%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM145+1 : TPTP v8.1.2. Released v6.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n022.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 : Wed Aug 30 18:44:36 EDT 2023 % Result : Theorem 27.41s 4.49s % Output : Proof 32.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : COM145+1 : TPTP v8.1.2. Released v6.4.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n022.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 : Tue Aug 29 13:06:08 EDT 2023 % 0.13/0.34 % CPUTime : % 0.44/0.67 ________ _____ % 0.44/0.67 ___ __ \_________(_)________________________________ % 0.44/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.44/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.44/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.44/0.67 % 0.44/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.44/0.67 (2023-06-19) % 0.44/0.67 % 0.44/0.67 (c) Philipp Rümmer, 2009-2023 % 0.44/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.44/0.67 Amanda Stjerna. % 0.44/0.67 Free software under BSD-3-Clause. % 0.44/0.67 % 0.44/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.44/0.67 % 0.44/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.44/0.68 Running up to 7 provers in parallel. % 0.44/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.44/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.44/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.44/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.44/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.44/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.44/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.08/1.34 Prover 4: Preprocessing ... % 4.08/1.35 Prover 1: Preprocessing ... % 4.64/1.38 Prover 0: Preprocessing ... % 4.64/1.38 Prover 6: Preprocessing ... % 4.64/1.38 Prover 5: Preprocessing ... % 4.64/1.38 Prover 2: Preprocessing ... % 4.64/1.38 Prover 3: Preprocessing ... % 10.96/2.29 Prover 6: Proving ... % 10.96/2.30 Prover 1: Constructing countermodel ... % 11.47/2.31 Prover 3: Constructing countermodel ... % 11.47/2.31 Prover 4: Constructing countermodel ... % 11.47/2.36 Prover 0: Proving ... % 11.47/2.43 Prover 5: Proving ... % 13.24/2.61 Prover 2: Proving ... % 27.41/4.49 Prover 6: proved (3798ms) % 27.41/4.49 % 27.41/4.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 27.41/4.49 % 27.41/4.49 Prover 3: stopped % 27.41/4.49 Prover 2: stopped % 27.41/4.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 27.41/4.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 27.41/4.50 Prover 0: stopped % 27.41/4.51 Prover 5: stopped % 28.19/4.52 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 28.19/4.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 28.19/4.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 28.84/4.65 Prover 7: Preprocessing ... % 28.84/4.65 Prover 10: Preprocessing ... % 29.76/4.73 Prover 8: Preprocessing ... % 29.76/4.74 Prover 11: Preprocessing ... % 29.76/4.77 Prover 13: Preprocessing ... % 30.51/4.83 Prover 10: Warning: ignoring some quantifiers % 30.51/4.86 Prover 1: Found proof (size 1174) % 30.51/4.86 Prover 1: proved (4170ms) % 30.51/4.86 Prover 11: stopped % 30.51/4.86 Prover 4: stopped % 30.51/4.87 Prover 10: Constructing countermodel ... % 30.51/4.88 Prover 10: stopped % 30.51/4.88 Prover 7: Warning: ignoring some quantifiers % 30.51/4.90 Prover 7: Constructing countermodel ... % 30.51/4.90 Prover 13: stopped % 30.51/4.90 Prover 8: Warning: ignoring some quantifiers % 30.51/4.90 Prover 7: stopped % 30.51/4.91 Prover 8: Constructing countermodel ... % 30.51/4.91 Prover 8: stopped % 30.51/4.91 % 30.51/4.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 30.51/4.91 % 30.51/4.94 % SZS output start Proof for theBenchmark % 30.51/4.95 Assumptions after simplification: % 30.51/4.95 --------------------------------- % 30.51/4.95 % 30.51/4.95 (DIFF-abs-app) % 31.28/4.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 31.28/4.97 $i] : ( ~ (vapp(v3, v4) = v5) | ~ (vabs(v0, v1, v2) = v5) | ~ $i(v4) | ~ % 31.28/4.97 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 31.28/4.97 % 31.28/4.97 (DIFF-noExp-someExp) % 31.28/4.97 $i(vnoExp) & ! [v0: $i] : ( ~ (vsomeExp(v0) = vnoExp) | ~ $i(v0)) % 31.28/4.97 % 31.28/4.97 (DIFF-var-abs) % 31.28/4.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 31.28/4.97 (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 31.28/4.97 $i(v1) | ~ $i(v0)) % 31.28/4.97 % 31.28/4.97 (DIFF-var-app) % 31.28/4.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vapp(v1, v2) = % 31.28/4.97 v3) | ~ (vvar(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 31.28/4.97 % 31.28/4.97 (EQ-abs) % 31.28/4.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 31.28/4.98 $i] : ! [v6: $i] : ( ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6) % 31.28/4.98 | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 31.28/4.98 (v5 = v2 & v4 = v1 & v3 = v0)) % 31.28/4.98 % 31.28/4.98 (EQ-app) % 31.28/4.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 31.28/4.98 (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 31.28/4.98 $i(v1) | ~ $i(v0) | (v3 = v1 & v2 = v0)) % 31.28/4.98 % 31.28/4.98 (EQ-arrow) % 31.28/4.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 31.28/4.98 (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 31.28/4.98 ~ $i(v1) | ~ $i(v0) | (v3 = v1 & v2 = v0)) % 31.28/4.98 % 31.28/4.98 (EQ-someExp) % 31.28/4.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v1) = v2) | % 31.28/4.98 ~ (vsomeExp(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 31.28/4.98 % 31.28/4.98 (T-Preservation-T-app) % 31.28/4.98 $i(ve2) & $i(ve1) & ? [v0: $i] : ? [v1: $i] : (vreduce(v0) = v1 & vapp(ve1, % 31.28/4.98 ve2) = v0 & $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 31.28/4.98 [v5: int] : ( ~ (v5 = 0) & vsomeExp(v3) = v1 & vtcheck(v2, v3, v4) = v5 & % 31.28/4.98 vtcheck(v2, v0, v4) = 0 & $i(v4) & $i(v3) & $i(v2))) % 31.28/4.98 % 31.28/4.98 (T-Preservation-T-app-IH1) % 31.28/4.98 $i(ve1) & ? [v0: $i] : (vreduce(ve1) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 31.28/4.98 $i] : ! [v3: $i] : ( ~ (vsomeExp(v2) = v0) | ~ (vtcheck(v1, ve1, v3) = % 31.28/4.98 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | vtcheck(v1, v2, v3) = 0)) % 31.28/4.98 % 31.28/4.98 (T-Preservation-T-app-IH2) % 31.28/4.99 $i(ve2) & ? [v0: $i] : (vreduce(ve2) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 31.28/4.99 $i] : ! [v3: $i] : ( ~ (vsomeExp(v2) = v0) | ~ (vtcheck(v1, ve2, v3) = % 31.28/4.99 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | vtcheck(v1, v2, v3) = 0)) % 31.28/4.99 % 31.28/4.99 (T-app) % 31.28/4.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 31.28/4.99 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (varrow(v0, v4) = v5) | ~ % 31.28/4.99 (vtcheck(v1, v6, v4) = v7) | ~ (vtcheck(v1, v2, v5) = 0) | ~ (vapp(v2, v3) % 31.28/4.99 = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 31.28/4.99 [v8: int] : ( ~ (v8 = 0) & vtcheck(v1, v3, v0) = v8)) % 31.28/4.99 % 31.28/4.99 (T-inv) % 31.28/4.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vtcheck(v2, v0, v1) = 0) | ~ % 31.28/4.99 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 31.28/4.99 ? [v6: $i] : ? [v7: $i] : (varrow(v5, v6) = v1 & vtcheck(v7, v4, v6) = 0 & % 31.28/4.99 vbind(v3, v5, v2) = v7 & vabs(v3, v5, v4) = v0 & $i(v7) & $i(v6) & $i(v5) % 31.28/4.99 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 31.28/4.99 : (varrow(v5, v1) = v6 & vtcheck(v2, v4, v5) = 0 & vtcheck(v2, v3, v6) = 0 & % 31.28/4.99 vapp(v3, v4) = v0 & $i(v6) & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : % 31.28/4.99 (vsomeType(v1) = v3 & $i(v3) & ? [v4: $i] : (vlookup(v4, v2) = v3 & % 31.28/4.99 vvar(v4) = v0 & $i(v4)))) % 31.28/4.99 % 31.28/4.99 (T-subst) % 31.28/4.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 31.28/4.99 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ (vsubst(v2, % 31.28/4.99 v3, v4) = v7) | ~ (vtcheck(v6, v4, v5) = 0) | ~ (vtcheck(v1, v7, v5) = % 31.28/4.99 v8) | ~ (vbind(v2, v0, v1) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 31.28/4.99 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: int] : ( ~ (v9 = 0) & vtcheck(v1, % 31.28/4.99 v3, v0) = v9)) % 31.28/4.99 % 31.28/4.99 (getSomeExp0) % 31.28/4.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (vgetSomeExp(v0) = v1) % 31.28/4.99 | ~ (vsomeExp(v2) = v0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 31.28/4.99 % 31.28/4.99 (isSomeExp0) % 31.28/4.99 $i(vnoExp) & ~ (visSomeExp(vnoExp) = 0) % 31.28/4.99 % 31.28/4.99 (isValue1) % 31.28/4.99 ! [v0: $i] : ! [v1: $i] : ( ~ (visValue(v1) = 0) | ~ (vvar(v0) = v1) | ~ % 31.28/4.99 $i(v1) | ~ $i(v0)) % 31.28/4.99 % 31.28/4.99 (isValue2) % 31.28/4.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (visValue(v2) = 0) | ~ % 31.28/4.99 (vapp(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 31.28/4.99 % 31.28/4.99 (reduce-INV) % 31.28/5.00 $i(vnoExp) & ! [v0: $i] : ! [v1: $i] : ( ~ (vreduce(v0) = v1) | ~ $i(v1) | % 31.28/5.00 ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 31.28/5.00 $i] : ? [v7: $i] : ? [v8: int] : ? [v9: int] : (v1 = vnoExp & ~ (v9 = % 31.28/5.00 0) & ~ (v8 = 0) & vreduce(v6) = v5 & visSomeExp(v5) = v8 & visValue(v6) % 31.28/5.00 = v9 & vapp(v7, v6) = v0 & vabs(v2, v3, v4) = v7 & $i(v7) & $i(v6) & % 31.28/5.00 $i(v5) & $i(v4) & $i(v3) & $i(v2)) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 31.28/5.00 $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] % 31.28/5.00 : ( ~ (v8 = 0) & vreduce(v5) = v3 & visSomeExp(v3) = v8 & vsomeExp(v9) = v1 % 31.28/5.00 & vsubst(v4, v5, v6) = v9 & visValue(v5) = 0 & vapp(v7, v5) = v0 & % 31.28/5.00 vabs(v4, v2, v6) = v7 & $i(v9) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 31.28/5.00 $i(v3) & $i(v2)) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 31.28/5.00 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (vreduce(v2) = v6 & % 31.28/5.00 vgetSomeExp(v6) = v8 & visSomeExp(v6) = 0 & vsomeExp(v9) = v1 & vapp(v7, % 31.28/5.00 v8) = v9 & vapp(v7, v2) = v0 & vabs(v3, v4, v5) = v7 & $i(v9) & $i(v8) & % 31.28/5.00 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)) | ? [v2: $i] : ? % 31.28/5.00 [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (vreduce(v2) = v3 & % 31.28/5.00 vgetSomeExp(v3) = v5 & visSomeExp(v3) = 0 & vsomeExp(v6) = v1 & vapp(v5, % 31.28/5.00 v4) = v6 & vapp(v2, v4) = v0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 31.28/5.00 $i(v2) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (vabs(v7, v8, v9) = % 31.28/5.00 v2) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7))) | ? [v2: $i] : ? [v3: $i] % 31.28/5.00 : ? [v4: $i] : ? [v5: int] : (v1 = vnoExp & ~ (v5 = 0) & vreduce(v3) = v4 % 31.28/5.00 & visSomeExp(v4) = v5 & vapp(v3, v2) = v0 & $i(v4) & $i(v3) & $i(v2) & ! % 31.28/5.00 [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (vabs(v6, v7, v8) = v3) | ~ % 31.28/5.00 $i(v8) | ~ $i(v7) | ~ $i(v6))) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 31.28/5.00 $i] : (v1 = vnoExp & vabs(v2, v3, v4) = v0 & $i(v4) & $i(v3) & $i(v2)) | % 31.28/5.00 ? [v2: $i] : (v1 = vnoExp & vvar(v2) = v0 & $i(v2))) % 31.28/5.00 % 31.28/5.00 (reduce0) % 31.28/5.00 $i(vnoExp) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = vnoExp | ~ % 31.28/5.00 (vreduce(v1) = v2) | ~ (vvar(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 31.28/5.00 % 31.28/5.00 (reduce1) % 31.28/5.00 $i(vnoExp) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 31.28/5.00 $i] : (v4 = vnoExp | ~ (vreduce(v3) = v4) | ~ (vabs(v0, v1, v2) = v3) | ~ % 31.28/5.00 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 31.28/5.00 % 31.28/5.00 (reduce3) % 31.28/5.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 31.28/5.00 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ (vreduce(v2) = % 31.28/5.00 v3) | ~ (visSomeExp(v1) = v8) | ~ (vapp(v7, v5) = v2) | ~ (vabs(v4, v0, % 31.28/5.00 v6) = v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 31.28/5.00 ~ $i(v1) | ~ $i(v0) | ? [v9: $i] : ? [v10: any] : ? [v11: $i] : ? [v12: % 31.28/5.00 $i] : (vreduce(v5) = v9 & vsomeExp(v11) = v12 & vsubst(v4, v5, v6) = v11 & % 31.28/5.00 visValue(v5) = v10 & $i(v12) & $i(v11) & $i(v9) & ( ~ (v10 = 0) | ~ (v9 = % 31.28/5.00 v1) | v12 = v3))) % 31.28/5.00 % 31.28/5.00 (function-axioms) % 31.28/5.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 31.28/5.00 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0: % 31.28/5.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 31.28/5.00 : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3, % 31.28/5.00 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 31.28/5.00 [v4: $i] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = % 31.28/5.00 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 31.28/5.00 : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & ! % 31.28/5.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3, % 31.28/5.00 v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 31.28/5.00 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~ % 31.28/5.00 (vlookup(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 31.28/5.00 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 31.28/5.00 (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0: $i] : ! % 31.28/5.00 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~ % 31.28/5.00 (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 31.28/5.00 ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 31.28/5.00 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0)) % 31.28/5.00 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 31.28/5.00 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: $i] : % 31.28/5.00 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~ % 31.28/5.00 (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 31.28/5.00 ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 31.28/5.00 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) = % 31.28/5.00 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 31.28/5.00 $i] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & ! % 31.28/5.