%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG100+2 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n007.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 13:57:52 EDT 2023 % Result : Theorem 19.48s 3.37s % Output : Proof 32.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : RNG100+2 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n007.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 : Sun Aug 27 02:23:42 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.16/1.15 Prover 4: Preprocessing ... % 3.16/1.15 Prover 1: Preprocessing ... % 3.16/1.18 Prover 3: Preprocessing ... % 3.16/1.18 Prover 0: Preprocessing ... % 3.16/1.18 Prover 5: Preprocessing ... % 3.16/1.19 Prover 2: Preprocessing ... % 3.16/1.19 Prover 6: Preprocessing ... % 9.93/2.08 Prover 1: Constructing countermodel ... % 9.93/2.09 Prover 3: Constructing countermodel ... % 9.93/2.10 Prover 5: Proving ... % 9.93/2.11 Prover 6: Proving ... % 10.37/2.13 Prover 2: Proving ... % 11.37/2.30 Prover 4: Constructing countermodel ... % 12.86/2.47 Prover 0: Proving ... % 19.48/3.37 Prover 3: proved (2723ms) % 19.48/3.37 % 19.48/3.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.48/3.37 % 19.48/3.38 Prover 5: stopped % 19.48/3.38 Prover 0: stopped % 19.48/3.39 Prover 6: stopped % 19.48/3.39 Prover 2: stopped % 19.48/3.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 19.48/3.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 19.48/3.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 19.48/3.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 19.93/3.41 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 20.35/3.46 Prover 8: Preprocessing ... % 20.35/3.49 Prover 10: Preprocessing ... % 20.35/3.49 Prover 7: Preprocessing ... % 20.35/3.50 Prover 11: Preprocessing ... % 20.35/3.51 Prover 13: Preprocessing ... % 21.73/3.64 Prover 8: Warning: ignoring some quantifiers % 21.79/3.66 Prover 8: Constructing countermodel ... % 21.79/3.67 Prover 10: Constructing countermodel ... % 22.28/3.71 Prover 7: Constructing countermodel ... % 22.28/3.76 Prover 13: Warning: ignoring some quantifiers % 22.68/3.78 Prover 13: Constructing countermodel ... % 24.26/4.01 Prover 11: Constructing countermodel ... % 31.43/4.89 Prover 1: Found proof (size 321) % 31.43/4.89 Prover 1: proved (4260ms) % 31.43/4.89 Prover 4: stopped % 31.43/4.89 Prover 8: stopped % 31.43/4.89 Prover 7: stopped % 31.43/4.89 Prover 10: stopped % 31.43/4.89 Prover 13: stopped % 31.43/4.89 Prover 11: stopped % 31.43/4.89 % 31.43/4.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 31.43/4.89 % 31.43/4.92 % SZS output start Proof for theBenchmark % 31.43/4.92 Assumptions after simplification: % 31.43/4.92 --------------------------------- % 31.43/4.92 % 31.43/4.92 (mAMDistr) % 31.43/4.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 31.43/4.95 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 31.43/4.95 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : % 31.43/4.95 ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? % 31.43/4.95 [v12: $i] : ? [v13: $i] : ? [v14: $i] : (sdtasdt0(v9, v0) = v11 & % 31.43/4.95 sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v9) = v10 & % 31.43/4.95 sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9 & aElement0(v2) = v8 & % 31.43/4.95 aElement0(v1) = v7 & aElement0(v0) = v6 & $i(v14) & $i(v13) & $i(v12) & % 31.43/4.95 $i(v11) & $i(v10) & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | % 31.43/4.95 (v14 = v11 & v10 = v5)))) % 31.43/4.95 % 31.43/4.95 (mAddComm) % 31.43/4.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 31.43/4.95 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 31.43/4.95 (sdtpldt0(v1, v0) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & $i(v5) & % 31.43/4.95 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 31.43/4.95 % 31.43/4.95 (mDefIdeal) % 31.43/4.96 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aIdeal0(v0) = v1) | ~ $i(v0) | ? % 31.43/4.96 [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2) | ? [v2: $i] : (aElementOf0(v2, % 31.43/4.96 v0) = 0 & $i(v2) & ( ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = % 31.43/4.96 0) & aElementOf0(v4, v0) = v5 & aElementOf0(v3, v0) = 0 & % 31.43/4.96 sdtpldt0(v2, v3) = v4 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] : % 31.43/4.96 ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v4, v0) = v5 & sdtasdt0(v3, % 31.43/4.96 v2) = v4 & aElement0(v3) = 0 & $i(v4) & $i(v3))))) & ! [v0: $i] : ( % 31.43/4.96 ~ (aIdeal0(v0) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i] : ( ~ % 31.43/4.96 (aElementOf0(v1, v0) = 0) | ~ $i(v1) | ( ! [v2: $i] : ! [v3: $i] : ! % 31.43/4.96 [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, v0) = v4) | ~ (sdtasdt0(v2, % 31.43/4.96 v1) = v3) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & % 31.43/4.96 aElement0(v2) = v5)) & ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 31.43/4.96 (v4 = 0 | ~ (aElementOf0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | % 31.43/4.96 ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v2, v0) = % 31.43/4.96 v5)))))) % 31.43/4.96 % 31.43/4.96 (mDefPrIdeal) % 31.43/4.96 ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~ $i(v0) | ? [v2: int] % 31.43/4.96 : ( ~ (v2 = 0) & aElement0(v0) = v2) | ( ! [v2: $i] : (v2 = v1 | ~ % 31.43/4.96 (aSet0(v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: any] : % 31.43/4.96 (aElementOf0(v3, v2) = v4 & $i(v3) & ( ~ (v4 = 0) | ! [v5: $i] : ( ~ % 31.43/4.96 (sdtasdt0(v0, v5) = v3) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) % 31.43/4.96 & aElement0(v5) = v6))) & (v4 = 0 | ? [v5: $i] : (sdtasdt0(v0, % 31.43/4.96 v5) = v3 & aElement0(v5) = 0 & $i(v5))))) & ! [v2: any] : ( ~ % 31.43/4.96 (aSet0(v1) = v2) | ~ $i(v1) | (v2 = 0 & ! [v3: $i] : ! [v4: int] : % 31.43/4.96 (v4 = 0 | ~ (aElementOf0(v3, v1) = v4) | ~ $i(v3) | ! [v5: $i] : ( % 31.43/4.96 ~ (sdtasdt0(v0, v5) = v3) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = % 31.43/4.96 0) & aElement0(v5) = v6))) & ! [v3: $i] : ( ~ % 31.43/4.96 (aElementOf0(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (sdtasdt0(v0, % 31.43/4.96 v4) = v3 & aElement0(v4) = 0 & $i(v4))))))) % 31.43/4.96 % 31.43/4.96 (mEOfElem) % 31.43/4.96 ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 31.43/4.96 (aElementOf0(v1, v0) = 0) | ~ $i(v1) | aElement0(v1) = 0)) % 31.43/4.96 % 31.43/4.96 (mMulAsso) % 31.43/4.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 31.43/4.96 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 31.43/4.96 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? % 31.43/4.96 [v9: $i] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & aElement0(v2) = % 31.43/4.96 v7 & aElement0(v1) = v6 & aElement0(v0) = v5 & $i(v9) & $i(v8) & ( ~ (v7 = % 31.43/4.96 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4))) % 31.43/4.96 % 31.43/4.96 (mMulComm) % 31.43/4.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 31.43/4.96 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 31.43/4.96 (sdtasdt0(v1, v0) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & $i(v5) & % 31.43/4.96 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 31.43/4.96 % 31.43/4.96 (mSortsB) % 31.43/4.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 31.43/4.96 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 31.43/4.96 (aElement0(v2) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & ( ~ (v4 = 0) % 31.43/4.96 | ~ (v3 = 0) | v5 = 0))) % 31.43/4.96 % 31.43/4.96 (mSortsB_02) % 31.43/4.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 31.43/4.97 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 31.43/4.97 (aElement0(v2) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & ( ~ (v4 = 0) % 31.43/4.97 | ~ (v3 = 0) | v5 = 0))) % 31.43/4.97 % 31.43/4.97 (m__) % 31.43/4.97 $i(xc) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & slsdtgt0(xc) = v0 & % 31.43/4.97 aIdeal0(v0) = v1 & aSet0(v0) = 0 & $i(v0) & ! [v2: $i] : ! [v3: int] : (v3 % 31.43/4.97 = 0 | ~ (aElementOf0(v2, v0) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ % 31.43/4.97 (sdtasdt0(xc, v4) = v2) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 31.43/4.97 aElement0(v4) = v5))) & ! [v2: $i] : ( ~ (aElementOf0(v2, v0) = 0) | % 31.43/4.97 ~ $i(v2) | ? [v3: $i] : (sdtasdt0(xc, v3) = v2 & aElement0(v3) = 0 & % 31.43/4.97 $i(v3))) & ? [v2: $i] : (aElementOf0(v2, v0) = 0 & $i(v2) & ( ? [v3: % 31.43/4.97 $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v4, v0) % 31.43/4.97 = v5 & aElementOf0(v3, v0) = 0 & sdtpldt0(v2, v3) = v4 & $i(v4) & % 31.43/4.97 $i(v3)) | ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 31.43/4.97 aElementOf0(v4, v0) = v5 & sdtasdt0(v3, v2) = v4 & aElement0(v3) = 0 & % 31.43/4.97 $i(v4) & $i(v3))))) % 31.43/4.97 % 31.43/4.97 (m__1905) % 31.43/4.97 aElement0(xc) = 0 & $i(xc) % 31.43/4.97 % 31.43/4.97 (function-axioms) % 31.82/4.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 31.82/4.97 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (aGcdOfAnd0(v4, v3, v2) = v1) | ~ % 31.82/4.97 (aGcdOfAnd0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 31.82/4.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 31.82/4.97 (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1) | ~ (sdteqdtlpzmzozddtrp0(v4, v3, % 31.82/4.97 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 31.82/4.97 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (misRelativelyPrime0(v3, v2) = v1) | % 31.82/4.97 ~ (misRelativelyPrime0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 31.82/4.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 31.82/4.97 (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & ! [v0: % 31.82/4.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 31.82/4.97 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 31.82/4.97 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 31.82/4.97 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 31.82/4.97 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 31.82/4.97 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 31.82/4.97 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 31.82/4.97 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 31.82/4.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 31.82/4.97 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: $i] : % 31.82/4.97 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) % 31.82/4.97 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 31.82/4.97 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 31.82/4.97 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) % 31.82/4.97 | ~ (slsdtgt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 31.82/4.97 v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: % 31.82/4.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 31.82/4.97 ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0: % 31.82/4.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 31.82/4.97 ~ (aIdeal0(v2) = v1) | ~ (aIdeal0(v2) = v0)) & ! [v0: MultipleValueBool] : % 31.82/4.97 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~ % 31.82/4.97 (aSet0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 31.82/4.97 (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 31.82/4.97 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | % 31.82/4.97 ~ (aElement0(v2) = v0)) % 31.82/4.97 % 31.82/4.97 Further assumptions not needed in the proof: % 31.82/4.97 -------------------------------------------- % 31.82/4.97 mAddAsso, mAddInvr, mAddZero, mCancel, mChineseRemainder, mDefDiv, mDefDvs, % 31.82/4.97 mDefGCD, mDefMod, mDefRel, mDefSInt, mDefSSum, mDivision, mElmSort, mEucSort, % 31.82/4.97 mIdeInt, mIdeSum, mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mSetEq, % 31.82/4.97 mSetSort, mSortsC, mSortsC_01, mSortsU, mUnNeZr % 31.82/4.97 % 31.82/4.97 Those formulas are unsatisfiable: % 31.82/4.97 --------------------------------- % 31.82/4.97 % 31.82/4.97 Begin of proof % 31.82/4.97 | % 31.82/4.97 | ALPHA: (mDefIdeal) implies: % 31.82/4.98 | (1) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aIdeal0(v0) = v1) | ~ % 31.82/4.98 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2) | ? [v2: $i] % 31.82/4.98 | : (aElementOf0(v2, v0) = 0 & $i(v2) & ( ? [v3: $i] : ? [v4: $i] : ? % 31.82/4.98 | [v5: int] : ( ~ (v5 = 0) & aElementOf0(v4, v0) = v5 & % 31.82/4.98 | aElementOf0(v3, v0) = 0 & sdtpldt0(v2, v3) = v4 & $i(v4) & % 31.82/4.98 | $i(v3)) | ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = % 31.82/4.98 | 0) & aElementOf0(v4, v0) = v5 & sdtasdt0(v3, v2) = v4 & % 31.82/4.98 | aElement0(v3) = 0 & $i(v4) & $i(v3))))) % 31.82/4.98 | % 31.82/4.98 | ALPHA: (m__1905) implies: % 31.85/4.98 | (2) aElement0(xc) = 0 % 31.85/4.98 | % 31.85/4.98 | ALPHA: (m__) implies: % 31.85/4.98 | (3) $i(xc) % 31.85/4.98 | (4) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & slsdtgt0(xc) = v0 & % 31.85/4.98 | aIdeal0(v0) = v1 & aSet0(v0) = 0 & $i(v0) & ! [v2: $i] : ! [v3: % 31.85/4.98 | int] : (v3 = 0 | ~ (aElementOf0(v2, v0) = v3) | ~ $i(v2) | ! % 31.85/4.98 | [v4: $i] : ( ~ (sdtasdt0(xc, v4) = v2) | ~ $i(v4) | ? [v5: int] : % 31.85/4.98 | ( ~ (v5 = 0) & aElement0(v4) = v5))) & ! [v2: $i] : ( ~ % 31.85/4.98 | (aElementOf0(v2, v0) = 0) | ~ $i(v2) | ? [v3: $i] : (sdtasdt0(xc, % 31.85/4.98 | v3) = v2 & aElement0(v3) = 0 & $i(v3))) & ? [v2: $i] : % 31.85/4.98 | (aElementOf0(v2, v0) = 0 & $i(v2) & ( ? [v3: $i] : ? [v4: $i] : ? % 31.85/4.98 | [v5: int] : ( ~ (v5 = 0) & aElementOf0(v4, v0) = v5 & % 31.85/4.98 | aElementOf0(v3, v0) = 0 & sdtpldt0(v2, v3) = v4 & $i(v4) & % 31.85/4.98 | $i(v3)) | ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = % 31.85/4.98 | 0) & aElementOf0(v4, v0) = v5 & sdtasdt0(v3, v2) = v4 & % 31.85/4.98 | aElement0(v3) = 0 & $i(v4) & $i(v3))))) % 31.85/4.98 | % 31.85/4.98 | ALPHA: (function-axioms) implies: % 31.85/4.98 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 31.85/4.98 | (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0)) % 31.85/4.98 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 31.85/4.98 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 31.85/4.98 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 31.85/4.98 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 31.85/4.98 | % 31.85/4.98 | DELTA: instantiating (4) with fresh symbols all_36_0, all_36_1 gives: % 31.85/4.98 | (8) ~ (all_36_0 = 0) & slsdtgt0(xc) = all_36_1 & aIdeal0(all_36_1) = % 31.85/4.98 | all_36_0 & aSet0(all_36_1) = 0 & $i(all_36_1) & ! [v0: $i] : ! [v1: % 31.85/4.98 | int] : (v1 = 0 | ~ (aElementOf0(v0, all_36_1) = v1) | ~ $i(v0) | ! % 31.85/4.98 | [v2: $i] : ( ~ (sdtasdt0(xc, v2) = v0) | ~ $i(v2) | ? [v3: int] : ( % 31.85/4.98 | ~ (v3 = 0) & aElement0(v2) = v3))) & ! [v0: $i] : ( ~ % 31.85/4.98 | (aElementOf0(v0, all_36_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 31.85/4.98 | (sdtasdt0(xc, v1) = v0 & aElement0(v1) = 0 & $i(v1))) & ? [v0: $i] : % 31.85/4.98 | (aElementOf0(v0, all_36_1) = 0 & $i(v0) & ( ? [v1: $i] : ? [v2: $i] : % 31.85/4.98 | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v2, all_36_1) = v3 & % 31.85/4.98 | aElementOf0(v1, all_36_1) = 0 & sdtpldt0(v0, v1) = v2 & $i(v2) & % 31.85/4.98 | $i(v1)) | ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) % 31.85/4.98 | & aElementOf0(v2, all_36_1) = v3 & sdtasdt0(v1, v0) = v2 & % 31.85/4.98 | aElement0(v1) = 0 & $i(v2) & $i(v1)))) % 31.85/4.98 | % 31.85/4.98 | ALPHA: (8) implies: % 31.85/4.99 | (9) ~ (all_36_0 = 0) % 31.85/4.99 | (10) $i(all_36_1) % 31.85/4.99 | (11) aSet0(all_36_1) = 0 % 31.85/4.99 | (12) aIdeal0(all_36_1) = all_36_0 % 31.85/4.99 | (13) slsdtgt0(xc) = all_36_1 % 31.85/4.99 | (14) ! [v0: $i] : ( ~ (aElementOf0(v0, all_36_1) = 0) | ~ $i(v0) | ? % 31.85/4.99 | [v1: $i] : (sdtasdt0(xc, v1) = v0 & aElement0(v1) = 0 & $i(v1))) % 31.85/4.99 | (15) ? [v0: $i] : (aElementOf0(v0, all_36_1) = 0 & $i(v0) & ( ? [v1: $i] : % 31.85/4.99 | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v2, % 31.85/4.99 | all_36_1) = v3 & aElementOf0(v1, all_36_1) = 0 & sdtpldt0(v0, % 31.85/4.99 | v1) = v2 & $i(v2) & $i(v1)) | ? [v1: $i] : ? [v2: $i] : ? % 31.85/4.99 | [v3: int] : ( ~ (v3 = 0) & aElementOf0(v2, all_36_1) = v3 & % 31.85/4.99 | sdtasdt0(v1, v0) = v2 & aElement0(v1) = 0 & $i(v2) & $i(v1)))) % 31.85/4.99 | % 31.85/4.99 | DELTA: instantiating (15) with fresh symbol all_39_0 gives: % 31.85/4.99 | (16) aElementOf0(all_39_0, all_36_1) = 0 & $i(all_39_0) & ( ? [v0: $i] : ? % 31.85/4.99 | [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v1, all_36_1) = % 31.85/4.99 | v2 & aElementOf0(v0, all_36_1) = 0 & sdtpldt0(all_39_0, v0) = v1 & % 31.85/4.99 | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ % 31.85/4.99 | (v2 = 0) & aElementOf0(v1, all_36_1) = v2 & sdtasdt0(v0, all_39_0) % 31.85/4.99 | = v1 & aElement0(v0) = 0 & $i(v1) & $i(v0))) % 31.85/4.99 | % 31.85/4.99 | ALPHA: (16) implies: % 31.85/4.99 | (17) $i(all_39_0) % 31.85/4.99 | (18) aElementOf0(all_39_0, all_36_1) = 0 % 31.85/4.99 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 31.85/4.99 | aElementOf0(v1, all_36_1) = v2 & aElementOf0(v0, all_36_1) = 0 & % 31.85/4.99 | sdtpldt0(all_39_0, v0) = v1 & $i(v1) & $i(v0)) | ? [v0: $i] : ? % 31.85/4.99 | [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v1, all_36_1) = % 31.85/4.99 | v2 & sdtasdt0(v0, all_39_0) = v1 & aElement0(v0) = 0 & $i(v1) & % 31.85/4.99 | $i(v0)) % 31.85/4.99 | % 31.85/4.99 | GROUND_INST: instantiating (14) with all_39_0, simplifying with (17), (18) % 31.85/4.99 | gives: % 31.85/4.99 | (20) ? [v0: $i] : (sdtasdt0(xc, v0) = all_39_0 & aElement0(v0) = 0 & % 31.85/4.99 | $i(v0)) % 31.85/4.99 | % 31.85/4.99 | GROUND_INST: instantiating (mEOfElem) with all_36_1, simplifying with (10), % 31.85/4.99 | (11) gives: % 31.85/4.99 | (21) ! [v0: $i] : ( ~ (aElementOf0(v0, all_36_1) = 0) | ~ $i(v0) | % 31.85/4.99 | aElement0(v0) = 0) % 31.85/4.99 | % 31.85/4.99 | GROUND_INST: instantiating (1) with all_36_1, all_36_0, simplifying with (10), % 31.85/4.99 | (12) gives: % 31.85/4.99 | (22) all_36_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & aSet0(all_36_1) = v0) | % 31.85/4.99 | ? [v0: $i] : (aElementOf0(v0, all_36_1) = 0 & $i(v0) & ( ? [v1: $i] : % 31.85/4.99 | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v2, % 31.85/4.99 | all_36_1) = v3 & aElementOf0(v1, all_36_1) = 0 & sdtpldt0(v0, % 31.85/4.99 | v1) = v2 & $i(v2) & $i(v1)) | ? [v1: $i] : ? [v2: $i] : ? % 31.85/4.99 | [v3: int] : ( ~ (v3 = 0) & aElementOf0(v2, all_36_1) = v3 & % 31.85/4.99 | sdtasdt0(v1, v0) = v2 & aElement0(v1) = 0 & $i(v2) & $i(v1)))) % 31.85/4.99 | % 31.85/4.99 | GROUND_INST: instantiating (mDefPrIdeal) with xc, all_36_1, simplifying with % 31.85/4.99 | (3), (13) gives: % 31.85/5.00 | (23) ? [v0: int] : ( ~ (v0 = 0) & aElement0(xc) = v0) | ( ! [v0: any] : % 31.85/5.00 | (v0 = all_36_1 | ~ (aSet0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 31.85/5.00 | [v2: any] : (aElementOf0(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! % 31.85/5.00 | [v3: $i] : ( ~ (sdtasdt0(xc, v3) = v1) | ~ $i(v3) | ? [v4: % 31.85/5.00 | int] : ( ~ (v4 = 0) & aElement0(v3) = v4))) & (v2 = 0 | ? % 31.85/5.00 | [v3: $i] : (sdtasdt0(xc, v3) = v1 & aElement0(v3) = 0 & % 31.85/5.00 | $i(v3))))) & ! [v0: any] : ( ~ (aSet0(all_36_1) = v0) | ~ % 31.85/5.00 | $i(all_36_1) | (v0 = 0 & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 31.85/5.00 | (aElementOf0(v1, all_36_1) = v2) | ~ $i(v1) | ! [v3: $i] : ( % 31.85/5.00 | ~ (sdtasdt0(xc, v3) = v1) | ~ $i(v3) | ? [v4: int] : ( ~ % 31.85/5.00 | (v4 = 0) & aElement0(v3) = v4))) & ! [v1: $i] : ( ~ % 31.85/5.00 | (aElementOf0(v1, all_36_1) = 0) | ~ $i(v1) | ? [v2: $i] : % 31.85/5.00 | (sdtasdt0(xc, v2) = v1 & aElement0(v2) = 0 & $i(v2)))))) % 31.85/5.00 | % 31.85/5.00 | GROUND_INST: instantiating (21) with all_39_0, simplifying with (17), (18) % 31.85/5.00 | gives: % 31.85/5.00 | (24) aElement0(all_39_0) = 0 % 31.85/5.00 | % 31.85/5.00 | DELTA: instantiating (20) with fresh symbol all_60_0 gives: % 31.85/5.00 | (25) sdtasdt0(xc, all_60_0) = all_39_0 & aElement0(all_60_0) = 0 & % 31.85/5.00 | $i(all_60_0) % 31.85/5.00 | % 31.85/5.00 | ALPHA: (25) implies: % 31.85/5.00 | (26) $i(all_60_0) % 31.85/5.00 | (27) aElement0(all_60_0) = 0 % 31.85/5.00 | (28) sdtasdt0(xc, all_60_0) = all_39_0 % 31.85/5.00 | % 31.85/5.00 | BETA: splitting (23) gives: % 31.85/5.00 | % 31.85/5.00 | Case 1: % 31.85/5.00 | | % 31.85/5.00 | | (29) ? [v0: int] : ( ~ (v0 = 0) & aElement0(xc) = v0) % 31.85/5.00 | | % 31.85/5.00 | | DELTA: instantiating (29) with fresh symbol all_67_0 gives: % 31.85/5.00 | | (30) ~ (all_67_0 = 0) & aElement0(xc) = all_67_0 % 31.85/5.00 | | % 31.85/5.00 | | ALPHA: (30) implies: % 31.85/5.00 | | (31) ~ (all_67_0 = 0) % 31.85/5.00 | | (32) aElement0(xc) = all_67_0 % 31.85/5.00 | | % 31.85/5.00 | | GROUND_INST: instantiating (5) with 0, all_67_0, xc, simplifying with (2), % 31.85/5.00 | | (32) gives: % 31.85/5.00 | | (33) all_67_0 = 0 % 31.85/5.00 | | % 31.85/5.00 | | REDUCE: (31), (33) imply: % 31.85/5.00 | | (34) $false % 31.85/5.00 | | % 31.85/5.00 | | CLOSE: (34) is inconsistent. % 31.85/5.00 | | % 31.85/5.00 | Case 2: % 31.85/5.00 | | % 31.97/5.00 | | (35) ! [v0: any] : (v0 = all_36_1 | ~ (aSet0(v0) = 0) | ~ $i(v0) | ? % 31.97/5.00 | | [v1: $i] : ? [v2: any] : (aElementOf0(v1, v0) = v2 & $i(v1) & ( ~ % 31.97/5.00 | | (v2 = 0) | ! [v3: $i] : ( ~ (sdtasdt0(xc, v3) = v1) | ~ % 31.97/5.00 | | $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aElement0(v3) = v4))) % 31.97/5.00 | | & (v2 = 0 | ? [v3: $i] : (sdtasdt0(xc, v3) = v1 & aElement0(v3) % 31.97/5.00 | | = 0 & $i(v3))))) & ! [v0: any] : ( ~ (aSet0(all_36_1) = v0) % 31.97/5.00 | | | ~ $i(all_36_1) | (v0 = 0 & ! [v1: $i] : ! [v2: int] : (v2 = 0 % 31.97/5.00 | | | ~ (aElementOf0(v1, all_36_1) = v2) | ~ $i(v1) | ! [v3: % 31.97/5.00 | | $i] : ( ~ (sdtasdt0(xc, v3) = v1) | ~ $i(v3) | ? [v4: int] % 31.97/5.00 | | : ( ~ (v4 = 0) & aElement0(v3) = v4))) & ! [v1: $i] : ( ~ % 31.97/5.00 | | (aElementOf0(v1, all_36_1) = 0) | ~ $i(v1) | ? [v2: $i] : % 31.97/5.00 | | (sdtasdt0(xc, v2) = v1 & aElement0(v2) = 0 & $i(v2))))) % 31.97/5.00 | | % 31.97/5.00 | | ALPHA: (35) implies: % 31.97/5.00 | | (36) ! [v0: any] : ( ~ (aSet0(all_36_1) = v0) | ~ $i(all_36_1) | (v0 = % 31.97/5.00 | | 0 & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, % 31.97/5.00 | | all_36_1) = v2) | ~ $i(v1) | ! [v3: $i] : ( ~ % 31.97/5.00 | | (sdtasdt0(xc, v3) = v1) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 % 31.97/5.00 | | = 0) & aElement0(v3) = v4))) & ! [v1: $i] : ( ~ % 31.97/5.00 | | (aElementOf0(v1, all_36_1) = 0) | ~ $i(v1) | ? [v2: $i] : % 31.97/5.00 | | (sdtasdt0(xc, v2) = v1 & aElement0(v2) = 0 & $i(v2))))) % 31.97/5.00 | | % 31.97/5.00 | | GROUND_INST: instantiating (36) with 0, simplifying with (10), (11) gives: % 31.97/5.01 | | (37) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_36_1) % 31.97/5.01 | | = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (sdtasdt0(xc, v2) = v0) | % 31.97/5.01 | | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & aElement0(v2) = v3))) & % 31.97/5.01 | | ! [v0: $i] : ( ~ (aElementOf0(v0, all_36_1) = 0) | ~ $i(v0) | ? % 31.97/5.01 | | [v1: $i] : (sdtasdt0(xc, v1) = v0 & aElement0(v1) = 0 & $i(v1))) % 31.97/5.01 | | % 31.97/5.01 | | ALPHA: (37) implies: % 31.97/5.01 | | (38) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_36_1) % 31.97/5.01 | | = v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (sdtasdt0(xc, v2) = v0) | % 31.97/5.01 | | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & aElement0(v2) = v3))) % 31.97/5.01 | | % 31.97/5.01 | | BETA: splitting (22) gives: % 31.97/5.01 | | % 31.97/5.01 | | Case 1: % 31.97/5.01 | | | % 31.97/5.01 | | | (39) all_36_0 = 0 % 31.97/5.01 | | | % 31.97/5.01 | | | REDUCE: (9), (39) imply: % 31.97/5.01 | | | (40) $false % 31.97/5.01 | | | % 31.97/5.01 | | | CLOSE: (40) is inconsistent. % 31.97/5.01 | | | % 31.97/5.01 | | Case 2: % 31.97/5.01 | | | % 31.97/5.01 | | | % 31.97/5.01 | | | DELTA: instantiating (15) with fresh symbol all_74_0 gives: % 31.97/5.01 | | | (41) aElementOf0(all_74_0, all_36_1) = 0 & $i(all_74_0) & ( ? [v0: $i] % 31.97/5.01 | | | : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v1, % 31.97/5.01 | | | all_36_1) = v2 & aElementOf0(v0, all_36_1) = 0 & % 31.97/5.01 | | | sdtpldt0(all_74_0, v0) = v1 & $i(v1) & $i(v0)) | ? [v0: $i] : % 31.97/5.01 | | | ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v1, % 31.97/5.01 | | | all_36_1) = v2 & sdtasdt0(v0, all_74_0) = v1 & aElement0(v0) % 31.97/5.01 | | | = 0 & $i(v1) & $i(v0))) % 31.97/5.01 | | | % 31.97/5.01 | | | ALPHA: (41) implies: % 31.97/5.01 | | | (42) $i(all_74_0) % 31.97/5.01 | | | (43) aElementOf0(all_74_0, all_36_1) = 0 % 31.97/5.01 | | | % 31.97/5.01 | | | GROUND_INST: instantiating (mMulComm) with xc, all_60_0, all_39_0, % 31.97/5.01 | | | simplifying with (3), (26), (28) gives: % 31.97/5.01 | | | (44) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_60_0, % 31.97/5.01 | | | xc) = v2 & aElement0(all_60_0) = v1 & aElement0(xc) = v0 & % 31.97/5.01 | | | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_39_0)) % 31.97/5.01 | | | % 31.97/5.01 | | | GROUND_INST: instantiating (14) with all_74_0, simplifying with (42), (43) % 31.97/5.01 | | | gives: % 31.97/5.01 | | | (45) ? [v0: $i] : (sdtasdt0(xc, v0) = all_74_0 & aElement0(v0) = 0 & % 31.97/5.01 | | | $i(v0)) % 31.97/5.01 | | | % 31.97/5.01 | | | DELTA: instantiating (45) with fresh symbol all_120_0 gives: % 31.97/5.01 | | | (46) sdtasdt0(xc, all_120_0) = all_74_0 & aElement0(all_120_0) = 0 & % 31.97/5.01 | | | $i(all_120_0) % 31.97/5.01 | | | % 31.97/5.01 | | | ALPHA: (46) implies: % 31.97/5.01 | | | (47) $i(all_120_0) % 31.97/5.01 | | | (48) sdtasdt0(xc, all_120_0) = all_74_0 % 31.97/5.01 | | | % 31.97/5.01 | | | DELTA: instantiating (44) with fresh symbols all_122_0, all_122_1, % 31.97/5.01 | | | all_122_2 gives: % 31.97/5.01 | | | (49) sdtasdt0(all_60_0, xc) = all_122_0 & aElement0(all_60_0) = % 31.97/5.01 | | | all_122_1 & aElement0(xc) = all_122_2 & $i(all_122_0) & ( ~ % 31.97/5.01 | | | (all_122_1 = 0) | ~ (all_122_2 = 0) | all_122_0 = all_39_0) % 31.97/5.01 | | | % 31.97/5.01 | | | ALPHA: (49) implies: % 31.97/5.01 | | | (50) $i(all_122_0) % 31.97/5.01 | | | (51) aElement0(xc) = all_122_2 % 31.97/5.01 | | | (52) aElement0(all_60_0) = all_122_1 % 31.97/5.01 | | | (53) sdtasdt0(all_60_0, xc) = all_122_0 % 31.97/5.01 | | | (54) ~ (all_122_1 = 0) | ~ (all_122_2 = 0) | all_122_0 = all_39_0 % 31.97/5.01 | | | % 31.97/5.01 | | | GROUND_INST: instantiating (5) with 0, all_122_2, xc, simplifying with % 31.97/5.01 | | | (2), (51) gives: % 31.97/5.01 | | | (55) all_122_2 = 0 % 31.97/5.01 | | | % 31.97/5.01 | | | GROUND_INST: instantiating (5) with 0, all_122_1, all_60_0, simplifying % 31.97/5.01 | | | with (27), (52) gives: % 31.97/5.01 | | | (56) all_122_1 = 0 % 31.97/5.01 | | | % 31.97/5.01 | | | BETA: splitting (54) gives: % 31.97/5.01 | | | % 31.97/5.01 | | | Case 1: % 31.97/5.01 | | | | % 31.97/5.01 | | | | (57) ~ (all_122_1 = 0) % 31.97/5.01 | | | | % 31.97/5.01 | | | | REDUCE: (56), (57) imply: % 31.97/5.01 | | | | (58) $false % 31.97/5.01 | | | | % 31.97/5.01 | | | | CLOSE: (58) is inconsistent. % 31.97/5.01 | | | | % 31.97/5.01 | | | Case 2: % 31.97/5.01 | | | | % 31.97/5.01 | | | | (59) ~ (all_122_2 = 0) | all_122_0 = all_39_0 % 31.97/5.01 | | | | % 31.97/5.01 | | | | BETA: splitting (59) gives: % 31.97/5.01 | | | | % 31.97/5.01 | | | | Case 1: % 31.97/5.01 | | | | | % 31.97/5.01 | | | | | (60) ~ (all_122_2 = 0) % 31.97/5.01 | | | | | % 31.97/5.01 | | | | | REDUCE: (55), (60) imply: % 31.97/5.01 | | | | | (61) $false % 31.97/5.01 | | | | | % 31.97/5.01 | | | | | CLOSE: (61) is inconsistent. % 31.97/5.01 | | | | | % 31.97/5.01 | | | | Case 2: % 31.97/5.01 | | | | | % 31.97/5.01 | | | | | (62) all_122_0 = all_39_0 % 31.97/5.01 | | | | | % 31.97/5.01 | | | | | REDUCE: (53), (62) imply: % 31.97/5.01 | | | | | (63) sdtasdt0(all_60_0, xc) = all_39_0 % 31.97/5.01 | | | | | % 31.97/5.01 | | | | | GROUND_INST: instantiating (mMulComm) with xc, all_120_0, all_74_0, % 31.97/5.01 | | | | | simplifying with (3), (47), (48) gives: % 31.97/5.01 | | | | | (64) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 31.97/5.01 | | | | | (sdtasdt0(all_120_0, xc) = v2 & aElement0(all_120_0) = v1 & % 31.97/5.02 | | | | | aElement0(xc) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | % 31.97/5.02 | | | | | v2 = all_74_0)) % 31.97/5.02 | | | | | % 31.97/5.02 | | | | | DELTA: instantiating (64) with fresh symbols all_171_0, all_171_1, % 31.97/5.02 | | | | | all_171_2 gives: % 31.97/5.02 | | | | | (65) sdtasdt0(all_120_0, xc) = all_171_0 & aElement0(all_120_0) = % 31.97/5.02 | | | | | all_171_1 & aElement0(xc) = all_171_2 & $i(all_171_0) & ( ~ % 31.97/5.02 | | | | | (all_171_1 = 0) | ~ (all_171_2 = 0) | all_171_0 = all_74_0) % 31.97/5.02 | | | | | % 31.97/5.02 | | | | | ALPHA: (65) implies: % 31.97/5.02 | | | | | (66) aElement0(xc) = all_171_2 % 31.97/5.02 | | | | | % 31.97/5.02 | | | | | GROUND_INST: instantiating (5) with 0, all_171_2, xc, simplifying with % 31.97/5.02 | | | | | (2), (66) gives: % 31.97/5.02 | | | | | (67) all_171_2 = 0 % 31.97/5.02 | | | | | % 31.97/5.02 | | | | | BETA: splitting (19) gives: % 31.97/5.02 | | | | | % 31.97/5.02 | | | | | Case 1: % 31.97/5.02 | | | | | | % 31.97/5.02 | | | | | | (68) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 31.97/5.02 | | | | | | aElementOf0(v1, all_36_1) = v2 & aElementOf0(v0, all_36_1) % 31.97/5.02 | | | | | | = 0 & sdtpldt0(all_39_0, v0) = v1 & $i(v1) & $i(v0)) % 31.97/5.02 | | | | | | % 31.97/5.02 | | | | | | DELTA: instantiating (68) with fresh symbols all_190_0, all_190_1, % 31.97/5.02 | | | | | | all_190_2 gives: % 31.97/5.02 | | | | | | (69) ~ (all_190_0 = 0) & aElementOf0(all_190_1, all_36_1) = % 31.97/5.02 | | | | | | all_190_0 & aElementOf0(all_190_2, all_36_1) = 0 & % 31.97/5.02 | | | | | | sdtpldt0(all_39_0, all_190_2) = all_190_1 & $i(all_190_1) & % 31.97/5.02 | | | | | | $i(all_190_2) % 31.97/5.02 | | | | | | % 31.97/5.02 | | | | | | ALPHA: (69) implies: % 31.97/5.02 | | | | | | (70) ~ (all_190_0 = 0) % 31.97/5.02 | | | | | | (71) $i(all_190_2) % 31.97/5.02 | | | | | | (72) $i(all_190_1) % 31.97/5.02 | | | | | | (73) sdtpldt0(all_39_0, all_190_2) = all_190_1 % 31.97/5.02 | | | | | | (74) aElementOf0(all_190_2, all_36_1) = 0 % 31.97/5.02 | | | | | | (75) aElementOf0(all_190_1, all_36_1) = all_190_0 % 31.97/5.02 | | | | | | % 31.97/5.02 | | | | | | GROUND_INST: instantiating (mAddComm) with all_39_0, all_190_2, % 31.97/5.02 | | | | | | all_190_1, simplifying with (17), (71), (73) gives: % 31.97/5.02 | | | | | | (76) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 31.97/5.02 | | | | | | (sdtpldt0(all_190_2, all_39_0) = v2 & aElement0(all_190_2) = % 31.97/5.02 | | | | | | v1 & aElement0(all_39_0) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ % 31.97/5.02 | | | | | | (v0 = 0) | v2 = all_190_1)) % 31.97/5.02 | | | | | | % 31.97/5.02 | | | | | | GROUND_INST: instantiating (mSortsB) with all_39_0, all_190_2, % 31.97/5.02 | | | | | | all_190_1, simplifying with (17), (71), (73) gives: % 31.97/5.02 | | | | | | (77) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 31.97/5.02 | | | | | | (aElement0(all_190_1) = v2 & aElement0(all_190_2) = v1 & % 31.97/5.02 | | | | | | aElement0(all_39_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 % 31.97/5.02 | | | | | | = 0)) % 31.97/5.02 | | | | | | % 31.97/5.02 | | | | | | GROUND_INST: instantiating (21) with all_190_2, simplifying with % 31.97/5.02 | | | | | | (71), (74) gives: % 31.97/5.02 | | | | | | (78) aElement0(all_190_2) = 0 % 31.97/5.02 | | | | | | % 31.97/5.02 | | | | | | GROUND_INST: instantiating (14) with all_190_2, simplifying with % 31.97/5.02 | | | | | | (71), (74) gives: % 31.97/5.02 | | | | | | (79) ? [v0: $i] : (sdtasdt0(xc, v0) = all_190_2 & aElement0(v0) % 31.97/5.02 | | | | | | = 0 & $i(v0)) % 31.97/5.02 | | | | | | % 31.97/5.02 | | | | | | GROUND_INST: instantiating (38) with all_190_1, all_190_0, % 31.97/5.02 | | | | | | simplifying with (72), (75) gives: % 31.97/5.02 | | | | | | (80) all_190_0 = 0 | ! [v0: $i] : ( ~ (sdtasdt0(xc, v0) = % 31.97/5.02 | | | | | | all_190_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 31.97/5.02 | | | | | | aElement0(v0) = v1)) % 32.07/5.02 | | | | | | % 32.07/5.02 | | | | | | DELTA: instantiating (79) with fresh symbol all_198_0 gives: % 32.07/5.02 | | | | | | (81) sdtasdt0(xc, all_198_0) = all_190_2 & aElement0(all_198_0) = % 32.07/5.02 | | | | | | 0 & $i(all_198_0) % 32.07/5.02 | | | | | | % 32.07/5.02 | | | | | | ALPHA: (81) implies: % 32.07/5.02 | | | | | | (82) $i(all_198_0) % 32.07/5.02 | | | | | | (83) aElement0(all_198_0) = 0 % 32.07/5.02 | | | | | | (84) sdtasdt0(xc, all_198_0) = all_190_2 % 32.07/5.02 | | | | | | % 32.07/5.02 | | | | | | DELTA: instantiating (77) with fresh symbols all_200_0, all_200_1, % 32.07/5.02 | | | | | | all_200_2 gives: % 32.07/5.02 | | | | | | (85) aElement0(all_190_1) = all_200_0 & aElement0(all_190_2) = % 32.07/5.02 | | | | | | all_200_1 & aElement0(all_39_0) = all_200_2 & ( ~ (all_200_1 % 32.07/5.02 | | | | | | = 0) | ~ (all_200_2 = 0) | all_200_0 = 0) % 32.07/5.02 | | | | | | % 32.07/5.02 | | | | | | ALPHA: (85) implies: % 32.07/5.02 | | | | | | (86) aElement0(all_39_0) = all_200_2 % 32.07/5.02 | | | | | | (87) aElement0(all_190_2) = all_200_1 % 32.07/5.02 | | | | | | (88) ~ (all_200_1 = 0) | ~ (all_200_2 = 0) | all_200_0 = 0 % 32.07/5.02 | | | | | | % 32.07/5.02 | | | | | | DELTA: instantiating (76) with fresh symbols all_202_0, all_202_1, % 32.07/5.02 | | | | | | all_202_2 gives: % 32.07/5.02 | | | | | | (89) sdtpldt0(all_190_2, all_39_0) = all_202_0 & % 32.07/5.02 | | | | | | aElement0(all_190_2) = all_202_1 & aElement0(all_39_0) = % 32.07/5.02 | | | | | | all_202_2 & $i(all_202_0) & ( ~ (all_202_1 = 0) | ~ % 32.07/5.02 | | | | | | (all_202_2 = 0) | all_202_0 = all_190_1) % 32.07/5.02 | | | | | | % 32.07/5.02 | | | | | | ALPHA: (89) implies: % 32.07/5.02 | | | | | | (90) aElement0(all_39_0) = all_202_2 % 32.07/5.02 | | | | | | (91) aElement0(all_190_2) = all_202_1 % 32.07/5.02 | | | | | | (92) sdtpldt0(all_190_2, all_39_0) = all_202_0 % 32.07/5.02 | | | | | | (93) ~ (all_202_1 = 0) | ~ (all_202_2 = 0) | all_202_0 = % 32.07/5.02 | | | | | | all_190_1 % 32.07/5.02 | | | | | | % 32.07/5.02 | | | | | | BETA: splitting (80) gives: % 32.07/5.02 | | | | | | % 32.07/5.02 | | | | | | Case 1: % 32.07/5.02 | | | | | | | % 32.07/5.02 | | | | | | | (94) all_190_0 = 0 % 32.07/5.02 | | | | | | | % 32.07/5.02 | | | | | | | REDUCE: (70), (94) imply: % 32.07/5.02 | | | | | | | (95) $false % 32.07/5.02 | | | | | | | % 32.07/5.02 | | | | | | | CLOSE: (95) is inconsistent. % 32.07/5.02 | | | | | | | % 32.07/5.02 | | | | | | Case 2: % 32.07/5.02 | | | | | | | % 32.07/5.02 | | | | | | | (96) ! [v0: $i] : ( ~ (sdtasdt0(xc, v0) = all_190_1) | ~ % 32.07/5.02 | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aElement0(v0) = % 32.07/5.02 | | | | | | | v1)) % 32.07/5.02 | | | | | | | % 32.07/5.02 | | | | | | | GROUND_INST: instantiating (5) with 0, all_202_2, all_39_0, % 32.07/5.02 | | | | | | | simplifying with (24), (90) gives: % 32.07/5.02 | | | | | | | (97) all_202_2 = 0 % 32.07/5.02 | | | | | | | % 32.07/5.02 | | | | | | | GROUND_INST: instantiating (5) with all_200_2, all_202_2, % 32.07/5.02 | | | | | | | all_39_0, simplifying with (86), (90) gives: % 32.07/5.02 | | | | | | | (98) all_202_2 = all_200_2 % 32.07/5.02 | | | | | | | % 32.07/5.02 | | | | | | | GROUND_INST: instantiating (5) with all_200_1, all_202_1, % 32.07/5.02 | | | | | | | all_190_2, simplifying with (87), (91) gives: % 32.07/5.03 | | | | | | | (99) all_202_1 = all_200_1 % 32.07/5.03 | | | | | | | % 32.07/5.03 | | | | | | | GROUND_INST: instantiating (5) with 0, all_202_1, all_190_2, % 32.07/5.03 | | | | | | | simplifying with (78), (91) gives: % 32.07/5.03 | | | | | | | (100) all_202_1 = 0 % 32.07/5.03 | | | | | | | % 32.07/5.03 | | | | | | | COMBINE_EQS: (99), (100) imply: % 32.07/5.03 | | | | | | | (101) all_200_1 = 0 % 32.07/5.03 | | | | | | | % 32.07/5.03 | | | | | | | SIMP: (101) implies: % 32.07/5.03 | | | | | | | (102) all_200_1 = 0 % 32.07/5.03 | | | | | | | % 32.07/5.03 | | | | | | | COMBINE_EQS: (97), (98) imply: % 32.07/5.03 | | | | | | | (103) all_200_2 = 0 % 32.07/5.03 | | | | | | | % 32.07/5.03 | | | | | | | BETA: splitting (93) gives: % 32.07/5.03 | | | | | | | % 32.07/5.03 | | | | | | | Case 1: % 32.07/5.03 | | | | | | | | % 32.07/5.03 | | | | | | | | (104) ~ (all_202_1 = 0) % 32.07/5.03 | | | | | | | | % 32.07/5.03 | | | | | | | | REDUCE: (100), (104) imply: % 32.07/5.03 | | | | | | | | (105) $false % 32.07/5.03 | | | | | | | | % 32.07/5.03 | | | | | | | | CLOSE: (105) is inconsistent. % 32.07/5.03 | | | | | | | | % 32.07/5.03 | | | | | | | Case 2: % 32.07/5.03 | | | | | | | | % 32.07/5.03 | | | | | | | | (106) ~ (all_202_2 = 0) | all_202_0 = all_190_1 % 32.07/5.03 | | | | | | | | % 32.07/5.03 | | | | | | | | BETA: splitting (106) gives: % 32.07/5.03 | | | | | | | | % 32.07/5.03 | | | | | | | | Case 1: % 32.07/5.03 | | | | | | | | | % 32.07/5.03 | | | | | | | | | (107) ~ (all_202_2 = 0) % 32.07/5.03 | | | | | | | | | % 32.07/5.03 | | | | | | | | | REDUCE: (97), (107) imply: % 32.07/5.03 | | | | | | | | | (108) $false % 32.07/5.03 | | | | | | | | | % 32.07/5.03 | | | | | | | | | CLOSE: (108) is inconsistent. % 32.07/5.03 | | | | | | | | | % 32.07/5.03 | | | | | | | | Case 2: % 32.07/5.03 | | | | | | | | | % 32.07/5.03 | | | | | | | | | (109) all_202_0 = all_190_1 % 32.07/5.03 | | | | | | | | | % 32.07/5.03 | | | | | | | | | REDUCE: (92), (109) imply: % 32.07/5.03 | | | | | | | | | (110) sdtpldt0(all_190_2, all_39_0) = all_190_1 % 32.07/5.03 | | | | | | | | | % 32.07/5.03 | | | | | | | | | BETA: splitting (88) gives: % 32.07/5.03 | | | | | | | | | % 32.07/5.03 | | | | | | | | | Case 1: % 32.07/5.03 | | | | | | | | | | % 32.07/5.03 | | | | | | | | | | (111) ~ (all_200_1 = 0) % 32.07/5.03 | | | | | | | | | | % 32.07/5.03 | | | | | | | | | | REDUCE: (102), (111) imply: % 32.07/5.03 | | | | | | | | | | (112) $false % 32.07/5.03 | | | | | | | | | | % 32.07/5.03 | | | | | | | | | | CLOSE: (112) is inconsistent. % 32.07/5.03 | | | | | | | | | | % 32.07/5.03 | | | | | | | | | Case 2: % 32.07/5.03 | | | | | | | | | | % 32.07/5.03 | | | | | | | | | | % 32.07/5.03 | | | | | | | | | | GROUND_INST: instantiating (mAMDistr) with xc, all_60_0, % 32.07/5.03 | | | | | | | | | | all_198_0, all_39_0, all_190_2, all_190_1, % 32.07/5.03 | | | | | | | | | | simplifying with (3), (26), (28), (73), (82), (84) % 32.07/5.03 | | | | | | | | | | gives: % 32.07/5.03 | | | | | | | | | | (113) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 32.07/5.03 | | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 32.07/5.03 | | | | | | | | | | : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v3, xc) = % 32.07/5.03 | | | | | | | | | | v5 & sdtasdt0(all_198_0, xc) = v7 & % 32.07/5.03 | | | | | | | | | | sdtasdt0(all_60_0, xc) = v6 & sdtasdt0(xc, v3) = % 32.07/5.03 | | | | | | | | | | v4 & sdtpldt0(v6, v7) = v8 & sdtpldt0(all_60_0, % 32.07/5.03 | | | | | | | | | | all_198_0) = v3 & aElement0(all_198_0) = v2 & % 32.07/5.03 | | | | | | | | | | aElement0(all_60_0) = v1 & aElement0(xc) = v0 & % 32.07/5.03 | | | | | | | | | | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 32.07/5.03 | | | | | | | | | | $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) % 32.07/5.03 | | | | | | | | | | | (v8 = v5 & v4 = all_190_1))) % 32.07/5.03 | | | | | | | | | | % 32.07/5.03 | | | | | | | | | | GROUND_INST: instantiating (mAMDistr) with xc, all_198_0, % 32.07/5.03 | | | | | | | | | | all_60_0, all_190_2, all_39_0, all_190_1, % 32.07/5.03 | | | | | | | | | | simplifying with (3), (26), (28), (82), (84), % 32.07/5.03 | | | | | | | | | | (110) gives: % 32.07/5.03 | | | | | | | | | | (114) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 32.07/5.03 | | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 32.07/5.03 | | | | | | | | | | : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v3, xc) = % 32.07/5.03 | | | | | | | | | | v5 & sdtasdt0(all_198_0, xc) = v6 & % 32.07/5.03 | | | | | | | | | | sdtasdt0(all_60_0, xc) = v7 & sdtasdt0(xc, v3) = % 32.07/5.03 | | | | | | | | | | v4 & sdtpldt0(v6, v7) = v8 & sdtpldt0(all_198_0, % 32.07/5.03 | | | | | | | | | | all_60_0) = v3 & aElement0(all_198_0) = v1 & % 32.07/5.03 | | | | | | | | | | aElement0(all_60_0) = v2 & aElement0(xc) = v0 & % 32.07/5.03 | | | | | | | | | | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 32.07/5.03 | | | | | | | | | | $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) % 32.07/5.03 | | | | | | | | | | | (v8 = v5 & v4 = all_190_1))) % 32.07/5.03 | | | | | | | | | | % 32.07/5.03 | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xc, all_198_0, % 32.07/5.03 | | | | | | | | | | all_190_2, simplifying with (3), (82), (84) gives: % 32.07/5.03 | | | | | | | | | | (115) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 32.07/5.03 | | | | | | | | | | (sdtasdt0(all_198_0, xc) = v2 & % 32.07/5.03 | | | | | | | | | | aElement0(all_198_0) = v1 & aElement0(xc) = v0 & % 32.07/5.03 | | | | | | | | | | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = % 32.07/5.03 | | | | | | | | | | all_190_2)) % 32.07/5.03 | | | | | | | | | | % 32.07/5.03 | | | | | | | | | | DELTA: instantiating (115) with fresh symbols all_308_0, % 32.07/5.03 | | | | | | | | | | all_308_1, all_308_2 gives: % 32.07/5.03 | | | | | | | | | | (116) sdtasdt0(all_198_0, xc) = all_308_0 & % 32.07/5.03 | | | | | | | | | | aElement0(all_198_0) = all_308_1 & aElement0(xc) = % 32.07/5.03 | | | | | | | | | | all_308_2 & $i(all_308_0) & ( ~ (all_308_1 = 0) | % 32.07/5.03 | | | | | | | | | | ~ (all_308_2 = 0) | all_308_0 = all_190_2) % 32.07/5.03 | | | | | | | | | | % 32.07/5.03 | | | | | | | | | | ALPHA: (116) implies: % 32.07/5.03 | | | | | | | | | | (117) aElement0(xc) = all_308_2 % 32.07/5.03 | | | | | | | | | | (118) aElement0(all_198_0) = all_308_1 % 32.07/5.03 | | | | | | | | | | (119) sdtasdt0(all_198_0, xc) = all_308_0 % 32.07/5.03 | | | | | | | | | | (120) ~ (all_308_1 = 0) | ~ (all_308_2 = 0) | all_308_0 % 32.07/5.03 | | | | | | | | | | = all_190_2 % 32.07/5.03 | | | | | | | | | | % 32.07/5.03 | | | | | | | | | | DELTA: instantiating (114) with fresh symbols all_310_0, % 32.07/5.03 | | | | | | | | | | all_310_1, all_310_2, all_310_3, all_310_4, % 32.07/5.03 | | | | | | | | | | all_310_5, all_310_6, all_310_7, all_310_8 gives: % 32.07/5.03 | | | | | | | | | | (121) sdtasdt0(all_310_5, xc) = all_310_3 & % 32.07/5.03 | | | | | | | | | | sdtasdt0(all_198_0, xc) = all_310_2 & % 32.07/5.03 | | | | | | | | | | sdtasdt0(all_60_0, xc) = all_310_1 & sdtasdt0(xc, % 32.07/5.03 | | | | | | | | | | all_310_5) = all_310_4 & sdtpldt0(all_310_2, % 32.07/5.03 | | | | | | | | | | all_310_1) = all_310_0 & sdtpldt0(all_198_0, % 32.07/5.03 | | | | | | | | | | all_60_0) = all_310_5 & aElement0(all_198_0) = % 32.07/5.03 | | | | | | | | | | all_310_7 & aElement0(all_60_0) = all_310_6 & % 32.07/5.03 | | | | | | | | | | aElement0(xc) = all_310_8 & $i(all_310_0) & % 32.07/5.03 | | | | | | | | | | $i(all_310_1) & $i(all_310_2) & $i(all_310_3) & % 32.07/5.03 | | | | | | | | | | $i(all_310_4) & $i(all_310_5) & ( ~ (all_310_6 = 0) % 32.07/5.03 | | | | | | | | | | | ~ (all_310_7 = 0) | ~ (all_310_8 = 0) | % 32.07/5.03 | | | | | | | | | | (all_310_0 = all_310_3 & all_310_4 = all_190_1)) % 32.07/5.03 | | | | | | | | | | % 32.07/5.03 | | | | | | | | | | ALPHA: (121) implies: % 32.07/5.03 | | | | | | | | | | (122) $i(all_310_5) % 32.07/5.03 | | | | | | | | | | (123) aElement0(xc) = all_310_8 % 32.07/5.03 | | | | | | | | | | (124) aElement0(all_60_0) = all_310_6 % 32.07/5.03 | | | | | | | | | | (125) aElement0(all_198_0) = all_310_7 % 32.07/5.03 | | | | | | | | | | (126) sdtpldt0(all_198_0, all_60_0) = all_310_5 % 32.07/5.03 | | | | | | | | | | (127) sdtpldt0(all_310_2, all_310_1) = all_310_0 % 32.07/5.03 | | | | | | | | | | (128) sdtasdt0(xc, all_310_5) = all_310_4 % 32.07/5.03 | | | | | | | | | | (129) sdtasdt0(all_60_0, xc) = all_310_1 % 32.07/5.03 | | | | | | | | | | (130) sdtasdt0(all_198_0, xc) = all_310_2 % 32.07/5.03 | | | | | | | | | | (131) sdtasdt0(all_310_5, xc) = all_310_3 % 32.07/5.03 | | | | | | | | | | (132) ~ (all_310_6 = 0) | ~ (all_310_7 = 0) | ~ % 32.07/5.03 | | | | | | | | | | (all_310_8 = 0) | (all_310_0 = all_310_3 & % 32.07/5.03 | | | | | | | | | | all_310_4 = all_190_1) % 32.07/5.03 | | | | | | | | | | % 32.07/5.03 | | | | | | | | | | DELTA: instantiating (113) with fresh symbols all_312_0, % 32.07/5.03 | | | | | | | | | | all_312_1, all_312_2, all_312_3, all_312_4, % 32.07/5.03 | | | | | | | | | | all_312_5, all_312_6, all_312_7, all_312_8 gives: % 32.07/5.03 | | | | | | | | | | (133) sdtasdt0(all_312_5, xc) = all_312_3 & % 32.07/5.03 | | | | | | | | | | sdtasdt0(all_198_0, xc) = all_312_1 & % 32.07/5.03 | | | | | | | | | | sdtasdt0(all_60_0, xc) = all_312_2 & sdtasdt0(xc, % 32.07/5.03 | | | | | | | | | | all_312_5) = all_312_4 & sdtpldt0(all_312_2, % 32.07/5.03 | | | | | | | | | | all_312_1) = all_312_0 & sdtpldt0(all_60_0, % 32.07/5.03 | | | | | | | | | | all_198_0) = all_312_5 & aElement0(all_198_0) = % 32.07/5.03 | | | | | | | | | | all_312_6 & aElement0(all_60_0) = all_312_7 & % 32.07/5.03 | | | | | | | | | | aElement0(xc) = all_312_8 & $i(all_312_0) & % 32.07/5.03 | | | | | | | | | | $i(all_312_1) & $i(all_312_2) & $i(all_312_3) & % 32.07/5.03 | | | | | | | | | | $i(all_312_4) & $i(all_312_5) & ( ~ (all_312_6 = 0) % 32.07/5.03 | | | | | | | | | | | ~ (all_312_7 = 0) | ~ (all_312_8 = 0) | % 32.07/5.03 | | | | | | | | | | (all_312_0 = all_312_3 & all_312_4 = all_190_1)) % 32.07/5.03 | | | | | | | | | | % 32.07/5.03 | | | | | | | | | | ALPHA: (133) implies: % 32.07/5.03 | | | | | | | | | | (134) aElement0(xc) = all_312_8 % 32.07/5.03 | | | | | | | | | | (135) aElement0(all_60_0) = all_312_7 % 32.07/5.03 | | | | | | | | | | (136) aElement0(all_198_0) = all_312_6 % 32.07/5.03 | | | | | | | | | | (137) sdtpldt0(all_60_0, all_198_0) = all_312_5 % 32.07/5.03 | | | | | | | | | | (138) sdtasdt0(all_60_0, xc) = all_312_2 % 32.07/5.03 | | | | | | | | | | (139) sdtasdt0(all_198_0, xc) = all_312_1 % 32.07/5.03 | | | | | | | | | | % 32.07/5.03 | | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_310_8, xc, % 32.07/5.03 | | | | | | | | | | simplifying with (2), (123) gives: % 32.07/5.03 | | | | | | | | | | (140) all_310_8 = 0 % 32.07/5.03 | | | | | | | | | | % 32.07/5.03 | | | | | | | | | | GROUND_INST: instantiating (5) with all_310_8, all_312_8, xc, % 32.07/5.03 | | | | | | | | | | simplifying with (123), (134) gives: % 32.07/5.04 | | | | | | | | | | (141) all_312_8 = all_310_8 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | GROUND_INST: instantiating (5) with all_308_2, all_312_8, xc, % 32.07/5.04 | | | | | | | | | | simplifying with (117), (134) gives: % 32.07/5.04 | | | | | | | | | | (142) all_312_8 = all_308_2 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_312_7, all_60_0, % 32.07/5.04 | | | | | | | | | | simplifying with (27), (135) gives: % 32.07/5.04 | | | | | | | | | | (143) all_312_7 = 0 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | GROUND_INST: instantiating (5) with all_310_6, all_312_7, % 32.07/5.04 | | | | | | | | | | all_60_0, simplifying with (124), (135) gives: % 32.07/5.04 | | | | | | | | | | (144) all_312_7 = all_310_6 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_312_6, all_198_0, % 32.07/5.04 | | | | | | | | | | simplifying with (83), (136) gives: % 32.07/5.04 | | | | | | | | | | (145) all_312_6 = 0 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | GROUND_INST: instantiating (5) with all_310_7, all_312_6, % 32.07/5.04 | | | | | | | | | | all_198_0, simplifying with (125), (136) gives: % 32.07/5.04 | | | | | | | | | | (146) all_312_6 = all_310_7 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | GROUND_INST: instantiating (5) with all_308_1, all_312_6, % 32.07/5.04 | | | | | | | | | | all_198_0, simplifying with (118), (136) gives: % 32.07/5.04 | | | | | | | | | | (147) all_312_6 = all_308_1 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | GROUND_INST: instantiating (7) with all_39_0, all_312_2, xc, % 32.07/5.04 | | | | | | | | | | all_60_0, simplifying with (63), (138) gives: % 32.07/5.04 | | | | | | | | | | (148) all_312_2 = all_39_0 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | GROUND_INST: instantiating (7) with all_310_1, all_312_2, xc, % 32.07/5.04 | | | | | | | | | | all_60_0, simplifying with (129), (138) gives: % 32.07/5.04 | | | | | | | | | | (149) all_312_2 = all_310_1 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | GROUND_INST: instantiating (7) with all_310_2, all_312_1, xc, % 32.07/5.04 | | | | | | | | | | all_198_0, simplifying with (130), (139) gives: % 32.07/5.04 | | | | | | | | | | (150) all_312_1 = all_310_2 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | GROUND_INST: instantiating (7) with all_308_0, all_312_1, xc, % 32.07/5.04 | | | | | | | | | | all_198_0, simplifying with (119), (139) gives: % 32.07/5.04 | | | | | | | | | | (151) all_312_1 = all_308_0 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | COMBINE_EQS: (150), (151) imply: % 32.07/5.04 | | | | | | | | | | (152) all_310_2 = all_308_0 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | SIMP: (152) implies: % 32.07/5.04 | | | | | | | | | | (153) all_310_2 = all_308_0 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | COMBINE_EQS: (148), (149) imply: % 32.07/5.04 | | | | | | | | | | (154) all_310_1 = all_39_0 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | COMBINE_EQS: (146), (147) imply: % 32.07/5.04 | | | | | | | | | | (155) all_310_7 = all_308_1 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | COMBINE_EQS: (145), (146) imply: % 32.07/5.04 | | | | | | | | | | (156) all_310_7 = 0 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | COMBINE_EQS: (143), (144) imply: % 32.07/5.04 | | | | | | | | | | (157) all_310_6 = 0 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | COMBINE_EQS: (141), (142) imply: % 32.07/5.04 | | | | | | | | | | (158) all_310_8 = all_308_2 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | SIMP: (158) implies: % 32.07/5.04 | | | | | | | | | | (159) all_310_8 = all_308_2 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | COMBINE_EQS: (155), (156) imply: % 32.07/5.04 | | | | | | | | | | (160) all_308_1 = 0 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | COMBINE_EQS: (140), (159) imply: % 32.07/5.04 | | | | | | | | | | (161) all_308_2 = 0 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | SIMP: (161) implies: % 32.07/5.04 | | | | | | | | | | (162) all_308_2 = 0 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | REDUCE: (127), (153), (154) imply: % 32.07/5.04 | | | | | | | | | | (163) sdtpldt0(all_308_0, all_39_0) = all_310_0 % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | BETA: splitting (132) gives: % 32.07/5.04 | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | Case 1: % 32.07/5.04 | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | (164) ~ (all_310_6 = 0) % 32.07/5.04 | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | REDUCE: (157), (164) imply: % 32.07/5.04 | | | | | | | | | | | (165) $false % 32.07/5.04 | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | CLOSE: (165) is inconsistent. % 32.07/5.04 | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | Case 2: % 32.07/5.04 | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | (166) ~ (all_310_7 = 0) | ~ (all_310_8 = 0) | % 32.07/5.04 | | | | | | | | | | | (all_310_0 = all_310_3 & all_310_4 = all_190_1) % 32.07/5.04 | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | BETA: splitting (120) gives: % 32.07/5.04 | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | Case 1: % 32.07/5.04 | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | (167) ~ (all_308_1 = 0) % 32.07/5.04 | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | REDUCE: (160), (167) imply: % 32.07/5.04 | | | | | | | | | | | | (168) $false % 32.07/5.04 | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | CLOSE: (168) is inconsistent. % 32.07/5.04 | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | Case 2: % 32.07/5.04 | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | (169) ~ (all_308_2 = 0) | all_308_0 = all_190_2 % 32.07/5.04 | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | BETA: splitting (166) gives: % 32.07/5.04 | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | Case 1: % 32.07/5.04 | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | (170) ~ (all_310_7 = 0) % 32.07/5.04 | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | REDUCE: (156), (170) imply: % 32.07/5.04 | | | | | | | | | | | | | (171) $false % 32.07/5.04 | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | CLOSE: (171) is inconsistent. % 32.07/5.04 | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | Case 2: % 32.07/5.04 | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | (172) ~ (all_310_8 = 0) | (all_310_0 = all_310_3 & % 32.07/5.04 | | | | | | | | | | | | | all_310_4 = all_190_1) % 32.07/5.04 | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | BETA: splitting (172) gives: % 32.07/5.04 | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | Case 1: % 32.07/5.04 | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | (173) ~ (all_310_8 = 0) % 32.07/5.04 | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | REDUCE: (140), (173) imply: % 32.07/5.04 | | | | | | | | | | | | | | (174) $false % 32.07/5.04 | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | CLOSE: (174) is inconsistent. % 32.07/5.04 | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | Case 2: % 32.07/5.04 | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | (175) all_310_0 = all_310_3 & all_310_4 = all_190_1 % 32.07/5.04 | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | ALPHA: (175) implies: % 32.07/5.04 | | | | | | | | | | | | | | (176) all_310_4 = all_190_1 % 32.07/5.04 | | | | | | | | | | | | | | (177) all_310_0 = all_310_3 % 32.07/5.04 | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | REDUCE: (128), (176) imply: % 32.07/5.04 | | | | | | | | | | | | | | (178) sdtasdt0(xc, all_310_5) = all_190_1 % 32.07/5.04 | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | REDUCE: (163), (177) imply: % 32.07/5.04 | | | | | | | | | | | | | | (179) sdtpldt0(all_308_0, all_39_0) = all_310_3 % 32.07/5.04 | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | BETA: splitting (169) gives: % 32.07/5.04 | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | Case 1: % 32.07/5.04 | | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | | (180) ~ (all_308_2 = 0) % 32.07/5.04 | | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | | REDUCE: (162), (180) imply: % 32.07/5.04 | | | | | | | | | | | | | | | (181) $false % 32.07/5.04 | | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | | CLOSE: (181) is inconsistent. % 32.07/5.04 | | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | Case 2: % 32.07/5.04 | | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | | (182) all_308_0 = all_190_2 % 32.07/5.04 | | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | | REDUCE: (179), (182) imply: % 32.07/5.04 | | | | | | | | | | | | | | | (183) sdtpldt0(all_190_2, all_39_0) = all_310_3 % 32.07/5.04 | | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_190_1, all_310_3, % 32.07/5.04 | | | | | | | | | | | | | | | all_39_0, all_190_2, simplifying with (110), (183) % 32.07/5.04 | | | | | | | | | | | | | | | gives: % 32.07/5.04 | | | | | | | | | | | | | | | (184) all_310_3 = all_190_1 % 32.07/5.04 | | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | | REDUCE: (131), (184) imply: % 32.07/5.04 | | | | | | | | | | | | | | | (185) sdtasdt0(all_310_5, xc) = all_190_1 % 32.07/5.04 | | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | | GROUND_INST: instantiating (mAddComm) with all_60_0, all_198_0, % 32.07/5.04 | | | | | | | | | | | | | | | all_312_5, simplifying with (26), (82), (137) % 32.07/5.04 | | | | | | | | | | | | | | | gives: % 32.07/5.04 | | | | | | | | | | | | | | | (186) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 32.07/5.04 | | | | | | | | | | | | | | | (sdtpldt0(all_198_0, all_60_0) = v2 & % 32.07/5.04 | | | | | | | | | | | | | | | aElement0(all_198_0) = v1 & aElement0(all_60_0) % 32.07/5.04 | | | | | | | | | | | | | | | = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 % 32.07/5.04 | | | | | | | | | | | | | | | = all_312_5)) % 32.07/5.04 | | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB) with all_60_0, all_198_0, % 32.07/5.04 | | | | | | | | | | | | | | | all_312_5, simplifying with (26), (82), (137) % 32.07/5.04 | | | | | | | | | | | | | | | gives: % 32.07/5.04 | | | | | | | | | | | | | | | (187) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 32.07/5.04 | | | | | | | | | | | | | | | (aElement0(all_312_5) = v2 & aElement0(all_198_0) % 32.07/5.04 | | | | | | | | | | | | | | | = v1 & aElement0(all_60_0) = v0 & ( ~ (v1 = 0) | % 32.07/5.04 | | | | | | | | | | | | | | | ~ (v0 = 0) | v2 = 0)) % 32.07/5.04 | | | | | | | | | | | | | | | % 32.07/5.04 | | | | | | | | | | | | | | | GROUND_INST: instantiating (mAddComm) with all_198_0, all_60_0, % 32.07/5.04 | | | | | | | | | | | | | | | all_310_5, simplifying with (26), (82), (126) % 32.07/5.04 | | | | | | | | | | | | | | | gives: % 32.07/5.04 | | | | | | | | | | | | | | | (188) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 32.07/5.04 | | | | | | | | | | | | | | | (sdtpldt0(all_60_0, all_198_0) = v2 & % 32.07/5.04 | | | | | | | | | | | | | | | aElement0(all_198_0) = v0 & aElement0(all_60_0) % 32.07/5.04 | | | | | | | | | | | | | | | = v1 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 % 32.07/5.04 | | | | | | | | | | | | | | | = all_310_5)) % 32.07/5.04 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB) with all_198_0, all_60_0, % 32.07/5.05 | | | | | | | | | | | | | | | all_310_5, simplifying with (26), (82), (126) % 32.07/5.05 | | | | | | | | | | | | | | | gives: % 32.07/5.05 | | | | | | | | | | | | | | | (189) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 32.07/5.05 | | | | | | | | | | | | | | | (aElement0(all_310_5) = v2 & aElement0(all_198_0) % 32.07/5.05 | | | | | | | | | | | | | | | = v0 & aElement0(all_60_0) = v1 & ( ~ (v1 = 0) | % 32.07/5.05 | | | | | | | | | | | | | | | ~ (v0 = 0) | v2 = 0)) % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | GROUND_INST: instantiating (96) with all_310_5, simplifying % 32.07/5.05 | | | | | | | | | | | | | | | with (122), (178) gives: % 32.07/5.05 | | | | | | | | | | | | | | | (190) ? [v0: int] : ( ~ (v0 = 0) & aElement0(all_310_5) % 32.07/5.05 | | | | | | | | | | | | | | | = v0) % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xc, all_310_5, % 32.07/5.05 | | | | | | | | | | | | | | | all_190_1, simplifying with (3), (122), (178) % 32.07/5.05 | | | | | | | | | | | | | | | gives: % 32.07/5.05 | | | | | | | | | | | | | | | (191) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 32.07/5.05 | | | | | | | | | | | | | | | (sdtasdt0(all_310_5, xc) = v2 & % 32.07/5.05 | | | | | | | | | | | | | | | aElement0(all_310_5) = v1 & aElement0(xc) = v0 & % 32.07/5.05 | | | | | | | | | | | | | | | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = % 32.07/5.05 | | | | | | | | | | | | | | | all_190_1)) % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with all_310_5, xc, % 32.07/5.05 | | | | | | | | | | | | | | | all_190_1, simplifying with (3), (122), (185) % 32.07/5.05 | | | | | | | | | | | | | | | gives: % 32.07/5.05 | | | | | | | | | | | | | | | (192) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 32.07/5.05 | | | | | | | | | | | | | | | (aElement0(all_310_5) = v0 & aElement0(all_190_1) % 32.07/5.05 | | | | | | | | | | | | | | | = v2 & aElement0(xc) = v1 & ( ~ (v1 = 0) | ~ % 32.07/5.05 | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | DELTA: instantiating (190) with fresh symbol all_460_0 % 32.07/5.05 | | | | | | | | | | | | | | | gives: % 32.07/5.05 | | | | | | | | | | | | | | | (193) ~ (all_460_0 = 0) & aElement0(all_310_5) = % 32.07/5.05 | | | | | | | | | | | | | | | all_460_0 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | ALPHA: (193) implies: % 32.07/5.05 | | | | | | | | | | | | | | | (194) ~ (all_460_0 = 0) % 32.07/5.05 | | | | | | | | | | | | | | | (195) aElement0(all_310_5) = all_460_0 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | DELTA: instantiating (189) with fresh symbols all_466_0, % 32.07/5.05 | | | | | | | | | | | | | | | all_466_1, all_466_2 gives: % 32.07/5.05 | | | | | | | | | | | | | | | (196) aElement0(all_310_5) = all_466_0 & % 32.07/5.05 | | | | | | | | | | | | | | | aElement0(all_198_0) = all_466_2 & % 32.07/5.05 | | | | | | | | | | | | | | | aElement0(all_60_0) = all_466_1 & ( ~ (all_466_1 = % 32.07/5.05 | | | | | | | | | | | | | | | 0) | ~ (all_466_2 = 0) | all_466_0 = 0) % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | ALPHA: (196) implies: % 32.07/5.05 | | | | | | | | | | | | | | | (197) aElement0(all_60_0) = all_466_1 % 32.07/5.05 | | | | | | | | | | | | | | | (198) aElement0(all_198_0) = all_466_2 % 32.07/5.05 | | | | | | | | | | | | | | | (199) aElement0(all_310_5) = all_466_0 % 32.07/5.05 | | | | | | | | | | | | | | | (200) ~ (all_466_1 = 0) | ~ (all_466_2 = 0) | % 32.07/5.05 | | | | | | | | | | | | | | | all_466_0 = 0 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | DELTA: instantiating (192) with fresh symbols all_470_0, % 32.07/5.05 | | | | | | | | | | | | | | | all_470_1, all_470_2 gives: % 32.07/5.05 | | | | | | | | | | | | | | | (201) aElement0(all_310_5) = all_470_2 & % 32.07/5.05 | | | | | | | | | | | | | | | aElement0(all_190_1) = all_470_0 & aElement0(xc) = % 32.07/5.05 | | | | | | | | | | | | | | | all_470_1 & ( ~ (all_470_1 = 0) | ~ (all_470_2 = % 32.07/5.05 | | | | | | | | | | | | | | | 0) | all_470_0 = 0) % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | ALPHA: (201) implies: % 32.07/5.05 | | | | | | | | | | | | | | | (202) aElement0(all_310_5) = all_470_2 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | DELTA: instantiating (187) with fresh symbols all_472_0, % 32.07/5.05 | | | | | | | | | | | | | | | all_472_1, all_472_2 gives: % 32.07/5.05 | | | | | | | | | | | | | | | (203) aElement0(all_312_5) = all_472_0 & % 32.07/5.05 | | | | | | | | | | | | | | | aElement0(all_198_0) = all_472_1 & % 32.07/5.05 | | | | | | | | | | | | | | | aElement0(all_60_0) = all_472_2 & ( ~ (all_472_1 = % 32.07/5.05 | | | | | | | | | | | | | | | 0) | ~ (all_472_2 = 0) | all_472_0 = 0) % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | ALPHA: (203) implies: % 32.07/5.05 | | | | | | | | | | | | | | | (204) aElement0(all_60_0) = all_472_2 % 32.07/5.05 | | | | | | | | | | | | | | | (205) aElement0(all_198_0) = all_472_1 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | DELTA: instantiating (191) with fresh symbols all_478_0, % 32.07/5.05 | | | | | | | | | | | | | | | all_478_1, all_478_2 gives: % 32.07/5.05 | | | | | | | | | | | | | | | (206) sdtasdt0(all_310_5, xc) = all_478_0 & % 32.07/5.05 | | | | | | | | | | | | | | | aElement0(all_310_5) = all_478_1 & aElement0(xc) = % 32.07/5.05 | | | | | | | | | | | | | | | all_478_2 & $i(all_478_0) & ( ~ (all_478_1 = 0) | % 32.07/5.05 | | | | | | | | | | | | | | | ~ (all_478_2 = 0) | all_478_0 = all_190_1) % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | ALPHA: (206) implies: % 32.07/5.05 | | | | | | | | | | | | | | | (207) aElement0(all_310_5) = all_478_1 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | DELTA: instantiating (186) with fresh symbols all_482_0, % 32.07/5.05 | | | | | | | | | | | | | | | all_482_1, all_482_2 gives: % 32.07/5.05 | | | | | | | | | | | | | | | (208) sdtpldt0(all_198_0, all_60_0) = all_482_0 & % 32.07/5.05 | | | | | | | | | | | | | | | aElement0(all_198_0) = all_482_1 & % 32.07/5.05 | | | | | | | | | | | | | | | aElement0(all_60_0) = all_482_2 & $i(all_482_0) & % 32.07/5.05 | | | | | | | | | | | | | | | ( ~ (all_482_1 = 0) | ~ (all_482_2 = 0) | % 32.07/5.05 | | | | | | | | | | | | | | | all_482_0 = all_312_5) % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | ALPHA: (208) implies: % 32.07/5.05 | | | | | | | | | | | | | | | (209) aElement0(all_60_0) = all_482_2 % 32.07/5.05 | | | | | | | | | | | | | | | (210) aElement0(all_198_0) = all_482_1 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | DELTA: instantiating (188) with fresh symbols all_486_0, % 32.07/5.05 | | | | | | | | | | | | | | | all_486_1, all_486_2 gives: % 32.07/5.05 | | | | | | | | | | | | | | | (211) sdtpldt0(all_60_0, all_198_0) = all_486_0 & % 32.07/5.05 | | | | | | | | | | | | | | | aElement0(all_198_0) = all_486_2 & % 32.07/5.05 | | | | | | | | | | | | | | | aElement0(all_60_0) = all_486_1 & $i(all_486_0) & % 32.07/5.05 | | | | | | | | | | | | | | | ( ~ (all_486_1 = 0) | ~ (all_486_2 = 0) | % 32.07/5.05 | | | | | | | | | | | | | | | all_486_0 = all_310_5) % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | ALPHA: (211) implies: % 32.07/5.05 | | | | | | | | | | | | | | | (212) aElement0(all_60_0) = all_486_1 % 32.07/5.05 | | | | | | | | | | | | | | | (213) aElement0(all_198_0) = all_486_2 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_482_2, all_60_0, % 32.07/5.05 | | | | | | | | | | | | | | | simplifying with (27), (209) gives: % 