%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM512+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n002.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 11:48:16 EDT 2023 % Result : Theorem 14.25s 2.74s % Output : Proof 52.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM512+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n002.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 09:10:17 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.54/1.24 Prover 4: Preprocessing ... % 3.54/1.24 Prover 1: Preprocessing ... % 3.54/1.28 Prover 3: Preprocessing ... % 3.54/1.28 Prover 5: Preprocessing ... % 3.54/1.28 Prover 0: Preprocessing ... % 3.54/1.28 Prover 2: Preprocessing ... % 3.54/1.28 Prover 6: Preprocessing ... % 9.95/2.13 Prover 1: Constructing countermodel ... % 9.95/2.14 Prover 3: Constructing countermodel ... % 9.95/2.17 Prover 6: Proving ... % 9.95/2.17 Prover 5: Constructing countermodel ... % 11.78/2.40 Prover 2: Proving ... % 13.01/2.50 Prover 4: Constructing countermodel ... % 13.01/2.54 Prover 0: Proving ... % 14.25/2.74 Prover 3: proved (2092ms) % 14.25/2.74 % 14.25/2.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.25/2.74 % 14.25/2.74 Prover 5: stopped % 14.25/2.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.25/2.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.25/2.74 Prover 6: stopped % 14.25/2.75 Prover 2: stopped % 14.25/2.75 Prover 0: stopped % 14.25/2.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.25/2.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.25/2.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.80/2.91 Prover 11: Preprocessing ... % 16.12/2.91 Prover 10: Preprocessing ... % 16.12/2.93 Prover 8: Preprocessing ... % 16.31/2.94 Prover 7: Preprocessing ... % 16.31/2.95 Prover 13: Preprocessing ... % 18.09/3.19 Prover 8: Warning: ignoring some quantifiers % 18.42/3.21 Prover 8: Constructing countermodel ... % 18.42/3.23 Prover 10: Constructing countermodel ... % 18.42/3.23 Prover 7: Constructing countermodel ... % 18.96/3.39 Prover 13: Constructing countermodel ... % 21.65/3.66 Prover 11: Constructing countermodel ... % 50.93/7.44 Prover 1: Found proof (size 390) % 50.93/7.44 Prover 1: proved (6816ms) % 50.93/7.44 Prover 13: stopped % 50.93/7.44 Prover 7: stopped % 50.93/7.44 Prover 11: stopped % 50.93/7.44 Prover 4: stopped % 50.93/7.44 Prover 8: stopped % 50.93/7.45 Prover 10: stopped % 50.93/7.45 % 50.93/7.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 50.93/7.45 % 51.30/7.54 % SZS output start Proof for theBenchmark % 51.30/7.55 Assumptions after simplification: % 51.30/7.55 --------------------------------- % 51.30/7.55 % 51.30/7.55 (mAddAsso) % 51.63/7.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 51.63/7.58 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 51.63/7.58 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? % 51.63/7.58 [v9: $i] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 & % 51.63/7.58 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) % 51.63/7.58 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = % 51.63/7.58 v4))) % 51.63/7.58 % 51.63/7.58 (mAddComm) % 51.63/7.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 51.63/7.58 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 51.63/7.58 (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 % 51.63/7.58 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 51.63/7.58 % 51.63/7.58 (mDivMin) % 51.76/7.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (doDivides0(v0, % 51.76/7.58 v3) = 0) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 51.76/7.58 $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: % 51.76/7.58 any] : (doDivides0(v0, v2) = v8 & doDivides0(v0, v1) = v7 & % 51.76/7.58 aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) % 51.76/7.58 = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v8 = 0))) % 51.76/7.58 % 51.76/7.58 (mLEAsym) % 51.76/7.58 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ $i(v1) % 51.76/7.58 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (sdtlseqdt0(v1, % 51.76/7.58 v0) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v4 % 51.76/7.58 = 0) | ~ (v3 = 0) | ~ (v2 = 0)))) % 51.76/7.58 % 51.76/7.58 (mMulAsso) % 51.76/7.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 51.76/7.59 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 51.76/7.59 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? % 51.76/7.59 [v9: $i] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & % 51.76/7.59 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) % 51.76/7.59 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = % 51.76/7.59 v4))) % 51.76/7.59 % 51.76/7.59 (mMulComm) % 51.76/7.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 51.76/7.59 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 51.76/7.59 (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 % 51.76/7.59 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 51.76/7.59 % 51.76/7.59 (mPrimDiv) % 51.76/7.59 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ % 51.76/7.59 (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (isPrime0(v1) = 0 & % 51.76/7.59 doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0 & $i(v1))) % 51.76/7.59 % 51.76/7.59 (mSortsB) % 51.76/7.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 51.76/7.59 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 51.76/7.59 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 51.76/7.59 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 51.76/7.59 % 51.76/7.59 (mSortsB_02) % 51.76/7.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 51.76/7.59 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 51.76/7.59 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 51.76/7.59 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 51.76/7.59 % 51.76/7.59 (m__) % 51.76/7.59 $i(xr) & $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: any] : ? % 51.76/7.59 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 51.76/7.59 : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : (sdtsldt0(v6, xr) = v7 & % 51.76/7.59 sdtsldt0(xn, xr) = v0 & sdtasdt0(v7, xr) = v10 & sdtasdt0(v3, xr) = v4 & % 51.76/7.59 sdtasdt0(v0, xm) = v3 & sdtasdt0(xr, v7) = v9 & sdtasdt0(xr, v0) = v2 & % 51.76/7.59 sdtasdt0(xp, xk) = v6 & sdtasdt0(xn, xm) = v5 & aNaturalNumber0(v7) = v8 & % 51.76/7.59 aNaturalNumber0(v0) = v1 & $i(v10) & $i(v9) & $i(v7) & $i(v6) & $i(v5) & % 51.76/7.59 $i(v4) & $i(v3) & $i(v2) & $i(v0) & ((v9 = v6 & v8 = 0 & ~ (v10 = v5)) | % 51.76/7.59 (v2 = xn & v1 = 0 & ~ (v5 = v4)))) % 51.76/7.59 % 51.76/7.59 (m__1799) % 51.76/7.60 $i(xp) & $i(xm) & $i(xn) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : % 51.76/7.60 (sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) = v0 & $i(v1) & $i(v0) & ! [v2: $i] % 51.76/7.60 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, % 51.76/7.60 v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 51.76/7.60 $i(v2) | ? [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10: any] : ? % 51.76/7.60 [v11: $i] : ? [v12: any] : ? [v13: any] : ? [v14: any] : ? [v15: any] % 51.76/7.60 : (isPrime0(v4) = v10 & doDivides0(v4, v11) = v12 & doDivides0(v4, v3) = % 51.76/7.60 v15 & doDivides0(v4, v2) = v14 & iLess0(v6, v1) = v13 & sdtasdt0(v2, v3) % 51.76/7.60 = v11 & aNaturalNumber0(v4) = v9 & aNaturalNumber0(v3) = v8 & % 51.76/7.60 aNaturalNumber0(v2) = v7 & $i(v11) & ( ~ (v13 = 0) | ~ (v9 = 0) | ~ % 51.76/7.60 (v8 = 0) | ~ (v7 = 0) | (v15 = 0 & ? [v16: $i] : (sdtasdt0(v4, v16) % 51.76/7.60 = v3 & aNaturalNumber0(v16) = 0 & $i(v16))) | (v14 = 0 & ? [v16: % 51.76/7.60 $i] : (sdtasdt0(v4, v16) = v2 & aNaturalNumber0(v16) = 0 & % 51.76/7.60 $i(v16))) | ( ~ (v12 = 0) & ! [v16: $i] : ( ~ (sdtasdt0(v4, v16) % 51.76/7.60 = v11) | ~ $i(v16) | ? [v17: int] : ( ~ (v17 = 0) & % 51.76/7.60 aNaturalNumber0(v16) = v17))) | ( ~ (v10 = 0) & (v4 = sz10 | v4 % 51.76/7.60 = sz00 | ? [v16: $i] : ( ~ (v16 = v4) & ~ (v16 = sz10) & % 51.76/7.60 doDivides0(v16, v4) = 0 & aNaturalNumber0(v16) = 0 & $i(v16) & % 51.76/7.60 ? [v17: $i] : (sdtasdt0(v16, v17) = v4 & aNaturalNumber0(v17) = % 51.76/7.60 0 & $i(v17))))))))) % 51.76/7.60 % 51.76/7.60 (m__1837) % 51.76/7.60 aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & % 51.76/7.60 $i(xp) & $i(xm) & $i(xn) % 51.76/7.60 % 51.76/7.60 (m__1860) % 51.76/7.60 $i(xp) & $i(xm) & $i(xn) & $i(sz10) & $i(sz00) & ? [v0: $i] : ( ~ (xp = sz10) % 51.76/7.60 & ~ (xp = sz00) & isPrime0(xp) = 0 & doDivides0(xp, v0) = 0 & sdtasdt0(xn, % 51.76/7.60 xm) = v0 & $i(v0) & ! [v1: $i] : ! [v2: any] : (v1 = xp | v1 = sz10 | ~ % 51.76/7.60 (doDivides0(v1, xp) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 51.76/7.60 aNaturalNumber0(v1) = v3) | ( ~ (v2 = 0) & ! [v3: $i] : ( ~ % 51.76/7.60 (sdtasdt0(v1, v3) = xp) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & % 51.76/7.60 aNaturalNumber0(v3) = v4)))) & ? [v1: $i] : (sdtasdt0(xp, v1) = v0 % 51.76/7.60 & aNaturalNumber0(v1) = 0 & $i(v1))) % 51.76/7.60 % 51.76/7.60 (m__2287) % 51.76/7.60 ~ (xp = xm) & ~ (xp = xn) & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0 % 51.76/7.60 & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (sdtpldt0(xm, v0) = xp & % 51.76/7.60 aNaturalNumber0(v0) = 0 & $i(v0)) & ? [v0: $i] : (sdtpldt0(xn, v0) = xp & % 51.76/7.60 aNaturalNumber0(v0) = 0 & $i(v0)) % 51.76/7.60 % 51.76/7.60 (m__2306) % 51.76/7.60 $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (sdtsldt0(v0, xp) = xk & % 51.76/7.60 sdtasdt0(xp, xk) = v0 & sdtasdt0(xn, xm) = v0 & aNaturalNumber0(xk) = 0 & % 51.76/7.60 $i(v0)) % 51.76/7.60 % 51.76/7.60 (m__2342) % 51.76/7.61 ~ (xr = sz10) & ~ (xr = sz00) & isPrime0(xr) = 0 & doDivides0(xr, xk) = 0 & % 51.76/7.61 aNaturalNumber0(xr) = 0 & $i(xr) & $i(xk) & $i(sz10) & $i(sz00) & ! [v0: $i] % 51.76/7.61 : ! [v1: any] : (v0 = xr | v0 = sz10 | ~ (doDivides0(v0, xr) = v1) | ~ % 51.76/7.61 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | ( ~ (v1 = % 51.76/7.61 0) & ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = xr) | ~ $i(v2) | ? [v3: % 51.76/7.61 int] : ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)))) & ? [v0: $i] : % 51.76/7.61 (sdtasdt0(xr, v0) = xk & aNaturalNumber0(v0) = 0 & $i(v0)) % 51.76/7.61 % 51.76/7.61 (m__2362) % 51.76/7.61 $i(xr) & $i(xk) & $i(xm) & $i(xn) & ? [v0: $i] : (doDivides0(xr, v0) = 0 & % 51.76/7.61 sdtasdt0(xn, xm) = v0 & $i(v0) & ? [v1: $i] : (sdtasdt0(xr, v1) = v0 & % 51.76/7.61 aNaturalNumber0(v1) = 0 & $i(v1)) & ? [v1: $i] : (sdtpldt0(xr, v1) = xk & % 51.76/7.61 aNaturalNumber0(v1) = 0 & $i(v1))) % 51.76/7.61 % 51.76/7.61 (m__2377) % 51.76/7.61 ~ (xk = xp) & sdtlseqdt0(xk, xp) = 0 & $i(xk) & $i(xp) & ? [v0: $i] : % 51.76/7.61 (sdtpldt0(xk, v0) = xp & aNaturalNumber0(v0) = 0 & $i(v0)) % 51.76/7.61 % 51.76/7.61 (m__2449) % 51.76/7.61 $i(xr) & $i(xm) & $i(xn) & ? [v0: any] : ? [v1: any] : (doDivides0(xr, xm) = % 51.76/7.61 v1 & doDivides0(xr, xn) = v0 & ((v1 = 0 & ? [v2: $i] : (sdtasdt0(xr, v2) = % 51.76/7.61 xm & aNaturalNumber0(v2) = 0 & $i(v2))) | (v0 = 0 & ? [v2: $i] : % 51.76/7.61 (sdtasdt0(xr, v2) = xn & aNaturalNumber0(v2) = 0 & $i(v2))))) % 51.76/7.61 % 51.76/7.61 (m__2487) % 51.76/7.61 doDivides0(xr, xn) = 0 & $i(xr) & $i(xn) & ? [v0: $i] : (sdtasdt0(xr, v0) = % 51.76/7.61 xn & aNaturalNumber0(v0) = 0 & $i(v0)) % 51.76/7.61 % 51.76/7.61 (m__2504) % 51.76/7.61 $i(xr) & $i(xn) & ? [v0: $i] : ( ~ (v0 = xn) & sdtsldt0(xn, xr) = v0 & % 51.76/7.61 sdtlseqdt0(v0, xn) = 0 & sdtasdt0(xr, v0) = xn & aNaturalNumber0(v0) = 0 & % 51.76/7.61 $i(v0) & ? [v1: $i] : (sdtpldt0(v0, v1) = xn & aNaturalNumber0(v1) = 0 & % 51.76/7.61 $i(v1))) % 51.76/7.61 % 51.76/7.61 (function-axioms) % 51.76/7.