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~ % 31.28/5.00 (vsomeType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 31.28/5.00 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ % 31.28/5.00 (visValue(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 31.28/5.00 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0)) % 31.28/5.00 % 31.28/5.00 Further assumptions not needed in the proof: % 31.28/5.00 -------------------------------------------- % 31.28/5.01 DIFF-empty-bind, DIFF-noType-someType, EQ-bind, EQ-empty, EQ-noExp, EQ-noType, % 31.28/5.01 EQ-someType, EQ-var, T-Context-Duplicate, T-Context-Swap, T-Strong, T-Weak, % 31.28/5.01 T-Weak-FreeVar, T-abs, T-var, gensym-is-fresh, getSomeType0, isFreeVar0, % 31.28/5.01 isFreeVar1, isFreeVar2, isSomeExp1, isSomeType0, isSomeType1, isValue0, % 31.28/5.01 lookup-INV, lookup0, lookup1, lookup2, reduce2, reduce4, reduce5, reduce6, % 31.28/5.01 subst-INV, subst0, subst1, subst2, subst3, subst4, subst5 % 31.28/5.01 % 31.28/5.01 Those formulas are unsatisfiable: % 31.28/5.01 --------------------------------- % 31.28/5.01 % 31.28/5.01 Begin of proof % 31.28/5.01 | % 31.28/5.01 | ALPHA: (DIFF-noExp-someExp) implies: % 31.28/5.01 | (1) ! [v0: $i] : ( ~ (vsomeExp(v0) = vnoExp) | ~ $i(v0)) % 31.28/5.01 | % 31.28/5.01 | ALPHA: (isSomeExp0) implies: % 31.28/5.01 | (2) ~ (visSomeExp(vnoExp) = 0) % 31.28/5.01 | % 31.28/5.01 | ALPHA: (reduce0) implies: % 31.28/5.01 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = vnoExp | ~ % 31.28/5.01 | (vreduce(v1) = v2) | ~ (vvar(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ % 31.28/5.01 | $i(v0)) % 31.28/5.01 | % 31.28/5.01 | ALPHA: (reduce1) implies: % 31.28/5.01 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 31.28/5.01 | (v4 = vnoExp | ~ (vreduce(v3) = v4) | ~ (vabs(v0, v1, v2) = v3) | ~ % 31.28/5.01 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 31.28/5.01 | % 31.28/5.01 | ALPHA: (reduce-INV) implies: % 31.28/5.01 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (vreduce(v0) = v1) | ~ $i(v1) | ~ % 31.28/5.01 | $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 31.28/5.01 | [v6: $i] : ? [v7: $i] : ? [v8: int] : ? [v9: int] : (v1 = vnoExp & % 31.28/5.01 | ~ (v9 = 0) & ~ (v8 = 0) & vreduce(v6) = v5 & visSomeExp(v5) = v8 % 31.28/5.01 | & visValue(v6) = v9 & vapp(v7, v6) = v0 & vabs(v2, v3, v4) = v7 & % 31.28/5.01 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)) | ? [v2: $i] % 31.28/5.01 | : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 31.28/5.01 | : ? [v8: int] : ? [v9: $i] : ( ~ (v8 = 0) & vreduce(v5) = v3 & % 31.28/5.01 | visSomeExp(v3) = v8 & vsomeExp(v9) = v1 & vsubst(v4, v5, v6) = v9 & % 31.28/5.01 | visValue(v5) = 0 & vapp(v7, v5) = v0 & vabs(v4, v2, v6) = v7 & % 31.28/5.01 | $i(v9) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)) | ? % 31.28/5.01 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? % 31.28/5.01 | [v7: $i] : ? [v8: $i] : ? [v9: $i] : (vreduce(v2) = v6 & % 31.28/5.01 | vgetSomeExp(v6) = v8 & visSomeExp(v6) = 0 & vsomeExp(v9) = v1 & % 31.28/5.01 | vapp(v7, v8) = v9 & vapp(v7, v2) = v0 & vabs(v3, v4, v5) = v7 & % 31.28/5.01 | $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 31.28/5.01 | $i(v2)) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 31.28/5.01 | ? [v6: $i] : (vreduce(v2) = v3 & vgetSomeExp(v3) = v5 & % 31.28/5.01 | visSomeExp(v3) = 0 & vsomeExp(v6) = v1 & vapp(v5, v4) = v6 & % 31.28/5.01 | vapp(v2, v4) = v0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ! % 31.28/5.01 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (vabs(v7, v8, v9) = v2) % 31.28/5.01 | | ~ $i(v9) | ~ $i(v8) | ~ $i(v7))) | ? [v2: $i] : ? [v3: $i] % 31.28/5.01 | : ? [v4: $i] : ? [v5: int] : (v1 = vnoExp & ~ (v5 = 0) & % 31.28/5.01 | vreduce(v3) = v4 & visSomeExp(v4) = v5 & vapp(v3, v2) = v0 & $i(v4) % 31.28/5.01 | & $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 31.28/5.01 | (vabs(v6, v7, v8) = v3) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6))) | % 31.28/5.01 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (v1 = vnoExp & vabs(v2, v3, % 31.28/5.01 | v4) = v0 & $i(v4) & $i(v3) & $i(v2)) | ? [v2: $i] : (v1 = vnoExp % 31.28/5.01 | & vvar(v2) = v0 & $i(v2))) % 31.28/5.01 | % 31.28/5.01 | ALPHA: (T-Preservation-T-app-IH1) implies: % 31.28/5.01 | (6) ? [v0: $i] : (vreduce(ve1) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 31.28/5.01 | ! [v3: $i] : ( ~ (vsomeExp(v2) = v0) | ~ (vtcheck(v1, ve1, v3) = 0) % 31.28/5.01 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | vtcheck(v1, v2, v3) = 0)) % 31.28/5.01 | % 31.28/5.01 | ALPHA: (T-Preservation-T-app-IH2) implies: % 31.28/5.02 | (7) ? [v0: $i] : (vreduce(ve2) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 31.28/5.02 | ! [v3: $i] : ( ~ (vsomeExp(v2) = v0) | ~ (vtcheck(v1, ve2, v3) = 0) % 31.28/5.02 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | vtcheck(v1, v2, v3) = 0)) % 31.28/5.02 | % 31.28/5.02 | ALPHA: (T-Preservation-T-app) implies: % 31.28/5.02 | (8) $i(ve1) % 31.28/5.02 | (9) $i(ve2) % 31.28/5.02 | (10) ? [v0: $i] : ? [v1: $i] : (vreduce(v0) = v1 & vapp(ve1, ve2) = v0 & % 31.28/5.02 | $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 31.28/5.02 | int] : ( ~ (v5 = 0) & vsomeExp(v3) = v1 & vtcheck(v2, v3, v4) = v5 % 31.28/5.02 | & vtcheck(v2, v0, v4) = 0 & $i(v4) & $i(v3) & $i(v2))) % 31.28/5.02 | % 31.28/5.02 | ALPHA: (function-axioms) implies: % 31.28/5.02 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 31.28/5.02 | : (v1 = v0 | ~ (visValue(v2) = v1) | ~ (visValue(v2) = v0)) % 31.28/5.02 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vreduce(v2) = % 31.28/5.02 | v1) | ~ (vreduce(v2) = v0)) % 31.28/5.02 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 31.28/5.02 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) % 31.28/5.02 | | ~ (vtcheck(v4, v3, v2) = v0)) % 31.28/5.02 | % 31.28/5.02 | DELTA: instantiating (6) with fresh symbol all_57_0 gives: % 31.28/5.02 | (14) vreduce(ve1) = all_57_0 & $i(all_57_0) & ! [v0: $i] : ! [v1: $i] : % 31.28/5.02 | ! [v2: $i] : ( ~ (vsomeExp(v1) = all_57_0) | ~ (vtcheck(v0, ve1, v2) % 31.28/5.02 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | vtcheck(v0, v1, v2) = % 31.28/5.02 | 0) % 31.28/5.02 | % 31.28/5.02 | ALPHA: (14) implies: % 31.28/5.02 | (15) $i(all_57_0) % 31.28/5.02 | (16) vreduce(ve1) = all_57_0 % 31.28/5.02 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vsomeExp(v1) = % 31.28/5.02 | all_57_0) | ~ (vtcheck(v0, ve1, v2) = 0) | ~ $i(v2) | ~ $i(v1) % 31.28/5.02 | | ~ $i(v0) | vtcheck(v0, v1, v2) = 0) % 31.28/5.02 | % 31.28/5.02 | DELTA: instantiating (7) with fresh symbol all_60_0 gives: % 31.28/5.02 | (18) vreduce(ve2) = all_60_0 & $i(all_60_0) & ! [v0: $i] : ! [v1: $i] : % 31.28/5.02 | ! [v2: $i] : ( ~ (vsomeExp(v1) = all_60_0) | ~ (vtcheck(v0, ve2, v2) % 31.28/5.02 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | vtcheck(v0, v1, v2) = % 31.28/5.02 | 0) % 31.28/5.02 | % 31.28/5.02 | ALPHA: (18) implies: % 31.28/5.02 | (19) $i(all_60_0) % 31.28/5.02 | (20) vreduce(ve2) = all_60_0 % 31.28/5.02 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vsomeExp(v1) = % 31.28/5.02 | all_60_0) | ~ (vtcheck(v0, ve2, v2) = 0) | ~ $i(v2) | ~ $i(v1) % 31.28/5.02 | | ~ $i(v0) | vtcheck(v0, v1, v2) = 0) % 31.28/5.02 | % 31.28/5.02 | DELTA: instantiating (10) with fresh symbols all_63_0, all_63_1 gives: % 31.28/5.02 | (22) vreduce(all_63_1) = all_63_0 & vapp(ve1, ve2) = all_63_1 & % 31.28/5.02 | $i(all_63_0) & $i(all_63_1) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 31.28/5.02 | : ? [v3: int] : ( ~ (v3 = 0) & vsomeExp(v1) = all_63_0 & vtcheck(v0, % 31.28/5.02 | v1, v2) = v3 & vtcheck(v0, all_63_1, v2) = 0 & $i(v2) & $i(v1) & % 31.28/5.02 | $i(v0)) % 31.28/5.02 | % 31.28/5.02 | ALPHA: (22) implies: % 31.28/5.02 | (23) $i(all_63_1) % 31.28/5.02 | (24) $i(all_63_0) % 31.28/5.02 | (25) vapp(ve1, ve2) = all_63_1 % 31.28/5.02 | (26) vreduce(all_63_1) = all_63_0 % 31.28/5.02 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) % 31.28/5.02 | & vsomeExp(v1) = all_63_0 & vtcheck(v0, v1, v2) = v3 & vtcheck(v0, % 31.28/5.02 | all_63_1, v2) = 0 & $i(v2) & $i(v1) & $i(v0)) % 31.28/5.02 | % 31.28/5.02 | DELTA: instantiating (27) with fresh symbols all_65_0, all_65_1, all_65_2, % 31.28/5.02 | all_65_3 gives: % 31.28/5.03 | (28) ~ (all_65_0 = 0) & vsomeExp(all_65_2) = all_63_0 & vtcheck(all_65_3, % 31.28/5.03 | all_65_2, all_65_1) = all_65_0 & vtcheck(all_65_3, all_63_1, % 31.28/5.03 | all_65_1) = 0 & $i(all_65_1) & $i(all_65_2) & $i(all_65_3) % 31.28/5.03 | % 31.28/5.03 | ALPHA: (28) implies: % 31.28/5.03 | (29) ~ (all_65_0 = 0) % 31.28/5.03 | (30) $i(all_65_3) % 31.28/5.03 | (31) $i(all_65_2) % 31.28/5.03 | (32) $i(all_65_1) % 31.28/5.03 | (33) vtcheck(all_65_3, all_63_1, all_65_1) = 0 % 31.28/5.03 | (34) vtcheck(all_65_3, all_65_2, all_65_1) = all_65_0 % 31.28/5.03 | (35) vsomeExp(all_65_2) = all_63_0 % 31.28/5.03 | % 31.28/5.03 | GROUND_INST: instantiating (T-inv) with all_63_1, all_65_1, all_65_3, % 31.28/5.03 | simplifying with (23), (30), (32), (33) gives: % 31.28/5.03 | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 31.28/5.03 | (varrow(v2, v3) = all_65_1 & vtcheck(v4, v1, v3) = 0 & vbind(v0, v2, % 31.28/5.03 | all_65_3) = v4 & vabs(v0, v2, v1) = all_63_1 & $i(v4) & $i(v3) & % 31.28/5.03 | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 31.28/5.03 | : ? [v3: $i] : (varrow(v2, all_65_1) = v3 & vtcheck(all_65_3, v1, v2) % 31.28/5.03 | = 0 & vtcheck(all_65_3, v0, v3) = 0 & vapp(v0, v1) = all_63_1 & % 31.28/5.03 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 31.28/5.03 | (vsomeType(all_65_1) = v0 & $i(v0) & ? [v1: $i] : (vlookup(v1, % 31.28/5.03 | all_65_3) = v0 & vvar(v1) = all_63_1 & $i(v1))) % 31.28/5.03 | % 31.28/5.03 | GROUND_INST: instantiating (5) with ve1, all_57_0, simplifying with (8), (15), % 31.28/5.03 | (16) gives: % 31.28/5.03 | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 31.28/5.03 | ? [v5: $i] : ? [v6: int] : ? [v7: int] : (all_57_0 = vnoExp & ~ (v7 % 31.28/5.03 | = 0) & ~ (v6 = 0) & vreduce(v4) = v3 & visSomeExp(v3) = v6 & % 31.28/5.03 | visValue(v4) = v7 & vapp(v5, v4) = ve1 & vabs(v0, v1, v2) = v5 & % 31.28/5.03 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 31.28/5.03 | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 31.28/5.03 | ? [v6: int] : ? [v7: $i] : ( ~ (v6 = 0) & vreduce(v3) = v1 & % 31.28/5.03 | visSomeExp(v1) = v6 & vsomeExp(v7) = all_57_0 & vsubst(v2, v3, v4) = % 31.28/5.03 | v7 & visValue(v3) = 0 & vapp(v5, v3) = ve1 & vabs(v2, v0, v4) = v5 & % 31.28/5.03 | $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? % 31.28/5.03 | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 31.28/5.03 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vreduce(v0) = v4 & % 31.28/5.03 | vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & vsomeExp(v7) = all_57_0 % 31.28/5.03 | & vapp(v5, v6) = v7 & vapp(v5, v0) = ve1 & vabs(v1, v2, v3) = v5 & % 31.28/5.03 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 31.28/5.03 | $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 31.28/5.03 | [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & visSomeExp(v1) = % 31.28/5.03 | 0 & vsomeExp(v4) = all_57_0 & vapp(v3, v2) = v4 & vapp(v0, v2) = ve1 % 31.28/5.03 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: % 31.28/5.04 | $i] : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ $i(v7) | ~ % 31.28/5.04 | $i(v6) | ~ $i(v5))) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 31.28/5.04 | ? [v3: int] : (all_57_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) = v2 & % 31.28/5.04 | visSomeExp(v2) = v3 & vapp(v1, v0) = ve1 & $i(v2) & $i(v1) & $i(v0) % 31.28/5.04 | & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (vabs(v4, v5, v6) = % 31.28/5.04 | v1) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4))) | ? [v0: $i] : ? % 31.28/5.04 | [v1: $i] : ? [v2: $i] : (all_57_0 = vnoExp & vabs(v0, v1, v2) = ve1 & % 31.28/5.04 | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : (all_57_0 = vnoExp & % 31.28/5.04 | vvar(v0) = ve1 & $i(v0)) % 31.28/5.04 | % 31.28/5.04 | GROUND_INST: instantiating (5) with ve2, all_60_0, simplifying with (9), (19), % 31.28/5.04 | (20) gives: % 31.28/5.04 | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 31.28/5.04 | ? [v5: $i] : ? [v6: int] : ? [v7: int] : (all_60_0 = vnoExp & ~ (v7 % 31.28/5.04 | = 0) & ~ (v6 = 0) & vreduce(v4) = v3 & visSomeExp(v3) = v6 & % 31.28/5.04 | visValue(v4) = v7 & vapp(v5, v4) = ve2 & vabs(v0, v1, v2) = v5 & % 31.28/5.04 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 31.28/5.04 | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 31.28/5.04 | ? [v6: int] : ? [v7: $i] : ( ~ (v6 = 0) & vreduce(v3) = v1 & % 31.28/5.04 | visSomeExp(v1) = v6 & vsomeExp(v7) = all_60_0 & vsubst(v2, v3, v4) = % 31.28/5.04 | v7 & visValue(v3) = 0 & vapp(v5, v3) = ve2 & vabs(v2, v0, v4) = v5 & % 31.28/5.04 | $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? % 31.28/5.04 | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 31.28/5.04 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vreduce(v0) = v4 & % 31.28/5.04 | vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & vsomeExp(v7) = all_60_0 % 31.28/5.04 | & vapp(v5, v6) = v7 & vapp(v5, v0) = ve2 & vabs(v1, v2, v3) = v5 & % 31.28/5.04 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 31.28/5.04 | $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 31.28/5.04 | [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & visSomeExp(v1) = % 31.28/5.04 | 0 & vsomeExp(v4) = all_60_0 & vapp(v3, v2) = v4 & vapp(v0, v2) = ve2 % 31.28/5.04 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: % 31.28/5.04 | $i] : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ $i(v7) | ~ % 31.28/5.04 | $i(v6) | ~ $i(v5))) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 31.28/5.04 | ? [v3: int] : (all_60_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) = v2 & % 31.28/5.04 | visSomeExp(v2) = v3 & vapp(v1, v0) = ve2 & $i(v2) & $i(v1) & $i(v0) % 31.28/5.04 | & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (vabs(v4, v5, v6) = % 31.28/5.04 | v1) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4))) | ? [v0: $i] : ? % 31.28/5.04 | [v1: $i] : ? [v2: $i] : (all_60_0 = vnoExp & vabs(v0, v1, v2) = ve2 & % 31.28/5.04 | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : (all_60_0 = vnoExp & % 31.28/5.04 | vvar(v0) = ve2 & $i(v0)) % 31.28/5.04 | % 31.28/5.04 | GROUND_INST: instantiating (5) with all_63_1, all_63_0, simplifying with (23), % 31.28/5.04 | (24), (26) gives: % 31.28/5.04 | (39) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 31.28/5.04 | ? [v5: $i] : ? [v6: int] : ? [v7: int] : (all_63_0 = vnoExp & ~ (v7 % 31.28/5.04 | = 0) & ~ (v6 = 0) & vreduce(v4) = v3 & visSomeExp(v3) = v6 & % 31.28/5.04 | visValue(v4) = v7 & vapp(v5, v4) = all_63_1 & vabs(v0, v1, v2) = v5 % 31.28/5.04 | & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] % 31.28/5.04 | : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] % 31.28/5.04 | : ? [v6: int] : ? [v7: $i] : ( ~ (v6 = 0) & vreduce(v3) = v1 & % 31.28/5.04 | visSomeExp(v1) = v6 & vsomeExp(v7) = all_63_0 & vsubst(v2, v3, v4) = % 31.28/5.04 | v7 & visValue(v3) = 0 & vapp(v5, v3) = all_63_1 & vabs(v2, v0, v4) = % 31.28/5.04 | v5 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | % 31.28/5.04 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 31.28/5.04 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vreduce(v0) = v4 & % 31.28/5.04 | vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & vsomeExp(v7) = all_63_0 % 31.28/5.04 | & vapp(v5, v6) = v7 & vapp(v5, v0) = all_63_1 & vabs(v1, v2, v3) = % 31.28/5.04 | v5 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 31.28/5.04 | $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 31.28/5.04 | [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & visSomeExp(v1) = % 31.28/5.04 | 0 & vsomeExp(v4) = all_63_0 & vapp(v3, v2) = v4 & vapp(v0, v2) = % 31.28/5.04 | all_63_1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] % 31.28/5.04 | : ! [v6: $i] : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ % 31.28/5.04 | $i(v7) | ~ $i(v6) | ~ $i(v5))) | ? [v0: $i] : ? [v1: $i] : ? % 31.28/5.04 | [v2: $i] : ? [v3: int] : (all_63_0 = vnoExp & ~ (v3 = 0) & % 31.28/5.04 | vreduce(v1) = v2 & visSomeExp(v2) = v3 & vapp(v1, v0) = all_63_1 & % 31.86/5.04 | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 31.86/5.04 | ( ~ (vabs(v4, v5, v6) = v1) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4))) | % 31.86/5.04 