%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM513+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n029.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 11:48:17 EDT 2023 % Result : Theorem 16.01s 2.98s % Output : Proof 48.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM513+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.36 % Computer : n029.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Fri Aug 25 08:57:24 EDT 2023 % 0.15/0.36 % CPUTime : % 0.22/0.61 ________ _____ % 0.22/0.61 ___ __ \_________(_)________________________________ % 0.22/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.61 % 0.22/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.61 (2023-06-19) % 0.22/0.61 % 0.22/0.61 (c) Philipp Rümmer, 2009-2023 % 0.22/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.61 Amanda Stjerna. % 0.22/0.61 Free software under BSD-3-Clause. % 0.22/0.61 % 0.22/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.61 % 0.22/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.63 Running up to 7 provers in parallel. % 0.22/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.58/1.18 Prover 1: Preprocessing ... % 3.58/1.18 Prover 4: Preprocessing ... % 3.91/1.23 Prover 3: Preprocessing ... % 3.91/1.23 Prover 2: Preprocessing ... % 3.91/1.23 Prover 5: Preprocessing ... % 3.91/1.23 Prover 6: Preprocessing ... % 3.91/1.23 Prover 0: Preprocessing ... % 9.57/2.04 Prover 1: Constructing countermodel ... % 9.57/2.05 Prover 3: Constructing countermodel ... % 9.57/2.07 Prover 6: Proving ... % 10.00/2.13 Prover 5: Constructing countermodel ... % 11.71/2.34 Prover 2: Proving ... % 12.05/2.39 Prover 4: Constructing countermodel ... % 12.58/2.45 Prover 0: Proving ... % 16.01/2.98 Prover 3: proved (2339ms) % 16.01/2.98 % 16.01/2.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.01/2.98 % 16.01/2.98 Prover 5: stopped % 16.01/2.99 Prover 6: stopped % 16.01/2.99 Prover 0: stopped % 16.62/3.01 Prover 2: stopped % 16.62/3.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.62/3.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.62/3.02 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.62/3.02 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.62/3.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.62/3.05 Prover 7: Preprocessing ... % 17.28/3.10 Prover 8: Preprocessing ... % 17.28/3.10 Prover 10: Preprocessing ... % 17.69/3.15 Prover 13: Preprocessing ... % 17.69/3.16 Prover 11: Preprocessing ... % 18.93/3.32 Prover 7: Constructing countermodel ... % 18.93/3.32 Prover 8: Warning: ignoring some quantifiers % 18.93/3.32 Prover 10: Constructing countermodel ... % 18.93/3.33 Prover 8: Constructing countermodel ... % 19.57/3.40 Prover 13: Constructing countermodel ... % 20.95/3.65 Prover 11: Constructing countermodel ... % 46.80/6.97 Prover 1: Found proof (size 484) % 46.80/6.97 Prover 1: proved (6337ms) % 46.80/6.97 Prover 7: stopped % 46.80/6.97 Prover 8: stopped % 46.80/6.97 Prover 13: stopped % 46.80/6.97 Prover 10: stopped % 46.80/6.97 Prover 11: stopped % 46.80/6.97 Prover 4: stopped % 46.80/6.97 % 46.80/6.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 46.80/6.97 % 46.80/7.05 % SZS output start Proof for theBenchmark % 46.80/7.06 Assumptions after simplification: % 46.80/7.06 --------------------------------- % 46.80/7.06 % 46.80/7.06 (mAddAsso) % 46.80/7.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 46.80/7.08 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 46.80/7.09 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? % 46.80/7.09 [v9: $i] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 & % 46.80/7.09 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) % 46.80/7.09 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = % 46.80/7.09 v4))) % 46.80/7.09 % 46.80/7.09 (mAddComm) % 46.80/7.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 46.80/7.09 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 46.80/7.09 (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 % 46.80/7.09 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 46.80/7.09 % 46.80/7.09 (mDefDiv) % 46.80/7.09 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (doDivides0(v0, v1) = v2) | ~ % 46.80/7.09 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aNaturalNumber0(v1) = v4 % 46.80/7.09 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (( ~ (v2 = 0) % 46.80/7.09 | ? [v3: $i] : (sdtasdt0(v0, v3) = v1 & aNaturalNumber0(v3) = 0 & % 46.80/7.09 $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = v1) | ~ % 46.80/7.09 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4))))) % 46.80/7.09 % 46.80/7.09 (mDefPrime) % 46.80/7.10 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: any] : ( ~ (isPrime0(v0) = v1) | % 46.80/7.10 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (( ~ % 46.80/7.10 (v1 = 0) | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v2: $i] : (v2 = v0 | % 46.80/7.10 v2 = sz10 | ~ (doDivides0(v2, v0) = 0) | ~ $i(v2) | ? [v3: int] : % 46.80/7.10 ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)))) & (v1 = 0 | v0 = sz10 | % 46.80/7.10 v0 = sz00 | ? [v2: $i] : ( ~ (v2 = v0) & ~ (v2 = sz10) & % 46.80/7.10 doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0 & $i(v2))))) % 46.80/7.10 % 46.80/7.10 (mDefQuot) % 46.80/7.10 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ % 46.80/7.10 (sdtsldt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 46.80/7.10 any] : ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 % 46.80/7.10 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))) | % 46.80/7.10 ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | ~ $i(v3) | ? [v4: % 46.80/7.10 int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) & ! [v3: $i] : ( ~ % 46.80/7.10 (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | (v3 = v1 & aNaturalNumber0(v2) = % 46.80/7.10 0)))) % 46.80/7.10 % 46.80/7.10 (mDivAsso) % 46.80/7.10 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ % 46.80/7.10 (sdtsldt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 46.80/7.10 any] : ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 % 46.80/7.10 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))) | % 46.80/7.10 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtsldt0(v4, v0) = v5) | ~ % 46.80/7.10 (sdtasdt0(v3, v1) = v4) | ~ $i(v3) | ? [v6: any] : ? [v7: $i] : % 46.80/7.10 (sdtasdt0(v3, v2) = v7 & aNaturalNumber0(v3) = v6 & $i(v7) & ( ~ (v6 = 0) % 46.80/7.10 | v7 = v5)))) % 46.80/7.10 % 46.80/7.10 (mDivLE) % 46.80/7.10 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (doDivides0(v0, v1) = % 46.80/7.10 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : % 46.80/7.10 (sdtlseqdt0(v0, v1) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = % 46.80/7.10 v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0))) % 46.80/7.10 % 46.80/7.10 (mLEAsym) % 46.80/7.10 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ $i(v1) % 46.80/7.10 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (sdtlseqdt0(v1, % 46.80/7.10 v0) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v4 % 46.80/7.10 = 0) | ~ (v3 = 0) | ~ (v2 = 0)))) % 46.80/7.10 % 46.80/7.10 (mMulAsso) % 46.80/7.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 46.80/7.11 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 46.80/7.11 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? % 46.80/7.11 [v9: $i] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & % 46.80/7.11 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) % 46.80/7.11 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = % 46.80/7.11 v4))) % 46.80/7.11 % 46.80/7.11 (mMulComm) % 46.80/7.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 46.80/7.11 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 46.80/7.11 (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 % 46.80/7.11 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 46.80/7.11 % 46.80/7.11 (mPrimDiv) % 46.80/7.11 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ % 46.80/7.11 (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (isPrime0(v1) = 0 & % 46.80/7.11 doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0 & $i(v1))) % 46.80/7.11 % 46.80/7.11 (mSortsB) % 46.80/7.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 46.80/7.11 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 46.80/7.11 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 46.80/7.11 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 46.80/7.11 % 46.80/7.11 (mSortsB_02) % 46.80/7.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 46.80/7.11 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 46.80/7.11 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 46.80/7.11 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 46.80/7.11 % 46.80/7.11 (m__) % 46.80/7.11 $i(xr) & $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? % 46.80/7.11 [v2: $i] : ? [v3: $i] : ( ~ (v3 = v1) & sdtsldt0(xk, xr) = v0 & sdtsldt0(xn, % 46.80/7.11 xr) = v2 & sdtasdt0(v2, xm) = v3 & sdtasdt0(xp, v0) = v1 & $i(v3) & $i(v2) % 46.80/7.11 & $i(v1) & $i(v0)) % 46.80/7.11 % 46.80/7.11 (m__1799) % 46.80/7.12 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, xp) = v1 % 46.80/7.12 & sdtpldt0(xn, xm) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! % 46.80/7.12 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) = v6) | ~ % 46.80/7.12 (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v7: any] % 46.80/7.12 : ? [v8: any] : ? [v9: any] : ? [v10: any] : ? [v11: $i] : ? [v12: % 46.80/7.12 any] : ? [v13: any] : ? [v14: any] : ? [v15: any] : (isPrime0(v4) = % 46.80/7.12 v10 & doDivides0(v4, v11) = v12 & doDivides0(v4, v3) = v15 & % 46.80/7.12 doDivides0(v4, v2) = v14 & iLess0(v6, v1) = v13 & sdtasdt0(v2, v3) = v11 % 46.80/7.12 & aNaturalNumber0(v4) = v9 & aNaturalNumber0(v3) = v8 & % 46.80/7.12 aNaturalNumber0(v2) = v7 & $i(v11) & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ % 46.80/7.12 (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v15 = 0 | v14 = % 46.80/7.12 0)))) % 46.80/7.12 % 46.80/7.12 (m__1837) % 46.80/7.12 aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & % 46.80/7.12 $i(xp) & $i(xm) & $i(xn) % 46.80/7.12 % 46.80/7.12 (m__1860) % 46.80/7.12 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (isPrime0(xp) = 0 & doDivides0(xp, % 46.80/7.12 v0) = 0 & sdtasdt0(xn, xm) = v0 & $i(v0)) % 46.80/7.12 % 46.80/7.12 (m__2306) % 46.80/7.12 $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (sdtsldt0(v0, xp) = xk & % 46.80/7.12 sdtasdt0(xn, xm) = v0 & $i(v0)) % 46.80/7.12 % 46.80/7.12 (m__2342) % 46.80/7.12 isPrime0(xr) = 0 & doDivides0(xr, xk) = 0 & aNaturalNumber0(xr) = 0 & $i(xr) & % 46.80/7.12 $i(xk) % 46.80/7.12 % 46.80/7.12 (m__2362) % 46.80/7.12 $i(xr) & $i(xk) & $i(xm) & $i(xn) & ? [v0: $i] : (doDivides0(xr, v0) = 0 & % 46.80/7.12 sdtlseqdt0(xr, xk) = 0 & sdtasdt0(xn, xm) = v0 & $i(v0)) % 46.80/7.12 % 46.80/7.12 (m__2377) % 46.80/7.12 ~ (xk = xp) & sdtlseqdt0(xk, xp) = 0 & $i(xk) & $i(xp) % 46.80/7.12 % 46.80/7.12 (m__2449) % 46.80/7.12 $i(xr) & $i(xm) & $i(xn) & ? [v0: any] : ? [v1: any] : (doDivides0(xr, xm) = % 46.80/7.12 v1 & doDivides0(xr, xn) = v0 & (v1 = 0 | v0 = 0)) % 46.80/7.12 % 46.80/7.12 (m__2487) % 46.80/7.12 doDivides0(xr, xn) = 0 & $i(xr) & $i(xn) % 46.80/7.12 % 46.80/7.12 (m__2504) % 46.80/7.12 $i(xr) & $i(xn) & ? [v0: $i] : ( ~ (v0 = xn) & sdtsldt0(xn, xr) = v0 & % 46.80/7.12 sdtlseqdt0(v0, xn) = 0 & $i(v0)) % 46.80/7.12 % 46.80/7.12 (m__2576) % 46.80/7.12 $i(xr) & $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? % 46.80/7.12 [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtsldt0(v3, xr) = v4 & sdtsldt0(xn, % 46.80/7.12 xr) = v0 & sdtasdt0(v4, xr) = v2 & sdtasdt0(v1, xr) = v2 & sdtasdt0(v0, % 46.80/7.12 xm) = v1 & sdtasdt0(xp, xk) = v3 & sdtasdt0(xn, xm) = v2 & $i(v4) & $i(v3) % 46.80/7.12 & $i(v2) & $i(v1) & $i(v0)) % 46.80/7.12 % 46.80/7.12 (function-axioms) % 46.80/7.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 46.80/7.13 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: % 46.80/7.13 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 46.80/7.13 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 46.80/7.13 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 46.80/7.13 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 46.80/7.13 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 46.80/7.13 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: % 46.80/7.13 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 46.80/7.13 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 46.80/7.13 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 46.80/7.13 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 46.80/7.13 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 46.80/7.13 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 46.80/7.13 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ % 46.80/7.13 (isPrime0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 46.80/7.13 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) % 46.80/7.13 | ~ (aNaturalNumber0(v2) = v0)) % 46.80/7.13 % 46.80/7.13 Further assumptions not needed in the proof: % 46.80/7.13 -------------------------------------------- % 46.80/7.13 mAMDistr, mAddCanc, mDefDiff, mDefLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, % 46.80/7.13 mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulCanc, % 46.80/7.13 mNatSort, mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, % 46.80/7.13 m_MulZero, m__1870, m__2075, m__2287, m__2315, m__2327 % 46.80/7.13 % 46.80/7.13 Those formulas are unsatisfiable: % 46.80/7.13 --------------------------------- % 46.80/7.13 % 46.80/7.13 Begin of proof % 46.80/7.13 | % 46.80/7.13 | ALPHA: (mDefQuot) implies: % 46.80/7.13 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ (sdtsldt0(v1, % 46.80/7.13 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 46.80/7.13 | ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & % 46.80/7.13 | aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 46.80/7.13 | 0))) | ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | % 46.80/7.13 | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = % 46.80/7.13 | v4)) & ! [v3: $i] : ( ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | % 46.80/7.13 | (v3 = v1 & aNaturalNumber0(v2) = 0)))) % 46.80/7.13 | % 46.80/7.13 | ALPHA: (mDivLE) implies: % 46.80/7.13 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (doDivides0(v0, v1) = 0) | % 46.80/7.13 | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : % 46.80/7.13 | (sdtlseqdt0(v0, v1) = v4 & aNaturalNumber0(v1) = v3 & % 46.80/7.13 | aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0))) % 46.80/7.13 | % 46.80/7.13 | ALPHA: (mDivAsso) implies: % 46.80/7.13 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ (sdtsldt0(v1, % 46.80/7.13 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 46.80/7.13 | ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & % 46.80/7.13 | aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 46.80/7.13 | 0))) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 46.80/7.13 | (sdtsldt0(v4, v0) = v5) | ~ (sdtasdt0(v3, v1) = v4) | ~ $i(v3) | % 46.80/7.13 | ? [v6: any] : ? [v7: $i] : (sdtasdt0(v3, v2) = v7 & % 46.80/7.13 | aNaturalNumber0(v3) = v6 & $i(v7) & ( ~ (v6 = 0) | v7 = v5)))) % 46.80/7.13 | % 46.80/7.13 | ALPHA: (mDefPrime) implies: % 46.80/7.14 | (4) ! [v0: $i] : ! [v1: any] : ( ~ (isPrime0(v0) = v1) | ~ $i(v0) | ? % 46.80/7.14 | [v2: int] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (( ~ (v1 = 0) % 46.80/7.14 | | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v2: $i] : (v2 = v0 | v2 % 46.80/7.14 | = sz10 | ~ (doDivides0(v2, v0) = 0) | ~ $i(v2) | ? [v3: % 46.80/7.14 | int] : ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)))) & (v1 = % 46.80/7.14 | 0 | v0 = sz10 | v0 = sz00 | ? [v2: $i] : ( ~ (v2 = v0) & ~ (v2 % 46.80/7.14 | = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0 & % 46.80/7.14 | $i(v2))))) % 46.80/7.14 | % 46.80/7.14 | ALPHA: (mPrimDiv) implies: % 46.80/7.14 | (5) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | % 46.80/7.14 | ~ $i(v0) | ? [v1: $i] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & % 46.80/7.14 | aNaturalNumber0(v1) = 0 & $i(v1))) % 46.80/7.14 | % 46.80/7.14 | ALPHA: (m__1837) implies: % 46.80/7.14 | (6) aNaturalNumber0(xn) = 0 % 46.80/7.14 | (7) aNaturalNumber0(xm) = 0 % 46.80/7.14 | (8) aNaturalNumber0(xp) = 0 % 46.80/7.14 | % 46.80/7.14 | ALPHA: (m__1799) implies: % 46.80/7.14 | (9) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) = % 46.80/7.14 | v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 46.80/7.14 | [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) = v6) | ~ % 46.80/7.14 | (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? % 46.80/7.14 | [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10: any] : ? [v11: % 46.80/7.14 | $i] : ? [v12: any] : ? [v13: any] : ? [v14: any] : ? [v15: % 46.80/7.14 | any] : (isPrime0(v4) = v10 & doDivides0(v4, v11) = v12 & % 46.80/7.14 | doDivides0(v4, v3) = v15 & doDivides0(v4, v2) = v14 & iLess0(v6, % 46.80/7.14 | v1) = v13 & sdtasdt0(v2, v3) = v11 & aNaturalNumber0(v4) = v9 & % 46.80/7.14 | aNaturalNumber0(v3) = v8 & aNaturalNumber0(v2) = v7 & $i(v11) & ( % 46.80/7.14 | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | ~ % 46.80/7.14 | (v8 = 0) | ~ (v7 = 0) | v15 = 0 | v14 = 0)))) % 46.80/7.14 | % 46.80/7.14 | ALPHA: (m__1860) implies: % 47.65/7.14 | (10) ? [v0: $i] : (isPrime0(xp) = 0 & doDivides0(xp, v0) = 0 & % 47.65/7.14 | sdtasdt0(xn, xm) = v0 & $i(v0)) % 47.65/7.14 | % 47.65/7.14 | ALPHA: (m__2306) implies: % 47.65/7.14 | (11) ? [v0: $i] : (sdtsldt0(v0, xp) = xk & sdtasdt0(xn, xm) = v0 & $i(v0)) % 47.65/7.14 | % 47.65/7.14 | ALPHA: (m__2342) implies: % 47.65/7.14 | (12) aNaturalNumber0(xr) = 0 % 47.65/7.14 | (13) doDivides0(xr, xk) = 0 % 47.65/7.14 | (14) isPrime0(xr) = 0 % 47.65/7.14 | % 47.65/7.14 | ALPHA: (m__2362) implies: % 47.65/7.14 | (15) ? [v0: $i] : (doDivides0(xr, v0) = 0 & sdtlseqdt0(xr, xk) = 0 & % 47.65/7.14 | sdtasdt0(xn, xm) = v0 & $i(v0)) % 47.65/7.14 | % 47.65/7.14 | ALPHA: (m__2377) implies: % 47.65/7.15 | (16) ~ (xk = xp) % 47.65/7.15 | (17) sdtlseqdt0(xk, xp) = 0 % 47.65/7.15 | % 47.65/7.15 | ALPHA: (m__2449) implies: % 47.65/7.15 | (18) ? [v0: any] : ? [v1: any] : (doDivides0(xr, xm) = v1 & % 47.65/7.15 | doDivides0(xr, xn) = v0 & (v1 = 0 | v0 = 0)) % 47.65/7.15 | % 47.65/7.15 | ALPHA: (m__2487) implies: % 47.65/7.15 | (19) doDivides0(xr, xn) = 0 % 47.65/7.15 | % 47.65/7.15 | ALPHA: (m__2504) implies: % 47.65/7.15 | (20) ? [v0: $i] : ( ~ (v0 = xn) & sdtsldt0(xn, xr) = v0 & sdtlseqdt0(v0, % 47.65/7.15 | xn) = 0 & $i(v0)) % 47.65/7.15 | % 47.65/7.15 | ALPHA: (m__2576) implies: % 47.65/7.15 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 47.65/7.15 | (sdtsldt0(v3, xr) = v4 & sdtsldt0(xn, xr) = v0 & sdtasdt0(v4, xr) = v2 % 47.65/7.15 | & sdtasdt0(v1, xr) = v2 & sdtasdt0(v0, xm) = v1 & sdtasdt0(xp, xk) = % 47.65/7.15 | v3 & sdtasdt0(xn, xm) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 47.65/7.15 | $i(v0)) % 47.65/7.15 | % 47.65/7.15 | ALPHA: (m__) implies: % 47.65/7.15 | (22) $i(xn) % 47.65/7.15 | (23) $i(xm) % 47.65/7.15 | (24) $i(xp) % 47.65/7.15 | (25) $i(xk) % 47.65/7.15 | (26) $i(xr) % 47.65/7.15 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v1) % 47.65/7.15 | & sdtsldt0(xk, xr) = v0 & sdtsldt0(xn, xr) = v2 & sdtasdt0(v2, xm) = % 47.65/7.15 | v3 & sdtasdt0(xp, v0) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 47.65/7.15 | % 47.65/7.15 | ALPHA: (function-axioms) implies: % 47.65/7.15 | (28) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 47.65/7.15 | : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = % 47.65/7.15 | v0)) % 47.65/7.15 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 47.65/7.15 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 47.65/7.15 | (30) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 47.65/7.15 | : ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ % 47.65/7.15 | (doDivides0(v3, v2) = v0)) % 47.65/7.15 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 47.65/7.15 | (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) % 47.65/7.15 | % 47.65/7.15 | DELTA: instantiating (11) with fresh symbol all_42_0 gives: % 47.65/7.15 | (32) sdtsldt0(all_42_0, xp) = xk & sdtasdt0(xn, xm) = all_42_0 & % 47.65/7.15 | $i(all_42_0) % 47.65/7.15 | % 47.65/7.15 | ALPHA: (32) implies: % 47.65/7.15 | (33) sdtasdt0(xn, xm) = all_42_0 % 47.65/7.15 | (34) sdtsldt0(all_42_0, xp) = xk % 47.65/7.15 | % 47.65/7.15 | DELTA: instantiating (20) with fresh symbol all_44_0 gives: % 47.65/7.15 | (35) ~ (all_44_0 = xn) & sdtsldt0(xn, xr) = all_44_0 & % 47.65/7.15 | sdtlseqdt0(all_44_0, xn) = 0 & $i(all_44_0) % 47.65/7.15 | % 47.65/7.15 | ALPHA: (35) implies: % 47.65/7.15 | (36) ~ (all_44_0 = xn) % 47.65/7.15 | (37) sdtlseqdt0(all_44_0, xn) = 0 % 47.65/7.15 | (38) sdtsldt0(xn, xr) = all_44_0 % 47.65/7.15 | % 47.65/7.15 | DELTA: instantiating (10) with fresh symbol all_46_0 gives: % 47.65/7.16 | (39) isPrime0(xp) = 0 & doDivides0(xp, all_46_0) = 0 & sdtasdt0(xn, xm) = % 47.65/7.16 | all_46_0 & $i(all_46_0) % 47.65/7.16 | % 47.65/7.16 | ALPHA: (39) implies: % 47.65/7.16 | (40) $i(all_46_0) % 47.65/7.16 | (41) sdtasdt0(xn, xm) = all_46_0 % 47.65/7.16 | (42) doDivides0(xp, all_46_0) = 0 % 47.65/7.16 | (43) isPrime0(xp) = 0 % 47.65/7.16 | % 47.65/7.16 | DELTA: instantiating (15) with fresh symbol all_48_0 gives: % 47.65/7.16 | (44) doDivides0(xr, all_48_0) = 0 & sdtlseqdt0(xr, xk) = 0 & sdtasdt0(xn, % 47.65/7.16 | xm) = all_48_0 & $i(all_48_0) % 47.65/7.16 | % 47.65/7.16 | ALPHA: (44) implies: % 47.65/7.16 | (45) sdtasdt0(xn, xm) = all_48_0 % 47.65/7.16 | % 47.65/7.16 | DELTA: instantiating (18) with fresh symbols all_50_0, all_50_1 gives: % 47.65/7.16 | (46) doDivides0(xr, xm) = all_50_0 & doDivides0(xr, xn) = all_50_1 & % 47.65/7.16 | (all_50_0 = 0 | all_50_1 = 0) % 47.65/7.16 | % 47.65/7.16 | ALPHA: (46) implies: % 47.65/7.16 | (47) doDivides0(xr, xn) = all_50_1 % 47.65/7.16 | % 47.65/7.16 | DELTA: instantiating (27) with fresh symbols all_52_0, all_52_1, all_52_2, % 47.65/7.16 | all_52_3 gives: % 47.65/7.16 | (48) ~ (all_52_0 = all_52_2) & sdtsldt0(xk, xr) = all_52_3 & sdtsldt0(xn, % 47.65/7.16 | xr) = all_52_1 & sdtasdt0(all_52_1, xm) = all_52_0 & sdtasdt0(xp, % 47.65/7.16 | all_52_3) = all_52_2 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & % 47.65/7.16 | $i(all_52_3) % 47.65/7.16 | % 47.65/7.16 | ALPHA: (48) implies: % 47.65/7.16 | (49) ~ (all_52_0 = all_52_2) % 47.65/7.16 | (50) $i(all_52_3) % 47.65/7.16 | (51) $i(all_52_1) % 47.65/7.16 | (52) sdtasdt0(xp, all_52_3) = all_52_2 % 47.65/7.16 | (53) sdtasdt0(all_52_1, xm) = all_52_0 % 47.65/7.16 | (54) sdtsldt0(xn, xr) = all_52_1 % 47.65/7.16 | (55) sdtsldt0(xk, xr) = all_52_3 % 47.65/7.16 | % 47.65/7.16 | DELTA: instantiating (21) with fresh symbols all_54_0, all_54_1, all_54_2, % 47.65/7.16 | all_54_3, all_54_4 gives: % 47.65/7.16 | (56) sdtsldt0(all_54_1, xr) = all_54_0 & sdtsldt0(xn, xr) = all_54_4 & % 47.65/7.16 | sdtasdt0(all_54_0, xr) = all_54_2 & sdtasdt0(all_54_3, xr) = all_54_2 % 47.65/7.16 | & sdtasdt0(all_54_4, xm) = all_54_3 & sdtasdt0(xp, xk) = all_54_1 & % 47.65/7.16 | sdtasdt0(xn, xm) = all_54_2 & $i(all_54_0) & $i(all_54_1) & % 47.65/7.16 | $i(all_54_2) & $i(all_54_3) & $i(all_54_4) % 47.65/7.16 | % 47.65/7.16 | ALPHA: (56) implies: % 47.65/7.16 | (57) $i(all_54_3) % 47.65/7.16 | (58) $i(all_54_0) % 47.65/7.16 | (59) sdtasdt0(xn, xm) = all_54_2 % 47.65/7.16 | (60) sdtasdt0(xp, xk) = all_54_1 % 47.65/7.16 | (61) sdtasdt0(all_54_4, xm) = all_54_3 % 47.65/7.16 | (62) sdtasdt0(all_54_3, xr) = all_54_2 % 47.65/7.16 | (63) sdtasdt0(all_54_0, xr) = all_54_2 % 47.65/7.16 | (64) sdtsldt0(xn, xr) = all_54_4 % 47.65/7.16 | (65) sdtsldt0(all_54_1, xr) = all_54_0 % 47.65/7.16 | % 47.65/7.16 | DELTA: instantiating (9) with fresh symbols all_56_0, all_56_1 gives: % 47.65/7.16 | (66) sdtpldt0(all_56_1, xp) = all_56_0 & sdtpldt0(xn, xm) = all_56_1 & % 47.65/7.16 | $i(all_56_0) & $i(all_56_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 47.65/7.16 | : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ % 47.65/7.16 | (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 47.65/7.16 | [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] % 47.65/7.16 | : ? [v10: any] : ? [v11: any] : ? [v12: any] : ? [v13: any] : % 47.65/7.16 | (isPrime0(v2) = v8 & doDivides0(v2, v9) = v10 & doDivides0(v2, v1) = % 47.65/7.16 | v13 & doDivides0(v2, v0) = v12 & iLess0(v4, all_56_0) = v11 & % 47.65/7.16 | sdtasdt0(v0, v1) = v9 & aNaturalNumber0(v2) = v7 & % 47.65/7.16 | aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & $i(v9) & ( ~ % 47.65/7.16 | (v11 = 0) | ~ (v10 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 47.65/7.16 | 0) | ~ (v5 = 0) | v13 = 0 | v12 = 0))) % 47.65/7.16 | % 47.65/7.16 | ALPHA: (66) implies: % 47.65/7.16 | (67) $i(all_56_1) % 47.65/7.16 | (68) sdtpldt0(xn, xm) = all_56_1 % 47.65/7.16 | (69) sdtpldt0(all_56_1, xp) = all_56_0 % 47.65/7.16 | (70) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 47.65/7.16 | ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | % 47.65/7.16 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : % 47.65/7.16 | ? [v8: any] : ? [v9: $i] : ? [v10: any] : ? [v11: any] : ? % 47.65/7.16 | [v12: any] : ? [v13: any] : (isPrime0(v2) = v8 & doDivides0(v2, v9) % 47.65/7.16 | = v10 & doDivides0(v2, v1) = v13 & doDivides0(v2, v0) = v12 & % 47.65/7.16 | iLess0(v4, all_56_0) = v11 & sdtasdt0(v0, v1) = v9 & % 47.65/7.16 | aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & % 47.65/7.16 | aNaturalNumber0(v0) = v5 & $i(v9) & ( ~ (v11 = 0) | ~ (v10 = 0) | % 47.65/7.16 | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v13 = 0 % 47.65/7.16 | | v12 = 0))) % 47.65/7.16 | % 47.65/7.17 | GROUND_INST: instantiating (29) with all_46_0, all_48_0, xm, xn, simplifying % 47.65/7.17 | with (41), (45) gives: % 47.65/7.17 | (71) all_48_0 = all_46_0 % 47.65/7.17 | % 47.65/7.17 | GROUND_INST: instantiating (29) with all_48_0, all_54_2, xm, xn, simplifying % 47.65/7.17 | with (45), (59) gives: % 47.65/7.17 | (72) all_54_2 = all_48_0 % 47.65/7.17 | % 47.65/7.17 | GROUND_INST: instantiating (29) with all_42_0, all_54_2, xm, xn, simplifying % 47.65/7.17 | with (33), (59) gives: % 47.65/7.17 | (73) all_54_2 = all_42_0 % 47.65/7.17 | % 47.65/7.17 | GROUND_INST: instantiating (30) with 0, all_50_1, xn, xr, simplifying with % 47.65/7.17 | (19), (47) gives: % 47.65/7.17 | (74) all_50_1 = 0 % 47.65/7.17 | % 47.65/7.17 | GROUND_INST: instantiating (31) with all_52_1, all_54_4, xr, xn, simplifying % 47.65/7.17 | with (54), (64) gives: % 47.65/7.17 | (75) all_54_4 = all_52_1 % 47.65/7.17 | % 47.65/7.17 | GROUND_INST: instantiating (31) with all_44_0, all_54_4, xr, xn, simplifying % 47.65/7.17 | with (38), (64) gives: % 47.65/7.17 | (76) all_54_4 = all_44_0 % 47.65/7.17 | % 47.65/7.17 | COMBINE_EQS: (72), (73) imply: % 47.65/7.17 | (77) all_48_0 = all_42_0 % 47.65/7.17 | % 47.65/7.17 | SIMP: (77) implies: % 47.65/7.17 | (78) all_48_0 = all_42_0 % 47.65/7.17 | % 47.65/7.17 | COMBINE_EQS: (75), (76) imply: % 47.65/7.17 | (79) all_52_1 = all_44_0 % 47.65/7.17 | % 47.65/7.17 | COMBINE_EQS: (71), (78) imply: % 47.65/7.17 | (80) all_46_0 = all_42_0 % 47.65/7.17 | % 47.65/7.17 | SIMP: (80) implies: % 47.65/7.17 | (81) all_46_0 = all_42_0 % 47.65/7.17 | % 47.65/7.17 | REDUCE: (42), (81) imply: % 47.65/7.17 | (82) doDivides0(xp, all_42_0) = 0 % 47.65/7.17 | % 47.65/7.17 | REDUCE: (63), (73) imply: % 47.65/7.17 | (83) sdtasdt0(all_54_0, xr) = all_42_0 % 47.65/7.17 | % 47.65/7.17 | REDUCE: (62), (73) imply: % 47.65/7.17 | (84) sdtasdt0(all_54_3, xr) = all_42_0 % 47.65/7.17 | % 47.65/7.17 | REDUCE: (61), (76) imply: % 47.65/7.17 | (85) sdtasdt0(all_44_0, xm) = all_54_3 % 47.65/7.17 | % 47.65/7.17 | REDUCE: (53), (79) imply: % 47.65/7.17 | (86) sdtasdt0(all_44_0, xm) = all_52_0 % 47.65/7.17 | % 47.65/7.17 | REDUCE: (51), (79) imply: % 47.65/7.17 | (87) $i(all_44_0) % 47.65/7.17 | % 47.65/7.17 | REDUCE: (40), (81) imply: % 47.65/7.17 | (88) $i(all_42_0) % 47.65/7.17 | % 47.65/7.17 | GROUND_INST: instantiating (29) with all_52_0, all_54_3, xm, all_44_0, % 47.65/7.17 | simplifying with (85), (86) gives: % 47.65/7.17 | (89) all_54_3 = all_52_0 % 47.65/7.17 | % 47.65/7.17 | REDUCE: (84), (89) imply: % 47.65/7.17 | (90) sdtasdt0(all_52_0, xr) = all_42_0 % 47.65/7.17 | % 47.65/7.17 | REDUCE: (57), (89) imply: % 47.65/7.17 | (91) $i(all_52_0) % 47.65/7.17 | % 47.65/7.17 | GROUND_INST: instantiating (5) with xp, simplifying with (8), (24) gives: % 47.65/7.17 | (92) xp = sz10 | xp = sz00 | ? [v0: $i] : (isPrime0(v0) = 0 & % 47.65/7.17 | doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0 & $i(v0)) % 47.65/7.17 | % 47.65/7.17 | GROUND_INST: instantiating (mAddComm) with xn, xm, all_56_1, simplifying with % 47.65/7.17 | (22), (23), (68) gives: % 47.65/7.17 | (93) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xm, xn) = v2 & % 47.65/7.17 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v2) & ( ~ % 47.65/7.17 | (v1 = 0) | ~ (v0 = 0) | v2 = all_56_1)) % 47.65/7.17 | % 47.65/7.17 | GROUND_INST: instantiating (mSortsB) with xn, xm, all_56_1, simplifying with % 47.65/7.17 | (22), (23), (68) gives: % 47.65/7.17 | (94) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 47.65/7.17 | (aNaturalNumber0(all_56_1) = v2 & aNaturalNumber0(xm) = v1 & % 47.65/7.17 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 47.65/7.17 | % 47.65/7.17 | GROUND_INST: instantiating (70) with xn, xm, xp, all_56_1, all_56_0, % 47.65/7.17 | simplifying with (22), (23), (24), (68), (69) gives: % 47.65/7.17 | (95) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 47.65/7.17 | $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 47.65/7.17 | (isPrime0(xp) = v3 & doDivides0(xp, v4) = v5 & doDivides0(xp, xm) = v8 % 47.65/7.17 | & doDivides0(xp, xn) = v7 & iLess0(all_56_0, all_56_0) = v6 & % 47.65/7.17 | sdtasdt0(xn, xm) = v4 & aNaturalNumber0(xp) = v2 & % 47.65/7.17 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v4) & ( ~ % 47.65/7.17 | (v6 = 0) | ~ (v5 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | % 47.65/7.17 | ~ (v0 = 0) | v8 = 0 | v7 = 0)) % 47.65/7.17 | % 47.65/7.17 | GROUND_INST: instantiating (mAddAsso) with xn, xm, xp, all_56_1, all_56_0, % 47.65/7.17 | simplifying with (22), (23), (24), (68), (69) gives: % 47.65/7.18 | (96) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 47.65/7.18 | : (sdtpldt0(xm, xp) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(xp) % 47.65/7.18 | = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v4) % 47.65/7.18 | & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = % 47.65/7.18 | all_56_0)) % 47.65/7.18 | % 47.65/7.18 | GROUND_INST: instantiating (mAddComm) with all_56_1, xp, all_56_0, simplifying % 47.65/7.18 | with (24), (67), (69) gives: % 47.65/7.18 | (97) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xp, all_56_1) = % 47.65/7.18 | v2 & aNaturalNumber0(all_56_1) = v0 & aNaturalNumber0(xp) = v1 & % 47.65/7.18 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_56_0)) % 47.65/7.18 | % 47.65/7.18 | GROUND_INST: instantiating (mSortsB) with all_56_1, xp, all_56_0, simplifying % 47.65/7.18 | with (24), (67), (69) gives: % 47.65/7.18 | (98) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 47.65/7.18 | (aNaturalNumber0(all_56_0) = v2 & aNaturalNumber0(all_56_1) = v0 & % 47.65/7.18 | aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 47.65/7.18 | % 47.65/7.18 | GROUND_INST: instantiating (mMulComm) with xn, xm, all_42_0, simplifying with % 47.65/7.18 | (22), (23), (33) gives: % 47.65/7.18 | (99) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xm, xn) = v2 & % 47.65/7.18 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v2) & ( ~ % 47.65/7.18 | (v1 = 0) | ~ (v0 = 0) | v2 = all_42_0)) % 47.65/7.18 | % 47.65/7.18 | GROUND_INST: instantiating (mSortsB_02) with xn, xm, all_42_0, simplifying % 47.65/7.18 | with (22), (23), (33) gives: % 47.65/7.18 | (100) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 47.65/7.18 | (aNaturalNumber0(all_42_0) = v2 & aNaturalNumber0(xm) = v1 & % 47.65/7.18 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 47.65/7.18 | % 47.65/7.18 | GROUND_INST: instantiating (mMulComm) with xp, xk, all_54_1, simplifying with % 47.65/7.18 | (24), (25), (60) gives: % 47.65/7.18 | (101) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xk, xp) = v2 & % 47.65/7.18 | aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & $i(v2) & ( ~ % 47.65/7.18 | (v1 = 0) | ~ (v0 = 0) | v2 = all_54_1)) % 47.65/7.18 | % 47.65/7.18 | GROUND_INST: instantiating (mSortsB_02) with xp, xk, all_54_1, simplifying % 47.65/7.18 | with (24), (25), (60) gives: % 47.65/7.18 | (102) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 47.65/7.18 | (aNaturalNumber0(all_54_1) = v2 & aNaturalNumber0(xk) = v1 & % 47.65/7.18 | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 47.65/7.18 | % 47.65/7.18 | GROUND_INST: instantiating (mMulComm) with xp, all_52_3, all_52_2, simplifying % 47.65/7.18 | with (24), (50), (52) gives: % 47.65/7.18 | (103) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_52_3, xp) = % 47.65/7.18 | v2 & aNaturalNumber0(all_52_3) = v1 & aNaturalNumber0(xp) = v0 & % 47.65/7.18 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_52_2)) % 47.65/7.18 | % 47.65/7.18 | GROUND_INST: instantiating (mSortsB_02) with xp, all_52_3, all_52_2, % 47.65/7.18 | simplifying with (24), (50), (52) gives: % 47.65/7.18 | (104) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 47.65/7.18 | (aNaturalNumber0(all_52_2) = v2 & aNaturalNumber0(all_52_3) = v1 & % 47.65/7.18 | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 47.65/7.18 | % 47.65/7.18 | GROUND_INST: instantiating (mMulComm) with all_44_0, xm, all_52_0, simplifying % 47.65/7.18 | with (23), (86), (87) gives: % 47.65/7.18 | (105) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xm, all_44_0) = % 47.65/7.18 | v2 & aNaturalNumber0(all_44_0) = v0 & aNaturalNumber0(xm) = v1 & % 47.65/7.18 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_52_0)) % 47.65/7.18 | % 47.65/7.18 | GROUND_INST: instantiating (mSortsB_02) with all_44_0, xm, all_52_0, % 47.65/7.18 | simplifying with (23), (86), (87) gives: % 47.65/7.18 | (106) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 47.65/7.18 | (aNaturalNumber0(all_52_0) = v2 & aNaturalNumber0(all_44_0) = v0 & % 47.65/7.18 | aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 47.65/7.18 | % 47.65/7.18 | GROUND_INST: instantiating (mMulAsso) with all_44_0, xm, xr, all_52_0, % 47.65/7.18 | all_42_0, simplifying with (23), (26), (86), (87), (90) gives: % 47.65/7.18 | (107) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 47.65/7.18 | $i] : (sdtasdt0(all_44_0, v3) = v4 & sdtasdt0(xm, xr) = v3 & % 47.65/7.18 | aNaturalNumber0(all_44_0) = v0 & aNaturalNumber0(xr) = v2 & % 47.65/7.18 | aNaturalNumber0(xm) = v1 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 % 47.65/7.18 | = 0) | ~ (v0 = 0) | v4 = all_42_0)) % 47.65/7.18 | % 47.65/7.18 | GROUND_INST: instantiating (mMulComm) with all_52_0, xr, all_42_0, simplifying % 47.65/7.18 | with (26), (90), (91) gives: % 47.65/7.18 | (108) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xr, all_52_0) = % 47.65/7.18 | v2 & aNaturalNumber0(all_52_0) = v0 & aNaturalNumber0(xr) = v1 & % 47.65/7.18 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_42_0)) % 47.65/7.18 | % 47.65/7.19 | GROUND_INST: instantiating (mSortsB_02) with all_52_0, xr, all_42_0, % 47.65/7.19 | simplifying with (26), (90), (91) gives: % 47.65/7.19 | (109) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 47.65/7.19 | (aNaturalNumber0(all_52_0) = v0 & aNaturalNumber0(all_42_0) = v2 & % 47.65/7.19 | aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 47.65/7.19 | % 47.65/7.19 | GROUND_INST: instantiating (mMulComm) with all_54_0, xr, all_42_0, simplifying % 47.65/7.19 | with (26), (58), (83) gives: % 47.65/7.19 | (110) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xr, all_54_0) = % 47.65/7.19 | v2 & aNaturalNumber0(all_54_0) = v0 & aNaturalNumber0(xr) = v1 & % 47.65/7.19 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_42_0)) % 47.65/7.19 | % 47.65/7.19 | GROUND_INST: instantiating (mSortsB_02) with all_54_0, xr, all_42_0, % 47.65/7.19 | simplifying with (26), (58), (83) gives: % 47.65/7.19 | (111) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 47.65/7.19 | (aNaturalNumber0(all_54_0) = v0 & aNaturalNumber0(all_42_0) = v2 & % 47.65/7.19 | aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 47.65/7.19 | % 47.65/7.19 | GROUND_INST: instantiating (mLEAsym) with xk, xp, simplifying with (17), (24), % 47.65/7.19 | (25) gives: % 47.65/7.19 | (112) xk = xp | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 47.65/7.19 | (sdtlseqdt0(xp, xk) = v2 & aNaturalNumber0(xk) = v0 & % 47.65/7.19 | aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 47.65/7.19 | 0))) % 47.65/7.19 | % 47.65/7.19 | GROUND_INST: instantiating (mLEAsym) with all_44_0, xn, simplifying with (22), % 47.65/7.19 | (37), (87) gives: % 47.65/7.19 | (113) all_44_0 = xn | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 47.65/7.19 | (sdtlseqdt0(xn, all_44_0) = v2 & aNaturalNumber0(all_44_0) = v0 & % 47.65/7.19 | aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 47.65/7.19 | 0))) % 47.65/7.19 | % 47.65/7.19 | GROUND_INST: instantiating (mDefDiv) with xr, xn, 0, simplifying with (19), % 47.65/7.19 | (22), (26) gives: % 47.65/7.19 | (114) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xr) = v0 & % 47.65/7.19 | aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0: % 47.65/7.19 | $i] : (sdtasdt0(xr, v0) = xn & aNaturalNumber0(v0) = 0 & $i(v0)) % 47.65/7.19 | % 47.65/7.19 | GROUND_INST: instantiating (3) with xr, xn, all_44_0, simplifying with (22), % 47.65/7.19 | (26), (38) gives: % 47.65/7.19 | (115) xr = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 47.65/7.19 | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & % 47.65/7.19 | aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 47.65/7.19 | 0))) | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 47.65/7.19 | (sdtsldt0(v1, xr) = v2) | ~ (sdtasdt0(v0, xn) = v1) | ~ $i(v0) | % 47.65/7.19 | ? [v3: any] : ? [v4: $i] : (sdtasdt0(v0, all_44_0) = v4 & % 47.65/7.19 | aNaturalNumber0(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v2))) % 47.65/7.19 | % 47.65/7.19 | GROUND_INST: instantiating (1) with xr, xn, all_44_0, simplifying with (22), % 47.65/7.19 | (26), (38) gives: % 47.65/7.19 | (116) xr = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 47.65/7.19 | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & % 47.65/7.19 | aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 47.65/7.19 | 0))) | ( ! [v0: any] : (v0 = all_44_0 | ~ (sdtasdt0(xr, v0) = % 47.65/7.19 | xn) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 47.65/7.19 | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xr, % 47.65/7.19 | all_44_0) = v0) | ~ $i(all_44_0) | (v0 = xn & % 47.65/7.19 | aNaturalNumber0(all_44_0) = 0))) % 47.65/7.19 | % 47.65/7.19 | GROUND_INST: instantiating (3) with xr, xk, all_52_3, simplifying with (25), % 47.65/7.19 | (26), (55) gives: % 47.65/7.19 | (117) xr = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 47.65/7.19 | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & % 47.65/7.19 | aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 47.65/7.19 | 0))) | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 47.65/7.19 | (sdtsldt0(v1, xr) = v2) | ~ (sdtasdt0(v0, xk) = v1) | ~ $i(v0) | % 47.65/7.19 | ? [v3: any] : ? [v4: $i] : (sdtasdt0(v0, all_52_3) = v4 & % 47.65/7.19 | aNaturalNumber0(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v2))) % 47.65/7.19 | % 47.65/7.19 | GROUND_INST: instantiating (1) with xr, xk, all_52_3, simplifying with (25), % 47.65/7.19 | (26), (55) gives: % 47.65/7.19 | (118) xr = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 47.65/7.19 | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & % 47.65/7.19 | aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 47.65/7.19 | 0))) | ( ! [v0: any] : (v0 = all_52_3 | ~ (sdtasdt0(xr, v0) = % 47.65/7.19 | xk) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 47.65/7.19 | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xr, % 47.65/7.19 | all_52_3) = v0) | ~ $i(all_52_3) | (v0 = xk & % 47.65/7.19 | aNaturalNumber0(all_52_3) = 0))) % 47.65/7.19 | % 47.65/7.19 | GROUND_INST: instantiating (1) with xp, all_42_0, xk, simplifying with (24), % 47.65/7.19 | (34), (88) gives: % 47.65/7.20 | (119) xp = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 47.65/7.20 | (doDivides0(xp, all_42_0) = v2 & aNaturalNumber0(all_42_0) = v1 & % 47.65/7.20 | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 47.65/7.20 | 0))) | ( ! [v0: $i] : (v0 = xk | ~ (sdtasdt0(xp, v0) = % 47.65/7.20 | all_42_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 47.65/7.20 | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xp, % 47.65/7.20 | xk) = v0) | ~ $i(xk) | (v0 = all_42_0 & aNaturalNumber0(xk) % 47.65/7.20 | = 0))) % 47.65/7.20 | % 47.65/7.20 | GROUND_INST: instantiating (4) with xp, 0, simplifying with (24), (43) gives: % 47.65/7.20 | (120) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0) | ( ~ (xp = % 47.65/7.20 | sz10) & ~ (xp = sz00) & ! [v0: $i] : (v0 = xp | v0 = sz10 | ~ % 47.65/7.20 | (doDivides0(v0, xp) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 47.65/7.20 | 0) & aNaturalNumber0(v0) = v1))) % 47.65/7.20 | % 47.65/7.20 | GROUND_INST: instantiating (4) with xr, 0, simplifying with (14), (26) gives: % 47.65/7.20 | (121) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xr) = v0) | ( ~ (xr = % 47.65/7.20 | sz10) & ~ (xr = sz00) & ! [v0: $i] : (v0 = xr | v0 = sz10 | ~ % 47.65/7.20 | (doDivides0(v0, xr) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 47.65/7.20 | 0) & aNaturalNumber0(v0) = v1))) % 47.65/7.20 | % 47.65/7.20 | DELTA: instantiating (111) with fresh symbols all_72_0, all_72_1, all_72_2 % 47.65/7.20 | gives: % 47.65/7.20 | (122) aNaturalNumber0(all_54_0) = all_72_2 & aNaturalNumber0(all_42_0) = % 47.65/7.20 | all_72_0 & aNaturalNumber0(xr) = all_72_1 & ( ~ (all_72_1 = 0) | ~ % 47.65/7.20 | (all_72_2 = 0) | all_72_0 = 0) % 47.65/7.20 | % 47.65/7.20 | ALPHA: (122) implies: % 47.65/7.20 | (123) aNaturalNumber0(xr) = all_72_1 % 47.65/7.20 | (124) aNaturalNumber0(all_42_0) = all_72_0 % 47.65/7.20 | % 47.65/7.20 | DELTA: instantiating (98) with fresh symbols all_74_0, all_74_1, all_74_2 % 47.65/7.20 | gives: % 47.65/7.20 | (125) aNaturalNumber0(all_56_0) = all_74_0 & aNaturalNumber0(all_56_1) = % 47.65/7.20 | all_74_2 & aNaturalNumber0(xp) = all_74_1 & ( ~ (all_74_1 = 0) | ~ % 47.65/7.20 | (all_74_2 = 0) | all_74_0 = 0) % 47.65/7.20 | % 47.65/7.20 | ALPHA: (125) implies: % 47.65/7.20 | (126) aNaturalNumber0(xp) = all_74_1 % 47.65/7.20 | % 47.65/7.20 | DELTA: instantiating (109) with fresh symbols all_76_0, all_76_1, all_76_2 % 47.65/7.20 | gives: % 47.65/7.20 | (127) aNaturalNumber0(all_52_0) = all_76_2 & aNaturalNumber0(all_42_0) = % 47.65/7.20 | all_76_0 & aNaturalNumber0(xr) = all_76_1 & ( ~ (all_76_1 = 0) | ~ % 47.65/7.20 | (all_76_2 = 0) | all_76_0 = 0) % 47.65/7.20 | % 47.65/7.20 | ALPHA: (127) implies: % 47.65/7.20 | (128) aNaturalNumber0(xr) = all_76_1 % 47.65/7.20 | (129) aNaturalNumber0(all_42_0) = all_76_0 % 47.65/7.20 | % 47.65/7.20 | DELTA: instantiating (106) with fresh symbols all_78_0, all_78_1, all_78_2 % 47.65/7.20 | gives: % 47.65/7.20 | (130) aNaturalNumber0(all_52_0) = all_78_0 & aNaturalNumber0(all_44_0) = % 47.65/7.20 | all_78_2 & aNaturalNumber0(xm) = all_78_1 & ( ~ (all_78_1 = 0) | ~ % 47.65/7.20 | (all_78_2 = 0) | all_78_0 = 0) % 47.65/7.20 | % 47.65/7.20 | ALPHA: (130) implies: % 47.65/7.20 | (131) aNaturalNumber0(xm) = all_78_1 % 47.65/7.20 | (132) aNaturalNumber0(all_44_0) = all_78_2 % 47.65/7.20 | % 47.65/7.20 | DELTA: instantiating (102) with fresh symbols all_80_0, all_80_1, all_80_2 % 