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 51.76/7.61 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: % 51.76/7.61 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 51.76/7.61 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 51.76/7.61 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 51.76/7.61 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 51.76/7.61 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 51.76/7.61 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: % 51.76/7.61 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 51.76/7.61 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 51.76/7.61 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 51.76/7.61 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 51.76/7.61 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 51.76/7.61 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 51.76/7.61 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ % 51.76/7.61 (isPrime0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 51.76/7.61 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) % 51.76/7.61 | ~ (aNaturalNumber0(v2) = v0)) % 51.76/7.61 % 51.76/7.61 Further assumptions not needed in the proof: % 51.76/7.62 -------------------------------------------- % 51.76/7.62 mAMDistr, mAddCanc, mDefDiff, mDefDiv, mDefLE, mDefPrime, mDefQuot, mDivAsso, % 51.76/7.62 mDivLE, mDivSum, mDivTrans, mIH, mIH_03, mLENTr, mLERefl, mLETotal, mLETran, % 51.76/7.62 mMonAdd, mMonMul, mMonMul2, mMulCanc, mNatSort, mSortsC, mSortsC_01, mZeroAdd, % 51.76/7.62 mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__1870, m__2075, m__2315, m__2327 % 51.76/7.62 % 51.76/7.62 Those formulas are unsatisfiable: % 51.76/7.62 --------------------------------- % 51.76/7.62 % 51.76/7.62 Begin of proof % 51.76/7.62 | % 51.76/7.62 | ALPHA: (mPrimDiv) implies: % 51.76/7.62 | (1) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | % 51.76/7.62 | ~ $i(v0) | ? [v1: $i] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & % 51.76/7.62 | aNaturalNumber0(v1) = 0 & $i(v1))) % 51.76/7.62 | % 51.76/7.62 | ALPHA: (m__1837) implies: % 51.76/7.62 | (2) aNaturalNumber0(xm) = 0 % 51.76/7.62 | (3) aNaturalNumber0(xp) = 0 % 51.76/7.62 | % 51.76/7.62 | ALPHA: (m__1799) implies: % 51.97/7.62 | (4) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) = % 51.97/7.62 | v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 51.97/7.62 | [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) = v6) | ~ % 51.97/7.62 | (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? % 51.97/7.62 | [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10: any] : ? [v11: % 51.97/7.62 | $i] : ? [v12: any] : ? [v13: any] : ? [v14: any] : ? [v15: % 51.97/7.62 | any] : (isPrime0(v4) = v10 & doDivides0(v4, v11) = v12 & % 51.97/7.62 | doDivides0(v4, v3) = v15 & doDivides0(v4, v2) = v14 & iLess0(v6, % 51.97/7.62 | v1) = v13 & sdtasdt0(v2, v3) = v11 & aNaturalNumber0(v4) = v9 & % 51.97/7.62 | aNaturalNumber0(v3) = v8 & aNaturalNumber0(v2) = v7 & $i(v11) & ( % 51.97/7.62 | ~ (v13 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | (v15 = % 51.97/7.62 | 0 & ? [v16: $i] : (sdtasdt0(v4, v16) = v3 & % 51.97/7.62 | aNaturalNumber0(v16) = 0 & $i(v16))) | (v14 = 0 & ? [v16: % 51.97/7.62 | $i] : (sdtasdt0(v4, v16) = v2 & aNaturalNumber0(v16) = 0 & % 51.97/7.62 | $i(v16))) | ( ~ (v12 = 0) & ! [v16: $i] : ( ~ % 51.97/7.62 | (sdtasdt0(v4, v16) = v11) | ~ $i(v16) | ? [v17: int] : ( % 51.97/7.62 | ~ (v17 = 0) & aNaturalNumber0(v16) = v17))) | ( ~ (v10 = % 51.97/7.62 | 0) & (v4 = sz10 | v4 = sz00 | ? [v16: $i] : ( ~ (v16 = v4) % 51.97/7.62 | & ~ (v16 = sz10) & doDivides0(v16, v4) = 0 & % 51.97/7.62 | aNaturalNumber0(v16) = 0 & $i(v16) & ? [v17: $i] : % 51.97/7.62 | (sdtasdt0(v16, v17) = v4 & aNaturalNumber0(v17) = 0 & % 51.97/7.63 | $i(v17))))))))) % 51.97/7.63 | % 51.97/7.63 | ALPHA: (m__1860) implies: % 51.97/7.63 | (5) ? [v0: $i] : ( ~ (xp = sz10) & ~ (xp = sz00) & isPrime0(xp) = 0 & % 51.97/7.63 | doDivides0(xp, v0) = 0 & sdtasdt0(xn, xm) = v0 & $i(v0) & ! [v1: $i] % 51.97/7.63 | : ! [v2: any] : (v1 = xp | v1 = sz10 | ~ (doDivides0(v1, xp) = v2) % 51.97/7.63 | | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aNaturalNumber0(v1) = % 51.97/7.63 | v3) | ( ~ (v2 = 0) & ! [v3: $i] : ( ~ (sdtasdt0(v1, v3) = xp) | % 51.97/7.63 | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = % 51.97/7.63 | v4)))) & ? [v1: $i] : (sdtasdt0(xp, v1) = v0 & % 51.97/7.63 | aNaturalNumber0(v1) = 0 & $i(v1))) % 51.97/7.63 | % 51.97/7.63 | ALPHA: (m__2287) implies: % 51.97/7.63 | (6) ? [v0: $i] : (sdtpldt0(xn, v0) = xp & aNaturalNumber0(v0) = 0 & % 51.97/7.63 | $i(v0)) % 51.97/7.63 | (7) ? [v0: $i] : (sdtpldt0(xm, v0) = xp & aNaturalNumber0(v0) = 0 & % 51.97/7.63 | $i(v0)) % 51.97/7.63 | % 51.97/7.63 | ALPHA: (m__2306) implies: % 51.97/7.63 | (8) ? [v0: $i] : (sdtsldt0(v0, xp) = xk & sdtasdt0(xp, xk) = v0 & % 51.97/7.63 | sdtasdt0(xn, xm) = v0 & aNaturalNumber0(xk) = 0 & $i(v0)) % 51.97/7.63 | % 51.97/7.63 | ALPHA: (m__2342) implies: % 51.97/7.63 | (9) aNaturalNumber0(xr) = 0 % 51.97/7.63 | (10) doDivides0(xr, xk) = 0 % 51.97/7.63 | (11) ? [v0: $i] : (sdtasdt0(xr, v0) = xk & aNaturalNumber0(v0) = 0 & % 51.97/7.63 | $i(v0)) % 51.97/7.63 | % 51.97/7.63 | ALPHA: (m__2362) implies: % 51.97/7.63 | (12) ? [v0: $i] : (doDivides0(xr, v0) = 0 & sdtasdt0(xn, xm) = v0 & $i(v0) % 51.97/7.63 | & ? [v1: $i] : (sdtasdt0(xr, v1) = v0 & aNaturalNumber0(v1) = 0 & % 51.97/7.63 | $i(v1)) & ? [v1: $i] : (sdtpldt0(xr, v1) = xk & % 51.97/7.63 | aNaturalNumber0(v1) = 0 & $i(v1))) % 51.97/7.63 | % 51.97/7.63 | ALPHA: (m__2377) implies: % 51.97/7.63 | (13) ? [v0: $i] : (sdtpldt0(xk, v0) = xp & aNaturalNumber0(v0) = 0 & % 51.97/7.63 | $i(v0)) % 51.97/7.63 | % 51.97/7.63 | ALPHA: (m__2449) implies: % 51.97/7.63 | (14) ? [v0: any] : ? [v1: any] : (doDivides0(xr, xm) = v1 & % 51.97/7.63 | doDivides0(xr, xn) = v0 & ((v1 = 0 & ? [v2: $i] : (sdtasdt0(xr, v2) % 51.97/7.63 | = xm & aNaturalNumber0(v2) = 0 & $i(v2))) | (v0 = 0 & ? [v2: % 51.97/7.63 | $i] : (sdtasdt0(xr, v2) = xn & aNaturalNumber0(v2) = 0 & % 51.97/7.63 | $i(v2))))) % 51.97/7.63 | % 51.97/7.63 | ALPHA: (m__2487) implies: % 51.97/7.63 | (15) doDivides0(xr, xn) = 0 % 51.97/7.63 | (16) ? [v0: $i] : (sdtasdt0(xr, v0) = xn & aNaturalNumber0(v0) = 0 & % 51.97/7.63 | $i(v0)) % 51.97/7.63 | % 51.97/7.63 | ALPHA: (m__2504) implies: % 51.97/7.64 | (17) ? [v0: $i] : ( ~ (v0 = xn) & sdtsldt0(xn, xr) = v0 & sdtlseqdt0(v0, % 51.97/7.64 | xn) = 0 & sdtasdt0(xr, v0) = xn & aNaturalNumber0(v0) = 0 & $i(v0) % 51.97/7.64 | & ? [v1: $i] : (sdtpldt0(v0, v1) = xn & aNaturalNumber0(v1) = 0 & % 51.97/7.64 | $i(v1))) % 51.97/7.64 | % 51.97/7.64 | ALPHA: (m__) implies: % 51.97/7.64 | (18) $i(xm) % 51.97/7.64 | (19) $i(xp) % 51.97/7.64 | (20) $i(xr) % 52.04/7.64 | (21) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 52.04/7.64 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : % 52.04/7.64 | ? [v10: $i] : (sdtsldt0(v6, xr) = v7 & sdtsldt0(xn, xr) = v0 & % 52.04/7.64 | sdtasdt0(v7, xr) = v10 & sdtasdt0(v3, xr) = v4 & sdtasdt0(v0, xm) = % 52.04/7.64 | v3 & sdtasdt0(xr, v7) = v9 & sdtasdt0(xr, v0) = v2 & sdtasdt0(xp, % 52.04/7.64 | xk) = v6 & sdtasdt0(xn, xm) = v5 & aNaturalNumber0(v7) = v8 & % 52.04/7.64 | aNaturalNumber0(v0) = v1 & $i(v10) & $i(v9) & $i(v7) & $i(v6) & % 52.04/7.64 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v0) & ((v9 = v6 & v8 = 0 & ~ % 52.04/7.64 | (v10 = v5)) | (v2 = xn & v1 = 0 & ~ (v5 = v4)))) % 52.04/7.64 | % 52.04/7.64 | ALPHA: (function-axioms) implies: % 52.04/7.64 | (22) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 52.04/7.64 | : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = % 52.04/7.64 | v0)) % 52.04/7.64 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.04/7.64 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 52.04/7.64 | (24) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 52.04/7.64 | : ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ % 52.04/7.64 | (doDivides0(v3, v2) = v0)) % 52.04/7.64 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.04/7.64 | (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) % 52.04/7.64 | % 52.04/7.64 | DELTA: instantiating (13) with fresh symbol all_39_0 gives: % 52.04/7.64 | (26) sdtpldt0(xk, all_39_0) = xp & aNaturalNumber0(all_39_0) = 0 & % 52.04/7.64 | $i(all_39_0) % 52.04/7.64 | % 52.04/7.64 | ALPHA: (26) implies: % 52.04/7.64 | (27) $i(all_39_0) % 52.04/7.64 | (28) sdtpldt0(xk, all_39_0) = xp % 52.04/7.64 | % 52.04/7.64 | DELTA: instantiating (11) with fresh symbol all_41_0 gives: % 52.04/7.64 | (29) sdtasdt0(xr, all_41_0) = xk & aNaturalNumber0(all_41_0) = 0 & % 52.04/7.64 | $i(all_41_0) % 52.04/7.64 | % 52.04/7.64 | ALPHA: (29) implies: % 52.04/7.64 | (30) $i(all_41_0) % 52.04/7.64 | (31) sdtasdt0(xr, all_41_0) = xk % 52.04/7.64 | % 52.04/7.64 | DELTA: instantiating (6) with fresh symbol all_43_0 gives: % 52.04/7.64 | (32) sdtpldt0(xn, all_43_0) = xp & aNaturalNumber0(all_43_0) = 0 & % 52.04/7.64 | $i(all_43_0) % 52.04/7.64 | % 52.04/7.64 | ALPHA: (32) implies: % 52.04/7.64 | (33) $i(all_43_0) % 52.04/7.64 | (34) sdtpldt0(xn, all_43_0) = xp % 52.04/7.64 | % 52.04/7.64 | DELTA: instantiating (7) with fresh symbol all_45_0 gives: % 52.04/7.64 | (35) sdtpldt0(xm, all_45_0) = xp & aNaturalNumber0(all_45_0) = 0 & % 52.04/7.64 | $i(all_45_0) % 52.04/7.64 | % 52.04/7.64 | ALPHA: (35) implies: % 52.04/7.64 | (36) $i(all_45_0) % 52.04/7.64 | (37) sdtpldt0(xm, all_45_0) = xp % 52.04/7.64 | % 52.04/7.64 | DELTA: instantiating (16) with fresh symbol all_47_0 gives: % 52.04/7.64 | (38) sdtasdt0(xr, all_47_0) = xn & aNaturalNumber0(all_47_0) = 0 & % 52.04/7.64 | $i(all_47_0) % 52.04/7.64 | % 52.04/7.64 | ALPHA: (38) implies: % 52.04/7.64 | (39) $i(all_47_0) % 52.04/7.64 | (40) sdtasdt0(xr, all_47_0) = xn % 52.04/7.64 | % 52.04/7.64 | DELTA: instantiating (8) with fresh symbol all_49_0 gives: % 52.04/7.64 | (41) sdtsldt0(all_49_0, xp) = xk & sdtasdt0(xp, xk) = all_49_0 & % 52.04/7.64 | sdtasdt0(xn, xm) = all_49_0 & aNaturalNumber0(xk) = 0 & $i(all_49_0) % 52.04/7.65 | % 52.04/7.65 | ALPHA: (41) implies: % 52.04/7.65 | (42) sdtasdt0(xn, xm) = all_49_0 % 52.04/7.65 | (43) sdtasdt0(xp, xk) = all_49_0 % 52.04/7.65 | % 52.04/7.65 | DELTA: instantiating (12) with fresh symbol all_57_0 gives: % 52.04/7.65 | (44) doDivides0(xr, all_57_0) = 0 & sdtasdt0(xn, xm) = all_57_0 & % 52.04/7.65 | $i(all_57_0) & ? [v0: $i] : (sdtasdt0(xr, v0) = all_57_0 & % 52.04/7.65 | aNaturalNumber0(v0) = 0 & $i(v0)) & ? [v0: $i] : (sdtpldt0(xr, v0) % 52.04/7.65 | = xk & aNaturalNumber0(v0) = 0 & $i(v0)) % 52.04/7.65 | % 52.04/7.65 | ALPHA: (44) implies: % 52.04/7.65 | (45) sdtasdt0(xn, xm) = all_57_0 % 52.04/7.65 | (46) ? [v0: $i] : (sdtpldt0(xr, v0) = xk & aNaturalNumber0(v0) = 0 & % 52.04/7.65 | $i(v0)) % 52.04/7.65 | (47) ? [v0: $i] : (sdtasdt0(xr, v0) = all_57_0 & aNaturalNumber0(v0) = 0 & % 52.04/7.65 | $i(v0)) % 52.04/7.65 | % 52.04/7.65 | DELTA: instantiating (17) with fresh symbol all_59_0 gives: % 52.04/7.65 | (48) ~ (all_59_0 = xn) & sdtsldt0(xn, xr) = all_59_0 & % 52.04/7.65 | sdtlseqdt0(all_59_0, xn) = 0 & sdtasdt0(xr, all_59_0) = xn & % 52.04/7.65 | aNaturalNumber0(all_59_0) = 0 & $i(all_59_0) & ? [v0: $i] : % 52.04/7.65 | (sdtpldt0(all_59_0, v0) = xn & aNaturalNumber0(v0) = 0 & $i(v0)) % 52.04/7.65 | % 52.04/7.65 | ALPHA: (48) implies: % 52.04/7.65 | (49) ~ (all_59_0 = xn) % 52.04/7.65 | (50) aNaturalNumber0(all_59_0) = 0 % 52.04/7.65 | (51) sdtasdt0(xr, all_59_0) = xn % 52.04/7.65 | (52) sdtlseqdt0(all_59_0, xn) = 0 % 52.04/7.65 | (53) sdtsldt0(xn, xr) = all_59_0 % 52.04/7.65 | (54) ? [v0: $i] : (sdtpldt0(all_59_0, v0) = xn & aNaturalNumber0(v0) = 0 & % 52.04/7.65 | $i(v0)) % 52.04/7.65 | % 52.04/7.65 | DELTA: instantiating (14) with fresh symbols all_61_0, all_61_1 gives: % 52.04/7.65 | (55) doDivides0(xr, xm) = all_61_0 & doDivides0(xr, xn) = all_61_1 & % 52.04/7.65 | ((all_61_0 = 0 & ? [v0: $i] : (sdtasdt0(xr, v0) = xm & % 52.04/7.65 | aNaturalNumber0(v0) = 0 & $i(v0))) | (all_61_1 = 0 & ? [v0: $i] % 52.04/7.65 | : (sdtasdt0(xr, v0) = xn & aNaturalNumber0(v0) = 0 & $i(v0)))) % 52.04/7.65 | % 52.04/7.65 | ALPHA: (55) implies: % 52.04/7.65 | (56) doDivides0(xr, xn) = all_61_1 % 52.04/7.65 | % 52.04/7.65 | DELTA: instantiating (5) with fresh symbol all_63_0 gives: % 52.04/7.65 | (57) ~ (xp = sz10) & ~ (xp = sz00) & isPrime0(xp) = 0 & doDivides0(xp, % 52.04/7.65 | all_63_0) = 0 & sdtasdt0(xn, xm) = all_63_0 & $i(all_63_0) & ! [v0: % 52.04/7.65 | $i] : ! [v1: any] : (v0 = xp | v0 = sz10 | ~ (doDivides0(v0, xp) = % 52.04/7.65 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 52.04/7.65 | aNaturalNumber0(v0) = v2) | ( ~ (v1 = 0) & ! [v2: $i] : ( ~ % 52.04/7.65 | (sdtasdt0(v0, v2) = xp) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = % 52.04/7.65 | 0) & aNaturalNumber0(v2) = v3)))) & ? [v0: $i] : % 52.04/7.65 | (sdtasdt0(xp, v0) = all_63_0 & aNaturalNumber0(v0) = 0 & $i(v0)) % 52.04/7.65 | % 52.04/7.65 | ALPHA: (57) implies: % 52.04/7.65 | (58) ~ (xp = sz00) % 52.04/7.65 | (59) ~ (xp = sz10) % 52.04/7.65 | (60) sdtasdt0(xn, xm) = all_63_0 % 52.04/7.65 | % 52.04/7.65 | DELTA: instantiating (21) with fresh symbols all_66_0, all_66_1, all_66_2, % 52.04/7.65 | all_66_3, all_66_4, all_66_5, all_66_6, all_66_7, all_66_8, all_66_9, % 52.04/7.65 | all_66_10 gives: % 52.04/7.65 | (61) sdtsldt0(all_66_4, xr) = all_66_3 & sdtsldt0(xn, xr) = all_66_10 & % 52.04/7.65 | sdtasdt0(all_66_3, xr) = all_66_0 & sdtasdt0(all_66_7, xr) = all_66_6 % 52.04/7.65 | & sdtasdt0(all_66_10, xm) = all_66_7 & sdtasdt0(xr, all_66_3) = % 52.04/7.65 | all_66_1 & sdtasdt0(xr, all_66_10) = all_66_8 & sdtasdt0(xp, xk) = % 52.04/7.65 | all_66_4 & sdtasdt0(xn, xm) = all_66_5 & aNaturalNumber0(all_66_3) = % 52.04/7.65 | all_66_2 & aNaturalNumber0(all_66_10) = all_66_9 & $i(all_66_0) & % 52.04/7.65 | $i(all_66_1) & $i(all_66_3) & $i(all_66_4) & $i(all_66_5) & % 52.04/7.65 | $i(all_66_6) & $i(all_66_7) & $i(all_66_8) & $i(all_66_10) & % 52.04/7.65 | ((all_66_1 = all_66_4 & all_66_2 = 0 & ~ (all_66_0 = all_66_5)) | % 52.04/7.65 | (all_66_8 = xn & all_66_9 = 0 & ~ (all_66_5 = all_66_6))) % 52.04/7.65 | % 52.04/7.65 | ALPHA: (61) implies: % 52.04/7.65 | (62) $i(all_66_10) % 52.04/7.65 | (63) $i(all_66_8) % 52.04/7.65 | (64) $i(all_66_7) % 52.04/7.65 | (65) $i(all_66_3) % 52.04/7.65 | (66) aNaturalNumber0(all_66_10) = all_66_9 % 52.04/7.65 | (67) aNaturalNumber0(all_66_3) = all_66_2 % 52.04/7.65 | (68) sdtasdt0(xn, xm) = all_66_5 % 52.04/7.65 | (69) sdtasdt0(xp, xk) = all_66_4 % 52.04/7.65 | (70) sdtasdt0(xr, all_66_10) = all_66_8 % 52.04/7.66 | (71) sdtasdt0(xr, all_66_3) = all_66_1 % 52.04/7.66 | (72) sdtasdt0(all_66_10, xm) = all_66_7 % 52.04/7.66 | (73) sdtasdt0(all_66_7, xr) = all_66_6 % 52.04/7.66 | (74) sdtasdt0(all_66_3, xr) = all_66_0 % 52.04/7.66 | (75) sdtsldt0(xn, xr) = all_66_10 % 52.04/7.66 | (76) (all_66_1 = all_66_4 & all_66_2 = 0 & ~ (all_66_0 = all_66_5)) | % 52.04/7.66 | (all_66_8 = xn & all_66_9 = 0 & ~ (all_66_5 = all_66_6)) % 52.04/7.66 | % 52.04/7.66 | DELTA: instantiating (4) with fresh symbols all_68_0, all_68_1 gives: % 52.04/7.66 | (77) sdtpldt0(all_68_1, xp) = all_68_0 & sdtpldt0(xn, xm) = all_68_1 & % 52.04/7.66 | $i(all_68_0) & $i(all_68_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 52.04/7.66 | : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ % 52.04/7.66 | (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.04/7.66 | [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] % 52.04/7.66 | : ? [v10: any] : ? [v11: any] : ? [v12: any] : ? [v13: any] : % 52.04/7.66 | (isPrime0(v2) = v8 & doDivides0(v2, v9) = v10 & doDivides0(v2, v1) = % 52.04/7.66 | v13 & doDivides0(v2, v0) = v12 & iLess0(v4, all_68_0) = v11 & % 52.04/7.66 | sdtasdt0(v0, v1) = v9 & aNaturalNumber0(v2) = v7 & % 52.04/7.66 | aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & $i(v9) & ( ~ % 52.04/7.66 | (v11 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | (v13 = 0 & % 52.04/7.66 | ? [v14: $i] : (sdtasdt0(v2, v14) = v1 & aNaturalNumber0(v14) % 52.04/7.66 | = 0 & $i(v14))) | (v12 = 0 & ? [v14: $i] : (sdtasdt0(v2, % 52.04/7.66 | v14) = v0 & aNaturalNumber0(v14) = 0 & $i(v14))) | ( ~ % 52.04/7.66 | (v10 = 0) & ! [v14: $i] : ( ~ (sdtasdt0(v2, v14) = v9) | ~ % 52.04/7.66 | $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & % 52.04/7.66 | aNaturalNumber0(v14) = v15))) | ( ~ (v8 = 0) & (v2 = sz10 % 52.04/7.66 | | v2 = sz00 | ? [v14: $i] : ( ~ (v14 = v2) & ~ (v14 = % 52.04/7.66 | sz10) & doDivides0(v14, v2) = 0 & aNaturalNumber0(v14) = % 52.04/7.66 | 0 & $i(v14) & ? [v15: $i] : (sdtasdt0(v14, v15) = v2 & % 52.04/7.66 | aNaturalNumber0(v15) = 0 & $i(v15)))))))) % 52.04/7.66 | % 52.04/7.66 | ALPHA: (77) implies: % 52.04/7.66 | (78) sdtpldt0(xn, xm) = all_68_1 % 52.04/7.66 | (79) sdtpldt0(all_68_1, xp) = all_68_0 % 52.04/7.66 | (80) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 52.04/7.66 | ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | % 52.04/7.66 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : % 52.04/7.66 | ? [v8: any] : ? [v9: $i] : ? [v10: any] : ? [v11: any] : ? % 52.04/7.66 | [v12: any] : ? [v13: any] : (isPrime0(v2) = v8 & doDivides0(v2, v9) % 52.04/7.66 | = v10 & doDivides0(v2, v1) = v13 & doDivides0(v2, v0) = v12 & % 52.04/7.66 | iLess0(v4, all_68_0) = v11 & sdtasdt0(v0, v1) = v9 & % 52.04/7.66 | aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & % 52.04/7.66 | aNaturalNumber0(v0) = v5 & $i(v9) & ( ~ (v11 = 0) | ~ (v7 = 0) | % 52.04/7.66 | ~ (v6 = 0) | ~ (v5 = 0) | (v13 = 0 & ? [v14: $i] : % 52.04/7.66 | (sdtasdt0(v2, v14) = v1 & aNaturalNumber0(v14) = 0 & $i(v14))) % 52.04/7.66 | | (v12 = 0 & ? [v14: $i] : (sdtasdt0(v2, v14) = v0 & % 52.04/7.66 | aNaturalNumber0(v14) = 0 & $i(v14))) | ( ~ (v10 = 0) & ! % 52.04/7.66 | [v14: $i] : ( ~ (sdtasdt0(v2, v14) = v9) | ~ $i(v14) | ? % 52.04/7.66 | [v15: int] : ( ~ (v15 = 0) & aNaturalNumber0(v14) = v15))) | % 52.04/7.66 | ( ~ (v8 = 0) & (v2 = sz10 | v2 = sz00 | ? [v14: $i] : ( ~ (v14 % 52.04/7.66 | = v2) & ~ (v14 = sz10) & doDivides0(v14, v2) = 0 & % 52.04/7.66 | aNaturalNumber0(v14) = 0 & $i(v14) & ? [v15: $i] : % 52.04/7.66 | (sdtasdt0(v14, v15) = v2 & aNaturalNumber0(v15) = 0 & % 52.04/7.66 | $i(v15)))))))) % 52.04/7.66 | % 52.04/7.66 | DELTA: instantiating (46) with fresh symbol all_71_0 gives: % 52.04/7.66 | (81) sdtpldt0(xr, all_71_0) = xk & aNaturalNumber0(all_71_0) = 0 & % 52.04/7.66 | $i(all_71_0) % 52.04/7.66 | % 52.04/7.66 | ALPHA: (81) implies: % 52.04/7.66 | (82) $i(all_71_0) % 52.04/7.66 | (83) sdtpldt0(xr, all_71_0) = xk % 52.04/7.66 | % 52.04/7.66 | DELTA: instantiating (47) with fresh symbol all_73_0 gives: % 52.04/7.66 | (84) sdtasdt0(xr, all_73_0) = all_57_0 & aNaturalNumber0(all_73_0) = 0 & % 52.04/7.66 | $i(all_73_0) % 52.04/7.66 | % 52.04/7.66 | ALPHA: (84) implies: % 52.04/7.66 | (85) $i(all_73_0) % 52.04/7.66 | (86) sdtasdt0(xr, all_73_0) = all_57_0 % 52.04/7.66 | % 52.04/7.66 | DELTA: instantiating (54) with fresh symbol all_75_0 gives: % 52.04/7.66 | (87) sdtpldt0(all_59_0, all_75_0) = xn & aNaturalNumber0(all_75_0) = 0 & % 52.04/7.66 | $i(all_75_0) % 52.04/7.66 | % 52.04/7.66 | ALPHA: (87) implies: % 52.04/7.66 | (88) $i(all_75_0) % 52.04/7.66 | (89) sdtpldt0(all_59_0, all_75_0) = xn % 52.04/7.66 | % 52.04/7.66 | GROUND_INST: instantiating (23) with all_63_0, all_66_5, xm, xn, simplifying % 52.04/7.66 | with (60), (68) gives: % 52.04/7.66 | (90) all_66_5 = all_63_0 % 52.04/7.66 | % 52.04/7.66 | GROUND_INST: instantiating (23) with all_57_0, all_66_5, xm, xn, simplifying % 52.04/7.66 | with (45), (68) gives: % 52.04/7.66 | (91) all_66_5 = all_57_0 % 52.04/7.66 | % 52.04/7.67 | GROUND_INST: instantiating (23) with all_49_0, all_66_5, xm, xn, simplifying % 52.04/7.67 | with (42), (68) gives: % 52.04/7.67 | (92) all_66_5 = all_49_0 % 52.04/7.67 | % 52.04/7.67 | GROUND_INST: instantiating (23) with all_49_0, all_66_4, xk, xp, simplifying % 52.04/7.67 | with (43), (69) gives: % 52.04/7.67 | (93) all_66_4 = all_49_0 % 52.04/7.67 | % 52.04/7.67 | GROUND_INST: instantiating (24) with 0, all_61_1, xn, xr, simplifying with % 52.04/7.67 | (15), (56) gives: % 52.04/7.67 | (94) all_61_1 = 0 % 52.04/7.67 | % 52.04/7.67 | GROUND_INST: instantiating (25) with all_59_0, all_66_10, xr, xn, simplifying % 52.04/7.67 | with (53), (75) gives: % 52.04/7.67 | (95) all_66_10 = all_59_0 % 52.04/7.67 | % 52.04/7.67 | COMBINE_EQS: (90), (91) imply: % 52.04/7.67 | (96) all_63_0 = all_57_0 % 52.04/7.67 | % 52.04/7.67 | COMBINE_EQS: (90), (92) imply: % 52.04/7.67 | (97) all_63_0 = all_49_0 % 52.04/7.67 | % 52.04/7.67 | COMBINE_EQS: (96), (97) imply: % 52.04/7.67 | (98) all_57_0 = all_49_0 % 52.04/7.67 | % 52.04/7.67 | SIMP: (98) implies: % 52.04/7.67 | (99) all_57_0 = all_49_0 % 52.04/7.67 | % 52.04/7.67 | REDUCE: (72), (95) imply: % 52.04/7.67 | (100) sdtasdt0(all_59_0, xm) = all_66_7 % 52.04/7.67 | % 52.04/7.67 | REDUCE: (86), (99) imply: % 52.04/7.67 | (101) sdtasdt0(xr, all_73_0) = all_49_0 % 52.04/7.67 | % 52.04/7.67 | REDUCE: (70), (95) imply: % 52.04/7.67 | (102) sdtasdt0(xr, all_59_0) = all_66_8 % 52.04/7.67 | % 52.04/7.67 | REDUCE: (66), (95) imply: % 52.04/7.67 | (103) aNaturalNumber0(all_59_0) = all_66_9 % 52.04/7.67 | % 52.04/7.67 | REDUCE: (62), (95) imply: % 52.04/7.67 | (104) $i(all_59_0) % 52.04/7.67 | % 52.04/7.67 | GROUND_INST: instantiating (22) with 0, all_66_9, all_59_0, simplifying with % 52.04/7.67 | (50), (103) gives: % 52.04/7.67 | (105) all_66_9 = 0 % 52.04/7.67 | % 52.04/7.67 | GROUND_INST: instantiating (23) with xn, all_66_8, all_59_0, xr, simplifying % 52.04/7.67 | with (51), (102) gives: % 52.04/7.67 | (106) all_66_8 = xn % 52.04/7.67 | % 52.04/7.67 | REDUCE: (63), (106) imply: % 52.04/7.67 | (107) $i(xn) % 52.04/7.67 | % 52.04/7.67 | GROUND_INST: instantiating (1) with xp, simplifying with (3), (19) gives: % 52.04/7.67 | (108) xp = sz10 | xp = sz00 | ? [v0: $i] : (isPrime0(v0) = 0 & % 52.04/7.67 | doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0 & $i(v0)) % 52.04/7.67 | % 52.04/7.67 | GROUND_INST: instantiating (mAddComm) with xn, xm, all_68_1, simplifying with % 52.04/7.67 | (18), (78), (107) gives: % 52.04/7.67 | (109) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xm, xn) = v2 & % 52.04/7.67 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v2) & ( ~ % 52.04/7.67 | (v1 = 0) | ~ (v0 = 0) | v2 = all_68_1)) % 52.04/7.67 | % 52.04/7.67 | GROUND_INST: instantiating (mSortsB) with xn, xm, all_68_1, simplifying with % 52.04/7.67 | (18), (78), (107) gives: % 52.04/7.67 | (110) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 52.04/7.67 | (aNaturalNumber0(all_68_1) = v2 & aNaturalNumber0(xm) = v1 & % 52.04/7.67 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 52.04/7.67 | % 52.04/7.67 | GROUND_INST: instantiating (mAddComm) with xm, all_45_0, xp, simplifying with % 52.04/7.67 | (18), (36), (37) gives: % 52.04/7.67 | (111) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(all_45_0, xm) = % 52.04/7.67 | v2 & aNaturalNumber0(all_45_0) = v1 & aNaturalNumber0(xm) = v0 & % 52.04/7.67 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xp)) % 52.04/7.67 | % 52.04/7.67 | GROUND_INST: instantiating (80) with xr, all_71_0, all_39_0, xk, xp, % 52.04/7.67 | simplifying with (20), (27), (28), (82), (83) gives: % 52.04/7.67 | (112) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 52.04/7.67 | $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 52.04/7.67 | (isPrime0(all_39_0) = v3 & doDivides0(all_39_0, v4) = v5 & % 52.04/7.67 | doDivides0(all_39_0, all_71_0) = v8 & doDivides0(all_39_0, xr) = v7 % 52.04/7.67 | & iLess0(xp, all_68_0) = v6 & sdtasdt0(xr, all_71_0) = v4 & % 52.04/7.67 | aNaturalNumber0(all_71_0) = v1 & aNaturalNumber0(all_39_0) = v2 & % 52.04/7.67 | aNaturalNumber0(xr) = v0 & $i(v4) & ( ~ (v6 = 0) | ~ (v2 = 0) | ~ % 52.04/7.67 | (v1 = 0) | ~ (v0 = 0) | (v8 = 0 & ? [v9: $i] : % 52.04/7.67 | (sdtasdt0(all_39_0, v9) = all_71_0 & aNaturalNumber0(v9) = 0 & % 52.04/7.67 | $i(v9))) | (v7 = 0 & ? [v9: $i] : (sdtasdt0(all_39_0, v9) = % 52.04/7.67 | xr & aNaturalNumber0(v9) = 0 & $i(v9))) | ( ~ (v5 = 0) & ! % 52.04/7.67 | [v9: $i] : ( ~ (sdtasdt0(all_39_0, v9) = v4) | ~ $i(v9) | ? % 52.04/7.67 | [v10: int] : ( ~ (v10 = 0) & aNaturalNumber0(v9) = v10))) | ( % 52.04/7.67 | ~ (v3 = 0) & (all_39_0 = sz10 | all_39_0 = sz00 | ? [v9: any] % 52.04/7.67 | : ( ~ (v9 = all_39_0) & ~ (v9 = sz10) & doDivides0(v9, % 52.04/7.67 | all_39_0) = 0 & aNaturalNumber0(v9) = 0 & $i(v9) & ? % 52.04/7.67 | [v10: $i] : (sdtasdt0(v9, v10) = all_39_0 & % 52.04/7.67 | aNaturalNumber0(v10) = 0 & $i(v10))))))) % 52.04/7.67 | % 52.04/7.67 | GROUND_INST: instantiating (mAddAsso) with xr, all_71_0, all_39_0, xk, xp, % 52.04/7.67 | simplifying with (20), (27), (28), (82), (83) gives: % 52.04/7.67 | (113) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 52.04/7.67 | $i] : (sdtpldt0(all_71_0, all_39_0) = v3 & sdtpldt0(xr, v3) = v4 & % 52.04/7.67 | aNaturalNumber0(all_71_0) = v1 & aNaturalNumber0(all_39_0) = v2 & % 52.04/7.67 | aNaturalNumber0(xr) = v0 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 % 52.04/7.67 | = 0) | ~ (v0 = 0) | v4 = xp)) % 52.04/7.67 | % 52.04/7.68 | GROUND_INST: instantiating (mAddComm) with xr, all_71_0, xk, simplifying with % 52.04/7.68 | (20), (82), (83) gives: % 52.04/7.68 | (114) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(all_71_0, xr) = % 52.04/7.68 | v2 & aNaturalNumber0(all_71_0) = v1 & aNaturalNumber0(xr) = v0 & % 52.04/7.68 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xk)) % 52.04/7.68 | % 52.04/7.68 | GROUND_INST: instantiating (80) with all_59_0, all_75_0, all_43_0, xn, xp, % 52.04/7.68 | simplifying with (33), (34), (88), (89), (104) gives: % 52.04/7.68 | (115) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 52.04/7.68 | $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 52.04/7.68 | (isPrime0(all_43_0) = v3 & doDivides0(all_43_0, v4) = v5 & % 52.04/7.68 | doDivides0(all_43_0, all_75_0) = v8 & doDivides0(all_43_0, % 52.04/7.68 | all_59_0) = v7 & iLess0(xp, all_68_0) = v6 & sdtasdt0(all_59_0, % 52.04/7.68 | all_75_0) = v4 & aNaturalNumber0(all_75_0) = v1 & % 52.04/7.68 | aNaturalNumber0(all_59_0) = v0 & aNaturalNumber0(all_43_0) = v2 & % 52.04/7.68 | $i(v4) & ( ~ (v6 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | % 52.04/7.68 | (v8 = 0 & ? [v9: $i] : (sdtasdt0(all_43_0, v9) = all_75_0 & % 52.04/7.68 | aNaturalNumber0(v9) = 0 & $i(v9))) | (v7 = 0 & ? [v9: $i] : % 52.04/7.68 | (sdtasdt0(all_43_0, v9) = all_59_0 & aNaturalNumber0(v9) = 0 & % 52.04/7.68 | $i(v9))) | ( ~ (v5 = 0) & ! [v9: $i] : ( ~ % 52.04/7.68 | (sdtasdt0(all_43_0, v9) = v4) | ~ $i(v9) | ? [v10: int] : ( % 52.04/7.68 | ~ (v10 = 0) & aNaturalNumber0(v9) = v10))) | ( ~ (v3 = 0) & % 52.04/7.68 | (all_43_0 = sz10 | all_43_0 = sz00 | ? [v9: any] : ( ~ (v9 = % 52.04/7.68 | all_43_0) & ~ (v9 = sz10) & doDivides0(v9, all_43_0) = 0 % 52.04/7.68 | & aNaturalNumber0(v9) = 0 & $i(v9) & ? [v10: $i] : % 52.04/7.68 | (sdtasdt0(v9, v10) = all_43_0 & aNaturalNumber0(v10) = 0 & % 52.04/7.68 | $i(v10))))))) % 52.04/7.68 | % 52.04/7.68 | GROUND_INST: instantiating (mAddAsso) with all_59_0, all_75_0, all_43_0, xn, % 52.04/7.68 | xp, simplifying with (33), (34), (88), (89), (104) gives: % 52.04/7.68 | (116) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 52.04/7.68 | $i] : (sdtpldt0(all_75_0, all_43_0) = v3 & sdtpldt0(all_59_0, v3) = % 52.04/7.68 | v4 & aNaturalNumber0(all_75_0) = v1 & aNaturalNumber0(all_59_0) = % 52.04/7.68 | v0 & aNaturalNumber0(all_43_0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = % 52.04/7.68 | 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = xp)) % 52.04/7.68 | % 52.04/7.68 | GROUND_INST: instantiating (80) with all_59_0, all_75_0, xm, xn, all_68_1, % 52.04/7.68 | simplifying with (18), (78), (88), (89), (104) gives: % 52.04/7.68 | (117) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 52.04/7.68 | $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 52.04/7.68 | (isPrime0(xm) = v3 & doDivides0(xm, v4) = v5 & doDivides0(xm, % 52.04/7.68 | all_75_0) = v8 & doDivides0(xm, all_59_0) = v7 & iLess0(all_68_1, % 52.04/7.68 | all_68_0) = v6 & sdtasdt0(all_59_0, all_75_0) = v4 & % 52.04/7.68 | aNaturalNumber0(all_75_0) = v1 & aNaturalNumber0(all_59_0) = v0 & % 52.04/7.68 | aNaturalNumber0(xm) = v2 & $i(v4) & ( ~ (v6 = 0) | ~ (v2 = 0) | ~ % 52.04/7.68 | (v1 = 0) | ~ (v0 = 0) | (v8 = 0 & ? [v9: $i] : (sdtasdt0(xm, % 52.04/7.68 | v9) = all_75_0 & aNaturalNumber0(v9) = 0 & $i(v9))) | (v7 = % 52.04/7.68 | 0 & ? [v9: $i] : (sdtasdt0(xm, v9) = all_59_0 & % 52.04/7.68 | aNaturalNumber0(v9) = 0 & $i(v9))) | ( ~ (v5 = 0) & ! [v9: % 52.04/7.68 | $i] : ( ~ (sdtasdt0(xm, v9) = v4) | ~ $i(v9) | ? [v10: int] % 52.04/7.68 | : ( ~ (v10 = 0) & aNaturalNumber0(v9) = v10))) | ( ~ (v3 = 0) % 52.04/7.68 | & (xm = sz10 | xm = sz00 | ? [v9: $i] : ( ~ (v9 = xm) & ~ (v9 % 52.04/7.68 | = sz10) & doDivides0(v9, xm) = 0 & aNaturalNumber0(v9) = % 52.04/7.68 | 0 & $i(v9) & ? [v10: $i] : (sdtasdt0(v9, v10) = xm & % 52.04/7.68 | aNaturalNumber0(v10) = 0 & $i(v10))))))) % 52.04/7.68 | % 52.04/7.68 | GROUND_INST: instantiating (mAddAsso) with all_59_0, all_75_0, xm, xn, % 52.04/7.68 | all_68_1, simplifying with (18), (78), (88), (89), (104) gives: % 52.04/7.68 | (118) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 