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_63_0 = vnoExp & vabs(v0, % 31.86/5.04 | v1, v2) = all_63_1 & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 31.86/5.04 | (all_63_0 = vnoExp & vvar(v0) = all_63_1 & $i(v0)) % 31.86/5.04 | % 31.86/5.04 | BETA: splitting (36) gives: % 31.86/5.04 | % 31.86/5.04 | Case 1: % 31.86/5.04 | | % 31.86/5.04 | | (40) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 31.86/5.04 | | : (varrow(v2, v3) = all_65_1 & vtcheck(v4, v1, v3) = 0 & vbind(v0, % 31.86/5.04 | | v2, all_65_3) = v4 & vabs(v0, v2, v1) = all_63_1 & $i(v4) & % 31.86/5.04 | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 31.86/5.04 | | % 31.86/5.04 | | DELTA: instantiating (40) with fresh symbols all_73_0, all_73_1, all_73_2, % 31.86/5.04 | | all_73_3, all_73_4 gives: % 31.86/5.04 | | (41) varrow(all_73_2, all_73_1) = all_65_1 & vtcheck(all_73_0, all_73_3, % 31.86/5.05 | | all_73_1) = 0 & vbind(all_73_4, all_73_2, all_65_3) = all_73_0 & % 31.86/5.05 | | vabs(all_73_4, all_73_2, all_73_3) = all_63_1 & $i(all_73_0) & % 31.86/5.05 | | $i(all_73_1) & $i(all_73_2) & $i(all_73_3) & $i(all_73_4) % 31.86/5.05 | | % 31.86/5.05 | | ALPHA: (41) implies: % 31.86/5.05 | | (42) $i(all_73_4) % 31.86/5.05 | | (43) $i(all_73_3) % 31.86/5.05 | | (44) $i(all_73_2) % 31.86/5.05 | | (45) vabs(all_73_4, all_73_2, all_73_3) = all_63_1 % 31.86/5.05 | | % 31.86/5.05 | | GROUND_INST: instantiating (DIFF-abs-app) with all_73_4, all_73_2, all_73_3, % 31.86/5.05 | | ve1, ve2, all_63_1, simplifying with (8), (9), (25), (42), % 31.86/5.05 | | (43), (44), (45) gives: % 31.86/5.05 | | (46) $false % 31.86/5.05 | | % 31.86/5.05 | | CLOSE: (46) is inconsistent. % 31.86/5.05 | | % 31.86/5.05 | Case 2: % 31.86/5.05 | | % 31.86/5.05 | | (47) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (varrow(v2, % 31.86/5.05 | | all_65_1) = v3 & vtcheck(all_65_3, v1, v2) = 0 & % 31.86/5.05 | | vtcheck(all_65_3, v0, v3) = 0 & vapp(v0, v1) = all_63_1 & $i(v3) & % 31.86/5.05 | | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : (vsomeType(all_65_1) = % 31.86/5.05 | | v0 & $i(v0) & ? [v1: $i] : (vlookup(v1, all_65_3) = v0 & vvar(v1) % 31.86/5.05 | | = all_63_1 & $i(v1))) % 31.86/5.05 | | % 31.86/5.05 | | BETA: splitting (47) gives: % 31.86/5.05 | | % 31.86/5.05 | | Case 1: % 31.86/5.05 | | | % 31.86/5.05 | | | (48) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 31.86/5.05 | | | (varrow(v2, all_65_1) = v3 & vtcheck(all_65_3, v1, v2) = 0 & % 31.86/5.05 | | | vtcheck(all_65_3, v0, v3) = 0 & vapp(v0, v1) = all_63_1 & $i(v3) % 31.86/5.05 | | | & $i(v2) & $i(v1) & $i(v0)) % 31.86/5.05 | | | % 31.86/5.05 | | | DELTA: instantiating (48) with fresh symbols all_73_0, all_73_1, all_73_2, % 31.86/5.05 | | | all_73_3 gives: % 31.86/5.05 | | | (49) varrow(all_73_1, all_65_1) = all_73_0 & vtcheck(all_65_3, % 31.86/5.05 | | | all_73_2, all_73_1) = 0 & vtcheck(all_65_3, all_73_3, all_73_0) % 31.86/5.05 | | | = 0 & vapp(all_73_3, all_73_2) = all_63_1 & $i(all_73_0) & % 31.86/5.05 | | | $i(all_73_1) & $i(all_73_2) & $i(all_73_3) % 31.86/5.05 | | | % 31.86/5.05 | | | ALPHA: (49) implies: % 31.86/5.05 | | | (50) $i(all_73_3) % 31.86/5.05 | | | (51) $i(all_73_2) % 31.86/5.05 | | | (52) $i(all_73_1) % 31.86/5.05 | | | (53) $i(all_73_0) % 31.86/5.05 | | | (54) vapp(all_73_3, all_73_2) = all_63_1 % 31.86/5.05 | | | (55) vtcheck(all_65_3, all_73_3, all_73_0) = 0 % 31.86/5.05 | | | (56) vtcheck(all_65_3, all_73_2, all_73_1) = 0 % 31.86/5.05 | | | (57) varrow(all_73_1, all_65_1) = all_73_0 % 31.86/5.05 | | | % 31.86/5.05 | | | GROUND_INST: instantiating (EQ-app) with ve1, ve2, all_73_3, all_73_2, % 31.86/5.05 | | | all_63_1, simplifying with (8), (9), (25), (50), (51), (54) % 31.86/5.05 | | | gives: % 31.86/5.05 | | | (58) all_73_2 = ve2 & all_73_3 = ve1 % 31.86/5.05 | | | % 31.86/5.05 | | | ALPHA: (58) implies: % 31.86/5.05 | | | (59) all_73_3 = ve1 % 31.86/5.05 | | | (60) all_73_2 = ve2 % 31.86/5.05 | | | % 31.86/5.05 | | | GROUND_INST: instantiating (T-inv) with all_73_3, all_73_0, all_65_3, % 31.86/5.05 | | | simplifying with (30), (50), (53), (55) gives: % 31.86/5.05 | | | (61) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 31.86/5.05 | | | $i] : (varrow(v2, v3) = all_73_0 & vtcheck(v4, v1, v3) = 0 & % 31.86/5.05 | | | vbind(v0, v2, all_65_3) = v4 & vabs(v0, v2, v1) = all_73_3 & % 31.86/5.05 | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? % 31.86/5.05 | | | [v1: $i] : ? [v2: $i] : ? [v3: $i] : (varrow(v2, all_73_0) = v3 % 31.86/5.05 | | | & vtcheck(all_65_3, v1, v2) = 0 & vtcheck(all_65_3, v0, v3) = 0 % 31.86/5.05 | | | & vapp(v0, v1) = all_73_3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | % 31.86/5.05 | | | ? [v0: $i] : (vsomeType(all_73_0) = v0 & $i(v0) & ? [v1: $i] : % 31.86/5.05 | | | (vlookup(v1, all_65_3) = v0 & vvar(v1) = all_73_3 & $i(v1))) % 31.86/5.05 | | | % 31.86/5.05 | | | GROUND_INST: instantiating (T-inv) with all_73_2, all_73_1, all_65_3, % 31.86/5.05 | | | simplifying with (30), (51), (52), (56) gives: % 31.86/5.05 | | | (62) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 31.86/5.05 | | | $i] : (varrow(v2, v3) = all_73_1 & vtcheck(v4, v1, v3) = 0 & % 31.86/5.05 | | | vbind(v0, v2, all_65_3) = v4 & vabs(v0, v2, v1) = all_73_2 & % 31.86/5.05 | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? % 31.86/5.05 | | | [v1: $i] : ? [v2: $i] : ? [v3: $i] : (varrow(v2, all_73_1) = v3 % 31.86/5.05 | | | & vtcheck(all_65_3, v1, v2) = 0 & vtcheck(all_65_3, v0, v3) = 0 % 31.86/5.05 | | | & vapp(v0, v1) = all_73_2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | % 31.86/5.05 | | | ? [v0: $i] : (vsomeType(all_73_1) = v0 & $i(v0) & ? [v1: $i] : % 31.86/5.05 | | | (vlookup(v1, all_65_3) = v0 & vvar(v1) = all_73_2 & $i(v1))) % 31.86/5.05 | | | % 31.86/5.05 | | | REDUCE: (56), (60) imply: % 31.86/5.05 | | | (63) vtcheck(all_65_3, ve2, all_73_1) = 0 % 31.86/5.05 | | | % 31.86/5.05 | | | REDUCE: (55), (59) imply: % 31.86/5.05 | | | (64) vtcheck(all_65_3, ve1, all_73_0) = 0 % 31.86/5.05 | | | % 31.86/5.05 | | | BETA: splitting (61) gives: % 31.86/5.05 | | | % 31.86/5.05 | | | Case 1: % 31.86/5.05 | | | | % 31.86/5.05 | | | | (65) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 31.86/5.05 | | | | $i] : (varrow(v2, v3) = all_73_0 & vtcheck(v4, v1, v3) = 0 & % 31.86/5.05 | | | | vbind(v0, v2, all_65_3) = v4 & vabs(v0, v2, v1) = all_73_3 & % 31.86/5.05 | | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 31.86/5.05 | | | | % 31.86/5.05 | | | | DELTA: instantiating (65) with fresh symbols all_87_0, all_87_1, % 31.86/5.05 | | | | all_87_2, all_87_3, all_87_4 gives: % 31.86/5.06 | | | | (66) varrow(all_87_2, all_87_1) = all_73_0 & vtcheck(all_87_0, % 31.86/5.06 | | | | all_87_3, all_87_1) = 0 & vbind(all_87_4, all_87_2, all_65_3) % 31.86/5.06 | | | | = all_87_0 & vabs(all_87_4, all_87_2, all_87_3) = all_73_3 & % 31.86/5.06 | | | | $i(all_87_0) & $i(all_87_1) & $i(all_87_2) & $i(all_87_3) & % 31.86/5.06 | | | | $i(all_87_4) % 31.86/5.06 | | | | % 31.86/5.06 | | | | ALPHA: (66) implies: % 31.86/5.06 | | | | (67) $i(all_87_4) % 31.86/5.06 | | | | (68) $i(all_87_3) % 31.86/5.06 | | | | (69) $i(all_87_2) % 31.86/5.06 | | | | (70) $i(all_87_1) % 31.86/5.06 | | | | (71) vabs(all_87_4, all_87_2, all_87_3) = all_73_3 % 31.86/5.06 | | | | (72) vbind(all_87_4, all_87_2, all_65_3) = all_87_0 % 31.86/5.06 | | | | (73) vtcheck(all_87_0, all_87_3, all_87_1) = 0 % 31.86/5.06 | | | | (74) varrow(all_87_2, all_87_1) = all_73_0 % 31.86/5.06 | | | | % 31.86/5.06 | | | | REDUCE: (59), (71) imply: % 31.86/5.06 | | | | (75) vabs(all_87_4, all_87_2, all_87_3) = ve1 % 31.86/5.06 | | | | % 31.86/5.06 | | | | GROUND_INST: instantiating (4) with all_87_4, all_87_2, all_87_3, ve1, % 31.86/5.06 | | | | all_57_0, simplifying with (8), (15), (16), (67), (68), % 31.86/5.06 | | | | (69), (75) gives: % 31.86/5.06 | | | | (76) all_57_0 = vnoExp % 31.86/5.06 | | | | % 31.86/5.06 | | | | GROUND_INST: instantiating (EQ-arrow) with all_73_1, all_65_1, all_87_2, % 31.86/5.06 | | | | all_87_1, all_73_0, simplifying with (32), (52), (57), % 31.86/5.06 | | | | (69), (70), (74) gives: % 31.86/5.06 | | | | (77) all_87_1 = all_65_1 & all_87_2 = all_73_1 % 31.86/5.06 | | | | % 31.86/5.06 | | | | ALPHA: (77) implies: % 31.86/5.06 | | | | (78) all_87_2 = all_73_1 % 31.86/5.06 | | | | (79) all_87_1 = all_65_1 % 31.86/5.06 | | | | % 31.86/5.06 | | | | REDUCE: (73), (79) imply: % 31.86/5.06 | | | | (80) vtcheck(all_87_0, all_87_3, all_65_1) = 0 % 31.86/5.06 | | | | % 31.86/5.06 | | | | REDUCE: (72), (78) imply: % 31.86/5.06 | | | | (81) vbind(all_87_4, all_73_1, all_65_3) = all_87_0 % 31.86/5.06 | | | | % 31.86/5.06 | | | | REDUCE: (75), (78) imply: % 31.86/5.06 | | | | (82) vabs(all_87_4, all_73_1, all_87_3) = ve1 % 31.86/5.06 | | | | % 31.86/5.06 | | | | BETA: splitting (62) gives: % 31.86/5.06 | | | | % 31.86/5.06 | | | | Case 1: % 31.86/5.06 | | | | | % 31.86/5.06 | | | | | (83) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 31.86/5.06 | | | | | [v4: $i] : (varrow(v2, v3) = all_73_1 & vtcheck(v4, v1, v3) = % 31.86/5.06 | | | | | 0 & vbind(v0, v2, all_65_3) = v4 & vabs(v0, v2, v1) = % 31.86/5.06 | | | | | all_73_2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 31.86/5.06 | | | | | % 31.86/5.06 | | | | | DELTA: instantiating (83) with fresh symbols all_114_0, all_114_1, % 31.86/5.06 | | | | | all_114_2, all_114_3, all_114_4 gives: % 31.86/5.06 | | | | | (84) varrow(all_114_2, all_114_1) = all_73_1 & vtcheck(all_114_0, % 31.86/5.06 | | | | | all_114_3, all_114_1) = 0 & vbind(all_114_4, all_114_2, % 31.86/5.06 | | | | | all_65_3) = all_114_0 & vabs(all_114_4, all_114_2, % 31.86/5.06 | | | | | all_114_3) = all_73_2 & $i(all_114_0) & $i(all_114_1) & % 31.86/5.06 | | | | | $i(all_114_2) & $i(all_114_3) & $i(all_114_4) % 31.86/5.06 | | | | | % 31.86/5.06 | | | | | ALPHA: (84) implies: % 31.86/5.06 | | | | | (85) $i(all_114_4) % 31.86/5.06 | | | | | (86) $i(all_114_3) % 31.86/5.06 | | | | | (87) $i(all_114_2) % 31.86/5.06 | | | | | (88) vabs(all_114_4, all_114_2, all_114_3) = all_73_2 % 31.86/5.06 | | | | | % 31.86/5.06 | | | | | REDUCE: (60), (88) imply: % 31.86/5.06 | | | | | (89) vabs(all_114_4, all_114_2, all_114_3) = ve2 % 31.86/5.06 | | | | | % 31.86/5.06 | | | | | GROUND_INST: instantiating (4) with all_114_4, all_114_2, all_114_3, % 31.86/5.06 | | | | | ve2, all_60_0, simplifying with (9), (19), (20), (85), % 31.86/5.06 | | | | | (86), (87), (89) gives: % 31.86/5.06 | | | | | (90) all_60_0 = vnoExp % 31.86/5.06 | | | | | % 31.86/5.06 | | | | | REDUCE: (20), (90) imply: % 31.86/5.06 | | | | | (91) vreduce(ve2) = vnoExp % 31.86/5.06 | | | | | % 31.86/5.06 | | | | | BETA: splitting (39) gives: % 31.86/5.06 | | | | | % 31.86/5.06 | | | | | Case 1: % 31.86/5.06 | | | | | | % 31.86/5.06 | | | | | | (92) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 31.86/5.06 | | | | | | [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : % 31.86/5.06 | | | | | | (all_63_0 = vnoExp & ~ (v7 = 0) & ~ (v6 = 0) & vreduce(v4) % 31.86/5.06 | | | | | | = v3 & visSomeExp(v3) = v6 & visValue(v4) = v7 & vapp(v5, % 31.86/5.06 | | | | | | v4) = all_63_1 & vabs(v0, v1, v2) = v5 & $i(v5) & $i(v4) % 31.86/5.06 | | | | | | & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? % 31.86/5.06 | | | | | | [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 31.86/5.06 | | | | | | $i] : ? [v6: int] : ? [v7: $i] : ( ~ (v6 = 0) & % 31.86/5.06 | | | | | | vreduce(v3) = v1 & visSomeExp(v1) = v6 & vsomeExp(v7) = % 31.86/5.06 | | | | | | all_63_0 & vsubst(v2, v3, v4) = v7 & visValue(v3) = 0 & % 31.86/5.06 | | | | | | vapp(v5, v3) = all_63_1 & vabs(v2, v0, v4) = v5 & $i(v7) & % 31.86/5.06 | | | | | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? % 31.86/5.06 | | | | | | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 31.86/5.06 | | | | | | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 31.86/5.06 | | | | | | (vreduce(v0) = v4 & vgetSomeExp(v4) = v6 & visSomeExp(v4) = % 31.86/5.06 | | | | | | 0 & vsomeExp(v7) = all_63_0 & vapp(v5, v6) = v7 & vapp(v5, % 31.86/5.06 | | | | | | v0) = all_63_1 & vabs(v1, v2, v3) = v5 & $i(v7) & $i(v6) % 31.86/5.06 | | | | | | & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 31.86/5.06 | | | | | | % 31.86/5.06 | | | | | | BETA: splitting (92) gives: % 31.86/5.06 | | | | | | % 31.86/5.06 | | | | | | Case 1: % 31.86/5.06 | | | | | | | % 31.86/5.06 | | | | | | | (93) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 31.86/5.06 | | | | | | | [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : % 31.86/5.06 | | | | | | | (all_63_0 = vnoExp & ~ (v7 = 0) & ~ (v6 = 0) & % 31.86/5.06 | | | | | | | vreduce(v4) = v3 & visSomeExp(v3) = v6 & visValue(v4) = % 31.86/5.06 | | | | | | | v7 & vapp(v5, v4) = all_63_1 & vabs(v0, v1, v2) = v5 & % 31.86/5.06 | | | | | | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 31.86/5.06 | | | | | | | % 31.86/5.06 | | | | | | | DELTA: instantiating (93) with fresh symbols all_111_0, all_111_1, % 31.86/5.06 | | | | | | | all_111_2, all_111_3, all_111_4, all_111_5, all_111_6, % 31.86/5.06 | | | | | | | all_111_7 gives: % 31.86/5.06 | | | | | | | (94) all_63_0 = vnoExp & ~ (all_111_0 = 0) & ~ (all_111_1 = % 31.86/5.06 | | | | | | | 0) & vreduce(all_111_3) = all_111_4 & % 31.86/5.06 | | | | | | | visSomeExp(all_111_4) = all_111_1 & visValue(all_111_3) = % 31.86/5.06 | | | | | | | all_111_0 & vapp(all_111_2, all_111_3) = all_63_1 & % 31.86/5.06 | | | | | | | vabs(all_111_7, all_111_6, all_111_5) = all_111_2 & % 31.86/5.06 | | | | | | | $i(all_111_2) & $i(all_111_3) & $i(all_111_4) & % 31.86/5.06 | | | | | | | $i(all_111_5) & $i(all_111_6) & $i(all_111_7) % 31.86/5.06 | | | | | | | % 31.86/5.06 | | | | | | | REF_CLOSE: (1), (31), (35), (94) are inconsistent by sub-proof #9. % 31.86/5.06 | | | | | | | % 31.86/5.06 | | | | | | Case 2: % 31.86/5.06 | | | | | | | % 31.86/5.06 | | | | | | | (95) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 31.86/5.06 | | | | | | | [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ( ~ % 31.86/5.06 | | | | | | | (v6 = 0) & vreduce(v3) = v1 & visSomeExp(v1) = v6 & % 31.86/5.06 | | | | | | | vsomeExp(v7) = all_63_0 & vsubst(v2, v3, v4) = v7 & % 31.86/5.06 | | | | | | | visValue(v3) = 0 & vapp(v5, v3) = all_63_1 & vabs(v2, % 31.86/5.06 | | | | | | | v0, v4) = v5 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & % 31.86/5.06 | | | | | | | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : % 31.86/5.06 | | | | | | | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 31.86/5.06 | | | | | | | [v6: $i] : ? [v7: $i] : (vreduce(v0) = v4 & % 31.86/5.06 | | | | | | | vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & vsomeExp(v7) % 31.86/5.06 | | | | | | | = all_63_0 & vapp(v5, v6) = v7 & vapp(v5, v0) = all_63_1 % 31.86/5.06 | | | | | | | & vabs(v1, v2, v3) = v5 & $i(v7) & $i(v6) & $i(v5) & % 31.86/5.06 | | | | | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 31.86/5.06 | | | | | | | % 31.86/5.06 | | | | | | | BETA: splitting (95) gives: % 31.86/5.06 | | | | | | | % 31.86/5.06 | | | | | | | Case 1: % 31.86/5.06 | | | | | | | | % 31.86/5.06 | | | | | | | | (96) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 31.86/5.06 | | | | | | | | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : % 31.86/5.06 | | | | | | | | ( ~ (v6 = 0) & vreduce(v3) = v1 & visSomeExp(v1) = v6 & % 