47.65/7.20 | gives: % 47.65/7.20 | (133) aNaturalNumber0(all_54_1) = all_80_0 & aNaturalNumber0(xk) = all_80_1 % 47.65/7.20 | & aNaturalNumber0(xp) = all_80_2 & ( ~ (all_80_1 = 0) | ~ (all_80_2 % 47.65/7.20 | = 0) | all_80_0 = 0) % 47.65/7.20 | % 47.65/7.20 | ALPHA: (133) implies: % 47.65/7.20 | (134) aNaturalNumber0(xp) = all_80_2 % 47.65/7.20 | % 47.65/7.20 | DELTA: instantiating (100) with fresh symbols all_82_0, all_82_1, all_82_2 % 47.65/7.20 | gives: % 47.65/7.20 | (135) aNaturalNumber0(all_42_0) = all_82_0 & aNaturalNumber0(xm) = all_82_1 % 47.65/7.20 | & aNaturalNumber0(xn) = all_82_2 & ( ~ (all_82_1 = 0) | ~ (all_82_2 % 47.65/7.20 | = 0) | all_82_0 = 0) % 47.65/7.20 | % 47.65/7.20 | ALPHA: (135) implies: % 47.65/7.20 | (136) aNaturalNumber0(xn) = all_82_2 % 47.65/7.20 | (137) aNaturalNumber0(xm) = all_82_1 % 47.65/7.20 | (138) aNaturalNumber0(all_42_0) = all_82_0 % 47.65/7.20 | (139) ~ (all_82_1 = 0) | ~ (all_82_2 = 0) | all_82_0 = 0 % 47.65/7.20 | % 47.65/7.20 | DELTA: instantiating (104) with fresh symbols all_84_0, all_84_1, all_84_2 % 47.65/7.20 | gives: % 48.11/7.20 | (140) aNaturalNumber0(all_52_2) = all_84_0 & aNaturalNumber0(all_52_3) = % 48.11/7.20 | all_84_1 & aNaturalNumber0(xp) = all_84_2 & ( ~ (all_84_1 = 0) | ~ % 48.11/7.20 | (all_84_2 = 0) | all_84_0 = 0) % 48.11/7.20 | % 48.11/7.20 | ALPHA: (140) implies: % 48.11/7.20 | (141) aNaturalNumber0(xp) = all_84_2 % 48.11/7.20 | % 48.11/7.20 | DELTA: instantiating (94) with fresh symbols all_86_0, all_86_1, all_86_2 % 48.11/7.20 | gives: % 48.11/7.20 | (142) aNaturalNumber0(all_56_1) = all_86_0 & aNaturalNumber0(xm) = all_86_1 % 48.11/7.20 | & aNaturalNumber0(xn) = all_86_2 & ( ~ (all_86_1 = 0) | ~ (all_86_2 % 48.11/7.20 | = 0) | all_86_0 = 0) % 48.11/7.20 | % 48.11/7.20 | ALPHA: (142) implies: % 48.11/7.20 | (143) aNaturalNumber0(xn) = all_86_2 % 48.11/7.20 | (144) aNaturalNumber0(xm) = all_86_1 % 48.11/7.20 | % 48.11/7.20 | DELTA: instantiating (97) with fresh symbols all_88_0, all_88_1, all_88_2 % 48.11/7.20 | gives: % 48.11/7.20 | (145) sdtpldt0(xp, all_56_1) = all_88_0 & aNaturalNumber0(all_56_1) = % 48.11/7.20 | all_88_2 & aNaturalNumber0(xp) = all_88_1 & $i(all_88_0) & ( ~ % 48.11/7.20 | (all_88_1 = 0) | ~ (all_88_2 = 0) | all_88_0 = all_56_0) % 48.11/7.20 | % 48.11/7.20 | ALPHA: (145) implies: % 48.11/7.20 | (146) aNaturalNumber0(xp) = all_88_1 % 48.11/7.20 | % 48.11/7.20 | DELTA: instantiating (108) with fresh symbols all_90_0, all_90_1, all_90_2 % 48.11/7.20 | gives: % 48.11/7.20 | (147) sdtasdt0(xr, all_52_0) = all_90_0 & aNaturalNumber0(all_52_0) = % 48.11/7.20 | all_90_2 & aNaturalNumber0(xr) = all_90_1 & $i(all_90_0) & ( ~ % 48.11/7.20 | (all_90_1 = 0) | ~ (all_90_2 = 0) | all_90_0 = all_42_0) % 48.11/7.20 | % 48.11/7.20 | ALPHA: (147) implies: % 48.11/7.20 | (148) aNaturalNumber0(xr) = all_90_1 % 48.11/7.20 | % 48.11/7.20 | DELTA: instantiating (101) with fresh symbols all_92_0, all_92_1, all_92_2 % 48.11/7.20 | gives: % 48.11/7.20 | (149) sdtasdt0(xk, xp) = all_92_0 & aNaturalNumber0(xk) = all_92_1 & % 48.11/7.20 | aNaturalNumber0(xp) = all_92_2 & $i(all_92_0) & ( ~ (all_92_1 = 0) | % 48.11/7.20 | ~ (all_92_2 = 0) | all_92_0 = all_54_1) % 48.11/7.20 | % 48.11/7.20 | ALPHA: (149) implies: % 48.11/7.20 | (150) aNaturalNumber0(xp) = all_92_2 % 48.11/7.20 | % 48.11/7.20 | DELTA: instantiating (110) with fresh symbols all_94_0, all_94_1, all_94_2 % 48.11/7.20 | gives: % 48.11/7.20 | (151) sdtasdt0(xr, all_54_0) = all_94_0 & aNaturalNumber0(all_54_0) = % 48.11/7.20 | all_94_2 & aNaturalNumber0(xr) = all_94_1 & $i(all_94_0) & ( ~ % 48.11/7.20 | (all_94_1 = 0) | ~ (all_94_2 = 0) | all_94_0 = all_42_0) % 48.11/7.20 | % 48.11/7.20 | ALPHA: (151) implies: % 48.11/7.20 | (152) aNaturalNumber0(xr) = all_94_1 % 48.11/7.20 | % 48.11/7.20 | DELTA: instantiating (93) with fresh symbols all_96_0, all_96_1, all_96_2 % 48.11/7.20 | gives: % 48.11/7.20 | (153) sdtpldt0(xm, xn) = all_96_0 & aNaturalNumber0(xm) = all_96_1 & % 48.11/7.20 | aNaturalNumber0(xn) = all_96_2 & $i(all_96_0) & ( ~ (all_96_1 = 0) | % 48.11/7.20 | ~ (all_96_2 = 0) | all_96_0 = all_56_1) % 48.11/7.20 | % 48.11/7.20 | ALPHA: (153) implies: % 48.11/7.20 | (154) aNaturalNumber0(xn) = all_96_2 % 48.11/7.20 | (155) aNaturalNumber0(xm) = all_96_1 % 48.11/7.20 | % 48.11/7.20 | DELTA: instantiating (105) with fresh symbols all_98_0, all_98_1, all_98_2 % 48.11/7.20 | gives: % 48.11/7.20 | (156) sdtasdt0(xm, all_44_0) = all_98_0 & aNaturalNumber0(all_44_0) = % 48.11/7.20 | all_98_2 & aNaturalNumber0(xm) = all_98_1 & $i(all_98_0) & ( ~ % 48.11/7.20 | (all_98_1 = 0) | ~ (all_98_2 = 0) | all_98_0 = all_52_0) % 48.11/7.20 | % 48.11/7.20 | ALPHA: (156) implies: % 48.11/7.20 | (157) aNaturalNumber0(xm) = all_98_1 % 48.11/7.20 | (158) aNaturalNumber0(all_44_0) = all_98_2 % 48.11/7.20 | (159) sdtasdt0(xm, all_44_0) = all_98_0 % 48.11/7.21 | (160) ~ (all_98_1 = 0) | ~ (all_98_2 = 0) | all_98_0 = all_52_0 % 48.11/7.21 | % 48.11/7.21 | DELTA: instantiating (103) with fresh symbols all_100_0, all_100_1, all_100_2 % 48.11/7.21 | gives: % 48.11/7.21 | (161) sdtasdt0(all_52_3, xp) = all_100_0 & aNaturalNumber0(all_52_3) = % 48.11/7.21 | all_100_1 & aNaturalNumber0(xp) = all_100_2 & $i(all_100_0) & ( ~ % 48.11/7.21 | (all_100_1 = 0) | ~ (all_100_2 = 0) | all_100_0 = all_52_2) % 48.11/7.21 | % 48.11/7.21 | ALPHA: (161) implies: % 48.11/7.21 | (162) aNaturalNumber0(xp) = all_100_2 % 48.11/7.21 | % 48.11/7.21 | DELTA: instantiating (99) with fresh symbols all_102_0, all_102_1, all_102_2 % 48.11/7.21 | gives: % 48.11/7.21 | (163) sdtasdt0(xm, xn) = all_102_0 & aNaturalNumber0(xm) = all_102_1 & % 48.11/7.21 | aNaturalNumber0(xn) = all_102_2 & $i(all_102_0) & ( ~ (all_102_1 = 0) % 48.11/7.21 | | ~ (all_102_2 = 0) | all_102_0 = all_42_0) % 48.11/7.21 | % 48.11/7.21 | ALPHA: (163) implies: % 48.11/7.21 | (164) aNaturalNumber0(xn) = all_102_2 % 48.11/7.21 | (165) aNaturalNumber0(xm) = all_102_1 % 48.11/7.21 | (166) sdtasdt0(xm, xn) = all_102_0 % 48.11/7.21 | (167) ~ (all_102_1 = 0) | ~ (all_102_2 = 0) | all_102_0 = all_42_0 % 48.11/7.21 | % 48.11/7.21 | DELTA: instantiating (96) with fresh symbols all_104_0, all_104_1, all_104_2, % 48.11/7.21 | all_104_3, all_104_4 gives: % 48.11/7.21 | (168) sdtpldt0(xm, xp) = all_104_1 & sdtpldt0(xn, all_104_1) = all_104_0 & % 48.11/7.21 | aNaturalNumber0(xp) = all_104_2 & aNaturalNumber0(xm) = all_104_3 & % 48.11/7.21 | aNaturalNumber0(xn) = all_104_4 & $i(all_104_0) & $i(all_104_1) & ( ~ % 48.11/7.21 | (all_104_2 = 0) | ~ (all_104_3 = 0) | ~ (all_104_4 = 0) | % 48.11/7.21 | all_104_0 = all_56_0) % 48.11/7.21 | % 48.11/7.21 | ALPHA: (168) implies: % 48.11/7.21 | (169) aNaturalNumber0(xn) = all_104_4 % 48.11/7.21 | (170) aNaturalNumber0(xm) = all_104_3 % 48.11/7.21 | (171) aNaturalNumber0(xp) = all_104_2 % 48.11/7.21 | % 48.11/7.21 | DELTA: instantiating (107) with fresh symbols all_106_0, all_106_1, all_106_2, % 48.11/7.21 | all_106_3, all_106_4 gives: % 48.11/7.21 | (172) sdtasdt0(all_44_0, all_106_1) = all_106_0 & sdtasdt0(xm, xr) = % 48.11/7.21 | all_106_1 & aNaturalNumber0(all_44_0) = all_106_4 & % 48.11/7.21 | aNaturalNumber0(xr) = all_106_2 & aNaturalNumber0(xm) = all_106_3 & % 48.11/7.21 | $i(all_106_0) & $i(all_106_1) & ( ~ (all_106_2 = 0) | ~ (all_106_3 = % 48.11/7.21 | 0) | ~ (all_106_4 = 0) | all_106_0 = all_42_0) % 48.11/7.21 | % 48.11/7.21 | ALPHA: (172) implies: % 48.11/7.21 | (173) aNaturalNumber0(xm) = all_106_3 % 48.11/7.21 | (174) aNaturalNumber0(xr) = all_106_2 % 48.11/7.21 | (175) aNaturalNumber0(all_44_0) = all_106_4 % 48.11/7.21 | % 48.11/7.21 | DELTA: instantiating (95) with fresh symbols all_108_0, all_108_1, all_108_2, % 48.11/7.21 | all_108_3, all_108_4, all_108_5, all_108_6, all_108_7, all_108_8 gives: % 48.11/7.21 | (176) isPrime0(xp) = all_108_5 & doDivides0(xp, all_108_4) = all_108_3 & % 48.11/7.21 | doDivides0(xp, xm) = all_108_0 & doDivides0(xp, xn) = all_108_1 & % 48.11/7.21 | iLess0(all_56_0, all_56_0) = all_108_2 & sdtasdt0(xn, xm) = all_108_4 % 48.11/7.21 | & aNaturalNumber0(xp) = all_108_6 & aNaturalNumber0(xm) = all_108_7 & % 48.11/7.21 | aNaturalNumber0(xn) = all_108_8 & $i(all_108_4) & ( ~ (all_108_2 = 0) % 48.11/7.21 | | ~ (all_108_3 = 0) | ~ (all_108_5 = 0) | ~ (all_108_6 = 0) | ~ % 48.11/7.21 | (all_108_7 = 0) | ~ (all_108_8 = 0) | all_108_0 = 0 | all_108_1 = % 48.11/7.21 | 0) % 48.11/7.21 | % 48.11/7.21 | ALPHA: (176) implies: % 48.11/7.21 | (177) aNaturalNumber0(xn) = all_108_8 % 48.11/7.21 | (178) aNaturalNumber0(xm) = all_108_7 % 48.11/7.21 | (179) aNaturalNumber0(xp) = all_108_6 % 48.11/7.21 | (180) sdtasdt0(xn, xm) = all_108_4 % 48.11/7.21 | (181) doDivides0(xp, all_108_4) = all_108_3 % 48.11/7.21 | % 48.11/7.21 | BETA: splitting (113) gives: % 48.11/7.21 | % 48.11/7.21 | Case 1: % 48.11/7.21 | | % 48.11/7.21 | | (182) all_44_0 = xn % 48.11/7.21 | | % 48.11/7.21 | | REDUCE: (36), (182) imply: % 48.11/7.21 | | (183) $false % 48.11/7.21 | | % 48.11/7.21 | | CLOSE: (183) is inconsistent. % 48.11/7.21 | | % 48.11/7.21 | Case 2: % 48.11/7.21 | | % 48.11/7.21 | | (184) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(xn, % 48.11/7.21 | | all_44_0) = v2 & aNaturalNumber0(all_44_0) = v0 & % 48.11/7.21 | | aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 48.11/7.21 | | 0))) % 48.11/7.21 | | % 48.11/7.21 | | DELTA: instantiating (184) with fresh symbols all_118_0, all_118_1, % 48.11/7.21 | | all_118_2 gives: % 48.11/7.21 | | (185) sdtlseqdt0(xn, all_44_0) = all_118_0 & aNaturalNumber0(all_44_0) = % 48.11/7.21 | | all_118_2 & aNaturalNumber0(xn) = all_118_1 & ( ~ (all_118_0 = 0) | % 48.11/7.21 | | ~ (all_118_1 = 0) | ~ (all_118_2 = 0)) % 48.11/7.21 | | % 48.11/7.21 | | ALPHA: (185) implies: % 48.11/7.21 | | (186) aNaturalNumber0(xn) = all_118_1 % 48.11/7.21 | | (187) aNaturalNumber0(all_44_0) = all_118_2 % 48.11/7.21 | | % 48.11/7.21 | | BETA: splitting (112) gives: % 48.11/7.21 | | % 48.11/7.21 | | Case 1: % 48.11/7.21 | | | % 48.11/7.21 | | | (188) xk = xp % 48.11/7.21 | | | % 48.11/7.21 | | | REDUCE: (16), (188) imply: % 48.11/7.21 | | | (189) $false % 48.11/7.21 | | | % 48.11/7.21 | | | CLOSE: (189) is inconsistent. % 48.11/7.21 | | | % 48.11/7.21 | | Case 2: % 48.11/7.21 | | | % 48.11/7.21 | | | (190) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(xp, xk) % 48.11/7.21 | | | = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( % 48.11/7.21 | | | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 48.11/7.21 | | | % 48.11/7.21 | | | DELTA: instantiating (190) with fresh symbols all_123_0, all_123_1, % 48.11/7.21 | | | all_123_2 gives: % 48.11/7.21 | | | (191) sdtlseqdt0(xp, xk) = all_123_0 & aNaturalNumber0(xk) = all_123_2 % 48.11/7.21 | | | & aNaturalNumber0(xp) = all_123_1 & ( ~ (all_123_0 = 0) | ~ % 48.11/7.21 | | | (all_123_1 = 0) | ~ (all_123_2 = 0)) % 48.11/7.21 | | | % 48.11/7.21 | | | ALPHA: (191) implies: % 48.11/7.21 | | | (192) aNaturalNumber0(xp) = all_123_1 % 48.11/7.21 | | | % 48.11/7.21 | | | GROUND_INST: instantiating (28) with 0, all_96_2, xn, simplifying with % 48.11/7.21 | | | (6), (154) gives: % 48.11/7.21 | | | (193) all_96_2 = 0 % 48.11/7.21 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_82_2, all_96_2, xn, simplifying % 48.11/7.22 | | | with (136), (154) gives: % 48.11/7.22 | | | (194) all_96_2 = all_82_2 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_102_2, all_104_4, xn, simplifying % 48.11/7.22 | | | with (164), (169) gives: % 48.11/7.22 | | | (195) all_104_4 = all_102_2 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_96_2, all_104_4, xn, simplifying % 48.11/7.22 | | | with (154), (169) gives: % 48.11/7.22 | | | (196) all_104_4 = all_96_2 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_108_8, all_118_1, xn, simplifying % 48.11/7.22 | | | with (177), (186) gives: % 48.11/7.22 | | | (197) all_118_1 = all_108_8 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_104_4, all_118_1, xn, simplifying % 48.11/7.22 | | | with (169), (186) gives: % 48.11/7.22 | | | (198) all_118_1 = all_104_4 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_86_2, all_118_1, xn, simplifying % 48.11/7.22 | | | with (143), (186) gives: % 48.11/7.22 | | | (199) all_118_1 = all_86_2 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_96_1, all_98_1, xm, simplifying % 48.11/7.22 | | | with (155), (157) gives: % 48.11/7.22 | | | (200) all_98_1 = all_96_1 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_86_1, all_98_1, xm, simplifying % 48.11/7.22 | | | with (144), (157) gives: % 48.11/7.22 | | | (201) all_98_1 = all_86_1 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_78_1, all_98_1, xm, simplifying % 48.11/7.22 | | | with (131), (157) gives: % 48.11/7.22 | | | (202) all_98_1 = all_78_1 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_96_1, all_102_1, xm, simplifying % 48.11/7.22 | | | with (155), (165) gives: % 48.11/7.22 | | | (203) all_102_1 = all_96_1 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with 0, all_106_3, xm, simplifying with % 48.11/7.22 | | | (7), (173) gives: % 48.11/7.22 | | | (204) all_106_3 = 0 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_104_3, all_106_3, xm, simplifying % 48.11/7.22 | | | with (170), (173) gives: % 48.11/7.22 | | | (205) all_106_3 = all_104_3 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_98_1, all_106_3, xm, simplifying % 48.11/7.22 | | | with (157), (173) gives: % 48.11/7.22 | | | (206) all_106_3 = all_98_1 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_102_1, all_108_7, xm, simplifying % 48.11/7.22 | | | with (165), (178) gives: % 48.11/7.22 | | | (207) all_108_7 = all_102_1 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_82_1, all_108_7, xm, simplifying % 48.11/7.22 | | | with (137), (178) gives: % 48.11/7.22 | | | (208) all_108_7 = all_82_1 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_84_2, all_88_1, xp, simplifying % 48.11/7.22 | | | with (141), (146) gives: % 48.11/7.22 | | | (209) all_88_1 = all_84_2 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_88_1, all_92_2, xp, simplifying % 48.11/7.22 | | | with (146), (150) gives: % 48.11/7.22 | | | (210) all_92_2 = all_88_1 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_92_2, all_100_2, xp, simplifying % 48.11/7.22 | | | with (150), (162) gives: % 48.11/7.22 | | | (211) all_100_2 = all_92_2 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_84_2, all_108_6, xp, simplifying % 48.11/7.22 | | | with (141), (179) gives: % 48.11/7.22 | | | (212) all_108_6 = all_84_2 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_80_2, all_108_6, xp, simplifying % 48.11/7.22 | | | with (134), (179) gives: % 48.11/7.22 | | | (213) all_108_6 = all_80_2 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_74_1, all_108_6, xp, simplifying % 48.11/7.22 | | | with (126), (179) gives: % 48.11/7.22 | | | (214) all_108_6 = all_74_1 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with 0, all_123_1, xp, simplifying with % 48.11/7.22 | | | (8), (192) gives: % 48.11/7.22 | | | (215) all_123_1 = 0 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_104_2, all_123_1, xp, simplifying % 48.11/7.22 | | | with (171), (192) gives: % 48.11/7.22 | | | (216) all_123_1 = all_104_2 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_100_2, all_123_1, xp, simplifying % 48.11/7.22 | | | with (162), (192) gives: % 48.11/7.22 | | | (217) all_123_1 = all_100_2 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_90_1, all_94_1, xr, simplifying % 48.11/7.22 | | | with (148), (152) gives: % 48.11/7.22 | | | (218) all_94_1 = all_90_1 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_76_1, all_94_1, xr, simplifying % 48.11/7.22 | | | with (128), (152) gives: % 48.11/7.22 | | | (219) all_94_1 = all_76_1 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_72_1, all_94_1, xr, simplifying % 48.11/7.22 | | | with (123), (152) gives: % 48.11/7.22 | | | (220) all_94_1 = all_72_1 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with 0, all_106_2, xr, simplifying with % 48.11/7.22 | | | (12), (174) gives: % 48.11/7.22 | | | (221) all_106_2 = 0 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_90_1, all_106_2, xr, simplifying % 48.11/7.22 | | | with (148), (174) gives: % 48.11/7.22 | | | (222) all_106_2 = all_90_1 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_76_0, all_82_0, all_42_0, % 48.11/7.22 | | | simplifying with (129), (138) gives: % 48.11/7.22 | | | (223) all_82_0 = all_76_0 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_72_0, all_82_0, all_42_0, % 48.11/7.22 | | | simplifying with (124), (138) gives: % 48.11/7.22 | | | (224) all_82_0 = all_72_0 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_78_2, all_106_4, all_44_0, % 48.11/7.22 | | | simplifying with (132), (175) gives: % 48.11/7.22 | | | (225) all_106_4 = all_78_2 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_106_4, all_118_2, all_44_0, % 48.11/7.22 | | | simplifying with (175), (187) gives: % 48.11/7.22 | | | (226) all_118_2 = all_106_4 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (28) with all_98_2, all_118_2, all_44_0, % 48.11/7.22 | | | simplifying with (158), (187) gives: % 48.11/7.22 | | | (227) all_118_2 = all_98_2 % 48.11/7.22 | | | % 48.11/7.22 | | | GROUND_INST: instantiating (29) with all_42_0, all_108_4, xm, xn, % 48.11/7.22 | | | simplifying with (33), (180) gives: % 48.11/7.22 | | | (228) all_108_4 = all_42_0 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (215), (216) imply: % 48.11/7.22 | | | (229) all_104_2 = 0 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (216), (217) imply: % 48.11/7.22 | | | (230) all_104_2 = all_100_2 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (197), (198) imply: % 48.11/7.22 | | | (231) all_108_8 = all_104_4 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (197), (199) imply: % 48.11/7.22 | | | (232) all_108_8 = all_86_2 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (226), (227) imply: % 48.11/7.22 | | | (233) all_106_4 = all_98_2 % 48.11/7.22 | | | % 48.11/7.22 | | | SIMP: (233) implies: % 48.11/7.22 | | | (234) all_106_4 = all_98_2 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (212), (213) imply: % 48.11/7.22 | | | (235) all_84_2 = all_80_2 % 48.11/7.22 | | | % 48.11/7.22 | | | SIMP: (235) implies: % 48.11/7.22 | | | (236) all_84_2 = all_80_2 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (213), (214) imply: % 48.11/7.22 | | | (237) all_80_2 = all_74_1 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (207), (208) imply: % 48.11/7.22 | | | (238) all_102_1 = all_82_1 % 48.11/7.22 | | | % 48.11/7.22 | | | SIMP: (238) implies: % 48.11/7.22 | | | (239) all_102_1 = all_82_1 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (231), (232) imply: % 48.11/7.22 | | | (240) all_104_4 = all_86_2 % 48.11/7.22 | | | % 48.11/7.22 | | | SIMP: (240) implies: % 48.11/7.22 | | | (241) all_104_4 = all_86_2 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (221), (222) imply: % 48.11/7.22 | | | (242) all_90_1 = 0 % 48.11/7.22 | | | % 48.11/7.22 | | | SIMP: (242) implies: % 48.11/7.22 | | | (243) all_90_1 = 0 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (204), (205) imply: % 48.11/7.22 | | | (244) all_104_3 = 0 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (205), (206) imply: % 48.11/7.22 | | | (245) all_104_3 = all_98_1 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (225), (234) imply: % 48.11/7.22 | | | (246) all_98_2 = all_78_2 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (229), (230) imply: % 48.11/7.22 | | | (247) all_100_2 = 0 % 48.11/7.22 | | | % 48.11/7.22 | | | SIMP: (247) implies: % 48.11/7.22 | | | (248) all_100_2 = 0 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (244), (245) imply: % 48.11/7.22 | | | (249) all_98_1 = 0 % 48.11/7.22 | | | % 48.11/7.22 | | | SIMP: (249) implies: % 48.11/7.22 | | | (250) all_98_1 = 0 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (195), (196) imply: % 48.11/7.22 | | | (251) all_102_2 = all_96_2 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (195), (241) imply: % 48.11/7.22 | | | (252) all_102_2 = all_86_2 % 48.11/7.22 | | | % 48.11/7.22 | | | COMBINE_EQS: (203), (239) imply: % 48.11/7.22 | | | (253) all_96_1 = all_82_1 % 48.11/7.22 | | | % 48.11/7.22 | | | SIMP: (253) implies: % 48.11/7.23 | | | (254) all_96_1 = all_82_1 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (251), (252) imply: % 48.11/7.23 | | | (255) all_96_2 = all_86_2 % 48.11/7.23 | | | % 48.11/7.23 | | | SIMP: (255) implies: % 48.11/7.23 | | | (256) all_96_2 = all_86_2 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (211), (248) imply: % 48.11/7.23 | | | (257) all_92_2 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | SIMP: (257) implies: % 48.11/7.23 | | | (258) all_92_2 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (200), (201) imply: % 48.11/7.23 | | | (259) all_96_1 = all_86_1 % 48.11/7.23 | | | % 48.11/7.23 | | | SIMP: (259) implies: % 48.11/7.23 | | | (260) all_96_1 = all_86_1 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (201), (202) imply: % 48.11/7.23 | | | (261) all_86_1 = all_78_1 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (201), (250) imply: % 48.11/7.23 | | | (262) all_86_1 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (254), (260) imply: % 48.11/7.23 | | | (263) all_86_1 = all_82_1 % 48.11/7.23 | | | % 48.11/7.23 | | | SIMP: (263) implies: % 48.11/7.23 | | | (264) all_86_1 = all_82_1 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (194), (256) imply: % 48.11/7.23 | | | (265) all_86_2 = all_82_2 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (193), (256) imply: % 48.11/7.23 | | | (266) all_86_2 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (219), (220) imply: % 48.11/7.23 | | | (267) all_76_1 = all_72_1 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (218), (219) imply: % 48.11/7.23 | | | (268) all_90_1 = all_76_1 % 48.11/7.23 | | | % 48.11/7.23 | | | SIMP: (268) implies: % 48.11/7.23 | | | (269) all_90_1 = all_76_1 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (210), (258) imply: % 48.11/7.23 | | | (270) all_88_1 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | SIMP: (270) implies: % 48.11/7.23 | | | (271) all_88_1 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (243), (269) imply: % 48.11/7.23 | | | (272) all_76_1 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | SIMP: (272) implies: % 48.11/7.23 | | | (273) all_76_1 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (209), (271) imply: % 48.11/7.23 | | | (274) all_84_2 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | SIMP: (274) implies: % 48.11/7.23 | | | (275) all_84_2 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (261), (264) imply: % 48.11/7.23 | | | (276) all_82_1 = all_78_1 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (262), (264) imply: % 48.11/7.23 | | | (277) all_82_1 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (265), (266) imply: % 48.11/7.23 | | | (278) all_82_2 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (236), (275) imply: % 48.11/7.23 | | | (279) all_80_2 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | SIMP: (279) implies: % 48.11/7.23 | | | (280) all_80_2 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (223), (224) imply: % 48.11/7.23 | | | (281) all_76_0 = all_72_0 % 48.11/7.23 | | | % 48.11/7.23 | | | SIMP: (281) implies: % 48.11/7.23 | | | (282) all_76_0 = all_72_0 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (276), (277) imply: % 48.11/7.23 | | | (283) all_78_1 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | SIMP: (283) implies: % 48.11/7.23 | | | (284) all_78_1 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (237), (280) imply: % 48.11/7.23 | | | (285) all_74_1 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | SIMP: (285) implies: % 48.11/7.23 | | | (286) all_74_1 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (267), (273) imply: % 48.11/7.23 | | | (287) all_72_1 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | SIMP: (287) implies: % 48.11/7.23 | | | (288) all_72_1 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (252), (266) imply: % 48.11/7.23 | | | (289) all_102_2 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | COMBINE_EQS: (239), (277) imply: % 48.11/7.23 | | | (290) all_102_1 = 0 % 48.11/7.23 | | | % 48.11/7.23 | | | REDUCE: (181), (228) imply: % 48.11/7.23 | | | (291) doDivides0(xp, all_42_0) = all_108_3 % 48.11/7.23 | | | % 48.11/7.23 | | | BETA: splitting (167) gives: % 48.11/7.23 | | | % 48.11/7.23 | | | Case 1: % 48.11/7.23 | | | | % 48.11/7.23 | | | | (292) ~ (all_102_1 = 0) % 48.11/7.23 | | | | % 48.11/7.23 | | | | REDUCE: (290), (292) imply: % 48.11/7.23 | | | | (293) $false % 48.11/7.23 | | | | % 48.11/7.23 | | | | CLOSE: (293) is inconsistent. % 48.11/7.23 | | | | % 48.11/7.23 | | | Case 2: % 48.11/7.23 | | | | % 48.11/7.23 | | | | (294) ~ (all_102_2 = 0) | all_102_0 = all_42_0 % 48.11/7.23 | | | | % 48.11/7.23 | | | | BETA: splitting (121) gives: % 48.11/7.23 | | | | % 48.11/7.23 | | | | Case 1: % 48.11/7.23 | | | | | % 48.11/7.23 | | | | | (295) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xr) = v0) % 48.11/7.23 | | | | | % 48.11/7.23 | | | | | DELTA: instantiating (295) with fresh symbol all_173_0 gives: % 48.11/7.23 | | | | | (296) ~ (all_173_0 = 0) & aNaturalNumber0(xr) = all_173_0 % 48.11/7.23 | | | | | % 48.11/7.23 | | | | | ALPHA: (296) implies: % 48.11/7.23 | | | | | (297) ~ (all_173_0 = 0) % 48.11/7.23 | | | | | (298) aNaturalNumber0(xr) = all_173_0 % 48.11/7.23 | | | | | % 48.11/7.23 | | | | | GROUND_INST: instantiating (28) with 0, all_173_0, xr, simplifying % 48.11/7.23 | | | | | with (12), (298) gives: % 48.11/7.23 | | | | | (299) all_173_0 = 0 % 48.11/7.23 | | | | | % 48.11/7.23 | | | | | REDUCE: (297), (299) imply: % 48.11/7.23 | | | | | (300) $false % 48.11/7.23 | | | | | % 48.11/7.23 | | | | | CLOSE: (300) is inconsistent. % 48.11/7.23 | | | | | % 48.11/7.23 | | | | Case 2: % 48.11/7.23 | | | | | % 48.11/7.23 | | | | | (301) ~ (xr = sz10) & ~ (xr = sz00) & ! [v0: $i] : (v0 = xr | v0 % 48.11/7.23 | | | | | = sz10 | ~ (doDivides0(v0, xr) = 0) | ~ $i(v0) | ? [v1: % 48.11/7.23 | | | | | int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) % 48.11/7.23 | | | | | % 48.11/7.23 | | | | | ALPHA: (301) implies: % 48.11/7.23 | | | | | (302) ~ (xr = sz00) % 48.11/7.23 | | | | | % 48.11/7.23 | | | | | BETA: splitting (294) gives: % 48.11/7.23 | | | | | % 48.11/7.23 | | | | | Case 1: % 48.11/7.23 | | | | | | % 48.11/7.23 | | | | | | (303) ~ (all_102_2 = 0) % 48.11/7.23 | | | | | | % 48.11/7.23 | | | | | | REDUCE: (289), (303) imply: % 48.11/7.23 | | | | | | (304) $false % 48.11/7.23 | | | | | | % 48.11/7.23 | | | | | | CLOSE: (304) is inconsistent. % 48.11/7.23 | | | | | | % 48.11/7.23 | | | | | Case 2: % 48.11/7.23 | | | | | | % 48.11/7.23 | | | | | | (305) all_102_0 = all_42_0 % 48.11/7.23 | | | | | | % 48.11/7.23 | | | | | | REDUCE: (166), (305) imply: % 48.11/7.23 | | | | | | (306) sdtasdt0(xm, xn) = all_42_0 % 48.11/7.23 | | | | | | % 48.11/7.23 | | | | | | BETA: splitting (120) gives: % 48.11/7.23 | | | | | | % 48.11/7.23 | | | | | | Case 1: % 48.11/7.23 | | | | | | | % 48.11/7.23 | | | | | | | (307) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0) % 48.11/7.23 | | | | | | | % 48.11/7.23 | | | | | | | DELTA: instantiating (307) with fresh symbol all_213_0 gives: % 48.11/7.23 | | | | | | | (308) ~ (all_213_0 = 0) & aNaturalNumber0(xp) = all_213_0 % 48.11/7.23 | | | | | | | % 48.11/7.23 | | | | | | | ALPHA: (308) implies: % 48.11/7.23 | | | | | | | (309) ~ (all_213_0 = 0) % 48.11/7.23 | | | | | | | (310) aNaturalNumber0(xp) = all_213_0 % 48.11/7.23 | | | | | | | % 48.11/7.23 | | | | | | | GROUND_INST: instantiating (28) with 0, all_213_0, xp, simplifying % 48.11/7.23 | | | | | | | with (8), (310) gives: % 48.11/7.23 | | | | | | | (311) all_213_0 = 0 % 48.11/7.23 | | | | | | | % 48.11/7.23 | | | | | | | REDUCE: (309), (311) imply: % 48.11/7.23 | | | | | | | (312) $false % 48.11/7.23 | | | | | | | % 48.11/7.23 | | | | | | | CLOSE: (312) is inconsistent. % 48.11/7.23 | | | | | | | % 48.11/7.23 | | | | | | Case 2: % 48.11/7.23 | | | | | | | % 48.11/7.23 | | | | | | | (313) ~ (xp = sz10) & ~ (xp = sz00) & ! [v0: $i] : (v0 = xp % 48.11/7.23 | | | | | | | | v0 = sz10 | ~ (doDivides0(v0, xp) = 0) | ~ $i(v0) | % 48.11/7.23 | | | | | | | ? [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = % 48.11/7.23 | | | | | | | v1)) % 48.11/7.23 | | | | | | | % 48.11/7.23 | | | | | | | ALPHA: (313) implies: % 48.11/7.23 | | | | | | | (314) ~ (xp = sz00) % 48.11/7.23 | | | | | | | (315) ~ (xp = sz10) % 48.11/7.23 | | | | | | | % 48.11/7.23 | | | | | | | BETA: splitting (139) gives: % 48.11/7.23 | | | | | | | % 48.11/7.23 | | | | | | | Case 1: % 48.11/7.23 | | | | | | | | % 48.11/7.23 | | | | | | | | (316) ~ (all_82_1 = 0) % 48.11/7.23 | | | | | | | | % 48.11/7.23 | | | | | | | | REDUCE: (277), (316) imply: % 48.11/7.23 | | | | | | | | (317) $false % 48.11/7.23 | | | | | | | | % 48.11/7.23 | | | | | | | | CLOSE: (317) is inconsistent. % 48.11/7.23 | | | | | | | | % 48.11/7.23 | | | | | | | Case 2: % 48.11/7.23 | | | | | | | | % 48.11/7.23 | | | | | | | | (318) ~ (all_82_2 = 0) | all_82_0 = 0 % 48.11/7.23 | | | | | | | | % 48.11/7.23 | | | | | | | | BETA: splitting (114) gives: % 48.11/7.23 | | | | | | | | % 48.11/7.23 | | | | | | | | Case 1: % 48.11/7.23 | | | | | | | | | % 48.11/7.23 | | | | | | | | | (319) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xr) = % 48.11/7.23 | | | | | | | | | v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ % 48.11/7.23 | | | | | | | | | (v0 = 0))) % 48.11/7.24 | | | | | | | | | % 48.11/7.24 | | | | | | | | | DELTA: instantiating (319) with fresh symbols all_233_0, % 48.11/7.24 | | | | | | | | | all_233_1 gives: % 48.11/7.24 | | | | | | | | | (320) aNaturalNumber0(xr) = all_233_1 & aNaturalNumber0(xn) % 48.11/7.24 | | | | | | | | | = all_233_0 & ( ~ (all_233_0 = 0) | ~ (all_233_1 = % 48.11/7.24 | | | | | | | | | 0)) % 48.11/7.24 | | | | | | | | | % 48.11/7.24 | | | | | | | | | ALPHA: (320) implies: % 48.11/7.24 | | | | | | | | | (321) aNaturalNumber0(xn) = all_233_0 % 48.11/7.24 | | | | | | | | | (322) aNaturalNumber0(xr) = all_233_1 % 48.11/7.24 | | | | | | | | | (323) ~ (all_233_0 = 0) | ~ (all_233_1 = 0) % 48.11/7.24 | | | | | | | | | % 48.11/7.24 | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_233_0, xn, % 48.11/7.24 | | | | | | | | | simplifying with (6), (321) gives: % 48.11/7.24 | | | | | | | | | (324) all_233_0 = 0 % 48.11/7.24 | | | | | | | | | % 48.11/7.24 | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_233_1, xr, % 48.11/7.24 | | | | | | | | | simplifying with (12), (322) gives: % 48.11/7.24 | | | | | | | | | (325) all_233_1 = 0 % 48.11/7.24 | | | | | | | | | % 48.11/7.24 | | | | | | | | | BETA: splitting (323) gives: % 48.11/7.24 | | | | | | | | | % 48.11/7.24 | | | | | | | | | Case 1: % 48.11/7.24 | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | (326) ~ (all_233_0 = 0) % 48.11/7.24 | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | REDUCE: (324), (326) imply: % 48.11/7.24 | | | | | | | | | | (327) $false % 48.11/7.24 | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | CLOSE: (327) is inconsistent. % 48.11/7.24 | | | | | | | | | | % 48.11/7.24 | | | | | | | | | Case 2: % 48.11/7.24 | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | (328) ~ (all_233_1 = 0) % 48.11/7.24 | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | REDUCE: (325), (328) imply: % 48.11/7.24 | | | | | | | | | | (329) $false % 48.11/7.24 | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | CLOSE: (329) is inconsistent. % 48.11/7.24 | | | | | | | | | | % 48.11/7.24 | | | | | | | | | End of split % 48.11/7.24 | | | | | | | | | % 48.11/7.24 | | | | | | | | Case 2: % 48.11/7.24 | | | | | | | | | % 48.11/7.24 | | | | | | | | | (330) ? [v0: $i] : (sdtasdt0(xr, v0) = xn & % 48.11/7.24 | | | | | | | | | aNaturalNumber0(v0) = 0 & $i(v0)) % 48.11/7.24 | | | | | | | | | % 48.11/7.24 | | | | | | | | | DELTA: instantiating (330) with fresh symbol all_233_0 gives: % 48.11/7.24 | | | | | | | | | (331) sdtasdt0(xr, all_233_0) = xn & % 48.11/7.24 | | | | | | | | | aNaturalNumber0(all_233_0) = 0 & $i(all_233_0) % 48.11/7.24 | | | | | | | | | % 48.11/7.24 | | | | | | | | | ALPHA: (331) implies: % 48.11/7.24 | | | | | | | | | (332) $i(all_233_0) % 48.11/7.24 | | | | | | | | | (333) aNaturalNumber0(all_233_0) = 0 % 48.11/7.24 | | | | | | | | | (334) sdtasdt0(xr, all_233_0) = xn % 48.11/7.24 | | | | | | | | | % 48.11/7.24 | | | | | | | | | BETA: splitting (92) gives: % 48.11/7.24 | | | | | | | | | % 48.11/7.24 | | | | | | | | | Case 1: % 48.11/7.24 | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | (335) xp = sz00 % 48.11/7.24 | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | REDUCE: (314), (335) imply: % 48.11/7.24 | | | | | | | | | | (336) $false % 48.11/7.24 | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | CLOSE: (336) is inconsistent. % 48.11/7.24 | | | | | | | | | | % 48.11/7.24 | | | | | | | | | Case 2: % 48.11/7.24 | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | (337) xp = sz10 | ? [v0: $i] : (isPrime0(v0) = 0 & % 48.11/7.24 | | | | | | | | | | doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0 % 48.11/7.24 | | | | | | | | | | & $i(v0)) % 48.11/7.24 | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | BETA: splitting (318) gives: % 48.11/7.24 | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | Case 1: % 48.11/7.24 | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | (338) ~ (all_82_2 = 0) % 48.11/7.24 | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | REDUCE: (278), (338) imply: % 48.11/7.24 | | | | | | | | | | | (339) $false % 48.11/7.24 | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | CLOSE: (339) is inconsistent. % 48.11/7.24 | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | Case 2: % 48.11/7.24 | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | (340) all_82_0 = 0 % 48.11/7.24 | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | COMBINE_EQS: (224), (340) imply: % 48.11/7.24 | | | | | | | | | | | (341) all_72_0 = 0 % 48.11/7.24 | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | SIMP: (341) implies: % 48.11/7.24 | | | | | | | | | | | (342) all_72_0 = 0 % 48.11/7.24 | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | REDUCE: (124), (342) imply: % 48.11/7.24 | | | | | | | | | | | (343) aNaturalNumber0(all_42_0) = 0 % 48.11/7.24 | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | BETA: splitting (337) gives: % 48.11/7.24 | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | Case 1: % 48.11/7.24 | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | (344) xp = sz10 % 48.11/7.24 | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | REDUCE: (315), (344) imply: % 48.11/7.24 | | | | | | | | | | | | (345) $false % 48.11/7.24 | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | CLOSE: (345) is inconsistent. % 48.11/7.24 | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | Case 2: % 48.11/7.24 | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | (346) ? [v0: $i] : (isPrime0(v0) = 0 & doDivides0(v0, % 48.11/7.24 | | | | | | | | | | | | xp) = 0 & aNaturalNumber0(v0) = 0 & $i(v0)) % 48.11/7.24 | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | DELTA: instantiating (346) with fresh symbol all_261_0 % 48.11/7.24 | | | | | | | | | | | | gives: % 48.11/7.24 | | | | | | | | | | | | (347) isPrime0(all_261_0) = 0 & doDivides0(all_261_0, % 48.11/7.24 | | | | | | | | | | | | xp) = 0 & aNaturalNumber0(all_261_0) = 0 & % 48.11/7.24 | | | | | | | | | | | | $i(all_261_0) % 48.11/7.24 | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | ALPHA: (347) implies: % 48.11/7.24 | | | | | | | | | | | | (348) $i(all_261_0) % 48.11/7.24 | | | | | | | | | | | | (349) doDivides0(all_261_0, xp) = 0 % 48.11/7.24 | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | BETA: splitting (119) gives: % 48.11/7.24 | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | Case 1: % 48.11/7.24 | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | (350) xp = sz00 % 48.11/7.24 | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | REDUCE: (314), (350) imply: % 48.11/7.24 | | | | | | | | | | | | | (351) $false % 48.11/7.24 | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | CLOSE: (351) is inconsistent. % 48.11/7.24 | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | Case 2: % 48.11/7.24 | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | (352) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 48.11/7.24 | | | | | | | | | | | | | (doDivides0(xp, all_42_0) = v2 & % 48.11/7.24 | | | | | | | | | | | | | aNaturalNumber0(all_42_0) = v1 & % 48.11/7.24 | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 % 48.11/7.24 | | | | | | | | | | | | | = 0) | ~ (v0 = 0))) | ( ! [v0: $i] : (v0 = % 48.11/7.24 | | | | | | | | | | | | | xk | ~ (sdtasdt0(xp, v0) = all_42_0) | ~ % 48.11/7.24 | | | | | | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 48.11/7.24 | | | | | | | | | | | | | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( % 48.11/7.24 | | | | | | | | | | | | | ~ (sdtasdt0(xp, xk) = v0) | ~ $i(xk) | (v0 = % 48.11/7.24 | | | | | | | | | | | | | all_42_0 & aNaturalNumber0(xk) = 0))) % 48.11/7.24 | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | BETA: splitting (115) gives: % 48.11/7.24 | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | Case 1: % 48.11/7.24 | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | | (353) xr = sz00 % 48.11/7.24 | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | | REDUCE: (302), (353) imply: % 48.11/7.24 | | | | | | | | | | | | | | (354) $false % 48.11/7.24 | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | | CLOSE: (354) is inconsistent. % 48.11/7.24 | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | Case 2: % 48.11/7.24 | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | | (355) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 48.11/7.24 | | | | | | | | | | | | | | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = % 48.11/7.24 | | | | | | | | | | | | | | v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | % 48.11/7.24 | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) | ! [v0: $i] : ! % 48.11/7.24 | | | | | | | | | | | | | | [v1: $i] : ! [v2: $i] : ( ~ (sdtsldt0(v1, xr) = % 48.11/7.24 | | | | | | | | | | | | | | v2) | ~ (sdtasdt0(v0, xn) = v1) | ~ $i(v0) | % 48.11/7.24 | | | | | | | | | | | | | | ? [v3: any] : ? [v4: $i] : (sdtasdt0(v0, % 48.11/7.24 | | | | | | | | | | | | | | all_44_0) = v4 & aNaturalNumber0(v0) = v3 & % 48.11/7.24 | | | | | | | | | | | | | | $i(v4) & ( ~ (v3 = 0) | v4 = v2))) % 48.11/7.24 | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | | BETA: splitting (116) gives: % 48.11/7.24 | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | | Case 1: % 48.11/7.24 | | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | | | (356) xr = sz00 % 48.11/7.24 | | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | | | REDUCE: (302), (356) imply: % 48.11/7.24 | | | | | | | | | | | | | | | (357) $false % 48.11/7.24 | | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | | | CLOSE: (357) is inconsistent. % 48.11/7.24 | | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | | Case 2: % 48.11/7.24 | | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | | | (358) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 48.11/7.24 | | | | | | | | | | | | | | | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = % 48.11/7.24 | | | | | | | | | | | | | | | v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | % 48.11/7.24 | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) | ( ! [v0: any] : % 48.11/7.24 | | | | | | | | | | | | | | | (v0 = all_44_0 | ~ (sdtasdt0(xr, v0) = xn) | ~ % 48.11/7.24 | | | | | | | | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 48.11/7.24 | | | | | | | | | | | | | | | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( % 48.11/7.24 | | | | | | | | | | | | | | | ~ (sdtasdt0(xr, all_44_0) = v0) | ~ % 48.11/7.24 | | | | | | | | | | | | | | | $i(all_44_0) | (v0 = xn & % 48.11/7.24 | | | | | | | | | | | | | | | aNaturalNumber0(all_44_0) = 0))) % 48.11/7.24 | | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | | | BETA: splitting (355) gives: % 48.11/7.24 | | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | | | Case 1: % 48.11/7.24 | | | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | | | | (359) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 48.11/7.24 | | | | | | | | | | | | | | | | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = % 48.11/7.24 | | | | | | | | | | | | | | | | v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | % 48.11/7.24 | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 48.11/7.24 | | | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (19), (28), (30), (359) are % 48.11/7.24 | | | | | | | | | | | | | | | | inconsistent by sub-proof #2. % 48.11/7.24 | | | | | | | | | | | | | | | | % 48.11/7.24 | | | | | | | | | | | | | | | Case 2: % 48.11/7.24 | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | (360) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 48.11/7.25 | | | | | | | | | | | | | | | | (sdtsldt0(v1, xr) = v2) | ~ (sdtasdt0(v0, xn) = % 48.11/7.25 | | | | | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : % 48.11/7.25 | | | | | | | | | | | | | | | | (sdtasdt0(v0, all_44_0) = v4 & % 48.11/7.25 | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = v3 & $i(v4) & ( ~ (v3 = % 48.11/7.25 | | | | | | | | | | | | | | | | 0) | v4 = v2))) % 48.11/7.25 | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | BETA: splitting (358) gives: % 48.11/7.25 | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | Case 1: % 48.11/7.25 | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | (361) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 48.11/7.25 | | | | | | | | | | | | | | | | | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = % 48.11/7.25 | | | | | | | | | | | | | | | | | v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | % 48.11/7.25 | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 48.11/7.25 | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (19), (28), (30), (361) are % 48.11/7.25 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #2. % 48.11/7.25 | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | Case 2: % 48.11/7.25 | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | (362) ! [v0: any] : (v0 = all_44_0 | ~ (sdtasdt0(xr, % 48.11/7.25 | | | | | | | | | | | | | | | | | v0) = xn) | ~ $i(v0) | ? [v1: int] : ( ~ % 48.11/7.25 | | | | | | | | | | | | | | | | | (v1 = 0) & aNaturalNumber0(v0) = v1)) & ! % 48.11/7.25 | | | | | | | | | | | | | | | | | [v0: $i] : ( ~ (sdtasdt0(xr, all_44_0) = v0) | ~ % 48.11/7.25 | | | | | | | | | | | | | | | | | $i(all_44_0) | (v0 = xn & % 48.11/7.25 | | | | | | | | | | | | | | | | | aNaturalNumber0(all_44_0) = 0)) % 48.11/7.25 | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | ALPHA: (362) implies: % 48.11/7.25 | | | | | | | | | | | | | | | | | (363) ! [v0: any] : (v0 = all_44_0 | ~ (sdtasdt0(xr, % 48.11/7.25 | | | | | | | | | | | | | | | | | v0) = xn) | ~ $i(v0) | ? [v1: int] : ( ~ % 48.11/7.25 | | | | | | | | | | | | | | | | | (v1 = 0) & aNaturalNumber0(v0) = v1)) % 48.11/7.25 | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with 0, all_108_3, all_42_0, % 48.11/7.25 | | | | | | | | | | | | | | | | | xp, simplifying with (82), (291) gives: % 48.11/7.25 | | | | | | | | | | | | | | | | | (364) all_108_3 = 0 % 48.11/7.25 | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | BETA: splitting (352) gives: % 48.11/7.25 | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | Case 1: % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | (365) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 48.11/7.25 | | | | | | | | | | | | | | | | | | (doDivides0(xp, all_42_0) = v2 & % 48.11/7.25 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_42_0) = v1 & % 48.11/7.25 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 % 48.11/7.25 | | | | | | | | | | | | | | | | | | = 0) | ~ (v0 = 0))) % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | DELTA: instantiating (365) with fresh symbols all_288_0, % 48.11/7.25 | | | | | | | | | | | | | | | | | | all_288_1, all_288_2 gives: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (366) doDivides0(xp, all_42_0) = all_288_0 & % 48.11/7.25 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_42_0) = all_288_1 & % 48.11/7.25 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_288_2 & ( ~ (all_288_0 = % 48.11/7.25 | | | | | | | | | | | | | | | | | | 0) | ~ (all_288_1 = 0) | ~ (all_288_2 = 0)) % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | ALPHA: (366) implies: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (367) aNaturalNumber0(xp) = all_288_2 % 48.11/7.25 | | | | | | | | | | | | | | | | | | (368) aNaturalNumber0(all_42_0) = all_288_1 % 48.11/7.25 | | | | | | | | | | | | | | | | | | (369) doDivides0(xp, all_42_0) = all_288_0 % 48.11/7.25 | | | | | | | | | | | | | | | | | | (370) ~ (all_288_0 = 0) | ~ (all_288_1 = 0) | ~ % 48.11/7.25 | | | | | | | | | | | | | | | | | | (all_288_2 = 0) % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | DELTA: instantiating (365) with fresh symbols all_293_0, % 48.11/7.25 | | | | | | | | | | | | | | | | | | all_293_1, all_293_2 gives: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (371) doDivides0(xp, all_42_0) = all_293_0 & % 48.11/7.25 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_42_0) = all_293_1 & % 48.11/7.25 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_293_2 & ( ~ (all_293_0 = % 48.11/7.25 | | | | | | | | | | | | | | | | | | 0) | ~ (all_293_1 = 0) | ~ (all_293_2 = 0)) % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | ALPHA: (371) implies: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (372) aNaturalNumber0(xp) = all_293_2 % 48.11/7.25 | | | | | | | | | | | | | | | | | | (373) aNaturalNumber0(all_42_0) = all_293_1 % 48.11/7.25 | | | | | | | | | | | | | | | | | | (374) doDivides0(xp, all_42_0) = all_293_0 % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_293_2, xp, % 48.11/7.25 | | | | | | | | | | | | | | | | | | simplifying with (8), (372) gives: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (375) all_293_2 = 0 % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_288_2, all_293_2, xp, % 48.11/7.25 | | | | | | | | | | | | | | | | | | simplifying with (367), (372) gives: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (376) all_293_2 = all_288_2 % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_293_1, all_42_0, % 48.11/7.25 | | | | | | | | | | | | | | | | | | simplifying with (343), (373) gives: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (377) all_293_1 = 0 % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_288_1, all_293_1, % 48.11/7.25 | | | | | | | | | | | | | | | | | | all_42_0, simplifying with (368), (373) gives: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (378) all_293_1 = all_288_1 % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with 0, all_293_0, all_42_0, % 48.11/7.25 | | | | | | | | | | | | | | | | | | xp, simplifying with (82), (374) gives: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (379) all_293_0 = 0 % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_288_0, all_293_0, % 48.11/7.25 | | | | | | | | | | | | | | | | | | all_42_0, xp, simplifying with (369), (374) gives: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (380) all_293_0 = all_288_0 % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (379), (380) imply: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (381) all_288_0 = 0 % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (377), (378) imply: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (382) all_288_1 = 0 % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (375), (376) imply: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (383) all_288_2 = 0 % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | BETA: splitting (370) gives: % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | Case 1: % 48.11/7.25 | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | (384) ~ (all_288_0 = 0) % 48.11/7.25 | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | REDUCE: (381), (384) imply: % 48.11/7.25 | | | | | | | | | | | | | | | | | | | (385) $false % 48.11/7.25 | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | CLOSE: (385) is inconsistent. % 48.11/7.25 | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | Case 2: % 48.11/7.25 | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | (386) ~ (all_288_1 = 0) | ~ (all_288_2 = 0) % 48.11/7.25 | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (386) gives: % 48.11/7.25 | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | Case 1: % 48.11/7.25 | | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | | (387) ~ (all_288_1 = 0) % 48.11/7.25 | | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (382), (387) imply: % 48.11/7.25 | | | | | | | | | | | | | | | | | | | | (388) $false % 48.11/7.25 | | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | | CLOSE: (388) is inconsistent. % 48.11/7.25 | | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | Case 2: % 48.11/7.25 | | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | | (389) ~ (all_288_2 = 0) % 48.11/7.25 | | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (383), (389) imply: % 48.11/7.25 | | | | | | | | | | | | | | | | | | | | (390) $false % 48.11/7.25 | | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | | CLOSE: (390) is inconsistent. % 48.11/7.25 | | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | End of split % 48.11/7.25 | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | End of split % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | Case 2: % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | (391) ! [v0: $i] : (v0 = xk | ~ (sdtasdt0(xp, v0) = % 48.11/7.25 | | | | | | | | | | | | | | | | | | all_42_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 48.11/7.25 | | | | | | | | | | | | | | | | | | = 0) & aNaturalNumber0(v0) = v1)) & ! [v0: % 48.11/7.25 | | | | | | | | | | | | | | | | | | $i] : ( ~ (sdtasdt0(xp, xk) = v0) | ~ $i(xk) | % 48.11/7.25 | | | | | | | | | | | | | | | | | | (v0 = all_42_0 & aNaturalNumber0(xk) = 0)) % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | ALPHA: (391) implies: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (392) ! [v0: $i] : ( ~ (sdtasdt0(xp, xk) = v0) | ~ % 48.11/7.25 | | | | | | | | | | | | | | | | | | $i(xk) | (v0 = all_42_0 & aNaturalNumber0(xk) = % 48.11/7.25 | | | | | | | | | | | | | | | | | | 0)) % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (392) with all_54_1, simplifying % 48.11/7.25 | | | | | | | | | | | | | | | | | | with (25), (60) gives: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (393) all_54_1 = all_42_0 & aNaturalNumber0(xk) = 0 % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | ALPHA: (393) implies: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (394) all_54_1 = all_42_0 % 48.11/7.25 | | | | | | | | | | | | | | | | | | (395) aNaturalNumber0(xk) = 0 % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | REDUCE: (65), (394) imply: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (396) sdtsldt0(all_42_0, xr) = all_54_0 % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | REDUCE: (60), (394) imply: % 48.11/7.25 | | | | | | | | | | | | | | | | | | (397) sdtasdt0(xp, xk) = all_42_0 % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives: % 48.11/7.25 | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | Case 1: % 48.11/7.25 | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | (398) xr = sz00 % 48.11/7.25 | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | REDUCE: (302), (398) imply: % 48.11/7.25 | | | | | | | | | | | | | | | | | | | (399) $false % 48.11/7.25 | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | CLOSE: (399) is inconsistent. % 48.11/7.25 | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | Case 2: % 48.11/7.25 | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | (400) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 48.11/7.25 | | | | | | | | | | | | | | | | | | | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = % 48.11/7.25 | | | | | | | | | | | | | | | | | | | v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) | ! [v0: $i] : ! % 48.11/7.25 | | | | | | | | | | | | | | | | | | | [v1: $i] : ! [v2: $i] : ( ~ (sdtsldt0(v1, xr) = % 48.11/7.25 | | | | | | | | | | | | | | | | | | | v2) | ~ (sdtasdt0(v0, xk) = v1) | ~ $i(v0) | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | ? [v3: any] : ? [v4: $i] : (sdtasdt0(v0, % 48.11/7.25 | | | | | | | | | | | | | | | | | | | all_52_3) = v4 & aNaturalNumber0(v0) = v3 & % 48.11/7.25 | | | | | | | | | | | | | | | | | | | $i(v4) & ( ~ (v3 = 0) | v4 = v2))) % 48.11/7.25 | | | | | | | | | | | | | | | | | | | % 48.11/7.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | Case 1: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | (401) xr = sz00 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | REDUCE: (302), (401) imply: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | (402) $false % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | CLOSE: (402) is inconsistent. % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | Case 2: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | (403) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) | ( ! [v0: any] : % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | (v0 = all_52_3 | ~ (sdtasdt0(xr, v0) = xk) | ~ % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | ~ (sdtasdt0(xr, all_52_3) = v0) | ~ % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | $i(all_52_3) | (v0 = xk & % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_52_3) = 0))) % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | BETA: splitting (400) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | Case 1: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | (404) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (28), (30), (395), (404) are % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | Case 2: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | (405) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | (sdtsldt0(v1, xr) = v2) | ~ (sdtasdt0(v0, xk) = % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | (sdtasdt0(v0, all_52_3) = v4 & % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = v3 & $i(v4) & ( ~ (v3 = % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | 0) | v4 = v2))) % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (403) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | (406) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (28), (30), (395), (406) are % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (363) with all_233_0, simplifying % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | with (332), (334) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | (407) all_233_0 = all_44_0 | ? [v0: int] : ( ~ (v0 = 0) % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | & aNaturalNumber0(all_233_0) = v0) % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_261_0, xp, simplifying % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | with (24), (348), (349) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | (408) xp = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | any] : (sdtlseqdt0(all_261_0, xp) = v2 & % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_261_0) = v0 & % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | = 0) | v2 = 0)) % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (405) with xp, all_42_0, all_54_0, % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | simplifying with (24), (396), (397) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | (409) ? [v0: any] : ? [v1: $i] : (sdtasdt0(xp, % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | all_52_3) = v1 & aNaturalNumber0(xp) = v0 & % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | $i(v1) & ( ~ (v0 = 0) | v1 = all_54_0)) % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (360) with xm, all_42_0, all_54_0, % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | simplifying with (23), (306), (396) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | (410) ? [v0: any] : ? [v1: $i] : (sdtasdt0(xm, % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | all_44_0) = v1 & aNaturalNumber0(xm) = v0 & % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | $i(v1) & ( ~ (v0 = 0) | v1 = all_54_0)) % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (410) with fresh symbols all_355_0, % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | all_355_1 gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | (411) sdtasdt0(xm, all_44_0) = all_355_0 & % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xm) = all_355_1 & $i(all_355_0) & % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_355_1 = 0) | all_355_0 = all_54_0) % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (411) implies: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | (412) aNaturalNumber0(xm) = all_355_1 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | (413) sdtasdt0(xm, all_44_0) = all_355_0 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | (414) ~ (all_355_1 = 0) | all_355_0 = all_54_0 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (409) with fresh symbols all_357_0, % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | all_357_1 gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | (415) sdtasdt0(xp, all_52_3) = all_357_0 & % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_357_1 & $i(all_357_0) & % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_357_1 = 0) | all_357_0 = all_54_0) % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (415) implies: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | (416) aNaturalNumber0(xp) = all_357_1 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | (417) sdtasdt0(xp, all_52_3) = all_357_0 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | (418) ~ (all_357_1 = 0) | all_357_0 = all_54_0 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (408) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | (419) xp = sz00 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (314), (419) imply: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | (420) $false % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (420) is inconsistent. % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_355_1, xm, % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (7), (412) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | (421) all_355_1 = 0 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_357_1, xp, % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (8), (416) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | (422) all_357_1 = 0 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_98_0, all_355_0, % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | all_44_0, xm, simplifying with (159), (413) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | (423) all_355_0 = all_98_0 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_52_2, all_357_0, % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | all_52_3, xp, simplifying with (52), (417) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | (424) all_357_0 = all_52_2 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (407) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | (425) all_233_0 = all_44_0 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (333), (425) imply: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | (426) aNaturalNumber0(all_44_0) = 0 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (414) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | (427) ~ (all_355_1 = 0) % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (421), (427) imply: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | (428) $false % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (428) is inconsistent. % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | (429) all_355_0 = all_54_0 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (423), (429) imply: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | (430) all_98_0 = all_54_0 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (418) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (431) ~ (all_357_1 = 0) % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (422), (431) imply: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (432) $false % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (432) is inconsistent. % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (433) all_357_0 = all_54_0 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (424), (433) imply: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (434) all_54_0 = all_52_2 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (434) implies: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (435) all_54_0 = all_52_2 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (430), (435) imply: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (436) all_98_0 = all_52_2 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) ~ (all_98_1 = 0) % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (250), (437) imply: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) $false % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (438) is inconsistent. % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) ~ (all_98_2 = 0) | all_98_0 = all_52_0 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (439) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) ~ (all_98_2 = 0) % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (246), (440) imply: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) ~ (all_78_2 = 0) % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_78_2, 0, all_44_0, % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (132), (426) gives: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) all_78_2 = 0 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (441), (442) imply: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) $false % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (443) is inconsistent. % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) all_98_0 = all_52_0 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (436), (444) imply: % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) all_52_0 = all_52_2 % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (445) implies: % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) all_52_0 = all_52_2 % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (49), (446) imply: % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) $false % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (447) is inconsistent. % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | (448) ? [v0: int] : ( ~ (v0 = 0) & % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_233_0) = v0) % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (448) with fresh symbol all_556_0 % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | (449) ~ (all_556_0 = 0) & aNaturalNumber0(all_233_0) = % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | all_556_0 % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | % 48.11/7.27 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (449) implies: % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | | | | (450) ~ (all_556_0 = 0) % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | | | | (451) aNaturalNumber0(all_233_0) = all_556_0 % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_556_0, all_233_0, % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (333), (451) gives: % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | | | | (452) all_556_0 = 0 % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (450), (452) imply: % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | | | | (453) $false % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (453) is inconsistent. % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | | | End of split % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | | End of split % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | End of split % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | End of split % 48.40/7.27 | | | | | | | | | | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | | | | | | | | | | End of split % 48.40/7.27 | | | | | | | | | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | | | | | | | | | End of split % 48.40/7.27 | | | | | | | | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | | | | | | | | End of split % 48.40/7.27 | | | | | | | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | | | | | | | End of split % 48.40/7.27 | | | | | | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | | | | | | End of split % 48.40/7.27 | | | | | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | | | | | End of split % 48.40/7.27 | | | | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | | | | End of split % 48.40/7.27 | | | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | | | End of split % 48.40/7.27 | | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | | End of split % 48.40/7.27 | | | | | | | | | | | % 48.40/7.27 | | | | | | | | | | End of split % 48.40/7.27 | | | | | | | | | | % 48.40/7.27 | | | | | | | | | End of split % 48.40/7.27 | | | | | | | | | % 48.40/7.27 | | | | | | | | End of split % 48.40/7.27 | | | | | | | | % 48.40/7.27 | | | | | | | End of split % 48.40/7.27 | | | | | | | % 48.40/7.27 | | | | | | End of split % 48.40/7.27 | | | | | | % 48.40/7.27 | | | | | End of split % 48.40/7.27 | | | | | % 48.40/7.27 | | | | End of split % 48.40/7.27 | | | | % 48.40/7.27 | | | End of split % 48.40/7.27 | | | % 48.40/7.27 | | End of split % 48.40/7.27 | | % 48.40/7.27 | End of split % 48.40/7.27 | % 48.40/7.27 End of proof % 48.40/7.27 % 48.40/7.27 Sub-proof #1 shows that the following formulas are inconsistent: % 48.40/7.27 ---------------------------------------------------------------- % 48.40/7.27 (1) aNaturalNumber0(xk) = 0 % 48.40/7.27 (2) aNaturalNumber0(xr) = 0 % 48.40/7.27 (3) doDivides0(xr, xk) = 0 % 48.40/7.27 (4) ? [v0: any] : ? [v1: any] : ? [v2: any] : (doDivides0(xr, xk) = v2 & % 48.40/7.27 aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | ~ % 48.40/7.27 (v1 = 0) | ~ (v0 = 0))) % 48.40/7.27 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 48.40/7.27 ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, % 48.40/7.27 v2) = v0)) % 48.40/7.27 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 48.40/7.27 (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) % 48.40/7.27 % 48.40/7.27 Begin of proof % 48.40/7.27 | % 48.40/7.27 | DELTA: instantiating (4) with fresh symbols all_349_0, all_349_1, all_349_2 % 48.40/7.27 | gives: % 48.40/7.27 | (7) doDivides0(xr, xk) = all_349_0 & aNaturalNumber0(xr) = all_349_2 & % 48.40/7.27 | aNaturalNumber0(xk) = all_349_1 & ( ~ (all_349_0 = 0) | ~ (all_349_1 = % 48.40/7.27 | 0) | ~ (all_349_2 = 0)) % 48.40/7.27 | % 48.40/7.27 | ALPHA: (7) implies: % 48.40/7.27 | (8) aNaturalNumber0(xk) = all_349_1 % 48.40/7.27 | (9) aNaturalNumber0(xr) = all_349_2 % 48.40/7.27 | (10) doDivides0(xr, xk) = all_349_0 % 48.40/7.27 | (11) ~ (all_349_0 = 0) | ~ (all_349_1 = 0) | ~ (all_349_2 = 0) % 48.40/7.27 | % 48.40/7.27 | GROUND_INST: instantiating (6) with 0, all_349_1, xk, simplifying with (1), % 48.40/7.27 | (8) gives: % 48.40/7.27 | (12) all_349_1 = 0 % 48.40/7.27 | % 48.40/7.27 | GROUND_INST: instantiating (6) with 0, all_349_2, xr, simplifying with (2), % 48.40/7.27 | (9) gives: % 48.40/7.27 | (13) all_349_2 = 0 % 48.40/7.27 | % 48.40/7.27 | GROUND_INST: instantiating (5) with 0, all_349_0, xk, xr, simplifying with % 48.40/7.27 | (3), (10) gives: % 48.40/7.27 | (14) all_349_0 = 0 % 48.40/7.27 | % 48.40/7.27 | BETA: splitting (11) gives: % 48.40/7.27 | % 48.40/7.27 | Case 1: % 48.40/7.27 | | % 48.40/7.27 | | (15) ~ (all_349_0 = 0) % 48.40/7.27 | | % 48.40/7.27 | | REDUCE: (14), (15) imply: % 48.40/7.27 | | (16) $false % 48.40/7.27 | | % 48.40/7.27 | | CLOSE: (16) is inconsistent. % 48.40/7.27 | | % 48.40/7.27 | Case 2: % 48.40/7.27 | | % 48.40/7.27 | | (17) ~ (all_349_1 = 0) | ~ (all_349_2 = 0) % 48.40/7.27 | | % 48.40/7.27 | | BETA: splitting (17) gives: % 48.40/7.27 | | % 48.40/7.27 | | Case 1: % 48.40/7.27 | | | % 48.40/7.27 | | | (18) ~ (all_349_1 = 0) % 48.40/7.27 | | | % 48.40/7.27 | | | REDUCE: (12), (18) imply: % 48.40/7.27 | | | (19) $false % 48.40/7.27 | | | % 48.40/7.27 | | | CLOSE: (19) is inconsistent. % 48.40/7.27 | | | % 48.40/7.27 | | Case 2: % 48.40/7.27 | | | % 48.40/7.27 | | | (20) ~ (all_349_2 = 0) % 48.40/7.27 | | | % 48.40/7.27 | | | REDUCE: (13), (20) imply: % 48.40/7.27 | | | (21) $false % 48.40/7.27 | | | % 48.40/7.27 | | | CLOSE: (21) is inconsistent. % 48.40/7.27 | | | % 48.40/7.27 | | End of split % 48.40/7.27 | | % 48.40/7.27 | End of split % 48.40/7.27 | % 48.40/7.27 End of proof % 48.40/7.27 % 48.40/7.27 Sub-proof #2 shows that the following formulas are inconsistent: % 48.40/7.27 ---------------------------------------------------------------- % 48.40/7.27 (1) aNaturalNumber0(xn) = 0 % 48.40/7.27 (2) doDivides0(xr, xn) = 0 % 48.40/7.27 (3) aNaturalNumber0(xr) = 0 % 48.40/7.27 (4) ? [v0: any] : ? [v1: any] : ? [v2: any] : (doDivides0(xr, xn) = v2 & % 48.40/7.27 aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ % 48.40/7.27 (v1 = 0) | ~ (v0 = 0))) % 48.40/7.27 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 48.40/7.27 ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, % 48.40/7.27 v2) = v0)) % 48.40/7.27 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 48.40/7.27 (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) % 48.40/7.27 % 48.40/7.27 Begin of proof % 48.40/7.27 | % 48.40/7.27 | DELTA: instantiating (4) with fresh symbols all_280_0, all_280_1, all_280_2 % 48.40/7.27 | gives: % 48.40/7.27 | (7) doDivides0(xr, xn) = all_280_0 & aNaturalNumber0(xr) = all_280_2 & % 48.40/7.27 | aNaturalNumber0(xn) = all_280_1 & ( ~ (all_280_0 = 0) | ~ (all_280_1 = % 48.40/7.27 | 0) | ~ (all_280_2 = 0)) % 48.40/7.27 | % 48.40/7.27 | ALPHA: (7) implies: % 48.40/7.27 | (8) aNaturalNumber0(xn) = all_280_1 % 48.40/7.27 | (9) doDivides0(xr, xn) = all_280_0 % 48.40/7.27 | % 48.40/7.27 | DELTA: instantiating (4) with fresh symbols all_282_0, all_282_1, all_282_2 % 48.40/7.27 | gives: % 48.40/7.27 | (10) doDivides0(xr, xn) = all_282_0 & aNaturalNumber0(xr) = all_282_2 & % 48.40/7.27 | aNaturalNumber0(xn) = all_282_1 & ( ~ (all_282_0 = 0) | ~ (all_282_1 % 48.40/7.27 | = 0) | ~ (all_282_2 = 0)) % 48.40/7.27 | % 48.40/7.27 | ALPHA: (10) implies: % 48.40/7.27 | (11) aNaturalNumber0(xn) = all_282_1 % 48.40/7.27 | (12) aNaturalNumber0(xr) = all_282_2 % 48.40/7.27 | (13) doDivides0(xr, xn) = all_282_0 % 48.40/7.27 | (14) ~ (all_282_0 = 0) | ~ (all_282_1 = 0) | ~ (all_282_2 = 0) % 48.40/7.27 | % 48.40/7.27 | GROUND_INST: instantiating (6) with 0, all_282_1, xn, simplifying with (1), % 48.40/7.27 | (11) gives: % 48.40/7.27 | (15) all_282_1 = 0 % 48.40/7.27 | % 48.40/7.28 | GROUND_INST: instantiating (6) with all_280_1, all_282_1, xn, simplifying with % 48.40/7.28 | (8), (11) gives: % 48.40/7.28 | (16) all_282_1 = all_280_1 % 48.40/7.28 | % 48.40/7.28 | GROUND_INST: instantiating (6) with 0, all_282_2, xr, simplifying with (3), % 48.40/7.28 | (12) gives: % 48.40/7.28 | (17) all_282_2 = 0 % 48.40/7.28 | % 48.40/7.28 | GROUND_INST: instantiating (5) with 0, all_282_0, xn, xr, simplifying with % 48.40/7.28 | (2), (13) gives: % 48.40/7.28 | (18) all_282_0 = 0 % 48.40/7.28 | % 48.40/7.28 | GROUND_INST: instantiating (5) with all_280_0, all_282_0, xn, xr, simplifying % 48.40/7.28 | with (9), (13) gives: % 48.40/7.28 | (19) all_282_0 = all_280_0 % 48.40/7.28 | % 48.40/7.28 | COMBINE_EQS: (18), (19) imply: % 48.40/7.28 | (20) all_280_0 = 0 % 48.40/7.28 | % 48.40/7.28 | COMBINE_EQS: (15), (16) imply: % 48.40/7.28 | (21) all_280_1 = 0 % 48.40/7.28 | % 48.40/7.28 | BETA: splitting (14) gives: % 48.40/7.28 | % 48.40/7.28 | Case 1: % 48.40/7.28 | | % 48.40/7.28 | | (22) ~ (all_282_0 = 0) % 48.40/7.28 | | % 48.40/7.28 | | REDUCE: (18), (22) imply: % 48.40/7.28 | | (23) $false % 48.40/7.28 | | % 48.40/7.28 | | CLOSE: (23) is inconsistent. % 48.40/7.28 | | % 48.40/7.28 | Case 2: % 48.40/7.28 | | % 48.40/7.28 | | (24) ~ (all_282_1 = 0) | ~ (all_282_2 = 0) % 48.40/7.28 | | % 48.40/7.28 | | BETA: splitting (24) gives: % 48.40/7.28 | | % 48.40/7.28 | | Case 1: % 48.40/7.28 | | | % 48.40/7.28 | | | (25) ~ (all_282_1 = 0) % 48.40/7.28 | | | % 48.40/7.28 | | | REDUCE: (15), (25) imply: % 48.40/7.28 | | | (26) $false % 48.40/7.28 | | | % 48.40/7.28 | | | CLOSE: (26) is inconsistent. % 48.40/7.28 | | | % 48.40/7.28 | | Case 2: % 48.40/7.28 | | | % 48.40/7.28 | | | (27) ~ (all_282_2 = 0) % 48.40/7.28 | | | % 48.40/7.28 | | | REDUCE: (17), (27) imply: % 48.40/7.28 | | | (28) $false % 48.40/7.28 | | | % 48.40/7.28 | | | CLOSE: (28) is inconsistent. % 48.40/7.28 | | | % 48.40/7.28 | | End of split % 48.40/7.28 | | % 48.40/7.28 | End of split % 48.40/7.28 | % 48.40/7.28 End of proof % 48.40/7.28 % SZS output end Proof for theBenchmark % 48.40/7.28 % 48.40/7.28 6662ms %------------------------------------------------------------------------------