructing countermodel ... % 27.70/4.67 Prover 13: Constructing countermodel ... % 28.62/4.75 Prover 11: Constructing countermodel ... % 64.79/9.49 Prover 13: stopped % 64.79/9.51 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 65.29/9.56 Prover 16: Preprocessing ... % 66.06/9.68 Prover 16: Constructing countermodel ... % 81.75/11.78 Prover 10: Found proof (size 117) % 81.75/11.78 Prover 10: proved (7763ms) % 81.75/11.78 Prover 11: stopped % 81.75/11.78 Prover 7: stopped % 81.75/11.78 Prover 8: stopped % 81.75/11.78 Prover 16: stopped % 81.75/11.78 Prover 1: stopped % 82.21/11.83 Prover 4: stopped % 82.21/11.83 % 82.21/11.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 82.21/11.83 % 82.21/11.84 % SZS output start Proof for theBenchmark % 82.21/11.84 Assumptions after simplification: % 82.21/11.84 --------------------------------- % 82.21/11.84 % 82.21/11.85 (mAddAsso) % 82.48/11.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 82.48/11.88 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 82.48/11.88 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 82.48/11.88 aNaturalNumber0(v0) | ? [v5: $i] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, % 82.48/11.88 v5) = v4 & $i(v5) & $i(v4))) % 82.48/11.88 % 82.48/11.88 (mAddCanc) % 82.48/11.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 % 82.48/11.89 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ % 82.48/11.89 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 82.48/11.89 aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & % 82.48/11.89 sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & $i(v6) & $i(v5))) & ! % 82.48/11.89 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 82.48/11.89 (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 82.48/11.89 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 82.48/11.89 aNaturalNumber0(v0)) % 82.48/11.89 % 82.48/11.89 (mAddComm) % 82.48/11.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 82.48/11.89 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 82.48/11.89 (sdtpldt0(v1, v0) = v2 & $i(v2))) % 82.48/11.89 % 82.48/11.89 (mDefDiff) % 82.48/11.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 82.48/11.90 (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ $i(v3) | ~ $i(v1) % 82.48/11.90 | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ % 82.48/11.90 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : % 82.48/11.90 ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ % 82.48/11.90 (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 82.48/11.90 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! % 82.48/11.90 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtmndt0(v1, v0) = % 82.48/11.90 v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 82.48/11.90 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 82.48/11.90 aNaturalNumber0(v2)) % 82.48/11.90 % 82.48/11.90 (mDefDiv) % 82.48/11.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ % 82.48/11.90 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 82.48/11.90 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0: % 82.48/11.90 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 82.48/11.90 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtasdt0(v0, % 82.48/11.90 v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 82.48/11.90 % 82.48/11.90 (mDefLE) % 82.48/11.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ % 82.48/11.91 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 82.48/11.91 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0: % 82.48/11.91 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ % 82.48/11.91 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtpldt0(v0, % 82.48/11.91 v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 82.48/11.91 % 82.48/11.91 (mDefPrime) % 82.48/11.91 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | v1 = sz10 | ~ % 82.48/11.91 $i(v1) | ~ $i(v0) | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ % 82.48/11.91 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = sz10 | % 82.48/11.91 v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1: $i] % 82.48/11.91 : ( ~ (v1 = v0) & ~ (v1 = sz10) & $i(v1) & doDivides0(v1, v0) & % 82.48/11.91 aNaturalNumber0(v1))) & ( ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)) & ( % 82.48/11.91 ~ isPrime0(sz00) | ~ aNaturalNumber0(sz00)) % 82.48/11.91 % 82.48/11.91 (mDivSum) % 82.48/11.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v1, v2) % 82.48/11.91 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v2) | ~ % 82.48/11.91 doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 82.48/11.91 aNaturalNumber0(v0) | doDivides0(v0, v3)) % 82.48/11.91 % 82.48/11.91 (mDivTrans) % 82.48/11.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 82.48/11.91 ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ % 82.48/11.91 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) % 82.48/11.91 % 82.48/11.91 (mMonAdd) % 82.48/11.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 82.48/11.92 (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 82.48/11.92 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 82.48/11.92 aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = % 82.48/11.92 v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & % 82.48/11.92 sdtpldt0(v1, v2) = v6 & $i(v6) & $i(v5) & $i(v4) & sdtlseqdt0(v4, v5) & % 82.48/11.92 sdtlseqdt0(v3, v6))) % 82.48/11.92 % 82.48/11.92 (mPrimDiv) % 82.48/11.92 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~ % 82.48/11.92 aNaturalNumber0(v0) | ? [v1: $i] : ($i(v1) & isPrime0(v1) & doDivides0(v1, % 82.48/11.92 v0) & aNaturalNumber0(v1))) % 82.48/11.92 % 82.48/11.92 (mSortsC_01) % 82.48/11.92 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10) % 82.48/11.92 % 82.48/11.92 (m__) % 82.48/11.92 $i(xp) & $i(xm) & $i(xn) & ~ doDivides0(xp, xm) & ~ doDivides0(xp, xn) & ! % 82.48/11.92 [v0: $i] : ( ~ (sdtasdt0(xp, v0) = xm) | ~ $i(v0) | ~ aNaturalNumber0(v0)) & % 82.48/11.92 ! [v0: $i] : ( ~ (sdtasdt0(xp, v0) = xn) | ~ $i(v0) | ~ % 82.48/11.92 aNaturalNumber0(v0)) % 82.48/11.92 % 82.48/11.92 (m__1799) % 82.48/11.95 $i(xp) & $i(xm) & $i(xn) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : % 82.48/11.95 (sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) = v0 & $i(v1) & $i(v0) & ! [v2: $i] % 82.48/11.95 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = % 82.48/11.95 sz00 | ~ (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) % 82.48/11.95 | ~ $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~ % 82.48/11.95 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3) | % 82.48/11.95 doDivides0(v4, v2) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: % 82.48/11.95 $i] : ($i(v9) & $i(v8) & ((v10 = v4 & ~ (v8 = v4) & ~ (v8 = sz10) & % 82.48/11.95 sdtasdt0(v8, v9) = v4 & doDivides0(v8, v4) & aNaturalNumber0(v9) & % 82.48/11.95 aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7) & ~ % 82.48/11.95 doDivides0(v4, v7) & ! [v11: $i] : ( ~ (sdtasdt0(v4, v11) = v7) | % 82.48/11.95 ~ $i(v11) | ~ aNaturalNumber0(v11)))))) & ! [v2: $i] : ! [v3: % 82.48/11.95 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 | % 82.48/11.95 ~ (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ % 82.48/11.95 $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~ % 82.48/11.95 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3) | ? % 82.48/11.95 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? % 82.48/11.95 [v12: $i] : ($i(v11) & $i(v10) & $i(v8) & ((v12 = v4 & ~ (v10 = v4) & ~ % 82.48/11.95 (v10 = sz10) & sdtasdt0(v10, v11) = v4 & doDivides0(v10, v4) & % 82.48/11.95 aNaturalNumber0(v11) & aNaturalNumber0(v10)) | (v9 = v2 & % 82.48/11.95 sdtasdt0(v4, v8) = v2 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = % 82.48/11.95 v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v13: $i] : ( ~ % 82.48/11.95 (sdtasdt0(v4, v13) = v7) | ~ $i(v13) | ~ % 82.48/11.95 aNaturalNumber0(v13)))))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 82.48/11.95 $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 | ~ % 82.48/11.95 (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ % 82.48/11.95 $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~ % 82.48/11.95 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v2) | ? % 82.48/11.95 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? % 82.48/11.95 [v12: $i] : ($i(v11) & $i(v10) & $i(v8) & ((v12 = v4 & ~ (v10 = v4) & ~ % 82.48/11.95 (v10 = sz10) & sdtasdt0(v10, v11) = v4 & doDivides0(v10, v4) & % 82.48/11.95 aNaturalNumber0(v11) & aNaturalNumber0(v10)) | (v9 = v3 & % 82.48/11.95 sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = % 82.48/11.95 v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v13: $i] : ( ~ % 82.48/11.95 (sdtasdt0(v4, v13) = v7) | ~ $i(v13) | ~ % 82.48/11.95 aNaturalNumber0(v13)))))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 82.48/11.95 $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 | ~ % 82.48/11.95 (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ % 82.48/11.95 $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~ % 82.48/11.95 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7: $i] : ? [v8: $i] : % 82.48/11.95 ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : % 82.48/11.95 ? [v14: $i] : ($i(v13) & $i(v12) & $i(v10) & $i(v8) & ((v14 = v4 & ~ (v12 % 82.48/11.95 = v4) & ~ (v12 = sz10) & sdtasdt0(v12, v13) = v4 & % 82.48/11.95 doDivides0(v12, v4) & aNaturalNumber0(v13) & aNaturalNumber0(v12)) | % 82.48/11.95 (v11 = v2 & sdtasdt0(v4, v10) = v2 & aNaturalNumber0(v10)) | (v9 = v3 % 82.48/11.95 & sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = % 82.48/11.95 v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v15: $i] : ( ~ % 82.48/11.95 (sdtasdt0(v4, v15) = v7) | ~ $i(v15) | ~ % 82.48/11.95 aNaturalNumber0(v15)))))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 82.48/11.95 $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) = v6) | ~ % 82.48/11.95 (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 82.48/11.95 isPrime0(v4) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~ % 82.48/11.95 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3) | % 82.48/11.95 doDivides0(v4, v2) | ? [v7: $i] : (sdtasdt0(v2, v3) = v7 & $i(v7) & ~ % 82.48/11.95 doDivides0(v4, v7) & ! [v8: $i] : ( ~ (sdtasdt0(v4, v8) = v7) | ~ % 82.48/11.95 $i(v8) | ~ aNaturalNumber0(v8)))) & ! [v2: $i] : ! [v3: $i] : ! % 82.48/11.95 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) = v6) | ~ % 82.48/11.95 (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 82.48/11.95 isPrime0(v4) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~ % 82.48/11.95 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3) | ? % 82.48/11.95 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v8) & ((v9 = v2 & sdtasdt0(v4, % 82.48/11.95 v8) = v2 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7) % 82.48/11.95 & ~ doDivides0(v4, v7) & ! [v10: $i] : ( ~ (sdtasdt0(v4, v10) = % 82.48/11.95 v7) | ~ $i(v10) | ~ aNaturalNumber0(v10)))))) & ! [v2: $i] : % 82.48/11.95 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) % 82.48/11.95 = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 82.48/11.95 ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~ % 82.48/11.95 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v2) | ? % 82.48/11.95 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v8) & ((v9 = v3 & sdtasdt0(v4, % 82.48/11.95 v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7) % 82.48/11.95 & ~ doDivides0(v4, v7) & ! [v10: $i] : ( ~ (sdtasdt0(v4, v10) = % 82.48/11.95 v7) | ~ $i(v10) | ~ aNaturalNumber0(v10)))))) & ! [v2: $i] : % 82.48/11.95 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) % 82.48/11.95 = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 82.48/11.95 ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~ % 82.48/11.95 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7: $i] : ? [v8: $i] : % 82.48/11.95 ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ($i(v10) & $i(v8) & ((v11 = v2 % 82.48/11.95 & sdtasdt0(v4, v10) = v2 & aNaturalNumber0(v10)) | (v9 = v3 & % 82.48/11.95 sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = % 82.48/11.95 v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v12: $i] : ( ~ % 82.48/11.95 (sdtasdt0(v4, v12) = v7) | ~ $i(v12) | ~ % 82.48/11.95 aNaturalNumber0(v12))))))) % 82.48/11.95 % 82.48/11.95 (m__1837) % 82.48/11.95 $i(xp) & $i(xm) & $i(xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & % 82.48/11.95 aNaturalNumber0(xn) % 82.48/11.95 % 82.48/11.95 (m__1860) % 82.48/11.95 $i(xp) & $i(xm) & $i(xn) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ( % 82.48/11.95 ~ (xp = sz10) & ~ (xp = sz00) & sdtasdt0(xp, v1) = v0 & sdtasdt0(xn, xm) = % 82.48/11.95 v0 & $i(v1) & $i(v0) & isPrime0(xp) & doDivides0(xp, v0) & % 82.48/11.95 aNaturalNumber0(v1) & ! [v2: $i] : ! [v3: $i] : (v2 = xp | v2 = sz10 | ~ % 82.48/11.95 (sdtasdt0(v2, v3) = xp) | ~ $i(v3) | ~ $i(v2) | ~ aNaturalNumber0(v3) | % 82.48/11.95 ~ aNaturalNumber0(v2)) & ! [v2: $i] : (v2 = xp | v2 = sz10 | ~ $i(v2) | % 82.48/11.95 ~ doDivides0(v2, xp) | ~ aNaturalNumber0(v2))) % 82.48/11.95 % 82.48/11.95 (m__1870) % 82.48/11.95 $i(xp) & $i(xn) & ? [v0: $i] : (sdtpldt0(xp, v0) = xn & $i(v0) & % 82.48/11.95 sdtlseqdt0(xp, xn) & aNaturalNumber0(v0)) % 82.48/11.95 % 82.48/11.95 (m__1883) % 82.48/11.96 sdtmndt0(xn, xp) = xr & sdtpldt0(xp, xr) = xn & $i(xr) & $i(xp) & $i(xn) & % 82.48/11.96 aNaturalNumber0(xr) % 82.48/11.96 % 82.48/11.96 (m__1894) % 82.48/11.96 $i(xr) & $i(xn) & ? [v0: $i] : ( ~ (xr = xn) & sdtpldt0(xr, v0) = xn & $i(v0) % 82.48/11.96 & sdtlseqdt0(xr, xn) & aNaturalNumber0(v0)) % 82.48/11.96 % 82.48/11.96 (m__2027) % 82.48/11.96 $i(xr) & $i(xp) & $i(xm) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 82.48/11.96 $i] : ($i(v2) & $i(v0) & ((v3 = xr & sdtasdt0(xp, v2) = xr & doDivides0(xp, % 82.48/11.96 xr) & aNaturalNumber0(v2)) | (v1 = xm & sdtasdt0(xp, v0) = xm & % 82.48/11.96 doDivides0(xp, xm) & aNaturalNumber0(v0)))) % 82.48/11.96 % 82.48/11.96 (function-axioms) % 82.73/11.