31.86/5.06 | | | | | | | | vsomeExp(v7) = all_63_0 & vsubst(v2, v3, v4) = v7 & % 31.86/5.06 | | | | | | | | visValue(v3) = 0 & vapp(v5, v3) = all_63_1 & vabs(v2, % 31.86/5.06 | | | | | | | | v0, v4) = v5 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & % 31.86/5.06 | | | | | | | | $i(v2) & $i(v1) & $i(v0)) % 31.86/5.06 | | | | | | | | % 31.86/5.06 | | | | | | | | DELTA: instantiating (96) with fresh symbols all_130_0, % 31.86/5.06 | | | | | | | | all_130_1, all_130_2, all_130_3, all_130_4, all_130_5, % 31.86/5.06 | | | | | | | | all_130_6, all_130_7 gives: % 31.86/5.07 | | | | | | | | (97) ~ (all_130_1 = 0) & vreduce(all_130_4) = all_130_6 & % 31.86/5.07 | | | | | | | | visSomeExp(all_130_6) = all_130_1 & vsomeExp(all_130_0) % 31.86/5.07 | | | | | | | | = all_63_0 & vsubst(all_130_5, all_130_4, all_130_3) = % 31.86/5.07 | | | | | | | | all_130_0 & visValue(all_130_4) = 0 & vapp(all_130_2, % 31.86/5.07 | | | | | | | | all_130_4) = all_63_1 & vabs(all_130_5, all_130_7, % 31.86/5.07 | | | | | | | | all_130_3) = all_130_2 & $i(all_130_0) & $i(all_130_2) % 31.86/5.07 | | | | | | | | & $i(all_130_3) & $i(all_130_4) & $i(all_130_5) & % 31.86/5.07 | | | | | | | | $i(all_130_6) & $i(all_130_7) % 31.86/5.07 | | | | | | | | % 31.86/5.07 | | | | | | | | ALPHA: (97) implies: % 31.86/5.07 | | | | | | | | (98) ~ (all_130_1 = 0) % 31.86/5.07 | | | | | | | | (99) $i(all_130_7) % 31.86/5.07 | | | | | | | | (100) $i(all_130_6) % 31.86/5.07 | | | | | | | | (101) $i(all_130_5) % 31.86/5.07 | | | | | | | | (102) $i(all_130_4) % 31.86/5.07 | | | | | | | | (103) $i(all_130_3) % 31.86/5.07 | | | | | | | | (104) $i(all_130_2) % 31.86/5.07 | | | | | | | | (105) $i(all_130_0) % 31.86/5.07 | | | | | | | | (106) vabs(all_130_5, all_130_7, all_130_3) = all_130_2 % 31.86/5.07 | | | | | | | | (107) vapp(all_130_2, all_130_4) = all_63_1 % 31.86/5.07 | | | | | | | | (108) visValue(all_130_4) = 0 % 31.86/5.07 | | | | | | | | (109) vsomeExp(all_130_0) = all_63_0 % 31.86/5.07 | | | | | | | | (110) visSomeExp(all_130_6) = all_130_1 % 31.86/5.07 | | | | | | | | (111) vreduce(all_130_4) = all_130_6 % 31.86/5.07 | | | | | | | | % 31.86/5.07 | | | | | | | | GROUND_INST: instantiating (EQ-app) with ve1, ve2, all_130_2, % 31.86/5.07 | | | | | | | | all_130_4, all_63_1, simplifying with (8), (9), % 31.86/5.07 | | | | | | | | (25), (102), (104), (107) gives: % 31.86/5.07 | | | | | | | | (112) all_130_2 = ve1 & all_130_4 = ve2 % 31.86/5.07 | | | | | | | | % 31.86/5.07 | | | | | | | | ALPHA: (112) implies: % 31.86/5.07 | | | | | | | | (113) all_130_4 = ve2 % 31.86/5.07 | | | | | | | | (114) all_130_2 = ve1 % 31.86/5.07 | | | | | | | | % 31.86/5.07 | | | | | | | | GROUND_INST: instantiating (EQ-someExp) with all_65_2, % 31.86/5.07 | | | | | | | | all_130_0, all_63_0, simplifying with (31), (35), % 31.86/5.07 | | | | | | | | (105), (109) gives: % 31.86/5.07 | | | | | | | | (115) all_130_0 = all_65_2 % 31.86/5.07 | | | | | | | | % 31.86/5.07 | | | | | | | | GROUND_INST: instantiating (reduce3) with all_73_1, all_130_6, % 31.86/5.07 | | | | | | | | all_63_1, all_63_0, all_87_4, ve2, all_87_3, ve1, % 31.86/5.07 | | | | | | | | all_130_1, simplifying with (9), (23), (24), (25), % 31.86/5.07 | | | | | | | | (26), (52), (67), (68), (82), (100), (110) gives: % 31.86/5.07 | | | | | | | | (116) all_130_1 = 0 | ? [v0: $i] : ? [v1: any] : ? [v2: % 31.86/5.07 | | | | | | | | $i] : ? [v3: $i] : (vreduce(ve2) = v0 & vsomeExp(v2) % 31.86/5.07 | | | | | | | | = v3 & vsubst(all_87_4, ve2, all_87_3) = v2 & % 31.86/5.07 | | | | | | | | visValue(ve2) = v1 & $i(v3) & $i(v2) & $i(v0) & ( ~ % 31.86/5.07 | | | | | | | | (v1 = 0) | ~ (v0 = all_130_6) | v3 = all_63_0)) % 31.86/5.07 | | | | | | | | % 31.86/5.07 | | | | | | | | REDUCE: (111), (113) imply: % 31.86/5.07 | | | | | | | | (117) vreduce(ve2) = all_130_6 % 31.86/5.07 | | | | | | | | % 31.86/5.07 | | | | | | | | REDUCE: (108), (113) imply: % 31.86/5.07 | | | | | | | | (118) visValue(ve2) = 0 % 31.86/5.07 | | | | | | | | % 31.86/5.07 | | | | | | | | REDUCE: (106), (114) imply: % 31.86/5.07 | | | | | | | | (119) vabs(all_130_5, all_130_7, all_130_3) = ve1 % 31.86/5.07 | | | | | | | | % 31.86/5.07 | | | | | | | | BETA: splitting (116) gives: % 31.86/5.07 | | | | | | | | % 31.86/5.07 | | | | | | | | Case 1: % 31.86/5.07 | | | | | | | | | % 31.86/5.07 | | | | | | | | | (120) all_130_1 = 0 % 31.86/5.07 | | | | | | | | | % 31.86/5.07 | | | | | | | | | REDUCE: (98), (120) imply: % 31.86/5.07 | | | | | | | | | (121) $false % 31.86/5.07 | | | | | | | | | % 31.86/5.07 | | | | | | | | | CLOSE: (121) is inconsistent. % 31.86/5.07 | | | | | | | | | % 31.86/5.07 | | | | | | | | Case 2: % 31.86/5.07 | | | | | | | | | % 31.86/5.07 | | | | | | | | | (122) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: % 31.86/5.07 | | | | | | | | | $i] : (vreduce(ve2) = v0 & vsomeExp(v2) = v3 & % 31.86/5.07 | | | | | | | | | vsubst(all_87_4, ve2, all_87_3) = v2 & % 31.86/5.07 | | | | | | | | | visValue(ve2) = v1 & $i(v3) & $i(v2) & $i(v0) & ( ~ % 31.86/5.07 | | | | | | | | | (v1 = 0) | ~ (v0 = all_130_6) | v3 = all_63_0)) % 31.86/5.07 | | | | | | | | | % 31.86/5.07 | | | | | | | | | DELTA: instantiating (122) with fresh symbols all_142_0, % 31.86/5.07 | | | | | | | | | all_142_1, all_142_2, all_142_3 gives: % 31.86/5.07 | | | | | | | | | (123) vreduce(ve2) = all_142_3 & vsomeExp(all_142_1) = % 31.86/5.07 | | | | | | | | | all_142_0 & vsubst(all_87_4, ve2, all_87_3) = % 31.86/5.07 | | | | | | | | | all_142_1 & visValue(ve2) = all_142_2 & $i(all_142_0) % 31.86/5.07 | | | | | | | | | & $i(all_142_1) & $i(all_142_3) & ( ~ (all_142_2 = 0) % 31.86/5.07 | | | | | | | | | | ~ (all_142_3 = all_130_6) | all_142_0 = % 31.86/5.07 | | | | | | | | | all_63_0) % 31.86/5.07 | | | | | | | | | % 31.86/5.07 | | | | | | | | | ALPHA: (123) implies: % 31.86/5.07 | | | | | | | | | (124) $i(all_142_1) % 31.86/5.07 | | | | | | | | | (125) visValue(ve2) = all_142_2 % 31.86/5.07 | | | | | | | | | (126) vsubst(all_87_4, ve2, all_87_3) = all_142_1 % 31.86/5.07 | | | | | | | | | (127) vsomeExp(all_142_1) = all_142_0 % 31.86/5.07 | | | | | | | | | (128) vreduce(ve2) = all_142_3 % 31.86/5.07 | | | | | | | | | (129) ~ (all_142_2 = 0) | ~ (all_142_3 = all_130_6) | % 31.86/5.07 | | | | | | | | | all_142_0 = all_63_0 % 31.86/5.07 | | | | | | | | | % 31.86/5.07 | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_142_2, ve2, % 31.86/5.07 | | | | | | | | | simplifying with (118), (125) gives: % 31.86/5.07 | | | | | | | | | (130) all_142_2 = 0 % 31.86/5.07 | | | | | | | | | % 31.86/5.07 | | | | | | | | | GROUND_INST: instantiating (12) with vnoExp, all_142_3, ve2, % 31.86/5.07 | | | | | | | | | simplifying with (91), (128) gives: % 31.86/5.07 | | | | | | | | | (131) all_142_3 = vnoExp % 31.86/5.07 | | | | | | | | | % 31.86/5.07 | | | | | | | | | GROUND_INST: instantiating (12) with all_130_6, all_142_3, ve2, % 31.86/5.07 | | | | | | | | | simplifying with (117), (128) gives: % 31.86/5.07 | | | | | | | | | (132) all_142_3 = all_130_6 % 31.86/5.07 | | | | | | | | | % 31.86/5.07 | | | | | | | | | COMBINE_EQS: (131), (132) imply: % 31.86/5.07 | | | | | | | | | (133) all_130_6 = vnoExp % 31.86/5.07 | | | | | | | | | % 31.86/5.07 | | | | | | | | | SIMP: (133) implies: % 31.86/5.07 | | | | | | | | | (134) all_130_6 = vnoExp % 31.86/5.07 | | | | | | | | | % 31.86/5.07 | | | | | | | | | BETA: splitting (129) gives: % 31.86/5.07 | | | | | | | | | % 31.86/5.07 | | | | | | | | | Case 1: % 31.86/5.07 | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | (135) ~ (all_142_2 = 0) % 31.86/5.07 | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | REDUCE: (130), (135) imply: % 31.86/5.07 | | | | | | | | | | (136) $false % 31.86/5.07 | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | CLOSE: (136) is inconsistent. % 31.86/5.07 | | | | | | | | | | % 31.86/5.07 | | | | | | | | | Case 2: % 31.86/5.07 | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | (137) ~ (all_142_3 = all_130_6) | all_142_0 = all_63_0 % 31.86/5.07 | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | BETA: splitting (137) gives: % 31.86/5.07 | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | Case 1: % 31.86/5.07 | | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | | (138) ~ (all_142_3 = all_130_6) % 31.86/5.07 | | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | | REDUCE: (131), (134), (138) imply: % 31.86/5.07 | | | | | | | | | | | (139) $false % 31.86/5.07 | | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | | CLOSE: (139) is inconsistent. % 31.86/5.07 | | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | Case 2: % 31.86/5.07 | | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | | (140) all_142_0 = all_63_0 % 31.86/5.07 | | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | | REDUCE: (127), (140) imply: % 31.86/5.07 | | | | | | | | | | | (141) vsomeExp(all_142_1) = all_63_0 % 31.86/5.07 | | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | | GROUND_INST: instantiating (EQ-abs) with all_87_4, all_73_1, % 31.86/5.07 | | | | | | | | | | | all_87_3, all_130_5, all_130_7, all_130_3, ve1, % 31.86/5.07 | | | | | | | | | | | simplifying with (52), (67), (68), (82), (99), % 31.86/5.07 | | | | | | | | | | | (101), (103), (119) gives: % 31.86/5.07 | | | | | | | | | | | (142) all_130_3 = all_87_3 & all_130_5 = all_87_4 & % 31.86/5.07 | | | | | | | | | | | all_130_7 = all_73_1 % 31.86/5.07 | | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | | ALPHA: (142) implies: % 31.86/5.07 | | | | | | | | | | | (143) all_130_3 = all_87_3 % 31.86/5.07 | | | | | | | | | | | (144) all_130_5 = all_87_4 % 31.86/5.07 | | | | | | | | | | | (145) all_130_7 = all_73_1 % 31.86/5.07 | | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | | GROUND_INST: instantiating (EQ-someExp) with all_65_2, % 31.86/5.07 | | | | | | | | | | | all_142_1, all_63_0, simplifying with (31), (35), % 31.86/5.07 | | | | | | | | | | | (124), (141) gives: % 31.86/5.07 | | | | | | | | | | | (146) all_142_1 = all_65_2 % 31.86/5.07 | | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | | REDUCE: (126), (146) imply: % 31.86/5.07 | | | | | | | | | | | (147) vsubst(all_87_4, ve2, all_87_3) = all_65_2 % 31.86/5.07 | | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | | GROUND_INST: instantiating (T-subst) with all_73_1, all_65_3, % 31.86/5.07 | | | | | | | | | | | all_87_4, ve2, all_87_3, all_65_1, all_87_0, % 31.86/5.07 | | | | | | | | | | | all_65_2, all_65_0, simplifying with (9), (30), % 31.86/5.07 | | | | | | | | | | | (32), (34), (52), (67), (68), (80), (81), (147) % 31.86/5.07 | | | | | | | | | | | gives: % 31.86/5.07 | | | | | | | | | | | (148) all_65_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 31.86/5.07 | | | | | | | | | | | vtcheck(all_65_3, ve2, all_73_1) = v0) % 31.86/5.07 | | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | | REF_CLOSE: (13), (29), (63), (148) are inconsistent by % 31.86/5.07 | | | | | | | | | | | sub-proof #8. % 31.86/5.07 | | | | | | | | | | | % 31.86/5.07 | | | | | | | | | | End of split % 31.86/5.07 | | | | | | | | | | % 31.86/5.07 | | | | | | | | | End of split % 31.86/5.07 | | | | | | | | | % 31.86/5.07 | | | | | | | | End of split % 31.86/5.07 | | | | | | | | % 31.86/5.08 | | | | | | | Case 2: % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | | (149) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 31.86/5.08 | | | | | | | | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 31.86/5.08 | | | | | | | | (vreduce(v0) = v4 & vgetSomeExp(v4) = v6 & % 31.86/5.08 | | | | | | | | visSomeExp(v4) = 0 & vsomeExp(v7) = all_63_0 & % 31.86/5.08 | | | | | | | | vapp(v5, v6) = v7 & vapp(v5, v0) = all_63_1 & % 31.86/5.08 | | | | | | | | vabs(v1, v2, v3) = v5 & $i(v7) & $i(v6) & $i(v5) & % 31.86/5.08 | | | | | | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | | DELTA: instantiating (149) with fresh symbols all_111_0, % 31.86/5.08 | | | | | | | | all_111_1, all_111_2, all_111_3, all_111_4, all_111_5, % 31.86/5.08 | | | | | | | | all_111_6, all_111_7 gives: % 31.86/5.08 | | | | | | | | (150) vreduce(all_111_7) = all_111_3 & vgetSomeExp(all_111_3) % 31.86/5.08 | | | | | | | | = all_111_1 & visSomeExp(all_111_3) = 0 & % 31.86/5.08 | | | | | | | | vsomeExp(all_111_0) = all_63_0 & vapp(all_111_2, % 31.86/5.08 | | | | | | | | all_111_1) = all_111_0 & vapp(all_111_2, all_111_7) = % 31.86/5.08 | | | | | | | | all_63_1 & vabs(all_111_6, all_111_5, all_111_4) = % 31.86/5.08 | | | | | | | | all_111_2 & $i(all_111_0) & $i(all_111_1) & % 31.86/5.08 | | | | | | | | $i(all_111_2) & $i(all_111_3) & $i(all_111_4) & % 31.86/5.08 | | | | | | | | $i(all_111_5) & $i(all_111_6) & $i(all_111_7) % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | | REF_CLOSE: (2), (8), (9), (12), (25), (91), (150), (EQ-app) are % 31.86/5.08 | | | | | | | | inconsistent by sub-proof #7. % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | End of split % 31.86/5.08 | | | | | | | % 31.86/5.08 | | | | | | End of split % 31.86/5.08 | | | | | | % 31.86/5.08 | | | | | Case 2: % 31.86/5.08 | | | | | | % 31.86/5.08 | | | | | | (151) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 31.86/5.08 | | | | | | [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & % 31.86/5.08 | | | | | | visSomeExp(v1) = 0 & vsomeExp(v4) = all_63_0 & vapp(v3, % 31.86/5.08 | | | | | | v2) = v4 & vapp(v0, v2) = all_63_1 & $i(v4) & $i(v3) & % 31.86/5.08 | | | | | | $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! % 31.86/5.08 | | | | | | [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ $i(v7) | ~ % 31.86/5.08 | | | | | | $i(v6) | ~ $i(v5))) | ? [v0: $i] : ? [v1: $i] : ? % 31.86/5.08 | | | | | | [v2: $i] : ? [v3: int] : (all_63_0 = vnoExp & ~ (v3 = 0) % 31.86/5.08 | | | | | | & vreduce(v1) = v2 & visSomeExp(v2) = v3 & vapp(v1, v0) = % 31.86/5.08 | | | | | | all_63_1 & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! % 31.86/5.08 | | | | | | [v5: $i] : ! [v6: $i] : ( ~ (vabs(v4, v5, v6) = v1) | ~ % 31.86/5.08 | | | | | | $i(v6) | ~ $i(v5) | ~ $i(v4))) | ? [v0: $i] : ? % 31.86/5.08 | | | | | | [v1: $i] : ? [v2: $i] : (all_63_0 = vnoExp & vabs(v0, v1, % 31.86/5.08 | | | | | | v2) = all_63_1 & $i(v2) & $i(v1) & $i(v0)) | ? [v0: % 31.86/5.08 | | | | | | $i] : (all_63_0 = vnoExp & vvar(v0) = all_63_1 & $i(v0)) % 31.86/5.08 | | | | | | % 31.86/5.08 | | | | | | BETA: splitting (151) gives: % 31.86/5.08 | | | | | | % 31.86/5.08 | | | | | | Case 1: % 31.86/5.08 | | | | | | | % 31.86/5.08 | | | | | | | (152) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 31.86/5.08 | | | | | | | ? [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & % 31.86/5.08 | | | | | | | visSomeExp(v1) = 0 & vsomeExp(v4) = all_63_0 & vapp(v3, % 31.86/5.08 | | | | | | | v2) = v4 & vapp(v0, v2) = all_63_1 & $i(v4) & $i(v3) % 31.86/5.08 | | | | | | | & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] % 31.86/5.08 | | | | | | | : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ $i(v7) % 31.86/5.08 | | | | | | | | ~ $i(v6) | ~ $i(v5))) | ? [v0: $i] : ? [v1: $i] % 31.86/5.08 | | | | | | | : ? [v2: $i] : ? [v3: int] : (all_63_0 = vnoExp & ~ % 31.86/5.08 | | | | | | | (v3 = 0) & vreduce(v1) = v2 & visSomeExp(v2) = v3 & % 31.86/5.08 | | | | | | | vapp(v1, v0) = all_63_1 & $i(v2) & $i(v1) & $i(v0) & ! % 31.86/5.08 | | | | | | | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (vabs(v4, % 