52.04/7.68 | $i] : (sdtpldt0(all_75_0, xm) = v3 & sdtpldt0(all_59_0, v3) = v4 & % 52.04/7.68 | aNaturalNumber0(all_75_0) = v1 & aNaturalNumber0(all_59_0) = v0 & % 52.04/7.68 | aNaturalNumber0(xm) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 % 52.04/7.68 | = 0) | ~ (v0 = 0) | v4 = all_68_1)) % 52.04/7.68 | % 52.04/7.68 | GROUND_INST: instantiating (mAddComm) with all_59_0, all_75_0, xn, simplifying % 52.04/7.68 | with (88), (89), (104) gives: % 52.04/7.68 | (119) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(all_75_0, % 52.04/7.68 | all_59_0) = v2 & aNaturalNumber0(all_75_0) = v1 & % 52.04/7.68 | aNaturalNumber0(all_59_0) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = % 52.04/7.68 | 0) | v2 = xn)) % 52.04/7.68 | % 52.04/7.68 | GROUND_INST: instantiating (80) with xn, xm, xp, all_68_1, all_68_0, % 52.04/7.68 | simplifying with (18), (19), (78), (79), (107) gives: % 52.04/7.69 | (120) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 52.04/7.69 | $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 52.04/7.69 | (isPrime0(xp) = v3 & doDivides0(xp, v4) = v5 & doDivides0(xp, xm) = % 52.04/7.69 | v8 & doDivides0(xp, xn) = v7 & iLess0(all_68_0, all_68_0) = v6 & % 52.04/7.69 | sdtasdt0(xn, xm) = v4 & aNaturalNumber0(xp) = v2 & % 52.04/7.69 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v4) & ( ~ % 52.04/7.69 | (v6 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v8 = 0 & ? % 52.04/7.69 | [v9: $i] : (sdtasdt0(xp, v9) = xm & aNaturalNumber0(v9) = 0 & % 52.04/7.69 | $i(v9))) | (v7 = 0 & ? [v9: $i] : (sdtasdt0(xp, v9) = xn & % 52.04/7.69 | aNaturalNumber0(v9) = 0 & $i(v9))) | ( ~ (v5 = 0) & ! [v9: % 52.04/7.69 | $i] : ( ~ (sdtasdt0(xp, v9) = v4) | ~ $i(v9) | ? [v10: int] % 52.04/7.69 | : ( ~ (v10 = 0) & aNaturalNumber0(v9) = v10))) | ( ~ (v3 = 0) % 52.04/7.69 | & (xp = sz10 | xp = sz00 | ? [v9: $i] : ( ~ (v9 = xp) & ~ (v9 % 52.04/7.69 | = sz10) & doDivides0(v9, xp) = 0 & aNaturalNumber0(v9) = % 52.04/7.69 | 0 & $i(v9) & ? [v10: $i] : (sdtasdt0(v9, v10) = xp & % 52.04/7.69 | aNaturalNumber0(v10) = 0 & $i(v10))))))) % 52.04/7.69 | % 52.04/7.69 | GROUND_INST: instantiating (mAddAsso) with xn, xm, xp, all_68_1, all_68_0, % 52.04/7.69 | simplifying with (18), (19), (78), (79), (107) gives: % 52.04/7.69 | (121) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 52.04/7.69 | $i] : (sdtpldt0(xm, xp) = v3 & sdtpldt0(xn, v3) = v4 & % 52.04/7.69 | aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & % 52.04/7.69 | aNaturalNumber0(xn) = v0 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 % 52.04/7.69 | = 0) | ~ (v0 = 0) | v4 = all_68_0)) % 52.04/7.69 | % 52.04/7.69 | GROUND_INST: instantiating (mMulComm) with xn, xm, all_49_0, simplifying with % 52.04/7.69 | (18), (42), (107) gives: % 52.04/7.69 | (122) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xm, xn) = v2 & % 52.04/7.69 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v2) & ( ~ % 52.04/7.69 | (v1 = 0) | ~ (v0 = 0) | v2 = all_49_0)) % 52.04/7.69 | % 52.04/7.69 | GROUND_INST: instantiating (mSortsB_02) with xn, xm, all_49_0, simplifying % 52.04/7.69 | with (18), (42), (107) gives: % 52.04/7.69 | (123) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 52.04/7.69 | (aNaturalNumber0(all_49_0) = v2 & aNaturalNumber0(xm) = v1 & % 52.04/7.69 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 52.04/7.69 | % 52.04/7.69 | GROUND_INST: instantiating (mMulComm) with xr, all_41_0, xk, simplifying with % 52.04/7.69 | (20), (30), (31) gives: % 52.04/7.69 | (124) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_41_0, xr) = % 52.04/7.69 | v2 & aNaturalNumber0(all_41_0) = v1 & aNaturalNumber0(xr) = v0 & % 52.04/7.69 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xk)) % 52.04/7.69 | % 52.04/7.69 | GROUND_INST: instantiating (mMulAsso) with xr, all_47_0, xm, xn, all_49_0, % 52.04/7.69 | simplifying with (18), (20), (39), (40), (42) gives: % 52.04/7.69 | (125) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 52.04/7.69 | $i] : (sdtasdt0(all_47_0, xm) = v3 & sdtasdt0(xr, v3) = v4 & % 52.04/7.69 | aNaturalNumber0(all_47_0) = v1 & aNaturalNumber0(xr) = v0 & % 52.04/7.69 | aNaturalNumber0(xm) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 % 52.04/7.69 | = 0) | ~ (v0 = 0) | v4 = all_49_0)) % 52.04/7.69 | % 52.04/7.69 | GROUND_INST: instantiating (mMulComm) with xr, all_47_0, xn, simplifying with % 52.04/7.69 | (20), (39), (40) gives: % 52.04/7.69 | (126) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_47_0, xr) = % 52.04/7.69 | v2 & aNaturalNumber0(all_47_0) = v1 & aNaturalNumber0(xr) = v0 & % 52.04/7.69 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xn)) % 52.04/7.69 | % 52.04/7.69 | GROUND_INST: instantiating (mMulAsso) with xr, all_59_0, xm, xn, all_49_0, % 52.04/7.69 | simplifying with (18), (20), (42), (51), (104) gives: % 52.04/7.69 | (127) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 52.04/7.69 | $i] : (sdtasdt0(all_59_0, xm) = v3 & sdtasdt0(xr, v3) = v4 & % 52.04/7.69 | aNaturalNumber0(all_59_0) = v1 & aNaturalNumber0(xr) = v0 & % 52.04/7.69 | aNaturalNumber0(xm) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 % 52.04/7.69 | = 0) | ~ (v0 = 0) | v4 = all_49_0)) % 52.04/7.69 | % 52.04/7.69 | GROUND_INST: instantiating (mMulComm) with xr, all_59_0, xn, simplifying with % 52.04/7.69 | (20), (51), (104) gives: % 52.04/7.69 | (128) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_59_0, xr) = % 52.04/7.69 | v2 & aNaturalNumber0(all_59_0) = v1 & aNaturalNumber0(xr) = v0 & % 52.04/7.69 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xn)) % 52.04/7.69 | % 52.04/7.69 | GROUND_INST: instantiating (mMulComm) with xr, all_66_3, all_66_1, simplifying % 52.04/7.69 | with (20), (65), (71) gives: % 52.04/7.69 | (129) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_66_3, xr) = % 52.04/7.69 | v2 & aNaturalNumber0(all_66_3) = v1 & aNaturalNumber0(xr) = v0 & % 52.04/7.69 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_66_1)) % 52.04/7.69 | % 52.04/7.69 | GROUND_INST: instantiating (mSortsB_02) with xr, all_66_3, all_66_1, % 52.04/7.69 | simplifying with (20), (65), (71) gives: % 52.04/7.69 | (130) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 52.04/7.69 | (aNaturalNumber0(all_66_1) = v2 & aNaturalNumber0(all_66_3) = v1 & % 52.04/7.69 | aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 52.04/7.69 | % 52.04/7.69 | GROUND_INST: instantiating (mMulComm) with xr, all_73_0, all_49_0, simplifying % 52.04/7.69 | with (20), (85), (101) gives: % 52.04/7.69 | (131) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_73_0, xr) = % 52.04/7.69 | v2 & aNaturalNumber0(all_73_0) = v1 & aNaturalNumber0(xr) = v0 & % 52.04/7.69 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_49_0)) % 52.04/7.69 | % 52.04/7.69 | GROUND_INST: instantiating (mSortsB_02) with xr, all_73_0, all_49_0, % 52.04/7.69 | simplifying with (20), (85), (101) gives: % 52.04/7.69 | (132) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 52.04/7.69 | (aNaturalNumber0(all_73_0) = v1 & aNaturalNumber0(all_49_0) = v2 & % 52.04/7.69 | aNaturalNumber0(xr) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 52.04/7.69 | % 52.04/7.69 | GROUND_INST: instantiating (mMulComm) with all_59_0, xm, all_66_7, simplifying % 52.04/7.69 | with (18), (100), (104) gives: % 52.04/7.69 | (133) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xm, all_59_0) = % 52.04/7.69 | v2 & aNaturalNumber0(all_59_0) = v0 & aNaturalNumber0(xm) = v1 & % 52.04/7.69 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_66_7)) % 52.04/7.69 | % 52.04/7.70 | GROUND_INST: instantiating (mSortsB_02) with all_59_0, xm, all_66_7, % 52.04/7.70 | simplifying with (18), (100), (104) gives: % 52.04/7.70 | (134) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 52.04/7.70 | (aNaturalNumber0(all_66_7) = v2 & aNaturalNumber0(all_59_0) = v0 & % 52.04/7.70 | aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 52.04/7.70 | % 52.04/7.70 | GROUND_INST: instantiating (mMulAsso) with all_59_0, xm, xr, all_66_7, % 52.04/7.70 | all_66_6, simplifying with (18), (20), (73), (100), (104) gives: % 52.04/7.70 | (135) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 52.04/7.70 | $i] : (sdtasdt0(all_59_0, v3) = v4 & sdtasdt0(xm, xr) = v3 & % 52.04/7.70 | aNaturalNumber0(all_59_0) = v0 & aNaturalNumber0(xr) = v2 & % 52.04/7.70 | aNaturalNumber0(xm) = v1 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 % 52.04/7.70 | = 0) | ~ (v0 = 0) | v4 = all_66_6)) % 52.04/7.70 | % 52.04/7.70 | GROUND_INST: instantiating (mMulComm) with all_66_7, xr, all_66_6, simplifying % 52.04/7.70 | with (20), (64), (73) gives: % 52.04/7.70 | (136) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xr, all_66_7) = % 52.04/7.70 | v2 & aNaturalNumber0(all_66_7) = v0 & aNaturalNumber0(xr) = v1 & % 52.04/7.70 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_66_6)) % 52.04/7.70 | % 52.04/7.70 | GROUND_INST: instantiating (mSortsB_02) with all_66_7, xr, all_66_6, % 52.04/7.70 | simplifying with (20), (64), (73) gives: % 52.04/7.70 | (137) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 52.04/7.70 | (aNaturalNumber0(all_66_6) = v2 & aNaturalNumber0(all_66_7) = v0 & % 52.04/7.70 | aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 52.04/7.70 | % 52.04/7.70 | GROUND_INST: instantiating (mMulComm) with all_66_3, xr, all_66_0, simplifying % 52.04/7.70 | with (20), (65), (74) gives: % 52.04/7.70 | (138) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xr, all_66_3) = % 52.04/7.70 | v2 & aNaturalNumber0(all_66_3) = v0 & aNaturalNumber0(xr) = v1 & % 52.04/7.70 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_66_0)) % 52.04/7.70 | % 52.04/7.70 | GROUND_INST: instantiating (mSortsB_02) with all_66_3, xr, all_66_0, % 52.04/7.70 | simplifying with (20), (65), (74) gives: % 52.04/7.70 | (139) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 52.04/7.70 | (aNaturalNumber0(all_66_0) = v2 & aNaturalNumber0(all_66_3) = v0 & % 52.04/7.70 | aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 52.04/7.70 | % 52.04/7.70 | GROUND_INST: instantiating (mLEAsym) with all_59_0, xn, simplifying with (52), % 52.04/7.70 | (104), (107) gives: % 52.04/7.70 | (140) all_59_0 = xn | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 52.04/7.70 | (sdtlseqdt0(xn, all_59_0) = v2 & aNaturalNumber0(all_59_0) = v0 & % 52.04/7.70 | aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 52.04/7.70 | 0))) % 52.04/7.70 | % 52.04/7.70 | GROUND_INST: instantiating (mDivMin) with xr, all_59_0, all_75_0, xn, % 52.04/7.70 | simplifying with (15), (20), (88), (89), (104) gives: % 52.04/7.70 | (141) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 52.04/7.70 | any] : (doDivides0(xr, all_75_0) = v4 & doDivides0(xr, all_59_0) = % 52.04/7.70 | v3 & aNaturalNumber0(all_75_0) = v2 & aNaturalNumber0(all_59_0) = % 52.04/7.70 | v1 & aNaturalNumber0(xr) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 % 52.04/7.70 | = 0) | ~ (v0 = 0) | v4 = 0)) % 52.04/7.70 | % 52.04/7.70 | GROUND_INST: instantiating (mDivMin) with xr, xr, all_71_0, xk, simplifying % 52.04/7.70 | with (10), (20), (82), (83) gives: % 52.04/7.70 | (142) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 52.04/7.70 | any] : (doDivides0(xr, all_71_0) = v4 & doDivides0(xr, xr) = v3 & % 52.04/7.70 | aNaturalNumber0(all_71_0) = v2 & aNaturalNumber0(xr) = v1 & % 52.04/7.70 | aNaturalNumber0(xr) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) % 52.04/7.70 | | ~ (v0 = 0) | v4 = 0)) % 52.04/7.70 | % 52.04/7.70 | DELTA: instantiating (139) with fresh symbols all_92_0, all_92_1, all_92_2 % 52.04/7.70 | gives: % 52.04/7.70 | (143) aNaturalNumber0(all_66_0) = all_92_0 & aNaturalNumber0(all_66_3) = % 52.04/7.70 | all_92_2 & aNaturalNumber0(xr) = all_92_1 & ( ~ (all_92_1 = 0) | ~ % 52.04/7.70 | (all_92_2 = 0) | all_92_0 = 0) % 52.04/7.70 | % 52.04/7.70 | ALPHA: (143) implies: % 52.04/7.70 | (144) aNaturalNumber0(xr) = all_92_1 % 52.04/7.70 | % 52.04/7.70 | DELTA: instantiating (123) with fresh symbols all_98_0, all_98_1, all_98_2 % 52.04/7.70 | gives: % 52.04/7.70 | (145) aNaturalNumber0(all_49_0) = all_98_0 & aNaturalNumber0(xm) = all_98_1 % 52.04/7.70 | & aNaturalNumber0(xn) = all_98_2 & ( ~ (all_98_1 = 0) | ~ (all_98_2 % 52.04/7.70 | = 0) | all_98_0 = 0) % 52.04/7.70 | % 52.04/7.70 | ALPHA: (145) implies: % 52.04/7.70 | (146) aNaturalNumber0(xm) = all_98_1 % 52.04/7.70 | % 52.04/7.70 | DELTA: instantiating (137) with fresh symbols all_100_0, all_100_1, all_100_2 % 52.04/7.70 | gives: % 52.04/7.70 | (147) aNaturalNumber0(all_66_6) = all_100_0 & aNaturalNumber0(all_66_7) = % 52.04/7.70 | all_100_2 & aNaturalNumber0(xr) = all_100_1 & ( ~ (all_100_1 = 0) | % 52.04/7.70 | ~ (all_100_2 = 0) | all_100_0 = 0) % 52.04/7.70 | % 52.04/7.70 | ALPHA: (147) implies: % 52.04/7.70 | (148) aNaturalNumber0(xr) = all_100_1 % 52.04/7.70 | (149) aNaturalNumber0(all_66_7) = all_100_2 % 52.04/7.70 | % 52.04/7.70 | DELTA: instantiating (134) with fresh symbols all_102_0, all_102_1, all_102_2 % 52.04/7.70 | gives: % 52.04/7.70 | (150) aNaturalNumber0(all_66_7) = all_102_0 & aNaturalNumber0(all_59_0) = % 52.04/7.70 | all_102_2 & aNaturalNumber0(xm) = all_102_1 & ( ~ (all_102_1 = 0) | % 52.04/7.70 | ~ (all_102_2 = 0) | all_102_0 = 0) % 52.04/7.70 | % 52.04/7.70 | ALPHA: (150) implies: % 52.04/7.70 | (151) aNaturalNumber0(xm) = all_102_1 % 52.04/7.70 | (152) aNaturalNumber0(all_59_0) = all_102_2 % 52.04/7.70 | (153) aNaturalNumber0(all_66_7) = all_102_0 % 52.04/7.70 | (154) ~ (all_102_1 = 0) | ~ (all_102_2 = 0) | all_102_0 = 0 % 52.04/7.70 | % 52.04/7.70 | DELTA: instantiating (110) with fresh symbols all_106_0, all_106_1, all_106_2 % 52.04/7.70 | gives: % 52.04/7.70 | (155) aNaturalNumber0(all_68_1) = all_106_0 & aNaturalNumber0(xm) = % 52.04/7.70 | all_106_1 & aNaturalNumber0(xn) = all_106_2 & ( ~ (all_106_1 = 0) | % 52.04/7.70 | ~ (all_106_2 = 0) | all_106_0 = 0) % 52.04/7.70 | % 52.04/7.70 | ALPHA: (155) implies: % 52.04/7.70 | (156) aNaturalNumber0(xm) = all_106_1 % 52.04/7.70 | % 52.04/7.70 | DELTA: instantiating (132) with fresh symbols all_108_0, all_108_1, all_108_2 % 52.04/7.70 | gives: % 52.04/7.70 | (157) aNaturalNumber0(all_73_0) = all_108_1 & aNaturalNumber0(all_49_0) = % 52.04/7.70 | all_108_0 & aNaturalNumber0(xr) = all_108_2 & ( ~ (all_108_1 = 0) | % 52.04/7.70 | ~ (all_108_2 = 0) | all_108_0 = 0) % 52.04/7.70 | % 52.04/7.70 | ALPHA: (157) implies: % 52.04/7.71 | (158) aNaturalNumber0(xr) = all_108_2 % 52.04/7.71 | % 52.04/7.71 | DELTA: instantiating (130) with fresh symbols all_110_0, all_110_1, all_110_2 % 52.04/7.71 | gives: % 52.04/7.71 | (159) aNaturalNumber0(all_66_1) = all_110_0 & aNaturalNumber0(all_66_3) = % 52.04/7.71 | all_110_1 & aNaturalNumber0(xr) = all_110_2 & ( ~ (all_110_1 = 0) | % 52.04/7.71 | ~ (all_110_2 = 0) | all_110_0 = 0) % 52.04/7.71 | % 52.04/7.71 | ALPHA: (159) implies: % 52.04/7.71 | (160) aNaturalNumber0(xr) = all_110_2 % 52.04/7.71 | % 52.04/7.71 | DELTA: instantiating (119) with fresh symbols all_112_0, all_112_1, all_112_2 % 52.04/7.71 | gives: % 52.04/7.71 | (161) sdtpldt0(all_75_0, all_59_0) = all_112_0 & aNaturalNumber0(all_75_0) % 52.04/7.71 | = all_112_1 & aNaturalNumber0(all_59_0) = all_112_2 & $i(all_112_0) & % 52.04/7.71 | ( ~ (all_112_1 = 0) | ~ (all_112_2 = 0) | all_112_0 = xn) % 52.04/7.71 | % 52.04/7.71 | ALPHA: (161) implies: % 52.04/7.71 | (162) aNaturalNumber0(all_59_0) = all_112_2 % 52.04/7.71 | % 52.04/7.71 | DELTA: instantiating (114) with fresh symbols all_114_0, all_114_1, all_114_2 % 52.04/7.71 | gives: % 52.04/7.71 | (163) sdtpldt0(all_71_0, xr) = all_114_0 & aNaturalNumber0(all_71_0) = % 52.04/7.71 | all_114_1 & aNaturalNumber0(xr) = all_114_2 & $i(all_114_0) & ( ~ % 52.04/7.71 | (all_114_1 = 0) | ~ (all_114_2 = 0) | all_114_0 = xk) % 52.04/7.71 | % 52.04/7.71 | ALPHA: (163) implies: % 52.04/7.71 | (164) aNaturalNumber0(xr) = all_114_2 % 52.04/7.71 | % 52.04/7.71 | DELTA: instantiating (109) with fresh symbols all_116_0, all_116_1, all_116_2 % 52.04/7.71 | gives: % 52.04/7.71 | (165) sdtpldt0(xm, xn) = all_116_0 & aNaturalNumber0(xm) = all_116_1 & % 52.04/7.71 | aNaturalNumber0(xn) = all_116_2 & $i(all_116_0) & ( ~ (all_116_1 = 0) % 52.04/7.71 | | ~ (all_116_2 = 0) | all_116_0 = all_68_1) % 52.04/7.71 | % 52.04/7.71 | ALPHA: (165) implies: % 52.04/7.71 | (166) aNaturalNumber0(xm) = all_116_1 % 52.04/7.71 | % 52.04/7.71 | DELTA: instantiating (138) with fresh symbols all_118_0, all_118_1, all_118_2 % 52.04/7.71 | gives: % 52.04/7.71 | (167) sdtasdt0(xr, all_66_3) = all_118_0 & aNaturalNumber0(all_66_3) = % 52.04/7.71 | all_118_2 & aNaturalNumber0(xr) = all_118_1 & $i(all_118_0) & ( ~ % 52.04/7.71 | (all_118_1 = 0) | ~ (all_118_2 = 0) | all_118_0 = all_66_0) % 52.04/7.71 | % 52.04/7.71 | ALPHA: (167) implies: % 52.04/7.71 | (168) aNaturalNumber0(xr) = all_118_1 % 52.04/7.71 | (169) aNaturalNumber0(all_66_3) = all_118_2 % 52.04/7.71 | (170) sdtasdt0(xr, all_66_3) = all_118_0 % 52.04/7.71 | (171) ~ (all_118_1 = 0) | ~ (all_118_2 = 0) | all_118_0 = all_66_0 % 52.04/7.71 | % 52.04/7.71 | DELTA: instantiating (122) with fresh symbols all_120_0, all_120_1, all_120_2 % 52.04/7.71 | gives: % 52.04/7.71 | (172) sdtasdt0(xm, xn) = all_120_0 & aNaturalNumber0(xm) = all_120_1 & % 52.04/7.71 | aNaturalNumber0(xn) = all_120_2 & $i(all_120_0) & ( ~ (all_120_1 = 0) % 52.04/7.71 | | ~ (all_120_2 = 0) | all_120_0 = all_49_0) % 52.04/7.71 | % 52.04/7.71 | ALPHA: (172) implies: % 52.04/7.71 | (173) aNaturalNumber0(xm) = all_120_1 % 52.04/7.71 | % 52.04/7.71 | DELTA: instantiating (129) with fresh symbols all_122_0, all_122_1, all_122_2 % 52.04/7.71 | gives: % 52.04/7.71 | (174) sdtasdt0(all_66_3, xr) = all_122_0 & aNaturalNumber0(all_66_3) = % 52.04/7.71 | all_122_1 & aNaturalNumber0(xr) = all_122_2 & $i(all_122_0) & ( ~ % 52.04/7.71 | (all_122_1 = 0) | ~ (all_122_2 = 0) | all_122_0 = all_66_1) % 52.04/7.71 | % 52.04/7.71 | ALPHA: (174) implies: % 52.04/7.71 | (175) aNaturalNumber0(xr) = all_122_2 % 52.04/7.71 | % 52.04/7.71 | DELTA: instantiating (128) with fresh symbols all_124_0, all_124_1, all_124_2 % 52.04/7.71 | gives: % 52.04/7.71 | (176) sdtasdt0(all_59_0, xr) = all_124_0 & aNaturalNumber0(all_59_0) = % 52.04/7.71 | all_124_1 & aNaturalNumber0(xr) = all_124_2 & $i(all_124_0) & ( ~ % 52.04/7.71 | (all_124_1 = 0) | ~ (all_124_2 = 0) | all_124_0 = xn) % 52.04/7.71 | % 52.04/7.71 | ALPHA: (176) implies: % 52.04/7.71 | (177) aNaturalNumber0(xr) = all_124_2 % 52.04/7.71 | (178) aNaturalNumber0(all_59_0) = all_124_1 % 52.04/7.71 | % 52.04/7.71 | DELTA: instantiating (126) with fresh symbols all_128_0, all_128_1, all_128_2 % 52.04/7.71 | gives: % 52.04/7.71 | (179) sdtasdt0(all_47_0, xr) = all_128_0 & aNaturalNumber0(all_47_0) = % 52.04/7.71 | all_128_1 & aNaturalNumber0(xr) = all_128_2 & $i(all_128_0) & ( ~ % 52.04/7.71 | (all_128_1 = 0) | ~ (all_128_2 = 0) | all_128_0 = xn) % 52.04/7.71 | % 52.04/7.71 | ALPHA: (179) implies: % 52.04/7.71 | (180) aNaturalNumber0(xr) = all_128_2 % 52.04/7.71 | % 52.04/7.71 | DELTA: instantiating (124) with fresh symbols all_130_0, all_130_1, all_130_2 % 52.04/7.71 | gives: % 52.04/7.71 | (181) sdtasdt0(all_41_0, xr) = all_130_0 & aNaturalNumber0(all_41_0) = % 52.04/7.71 | all_130_1 & aNaturalNumber0(xr) = all_130_2 & $i(all_130_0) & ( ~ % 52.04/7.71 | (all_130_1 = 0) | ~ (all_130_2 = 0) | all_130_0 = xk) % 52.04/7.71 | % 52.04/7.71 | ALPHA: (181) implies: % 52.04/7.71 | (182) aNaturalNumber0(xr) = all_130_2 % 52.04/7.71 | % 52.04/7.71 | DELTA: instantiating (131) with fresh symbols all_140_0, all_140_1, all_140_2 % 52.04/7.71 | gives: % 52.39/7.71 | (183) sdtasdt0(all_73_0, xr) = all_140_0 & aNaturalNumber0(all_73_0) = % 52.39/7.71 | all_140_1 & aNaturalNumber0(xr) = all_140_2 & $i(all_140_0) & ( ~ % 52.39/7.71 | (all_140_1 = 0) | ~ (all_140_2 = 0) | all_140_0 = all_49_0) % 52.39/7.71 | % 52.39/7.71 | ALPHA: (183) implies: % 52.39/7.71 | (184) aNaturalNumber0(xr) = all_140_2 % 52.39/7.71 | % 52.39/7.71 | DELTA: instantiating (136) with fresh symbols all_142_0, all_142_1, all_142_2 % 52.39/7.71 | gives: % 52.39/7.71 | (185) sdtasdt0(xr, all_66_7) = all_142_0 & aNaturalNumber0(all_66_7) = % 52.39/7.71 | all_142_2 & aNaturalNumber0(xr) = all_142_1 & $i(all_142_0) & ( ~ % 52.39/7.71 | (all_142_1 = 0) | ~ (all_142_2 = 0) | all_142_0 = all_66_6) % 52.39/7.71 | % 52.39/7.71 | ALPHA: (185) implies: % 52.39/7.71 | (186) aNaturalNumber0(xr) = all_142_1 % 52.39/7.71 | (187) aNaturalNumber0(all_66_7) = all_142_2 % 52.39/7.71 | (188) sdtasdt0(xr, all_66_7) = all_142_0 % 52.39/7.71 | (189) ~ (all_142_1 = 0) | ~ (all_142_2 = 0) | all_142_0 = all_66_6 % 52.39/7.71 | % 52.39/7.71 | DELTA: instantiating (133) with fresh symbols all_144_0, all_144_1, all_144_2 % 52.39/7.71 | gives: % 52.39/7.71 | (190) sdtasdt0(xm, all_59_0) = all_144_0 & aNaturalNumber0(all_59_0) = % 52.39/7.71 | all_144_2 & aNaturalNumber0(xm) = all_144_1 & $i(all_144_0) & ( ~ % 52.39/7.71 | (all_144_1 = 0) | ~ (all_144_2 = 0) | all_144_0 = all_66_7) % 52.39/7.71 | % 52.39/7.71 | ALPHA: (190) implies: % 52.39/7.71 | (191) aNaturalNumber0(xm) = all_144_1 % 52.39/7.71 | (192) aNaturalNumber0(all_59_0) = all_144_2 % 52.39/7.71 | % 52.39/7.71 | DELTA: instantiating (111) with fresh symbols all_146_0, all_146_1, all_146_2 % 52.39/7.71 | gives: % 52.39/7.71 | (193) sdtpldt0(all_45_0, xm) = all_146_0 & aNaturalNumber0(all_45_0) = % 52.39/7.71 | all_146_1 & aNaturalNumber0(xm) = all_146_2 & $i(all_146_0) & ( ~ % 52.39/7.71 | (all_146_1 = 0) | ~ (all_146_2 = 0) | all_146_0 = xp) % 52.39/7.71 | % 52.39/7.71 | ALPHA: (193) implies: % 52.39/7.71 | (194) aNaturalNumber0(xm) = all_146_2 % 52.39/7.71 | % 52.39/7.71 | DELTA: instantiating (142) with fresh symbols all_148_0, all_148_1, all_148_2, % 52.39/7.71 | all_148_3, all_148_4 gives: % 52.39/7.71 | (195) doDivides0(xr, all_71_0) = all_148_0 & doDivides0(xr, xr) = all_148_1 % 52.39/7.71 | & aNaturalNumber0(all_71_0) = all_148_2 & aNaturalNumber0(xr) = % 52.39/7.71 | all_148_3 & aNaturalNumber0(xr) = all_148_4 & ( ~ (all_148_1 = 0) | % 52.39/7.71 | ~ (all_148_2 = 0) | ~ (all_148_3 = 0) | ~ (all_148_4 = 0) | % 52.39/7.71 | all_148_0 = 0) % 52.39/7.71 | % 52.39/7.71 | ALPHA: (195) implies: % 52.39/7.71 | (196) aNaturalNumber0(xr) = all_148_4 % 52.39/7.71 | (197) aNaturalNumber0(xr) = all_148_3 % 52.39/7.71 | % 52.39/7.71 | DELTA: instantiating (141) with fresh symbols all_150_0, all_150_1, all_150_2, % 52.39/7.71 | all_150_3, all_150_4 gives: % 52.39/7.72 | (198) doDivides0(xr, all_75_0) = all_150_0 & doDivides0(xr, all_59_0) = % 52.39/7.72 | all_150_1 & aNaturalNumber0(all_75_0) = all_150_2 & % 52.39/7.72 | aNaturalNumber0(all_59_0) = all_150_3 & aNaturalNumber0(xr) = % 52.39/7.72 | all_150_4 & ( ~ (all_150_1 = 0) | ~ (all_150_2 = 0) | ~ (all_150_3 % 52.39/7.72 | = 0) | ~ (all_150_4 = 0) | all_150_0 = 0) % 52.39/7.72 | % 52.39/7.72 | ALPHA: (198) implies: % 52.39/7.72 | (199) aNaturalNumber0(xr) = all_150_4 % 52.39/7.72 | (200) aNaturalNumber0(all_59_0) = all_150_3 % 52.39/7.72 | % 52.39/7.72 | DELTA: instantiating (127) with fresh symbols all_152_0, all_152_1, all_152_2, % 52.39/7.72 | all_152_3, all_152_4 gives: % 52.39/7.72 | (201) sdtasdt0(all_59_0, xm) = all_152_1 & sdtasdt0(xr, all_152_1) = % 52.39/7.72 | all_152_0 & aNaturalNumber0(all_59_0) = all_152_3 & % 52.39/7.72 | aNaturalNumber0(xr) = all_152_4 & aNaturalNumber0(xm) = all_152_2 & % 52.39/7.72 | $i(all_152_0) & $i(all_152_1) & ( ~ (all_152_2 = 0) | ~ (all_152_3 = % 52.39/7.72 | 0) | ~ (all_152_4 = 0) | all_152_0 = all_49_0) % 52.39/7.72 | % 52.39/7.72 | ALPHA: (201) implies: % 52.39/7.72 | (202) aNaturalNumber0(xm) = all_152_2 % 52.39/7.72 | (203) aNaturalNumber0(xr) = all_152_4 % 52.39/7.72 | (204) aNaturalNumber0(all_59_0) = all_152_3 % 52.39/7.72 | (205) sdtasdt0(xr, all_152_1) = all_152_0 % 52.39/7.72 | (206) sdtasdt0(all_59_0, xm) = all_152_1 % 52.39/7.72 | (207) ~ (all_152_2 = 0) | ~ (all_152_3 = 0) | ~ (all_152_4 = 0) | % 52.39/7.72 | all_152_0 = all_49_0 % 52.39/7.72 | % 52.39/7.72 | DELTA: instantiating (118) with fresh symbols all_154_0, all_154_1, all_154_2, % 52.39/7.72 | all_154_3, all_154_4 gives: % 52.39/7.72 | (208) sdtpldt0(all_75_0, xm) = all_154_1 & sdtpldt0(all_59_0, all_154_1) = % 52.39/7.72 | all_154_0 & aNaturalNumber0(all_75_0) = all_154_3 & % 52.39/7.72 | aNaturalNumber0(all_59_0) = all_154_4 & aNaturalNumber0(xm) = % 52.39/7.72 | all_154_2 & $i(all_154_0) & $i(all_154_1) & ( ~ (all_154_2 = 0) | ~ % 52.39/7.72 | (all_154_3 = 0) | ~ (all_154_4 = 0) | all_154_0 = all_68_1) % 52.39/7.72 | % 52.39/7.72 | ALPHA: (208) implies: % 52.39/7.72 | (209) aNaturalNumber0(xm) = all_154_2 % 52.39/7.72 | (210) aNaturalNumber0(all_59_0) = all_154_4 % 52.39/7.72 | % 52.39/7.72 | DELTA: instantiating (121) with fresh symbols all_156_0, all_156_1, all_156_2, % 52.39/7.72 | all_156_3, all_156_4 gives: % 52.39/7.72 | (211) sdtpldt0(xm, xp) = all_156_1 & sdtpldt0(xn, all_156_1) = all_156_0 & % 52.39/7.72 | aNaturalNumber0(xp) = all_156_2 & aNaturalNumber0(xm) = all_156_3 & % 52.39/7.72 | aNaturalNumber0(xn) = all_156_4 & $i(all_156_0) & $i(all_156_1) & ( ~ % 52.39/7.72 | (all_156_2 = 0) | ~ (all_156_3 = 0) | ~ (all_156_4 = 0) | % 52.39/7.72 | all_156_0 = all_68_0) % 52.39/7.72 | % 52.39/7.72 | ALPHA: (211) implies: % 52.39/7.72 | (212) aNaturalNumber0(xm) = all_156_3 % 52.39/7.72 | % 52.39/7.72 | DELTA: instantiating (113) with fresh symbols all_158_0, all_158_1, all_158_2, % 52.39/7.72 | all_158_3, all_158_4 gives: % 52.39/7.72 | (213) sdtpldt0(all_71_0, all_39_0) = all_158_1 & sdtpldt0(xr, all_158_1) = % 52.39/7.72 | all_158_0 & aNaturalNumber0(all_71_0) = all_158_3 & % 52.39/7.72 | aNaturalNumber0(all_39_0) = all_158_2 & aNaturalNumber0(xr) = % 52.39/7.72 | all_158_4 & $i(all_158_0) & $i(all_158_1) & ( ~ (all_158_2 = 0) | ~ % 52.39/7.72 | (all_158_3 = 0) | ~ (all_158_4 = 0) | all_158_0 = xp) % 52.39/7.72 | % 52.39/7.72 | ALPHA: (213) implies: % 52.39/7.72 | (214) aNaturalNumber0(xr) = all_158_4 % 52.39/7.72 | % 52.39/7.72 | DELTA: instantiating (116) with fresh symbols all_160_0, all_160_1, all_160_2, % 52.39/7.72 | all_160_3, all_160_4 gives: % 52.39/7.72 | (215) sdtpldt0(all_75_0, all_43_0) = all_160_1 & sdtpldt0(all_59_0, % 52.39/7.72 | all_160_1) = all_160_0 & aNaturalNumber0(all_75_0) = all_160_3 & % 52.39/7.72 | aNaturalNumber0(all_59_0) = all_160_4 & aNaturalNumber0(all_43_0) = % 52.39/7.72 | all_160_2 & $i(all_160_0) & $i(all_160_1) & ( ~ (all_160_2 = 0) | ~ % 52.39/7.72 | (all_160_3 = 0) | ~ (all_160_4 = 0) | all_160_0 = xp) % 52.39/7.72 | % 52.39/7.72 | ALPHA: (215) implies: % 52.39/7.72 | (216) aNaturalNumber0(all_59_0) = all_160_4 % 52.39/7.72 | % 52.39/7.72 | DELTA: instantiating (135) with fresh symbols all_162_0, all_162_1, all_162_2, % 52.39/7.72 | all_162_3, all_162_4 gives: % 52.39/7.72 | (217) sdtasdt0(all_59_0, all_162_1) = all_162_0 & sdtasdt0(xm, xr) = % 52.39/7.72 | all_162_1 & aNaturalNumber0(all_59_0) = all_162_4 & % 52.39/7.72 | aNaturalNumber0(xr) = all_162_2 & aNaturalNumber0(xm) = all_162_3 & % 52.39/7.72 | $i(all_162_0) & $i(all_162_1) & ( ~ (all_162_2 = 0) | ~ (all_162_3 = % 52.39/7.72 | 0) | ~ (all_162_4 = 0) | all_162_0 = all_66_6) % 52.39/7.72 | % 52.39/7.72 | ALPHA: (217) implies: % 52.39/7.72 | (218) aNaturalNumber0(xm) = all_162_3 % 52.39/7.72 | (219) aNaturalNumber0(xr) = all_162_2 % 52.39/7.72 | (220) aNaturalNumber0(all_59_0) = all_162_4 % 52.39/7.72 | % 52.39/7.72 | DELTA: instantiating (125) with fresh symbols all_164_0, all_164_1, all_164_2, % 52.39/7.72 | all_164_3, all_164_4 gives: % 52.39/7.72 | (221) sdtasdt0(all_47_0, xm) = all_164_1 & sdtasdt0(xr, all_164_1) = % 52.39/7.72 | all_164_0 & aNaturalNumber0(all_47_0) = all_164_3 & % 52.39/7.72 | aNaturalNumber0(xr) = all_164_4 & aNaturalNumber0(xm) = all_164_2 & % 52.39/7.72 | $i(all_164_0) & $i(all_164_1) & ( ~ (all_164_2 = 0) | ~ (all_164_3 = % 52.39/7.72 | 0) | ~ (all_164_4 = 0) | all_164_0 = all_49_0) % 52.39/7.72 | % 52.39/7.72 | ALPHA: (221) implies: % 52.39/7.72 | (222) aNaturalNumber0(xm) = all_164_2 % 52.39/7.72 | (223) aNaturalNumber0(xr) = all_164_4 % 52.39/7.72 | % 52.39/7.72 | DELTA: instantiating (112) with fresh symbols all_166_0, all_166_1, all_166_2, % 52.39/7.72 | all_166_3, all_166_4, all_166_5, all_166_6, all_166_7, all_166_8 gives: % 52.39/7.72 | (224) isPrime0(all_39_0) = all_166_5 & doDivides0(all_39_0, all_166_4) = % 52.39/7.72 | all_166_3 & doDivides0(all_39_0, all_71_0) = all_166_0 & % 52.39/7.72 | doDivides0(all_39_0, xr) = all_166_1 & iLess0(xp, all_68_0) = % 52.39/7.72 | all_166_2 & sdtasdt0(xr, all_71_0) = all_166_4 & % 52.39/7.72 | aNaturalNumber0(all_71_0) = all_166_7 & aNaturalNumber0(all_39_0) = % 52.39/7.72 | all_166_6 & aNaturalNumber0(xr) = all_166_8 & $i(all_166_4) & ( ~ % 52.39/7.72 | (all_166_2 = 0) | ~ (all_166_6 = 0) | ~ (all_166_7 = 0) | ~ % 52.39/7.72 | (all_166_8 = 0) | (all_166_0 = 0 & ? [v0: $i] : % 52.39/7.72 | (sdtasdt0(all_39_0, v0) = all_71_0 & aNaturalNumber0(v0) = 0 & % 52.39/7.72 | $i(v0))) | (all_166_1 = 0 & ? [v0: $i] : (sdtasdt0(all_39_0, % 52.39/7.72 | v0) = xr & aNaturalNumber0(v0) = 0 & $i(v0))) | ( ~ % 52.39/7.72 | (all_166_3 = 0) & ! [v0: $i] : ( ~ (sdtasdt0(all_39_0, v0) = % 52.39/7.72 | all_166_4) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 52.39/7.72 | aNaturalNumber0(v0) = v1))) | ( ~ (all_166_5 = 0) & (all_39_0 % 52.39/7.72 | = sz10 | all_39_0 = sz00 | ? [v0: any] : ( ~ (v0 = all_39_0) & % 52.39/7.72 | ~ (v0 = sz10) & doDivides0(v0, all_39_0) = 0 & % 52.39/7.72 | aNaturalNumber0(v0) = 0 & $i(v0) & ? [v1: $i] : % 52.39/7.72 | (sdtasdt0(v0, v1) = all_39_0 & aNaturalNumber0(v1) = 0 & % 52.39/7.72 | $i(v1)))))) % 52.39/7.72 | % 52.39/7.72 | ALPHA: (224) implies: % 52.39/7.72 | (225) aNaturalNumber0(xr) = all_166_8 % 52.39/7.72 | % 52.39/7.72 | DELTA: instantiating (115) with fresh symbols all_168_0, all_168_1, all_168_2, % 52.39/7.72 | all_168_3, all_168_4, all_168_5, all_168_6, all_168_7, all_168_8 gives: % 52.39/7.73 | (226) isPrime0(all_43_0) = all_168_5 & doDivides0(all_43_0, all_168_4) = % 52.39/7.73 | all_168_3 & doDivides0(all_43_0, all_75_0) = all_168_0 & % 52.39/7.73 | doDivides0(all_43_0, all_59_0) = all_168_1 & iLess0(xp, all_68_0) = % 52.39/7.73 | all_168_2 & sdtasdt0(all_59_0, all_75_0) = all_168_4 & % 52.39/7.73 | aNaturalNumber0(all_75_0) = all_168_7 & aNaturalNumber0(all_59_0) = % 52.39/7.73 | all_168_8 & aNaturalNumber0(all_43_0) = all_168_6 & $i(all_168_4) & ( % 52.39/7.73 | ~ (all_168_2 = 0) | ~ (all_168_6 = 0) | ~ (all_168_7 = 0) | ~ % 52.39/7.73 | (all_168_8 = 0) | (all_168_0 = 0 & ? [v0: $i] : % 52.39/7.73 | (sdtasdt0(all_43_0, v0) = all_75_0 & aNaturalNumber0(v0) = 0 & % 52.39/7.73 | $i(v0))) | (all_168_1 = 0 & ? [v0: $i] : (sdtasdt0(all_43_0, % 52.39/7.73 | v0) = all_59_0 & aNaturalNumber0(v0) = 0 & $i(v0))) | ( ~ % 52.39/7.73 | (all_168_3 = 0) & ! [v0: $i] : ( ~ (sdtasdt0(all_43_0, v0) = % 52.39/7.73 | all_168_4) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 52.39/7.73 | aNaturalNumber0(v0) = v1))) | ( ~ (all_168_5 = 0) & (all_43_0 % 52.39/7.73 | = sz10 | all_43_0 = sz00 | ? [v0: any] : ( ~ (v0 = all_43_0) & % 52.39/7.73 | ~ (v0 = sz10) & doDivides0(v0, all_43_0) = 0 & % 52.39/7.73 | aNaturalNumber0(v0) = 0 & $i(v0) & ? [v1: $i] : % 52.39/7.73 | (sdtasdt0(v0, v1) = all_43_0 & aNaturalNumber0(v1) = 0 & % 52.39/7.73 | $i(v1)))))) % 52.39/7.73 | % 52.39/7.73 | ALPHA: (226) implies: % 52.39/7.73 | (227) aNaturalNumber0(all_59_0) = all_168_8 % 52.39/7.73 | % 52.39/7.73 | DELTA: instantiating (117) with fresh symbols all_170_0, all_170_1, all_170_2, % 52.39/7.73 | all_170_3, all_170_4, all_170_5, all_170_6, all_170_7, all_170_8 gives: % 52.39/7.73 | (228) isPrime0(xm) = all_170_5 & doDivides0(xm, all_170_4) = all_170_3 & % 52.39/7.73 | doDivides0(xm, all_75_0) = all_170_0 & doDivides0(xm, all_59_0) = % 52.39/7.73 | all_170_1 & iLess0(all_68_1, all_68_0) = all_170_2 & % 52.39/7.73 | sdtasdt0(all_59_0, all_75_0) = all_170_4 & aNaturalNumber0(all_75_0) % 52.39/7.73 | = all_170_7 & aNaturalNumber0(all_59_0) = all_170_8 & % 52.39/7.73 | aNaturalNumber0(xm) = all_170_6 & $i(all_170_4) & ( ~ (all_170_2 = 0) % 52.39/7.73 | | ~ (all_170_6 = 0) | ~ (all_170_7 = 0) | ~ (all_170_8 = 0) | % 52.39/7.73 | (all_170_0 = 0 & ? [v0: $i] : (sdtasdt0(xm, v0) = all_75_0 & % 52.39/7.73 | aNaturalNumber0(v0) = 0 & $i(v0))) | (all_170_1 = 0 & ? [v0: % 52.39/7.73 | $i] : (sdtasdt0(xm, v0) = all_59_0 & aNaturalNumber0(v0) = 0 & % 52.39/7.73 | $i(v0))) | ( ~ (all_170_3 = 0) & ! [v0: $i] : ( ~ % 52.39/7.73 | (sdtasdt0(xm, v0) = all_170_4) | ~ $i(v0) | ? [v1: int] : ( ~ % 52.39/7.73 | (v1 = 0) & aNaturalNumber0(v0) = v1))) | ( ~ (all_170_5 = 0) % 52.39/7.73 | & (xm = sz10 | xm = sz00 | ? [v0: $i] : ( ~ (v0 = xm) & ~ (v0 = % 52.39/7.73 | sz10) & doDivides0(v0, xm) = 0 & aNaturalNumber0(v0) = 0 & % 52.39/7.73 | $i(v0) & ? [v1: $i] : (sdtasdt0(v0, v1) = xm & % 52.39/7.73 | aNaturalNumber0(v1) = 0 & $i(v1)))))) % 52.39/7.73 | % 52.39/7.73 | ALPHA: (228) implies: % 52.39/7.73 | (229) aNaturalNumber0(xm) = all_170_6 % 52.39/7.73 | (230) aNaturalNumber0(all_59_0) = all_170_8 % 52.39/7.73 | % 52.39/7.73 | DELTA: instantiating (120) with fresh symbols all_172_0, all_172_1, all_172_2, % 52.39/7.73 | all_172_3, all_172_4, all_172_5, all_172_6, all_172_7, all_172_8 gives: % 52.39/7.73 | (231) isPrime0(xp) = all_172_5 & doDivides0(xp, all_172_4) = all_172_3 & % 52.39/7.73 | doDivides0(xp, xm) = all_172_0 & doDivides0(xp, xn) = all_172_1 & % 52.39/7.73 | iLess0(all_68_0, all_68_0) = all_172_2 & sdtasdt0(xn, xm) = all_172_4 % 52.39/7.73 | & aNaturalNumber0(xp) = all_172_6 & aNaturalNumber0(xm) = all_172_7 & % 52.39/7.73 | aNaturalNumber0(xn) = all_172_8 & $i(all_172_4) & ( ~ (all_172_2 = 0) % 52.39/7.73 | | ~ (all_172_6 = 0) | ~ (all_172_7 = 0) | ~ (all_172_8 = 0) | % 52.39/7.73 | (all_172_0 = 0 & ? [v0: $i] : (sdtasdt0(xp, v0) = xm & % 52.39/7.73 | aNaturalNumber0(v0) = 0 & $i(v0))) | (all_172_1 = 0 & ? [v0: % 52.39/7.73 | $i] : (sdtasdt0(xp, v0) = xn & aNaturalNumber0(v0) = 0 & % 52.39/7.73 | $i(v0))) | ( ~ (all_172_3 = 0) & ! [v0: $i] : ( ~ % 52.39/7.73 | (sdtasdt0(xp, v0) = all_172_4) | ~ $i(v0) | ? [v1: int] : ( ~ % 52.39/7.73 | (v1 = 0) & aNaturalNumber0(v0) = v1))) | ( ~ (all_172_5 = 0) % 52.39/7.73 | & (xp = sz10 | xp = sz00 | ? [v0: $i] : ( ~ (v0 = xp) & ~ (v0 = % 52.39/7.73 | sz10) & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0 & % 52.39/7.73 | $i(v0) & ? [v1: $i] : (sdtasdt0(v0, v1) = xp & % 52.39/7.73 | aNaturalNumber0(v1) = 0 & $i(v1)))))) % 52.39/7.73 | % 52.39/7.73 | ALPHA: (231) implies: % 52.39/7.73 | (232) aNaturalNumber0(xm) = all_172_7 % 52.39/7.73 | % 52.39/7.73 | BETA: splitting (140) gives: % 52.39/7.73 | % 52.39/7.73 | Case 1: % 52.39/7.73 | | % 52.39/7.73 | | (233) all_59_0 = xn % 52.39/7.73 | | % 52.39/7.73 | | REDUCE: (49), (233) imply: % 52.39/7.73 | | (234) $false % 52.39/7.73 | | % 52.39/7.73 | | CLOSE: (234) is inconsistent. % 52.39/7.73 | | % 52.39/7.73 | Case 2: % 52.39/7.73 | | % 52.39/7.73 | | (235) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(xn, % 52.39/7.73 | | all_59_0) = v2 & aNaturalNumber0(all_59_0) = v0 & % 52.39/7.73 | | aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 52.39/7.73 | | 0))) % 52.39/7.73 | | % 52.39/7.73 | | DELTA: instantiating (235) with fresh symbols all_194_0, all_194_1, % 52.39/7.73 | | all_194_2 gives: % 52.39/7.73 | | (236) sdtlseqdt0(xn, all_59_0) = all_194_0 & aNaturalNumber0(all_59_0) = % 52.39/7.73 | | all_194_2 & aNaturalNumber0(xn) = all_194_1 & ( ~ (all_194_0 = 0) | % 52.39/7.73 | | ~ (all_194_1 = 0) | ~ (all_194_2 = 0)) % 52.39/7.73 | | % 52.39/7.73 | | ALPHA: (236) implies: % 52.39/7.73 | | (237) aNaturalNumber0(all_59_0) = all_194_2 % 52.39/7.73 | | % 52.39/7.73 | | BETA: splitting (108) gives: % 52.39/7.73 | | % 52.39/7.73 | | Case 1: % 52.39/7.73 | | | % 52.39/7.73 | | | (238) xp = sz00 % 52.39/7.73 | | | % 52.39/7.73 | | | REDUCE: (58), (238) imply: % 52.39/7.73 | | | (239) $false % 52.39/7.73 | | | % 52.39/7.73 | | | CLOSE: (239) is inconsistent. % 52.39/7.73 | | | % 52.39/7.73 | | Case 2: % 52.39/7.73 | | | % 52.39/7.73 | | | (240) xp = sz10 | ? [v0: $i] : (isPrime0(v0) = 0 & doDivides0(v0, xp) % 52.39/7.73 | | | = 0 & aNaturalNumber0(v0) = 0 & $i(v0)) % 52.39/7.73 | | | % 52.39/7.73 | | | BETA: splitting (240) gives: % 52.39/7.73 | | | % 52.39/7.73 | | | Case 1: % 52.39/7.73 | | | | % 52.39/7.73 | | | | (241) xp = sz10 % 52.39/7.73 | | | | % 52.39/7.73 | | | | REDUCE: (59), (241) imply: % 52.39/7.73 | | | | (242) $false % 52.39/7.73 | | | | % 52.39/7.73 | | | | CLOSE: (242) is inconsistent. % 52.39/7.73 | | | | % 52.39/7.73 | | | Case 2: % 52.39/7.73 | | | | % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with 0, all_106_1, xm, simplifying with % 52.39/7.74 | | | | (2), (156) gives: % 52.39/7.74 | | | | (243) all_106_1 = 0 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_98_1, all_106_1, xm, % 52.39/7.74 | | | | simplifying with (146), (156) gives: % 52.39/7.74 | | | | (244) all_106_1 = all_98_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_106_1, all_120_1, xm, % 52.39/7.74 | | | | simplifying with (156), (173) gives: % 52.39/7.74 | | | | (245) all_120_1 = all_106_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_102_1, all_120_1, xm, % 52.39/7.74 | | | | simplifying with (151), (173) gives: % 52.39/7.74 | | | | (246) all_120_1 = all_102_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_120_1, all_146_2, xm, % 52.39/7.74 | | | | simplifying with (173), (194) gives: % 52.39/7.74 | | | | (247) all_146_2 = all_120_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_146_2, all_152_2, xm, % 52.39/7.74 | | | | simplifying with (194), (202) gives: % 52.39/7.74 | | | | (248) all_152_2 = all_146_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_144_1, all_152_2, xm, % 52.39/7.74 | | | | simplifying with (191), (202) gives: % 52.39/7.74 | | | | (249) all_152_2 = all_144_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_146_2, all_154_2, xm, % 52.39/7.74 | | | | simplifying with (194), (209) gives: % 52.39/7.74 | | | | (250) all_154_2 = all_146_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_154_2, all_156_3, xm, % 52.39/7.74 | | | | simplifying with (209), (212) gives: % 52.39/7.74 | | | | (251) all_156_3 = all_154_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_156_3, all_162_3, xm, % 52.39/7.74 | | | | simplifying with (212), (218) gives: % 52.39/7.74 | | | | (252) all_162_3 = all_156_3 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_162_3, all_164_2, xm, % 52.39/7.74 | | | | simplifying with (218), (222) gives: % 52.39/7.74 | | | | (253) all_164_2 = all_162_3 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_164_2, all_170_6, xm, % 52.39/7.74 | | | | simplifying with (222), (229) gives: % 52.39/7.74 | | | | (254) all_170_6 = all_164_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_170_6, all_172_7, xm, % 52.39/7.74 | | | | simplifying with (229), (232) gives: % 52.39/7.74 | | | | (255) all_172_7 = all_170_6 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_116_1, all_172_7, xm, % 52.39/7.74 | | | | simplifying with (166), (232) gives: % 52.39/7.74 | | | | (256) all_172_7 = all_116_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with 0, all_100_1, xr, simplifying with % 52.39/7.74 | | | | (9), (148) gives: % 52.39/7.74 | | | | (257) all_100_1 = 0 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_110_2, all_118_1, xr, % 52.39/7.74 | | | | simplifying with (160), (168) gives: % 52.39/7.74 | | | | (258) all_118_1 = all_110_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_118_1, all_124_2, xr, % 52.39/7.74 | | | | simplifying with (168), (177) gives: % 52.39/7.74 | | | | (259) all_124_2 = all_118_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_128_2, all_130_2, xr, % 52.39/7.74 | | | | simplifying with (180), (182) gives: % 52.39/7.74 | | | | (260) all_130_2 = all_128_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_110_2, all_140_2, xr, % 52.39/7.74 | | | | simplifying with (160), (184) gives: % 52.39/7.74 | | | | (261) all_140_2 = all_110_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_108_2, all_140_2, xr, % 52.39/7.74 | | | | simplifying with (158), (184) gives: % 52.39/7.74 | | | | (262) all_140_2 = all_108_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_100_1, all_140_2, xr, % 52.39/7.74 | | | | simplifying with (148), (184) gives: % 52.39/7.74 | | | | (263) all_140_2 = all_100_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_124_2, all_142_1, xr, % 52.39/7.74 | | | | simplifying with (177), (186) gives: % 52.39/7.74 | | | | (264) all_142_1 = all_124_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_114_2, all_142_1, xr, % 52.39/7.74 | | | | simplifying with (164), (186) gives: % 52.39/7.74 | | | | (265) all_142_1 = all_114_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_130_2, all_148_4, xr, % 52.39/7.74 | | | | simplifying with (182), (196) gives: % 52.39/7.74 | | | | (266) all_148_4 = all_130_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_148_4, all_148_3, xr, % 