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 82.73/11.96 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 82.73/11.96 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 82.73/11.96 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 82.73/11.96 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 82.73/11.96 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 82.73/11.96 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 82.73/11.96 % 82.73/11.96 Further assumptions not needed in the proof: % 82.73/11.96 -------------------------------------------- % 82.73/11.96 mAMDistr, mDefQuot, mDivAsso, mDivLE, mDivMin, mIH, mIH_03, mLEAsym, mLENTr, % 82.73/11.96 mLERefl, mLETotal, mLETran, mMonMul, mMonMul2, mMulAsso, mMulCanc, mMulComm, % 82.73/11.96 mNatSort, mSortsB, mSortsB_02, mSortsC, mZeroAdd, mZeroMul, m_AddZero, % 82.73/11.96 m_MulUnit, m_MulZero, m__1913 % 82.73/11.96 % 82.73/11.96 Those formulas are unsatisfiable: % 82.73/11.96 --------------------------------- % 82.73/11.96 % 82.73/11.96 Begin of proof % 82.73/11.96 | % 82.73/11.96 | ALPHA: (mSortsC_01) implies: % 82.73/11.96 | (1) aNaturalNumber0(sz10) % 82.73/11.96 | % 82.73/11.96 | ALPHA: (mAddCanc) implies: % 82.73/11.96 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 82.73/11.96 | (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ % 82.73/11.96 | $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) % 82.73/11.96 | | ~ aNaturalNumber0(v0)) % 82.73/11.97 | % 82.73/11.97 | ALPHA: (mDefLE) implies: % 82.73/11.97 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, % 82.73/11.97 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] % 82.73/11.97 | : (sdtpldt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 82.73/11.97 | % 82.73/11.97 | ALPHA: (mDefDiff) implies: % 82.73/11.97 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 82.73/11.97 | (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ $i(v3) | ~ % 82.73/11.97 | $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | % 82.73/11.97 | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 82.73/11.97 | % 82.73/11.97 | ALPHA: (mDefDiv) implies: % 82.73/11.97 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, % 82.73/11.97 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] % 82.73/11.97 | : (sdtasdt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 82.73/11.97 | % 82.73/11.97 | ALPHA: (mDefPrime) implies: % 82.73/11.97 | (6) ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10) % 82.73/11.97 | % 82.73/11.97 | ALPHA: (mPrimDiv) implies: % 82.73/11.97 | (7) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~ % 82.73/11.97 | aNaturalNumber0(v0) | ? [v1: $i] : ($i(v1) & isPrime0(v1) & % 82.73/11.97 | doDivides0(v1, v0) & aNaturalNumber0(v1))) % 82.73/11.97 | % 82.73/11.97 | ALPHA: (m__1837) implies: % 82.73/11.97 | (8) aNaturalNumber0(xn) % 82.73/11.97 | (9) aNaturalNumber0(xm) % 82.73/11.97 | (10) aNaturalNumber0(xp) % 82.73/11.97 | % 82.73/11.97 | ALPHA: (m__1799) implies: % 82.73/11.99 | (11) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) % 82.73/11.99 | = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 82.73/11.99 | ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 | ~ (sdtpldt0(v5, % 82.73/11.99 | v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) % 82.73/11.99 | | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~ % 82.73/11.99 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3) % 82.73/11.99 | | doDivides0(v4, v2) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 82.73/11.99 | ? [v10: $i] : ($i(v9) & $i(v8) & ((v10 = v4 & ~ (v8 = v4) & ~ % 82.73/11.99 | (v8 = sz10) & sdtasdt0(v8, v9) = v4 & doDivides0(v8, v4) & % 82.73/11.99 | aNaturalNumber0(v9) & aNaturalNumber0(v8)) | (sdtasdt0(v2, % 82.73/11.99 | v3) = v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v11: $i] : % 82.73/11.99 | ( ~ (sdtasdt0(v4, v11) = v7) | ~ $i(v11) | ~ % 82.73/11.99 | aNaturalNumber0(v11)))))) & ! [v2: $i] : ! [v3: $i] : ! % 82.73/11.99 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 | ~ % 82.73/11.99 | (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | % 82.73/11.99 | ~ $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) % 82.73/11.99 | | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, % 82.73/11.99 | v3) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 82.73/11.99 | ? [v11: $i] : ? [v12: $i] : ($i(v11) & $i(v10) & $i(v8) & ((v12 = % 82.73/11.99 | v4 & ~ (v10 = v4) & ~ (v10 = sz10) & sdtasdt0(v10, v11) = % 82.73/11.99 | v4 & doDivides0(v10, v4) & aNaturalNumber0(v11) & % 82.73/11.99 | aNaturalNumber0(v10)) | (v9 = v2 & sdtasdt0(v4, v8) = v2 & % 82.73/11.99 | aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7) & ~ % 82.73/11.99 | doDivides0(v4, v7) & ! [v13: $i] : ( ~ (sdtasdt0(v4, v13) = % 82.73/11.99 | v7) | ~ $i(v13) | ~ aNaturalNumber0(v13)))))) & ! % 82.73/11.99 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 82.73/11.99 | (v4 = sz10 | v4 = sz00 | ~ (sdtpldt0(v5, v4) = v6) | ~ % 82.73/11.99 | (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 82.73/11.99 | iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | % 82.73/11.99 | ~ aNaturalNumber0(v2) | doDivides0(v4, v2) | ? [v7: $i] : ? % 82.73/11.99 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: % 82.73/11.99 | $i] : ($i(v11) & $i(v10) & $i(v8) & ((v12 = v4 & ~ (v10 = v4) & % 82.73/11.99 | ~ (v10 = sz10) & sdtasdt0(v10, v11) = v4 & doDivides0(v10, % 82.73/11.99 | v4) & aNaturalNumber0(v11) & aNaturalNumber0(v10)) | (v9 = % 82.73/11.99 | v3 & sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | % 82.73/11.99 | (sdtasdt0(v2, v3) = v7 & $i(v7) & ~ doDivides0(v4, v7) & ! % 82.73/11.99 | [v13: $i] : ( ~ (sdtasdt0(v4, v13) = v7) | ~ $i(v13) | ~ % 82.73/11.99 | aNaturalNumber0(v13)))))) & ! [v2: $i] : ! [v3: $i] : ! % 82.73/11.99 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 | ~ % 82.73/11.99 | (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | % 82.73/11.99 | ~ $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) % 82.73/11.99 | | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7: $i] : % 82.73/11.99 | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: % 82.73/11.99 | $i] : ? [v13: $i] : ? [v14: $i] : ($i(v13) & $i(v12) & $i(v10) % 82.73/11.99 | & $i(v8) & ((v14 = v4 & ~ (v12 = v4) & ~ (v12 = sz10) & % 82.73/11.99 | sdtasdt0(v12, v13) = v4 & doDivides0(v12, v4) & % 82.73/11.99 | aNaturalNumber0(v13) & aNaturalNumber0(v12)) | (v11 = v2 & % 82.73/11.99 | sdtasdt0(v4, v10) = v2 & aNaturalNumber0(v10)) | (v9 = v3 & % 82.73/11.99 | sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2, % 82.73/11.99 | v3) = v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v15: $i] : % 82.73/11.99 | ( ~ (sdtasdt0(v4, v15) = v7) | ~ $i(v15) | ~ % 82.73/11.99 | aNaturalNumber0(v15)))))) & ! [v2: $i] : ! [v3: $i] : ! % 82.73/11.99 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) = v6) | % 82.73/11.99 | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 82.73/11.99 | ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~ % 82.73/11.99 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3) % 82.73/11.99 | | doDivides0(v4, v2) | ? [v7: $i] : (sdtasdt0(v2, v3) = v7 & % 82.73/11.99 | $i(v7) & ~ doDivides0(v4, v7) & ! [v8: $i] : ( ~ (sdtasdt0(v4, % 82.73/11.99 | v8) = v7) | ~ $i(v8) | ~ aNaturalNumber0(v8)))) & ! % 82.73/11.99 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 82.73/11.99 | ~ (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) % 82.73/11.99 | | ~ $i(v3) | ~ $i(v2) | ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~ % 82.73/11.99 | aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ % 82.73/11.99 | aNaturalNumber0(v2) | doDivides0(v4, v3) | ? [v7: $i] : ? [v8: % 82.73/11.99 | $i] : ? [v9: $i] : ($i(v8) & ((v9 = v2 & sdtasdt0(v4, v8) = v2 % 82.73/11.99 | & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7) & % 82.73/11.99 | ~ doDivides0(v4, v7) & ! [v10: $i] : ( ~ (sdtasdt0(v4, v10) % 82.73/11.99 | = v7) | ~ $i(v10) | ~ aNaturalNumber0(v10)))))) & ! % 82.73/11.99 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 82.73/11.99 | ~ (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) % 82.73/11.99 | | ~ $i(v3) | ~ $i(v2) | ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~ % 82.73/11.99 | aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ % 82.73/11.99 | aNaturalNumber0(v2) | doDivides0(v4, v2) | ? [v7: $i] : ? [v8: % 82.73/11.99 | $i] : ? [v9: $i] : ($i(v8) & ((v9 = v3 & sdtasdt0(v4, v8) = v3 % 82.73/11.99 | & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7) & % 82.73/11.99 | ~ doDivides0(v4, v7) & ! [v10: $i] : ( ~ (sdtasdt0(v4, v10) % 82.73/11.99 | = v7) | ~ $i(v10) | ~ aNaturalNumber0(v10)))))) & ! % 82.73/11.99 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 82.73/11.99 | ~ (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) % 82.73/11.99 | | ~ $i(v3) | ~ $i(v2) | ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~ % 82.73/11.99 | aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~ % 82.73/11.99 | aNaturalNumber0(v2) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 82.73/11.99 | [v10: $i] : ? [v11: $i] : ($i(v10) & $i(v8) & ((v11 = v2 & % 82.73/11.99 | sdtasdt0(v4, v10) = v2 & aNaturalNumber0(v10)) | (v9 = v3 & % 82.73/11.99 | sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2, % 82.73/11.99 | v3) = v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v12: $i] : % 82.73/11.99 | ( ~ (sdtasdt0(v4, v12) = v7) | ~ $i(v12) | ~ % 82.73/11.99 | aNaturalNumber0(v12))))))) % 82.73/11.99 | % 82.73/11.99 | ALPHA: (m__1860) implies: % 82.73/11.99 | (12) ? [v0: $i] : ? [v1: $i] : ( ~ (xp = sz10) & ~ (xp = sz00) & % 82.73/11.99 | sdtasdt0(xp, v1) = v0 & sdtasdt0(xn, xm) = v0 & $i(v1) & $i(v0) & % 82.73/11.99 | isPrime0(xp) & doDivides0(xp, v0) & aNaturalNumber0(v1) & ! [v2: % 82.73/11.99 | $i] : ! [v3: $i] : (v2 = xp | v2 = sz10 | ~ (sdtasdt0(v2, v3) = % 82.73/11.99 | xp) | ~ $i(v3) | ~ $i(v2) | ~ aNaturalNumber0(v3) | ~ % 82.73/11.99 | aNaturalNumber0(v2)) & ! [v2: $i] : (v2 = xp | v2 = sz10 | ~ % 82.73/11.99 | $i(v2) | ~ doDivides0(v2, xp) | ~ aNaturalNumber0(v2))) % 82.73/11.99 | % 82.73/11.99 | ALPHA: (m__1870) implies: % 82.73/12.00 | (13) ? [v0: $i] : (sdtpldt0(xp, v0) = xn & $i(v0) & sdtlseqdt0(xp, xn) & % 82.73/12.00 | aNaturalNumber0(v0)) % 82.73/12.00 | % 82.73/12.00 | ALPHA: (m__1883) implies: % 82.73/12.00 | (14) aNaturalNumber0(xr) % 82.73/12.00 | (15) sdtpldt0(xp, xr) = xn % 82.73/12.00 | (16) sdtmndt0(xn, xp) = xr % 82.73/12.00 | % 82.73/12.00 | ALPHA: (m__1894) implies: % 82.73/12.00 | (17) ? [v0: $i] : ( ~ (xr = xn) & sdtpldt0(xr, v0) = xn & $i(v0) & % 82.73/12.00 | sdtlseqdt0(xr, xn) & aNaturalNumber0(v0)) % 82.73/12.00 | % 82.73/12.00 | ALPHA: (m__2027) implies: % 82.73/12.00 | (18) $i(xr) % 82.73/12.00 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v2) & % 82.73/12.00 | $i(v0) & ((v3 = xr & sdtasdt0(xp, v2) = xr & doDivides0(xp, xr) & % 82.73/12.00 | aNaturalNumber0(v2)) | (v1 = xm & sdtasdt0(xp, v0) = xm & % 82.73/12.00 | doDivides0(xp, xm) & aNaturalNumber0(v0)))) % 82.73/12.00 | % 82.73/12.00 | ALPHA: (m__) implies: % 83.10/12.00 | (20) ~ doDivides0(xp, xn) % 83.10/12.00 | (21) ~ doDivides0(xp, xm) % 83.10/12.00 | (22) $i(xn) % 83.10/12.00 | (23) $i(xm) % 83.10/12.00 | (24) $i(xp) % 83.10/12.00 | % 83.10/12.00 | ALPHA: (function-axioms) implies: % 83.10/12.00 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 83.10/12.00 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 83.10/12.00 | % 83.10/12.00 | DELTA: instantiating (13) with fresh symbol all_39_0 gives: % 83.10/12.00 | (26) sdtpldt0(xp, all_39_0) = xn & $i(all_39_0) & sdtlseqdt0(xp, xn) & % 83.10/12.00 | aNaturalNumber0(all_39_0) % 83.10/12.00 | % 83.10/12.00 | ALPHA: (26) implies: % 83.10/12.00 | (27) aNaturalNumber0(all_39_0) % 83.10/12.00 | (28) sdtlseqdt0(xp, xn) % 83.10/12.00 | (29) $i(all_39_0) % 83.10/12.00 | (30) sdtpldt0(xp, all_39_0) = xn % 83.10/12.00 | % 83.10/12.00 | DELTA: instantiating (17) with fresh symbol all_41_0 gives: % 83.10/12.00 | (31) ~ (xr = xn) & sdtpldt0(xr, all_41_0) = xn & $i(all_41_0) & % 83.10/12.00 | sdtlseqdt0(xr, xn) & aNaturalNumber0(all_41_0) % 83.10/12.00 | % 83.10/12.00 | ALPHA: (31) implies: % 83.10/12.00 | (32) ~ (xr = xn) % 83.10/12.00 | (33) aNaturalNumber0(all_41_0) % 83.10/12.00 | (34) sdtlseqdt0(xr, xn) % 83.10/12.00 | (35) $i(all_41_0) % 83.10/12.00 | (36) sdtpldt0(xr, all_41_0) = xn % 83.10/12.00 | % 83.10/12.00 | DELTA: instantiating (19) with fresh symbols all_45_0, all_45_1, all_45_2, % 83.10/12.00 | all_45_3 gives: % 83.10/12.00 | (37) $i(all_45_1) & $i(all_45_3) & ((all_45_0 = xr & sdtasdt0(xp, all_45_1) % 83.10/12.00 | = xr & doDivides0(xp, xr) & aNaturalNumber0(all_45_1)) | (all_45_2 % 83.10/12.00 | = xm & sdtasdt0(xp, all_45_3) = xm & doDivides0(xp, xm) & % 83.10/12.00 | aNaturalNumber0(all_45_3))) % 83.10/12.00 | % 83.10/12.00 | ALPHA: (37) implies: % 83.10/12.00 | (38) (all_45_0 = xr & sdtasdt0(xp, all_45_1) = xr & doDivides0(xp, xr) & % 83.10/12.00 | aNaturalNumber0(all_45_1)) | (all_45_2 = xm & sdtasdt0(xp, all_45_3) % 83.10/12.00 | = xm & doDivides0(xp, xm) & aNaturalNumber0(all_45_3)) % 83.10/12.00 | % 83.10/12.00 | DELTA: instantiating (12) with fresh symbols all_47_0, all_47_1 gives: % 83.10/12.00 | (39) ~ (xp = sz10) & ~ (xp = sz00) & sdtasdt0(xp, all_47_0) = all_47_1 & % 83.10/12.00 | sdtasdt0(xn, xm) = all_47_1 & $i(all_47_0) & $i(all_47_1) & % 83.10/12.00 | isPrime0(xp) & doDivides0(xp, all_47_1) & aNaturalNumber0(all_47_0) & % 83.10/12.00 | ! [v0: $i] : ! [v1: $i] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) % 83.10/12.00 | = xp) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ % 83.10/12.00 | aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = xp | v0 = sz10 | ~ % 83.10/12.00 | $i(v0) | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0)) % 83.10/12.00 | % 83.10/12.00 | ALPHA: (39) implies: % 83.10/12.00 | (40) ~ (xp = sz00) % 83.10/12.00 | (41) ~ (xp = sz10) % 83.10/12.00 | (42) ! [v0: $i] : ! [v1: $i] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, % 83.10/12.00 | v1) = xp) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ % 83.10/12.00 | aNaturalNumber0(v0)) % 83.10/12.00 | % 83.10/12.00 | DELTA: instantiating (11) with fresh symbols all_50_0, all_50_1 gives: % 83.10/12.01 | (43) sdtpldt0(all_50_1, xp) = all_50_0 & sdtpldt0(xn, xm) = all_50_1 & % 83.10/12.01 | $i(all_50_0) & $i(all_50_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 83.10/12.01 | : ! [v3: $i] : ! [v4: $i] : (v2 = sz10 | v2 = sz00 | ~ % 83.10/12.01 | (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | % 83.10/12.01 | ~ $i(v1) | ~ $i(v0) | ~ iLess0(v4, all_50_0) | ~ % 83.10/12.01 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 83.10/12.01 | aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ? % 83.10/12.01 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v7) & % 83.10/12.01 | $i(v6) & ((v8 = v2 & ~ (v6 = v2) & ~ (v6 = sz10) & sdtasdt0(v6, % 83.10/12.01 | v7) = v2 & doDivides0(v6, v2) & aNaturalNumber0(v7) & % 83.10/12.01 | aNaturalNumber0(v6)) | (sdtasdt0(v0, v1) = v5 & $i(v5) & ~ % 83.10/12.01 | doDivides0(v2, v5) & ! [v9: $i] : ( ~ (sdtasdt0(v2, v9) = v5) % 83.10/12.01 | | ~ $i(v9) | ~ aNaturalNumber0(v9)))))) & ! [v0: $i] : ! % 83.10/12.01 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = sz10 | v2 = % 83.10/12.01 | sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ % 83.10/12.01 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ iLess0(v4, all_50_0) | ~ % 83.10/12.01 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 83.10/12.01 | aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5: $i] : ? [v6: $i] % 83.10/12.01 | : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ($i(v9) & % 83.10/12.01 | $i(v8) & $i(v6) & ((v10 = v2 & ~ (v8 = v2) & ~ (v8 = sz10) & % 83.10/12.01 | sdtasdt0(v8, v9) = v2 & doDivides0(v8, v2) & % 83.10/12.01 | aNaturalNumber0(v9) & aNaturalNumber0(v8)) | (v7 = v0 & % 83.10/12.01 | sdtasdt0(v2, v6) = v0 & aNaturalNumber0(v6)) | (sdtasdt0(v0, % 83.10/12.01 | v1) = v5 & $i(v5) & ~ doDivides0(v2, v5) & ! [v11: $i] : ( % 83.10/12.01 | ~ (sdtasdt0(v2, v11) = v5) | ~ $i(v11) | ~ % 83.10/12.01 | aNaturalNumber0(v11)))))) & ! [v0: $i] : ! [v1: $i] : ! % 83.10/12.01 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = sz10 | v2 = sz00 | ~ % 83.10/12.01 | (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | % 83.10/12.01 | ~ $i(v1) | ~ $i(v0) | ~ iLess0(v4, all_50_0) | ~ % 83.10/12.01 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 83.10/12.01 | aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5: $i] : ? [v6: $i] % 83.10/12.01 | : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ($i(v9) & % 83.10/12.01 | $i(v8) & $i(v6) & ((v10 = v2 & ~ (v8 = v2) & ~ (v8 = sz10) & % 83.10/12.01 | sdtasdt0(v8, v9) = v2 & doDivides0(v8, v2) & % 83.10/12.01 | aNaturalNumber0(v9) & aNaturalNumber0(v8)) | (v7 = v1 & % 83.10/12.01 | sdtasdt0(v2, v6) = v1 & aNaturalNumber0(v6)) | (sdtasdt0(v0, % 83.10/12.01 | v1) = v5 & $i(v5) & ~ doDivides0(v2, v5) & ! [v11: $i] : ( % 83.10/12.01 | ~ (sdtasdt0(v2, v11) = v5) | ~ $i(v11) | ~ % 83.10/12.01 | aNaturalNumber0(v11)))))) & ! [v0: $i] : ! [v1: $i] : ! % 83.10/12.01 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = sz10 | v2 = sz00 | ~ % 83.10/12.01 | (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | % 83.10/12.01 | ~ $i(v1) | ~ $i(v0) | ~ iLess0(v4, all_50_0) | ~ % 83.10/12.01 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 83.10/12.01 | aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? % 83.10/12.01 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] % 83.10/12.01 | : ($i(v11) & $i(v10) & $i(v8) & $i(v6) & ((v12 = v2 & ~ (v10 = v2) % 83.10/12.01 | & ~ (v10 = sz10) & sdtasdt0(v10, v11) = v2 & doDivides0(v10, % 83.10/12.01 | v2) & aNaturalNumber0(v11) & aNaturalNumber0(v10)) | (v9 = % 83.10/12.01 | v0 & sdtasdt0(v2, v8) = v0 & aNaturalNumber0(v8)) | (v7 = v1 & % 83.10/12.01 | sdtasdt0(v2, v6) = v1 & aNaturalNumber0(v6)) | (sdtasdt0(v0, % 83.10/12.01 | v1) = v5 & $i(v5) & ~ doDivides0(v2, v5) & ! [v13: $i] : ( % 83.10/12.01 | ~ (sdtasdt0(v2, v13) = v5) | ~ $i(v13) | ~ % 83.10/12.01 | aNaturalNumber0(v13)))))) & ! [v0: $i] : ! [v1: $i] : ! % 83.10/12.01 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3, v2) = v4) | % 83.10/12.01 | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 83.10/12.01 | isPrime0(v2) | ~ iLess0(v4, all_50_0) | ~ aNaturalNumber0(v2) | ~ % 83.10/12.01 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) | % 83.10/12.01 | doDivides0(v2, v0) | ? [v5: $i] : (sdtasdt0(v0, v1) = v5 & $i(v5) & % 83.10/12.01 | ~ doDivides0(v2, v5) & ! [v6: $i] : ( ~ (sdtasdt0(v2, v6) = v5) % 83.10/12.01 | | ~ $i(v6) | ~ aNaturalNumber0(v6)))) & ! [v0: $i] : ! [v1: % 83.10/12.01 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3, % 83.10/12.01 | v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 83.10/12.01 | ~ $i(v0) | ~ isPrime0(v2) | ~ iLess0(v4, all_50_0) | ~ % 83.10/12.01 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 83.10/12.01 | aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5: $i] : ? [v6: $i] % 83.10/12.01 | : ? [v7: $i] : ($i(v6) & ((v7 = v0 & sdtasdt0(v2, v6) = v0 & % 83.10/12.01 | aNaturalNumber0(v6)) | (sdtasdt0(v0, v1) = v5 & $i(v5) & ~ % 83.10/12.01 | doDivides0(v2, v5) & ! [v8: $i] : ( ~ (sdtasdt0(v2, v8) = v5) % 