32.07/5.05 | | | | | | | | | | | | | | | (214) all_482_2 = 0 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_466_1, all_482_2, % 32.07/5.05 | | | | | | | | | | | | | | | all_60_0, simplifying with (197), (209) gives: % 32.07/5.05 | | | | | | | | | | | | | | | (215) all_482_2 = all_466_1 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_482_2, all_486_1, % 32.07/5.05 | | | | | | | | | | | | | | | all_60_0, simplifying with (209), (212) gives: % 32.07/5.05 | | | | | | | | | | | | | | | (216) all_486_1 = all_482_2 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_472_2, all_486_1, % 32.07/5.05 | | | | | | | | | | | | | | | all_60_0, simplifying with (204), (212) gives: % 32.07/5.05 | | | | | | | | | | | | | | | (217) all_486_1 = all_472_2 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_482_1, all_198_0, % 32.07/5.05 | | | | | | | | | | | | | | | simplifying with (83), (210) gives: % 32.07/5.05 | | | | | | | | | | | | | | | (218) all_482_1 = 0 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_466_2, all_482_1, % 32.07/5.05 | | | | | | | | | | | | | | | all_198_0, simplifying with (198), (210) gives: % 32.07/5.05 | | | | | | | | | | | | | | | (219) all_482_1 = all_466_2 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_482_1, all_486_2, % 32.07/5.05 | | | | | | | | | | | | | | | all_198_0, simplifying with (210), (213) gives: % 32.07/5.05 | | | | | | | | | | | | | | | (220) all_486_2 = all_482_1 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_472_1, all_486_2, % 32.07/5.05 | | | | | | | | | | | | | | | all_198_0, simplifying with (205), (213) gives: % 32.07/5.05 | | | | | | | | | | | | | | | (221) all_486_2 = all_472_1 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_460_0, all_470_2, % 32.07/5.05 | | | | | | | | | | | | | | | all_310_5, simplifying with (195), (202) gives: % 32.07/5.05 | | | | | | | | | | | | | | | (222) all_470_2 = all_460_0 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_470_2, all_478_1, % 32.07/5.05 | | | | | | | | | | | | | | | all_310_5, simplifying with (202), (207) gives: % 32.07/5.05 | | | | | | | | | | | | | | | (223) all_478_1 = all_470_2 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_466_0, all_478_1, % 32.07/5.05 | | | | | | | | | | | | | | | all_310_5, simplifying with (199), (207) gives: % 32.07/5.05 | | | | | | | | | | | | | | | (224) all_478_1 = all_466_0 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | COMBINE_EQS: (216), (217) imply: % 32.07/5.05 | | | | | | | | | | | | | | | (225) all_482_2 = all_472_2 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | SIMP: (225) implies: % 32.07/5.05 | | | | | | | | | | | | | | | (226) all_482_2 = all_472_2 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | COMBINE_EQS: (220), (221) imply: % 32.07/5.05 | | | | | | | | | | | | | | | (227) all_482_1 = all_472_1 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | SIMP: (227) implies: % 32.07/5.05 | | | | | | | | | | | | | | | (228) all_482_1 = all_472_1 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | COMBINE_EQS: (219), (228) imply: % 32.07/5.05 | | | | | | | | | | | | | | | (229) all_472_1 = all_466_2 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | COMBINE_EQS: (218), (228) imply: % 32.07/5.05 | | | | | | | | | | | | | | | (230) all_472_1 = 0 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | COMBINE_EQS: (214), (226) imply: % 32.07/5.05 | | | | | | | | | | | | | | | (231) all_472_2 = 0 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | COMBINE_EQS: (215), (226) imply: % 32.07/5.05 | | | | | | | | | | | | | | | (232) all_472_2 = all_466_1 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | COMBINE_EQS: (223), (224) imply: % 32.07/5.05 | | | | | | | | | | | | | | | (233) all_470_2 = all_466_0 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | SIMP: (233) implies: % 32.07/5.05 | | | | | | | | | | | | | | | (234) all_470_2 = all_466_0 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | COMBINE_EQS: (229), (230) imply: % 32.07/5.05 | | | | | | | | | | | | | | | (235) all_466_2 = 0 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | SIMP: (235) implies: % 32.07/5.05 | | | | | | | | | | | | | | | (236) all_466_2 = 0 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | COMBINE_EQS: (231), (232) imply: % 32.07/5.05 | | | | | | | | | | | | | | | (237) all_466_1 = 0 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | SIMP: (237) implies: % 32.07/5.05 | | | | | | | | | | | | | | | (238) all_466_1 = 0 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | COMBINE_EQS: (222), (234) imply: % 32.07/5.05 | | | | | | | | | | | | | | | (239) all_466_0 = all_460_0 % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 32.07/5.05 | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | Case 1: % 32.07/5.05 | | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | | (240) ~ (all_466_1 = 0) % 32.07/5.05 | | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | | REDUCE: (238), (240) imply: % 32.07/5.05 | | | | | | | | | | | | | | | | (241) $false % 32.07/5.05 | | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | | CLOSE: (241) is inconsistent. % 32.07/5.05 | | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | Case 2: % 32.07/5.05 | | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | | (242) ~ (all_466_2 = 0) | all_466_0 = 0 % 32.07/5.05 | | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 32.07/5.05 | | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | | Case 1: % 32.07/5.05 | | | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | | | (243) ~ (all_466_2 = 0) % 32.07/5.05 | | | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | | | REDUCE: (236), (243) imply: % 32.07/5.05 | | | | | | | | | | | | | | | | | (244) $false % 32.07/5.05 | | | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | | | CLOSE: (244) is inconsistent. % 32.07/5.05 | | | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | | Case 2: % 32.07/5.05 | | | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | | | (245) all_466_0 = 0 % 32.07/5.05 | | | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (245) imply: % 32.07/5.05 | | | | | | | | | | | | | | | | | (246) all_460_0 = 0 % 32.07/5.05 | | | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | | | SIMP: (246) implies: % 32.07/5.05 | | | | | | | | | | | | | | | | | (247) all_460_0 = 0 % 32.07/5.05 | | | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | | | REDUCE: (194), (247) imply: % 32.07/5.05 | | | | | | | | | | | | | | | | | (248) $false % 32.07/5.05 | | | | | | | | | | | | | | | | | % 32.07/5.05 | | | | | | | | | | | | | | | | | CLOSE: (248) is inconsistent. % 32.07/5.05 | | | | | | | | | | | | | | | | | % 32.07/5.06 | | | | | | | | | | | | | | | | End of split % 32.07/5.06 | | | | | | | | | | | | | | | | % 32.07/5.06 | | | | | | | | | | | | | | | End of split % 32.07/5.06 | | | | | | | | | | | | | | | % 32.07/5.06 | | | | | | | | | | | | | | End of split % 32.07/5.06 | | | | | | | | | | | | | | % 32.07/5.06 | | | | | | | | | | | | | End of split % 32.07/5.06 | | | | | | | | | | | | | % 32.07/5.06 | | | | | | | | | | | | End of split % 32.07/5.06 | | | | | | | | | | | | % 32.07/5.06 | | | | | | | | | | | End of split % 32.07/5.06 | | | | | | | | | | | % 32.07/5.06 | | | | | | | | | | End of split % 32.07/5.06 | | | | | | | | | | % 32.07/5.06 | | | | | | | | | End of split % 32.07/5.06 | | | | | | | | | % 32.07/5.06 | | | | | | | | End of split % 32.07/5.06 | | | | | | | | % 32.07/5.06 | | | | | | | End of split % 32.07/5.06 | | | | | | | % 32.07/5.06 | | | | | | End of split % 32.07/5.06 | | | | | | % 32.07/5.06 | | | | | Case 2: % 32.07/5.06 | | | | | | % 32.07/5.06 | | | | | | (249) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 32.07/5.06 | | | | | | aElementOf0(v1, all_36_1) = v2 & sdtasdt0(v0, all_39_0) = % 32.07/5.06 | | | | | | v1 & aElement0(v0) = 0 & $i(v1) & $i(v0)) % 32.07/5.06 | | | | | | % 32.07/5.06 | | | | | | DELTA: instantiating (249) with fresh symbols all_190_0, all_190_1, % 32.07/5.06 | | | | | | all_190_2 gives: % 32.07/5.06 | | | | | | (250) ~ (all_190_0 = 0) & aElementOf0(all_190_1, all_36_1) = % 32.07/5.06 | | | | | | all_190_0 & sdtasdt0(all_190_2, all_39_0) = all_190_1 & % 32.07/5.06 | | | | | | aElement0(all_190_2) = 0 & $i(all_190_1) & $i(all_190_2) % 32.07/5.06 | | | | | | % 32.07/5.06 | | | | | | ALPHA: (250) implies: % 32.07/5.06 | | | | | | (251) ~ (all_190_0 = 0) % 32.07/5.06 | | | | | | (252) $i(all_190_2) % 32.07/5.06 | | | | | | (253) $i(all_190_1) % 32.07/5.06 | | | | | | (254) aElement0(all_190_2) = 0 % 32.07/5.06 | | | | | | (255) sdtasdt0(all_190_2, all_39_0) = all_190_1 % 32.07/5.06 | | | | | | (256) aElementOf0(all_190_1, all_36_1) = all_190_0 % 32.07/5.06 | | | | | | % 32.07/5.06 | | | | | | GROUND_INST: instantiating (mMulComm) with all_190_2, all_39_0, % 32.07/5.06 | | | | | | all_190_1, simplifying with (17), (252), (255) gives: % 32.07/5.06 | | | | | | (257) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 32.07/5.06 | | | | | | (sdtasdt0(all_39_0, all_190_2) = v2 & aElement0(all_190_2) % 32.07/5.06 | | | | | | = v0 & aElement0(all_39_0) = v1 & $i(v2) & ( ~ (v1 = 0) | % 32.07/5.06 | | | | | | ~ (v0 = 0) | v2 = all_190_1)) % 32.07/5.06 | | | | | | % 32.07/5.06 | | | | | | GROUND_INST: instantiating (mSortsB_02) with all_190_2, all_39_0, % 32.07/5.06 | | | | | | all_190_1, simplifying with (17), (252), (255) gives: % 32.07/5.06 | | | | | | (258) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 32.07/5.06 | | | | | | (aElement0(all_190_1) = v2 & aElement0(all_190_2) = v0 & % 32.07/5.06 | | | | | | aElement0(all_39_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | % 32.07/5.06 | | | | | | v2 = 0)) % 32.07/5.06 | | | | | | % 32.07/5.06 | | | | | | GROUND_INST: instantiating (38) with all_190_1, all_190_0, % 32.07/5.06 | | | | | | simplifying with (253), (256) gives: % 32.07/5.06 | | | | | | (259) all_190_0 = 0 | ! [v0: $i] : ( ~ (sdtasdt0(xc, v0) = % 32.07/5.06 | | | | | | all_190_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 32.07/5.06 | | | | | | aElement0(v0) = v1)) % 32.07/5.06 | | | | | | % 32.07/5.06 | | | | | | DELTA: instantiating (258) with fresh symbols all_215_0, all_215_1, % 32.07/5.06 | | | | | | all_215_2 gives: % 32.07/5.06 | | | | | | (260) aElement0(all_190_1) = all_215_0 & aElement0(all_190_2) = % 32.07/5.06 | | | | | | all_215_2 & aElement0(all_39_0) = all_215_1 & ( ~ % 32.07/5.06 | | | | | | (all_215_1 = 0) | ~ (all_215_2 = 0) | all_215_0 = 0) % 32.07/5.06 | | | | | | % 32.07/5.06 | | | | | | ALPHA: (260) implies: % 32.07/5.06 | | | | | | (261) aElement0(all_39_0) = all_215_1 % 32.07/5.06 | | | | | | (262) aElement0(all_190_2) = all_215_2 % 32.07/5.06 | | | | | | (263) ~ (all_215_1 = 0) | ~ (all_215_2 = 0) | all_215_0 = 0 % 32.07/5.06 | | | | | | % 32.07/5.06 | | | | | | DELTA: instantiating (257) with fresh symbols all_217_0, all_217_1, % 32.07/5.06 | | | | | | all_217_2 gives: % 32.07/5.06 | | | | | | (264) sdtasdt0(all_39_0, all_190_2) = all_217_0 & % 32.07/5.06 | | | | | | aElement0(all_190_2) = all_217_2 & aElement0(all_39_0) = % 32.07/5.06 | | | | | | all_217_1 & $i(all_217_0) & ( ~ (all_217_1 = 0) | ~ % 32.07/5.06 | | | | | | (all_217_2 = 0) | all_217_0 = all_190_1) % 32.07/5.06 | | | | | | % 32.07/5.06 | | | | | | ALPHA: (264) implies: % 32.07/5.06 | | | | | | (265) aElement0(all_39_0) = all_217_1 % 32.07/5.06 | | | | | | (266) aElement0(all_190_2) = all_217_2 % 32.07/5.06 | | | | | | (267) sdtasdt0(all_39_0, all_190_2) = all_217_0 % 32.07/5.06 | | | | | | (268) ~ (all_217_1 = 0) | ~ (all_217_2 = 0) | all_217_0 = % 32.07/5.06 | | | | | | all_190_1 % 32.07/5.06 | | | | | | % 32.07/5.06 | | | | | | BETA: splitting (259) gives: % 32.07/5.06 | | | | | | % 32.07/5.06 | | | | | | Case 1: % 32.07/5.06 | | | | | | | % 32.07/5.06 | | | | | | | (269) all_190_0 = 0 % 32.07/5.06 | | | | | | | % 32.07/5.06 | | | | | | | REDUCE: (251), (269) imply: % 32.07/5.06 | | | | | | | (270) $false % 32.07/5.06 | | | | | | | % 32.07/5.06 | | | | | | | CLOSE: (270) is inconsistent. % 32.07/5.06 | | | | | | | % 32.07/5.06 | | | | | | Case 2: % 32.07/5.06 | | | | | | | % 32.07/5.06 | | | | | | | (271) ! [v0: $i] : ( ~ (sdtasdt0(xc, v0) = all_190_1) | ~ % 32.07/5.06 | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aElement0(v0) = % 32.07/5.06 | | | | | | | v1)) % 32.07/5.06 | | | | | | | % 32.07/5.06 | | | | | | | GROUND_INST: instantiating (5) with 0, all_217_1, all_39_0, % 32.07/5.06 | | | | | | | simplifying with (24), (265) gives: % 32.07/5.06 | | | | | | | (272) all_217_1 = 0 % 32.07/5.06 | | | | | | | % 32.07/5.06 | | | | | | | GROUND_INST: instantiating (5) with all_215_1, all_217_1, % 32.07/5.06 | | | | | | | all_39_0, simplifying with (261), (265) gives: % 32.07/5.06 | | | | | | | (273) all_217_1 = all_215_1 % 32.07/5.06 | | | | | | | % 32.07/5.06 | | | | | | | GROUND_INST: instantiating (5) with 0, all_217_2, all_190_2, % 32.07/5.06 | | | | | | | simplifying with (254), (266) gives: % 32.07/5.06 | | | | | | | (274) all_217_2 = 0 % 32.07/5.06 | | | | | | | % 32.07/5.06 | | | | | | | GROUND_INST: instantiating (5) with all_215_2, all_217_2, % 32.07/5.06 | | | | | | | all_190_2, simplifying with (262), (266) gives: % 32.07/5.06 | | | | | | | (275) all_217_2 = all_215_2 % 32.07/5.06 | | | | | | | % 32.07/5.06 | | | | | | | COMBINE_EQS: (272), (273) imply: % 32.07/5.06 | | | | | | | (276) all_215_1 = 0 % 32.07/5.06 | | | | | | | % 32.07/5.06 | | | | | | | SIMP: (276) implies: % 32.07/5.06 | | | | | | | (277) all_215_1 = 0 % 32.07/5.06 | | | | | | | % 32.07/5.06 | | | | | | | COMBINE_EQS: (274), (275) imply: % 32.07/5.06 | | | | | | | (278) all_215_2 = 0 % 32.07/5.06 | | | | | | | % 32.07/5.06 | | | | | | | SIMP: (278) implies: % 32.07/5.06 | | | | | | | (279) all_215_2 = 0 % 32.07/5.06 | | | | | | | % 32.07/5.06 | | | | | | | BETA: splitting (268) gives: % 32.07/5.06 | | | | | | | % 32.07/5.06 | | | | | | | Case 1: % 32.07/5.06 | | | | | | | | % 32.07/5.06 | | | | | | | | (280) ~ (all_217_1 = 0) % 32.07/5.06 | | | | | | | | % 32.07/5.06 | | | | | | | | REDUCE: (272), (280) imply: % 32.07/5.06 | | | | | | | | (281) $false % 32.07/5.06 | | | | | | | | % 32.07/5.06 | | | | | | | | CLOSE: (281) is inconsistent. % 32.07/5.06 | | | | | | | | % 32.07/5.06 | | | | | | | Case 2: % 32.07/5.06 | | | | | | | | % 32.07/5.06 | | | | | | | | (282) ~ (all_217_2 = 0) | all_217_0 = all_190_1 % 32.07/5.06 | | | | | | | | % 32.07/5.06 | | | | | | | | BETA: splitting (282) gives: % 32.07/5.06 | | | | | | | | % 32.07/5.06 | | | | | | | | Case 1: % 32.07/5.06 | | | | | | | | | % 32.07/5.06 | | | | | | | | | (283) ~ (all_217_2 = 0) % 32.07/5.06 | | | | | | | | | % 32.07/5.06 | | | | | | | | | REDUCE: (274), (283) imply: % 32.07/5.06 | | | | | | | | | (284) $false % 32.07/5.06 | | | | | | | | | % 32.07/5.06 | | | | | | | | | CLOSE: (284) is inconsistent. % 32.07/5.06 | | | | | | | | | % 32.07/5.06 | | | | | | | | Case 2: % 32.07/5.06 | | | | | | | | | % 32.07/5.06 | | | | | | | | | (285) all_217_0 = all_190_1 % 32.07/5.06 | | | | | | | | | % 32.07/5.06 | | | | | | | | | REDUCE: (267), (285) imply: % 32.07/5.06 | | | | | | | | | (286) sdtasdt0(all_39_0, all_190_2) = all_190_1 % 32.07/5.06 | | | | | | | | | % 32.07/5.06 | | | | | | | | | BETA: splitting (263) gives: % 32.07/5.06 | | | | | | | | | % 32.07/5.06 | | | | | | | | | Case 1: % 32.07/5.06 | | | | | | | | | | % 32.07/5.06 | | | | | | | | | | (287) ~ (all_215_1 = 0) % 32.07/5.06 | | | | | | | | | | % 32.07/5.06 | | | | | | | | | | REDUCE: (277), (287) imply: % 32.07/5.06 | | | | | | | | | | (288) $false % 32.07/5.06 | | | | | | | | | | % 32.07/5.06 | | | | | | | | | | CLOSE: (288) is inconsistent. % 32.07/5.06 | | | | | | | | | | % 32.07/5.06 | | | | | | | | | Case 2: % 32.07/5.06 | | | | | | | | | | % 32.07/5.06 | | | | | | | | | | % 32.07/5.06 | | | | | | | | | | GROUND_INST: instantiating (mMulAsso) with all_60_0, xc, % 32.07/5.06 | | | | | | | | | | all_190_2, all_39_0, all_190_1, simplifying with % 32.07/5.06 | | | | | | | | | | (3), (26), (63), (252), (286) gives: % 32.07/5.06 | | | | | | | | | | (289) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 32.07/5.06 | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtasdt0(all_60_0, v3) = % 32.07/5.06 | | | | | | | | | | v4 & sdtasdt0(xc, all_190_2) = v3 & % 32.07/5.06 | | | | | | | | | | aElement0(all_190_2) = v2 & aElement0(all_60_0) = % 32.07/5.06 | | | | | | | | | | v0 & aElement0(xc) = v1 & $i(v4) & $i(v3) & ( ~ % 32.07/5.06 | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = % 32.07/5.06 | | | | | | | | | | all_190_1)) % 32.07/5.06 | | | | | | | | | | % 32.07/5.06 | | | | | | | | | | GROUND_INST: instantiating (mMulAsso) with xc, all_60_0, % 32.07/5.06 | | | | | | | | | | all_190_2, all_39_0, all_190_1, simplifying with % 32.07/5.06 | | | | | | | | | | (3), (26), (28), (252), (286) gives: % 32.07/5.06 | | | | | | | | | | (290) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 32.07/5.06 | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtasdt0(all_60_0, % 32.07/5.06 | | | | | | | | | | all_190_2) = v3 & sdtasdt0(xc, v3) = v4 & % 32.07/5.06 | | | | | | | | | | aElement0(all_190_2) = v2 & aElement0(all_60_0) = % 32.07/5.06 | | | | | | | | | | v1 & aElement0(xc) = v0 & $i(v4) & $i(v3) & ( ~ % 32.07/5.06 | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = % 32.07/5.06 | | | | | | | | | | all_190_1)) % 32.07/5.06 | | | | | | | | | | % 32.07/5.06 | | | | | | | | | | DELTA: instantiating (290) with fresh symbols all_302_0, % 32.07/5.06 | | | | | | | | | | all_302_1, all_302_2, all_302_3, all_302_4 gives: % 32.07/5.06 | | | | | | | | | | (291) sdtasdt0(all_60_0, all_190_2) = all_302_1 & % 32.07/5.06 | | | | | | | | | | sdtasdt0(xc, all_302_1) = all_302_0 & % 32.07/5.06 | | | | | | | | | | aElement0(all_190_2) = all_302_2 & % 32.07/5.06 | | | | | | | | | | aElement0(all_60_0) = all_302_3 & aElement0(xc) = % 32.07/5.06 | | | | | | | | | | all_302_4 & $i(all_302_0) & $i(all_302_1) & ( ~ % 32.07/5.06 | | | | | | | | | | (all_302_2 = 0) | ~ (all_302_3 = 0) | ~ % 32.07/5.06 | | | | | | | | | | (all_302_4 = 0) | all_302_0 = all_190_1) % 32.07/5.06 | | | | | | | | | | % 32.07/5.06 | | | | | | | | | | ALPHA: (291) implies: % 32.07/5.07 | | | | | | | | | | (292) $i(all_302_1) % 32.07/5.07 | | | | | | | | | | (293) aElement0(xc) = all_302_4 % 32.07/5.07 | | | | | | | | | | (294) aElement0(all_60_0) = all_302_3 % 32.07/5.07 | | | | | | | | | | (295) aElement0(all_190_2) = all_302_2 % 32.07/5.07 | | | | | | | | | | (296) sdtasdt0(xc, all_302_1) = all_302_0 % 32.07/5.07 | | | | | | | | | | (297) sdtasdt0(all_60_0, all_190_2) = all_302_1 % 32.07/5.07 | | | | | | | | | | (298) ~ (all_302_2 = 0) | ~ (all_302_3 = 0) | ~ % 32.07/5.07 | | | | | | | | | | (all_302_4 = 0) | all_302_0 = all_190_1 % 32.07/5.07 | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | DELTA: instantiating (289) with fresh symbols all_304_0, % 32.07/5.07 | | | | | | | | | | all_304_1, all_304_2, all_304_3, all_304_4 gives: % 32.07/5.07 | | | | | | | | | | (299) sdtasdt0(all_60_0, all_304_1) = all_304_0 & % 32.07/5.07 | | | | | | | | | | sdtasdt0(xc, all_190_2) = all_304_1 & % 32.07/5.07 | | | | | | | | | | aElement0(all_190_2) = all_304_2 & % 32.07/5.07 | | | | | | | | | | aElement0(all_60_0) = all_304_4 & aElement0(xc) = % 32.07/5.07 | | | | | | | | | | all_304_3 & $i(all_304_0) & $i(all_304_1) & ( ~ % 32.07/5.07 | | | | | | | | | | (all_304_2 = 0) | ~ (all_304_3 = 0) | ~ % 32.07/5.07 | | | | | | | | | | (all_304_4 = 0) | all_304_0 = all_190_1) % 32.07/5.07 | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | ALPHA: (299) implies: % 32.07/5.07 | | | | | | | | | | (300) aElement0(xc) = all_304_3 % 32.07/5.07 | | | | | | | | | | (301) aElement0(all_60_0) = all_304_4 % 32.07/5.07 | | | | | | | | | | (302) aElement0(all_190_2) = all_304_2 % 32.07/5.07 | | | | | | | | | | (303) ~ (all_304_2 = 0) | ~ (all_304_3 = 0) | ~ % 32.07/5.07 | | | | | | | | | | (all_304_4 = 0) | all_304_0 = all_190_1 % 32.07/5.07 | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_304_3, xc, % 32.07/5.07 | | | | | | | | | | simplifying with (2), (300) gives: % 32.07/5.07 | | | | | | | | | | (304) all_304_3 = 0 % 32.07/5.07 | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | GROUND_INST: instantiating (5) with all_302_4, all_304_3, xc, % 32.07/5.07 | | | | | | | | | | simplifying with (293), (300) gives: % 32.07/5.07 | | | | | | | | | | (305) all_304_3 = all_302_4 % 32.07/5.07 | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_304_4, all_60_0, % 32.07/5.07 | | | | | | | | | | simplifying with (27), (301) gives: % 32.07/5.07 | | | | | | | | | | (306) all_304_4 = 0 % 32.07/5.07 | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | GROUND_INST: instantiating (5) with all_302_3, all_304_4, % 32.07/5.07 | | | | | | | | | | all_60_0, simplifying with (294), (301) gives: % 32.07/5.07 | | | | | | | | | | (307) all_304_4 = all_302_3 % 32.07/5.07 | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_304_2, all_190_2, % 32.07/5.07 | | | | | | | | | | simplifying with (254), (302) gives: % 32.07/5.07 | | | | | | | | | | (308) all_304_2 = 0 % 32.07/5.07 | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | GROUND_INST: instantiating (5) with all_302_2, all_304_2, % 32.07/5.07 | | | | | | | | | | all_190_2, simplifying with (295), (302) gives: % 32.07/5.07 | | | | | | | | | | (309) all_304_2 = all_302_2 % 32.07/5.07 | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | COMBINE_EQS: (308), (309) imply: % 32.07/5.07 | | | | | | | | | | (310) all_302_2 = 0 % 32.07/5.07 | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | COMBINE_EQS: (304), (305) imply: % 32.07/5.07 | | | | | | | | | | (311) all_302_4 = 0 % 32.07/5.07 | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | COMBINE_EQS: (306), (307) imply: % 32.07/5.07 | | | | | | | | | | (312) all_302_3 = 0 % 32.07/5.07 | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | SIMP: (312) implies: % 32.07/5.07 | | | | | | | | | | (313) all_302_3 = 0 % 32.07/5.07 | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | BETA: splitting (298) gives: % 32.07/5.07 | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | Case 1: % 32.07/5.07 | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | (314) ~ (all_302_2 = 0) % 32.07/5.07 | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | REDUCE: (310), (314) imply: % 32.07/5.07 | | | | | | | | | | | (315) $false % 32.07/5.07 | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | CLOSE: (315) is inconsistent. % 32.07/5.07 | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | Case 2: % 32.07/5.07 | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | (316) ~ (all_302_3 = 0) | ~ (all_302_4 = 0) | % 32.07/5.07 | | | | | | | | | | | all_302_0 = all_190_1 % 32.07/5.07 | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | BETA: splitting (303) gives: % 32.07/5.07 | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | Case 1: % 32.07/5.07 | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | (317) ~ (all_304_2 = 0) % 32.07/5.07 | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | REDUCE: (308), (317) imply: % 32.07/5.07 | | | | | | | | | | | | (318) $false % 32.07/5.07 | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | CLOSE: (318) is inconsistent. % 32.07/5.07 | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | Case 2: % 32.07/5.07 | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | (319) ~ (all_304_3 = 0) | ~ (all_304_4 = 0) | % 32.07/5.07 | | | | | | | | | | | | all_304_0 = all_190_1 % 32.07/5.07 | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | BETA: splitting (316) gives: % 32.07/5.07 | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | Case 1: % 32.07/5.07 | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | (320) ~ (all_302_3 = 0) % 32.07/5.07 | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | REDUCE: (313), (320) imply: % 32.07/5.07 | | | | | | | | | | | | | (321) $false % 32.07/5.07 | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | CLOSE: (321) is inconsistent. % 32.07/5.07 | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | Case 2: % 32.07/5.07 | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | (322) ~ (all_302_4 = 0) | all_302_0 = all_190_1 % 32.07/5.07 | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | BETA: splitting (322) gives: % 32.07/5.07 | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | Case 1: % 32.07/5.07 | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | (323) ~ (all_302_4 = 0) % 32.07/5.07 | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | REDUCE: (311), (323) imply: % 32.07/5.07 | | | | | | | | | | | | | | (324) $false % 32.07/5.07 | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | CLOSE: (324) is inconsistent. % 32.07/5.07 | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | Case 2: % 32.07/5.07 | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | (325) all_302_0 = all_190_1 % 32.07/5.07 | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | REDUCE: (296), (325) imply: % 32.07/5.07 | | | | | | | | | | | | | | (326) sdtasdt0(xc, all_302_1) = all_190_1 % 32.07/5.07 | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | BETA: splitting (319) gives: % 32.07/5.07 | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | Case 1: % 32.07/5.07 | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | (327) ~ (all_304_3 = 0) % 32.07/5.07 | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | REDUCE: (304), (327) imply: % 32.07/5.07 | | | | | | | | | | | | | | | (328) $false % 32.07/5.07 | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | CLOSE: (328) is inconsistent. % 32.07/5.07 | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | Case 2: % 32.07/5.07 | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | (329) ~ (all_304_4 = 0) | all_304_0 = all_190_1 % 32.07/5.07 | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | BETA: splitting (329) gives: % 32.07/5.07 | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | Case 1: % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | (330) ~ (all_304_4 = 0) % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | REDUCE: (306), (330) imply: % 32.07/5.07 | | | | | | | | | | | | | | | | (331) $false % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | CLOSE: (331) is inconsistent. % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | Case 2: % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (271) with all_302_1, simplifying % 32.07/5.07 | | | | | | | | | | | | | | | | with (292), (326) gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (332) ? [v0: int] : ( ~ (v0 = 0) & aElement0(all_302_1) % 32.07/5.07 | | | | | | | | | | | | | | | | = v0) % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xc, all_302_1, % 32.07/5.07 | | | | | | | | | | | | | | | | all_190_1, simplifying with (3), (292), (326) % 32.07/5.07 | | | | | | | | | | | | | | | | gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (333) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 32.07/5.07 | | | | | | | | | | | | | | | | (sdtasdt0(all_302_1, xc) = v2 & % 32.07/5.07 | | | | | | | | | | | | | | | | aElement0(all_302_1) = v1 & aElement0(xc) = v0 & % 32.07/5.07 | | | | | | | | | | | | | | | | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = % 32.07/5.07 | | | | | | | | | | | | | | | | all_190_1)) % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with xc, all_302_1, % 32.07/5.07 | | | | | | | | | | | | | | | | all_190_1, simplifying with (3), (292), (326) % 32.07/5.07 | | | | | | | | | | | | | | | | gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (334) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 32.07/5.07 | | | | | | | | | | | | | | | | (aElement0(all_302_1) = v1 & aElement0(all_190_1) % 32.07/5.07 | | | | | | | | | | | | | | | | = v2 & aElement0(xc) = v0 & ( ~ (v1 = 0) | ~ % 32.07/5.07 | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with all_60_0, all_190_2, % 32.07/5.07 | | | | | | | | | | | | | | | | all_302_1, simplifying with (26), (252), (297) % 32.07/5.07 | | | | | | | | | | | | | | | | gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (335) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 32.07/5.07 | | | | | | | | | | | | | | | | (sdtasdt0(all_190_2, all_60_0) = v2 & % 32.07/5.07 | | | | | | | | | | | | | | | | aElement0(all_190_2) = v1 & aElement0(all_60_0) % 32.07/5.07 | | | | | | | | | | | | | | | | = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 % 32.07/5.07 | | | | | | | | | | | | | | | | = all_302_1)) % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with all_60_0, % 32.07/5.07 | | | | | | | | | | | | | | | | all_190_2, all_302_1, simplifying with (26), % 32.07/5.07 | | | | | | | | | | | | | | | | (252), (297) gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (336) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 32.07/5.07 | | | | | | | | | | | | | | | | (aElement0(all_302_1) = v2 & aElement0(all_190_2) % 32.07/5.07 | | | | | | | | | | | | | | | | = v1 & aElement0(all_60_0) = v0 & ( ~ (v1 = 0) | % 32.07/5.07 | | | | | | | | | | | | | | | | ~ (v0 = 0) | v2 = 0)) % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | DELTA: instantiating (332) with fresh symbol all_384_0 % 32.07/5.07 | | | | | | | | | | | | | | | | gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (337) ~ (all_384_0 = 0) & aElement0(all_302_1) = % 32.07/5.07 | | | | | | | | | | | | | | | | all_384_0 % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | ALPHA: (337) implies: % 32.07/5.07 | | | | | | | | | | | | | | | | (338) ~ (all_384_0 = 0) % 32.07/5.07 | | | | | | | | | | | | | | | | (339) aElement0(all_302_1) = all_384_0 % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | DELTA: instantiating (336) with fresh symbols all_390_0, % 32.07/5.07 | | | | | | | | | | | | | | | | all_390_1, all_390_2 gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (340) aElement0(all_302_1) = all_390_0 & % 32.07/5.07 | | | | | | | | | | | | | | | | aElement0(all_190_2) = all_390_1 & % 32.07/5.07 | | | | | | | | | | | | | | | | aElement0(all_60_0) = all_390_2 & ( ~ (all_390_1 = % 32.07/5.07 | | | | | | | | | | | | | | | | 0) | ~ (all_390_2 = 0) | all_390_0 = 0) % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | ALPHA: (340) implies: % 32.07/5.07 | | | | | | | | | | | | | | | | (341) aElement0(all_60_0) = all_390_2 % 32.07/5.07 | | | | | | | | | | | | | | | | (342) aElement0(all_190_2) = all_390_1 % 32.07/5.07 | | | | | | | | | | | | | | | | (343) aElement0(all_302_1) = all_390_0 % 32.07/5.07 | | | | | | | | | | | | | | | | (344) ~ (all_390_1 = 0) | ~ (all_390_2 = 0) | % 32.07/5.07 | | | | | | | | | | | | | | | | all_390_0 = 0 % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | DELTA: instantiating (334) with fresh symbols all_392_0, % 32.07/5.07 | | | | | | | | | | | | | | | | all_392_1, all_392_2 gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (345) aElement0(all_302_1) = all_392_1 & % 32.07/5.07 | | | | | | | | | | | | | | | | aElement0(all_190_1) = all_392_0 & aElement0(xc) = % 32.07/5.07 | | | | | | | | | | | | | | | | all_392_2 & ( ~ (all_392_1 = 0) | ~ (all_392_2 = % 32.07/5.07 | | | | | | | | | | | | | | | | 0) | all_392_0 = 0) % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | ALPHA: (345) implies: % 32.07/5.07 | | | | | | | | | | | | | | | | (346) aElement0(all_302_1) = all_392_1 % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | DELTA: instantiating (335) with fresh symbols all_394_0, % 32.07/5.07 | | | | | | | | | | | | | | | | all_394_1, all_394_2 gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (347) sdtasdt0(all_190_2, all_60_0) = all_394_0 & % 32.07/5.07 | | | | | | | | | | | | | | | | aElement0(all_190_2) = all_394_1 & % 32.07/5.07 | | | | | | | | | | | | | | | | aElement0(all_60_0) = all_394_2 & $i(all_394_0) & % 32.07/5.07 | | | | | | | | | | | | | | | | ( ~ (all_394_1 = 0) | ~ (all_394_2 = 0) | % 32.07/5.07 | | | | | | | | | | | | | | | | all_394_0 = all_302_1) % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | ALPHA: (347) implies: % 32.07/5.07 | | | | | | | | | | | | | | | | (348) aElement0(all_60_0) = all_394_2 % 32.07/5.07 | | | | | | | | | | | | | | | | (349) aElement0(all_190_2) = all_394_1 % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | DELTA: instantiating (333) with fresh symbols all_398_0, % 32.07/5.07 | | | | | | | | | | | | | | | | all_398_1, all_398_2 gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (350) sdtasdt0(all_302_1, xc) = all_398_0 & % 32.07/5.07 | | | | | | | | | | | | | | | | aElement0(all_302_1) = all_398_1 & aElement0(xc) = % 32.07/5.07 | | | | | | | | | | | | | | | | all_398_2 & $i(all_398_0) & ( ~ (all_398_1 = 0) | % 32.07/5.07 | | | | | | | | | | | | | | | | ~ (all_398_2 = 0) | all_398_0 = all_190_1) % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | ALPHA: (350) implies: % 32.07/5.07 | | | | | | | | | | | | | | | | (351) aElement0(all_302_1) = all_398_1 % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_394_2, all_60_0, % 32.07/5.07 | | | | | | | | | | | | | | | | simplifying with (27), (348) gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (352) all_394_2 = 0 % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_390_2, all_394_2, % 32.07/5.07 | | | | | | | | | | | | | | | | all_60_0, simplifying with (341), (348) gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (353) all_394_2 = all_390_2 % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_394_1, all_190_2, % 32.07/5.07 | | | | | | | | | | | | | | | | simplifying with (254), (349) gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (354) all_394_1 = 0 % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_390_1, all_394_1, % 32.07/5.07 | | | | | | | | | | | | | | | | all_190_2, simplifying with (342), (349) gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (355) all_394_1 = all_390_1 % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_392_1, all_398_1, % 32.07/5.07 | | | | | | | | | | | | | | | | all_302_1, simplifying with (346), (351) gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (356) all_398_1 = all_392_1 % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_390_0, all_398_1, % 32.07/5.07 | | | | | | | | | | | | | | | | all_302_1, simplifying with (343), (351) gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (357) all_398_1 = all_390_0 % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_384_0, all_398_1, % 32.07/5.07 | | | | | | | | | | | | | | | | all_302_1, simplifying with (339), (351) gives: % 32.07/5.07 | | | | | | | | | | | | | | | | (358) all_398_1 = all_384_0 % 32.07/5.07 | | | | | | | | | | | | | | | | % 32.07/5.07 | | | | | | | | | | | | | | | | COMBINE_EQS: (356), (358) imply: % 32.07/5.08 | | | | | | | | | | | | | | | | (359) all_392_1 = all_384_0 % 32.07/5.08 | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | COMBINE_EQS: (356), (357) imply: % 32.07/5.08 | | | | | | | | | | | | | | | | (360) all_392_1 = all_390_0 % 32.07/5.08 | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | COMBINE_EQS: (354), (355) imply: % 32.07/5.08 | | | | | | | | | | | | | | | | (361) all_390_1 = 0 % 32.07/5.08 | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | SIMP: (361) implies: % 32.07/5.08 | | | | | | | | | | | | | | | | (362) all_390_1 = 0 % 32.07/5.08 | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | COMBINE_EQS: (352), (353) imply: % 32.07/5.08 | | | | | | | | | | | | | | | | (363) all_390_2 = 0 % 32.07/5.08 | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | SIMP: (363) implies: % 32.07/5.08 | | | | | | | | | | | | | | | | (364) all_390_2 = 0 % 32.07/5.08 | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | COMBINE_EQS: (359), (360) imply: % 32.07/5.08 | | | | | | | | | | | | | | | | (365) all_390_0 = all_384_0 % 32.07/5.08 | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | BETA: splitting (344) gives: % 32.07/5.08 | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | Case 1: % 32.07/5.08 | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | | (366) ~ (all_390_1 = 0) % 32.07/5.08 | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | | REDUCE: (362), (366) imply: % 32.07/5.08 | | | | | | | | | | | | | | | | | (367) $false % 32.07/5.08 | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | | CLOSE: (367) is inconsistent. % 32.07/5.08 | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | Case 2: % 32.07/5.08 | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | | (368) ~ (all_390_2 = 0) | all_390_0 = 0 % 32.07/5.08 | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | | BETA: splitting (368) gives: % 32.07/5.08 | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | | Case 1: % 32.07/5.08 | | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | | | (369) ~ (all_390_2 = 0) % 32.07/5.08 | | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | | | REDUCE: (364), (369) imply: % 32.07/5.08 | | | | | | | | | | | | | | | | | | (370) $false % 32.07/5.08 | | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | | | CLOSE: (370) is inconsistent. % 32.07/5.08 | | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | | Case 2: % 32.07/5.08 | | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | | | (371) all_390_0 = 0 % 32.07/5.08 | | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (371) imply: % 32.07/5.08 | | | | | | | | | | | | | | | | | | (372) all_384_0 = 0 % 32.07/5.08 | | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | | | SIMP: (372) implies: % 32.07/5.08 | | | | | | | | | | | | | | | | | | (373) all_384_0 = 0 % 32.07/5.08 | | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | | | REDUCE: (338), (373) imply: % 32.07/5.08 | | | | | | | | | | | | | | | | | | (374) $false % 32.07/5.08 | | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | | | CLOSE: (374) is inconsistent. % 32.07/5.08 | | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | | End of split % 32.07/5.08 | | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | | End of split % 32.07/5.08 | | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | | End of split % 32.07/5.08 | | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | | End of split % 32.07/5.08 | | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | | End of split % 32.07/5.08 | | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | | End of split % 32.07/5.08 | | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | | End of split % 32.07/5.08 | | | | | | | | | | | % 32.07/5.08 | | | | | | | | | | End of split % 32.07/5.08 | | | | | | | | | | % 32.07/5.08 | | | | | | | | | End of split % 32.07/5.08 | | | | | | | | | % 32.07/5.08 | | | | | | | | End of split % 32.07/5.08 | | | | | | | | % 32.07/5.08 | | | | | | | End of split % 32.07/5.08 | | | | | | | % 32.07/5.08 | | | | | | End of split % 32.07/5.08 | | | | | | % 32.07/5.08 | | | | | End of split % 32.07/5.08 | | | | | % 32.07/5.08 | | | | End of split % 32.07/5.08 | | | | % 32.07/5.08 | | | End of split % 32.07/5.08 | | | % 32.07/5.08 | | End of split % 32.07/5.08 | | % 32.07/5.08 | End of split % 32.07/5.08 | % 32.07/5.08 End of proof % 32.07/5.08 % SZS output end Proof for theBenchmark % 32.07/5.08 % 32.07/5.08 4464ms %------------------------------------------------------------------------------