52.39/7.74 | | | | simplifying with (196), (197) gives: % 52.39/7.74 | | | | (267) all_148_3 = all_148_4 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_148_3, all_150_4, xr, % 52.39/7.74 | | | | simplifying with (197), (199) gives: % 52.39/7.74 | | | | (268) all_150_4 = all_148_3 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_150_4, all_152_4, xr, % 52.39/7.74 | | | | simplifying with (199), (203) gives: % 52.39/7.74 | | | | (269) all_152_4 = all_150_4 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_152_4, all_158_4, xr, % 52.39/7.74 | | | | simplifying with (203), (214) gives: % 52.39/7.74 | | | | (270) all_158_4 = all_152_4 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_162_2, all_164_4, xr, % 52.39/7.74 | | | | simplifying with (219), (223) gives: % 52.39/7.74 | | | | (271) all_164_4 = all_162_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_158_4, all_164_4, xr, % 52.39/7.74 | | | | simplifying with (214), (223) gives: % 52.39/7.74 | | | | (272) all_164_4 = all_158_4 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_92_1, all_164_4, xr, % 52.39/7.74 | | | | simplifying with (144), (223) gives: % 52.39/7.74 | | | | (273) all_164_4 = all_92_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_128_2, all_166_8, xr, % 52.39/7.74 | | | | simplifying with (180), (225) gives: % 52.39/7.74 | | | | (274) all_166_8 = all_128_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_122_2, all_166_8, xr, % 52.39/7.74 | | | | simplifying with (175), (225) gives: % 52.39/7.74 | | | | (275) all_166_8 = all_122_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_118_1, all_166_8, xr, % 52.39/7.74 | | | | simplifying with (168), (225) gives: % 52.39/7.74 | | | | (276) all_166_8 = all_118_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_102_2, all_112_2, all_59_0, % 52.39/7.74 | | | | simplifying with (152), (162) gives: % 52.39/7.74 | | | | (277) all_112_2 = all_102_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_150_3, all_160_4, all_59_0, % 52.39/7.74 | | | | simplifying with (200), (216) gives: % 52.39/7.74 | | | | (278) all_160_4 = all_150_3 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_150_3, all_162_4, all_59_0, % 52.39/7.74 | | | | simplifying with (200), (220) gives: % 52.39/7.74 | | | | (279) all_162_4 = all_150_3 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_144_2, all_162_4, all_59_0, % 52.39/7.74 | | | | simplifying with (192), (220) gives: % 52.39/7.74 | | | | (280) all_162_4 = all_144_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_162_4, all_168_8, all_59_0, % 52.39/7.74 | | | | simplifying with (220), (227) gives: % 52.39/7.74 | | | | (281) all_168_8 = all_162_4 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_154_4, all_168_8, all_59_0, % 52.39/7.74 | | | | simplifying with (210), (227) gives: % 52.39/7.74 | | | | (282) all_168_8 = all_154_4 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_152_3, all_170_8, all_59_0, % 52.39/7.74 | | | | simplifying with (204), (230) gives: % 52.39/7.74 | | | | (283) all_170_8 = all_152_3 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_150_3, all_170_8, all_59_0, % 52.39/7.74 | | | | simplifying with (200), (230) gives: % 52.39/7.74 | | | | (284) all_170_8 = all_150_3 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_124_1, all_170_8, all_59_0, % 52.39/7.74 | | | | simplifying with (178), (230) gives: % 52.39/7.74 | | | | (285) all_170_8 = all_124_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_112_2, all_170_8, all_59_0, % 52.39/7.74 | | | | simplifying with (162), (230) gives: % 52.39/7.74 | | | | (286) all_170_8 = all_112_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with 0, all_194_2, all_59_0, simplifying % 52.39/7.74 | | | | with (50), (237) gives: % 52.39/7.74 | | | | (287) all_194_2 = 0 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_160_4, all_194_2, all_59_0, % 52.39/7.74 | | | | simplifying with (216), (237) gives: % 52.39/7.74 | | | | (288) all_194_2 = all_160_4 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_102_0, all_142_2, all_66_7, % 52.39/7.74 | | | | simplifying with (153), (187) gives: % 52.39/7.74 | | | | (289) all_142_2 = all_102_0 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_100_2, all_142_2, all_66_7, % 52.39/7.74 | | | | simplifying with (149), (187) gives: % 52.39/7.74 | | | | (290) all_142_2 = all_100_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (22) with all_66_2, all_118_2, all_66_3, % 52.39/7.74 | | | | simplifying with (67), (169) gives: % 52.39/7.74 | | | | (291) all_118_2 = all_66_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (23) with all_66_1, all_118_0, all_66_3, xr, % 52.39/7.74 | | | | simplifying with (71), (170) gives: % 52.39/7.74 | | | | (292) all_118_0 = all_66_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | GROUND_INST: instantiating (23) with all_66_7, all_152_1, xm, all_59_0, % 52.39/7.74 | | | | simplifying with (100), (206) gives: % 52.39/7.74 | | | | (293) all_152_1 = all_66_7 % 52.39/7.74 | | | | % 52.39/7.74 | | | | COMBINE_EQS: (287), (288) imply: % 52.39/7.74 | | | | (294) all_160_4 = 0 % 52.39/7.74 | | | | % 52.39/7.74 | | | | SIMP: (294) implies: % 52.39/7.74 | | | | (295) all_160_4 = 0 % 52.39/7.74 | | | | % 52.39/7.74 | | | | COMBINE_EQS: (255), (256) imply: % 52.39/7.74 | | | | (296) all_170_6 = all_116_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | SIMP: (296) implies: % 52.39/7.74 | | | | (297) all_170_6 = all_116_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | COMBINE_EQS: (254), (297) imply: % 52.39/7.74 | | | | (298) all_164_2 = all_116_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | SIMP: (298) implies: % 52.39/7.74 | | | | (299) all_164_2 = all_116_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | COMBINE_EQS: (283), (284) imply: % 52.39/7.74 | | | | (300) all_152_3 = all_150_3 % 52.39/7.74 | | | | % 52.39/7.74 | | | | COMBINE_EQS: (283), (285) imply: % 52.39/7.74 | | | | (301) all_152_3 = all_124_1 % 52.39/7.74 | | | | % 52.39/7.74 | | | | COMBINE_EQS: (283), (286) imply: % 52.39/7.74 | | | | (302) all_152_3 = all_112_2 % 52.39/7.74 | | | | % 52.39/7.74 | | | | COMBINE_EQS: (281), (282) imply: % 52.39/7.74 | | | | (303) all_162_4 = all_154_4 % 52.39/7.74 | | | | % 52.39/7.74 | | | | SIMP: (303) implies: % 52.39/7.74 | | | | (304) all_162_4 = all_154_4 % 52.39/7.74 | | | | % 52.39/7.74 | | | | COMBINE_EQS: (275), (276) imply: % 52.39/7.75 | | | | (305) all_122_2 = all_118_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (274), (275) imply: % 52.39/7.75 | | | | (306) all_128_2 = all_122_2 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (306) implies: % 52.39/7.75 | | | | (307) all_128_2 = all_122_2 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (253), (299) imply: % 52.39/7.75 | | | | (308) all_162_3 = all_116_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (308) implies: % 52.39/7.75 | | | | (309) all_162_3 = all_116_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (271), (273) imply: % 52.39/7.75 | | | | (310) all_162_2 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (271), (272) imply: % 52.39/7.75 | | | | (311) all_162_2 = all_158_4 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (310), (311) imply: % 52.39/7.75 | | | | (312) all_158_4 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (312) implies: % 52.39/7.75 | | | | (313) all_158_4 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (252), (309) imply: % 52.39/7.75 | | | | (314) all_156_3 = all_116_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (314) implies: % 52.39/7.75 | | | | (315) all_156_3 = all_116_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (280), (304) imply: % 52.39/7.75 | | | | (316) all_154_4 = all_144_2 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (279), (304) imply: % 52.39/7.75 | | | | (317) all_154_4 = all_150_3 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (278), (295) imply: % 52.39/7.75 | | | | (318) all_150_3 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (318) implies: % 52.39/7.75 | | | | (319) all_150_3 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (270), (313) imply: % 52.39/7.75 | | | | (320) all_152_4 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (320) implies: % 52.39/7.75 | | | | (321) all_152_4 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (251), (315) imply: % 52.39/7.75 | | | | (322) all_154_2 = all_116_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (322) implies: % 52.39/7.75 | | | | (323) all_154_2 = all_116_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (250), (323) imply: % 52.39/7.75 | | | | (324) all_146_2 = all_116_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (324) implies: % 52.39/7.75 | | | | (325) all_146_2 = all_116_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (316), (317) imply: % 52.39/7.75 | | | | (326) all_150_3 = all_144_2 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (326) implies: % 52.39/7.75 | | | | (327) all_150_3 = all_144_2 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (248), (249) imply: % 52.39/7.75 | | | | (328) all_146_2 = all_144_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (328) implies: % 52.39/7.75 | | | | (329) all_146_2 = all_144_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (300), (301) imply: % 52.39/7.75 | | | | (330) all_150_3 = all_124_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (330) implies: % 52.39/7.75 | | | | (331) all_150_3 = all_124_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (301), (302) imply: % 52.39/7.75 | | | | (332) all_124_1 = all_112_2 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (269), (321) imply: % 52.39/7.75 | | | | (333) all_150_4 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (333) implies: % 52.39/7.75 | | | | (334) all_150_4 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (319), (327) imply: % 52.39/7.75 | | | | (335) all_144_2 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (327), (331) imply: % 52.39/7.75 | | | | (336) all_144_2 = all_124_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (268), (334) imply: % 52.39/7.75 | | | | (337) all_148_3 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (337) implies: % 52.39/7.75 | | | | (338) all_148_3 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (267), (338) imply: % 52.39/7.75 | | | | (339) all_148_4 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (339) implies: % 52.39/7.75 | | | | (340) all_148_4 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (266), (340) imply: % 52.39/7.75 | | | | (341) all_130_2 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (341) implies: % 52.39/7.75 | | | | (342) all_130_2 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (247), (329) imply: % 52.39/7.75 | | | | (343) all_144_1 = all_120_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (325), (329) imply: % 52.39/7.75 | | | | (344) all_144_1 = all_116_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (343), (344) imply: % 52.39/7.75 | | | | (345) all_120_1 = all_116_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (345) implies: % 52.39/7.75 | | | | (346) all_120_1 = all_116_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (335), (336) imply: % 52.39/7.75 | | | | (347) all_124_1 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (347) implies: % 52.39/7.75 | | | | (348) all_124_1 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (264), (265) imply: % 52.39/7.75 | | | | (349) all_124_2 = all_114_2 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (349) implies: % 52.39/7.75 | | | | (350) all_124_2 = all_114_2 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (289), (290) imply: % 52.39/7.75 | | | | (351) all_102_0 = all_100_2 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (261), (262) imply: % 52.39/7.75 | | | | (352) all_110_2 = all_108_2 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (352) implies: % 52.39/7.75 | | | | (353) all_110_2 = all_108_2 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (262), (263) imply: % 52.39/7.75 | | | | (354) all_108_2 = all_100_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (260), (342) imply: % 52.39/7.75 | | | | (355) all_128_2 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (355) implies: % 52.39/7.75 | | | | (356) all_128_2 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (307), (356) imply: % 52.39/7.75 | | | | (357) all_122_2 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (357) implies: % 52.39/7.75 | | | | (358) all_122_2 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (332), (348) imply: % 52.39/7.75 | | | | (359) all_112_2 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (359) implies: % 52.39/7.75 | | | | (360) all_112_2 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (259), (350) imply: % 52.39/7.75 | | | | (361) all_118_1 = all_114_2 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (361) implies: % 52.39/7.75 | | | | (362) all_118_1 = all_114_2 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (305), (358) imply: % 52.39/7.75 | | | | (363) all_118_1 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (363) implies: % 52.39/7.75 | | | | (364) all_118_1 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (246), (346) imply: % 52.39/7.75 | | | | (365) all_116_1 = all_102_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (245), (346) imply: % 52.39/7.75 | | | | (366) all_116_1 = all_106_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (258), (362) imply: % 52.39/7.75 | | | | (367) all_114_2 = all_110_2 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (362), (364) imply: % 