83.10/12.01 | | ~ $i(v8) | ~ aNaturalNumber0(v8)))))) & ! [v0: $i] : ! % 83.10/12.01 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3, % 83.10/12.01 | v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 83.10/12.01 | ~ $i(v0) | ~ isPrime0(v2) | ~ iLess0(v4, all_50_0) | ~ % 83.10/12.01 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 83.10/12.01 | aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5: $i] : ? [v6: $i] % 83.10/12.01 | : ? [v7: $i] : ($i(v6) & ((v7 = v1 & sdtasdt0(v2, v6) = v1 & % 83.10/12.01 | aNaturalNumber0(v6)) | (sdtasdt0(v0, v1) = v5 & $i(v5) & ~ % 83.10/12.01 | doDivides0(v2, v5) & ! [v8: $i] : ( ~ (sdtasdt0(v2, v8) = v5) % 83.10/12.01 | | ~ $i(v8) | ~ aNaturalNumber0(v8)))))) & ! [v0: $i] : ! % 83.10/12.01 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3, % 83.10/12.01 | v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 83.10/12.01 | ~ $i(v0) | ~ isPrime0(v2) | ~ iLess0(v4, all_50_0) | ~ % 83.10/12.01 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 83.10/12.01 | aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? % 83.10/12.01 | [v8: $i] : ? [v9: $i] : ($i(v8) & $i(v6) & ((v9 = v0 & sdtasdt0(v2, % 83.10/12.01 | v8) = v0 & aNaturalNumber0(v8)) | (v7 = v1 & sdtasdt0(v2, % 83.10/12.01 | v6) = v1 & aNaturalNumber0(v6)) | (sdtasdt0(v0, v1) = v5 & % 83.10/12.01 | $i(v5) & ~ doDivides0(v2, v5) & ! [v10: $i] : ( ~ % 83.10/12.01 | (sdtasdt0(v2, v10) = v5) | ~ $i(v10) | ~ % 83.10/12.01 | aNaturalNumber0(v10)))))) % 83.10/12.01 | % 83.10/12.01 | ALPHA: (43) implies: % 83.10/12.01 | (44) sdtpldt0(xn, xm) = all_50_1 % 83.10/12.01 | % 83.10/12.01 | BETA: splitting (38) gives: % 83.10/12.01 | % 83.10/12.01 | Case 1: % 83.10/12.01 | | % 83.10/12.01 | | (45) all_45_0 = xr & sdtasdt0(xp, all_45_1) = xr & doDivides0(xp, xr) & % 83.10/12.01 | | aNaturalNumber0(all_45_1) % 83.10/12.01 | | % 83.10/12.01 | | ALPHA: (45) implies: % 83.10/12.01 | | (46) doDivides0(xp, xr) % 83.10/12.01 | | % 83.10/12.01 | | BETA: splitting (6) gives: % 83.10/12.01 | | % 83.10/12.01 | | Case 1: % 83.10/12.01 | | | % 83.10/12.02 | | | (47) ~ aNaturalNumber0(sz10) % 83.10/12.02 | | | % 83.10/12.02 | | | PRED_UNIFY: (1), (47) imply: % 83.10/12.02 | | | (48) $false % 83.10/12.02 | | | % 83.10/12.02 | | | CLOSE: (48) is inconsistent. % 83.10/12.02 | | | % 83.10/12.02 | | Case 2: % 83.10/12.02 | | | % 83.10/12.02 | | | (49) ~ isPrime0(sz10) % 83.10/12.02 | | | % 83.10/12.02 | | | GROUND_INST: instantiating (7) with xp, simplifying with (10), (24) gives: % 83.10/12.02 | | | (50) xp = sz10 | xp = sz00 | ? [v0: $i] : ($i(v0) & isPrime0(v0) & % 83.10/12.02 | | | doDivides0(v0, xp) & aNaturalNumber0(v0)) % 83.10/12.02 | | | % 83.10/12.02 | | | GROUND_INST: instantiating (3) with xp, xn, simplifying with (8), (10), % 83.10/12.02 | | | (22), (24), (28) gives: % 83.10/12.02 | | | (51) ? [v0: $i] : (sdtpldt0(xp, v0) = xn & $i(v0) & % 83.10/12.02 | | | aNaturalNumber0(v0)) % 83.10/12.02 | | | % 83.10/12.02 | | | GROUND_INST: instantiating (3) with xr, xn, simplifying with (8), (14), % 83.10/12.02 | | | (18), (22), (34) gives: % 83.10/12.02 | | | (52) ? [v0: $i] : (sdtpldt0(xr, v0) = xn & $i(v0) & % 83.10/12.02 | | | aNaturalNumber0(v0)) % 83.10/12.02 | | | % 83.10/12.02 | | | GROUND_INST: instantiating (mAddAsso) with xp, xr, xm, xn, all_50_1, % 83.10/12.02 | | | simplifying with (9), (10), (14), (15), (18), (23), (24), % 83.10/12.02 | | | (44) gives: % 83.10/12.02 | | | (53) ? [v0: $i] : (sdtpldt0(xr, xm) = v0 & sdtpldt0(xp, v0) = all_50_1 % 83.10/12.02 | | | & $i(v0) & $i(all_50_1)) % 83.10/12.02 | | | % 83.10/12.02 | | | GROUND_INST: instantiating (mAddAsso) with xp, all_39_0, xm, xn, all_50_1, % 83.10/12.02 | | | simplifying with (9), (10), (23), (24), (27), (29), (30), % 83.10/12.02 | | | (44) gives: % 83.10/12.02 | | | (54) ? [v0: $i] : (sdtpldt0(all_39_0, xm) = v0 & sdtpldt0(xp, v0) = % 83.10/12.02 | | | all_50_1 & $i(v0) & $i(all_50_1)) % 83.10/12.02 | | | % 83.10/12.02 | | | GROUND_INST: instantiating (mAddComm) with xp, all_39_0, xn, simplifying % 83.10/12.02 | | | with (10), (24), (27), (29), (30) gives: % 83.10/12.02 | | | (55) sdtpldt0(all_39_0, xp) = xn & $i(xn) % 83.10/12.02 | | | % 83.10/12.02 | | | ALPHA: (55) implies: % 83.10/12.02 | | | (56) sdtpldt0(all_39_0, xp) = xn % 83.10/12.02 | | | % 83.10/12.02 | | | GROUND_INST: instantiating (mMonAdd) with xr, xn, all_41_0, xn, % 83.10/12.02 | | | simplifying with (8), (14), (18), (22), (33), (34), (35), % 83.10/12.02 | | | (36) gives: % 83.10/12.02 | | | (57) xr = xn | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = xn) % 83.10/12.02 | | | & ~ (v1 = v0) & sdtpldt0(all_41_0, xr) = v0 & % 83.10/12.02 | | | sdtpldt0(all_41_0, xn) = v1 & sdtpldt0(xn, all_41_0) = v2 & % 83.10/12.02 | | | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) & sdtlseqdt0(xn, % 83.10/12.02 | | | v2)) % 83.10/12.02 | | | % 83.10/12.02 | | | GROUND_INST: instantiating (mAddComm) with xr, all_41_0, xn, simplifying % 83.10/12.02 | | | with (14), (18), (33), (35), (36) gives: % 83.10/12.02 | | | (58) sdtpldt0(all_41_0, xr) = xn & $i(xn) % 83.10/12.02 | | | % 83.10/12.02 | | | ALPHA: (58) implies: % 83.10/12.02 | | | (59) sdtpldt0(all_41_0, xr) = xn % 83.10/12.02 | | | % 83.10/12.02 | | | GROUND_INST: instantiating (4) with xp, xn, xr, all_39_0, simplifying with % 83.10/12.02 | | | (8), (10), (16), (22), (24), (27), (28), (29), (30) gives: % 83.10/12.02 | | | (60) all_39_0 = xr % 83.10/12.02 | | | % 83.10/12.02 | | | DELTA: instantiating (52) with fresh symbol all_73_0 gives: % 83.10/12.02 | | | (61) sdtpldt0(xr, all_73_0) = xn & $i(all_73_0) & % 83.10/12.02 | | | aNaturalNumber0(all_73_0) % 83.10/12.02 | | | % 83.10/12.02 | | | ALPHA: (61) implies: % 83.10/12.02 | | | (62) aNaturalNumber0(all_73_0) % 83.10/12.02 | | | (63) $i(all_73_0) % 83.10/12.02 | | | (64) sdtpldt0(xr, all_73_0) = xn % 83.10/12.02 | | | % 83.10/12.02 | | | DELTA: instantiating (51) with fresh symbol all_75_0 gives: % 83.10/12.02 | | | (65) sdtpldt0(xp, all_75_0) = xn & $i(all_75_0) & % 83.10/12.02 | | | aNaturalNumber0(all_75_0) % 83.10/12.02 | | | % 83.10/12.02 | | | ALPHA: (65) implies: % 83.10/12.02 | | | (66) aNaturalNumber0(all_75_0) % 83.10/12.02 | | | (67) $i(all_75_0) % 83.10/12.02 | | | (68) sdtpldt0(xp, all_75_0) = xn % 83.10/12.02 | | | % 83.10/12.02 | | | DELTA: instantiating (53) with fresh symbol all_81_0 gives: % 83.10/12.02 | | | (69) sdtpldt0(xr, xm) = all_81_0 & sdtpldt0(xp, all_81_0) = all_50_1 & % 83.10/12.02 | | | $i(all_81_0) & $i(all_50_1) % 83.10/12.02 | | | % 83.10/12.02 | | | ALPHA: (69) implies: % 83.10/12.02 | | | (70) sdtpldt0(xr, xm) = all_81_0 % 83.10/12.02 | | | % 83.10/12.02 | | | DELTA: instantiating (54) with fresh symbol all_85_0 gives: % 83.10/12.03 | | | (71) sdtpldt0(all_39_0, xm) = all_85_0 & sdtpldt0(xp, all_85_0) = % 83.10/12.03 | | | all_50_1 & $i(all_85_0) & $i(all_50_1) % 83.10/12.03 | | | % 83.10/12.03 | | | ALPHA: (71) implies: % 83.10/12.03 | | | (72) sdtpldt0(all_39_0, xm) = all_85_0 % 83.10/12.03 | | | % 83.10/12.03 | | | REDUCE: (56), (60) imply: % 83.10/12.03 | | | (73) sdtpldt0(xr, xp) = xn % 83.10/12.03 | | | % 83.10/12.03 | | | REDUCE: (60), (72) imply: % 83.10/12.03 | | | (74) sdtpldt0(xr, xm) = all_85_0 % 83.10/12.03 | | | % 83.10/12.03 | | | BETA: splitting (50) gives: % 83.10/12.03 | | | % 83.10/12.03 | | | Case 1: % 83.10/12.03 | | | | % 83.10/12.03 | | | | (75) xp = sz00 % 83.10/12.03 | | | | % 83.10/12.03 | | | | REDUCE: (40), (75) imply: % 83.10/12.03 | | | | (76) $false % 83.10/12.03 | | | | % 83.10/12.03 | | | | CLOSE: (76) is inconsistent. % 83.10/12.03 | | | | % 83.10/12.03 | | | Case 2: % 83.10/12.03 | | | | % 83.10/12.03 | | | | (77) xp = sz10 | ? [v0: $i] : ($i(v0) & isPrime0(v0) & % 83.10/12.03 | | | | doDivides0(v0, xp) & aNaturalNumber0(v0)) % 83.10/12.03 | | | | % 83.10/12.03 | | | | BETA: splitting (57) gives: % 83.10/12.03 | | | | % 83.10/12.03 | | | | Case 1: % 83.10/12.03 | | | | | % 83.10/12.03 | | | | | (78) xr = xn % 83.10/12.03 | | | | | % 83.10/12.03 | | | | | REDUCE: (32), (78) imply: % 83.10/12.03 | | | | | (79) $false % 83.10/12.03 | | | | | % 83.10/12.03 | | | | | CLOSE: (79) is inconsistent. % 83.10/12.03 | | | | | % 83.10/12.03 | | | | Case 2: % 83.10/12.03 | | | | | % 83.10/12.03 | | | | | (80) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = xn) & ~ % 83.10/12.03 | | | | | (v1 = v0) & sdtpldt0(all_41_0, xr) = v0 & sdtpldt0(all_41_0, % 83.10/12.03 | | | | | xn) = v1 & sdtpldt0(xn, all_41_0) = v2 & $i(v2) & $i(v1) & % 83.10/12.03 | | | | | $i(v0) & sdtlseqdt0(v0, v1) & sdtlseqdt0(xn, v2)) % 83.10/12.03 | | | | | % 83.10/12.03 | | | | | DELTA: instantiating (80) with fresh symbols all_102_0, all_102_1, % 83.10/12.03 | | | | | all_102_2 gives: % 83.10/12.03 | | | | | (81) ~ (all_102_0 = xn) & ~ (all_102_1 = all_102_2) & % 83.10/12.03 | | | | | sdtpldt0(all_41_0, xr) = all_102_2 & sdtpldt0(all_41_0, xn) = % 83.10/12.03 | | | | | all_102_1 & sdtpldt0(xn, all_41_0) = all_102_0 & $i(all_102_0) % 83.10/12.03 | | | | | & $i(all_102_1) & $i(all_102_2) & sdtlseqdt0(all_102_2, % 83.10/12.03 | | | | | all_102_1) & sdtlseqdt0(xn, all_102_0) % 83.10/12.03 | | | | | % 83.10/12.03 | | | | | ALPHA: (81) implies: % 83.10/12.03 | | | | | (82) $i(all_102_2) % 83.10/12.03 | | | | | (83) sdtpldt0(all_41_0, xr) = all_102_2 % 83.10/12.03 | | | | | % 83.10/12.03 | | | | | BETA: splitting (77) gives: % 83.10/12.03 | | | | | % 83.10/12.03 | | | | | Case 1: % 83.10/12.03 | | | | | | % 83.10/12.03 | | | | | | (84) xp = sz10 % 83.10/12.03 | | | | | | % 83.10/12.03 | | | | | | REDUCE: (41), (84) imply: % 83.10/12.03 | | | | | | (85) $false % 83.10/12.03 | | | | | | % 83.10/12.03 | | | | | | CLOSE: (85) is inconsistent. % 83.10/12.03 | | | | | | % 83.10/12.03 | | | | | Case 2: % 83.10/12.03 | | | | | | % 83.10/12.03 | | | | | | (86) ? [v0: $i] : ($i(v0) & isPrime0(v0) & doDivides0(v0, xp) & % 83.10/12.03 | | | | | | aNaturalNumber0(v0)) % 83.10/12.03 | | | | | | % 83.10/12.03 | | | | | | DELTA: instantiating (86) with fresh symbol all_107_0 gives: % 83.10/12.03 | | | | | | (87) $i(all_107_0) & isPrime0(all_107_0) & doDivides0(all_107_0, % 83.10/12.03 | | | | | | xp) & aNaturalNumber0(all_107_0) % 83.10/12.03 | | | | | | % 83.10/12.03 | | | | | | ALPHA: (87) implies: % 83.10/12.03 | | | | | | (88) aNaturalNumber0(all_107_0) % 83.10/12.03 | | | | | | (89) doDivides0(all_107_0, xp) % 83.10/12.03 | | | | | | (90) isPrime0(all_107_0) % 83.10/12.03 | | | | | | (91) $i(all_107_0) % 83.10/12.03 | | | | | | % 83.10/12.03 | | | | | | GROUND_INST: instantiating (25) with all_81_0, all_85_0, xm, xr, % 83.10/12.03 | | | | | | simplifying with (70), (74) gives: % 83.10/12.03 | | | | | | (92) all_85_0 = all_81_0 % 83.10/12.03 | | | | | | % 83.10/12.03 | | | | | | GROUND_INST: instantiating (25) with xn, all_102_2, xr, all_41_0, % 83.10/12.03 | | | | | | simplifying with (59), (83) gives: % 83.10/12.03 | | | | | | (93) all_102_2 = xn % 83.10/12.03 | | | | | | % 83.25/12.03 | | | | | | GROUND_INST: instantiating (mDivTrans) with all_107_0, xp, xr, % 83.25/12.03 | | | | | | simplifying with (10), (14), (18), (24), (46), (88), % 83.25/12.03 | | | | | | (89), (91) gives: % 83.25/12.03 | | | | | | (94) doDivides0(all_107_0, xr) % 83.25/12.03 | | | | | | % 83.25/12.03 | | | | | | GROUND_INST: instantiating (5) with all_107_0, xp, simplifying with % 83.25/12.03 | | | | | | (10), (24), (88), (89), (91) gives: % 83.25/12.03 | | | | | | (95) ? [v0: $i] : (sdtasdt0(all_107_0, v0) = xp & $i(v0) & % 83.25/12.03 | | | | | | aNaturalNumber0(v0)) % 83.25/12.03 | | | | | | % 83.25/12.03 | | | | | | GROUND_INST: instantiating (4) with xp, xn, xr, all_75_0, % 83.25/12.03 | | | | | | simplifying with (8), (10), (16), (22), (24), (28), % 83.25/12.03 | | | | | | (66), (67), (68) gives: % 83.25/12.03 | | | | | | (96) all_75_0 = xr % 83.25/12.03 | | | | | | % 83.25/12.03 | | | | | | GROUND_INST: instantiating (mAddComm) with xp, all_75_0, xn, % 83.25/12.03 | | | | | | simplifying with (10), (24), (66), (67), (68) gives: % 83.25/12.03 | | | | | | (97) sdtpldt0(all_75_0, xp) = xn & $i(xn) % 83.25/12.03 | | | | | | % 83.25/12.03 | | | | | | GROUND_INST: instantiating (mMonAdd) with xr, xn, xm, all_81_0, % 83.25/12.03 | | | | | | simplifying with (8), (9), (14), (18), (22), (23), % 83.25/12.03 | | | | | | (34), (70) gives: % 83.25/12.03 | | | | | | (98) xr = xn | ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ( ~ (v2 % 83.25/12.03 | | | | | | = all_81_0) & ~ (v1 = v0) & sdtpldt0(xm, xr) = v0 & % 83.25/12.03 | | | | | | sdtpldt0(xm, xn) = v1 & sdtpldt0(xn, xm) = v2 & $i(v2) & % 83.25/12.03 | | | | | | $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) & % 83.25/12.03 | | | | | | sdtlseqdt0(all_81_0, v2)) % 83.25/12.03 | | | | | | % 83.25/12.03 | | | | | | GROUND_INST: instantiating (2) with xr, all_73_0, all_41_0, xn, % 83.25/12.03 | | | | | | simplifying with (14), (18), (33), (35), (36), (62), % 83.25/12.03 | | | | | | (63), (64) gives: % 83.25/12.03 | | | | | | (99) all_73_0 = all_41_0 % 83.25/12.03 | | | | | | % 83.25/12.03 | | | | | | GROUND_INST: instantiating (2) with xr, all_73_0, xp, xn, % 83.25/12.03 | | | | | | simplifying with (10), (14), (18), (24), (62), (63), % 83.25/12.03 | | | | | | (64), (73) gives: % 83.25/12.03 | | | | | | (100) all_73_0 = xp % 83.25/12.03 | | | | | | % 83.25/12.03 | | | | | | GROUND_INST: instantiating (mMonAdd) with