52.39/7.75 | | | | (368) all_114_2 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (365), (366) imply: % 52.39/7.75 | | | | (369) all_106_1 = all_102_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (369) implies: % 52.39/7.75 | | | | (370) all_106_1 = all_102_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (367), (368) imply: % 52.39/7.75 | | | | (371) all_110_2 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (371) implies: % 52.39/7.75 | | | | (372) all_110_2 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (277), (360) imply: % 52.39/7.75 | | | | (373) all_102_2 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (373) implies: % 52.39/7.75 | | | | (374) all_102_2 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (353), (372) imply: % 52.39/7.75 | | | | (375) all_108_2 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (375) implies: % 52.39/7.75 | | | | (376) all_108_2 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (354), (376) imply: % 52.39/7.75 | | | | (377) all_100_1 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | SIMP: (377) implies: % 52.39/7.75 | | | | (378) all_100_1 = all_92_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (244), (370) imply: % 52.39/7.75 | | | | (379) all_102_1 = all_98_1 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (243), (370) imply: % 52.39/7.75 | | | | (380) all_102_1 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (379), (380) imply: % 52.39/7.75 | | | | (381) all_98_1 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (257), (378) imply: % 52.39/7.75 | | | | (382) all_92_1 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (368), (382) imply: % 52.39/7.75 | | | | (383) all_114_2 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (365), (380) imply: % 52.39/7.75 | | | | (384) all_116_1 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (362), (383) imply: % 52.39/7.75 | | | | (385) all_118_1 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (265), (383) imply: % 52.39/7.75 | | | | (386) all_142_1 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (344), (384) imply: % 52.39/7.75 | | | | (387) all_144_1 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (321), (382) imply: % 52.39/7.75 | | | | (388) all_152_4 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (301), (348) imply: % 52.39/7.75 | | | | (389) all_152_3 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | COMBINE_EQS: (249), (387) imply: % 52.39/7.75 | | | | (390) all_152_2 = 0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | REDUCE: (205), (293) imply: % 52.39/7.75 | | | | (391) sdtasdt0(xr, all_66_7) = all_152_0 % 52.39/7.75 | | | | % 52.39/7.75 | | | | BETA: splitting (154) gives: % 52.39/7.75 | | | | % 52.39/7.75 | | | | Case 1: % 52.39/7.75 | | | | | % 52.39/7.75 | | | | | (392) ~ (all_102_1 = 0) % 52.39/7.75 | | | | | % 52.39/7.75 | | | | | REDUCE: (380), (392) imply: % 52.39/7.75 | | | | | (393) $false % 52.39/7.75 | | | | | % 52.39/7.75 | | | | | CLOSE: (393) is inconsistent. % 52.39/7.75 | | | | | % 52.39/7.75 | | | | Case 2: % 52.39/7.75 | | | | | % 52.39/7.75 | | | | | (394) ~ (all_102_2 = 0) | all_102_0 = 0 % 52.39/7.75 | | | | | % 52.39/7.75 | | | | | BETA: splitting (394) gives: % 52.39/7.75 | | | | | % 52.39/7.75 | | | | | Case 1: % 52.39/7.75 | | | | | | % 52.39/7.75 | | | | | | (395) ~ (all_102_2 = 0) % 52.39/7.75 | | | | | | % 52.39/7.75 | | | | | | REDUCE: (374), (395) imply: % 52.39/7.75 | | | | | | (396) $false % 52.39/7.75 | | | | | | % 52.39/7.75 | | | | | | CLOSE: (396) is inconsistent. % 52.39/7.75 | | | | | | % 52.39/7.75 | | | | | Case 2: % 52.39/7.75 | | | | | | % 52.39/7.75 | | | | | | (397) all_102_0 = 0 % 52.39/7.75 | | | | | | % 52.39/7.75 | | | | | | COMBINE_EQS: (351), (397) imply: % 52.39/7.75 | | | | | | (398) all_100_2 = 0 % 52.39/7.75 | | | | | | % 52.39/7.75 | | | | | | SIMP: (398) implies: % 52.39/7.75 | | | | | | (399) all_100_2 = 0 % 52.39/7.75 | | | | | | % 52.39/7.75 | | | | | | COMBINE_EQS: (290), (399) imply: % 52.39/7.75 | | | | | | (400) all_142_2 = 0 % 52.39/7.75 | | | | | | % 52.39/7.75 | | | | | | BETA: splitting (189) gives: % 52.39/7.75 | | | | | | % 52.39/7.75 | | | | | | Case 1: % 52.39/7.75 | | | | | | | % 52.39/7.75 | | | | | | | (401) ~ (all_142_1 = 0) % 52.39/7.75 | | | | | | | % 52.39/7.75 | | | | | | | REDUCE: (386), (401) imply: % 52.39/7.75 | | | | | | | (402) $false % 52.39/7.75 | | | | | | | % 52.39/7.75 | | | | | | | CLOSE: (402) is inconsistent. % 52.39/7.75 | | | | | | | % 52.39/7.75 | | | | | | Case 2: % 52.39/7.75 | | | | | | | % 52.39/7.75 | | | | | | | (403) ~ (all_142_2 = 0) | all_142_0 = all_66_6 % 52.39/7.75 | | | | | | | % 52.39/7.75 | | | | | | | BETA: splitting (403) gives: % 52.39/7.75 | | | | | | | % 52.39/7.75 | | | | | | | Case 1: % 52.39/7.75 | | | | | | | | % 52.39/7.75 | | | | | | | | (404) ~ (all_142_2 = 0) % 52.39/7.75 | | | | | | | | % 52.39/7.75 | | | | | | | | REDUCE: (400), (404) imply: % 52.39/7.75 | | | | | | | | (405) $false % 52.39/7.75 | | | | | | | | % 52.39/7.75 | | | | | | | | CLOSE: (405) is inconsistent. % 52.39/7.75 | | | | | | | | % 52.39/7.75 | | | | | | | Case 2: % 52.39/7.75 | | | | | | | | % 52.39/7.76 | | | | | | | | (406) all_142_0 = all_66_6 % 52.39/7.76 | | | | | | | | % 52.39/7.76 | | | | | | | | REDUCE: (188), (406) imply: % 52.39/7.76 | | | | | | | | (407) sdtasdt0(xr, all_66_7) = all_66_6 % 52.39/7.76 | | | | | | | | % 52.39/7.76 | | | | | | | | BETA: splitting (207) gives: % 52.39/7.76 | | | | | | | | % 52.39/7.76 | | | | | | | | Case 1: % 52.39/7.76 | | | | | | | | | % 52.39/7.76 | | | | | | | | | (408) ~ (all_152_2 = 0) % 52.39/7.76 | | | | | | | | | % 52.39/7.76 | | | | | | | | | REDUCE: (390), (408) imply: % 52.39/7.76 | | | | | | | | | (409) $false % 52.39/7.76 | | | | | | | | | % 52.39/7.76 | | | | | | | | | CLOSE: (409) is inconsistent. % 52.39/7.76 | | | | | | | | | % 52.39/7.76 | | | | | | | | Case 2: % 52.39/7.76 | | | | | | | | | % 52.39/7.76 | | | | | | | | | (410) ~ (all_152_3 = 0) | ~ (all_152_4 = 0) | all_152_0 = % 52.39/7.76 | | | | | | | | | all_49_0 % 52.39/7.76 | | | | | | | | | % 52.39/7.76 | | | | | | | | | BETA: splitting (410) gives: % 52.39/7.76 | | | | | | | | | % 52.39/7.76 | | | | | | | | | Case 1: % 52.39/7.76 | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | (411) ~ (all_152_3 = 0) % 52.39/7.76 | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | REDUCE: (389), (411) imply: % 52.39/7.76 | | | | | | | | | | (412) $false % 52.39/7.76 | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | CLOSE: (412) is inconsistent. % 52.39/7.76 | | | | | | | | | | % 52.39/7.76 | | | | | | | | | Case 2: % 52.39/7.76 | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | (413) ~ (all_152_4 = 0) | all_152_0 = all_49_0 % 52.39/7.76 | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | BETA: splitting (413) gives: % 52.39/7.76 | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | Case 1: % 52.39/7.76 | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | (414) ~ (all_152_4 = 0) % 52.39/7.76 | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | REDUCE: (388), (414) imply: % 52.39/7.76 | | | | | | | | | | | (415) $false % 52.39/7.76 | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | CLOSE: (415) is inconsistent. % 52.39/7.76 | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | Case 2: % 52.39/7.76 | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | (416) all_152_0 = all_49_0 % 52.39/7.76 | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | REDUCE: (391), (416) imply: % 52.39/7.76 | | | | | | | | | | | (417) sdtasdt0(xr, all_66_7) = all_49_0 % 52.39/7.76 | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | GROUND_INST: instantiating (23) with all_49_0, all_66_6, % 52.39/7.76 | | | | | | | | | | | all_66_7, xr, simplifying with (407), (417) gives: % 52.39/7.76 | | | | | | | | | | | (418) all_66_6 = all_49_0 % 52.39/7.76 | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | BETA: splitting (76) gives: % 52.39/7.76 | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | Case 1: % 52.39/7.76 | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | (419) all_66_1 = all_66_4 & all_66_2 = 0 & ~ (all_66_0 % 52.39/7.76 | | | | | | | | | | | | = all_66_5) % 52.39/7.76 | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | ALPHA: (419) implies: % 52.39/7.76 | | | | | | | | | | | | (420) all_66_2 = 0 % 52.39/7.76 | | | | | | | | | | | | (421) all_66_1 = all_66_4 % 52.39/7.76 | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | COMBINE_EQS: (93), (421) imply: % 52.39/7.76 | | | | | | | | | | | | (422) all_66_1 = all_49_0 % 52.39/7.76 | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | COMBINE_EQS: (291), (420) imply: % 52.39/7.76 | | | | | | | | | | | | (423) all_118_2 = 0 % 52.39/7.76 | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | COMBINE_EQS: (292), (422) imply: % 52.39/7.76 | | | | | | | | | | | | (424) all_118_0 = all_49_0 % 52.39/7.76 | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | BETA: splitting (171) gives: % 52.39/7.76 | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | Case 1: % 52.39/7.76 | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | (425) ~ (all_118_1 = 0) % 52.39/7.76 | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | REDUCE: (385), (425) imply: % 52.39/7.76 | | | | | | | | | | | | | (426) $false % 52.39/7.76 | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | CLOSE: (426) is inconsistent. % 52.39/7.76 | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | Case 2: % 52.39/7.76 | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | (427) ~ (all_118_2 = 0) | all_118_0 = all_66_0 % 52.39/7.76 | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | BETA: splitting (427) gives: % 52.39/7.76 | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | Case 1: % 52.39/7.76 | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | (428) ~ (all_118_2 = 0) % 52.39/7.76 | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | REDUCE: (423), (428) imply: % 52.39/7.76 | | | | | | | | | | | | | | (429) $false % 52.39/7.76 | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | CLOSE: (429) is inconsistent. % 52.39/7.76 | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | Case 2: % 52.39/7.76 | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | (430) all_118_0 = all_66_0 % 52.39/7.76 | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | COMBINE_EQS: (424), (430) imply: % 52.39/7.76 | | | | | | | | | | | | | | (431) all_66_0 = all_49_0 % 52.39/7.76 | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | BETA: splitting (76) gives: % 52.39/7.76 | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | Case 1: % 52.39/7.76 | | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | | ALPHA: (419) implies: % 52.39/7.76 | | | | | | | | | | | | | | | (432) ~ (all_66_0 = all_66_5) % 52.39/7.76 | | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | | REDUCE: (92), (431), (432) imply: % 52.39/7.76 | | | | | | | | | | | | | | | (433) $false % 52.39/7.76 | | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | | CLOSE: (433) is inconsistent. % 52.39/7.76 | | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | Case 2: % 52.39/7.76 | | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | | (434) all_66_8 = xn & all_66_9 = 0 & ~ (all_66_5 = % 52.39/7.76 | | | | | | | | | | | | | | | all_66_6) % 52.39/7.76 | | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | | ALPHA: (434) implies: % 52.39/7.76 | | | | | | | | | | | | | | | (435) ~ (all_66_5 = all_66_6) % 52.39/7.76 | | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | | REDUCE: (92), (418), (435) imply: % 52.39/7.76 | | | | | | | | | | | | | | | (436) $false % 52.39/7.76 | | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | | CLOSE: (436) is inconsistent. % 52.39/7.76 | | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | | End of split % 52.39/7.76 | | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | | End of split % 52.39/7.76 | | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | End of split % 52.39/7.76 | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | Case 2: % 52.39/7.76 | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | (437) all_66_8 = xn & all_66_9 = 0 & ~ (all_66_5 = % 52.39/7.76 | | | | | | | | | | | | all_66_6) % 52.39/7.76 | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | ALPHA: (437) implies: % 52.39/7.76 | | | | | | | | | | | | (438) ~ (all_66_5 = all_66_6) % 52.39/7.76 | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | REDUCE: (92), (418), (438) imply: % 52.39/7.76 | | | | | | | | | | | | (439) $false % 52.39/7.76 | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | | CLOSE: (439) is inconsistent. % 52.39/7.76 | | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | | End of split % 52.39/7.76 | | | | | | | | | | | % 52.39/7.76 | | | | | | | | | | End of split % 52.39/7.76 | | | | | | | | | | % 52.39/7.76 | | | | | | | | | End of split % 52.39/7.76 | | | | | | | | | % 52.39/7.76 | | | | | | | | End of split % 52.39/7.76 | | | | | | | | % 52.39/7.76 | | | | | | | End of split % 52.39/7.76 | | | | | | | % 52.39/7.76 | | | | | | End of split % 52.39/7.76 | | | | | | % 52.39/7.76 | | | | | End of split % 52.39/7.76 | | | | | % 52.39/7.76 | | | | End of split % 52.39/7.76 | | | | % 52.39/7.76 | | | End of split % 52.39/7.76 | | | % 52.39/7.76 | | End of split % 52.39/7.76 | | % 52.39/7.76 | End of split % 52.39/7.76 | % 52.39/7.76 End of proof % 52.39/7.76 % SZS output end Proof for theBenchmark % 52.39/7.76 % 52.39/7.76 7154ms %------------------------------------------------------------------------------