xr, xn, all_73_0, xn, % 83.25/12.03 | | | | | | simplifying with (8), (14), (18), (22), (34), (62), % 83.25/12.03 | | | | | | (63), (64) gives: % 83.25/12.04 | | | | | | (101) xr = xn | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 % 83.25/12.04 | | | | | | = xn) & ~ (v1 = v0) & sdtpldt0(all_73_0, xr) = v0 & % 83.25/12.04 | | | | | | sdtpldt0(all_73_0, xn) = v1 & sdtpldt0(xn, all_73_0) = v2 % 83.25/12.04 | | | | | | & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) & % 83.25/12.04 | | | | | | sdtlseqdt0(xn, v2)) % 83.25/12.04 | | | | | | % 83.25/12.04 | | | | | | COMBINE_EQS: (99), (100) imply: % 83.25/12.04 | | | | | | (102) all_41_0 = xp % 83.25/12.04 | | | | | | % 83.25/12.04 | | | | | | DELTA: instantiating (95) with fresh symbol all_129_0 gives: % 83.25/12.04 | | | | | | (103) sdtasdt0(all_107_0, all_129_0) = xp & $i(all_129_0) & % 83.25/12.04 | | | | | | aNaturalNumber0(all_129_0) % 83.25/12.04 | | | | | | % 83.25/12.04 | | | | | | ALPHA: (103) implies: % 83.25/12.04 | | | | | | (104) aNaturalNumber0(all_129_0) % 83.25/12.04 | | | | | | (105) $i(all_129_0) % 83.25/12.04 | | | | | | (106) sdtasdt0(all_107_0, all_129_0) = xp % 83.25/12.04 | | | | | | % 83.25/12.04 | | | | | | BETA: splitting (101) gives: % 83.25/12.04 | | | | | | % 83.25/12.04 | | | | | | Case 1: % 83.25/12.04 | | | | | | | % 83.25/12.04 | | | | | | | (107) xr = xn % 83.25/12.04 | | | | | | | % 83.25/12.04 | | | | | | | REDUCE: (32), (107) imply: % 83.25/12.04 | | | | | | | (108) $false % 83.25/12.04 | | | | | | | % 83.25/12.04 | | | | | | | CLOSE: (108) is inconsistent. % 83.25/12.04 | | | | | | | % 83.25/12.04 | | | | | | Case 2: % 83.25/12.04 | | | | | | | % 83.25/12.04 | | | | | | | (109) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = xn) & % 83.25/12.04 | | | | | | | ~ (v1 = v0) & sdtpldt0(all_73_0, xr) = v0 & % 83.25/12.04 | | | | | | | sdtpldt0(all_73_0, xn) = v1 & sdtpldt0(xn, all_73_0) = % 83.25/12.04 | | | | | | | v2 & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) & % 83.25/12.04 | | | | | | | sdtlseqdt0(xn, v2)) % 83.25/12.04 | | | | | | | % 83.25/12.04 | | | | | | | DELTA: instantiating (109) with fresh symbols all_192_0, % 83.25/12.04 | | | | | | | all_192_1, all_192_2 gives: % 83.25/12.04 | | | | | | | (110) ~ (all_192_0 = xn) & ~ (all_192_1 = all_192_2) & % 83.25/12.04 | | | | | | | sdtpldt0(all_73_0, xr) = all_192_2 & sdtpldt0(all_73_0, % 83.25/12.04 | | | | | | | xn) = all_192_1 & sdtpldt0(xn, all_73_0) = all_192_0 & % 83.25/12.04 | | | | | | | $i(all_192_0) & $i(all_192_1) & $i(all_192_2) & % 83.25/12.04 | | | | | | | sdtlseqdt0(all_192_2, all_192_1) & sdtlseqdt0(xn, % 83.25/12.04 | | | | | | | all_192_0) % 83.25/12.04 | | | | | | | % 83.25/12.04 | | | | | | | ALPHA: (110) implies: % 83.25/12.04 | | | | | | | (111) sdtpldt0(all_73_0, xr) = all_192_2 % 83.25/12.04 | | | | | | | % 83.25/12.04 | | | | | | | REDUCE: (100), (111) imply: % 83.25/12.04 | | | | | | | (112) sdtpldt0(xp, xr) = all_192_2 % 83.25/12.04 | | | | | | | % 83.25/12.04 | | | | | | | BETA: splitting (98) gives: % 83.25/12.04 | | | | | | | % 83.25/12.04 | | | | | | | Case 1: % 83.25/12.04 | | | | | | | | % 83.25/12.04 | | | | | | | | (113) xr = xn % 83.25/12.04 | | | | | | | | % 83.25/12.04 | | | | | | | | REDUCE: (32), (113) imply: % 83.25/12.04 | | | | | | | | (114) $false % 83.25/12.04 | | | | | | | | % 83.25/12.04 | | | | | | | | CLOSE: (114) is inconsistent. % 83.25/12.04 | | | | | | | | % 83.25/12.04 | | | | | | | Case 2: % 83.25/12.04 | | | | | | | | % 83.25/12.04 | | | | | | | | % 83.25/12.04 | | | | | | | | GROUND_INST: instantiating (25) with xn, all_192_2, xr, xp, % 83.25/12.04 | | | | | | | | simplifying with (15), (112) gives: % 83.25/12.04 | | | | | | | | (115) all_192_2 = xn % 83.25/12.04 | | | | | | | | % 83.25/12.04 | | | | | | | | GROUND_INST: instantiating (mDivSum) with all_107_0, xp, xr, xn, % 83.25/12.04 | | | | | | | | simplifying with (10), (14), (15), (18), (24), % 83.25/12.04 | | | | | | | | (88), (89), (91), (94) gives: % 83.25/12.04 | | | | | | | | (116) doDivides0(all_107_0, xn) % 83.25/12.04 | | | | | | | | % 83.25/12.04 | | | | | | | | GROUND_INST: instantiating (42) with all_107_0, all_129_0, % 83.25/12.04 | | | | | | | | simplifying with (88), (91), (104), (105), (106) % 83.25/12.04 | | | | | | | | gives: % 83.25/12.04 | | | | | | | | (117) all_107_0 = xp | all_107_0 = sz10 % 83.25/12.04 | | | | | | | | % 83.25/12.04 | | | | | | | | BETA: splitting (117) gives: % 83.25/12.04 | | | | | | | | % 83.25/12.04 | | | | | | | | Case 1: % 83.25/12.04 | | | | | | | | | % 83.25/12.04 | | | | | | | | | (118) all_107_0 = xp % 83.25/12.04 | | | | | | | | | % 83.25/12.04 | | | | | | | | | REDUCE: (116), (118) imply: % 83.25/12.04 | | | | | | | | | (119) doDivides0(xp, xn) % 83.25/12.04 | | | | | | | | | % 83.25/12.04 | | | | | | | | | PRED_UNIFY: (20), (119) imply: % 83.25/12.04 | | | | | | | | | (120) $false % 83.25/12.04 | | | | | | | | | % 83.25/12.04 | | | | | | | | | CLOSE: (120) is inconsistent. % 83.25/12.04 | | | | | | | | | % 83.25/12.04 | | | | | | | | Case 2: % 83.25/12.04 | | | | | | | | | % 83.25/12.04 | | | | | | | | | (121) all_107_0 = sz10 % 83.25/12.04 | | | | | | | | | % 83.25/12.04 | | | | | | | | | REDUCE: (90), (121) imply: % 83.25/12.04 | | | | | | | | | (122) isPrime0(sz10) % 83.25/12.04 | | | | | | | | | % 83.25/12.04 | | | | | | | | | PRED_UNIFY: (49), (122) imply: % 83.25/12.04 | | | | | | | | | (123) $false % 83.25/12.04 | | | | | | | | | % 83.25/12.04 | | | | | | | | | CLOSE: (123) is inconsistent. % 83.25/12.04 | | | | | | | | | % 83.25/12.04 | | | | | | | | End of split % 83.25/12.04 | | | | | | | | % 83.25/12.04 | | | | | | | End of split % 83.25/12.04 | | | | | | | % 83.25/12.04 | | | | | | End of split % 83.25/12.04 | | | | | | % 83.25/12.04 | | | | | End of split % 83.25/12.04 | | | | | % 83.25/12.04 | | | | End of split % 83.25/12.04 | | | | % 83.25/12.04 | | | End of split % 83.25/12.04 | | | % 83.25/12.04 | | End of split % 83.25/12.04 | | % 83.25/12.04 | Case 2: % 83.25/12.04 | | % 83.25/12.04 | | (124) all_45_2 = xm & sdtasdt0(xp, all_45_3) = xm & doDivides0(xp, xm) & % 83.25/12.04 | | aNaturalNumber0(all_45_3) % 83.25/12.04 | | % 83.25/12.04 | | ALPHA: (124) implies: % 83.25/12.04 | | (125) doDivides0(xp, xm) % 83.25/12.04 | | % 83.25/12.04 | | PRED_UNIFY: (21), (125) imply: % 83.25/12.04 | | (126) $false % 83.25/12.04 | | % 83.25/12.04 | | CLOSE: (126) is inconsistent. % 83.25/12.04 | | % 83.25/12.04 | End of split % 83.25/12.04 | % 83.25/12.04 End of proof % 83.25/12.04 % SZS output end Proof for theBenchmark % 83.25/12.04 % 83.25/12.04 11412ms %------------------------------------------------------------------------------