31.86/5.08 | | | | | | | v5, v6) = v1) | ~ $i(v6) | ~ $i(v5) | ~ % 31.86/5.08 | | | | | | | $i(v4))) % 31.86/5.08 | | | | | | | % 31.86/5.08 | | | | | | | BETA: splitting (152) gives: % 31.86/5.08 | | | | | | | % 31.86/5.08 | | | | | | | Case 1: % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | | (153) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 31.86/5.08 | | | | | | | | ? [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 % 31.86/5.08 | | | | | | | | & visSomeExp(v1) = 0 & vsomeExp(v4) = all_63_0 & % 31.86/5.08 | | | | | | | | vapp(v3, v2) = v4 & vapp(v0, v2) = all_63_1 & $i(v4) % 31.86/5.08 | | | | | | | | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : % 31.86/5.08 | | | | | | | | ! [v6: $i] : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = % 31.86/5.08 | | | | | | | | v0) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5))) % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | | DELTA: instantiating (153) with fresh symbols all_111_0, % 31.86/5.08 | | | | | | | | all_111_1, all_111_2, all_111_3, all_111_4 gives: % 31.86/5.08 | | | | | | | | (154) vreduce(all_111_4) = all_111_3 & vgetSomeExp(all_111_3) % 31.86/5.08 | | | | | | | | = all_111_1 & visSomeExp(all_111_3) = 0 & % 31.86/5.08 | | | | | | | | vsomeExp(all_111_0) = all_63_0 & vapp(all_111_1, % 31.86/5.08 | | | | | | | | all_111_2) = all_111_0 & vapp(all_111_4, all_111_2) = % 31.86/5.08 | | | | | | | | all_63_1 & $i(all_111_0) & $i(all_111_1) & % 31.86/5.08 | | | | | | | | $i(all_111_2) & $i(all_111_3) & $i(all_111_4) & ! [v0: % 31.86/5.08 | | | | | | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vabs(v0, v1, % 31.86/5.08 | | | | | | | | v2) = all_111_4) | ~ $i(v2) | ~ $i(v1) | ~ % 31.86/5.08 | | | | | | | | $i(v0)) % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | | REF_CLOSE: (2), (8), (9), (12), (13), (16), (17), (25), (29), % 31.86/5.08 | | | | | | | | (30), (31), (32), (34), (35), (37), (52), (53), (57), % 31.86/5.08 | | | | | | | | (63), (64), (154), (EQ-app), (EQ-someExp), (T-app), % 31.86/5.08 | | | | | | | | (getSomeExp0) are inconsistent by sub-proof #6. % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | Case 2: % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | | (155) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] % 31.86/5.08 | | | | | | | | : (all_63_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) = v2 & % 31.86/5.08 | | | | | | | | visSomeExp(v2) = v3 & vapp(v1, v0) = all_63_1 & % 31.86/5.08 | | | | | | | | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] % 31.86/5.08 | | | | | | | | : ! [v6: $i] : ( ~ (vabs(v4, v5, v6) = v1) | ~ % 31.86/5.08 | | | | | | | | $i(v6) | ~ $i(v5) | ~ $i(v4))) % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | | DELTA: instantiating (155) with fresh symbols all_111_0, % 31.86/5.08 | | | | | | | | all_111_1, all_111_2, all_111_3 gives: % 31.86/5.08 | | | | | | | | (156) all_63_0 = vnoExp & ~ (all_111_0 = 0) & % 31.86/5.08 | | | | | | | | vreduce(all_111_2) = all_111_1 & visSomeExp(all_111_1) % 31.86/5.08 | | | | | | | | = all_111_0 & vapp(all_111_2, all_111_3) = all_63_1 & % 31.86/5.08 | | | | | | | | $i(all_111_1) & $i(all_111_2) & $i(all_111_3) & ! [v0: % 31.86/5.08 | | | | | | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vabs(v0, v1, % 31.86/5.08 | | | | | | | | v2) = all_111_2) | ~ $i(v2) | ~ $i(v1) | ~ % 31.86/5.08 | | | | | | | | $i(v0)) % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | | REF_CLOSE: (1), (31), (35), (156) are inconsistent by sub-proof % 31.86/5.08 | | | | | | | | #5. % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | End of split % 31.86/5.08 | | | | | | | % 31.86/5.08 | | | | | | Case 2: % 31.86/5.08 | | | | | | | % 31.86/5.08 | | | | | | | (157) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_63_0 = % 31.86/5.08 | | | | | | | vnoExp & vabs(v0, v1, v2) = all_63_1 & $i(v2) & $i(v1) % 31.86/5.08 | | | | | | | & $i(v0)) | ? [v0: $i] : (all_63_0 = vnoExp & vvar(v0) % 31.86/5.08 | | | | | | | = all_63_1 & $i(v0)) % 31.86/5.08 | | | | | | | % 31.86/5.08 | | | | | | | BETA: splitting (157) gives: % 31.86/5.08 | | | | | | | % 31.86/5.08 | | | | | | | Case 1: % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | | (158) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_63_0 = % 31.86/5.08 | | | | | | | | vnoExp & vabs(v0, v1, v2) = all_63_1 & $i(v2) & % 31.86/5.08 | | | | | | | | $i(v1) & $i(v0)) % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | | DELTA: instantiating (158) with fresh symbols all_111_0, % 31.86/5.08 | | | | | | | | all_111_1, all_111_2 gives: % 31.86/5.08 | | | | | | | | (159) all_63_0 = vnoExp & vabs(all_111_2, all_111_1, % 31.86/5.08 | | | | | | | | all_111_0) = all_63_1 & $i(all_111_0) & $i(all_111_1) % 31.86/5.08 | | | | | | | | & $i(all_111_2) % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | | REF_CLOSE: (1), (31), (35), (159) are inconsistent by sub-proof % 31.86/5.08 | | | | | | | | #4. % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | Case 2: % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | | (160) ? [v0: $i] : (all_63_0 = vnoExp & vvar(v0) = all_63_1 % 31.86/5.08 | | | | | | | | & $i(v0)) % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | | DELTA: instantiating (160) with fresh symbol all_111_0 gives: % 31.86/5.08 | | | | | | | | (161) all_63_0 = vnoExp & vvar(all_111_0) = all_63_1 & % 31.86/5.08 | | | | | | | | $i(all_111_0) % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | | REF_CLOSE: (1), (31), (35), (161) are inconsistent by sub-proof % 31.86/5.08 | | | | | | | | #3. % 31.86/5.08 | | | | | | | | % 31.86/5.08 | | | | | | | End of split % 31.86/5.08 | | | | | | | % 31.86/5.08 | | | | | | End of split % 31.86/5.08 | | | | | | % 31.86/5.08 | | | | | End of split % 31.86/5.08 | | | | | % 31.86/5.08 | | | | Case 2: % 31.86/5.08 | | | | | % 31.86/5.08 | | | | | (162) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 31.86/5.08 | | | | | (varrow(v2, all_73_1) = v3 & vtcheck(all_65_3, v1, v2) = 0 & % 31.86/5.08 | | | | | vtcheck(all_65_3, v0, v3) = 0 & vapp(v0, v1) = all_73_2 & % 31.86/5.08 | | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 31.86/5.08 | | | | | (vsomeType(all_73_1) = v0 & $i(v0) & ? [v1: $i] : % 31.86/5.08 | | | | | (vlookup(v1, all_65_3) = v0 & vvar(v1) = all_73_2 & % 31.86/5.08 | | | | | $i(v1))) % 31.86/5.08 | | | | | % 31.86/5.08 | | | | | BETA: splitting (162) gives: % 31.86/5.08 | | | | | % 31.86/5.08 | | | | | Case 1: % 31.86/5.08 | | | | | | % 31.86/5.08 | | | | | | (163) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 31.86/5.08 | | | | | | (varrow(v2, all_73_1) = v3 & vtcheck(all_65_3, v1, v2) = 0 % 31.86/5.08 | | | | | | & vtcheck(all_65_3, v0, v3) = 0 & vapp(v0, v1) = all_73_2 % 31.86/5.08 | | | | | | & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 31.86/5.08 | | | | | | % 31.86/5.08 | | | | | | DELTA: instantiating (163) with fresh symbols all_114_0, all_114_1, % 31.86/5.08 | | | | | | all_114_2, all_114_3 gives: % 31.86/5.08 | | | | | | (164) varrow(all_114_1, all_73_1) = all_114_0 & vtcheck(all_65_3, % 31.86/5.08 | | | | | | all_114_2, all_114_1) = 0 & vtcheck(all_65_3, all_114_3, % 31.86/5.08 | | | | | | all_114_0) = 0 & vapp(all_114_3, all_114_2) = all_73_2 & % 31.86/5.08 | | | | | | $i(all_114_0) & $i(all_114_1) & $i(all_114_2) & % 31.86/5.08 | | | | | | $i(all_114_3) % 31.86/5.08 | | | | | | % 31.86/5.08 | | | | | | ALPHA: (164) implies: % 31.86/5.08 | | | | | | (165) $i(all_114_3) % 31.86/5.08 | | | | | | (166) $i(all_114_2) % 31.86/5.08 | | | | | | (167) vapp(all_114_3, all_114_2) = all_73_2 % 31.86/5.08 | | | | | | % 31.86/5.08 | | | | | | REDUCE: (60), (167) imply: % 31.86/5.08 | | | | | | (168) vapp(all_114_3, all_114_2) = ve2 % 31.86/5.08 | | | | | | % 31.86/5.08 | | | | | | BETA: splitting (39) gives: % 31.86/5.08 | | | | | | % 31.86/5.08 | | | | | | Case 1: % 31.86/5.08 | | | | | | | % 31.86/5.08 | | | | | | | (169) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 31.86/5.08 | | | | | | | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : % 31.86/5.08 | | | | | | | (all_63_0 = vnoExp & ~ (v7 = 0) & ~ (v6 = 0) & % 31.86/5.08 | | | | | | | vreduce(v4) = v3 & visSomeExp(v3) = v6 & visValue(v4) = % 31.86/5.08 | | | | | | | v7 & vapp(v5, v4) = all_63_1 & vabs(v0, v1, v2) = v5 & % 31.86/5.08 | | | | | | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | % 31.86/5.08 | | | | | | | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 31.86/5.08 | | | | | | | [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ( ~ % 31.86/5.08 | | | | | | | (v6 = 0) & vreduce(v3) = v1 & visSomeExp(v1) = v6 & % 31.86/5.08 | | | | | | | vsomeExp(v7) = all_63_0 & vsubst(v2, v3, v4) = v7 & % 31.86/5.08 | | | | | | | visValue(v3) = 0 & vapp(v5, v3) = all_63_1 & vabs(v2, % 31.86/5.08 | | | | | | | v0, v4) = v5 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & % 31.86/5.08 | | | | | | | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : % 31.86/5.08 | | | | | | | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 31.86/5.08 | | | | | | | ? [v6: $i] : ? [v7: $i] : (vreduce(v0) = v4 & % 31.86/5.08 | | | | | | | vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & % 31.86/5.08 | | | | | | | vsomeExp(v7) = all_63_0 & vapp(v5, v6) = v7 & vapp(v5, % 31.86/5.08 | | | | | | | v0) = all_63_1 & vabs(v1, v2, v3) = v5 & $i(v7) & % 31.86/5.08 | | | | | | | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 31.86/5.08 | | | | | | | $i(v0)) % 31.86/5.08 | | | | | | | % 31.86/5.08 | | | | | | | BETA: splitting (169) gives: % 31.86/5.08 | | | | | | | % 31.86/5.08 | | | | | | | Case 1: % 31.86/5.08 | | | | | | | | % 31.86/5.09 | | | | | | | | (170) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 31.86/5.09 | | | | | | | | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] % 31.86/5.09 | | | | | | | | : (all_63_0 = vnoExp & ~ (v7 = 0) & ~ (v6 = 0) & % 31.86/5.09 | | | | | | | | vreduce(v4) = v3 & visSomeExp(v3) = v6 & visValue(v4) % 31.86/5.09 | | | | | | | | = v7 & vapp(v5, v4) = all_63_1 & vabs(v0, v1, v2) = % 31.86/5.09 | | | | | | | | v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 31.86/5.09 | | | | | | | | $i(v0)) % 31.86/5.09 | | | | | | | | % 31.86/5.09 | | | | | | | | DELTA: instantiating (170) with fresh symbols all_111_0, % 31.86/5.09 | | | | | | | | all_111_1, all_111_2, all_111_3, all_111_4, all_111_5, % 31.86/5.09 | | | | | | | | all_111_6, all_111_7 gives: % 31.86/5.09 | | | | | | | | (171) all_63_0 = vnoExp & ~ (all_111_0 = 0) & ~ (all_111_1 % 31.86/5.09 | | | | | | | | = 0) & vreduce(all_111_3) = all_111_4 & % 31.86/5.09 | | | | | | | | visSomeExp(all_111_4) = all_111_1 & visValue(all_111_3) % 31.86/5.09 | | | | | | | | = all_111_0 & vapp(all_111_2, all_111_3) = all_63_1 & % 31.86/5.09 | | | | | | | | vabs(all_111_7, all_111_6, all_111_5) = all_111_2 & % 31.86/5.09 | | | | | | | | $i(all_111_2) & $i(all_111_3) & $i(all_111_4) & % 31.86/5.09 | | | | | | | | $i(all_111_5) & $i(all_111_6) & $i(all_111_7) % 31.86/5.09 | | | | | | | | % 31.86/5.09 | | | | | | | | REF_CLOSE: (1), (31), (35), (171) are inconsistent by sub-proof % 31.86/5.09 | | | | | | | | #9. % 31.86/5.09 | | | | | | | | % 31.86/5.09 | | | | | | | Case 2: % 31.86/5.09 | | | | | | | | % 31.86/5.09 | | | | | | | | (172) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 31.86/5.09 | | | | | | | | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] % 31.86/5.09 | | | | | | | | : ( ~ (v6 = 0) & vreduce(v3) = v1 & visSomeExp(v1) = v6 % 31.86/5.09 | | | | | | | | & vsomeExp(v7) = all_63_0 & vsubst(v2, v3, v4) = v7 & % 31.86/5.09 | | | | | | | | visValue(v3) = 0 & vapp(v5, v3) = all_63_1 & vabs(v2, % 31.86/5.09 | | | | | | | | v0, v4) = v5 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & % 31.86/5.09 | | | | | | | | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] % 31.86/5.09 | | | | | | | | : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] % 31.86/5.09 | | | | | | | | : ? [v6: $i] : ? [v7: $i] : (vreduce(v0) = v4 & % 31.86/5.09 | | | | | | | | vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & % 31.86/5.09 | | | | | | | | vsomeExp(v7) = all_63_0 & vapp(v5, v6) = v7 & % 31.86/5.09 | | | | | | | | vapp(v5, v0) = all_63_1 & vabs(v1, v2, v3) = v5 & % 31.86/5.09 | | | | | | | | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 31.86/5.09 | | | | | | | | $i(v1) & $i(v0)) % 31.86/5.09 | | | | | | | | % 31.86/5.09 | | | | | | | | BETA: splitting (172) gives: % 31.86/5.09 | | | | | | | | % 31.86/5.09 | | | | | | | | Case 1: % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | (173) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 31.86/5.09 | | | | | | | | | : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: % 31.86/5.09 | | | | | | | | | $i] : ( ~ (v6 = 0) & vreduce(v3) = v1 & % 31.86/5.09 | | | | | | | | | visSomeExp(v1) = v6 & vsomeExp(v7) = all_63_0 & % 31.86/5.09 | | | | | | | | | vsubst(v2, v3, v4) = v7 & visValue(v3) = 0 & % 31.86/5.09 | | | | | | | | | vapp(v5, v3) = all_63_1 & vabs(v2, v0, v4) = v5 & % 31.86/5.09 | | | | | | | | | $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 31.86/5.09 | | | | | | | | | & $i(v0)) % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | DELTA: instantiating (173) with fresh symbols all_122_0, % 31.86/5.09 | | | | | | | | | all_122_1, all_122_2, all_122_3, all_122_4, all_122_5, % 31.86/5.09 | | | | | | | | | all_122_6, all_122_7 gives: % 31.86/5.09 | | | | | | | | | (174) ~ (all_122_1 = 0) & vreduce(all_122_4) = all_122_6 & % 31.86/5.09 | | | | | | | | | visSomeExp(all_122_6) = all_122_1 & % 31.86/5.09 | | | | | | | | | vsomeExp(all_122_0) = all_63_0 & vsubst(all_122_5, % 31.86/5.09 | | | | | | | | | all_122_4, all_122_3) = all_122_0 & % 31.86/5.09 | | | | | | | | | visValue(all_122_4) = 0 & vapp(all_122_2, all_122_4) % 31.86/5.09 | | | | | | | | | = all_63_1 & vabs(all_122_5, all_122_7, all_122_3) = % 31.86/5.09 | | | | | | | | | all_122_2 & $i(all_122_0) & $i(all_122_2) & % 31.86/5.09 | | | | | | | | | $i(all_122_3) & $i(all_122_4) & $i(all_122_5) & % 31.86/5.09 | | | | | | | | | $i(all_122_6) & $i(all_122_7) % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | ALPHA: (174) implies: % 31.86/5.09 | | | | | | | | | (175) $i(all_122_4) % 31.86/5.09 | | | | | | | | | (176) $i(all_122_2) % 31.86/5.09 | | | | | | | | | (177) vapp(all_122_2, all_122_4) = all_63_1 % 31.86/5.09 | | | | | | | | | (178) visValue(all_122_4) = 0 % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | GROUND_INST: instantiating (EQ-app) with ve1, ve2, all_122_2, % 31.86/5.09 | | | | | | | | | all_122_4, all_63_1, simplifying with (8), (9), % 31.86/5.09 | | | | | | | | | (25), (175), (176), (177) gives: % 31.86/5.09 | | | | | | | | | (179) all_122_2 = ve1 & all_122_4 = ve2 % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | ALPHA: (179) implies: % 31.86/5.09 | | | | | | | | | (180) all_122_4 = ve2 % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | REDUCE: (178), (180) imply: % 31.86/5.09 | | | | | | | | | (181) visValue(ve2) = 0 % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | GROUND_INST: instantiating (isValue2) with all_114_3, % 31.86/5.09 | | | | | | | | | all_114_2, ve2, simplifying with (9), (165), % 31.86/5.09 | | | | | | | | | (166), (168), (181) gives: % 31.86/5.09 | | | | | | | | | (182) $false % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | CLOSE: (182) is inconsistent. % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | Case 2: % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | (183) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 31.86/5.09 | | | | | | | | | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 31.86/5.09 | | | | | | | | | $i] : (vreduce(v0) = v4 & vgetSomeExp(v4) = v6 & % 31.86/5.09 | | | | | | | | | visSomeExp(v4) = 0 & vsomeExp(v7) = all_63_0 & % 31.86/5.09 | | | | | | | | | vapp(v5, v6) = v7 & vapp(v5, v0) = all_63_1 & % 31.86/5.09 | | | | | | | | | vabs(v1, v2, v3) = v5 & $i(v7) & $i(v6) & $i(v5) & % 31.86/5.09 | | | | | | | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | DELTA: instantiating (183) with fresh symbols all_122_0, % 31.86/5.09 | | | | | | | | | all_122_1, all_122_2, all_122_3, all_122_4, all_122_5, % 31.86/5.09 | | | | | | | | | all_122_6, all_122_7 gives: % 31.86/5.09 | | | | | | | | | (184) vreduce(all_122_7) = all_122_3 & % 31.86/5.09 | | | | | | | | | vgetSomeExp(all_122_3) = all_122_1 & % 31.86/5.09 | | | | | | | | | visSomeExp(all_122_3) = 0 & vsomeExp(all_122_0) = % 31.86/5.09 | | | | | | | | | all_63_0 & vapp(all_122_2, all_122_1) = all_122_0 & % 31.86/5.09 | | | | | | | | | vapp(all_122_2, all_122_7) = all_63_1 & % 31.86/5.09 | | | | | | | | | vabs(all_122_6, all_122_5, all_122_4) = all_122_2 & % 31.86/5.09 | | | | | | | | | $i(all_122_0) & $i(all_122_1) & $i(all_122_2) & % 31.86/5.09 | | | | | | | | | $i(all_122_3) & $i(all_122_4) & $i(all_122_5) & % 31.86/5.09 | | | | | | | | | $i(all_122_6) & $i(all_122_7) % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | ALPHA: (184) implies: % 31.86/5.09 | | | | | | | | | (185) $i(all_122_7) % 31.86/5.09 | | | | | | | | | (186) $i(all_122_6) % 31.86/5.09 | | | | | | | | | (187) $i(all_122_5) % 31.86/5.09 | | | | | | | | | (188) $i(all_122_4) % 31.86/5.09 | | | | | | | | | (189) $i(all_122_3) % 31.86/5.09 | | | | | | | | | (190) $i(all_122_2) % 31.86/5.09 | | | | | | | | | (191) $i(all_122_1) % 31.86/5.09 | | | | | | | | | (192) $i(all_122_0) % 31.86/5.09 | | | | | | | | | (193) vabs(all_122_6, all_122_5, all_122_4) = all_122_2 % 31.86/5.09 | | | | | | | | | (194) vapp(all_122_2, all_122_7) = all_63_1 % 31.86/5.09 | | | | | | | | | (195) vapp(all_122_2, all_122_1) = all_122_0 % 31.86/5.09 | | | | | | | | | (196) vsomeExp(all_122_0) = all_63_0 % 31.86/5.09 | | | | | | | | | (197) visSomeExp(all_122_3) = 0 % 31.86/5.09 | | | | | | | | | (198) vgetSomeExp(all_122_3) = all_122_1 % 31.86/5.09 | | | | | | | | | (199) vreduce(all_122_7) = all_122_3 % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | GROUND_INST: instantiating (EQ-app) with ve1, ve2, all_122_2, % 31.86/5.09 | | | | | | | | | all_122_7, all_63_1, simplifying with (8), (9), % 31.86/5.09 | | | | | | | | | (25), (185), (190), (194) gives: % 31.86/5.09 | | | | | | | | | (200) all_122_2 = ve1 & all_122_7 = ve2 % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | ALPHA: (200) implies: % 31.86/5.09 | | | | | | | | | (201) all_122_7 = ve2 % 31.86/5.09 | | | | | | | | | (202) all_122_2 = ve1 % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | GROUND_INST: instantiating (EQ-someExp) with all_65_2, % 31.86/5.09 | | | | | | | | | all_122_0, all_63_0, simplifying with (31), (35), % 31.86/5.09 | | | | | | | | | (192), (196) gives: % 31.86/5.09 | | | | | | | | | (203) all_122_0 = all_65_2 % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | REDUCE: (199), (201) imply: % 31.86/5.09 | | | | | | | | | (204) vreduce(ve2) = all_122_3 % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | REDUCE: (195), (202), (203) imply: % 31.86/5.09 | | | | | | | | | (205) vapp(ve1, all_122_1) = all_65_2 % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | REDUCE: (193), (202) imply: % 31.86/5.09 | | | | | | | | | (206) vabs(all_122_6, all_122_5, all_122_4) = ve1 % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | GROUND_INST: instantiating (12) with all_60_0, all_122_3, ve2, % 31.86/5.09 | | | | | | | | | simplifying with (20), (204) gives: % 31.86/5.09 | | | | | | | | | (207) all_122_3 = all_60_0 % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | REDUCE: (198), (207) imply: % 31.86/5.09 | | | | | | | | | (208) vgetSomeExp(all_60_0) = all_122_1 % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | REDUCE: (197), (207) imply: % 31.86/5.09 | | | | | | | | | (209) visSomeExp(all_60_0) = 0 % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | GROUND_INST: instantiating (EQ-abs) with all_87_4, all_73_1, % 31.86/5.09 | | | | | | | | | all_87_3, all_122_6, all_122_5, all_122_4, ve1, % 31.86/5.09 | | | | | | | | | simplifying with (52), (67), (68), (82), (186), % 31.86/5.09 | | | | | | | | | (187), (188), (206) gives: % 31.86/5.09 | | | | | | | | | (210) all_122_4 = all_87_3 & all_122_5 = all_73_1 & % 31.86/5.09 | | | | | | | | | all_122_6 = all_87_4 % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | ALPHA: (210) implies: % 31.86/5.09 | | | | | | | | | (211) all_122_6 = all_87_4 % 31.86/5.09 | | | | | | | | | (212) all_122_5 = all_73_1 % 31.86/5.09 | | | | | | | | | (213) all_122_4 = all_87_3 % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | GROUND_INST: instantiating (T-app) with all_73_1, all_65_3, % 31.86/5.09 | | | | | | | | | ve1, all_122_1, all_65_1, all_73_0, all_65_2, % 31.86/5.09 | | | | | | | | | all_65_0, simplifying with (8), (30), (32), (34), % 31.86/5.09 | | | | | | | | | (52), (57), (64), (191), (205) gives: % 31.86/5.09 | | | | | | | | | (214) all_65_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 31.86/5.09 | | | | | | | | | vtcheck(all_65_3, all_122_1, all_73_1) = v0) % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | BETA: splitting (214) gives: % 31.86/5.09 | | | | | | | | | % 31.86/5.09 | | | | | | | | | Case 1: % 31.86/5.09 | | | | | | | | | | % 31.86/5.09 | | | | | | | | | | (215) all_65_0 = 0 % 31.86/5.09 | | | | | | | | | | % 31.86/5.09 | | | | | | | | | | REDUCE: (29), (215) imply: % 31.86/5.09 | | | | | | | | | | (216) $false % 31.86/5.09 | | | | | | | | | | % 31.86/5.09 | | | | | | | | | | CLOSE: (216) is inconsistent. % 31.86/5.09 | | | | | | | | | | % 31.86/5.09 | | | | | | | | | Case 2: % 31.86/5.09 | | | | | | | | | | % 31.86/5.09 | | | | | | | | | | (217) ? [v0: int] : ( ~ (v0 = 0) & vtcheck(all_65_3, % 31.86/5.09 | | | | | | | | | | all_122_1, all_73_1) = v0) % 31.86/5.09 | | | | | | | | | | % 31.86/5.09 | | | | | | | | | | DELTA: instantiating (217) with fresh symbol all_144_0 % 31.86/5.09 | | | | | | | | | | gives: % 31.86/5.09 | | | | | | | | | | (218) ~ (all_144_0 = 0) & vtcheck(all_65_3, all_122_1, % 31.86/5.09 | | | | | | | | | | all_73_1) = all_144_0 % 31.86/5.09 | | | | | | | | | | % 31.86/5.09 | | | | | | | | | | ALPHA: (218) implies: % 31.86/5.09 | | | | | | | | | | (219) ~ (all_144_0 = 0) % 31.86/5.09 | | | | | | | | | | (220) vtcheck(all_65_3, all_122_1, all_73_1) = all_144_0 % 31.86/5.09 | | | | | | | | | | % 31.86/5.09 | | | | | | | | | | BETA: splitting (37) gives: % 31.86/5.09 | | | | | | | | | | % 31.86/5.09 | | | | | | | | | | Case 1: % 31.86/5.09 | | | | | | | | | | | % 31.86/5.10 | | | | | | | | | | | (221) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 31.86/5.10 | | | | | | | | | | | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : % 31.86/5.10 | | | | | | | | | | | ? [v7: int] : (all_57_0 = vnoExp & ~ (v7 = 0) & % 31.86/5.10 | | | | | | | | | | | ~ (v6 = 0) & vreduce(v4) = v3 & visSomeExp(v3) = % 31.86/5.10 | | | | | | | | | | | v6 & visValue(v4) = v7 & vapp(v5, v4) = ve1 & % 31.86/5.10 | | | | | | | | | | | vabs(v0, v1, v2) = v5 & $i(v5) & $i(v4) & $i(v3) % 31.86/5.10 | | | | | | | | | | | & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? % 31.86/5.10 | | | | | | | | | | | [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 31.86/5.10 | | | | | | | | | | | : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ( ~ % 31.86/5.10 | | | | | | | | | | | (v6 = 0) & vreduce(v3) = v1 & visSomeExp(v1) = % 31.86/5.10 | | | | | | | | | | | v6 & vsomeExp(v7) = all_57_0 & vsubst(v2, v3, % 31.86/5.10 | | | | | | | | | | | v4) = v7 & visValue(v3) = 0 & vapp(v5, v3) = % 31.86/5.10 | | | | | | | | | | | ve1 & vabs(v2, v0, v4) = v5 & $i(v7) & $i(v5) & % 31.86/5.10 | | | | | | | | | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? % 31.86/5.10 | | | | | | | | | | | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 31.86/5.10 | | | | | | | | | | | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? % 31.86/5.10 | | | | | | | | | | | [v7: $i] : (vreduce(v0) = v4 & vgetSomeExp(v4) = % 31.86/5.10 | | | | | | | | | | | v6 & visSomeExp(v4) = 0 & vsomeExp(v7) = % 31.86/5.10 | | | | | | | | | | | all_57_0 & vapp(v5, v6) = v7 & vapp(v5, v0) = % 31.86/5.10 | | | | | | | | | | | ve1 & vabs(v1, v2, v3) = v5 & $i(v7) & $i(v6) & % 31.86/5.10 | | | | | | | | | | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 31.86/5.10 | | | | | | | | | | | $i(v0)) % 31.86/5.10 | | | | | | | | | | | % 31.86/5.10 | | | | | | | | | | | BETA: splitting (221) gives: % 31.86/5.10 | | | | | | | | | | | % 31.86/5.10 | | | | | | | | | | | Case 1: % 31.86/5.10 | | | | | | | | | | | | % 31.86/5.10 | | | | | | | | | | | | (222) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 31.86/5.10 | | | | | | | | | | | | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : % 31.86/5.10 | | | | | | | | | | | | ? [v7: int] : (all_57_0 = vnoExp & ~ (v7 = 0) & % 31.86/5.10 | | | | | | | | | | | | ~ (v6 = 0) & vreduce(v4) = v3 & visSomeExp(v3) = % 31.86/5.10 | | | | | | | | | | | | v6 & visValue(v4) = v7 & vapp(v5, v4) = ve1 & % 31.86/5.10 | | | | | | | | | | | | vabs(v0, v1, v2) = v5 & $i(v5) & $i(v4) & $i(v3) % 31.86/5.10 | | | | | | | | | | | | & $i(v2) & $i(v1) & $i(v0)) % 31.86/5.10 | | | | | | | | | | | | % 31.86/5.10 | | | | | | | | | | | | DELTA: instantiating (222) with fresh symbols all_152_0, % 31.86/5.10 | | | | | | | | | | | | all_152_1, all_152_2, all_152_3, all_152_4, % 31.86/5.10 | | | | | | | | | | | | all_152_5, all_152_6, all_152_7 gives: % 31.86/5.10 | | | | | | | | | | | | (223) all_57_0 = vnoExp & ~ (all_152_0 = 0) & ~ % 31.86/5.10 | | | | | | | | | | | | (all_152_1 = 0) & vreduce(all_152_3) = all_152_4 & % 31.86/5.10 | | | | | | | | | | | | visSomeExp(all_152_4) = all_152_1 & % 31.86/5.10 | | | | | | | | | | | | visValue(all_152_3) = all_152_0 & vapp(all_152_2, % 31.86/5.10 | | | | | | | | | | | | all_152_3) = ve1 & vabs(all_152_7, all_152_6, % 31.86/5.10 | | | | | | | | | | | | all_152_5) = all_152_2 & $i(all_152_2) & % 31.86/5.10 | | | | | | | | | | | | $i(all_152_3) & $i(all_152_4) & $i(all_152_5) & % 31.86/5.10 | | | | | | | | | | | | $i(all_152_6) & $i(all_152_7) % 31.86/5.10 | | | | | | | | | | | | % 31.86/5.10 | | | | | | | | | | | | ALPHA: (223) implies: % 31.86/5.10 | | | | | | | | | | | | (224) $i(all_152_3) % 31.86/5.10 | | | | | | | | | | | | (225) $i(all_152_2) % 31.86/5.10 | | | | | | | | | | | | (226) vapp(all_152_2, all_152_3) = ve1 % 31.86/5.10 | | | | | | | | | | | | % 31.86/5.10 | | | | | | | | | | | | GROUND_INST: instantiating (DIFF-abs-app) with all_87_4, % 31.86/5.10 | | | | | | | | | | | | all_73_1, all_87_3, all_152_2, all_152_3, ve1, % 31.86/5.10 | | | | | | | | | | | | simplifying with (52), (67), (68), (82), (224), % 31.86/5.10 | | | | | | | | | | | | (225), (226) gives: % 31.86/5.10 | | | | | | | | | | | | (227) $false % 31.86/5.10 | | | | | | | | | | | | % 31.86/5.10 | | | | | | | | | | | | CLOSE: (227) is inconsistent. % 31.86/5.10 | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | Case 2: % 32.11/5.10 | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | (228) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.10 | | | | | | | | | | | | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : % 32.11/5.10 | | | | | | | | | | | | ? [v7: $i] : ( ~ (v6 = 0) & vreduce(v3) = v1 & % 32.11/5.10 | | | | | | | | | | | | visSomeExp(v1) = v6 & vsomeExp(v7) = all_57_0 & % 32.11/5.10 | | | | | | | | | | | | vsubst(v2, v3, v4) = v7 & visValue(v3) = 0 & % 32.11/5.10 | | | | | | | | | | | | vapp(v5, v3) = ve1 & vabs(v2, v0, v4) = v5 & % 32.11/5.10 | | | | | | | | | | | | $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 32.11/5.10 | | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : % 32.11/5.10 | | | | | | | | | | | | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 32.11/5.10 | | | | | | | | | | | | $i] : ? [v6: $i] : ? [v7: $i] : (vreduce(v0) = % 32.11/5.10 | | | | | | | | | | | | v4 & vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & % 32.11/5.10 | | | | | | | | | | | | vsomeExp(v7) = all_57_0 & vapp(v5, v6) = v7 & % 32.11/5.10 | | | | | | | | | | | | vapp(v5, v0) = ve1 & vabs(v1, v2, v3) = v5 & % 32.11/5.10 | | | | | | | | | | | | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 32.11/5.10 | | | | | | | | | | | | $i(v2) & $i(v1) & $i(v0)) % 32.11/5.10 | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | BETA: splitting (228) gives: % 32.11/5.10 | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | Case 1: % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | | (229) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.10 | | | | | | | | | | | | | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : % 32.11/5.10 | | | | | | | | | | | | | ? [v7: $i] : ( ~ (v6 = 0) & vreduce(v3) = v1 & % 32.11/5.10 | | | | | | | | | | | | | visSomeExp(v1) = v6 & vsomeExp(v7) = all_57_0 & % 32.11/5.10 | | | | | | | | | | | | | vsubst(v2, v3, v4) = v7 & visValue(v3) = 0 & % 32.11/5.10 | | | | | | | | | | | | | vapp(v5, v3) = ve1 & vabs(v2, v0, v4) = v5 & % 32.11/5.10 | | | | | | | | | | | | | $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 32.11/5.10 | | | | | | | | | | | | | $i(v1) & $i(v0)) % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | | DELTA: instantiating (229) with fresh symbols all_152_0, % 32.11/5.10 | | | | | | | | | | | | | all_152_1, all_152_2, all_152_3, all_152_4, % 32.11/5.10 | | | | | | | | | | | | | all_152_5, all_152_6, all_152_7 gives: % 32.11/5.10 | | | | | | | | | | | | | (230) ~ (all_152_1 = 0) & vreduce(all_152_4) = % 32.11/5.10 | | | | | | | | | | | | | all_152_6 & visSomeExp(all_152_6) = all_152_1 & % 32.11/5.10 | | | | | | | | | | | | | vsomeExp(all_152_0) = all_57_0 & vsubst(all_152_5, % 32.11/5.10 | | | | | | | | | | | | | all_152_4, all_152_3) = all_152_0 & % 32.11/5.10 | | | | | | | | | | | | | visValue(all_152_4) = 0 & vapp(all_152_2, % 32.11/5.10 | | | | | | | | | | | | | all_152_4) = ve1 & vabs(all_152_5, all_152_7, % 32.11/5.10 | | | | | | | | | | | | | all_152_3) = all_152_2 & $i(all_152_0) & % 32.11/5.10 | | | | | | | | | | | | | $i(all_152_2) & $i(all_152_3) & $i(all_152_4) & % 32.11/5.10 | | | | | | | | | | | | | $i(all_152_5) & $i(all_152_6) & $i(all_152_7) % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | | ALPHA: (230) implies: % 32.11/5.10 | | | | | | | | | | | | | (231) $i(all_152_0) % 32.11/5.10 | | | | | | | | | | | | | (232) vsomeExp(all_152_0) = all_57_0 % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | | REDUCE: (76), (232) imply: % 32.11/5.10 | | | | | | | | | | | | | (233) vsomeExp(all_152_0) = vnoExp % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_152_0, simplifying with % 32.11/5.10 | | | | | | | | | | | | | (231), (233) gives: % 32.11/5.10 | | | | | | | | | | | | | (234) $false % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | | CLOSE: (234) is inconsistent. % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | Case 2: % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | | (235) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.10 | | | | | | | | | | | | | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 32.11/5.10 | | | | | | | | | | | | | ? [v7: $i] : (vreduce(v0) = v4 & vgetSomeExp(v4) = % 32.11/5.10 | | | | | | | | | | | | | v6 & visSomeExp(v4) = 0 & vsomeExp(v7) = % 32.11/5.10 | | | | | | | | | | | | | all_57_0 & vapp(v5, v6) = v7 & vapp(v5, v0) = % 32.11/5.10 | | | | | | | | | | | | | ve1 & vabs(v1, v2, v3) = v5 & $i(v7) & $i(v6) & % 32.11/5.10 | | | | | | | | | | | | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 32.11/5.10 | | | | | | | | | | | | | $i(v0)) % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | | DELTA: instantiating (235) with fresh symbols all_152_0, % 32.11/5.10 | | | | | | | | | | | | | all_152_1, all_152_2, all_152_3, all_152_4, % 32.11/5.10 | | | | | | | | | | | | | all_152_5, all_152_6, all_152_7 gives: % 32.11/5.10 | | | | | | | | | | | | | (236) vreduce(all_152_7) = all_152_3 & % 32.11/5.10 | | | | | | | | | | | | | vgetSomeExp(all_152_3) = all_152_1 & % 32.11/5.10 | | | | | | | | | | | | | visSomeExp(all_152_3) = 0 & vsomeExp(all_152_0) = % 32.11/5.10 | | | | | | | | | | | | | all_57_0 & vapp(all_152_2, all_152_1) = all_152_0 % 32.11/5.10 | | | | | | | | | | | | | & vapp(all_152_2, all_152_7) = ve1 & % 32.11/5.10 | | | | | | | | | | | | | vabs(all_152_6, all_152_5, all_152_4) = all_152_2 % 32.11/5.10 | | | | | | | | | | | | | & $i(all_152_0) & $i(all_152_1) & $i(all_152_2) & % 32.11/5.10 | | | | | | | | | | | | | $i(all_152_3) & $i(all_152_4) & $i(all_152_5) & % 32.11/5.10 | | | | | | | | | | | | | $i(all_152_6) & $i(all_152_7) % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | | ALPHA: (236) implies: % 32.11/5.10 | | | | | | | | | | | | | (237) $i(all_152_0) % 32.11/5.10 | | | | | | | | | | | | | (238) vsomeExp(all_152_0) = all_57_0 % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | | REDUCE: (76), (238) imply: % 32.11/5.10 | | | | | | | | | | | | | (239) vsomeExp(all_152_0) = vnoExp % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_152_0, simplifying with % 32.11/5.10 | | | | | | | | | | | | | (237), (239) gives: % 32.11/5.10 | | | | | | | | | | | | | (240) $false % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | | CLOSE: (240) is inconsistent. % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | End of split % 32.11/5.10 | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | End of split % 32.11/5.10 | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | Case 2: % 32.11/5.10 | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | (241) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.10 | | | | | | | | | | | $i] : ? [v4: $i] : (vreduce(v0) = v1 & % 32.11/5.10 | | | | | | | | | | | vgetSomeExp(v1) = v3 & visSomeExp(v1) = 0 & % 32.11/5.10 | | | | | | | | | | | vsomeExp(v4) = all_57_0 & vapp(v3, v2) = v4 & % 32.11/5.10 | | | | | | | | | | | vapp(v0, v2) = ve1 & $i(v4) & $i(v3) & $i(v2) & % 32.11/5.10 | | | | | | | | | | | $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! % 32.11/5.10 | | | | | | | | | | | [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ % 32.11/5.10 | | | | | | | | | | | $i(v7) | ~ $i(v6) | ~ $i(v5))) | ? [v0: $i] % 32.11/5.10 | | | | | | | | | | | : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : % 32.11/5.10 | | | | | | | | | | | (all_57_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) = % 32.11/5.10 | | | | | | | | | | | v2 & visSomeExp(v2) = v3 & vapp(v1, v0) = ve1 & % 32.11/5.10 | | | | | | | | | | | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: % 32.11/5.10 | | | | | | | | | | | $i] : ! [v6: $i] : ( ~ (vabs(v4, v5, v6) = % 32.11/5.10 | | | | | | | | | | | v1) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4))) | % 32.11/5.10 | | | | | | | | | | | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_57_0 % 32.11/5.10 | | | | | | | | | | | = vnoExp & vabs(v0, v1, v2) = ve1 & $i(v2) & % 32.11/5.10 | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (all_57_0 = % 32.11/5.10 | | | | | | | | | | | vnoExp & vvar(v0) = ve1 & $i(v0)) % 32.11/5.10 | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | BETA: splitting (241) gives: % 32.11/5.10 | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | Case 1: % 32.11/5.10 | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | (242) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.10 | | | | | | | | | | | | $i] : ? [v4: $i] : (vreduce(v0) = v1 & % 32.11/5.10 | | | | | | | | | | | | vgetSomeExp(v1) = v3 & visSomeExp(v1) = 0 & % 32.11/5.10 | | | | | | | | | | | | vsomeExp(v4) = all_57_0 & vapp(v3, v2) = v4 & % 32.11/5.10 | | | | | | | | | | | | vapp(v0, v2) = ve1 & $i(v4) & $i(v3) & $i(v2) & % 32.11/5.10 | | | | | | | | | | | | $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! % 32.11/5.10 | | | | | | | | | | | | [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ % 32.11/5.10 | | | | | | | | | | | | $i(v7) | ~ $i(v6) | ~ $i(v5))) | ? [v0: $i] % 32.11/5.10 | | | | | | | | | | | | : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : % 32.11/5.10 | | | | | | | | | | | | (all_57_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) = % 32.11/5.10 | | | | | | | | | | | | v2 & visSomeExp(v2) = v3 & vapp(v1, v0) = ve1 & % 32.11/5.10 | | | | | | | | | | | | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: % 32.11/5.10 | | | | | | | | | | | | $i] : ! [v6: $i] : ( ~ (vabs(v4, v5, v6) = % 32.11/5.10 | | | | | | | | | | | | v1) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4))) % 32.11/5.10 | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | BETA: splitting (242) gives: % 32.11/5.10 | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | Case 1: % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | | (243) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.10 | | | | | | | | | | | | | $i] : ? [v4: $i] : (vreduce(v0) = v1 & % 32.11/5.10 | | | | | | | | | | | | | vgetSomeExp(v1) = v3 & visSomeExp(v1) = 0 & % 32.11/5.10 | | | | | | | | | | | | | vsomeExp(v4) = all_57_0 & vapp(v3, v2) = v4 & % 32.11/5.10 | | | | | | | | | | | | | vapp(v0, v2) = ve1 & $i(v4) & $i(v3) & $i(v2) & % 32.11/5.10 | | | | | | | | | | | | | $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! % 32.11/5.10 | | | | | | | | | | | | | [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ % 32.11/5.10 | | | | | | | | | | | | | $i(v7) | ~ $i(v6) | ~ $i(v5))) % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | | DELTA: instantiating (243) with fresh symbols all_152_0, % 32.11/5.10 | | | | | | | | | | | | | all_152_1, all_152_2, all_152_3, all_152_4 gives: % 32.11/5.10 | | | | | | | | | | | | | (244) vreduce(all_152_4) = all_152_3 & % 32.11/5.10 | | | | | | | | | | | | | vgetSomeExp(all_152_3) = all_152_1 & % 32.11/5.10 | | | | | | | | | | | | | visSomeExp(all_152_3) = 0 & vsomeExp(all_152_0) = % 32.11/5.10 | | | | | | | | | | | | | all_57_0 & vapp(all_152_1, all_152_2) = all_152_0 % 32.11/5.10 | | | | | | | | | | | | | & vapp(all_152_4, all_152_2) = ve1 & $i(all_152_0) % 32.11/5.10 | | | | | | | | | | | | | & $i(all_152_1) & $i(all_152_2) & $i(all_152_3) & % 32.11/5.10 | | | | | | | | | | | | | $i(all_152_4) & ! [v0: $i] : ! [v1: $i] : ! % 32.11/5.10 | | | | | | | | | | | | | [v2: $i] : ( ~ (vabs(v0, v1, v2) = all_152_4) | ~ % 32.11/5.10 | | | | | | | | | | | | | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | | ALPHA: (244) implies: % 32.11/5.10 | | | | | | | | | | | | | (245) $i(all_152_0) % 32.11/5.10 | | | | | | | | | | | | | (246) vsomeExp(all_152_0) = all_57_0 % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.10 | | | | | | | | | | | | | REDUCE: (76), (246) imply: % 32.11/5.10 | | | | | | | | | | | | | (247) vsomeExp(all_152_0) = vnoExp % 32.11/5.10 | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_152_0, simplifying with % 32.11/5.11 | | | | | | | | | | | | | (245), (247) gives: % 32.11/5.11 | | | | | | | | | | | | | (248) $false % 32.11/5.11 | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | CLOSE: (248) is inconsistent. % 32.11/5.11 | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | Case 2: % 32.11/5.11 | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | (249) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.11 | | | | | | | | | | | | | int] : (all_57_0 = vnoExp & ~ (v3 = 0) & % 32.11/5.11 | | | | | | | | | | | | | vreduce(v1) = v2 & visSomeExp(v2) = v3 & % 32.11/5.11 | | | | | | | | | | | | | vapp(v1, v0) = ve1 & $i(v2) & $i(v1) & $i(v0) & % 32.11/5.11 | | | | | | | | | | | | | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 32.11/5.11 | | | | | | | | | | | | | (vabs(v4, v5, v6) = v1) | ~ $i(v6) | ~ % 32.11/5.11 | | | | | | | | | | | | | $i(v5) | ~ $i(v4))) % 32.11/5.11 | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | DELTA: instantiating (249) with fresh symbols all_152_0, % 32.11/5.11 | | | | | | | | | | | | | all_152_1, all_152_2, all_152_3 gives: % 32.11/5.11 | | | | | | | | | | | | | (250) all_57_0 = vnoExp & ~ (all_152_0 = 0) & % 32.11/5.11 | | | | | | | | | | | | | vreduce(all_152_2) = all_152_1 & % 32.11/5.11 | | | | | | | | | | | | | visSomeExp(all_152_1) = all_152_0 & % 32.11/5.11 | | | | | | | | | | | | | vapp(all_152_2, all_152_3) = ve1 & $i(all_152_1) & % 32.11/5.11 | | | | | | | | | | | | | $i(all_152_2) & $i(all_152_3) & ! [v0: $i] : ! % 32.11/5.11 | | | | | | | | | | | | | [v1: $i] : ! [v2: $i] : ( ~ (vabs(v0, v1, v2) = % 32.11/5.11 | | | | | | | | | | | | | all_152_2) | ~ $i(v2) | ~ $i(v1) | ~ % 32.11/5.11 | | | | | | | | | | | | | $i(v0)) % 32.11/5.11 | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | ALPHA: (250) implies: % 32.11/5.11 | | | | | | | | | | | | | (251) $i(all_152_3) % 32.11/5.11 | | | | | | | | | | | | | (252) $i(all_152_2) % 32.11/5.11 | | | | | | | | | | | | | (253) vapp(all_152_2, all_152_3) = ve1 % 32.11/5.11 | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | GROUND_INST: instantiating (DIFF-abs-app) with all_87_4, % 32.11/5.11 | | | | | | | | | | | | | all_73_1, all_87_3, all_152_2, all_152_3, ve1, % 32.11/5.11 | | | | | | | | | | | | | simplifying with (52), (67), (68), (82), (251), % 32.11/5.11 | | | | | | | | | | | | | (252), (253) gives: % 32.11/5.11 | | | | | | | | | | | | | (254) $false % 32.11/5.11 | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | CLOSE: (254) is inconsistent. % 32.11/5.11 | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | End of split % 32.11/5.11 | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | Case 2: % 32.11/5.11 | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | (255) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 32.11/5.11 | | | | | | | | | | | | (all_57_0 = vnoExp & vabs(v0, v1, v2) = ve1 & % 32.11/5.11 | | | | | | | | | | | | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 32.11/5.11 | | | | | | | | | | | | (all_57_0 = vnoExp & vvar(v0) = ve1 & $i(v0)) % 32.11/5.11 | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | BETA: splitting (255) gives: % 32.11/5.11 | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | Case 1: % 32.11/5.11 | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | (256) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 32.11/5.11 | | | | | | | | | | | | | (all_57_0 = vnoExp & vabs(v0, v1, v2) = ve1 & % 32.11/5.11 | | | | | | | | | | | | | $i(v2) & $i(v1) & $i(v0)) % 32.11/5.11 | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | DELTA: instantiating (256) with fresh symbols all_152_0, % 32.11/5.11 | | | | | | | | | | | | | all_152_1, all_152_2 gives: % 32.11/5.11 | | | | | | | | | | | | | (257) all_57_0 = vnoExp & vabs(all_152_2, all_152_1, % 32.11/5.11 | | | | | | | | | | | | | all_152_0) = ve1 & $i(all_152_0) & $i(all_152_1) % 32.11/5.11 | | | | | | | | | | | | | & $i(all_152_2) % 32.11/5.11 | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | ALPHA: (257) implies: % 32.11/5.11 | | | | | | | | | | | | | (258) $i(all_152_2) % 32.11/5.11 | | | | | | | | | | | | | (259) $i(all_152_1) % 32.11/5.11 | | | | | | | | | | | | | (260) $i(all_152_0) % 32.11/5.11 | | | | | | | | | | | | | (261) vabs(all_152_2, all_152_1, all_152_0) = ve1 % 32.11/5.11 | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | GROUND_INST: instantiating (EQ-abs) with all_87_4, all_73_1, % 32.11/5.11 | | | | | | | | | | | | | all_87_3, all_152_2, all_152_1, all_152_0, ve1, % 32.11/5.11 | | | | | | | | | | | | | simplifying with (52), (67), (68), (82), (258), % 32.11/5.11 | | | | | | | | | | | | | (259), (260), (261) gives: % 32.11/5.11 | | | | | | | | | | | | | (262) all_152_0 = all_87_3 & all_152_1 = all_73_1 & % 32.11/5.11 | | | | | | | | | | | | | all_152_2 = all_87_4 % 32.11/5.11 | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | ALPHA: (262) implies: % 32.11/5.11 | | | | | | | | | | | | | (263) all_152_1 = all_73_1 % 32.11/5.11 | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | BETA: splitting (38) gives: % 32.11/5.11 | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | Case 1: % 32.11/5.11 | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | (264) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.11 | | | | | | | | | | | | | | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : % 32.11/5.11 | | | | | | | | | | | | | | ? [v7: int] : (all_60_0 = vnoExp & ~ (v7 = 0) & % 32.11/5.11 | | | | | | | | | | | | | | ~ (v6 = 0) & vreduce(v4) = v3 & visSomeExp(v3) = % 32.11/5.11 | | | | | | | | | | | | | | v6 & visValue(v4) = v7 & vapp(v5, v4) = ve2 & % 32.11/5.11 | | | | | | | | | | | | | | vabs(v0, v1, v2) = v5 & $i(v5) & $i(v4) & $i(v3) % 32.11/5.11 | | | | | | | | | | | | | | & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? % 32.11/5.11 | | | | | | | | | | | | | | [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 32.11/5.11 | | | | | | | | | | | | | | : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ( ~ % 32.11/5.11 | | | | | | | | | | | | | | (v6 = 0) & vreduce(v3) = v1 & visSomeExp(v1) = % 32.11/5.11 | | | | | | | | | | | | | | v6 & vsomeExp(v7) = all_60_0 & vsubst(v2, v3, % 32.11/5.11 | | | | | | | | | | | | | | v4) = v7 & visValue(v3) = 0 & vapp(v5, v3) = % 32.11/5.11 | | | | | | | | | | | | | | ve2 & vabs(v2, v0, v4) = v5 & $i(v7) & $i(v5) & % 32.11/5.11 | | | | | | | | | | | | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? % 32.11/5.11 | | | | | | | | | | | | | | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 32.11/5.11 | | | | | | | | | | | | | | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? % 32.11/5.11 | | | | | | | | | | | | | | [v7: $i] : (vreduce(v0) = v4 & vgetSomeExp(v4) = % 32.11/5.11 | | | | | | | | | | | | | | v6 & visSomeExp(v4) = 0 & vsomeExp(v7) = % 32.11/5.11 | | | | | | | | | | | | | | all_60_0 & vapp(v5, v6) = v7 & vapp(v5, v0) = % 32.11/5.11 | | | | | | | | | | | | | | ve2 & vabs(v1, v2, v3) = v5 & $i(v7) & $i(v6) & % 32.11/5.11 | | | | | | | | | | | | | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 32.11/5.11 | | | | | | | | | | | | | | $i(v0)) % 32.11/5.11 | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | BETA: splitting (264) gives: % 32.11/5.11 | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | Case 1: % 32.11/5.11 | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | (265) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.11 | | | | | | | | | | | | | | | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : % 32.11/5.11 | | | | | | | | | | | | | | | ? [v7: int] : (all_60_0 = vnoExp & ~ (v7 = 0) & % 32.11/5.11 | | | | | | | | | | | | | | | ~ (v6 = 0) & vreduce(v4) = v3 & visSomeExp(v3) = % 32.11/5.11 | | | | | | | | | | | | | | | v6 & visValue(v4) = v7 & vapp(v5, v4) = ve2 & % 32.11/5.11 | | | | | | | | | | | | | | | vabs(v0, v1, v2) = v5 & $i(v5) & $i(v4) & $i(v3) % 32.11/5.11 | | | | | | | | | | | | | | | & $i(v2) & $i(v1) & $i(v0)) % 32.11/5.11 | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | DELTA: instantiating (265) with fresh symbols all_166_0, % 32.11/5.11 | | | | | | | | | | | | | | | all_166_1, all_166_2, all_166_3, all_166_4, % 32.11/5.11 | | | | | | | | | | | | | | | all_166_5, all_166_6, all_166_7 gives: % 32.11/5.11 | | | | | | | | | | | | | | | (266) all_60_0 = vnoExp & ~ (all_166_0 = 0) & ~ % 32.11/5.11 | | | | | | | | | | | | | | | (all_166_1 = 0) & vreduce(all_166_3) = all_166_4 & % 32.11/5.11 | | | | | | | | | | | | | | | visSomeExp(all_166_4) = all_166_1 & % 32.11/5.11 | | | | | | | | | | | | | | | visValue(all_166_3) = all_166_0 & vapp(all_166_2, % 32.11/5.11 | | | | | | | | | | | | | | | all_166_3) = ve2 & vabs(all_166_7, all_166_6, % 32.11/5.11 | | | | | | | | | | | | | | | all_166_5) = all_166_2 & $i(all_166_2) & % 32.11/5.11 | | | | | | | | | | | | | | | $i(all_166_3) & $i(all_166_4) & $i(all_166_5) & % 32.11/5.11 | | | | | | | | | | | | | | | $i(all_166_6) & $i(all_166_7) % 32.11/5.11 | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | ALPHA: (266) implies: % 32.11/5.11 | | | | | | | | | | | | | | | (267) all_60_0 = vnoExp % 32.11/5.11 | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | REDUCE: (209), (267) imply: % 32.11/5.11 | | | | | | | | | | | | | | | (268) visSomeExp(vnoExp) = 0 % 32.11/5.11 | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | PRED_UNIFY: (2), (268) imply: % 32.11/5.11 | | | | | | | | | | | | | | | (269) $false % 32.11/5.11 | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | CLOSE: (269) is inconsistent. % 32.11/5.11 | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | Case 2: % 32.11/5.11 | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | (270) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.11 | | | | | | | | | | | | | | | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : % 32.11/5.11 | | | | | | | | | | | | | | | ? [v7: $i] : ( ~ (v6 = 0) & vreduce(v3) = v1 & % 32.11/5.11 | | | | | | | | | | | | | | | visSomeExp(v1) = v6 & vsomeExp(v7) = all_60_0 & % 32.11/5.11 | | | | | | | | | | | | | | | vsubst(v2, v3, v4) = v7 & visValue(v3) = 0 & % 32.11/5.11 | | | | | | | | | | | | | | | vapp(v5, v3) = ve2 & vabs(v2, v0, v4) = v5 & % 32.11/5.11 | | | | | | | | | | | | | | | $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 32.11/5.11 | | | | | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : % 32.11/5.11 | | | | | | | | | | | | | | | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 32.11/5.11 | | | | | | | | | | | | | | | $i] : ? [v6: $i] : ? [v7: $i] : (vreduce(v0) = % 32.11/5.11 | | | | | | | | | | | | | | | v4 & vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & % 32.11/5.11 | | | | | | | | | | | | | | | vsomeExp(v7) = all_60_0 & vapp(v5, v6) = v7 & % 32.11/5.11 | | | | | | | | | | | | | | | vapp(v5, v0) = ve2 & vabs(v1, v2, v3) = v5 & % 32.11/5.11 | | | | | | | | | | | | | | | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 32.11/5.11 | | | | | | | | | | | | | | | $i(v2) & $i(v1) & $i(v0)) % 32.11/5.11 | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | BETA: splitting (270) gives: % 32.11/5.11 | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | Case 1: % 32.11/5.11 | | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | | (271) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.11 | | | | | | | | | | | | | | | | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : % 32.11/5.11 | | | | | | | | | | | | | | | | ? [v7: $i] : ( ~ (v6 = 0) & vreduce(v3) = v1 & % 32.11/5.11 | | | | | | | | | | | | | | | | visSomeExp(v1) = v6 & vsomeExp(v7) = all_60_0 & % 32.11/5.11 | | | | | | | | | | | | | | | | vsubst(v2, v3, v4) = v7 & visValue(v3) = 0 & % 32.11/5.11 | | | | | | | | | | | | | | | | vapp(v5, v3) = ve2 & vabs(v2, v0, v4) = v5 & % 32.11/5.11 | | | | | | | | | | | | | | | | $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 32.11/5.11 | | | | | | | | | | | | | | | | $i(v1) & $i(v0)) % 32.11/5.11 | | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | | DELTA: instantiating (271) with fresh symbols all_166_0, % 32.11/5.11 | | | | | | | | | | | | | | | | all_166_1, all_166_2, all_166_3, all_166_4, % 32.11/5.11 | | | | | | | | | | | | | | | | all_166_5, all_166_6, all_166_7 gives: % 32.11/5.11 | | | | | | | | | | | | | | | | (272) ~ (all_166_1 = 0) & vreduce(all_166_4) = % 32.11/5.11 | | | | | | | | | | | | | | | | all_166_6 & visSomeExp(all_166_6) = all_166_1 & % 32.11/5.11 | | | | | | | | | | | | | | | | vsomeExp(all_166_0) = all_60_0 & vsubst(all_166_5, % 32.11/5.11 | | | | | | | | | | | | | | | | all_166_4, all_166_3) = all_166_0 & % 32.11/5.11 | | | | | | | | | | | | | | | | visValue(all_166_4) = 0 & vapp(all_166_2, % 32.11/5.11 | | | | | | | | | | | | | | | | all_166_4) = ve2 & vabs(all_166_5, all_166_7, % 32.11/5.11 | | | | | | | | | | | | | | | | all_166_3) = all_166_2 & $i(all_166_0) & % 32.11/5.11 | | | | | | | | | | | | | | | | $i(all_166_2) & $i(all_166_3) & $i(all_166_4) & % 32.11/5.11 | | | | | | | | | | | | | | | | $i(all_166_5) & $i(all_166_6) & $i(all_166_7) % 32.11/5.11 | | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | | ALPHA: (272) implies: % 32.11/5.11 | | | | | | | | | | | | | | | | (273) $i(all_166_0) % 32.11/5.11 | | | | | | | | | | | | | | | | (274) vsomeExp(all_166_0) = all_60_0 % 32.11/5.11 | | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (getSomeExp0) with all_60_0, % 32.11/5.11 | | | | | | | | | | | | | | | | all_122_1, all_166_0, simplifying with (19), % 32.11/5.11 | | | | | | | | | | | | | | | | (191), (208), (273), (274) gives: % 32.11/5.11 | | | | | | | | | | | | | | | | (275) all_166_0 = all_122_1 % 32.11/5.11 | | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_65_3, all_166_0, % 32.11/5.11 | | | | | | | | | | | | | | | | all_73_1, simplifying with (30), (52), (63), % 32.11/5.11 | | | | | | | | | | | | | | | | (273), (274) gives: % 32.11/5.11 | | | | | | | | | | | | | | | | (276) vtcheck(all_65_3, all_166_0, all_73_1) = 0 % 32.11/5.11 | | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | | REDUCE: (275), (276) imply: % 32.11/5.11 | | | | | | | | | | | | | | | | (277) vtcheck(all_65_3, all_122_1, all_73_1) = 0 % 32.11/5.11 | | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (219), (220), (277) are inconsistent by % 32.11/5.11 | | | | | | | | | | | | | | | | sub-proof #2. % 32.11/5.11 | | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | Case 2: % 32.11/5.11 | | | | | | | | | | | | | | | | % 32.11/5.11 | | | | | | | | | | | | | | | | (278) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.11 | | | | | | | | | | | | | | | | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 32.11/5.11 | | | | | | | | | | | | | | | | ? [v7: $i] : (vreduce(v0) = v4 & vgetSomeExp(v4) = % 32.11/5.11 | | | | | | | | | | | | | | | | v6 & visSomeExp(v4) = 0 & vsomeExp(v7) = % 32.11/5.11 | | | | | | | | | | | | | | | | all_60_0 & vapp(v5, v6) = v7 & vapp(v5, v0) = % 32.11/5.11 | | | | | | | | | | | | | | | | ve2 & vabs(v1, v2, v3) = v5 & $i(v7) & $i(v6) & % 32.11/5.11 | | | | | | | | | | | | | | | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 32.11/5.11 | | | | | | | | | | | | | | | | $i(v0)) % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | DELTA: instantiating (278) with fresh symbols all_166_0, % 32.11/5.12 | | | | | | | | | | | | | | | | all_166_1, all_166_2, all_166_3, all_166_4, % 32.11/5.12 | | | | | | | | | | | | | | | | all_166_5, all_166_6, all_166_7 gives: % 32.11/5.12 | | | | | | | | | | | | | | | | (279) vreduce(all_166_7) = all_166_3 & % 32.11/5.12 | | | | | | | | | | | | | | | | vgetSomeExp(all_166_3) = all_166_1 & % 32.11/5.12 | | | | | | | | | | | | | | | | visSomeExp(all_166_3) = 0 & vsomeExp(all_166_0) = % 32.11/5.12 | | | | | | | | | | | | | | | | all_60_0 & vapp(all_166_2, all_166_1) = all_166_0 % 32.11/5.12 | | | | | | | | | | | | | | | | & vapp(all_166_2, all_166_7) = ve2 & % 32.11/5.12 | | | | | | | | | | | | | | | | vabs(all_166_6, all_166_5, all_166_4) = all_166_2 % 32.11/5.12 | | | | | | | | | | | | | | | | & $i(all_166_0) & $i(all_166_1) & $i(all_166_2) & % 32.11/5.12 | | | | | | | | | | | | | | | | $i(all_166_3) & $i(all_166_4) & $i(all_166_5) & % 32.11/5.12 | | | | | | | | | | | | | | | | $i(all_166_6) & $i(all_166_7) % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | ALPHA: (279) implies: % 32.11/5.12 | | | | | | | | | | | | | | | | (280) $i(all_166_0) % 32.11/5.12 | | | | | | | | | | | | | | | | (281) vsomeExp(all_166_0) = all_60_0 % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (getSomeExp0) with all_60_0, % 32.11/5.12 | | | | | | | | | | | | | | | | all_122_1, all_166_0, simplifying with (19), % 32.11/5.12 | | | | | | | | | | | | | | | | (191), (208), (280), (281) gives: % 32.11/5.12 | | | | | | | | | | | | | | | | (282) all_166_0 = all_122_1 % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_65_3, all_166_0, % 32.11/5.12 | | | | | | | | | | | | | | | | all_73_1, simplifying with (30), (52), (63), % 32.11/5.12 | | | | | | | | | | | | | | | | (280), (281) gives: % 32.11/5.12 | | | | | | | | | | | | | | | | (283) vtcheck(all_65_3, all_166_0, all_73_1) = 0 % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | REDUCE: (282), (283) imply: % 32.11/5.12 | | | | | | | | | | | | | | | | (284) vtcheck(all_65_3, all_122_1, all_73_1) = 0 % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (219), (220), (284) are inconsistent by % 32.11/5.12 | | | | | | | | | | | | | | | | sub-proof #2. % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | End of split % 32.11/5.12 | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | End of split % 32.11/5.12 | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | Case 2: % 32.11/5.12 | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | (285) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.12 | | | | | | | | | | | | | | $i] : ? [v4: $i] : (vreduce(v0) = v1 & % 32.11/5.12 | | | | | | | | | | | | | | vgetSomeExp(v1) = v3 & visSomeExp(v1) = 0 & % 32.11/5.12 | | | | | | | | | | | | | | vsomeExp(v4) = all_60_0 & vapp(v3, v2) = v4 & % 32.11/5.12 | | | | | | | | | | | | | | vapp(v0, v2) = ve2 & $i(v4) & $i(v3) & $i(v2) & % 32.11/5.12 | | | | | | | | | | | | | | $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! % 32.11/5.12 | | | | | | | | | | | | | | [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ % 32.11/5.12 | | | | | | | | | | | | | | $i(v7) | ~ $i(v6) | ~ $i(v5))) | ? [v0: $i] % 32.11/5.12 | | | | | | | | | | | | | | : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : % 32.11/5.12 | | | | | | | | | | | | | | (all_60_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) = % 32.11/5.12 | | | | | | | | | | | | | | v2 & visSomeExp(v2) = v3 & vapp(v1, v0) = ve2 & % 32.11/5.12 | | | | | | | | | | | | | | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: % 32.11/5.12 | | | | | | | | | | | | | | $i] : ! [v6: $i] : ( ~ (vabs(v4, v5, v6) = % 32.11/5.12 | | | | | | | | | | | | | | v1) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4))) | % 32.11/5.12 | | | | | | | | | | | | | | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_60_0 % 32.11/5.12 | | | | | | | | | | | | | | = vnoExp & vabs(v0, v1, v2) = ve2 & $i(v2) & % 32.11/5.12 | | | | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (all_60_0 = % 32.11/5.12 | | | | | | | | | | | | | | vnoExp & vvar(v0) = ve2 & $i(v0)) % 32.11/5.12 | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | BETA: splitting (285) gives: % 32.11/5.12 | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | Case 1: % 32.11/5.12 | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | (286) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.12 | | | | | | | | | | | | | | | $i] : ? [v4: $i] : (vreduce(v0) = v1 & % 32.11/5.12 | | | | | | | | | | | | | | | vgetSomeExp(v1) = v3 & visSomeExp(v1) = 0 & % 32.11/5.12 | | | | | | | | | | | | | | | vsomeExp(v4) = all_60_0 & vapp(v3, v2) = v4 & % 32.11/5.12 | | | | | | | | | | | | | | | vapp(v0, v2) = ve2 & $i(v4) & $i(v3) & $i(v2) & % 32.11/5.12 | | | | | | | | | | | | | | | $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! % 32.11/5.12 | | | | | | | | | | | | | | | [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ % 32.11/5.12 | | | | | | | | | | | | | | | $i(v7) | ~ $i(v6) | ~ $i(v5))) | ? [v0: $i] % 32.11/5.12 | | | | | | | | | | | | | | | : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : % 32.11/5.12 | | | | | | | | | | | | | | | (all_60_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) = % 32.11/5.12 | | | | | | | | | | | | | | | v2 & visSomeExp(v2) = v3 & vapp(v1, v0) = ve2 & % 32.11/5.12 | | | | | | | | | | | | | | | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: % 32.11/5.12 | | | | | | | | | | | | | | | $i] : ! [v6: $i] : ( ~ (vabs(v4, v5, v6) = % 32.11/5.12 | | | | | | | | | | | | | | | v1) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4))) % 32.11/5.12 | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 32.11/5.12 | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | Case 1: % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | (287) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.12 | | | | | | | | | | | | | | | | $i] : ? [v4: $i] : (vreduce(v0) = v1 & % 32.11/5.12 | | | | | | | | | | | | | | | | vgetSomeExp(v1) = v3 & visSomeExp(v1) = 0 & % 32.11/5.12 | | | | | | | | | | | | | | | | vsomeExp(v4) = all_60_0 & vapp(v3, v2) = v4 & % 32.11/5.12 | | | | | | | | | | | | | | | | vapp(v0, v2) = ve2 & $i(v4) & $i(v3) & $i(v2) & % 32.11/5.12 | | | | | | | | | | | | | | | | $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! % 32.11/5.12 | | | | | | | | | | | | | | | | [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ % 32.11/5.12 | | | | | | | | | | | | | | | | $i(v7) | ~ $i(v6) | ~ $i(v5))) % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | DELTA: instantiating (287) with fresh symbols all_166_0, % 32.11/5.12 | | | | | | | | | | | | | | | | all_166_1, all_166_2, all_166_3, all_166_4 gives: % 32.11/5.12 | | | | | | | | | | | | | | | | (288) vreduce(all_166_4) = all_166_3 & % 32.11/5.12 | | | | | | | | | | | | | | | | vgetSomeExp(all_166_3) = all_166_1 & % 32.11/5.12 | | | | | | | | | | | | | | | | visSomeExp(all_166_3) = 0 & vsomeExp(all_166_0) = % 32.11/5.12 | | | | | | | | | | | | | | | | all_60_0 & vapp(all_166_1, all_166_2) = all_166_0 % 32.11/5.12 | | | | | | | | | | | | | | | | & vapp(all_166_4, all_166_2) = ve2 & $i(all_166_0) % 32.11/5.12 | | | | | | | | | | | | | | | | & $i(all_166_1) & $i(all_166_2) & $i(all_166_3) & % 32.11/5.12 | | | | | | | | | | | | | | | | $i(all_166_4) & ! [v0: $i] : ! [v1: $i] : ! % 32.11/5.12 | | | | | | | | | | | | | | | | [v2: $i] : ( ~ (vabs(v0, v1, v2) = all_166_4) | ~ % 32.11/5.12 | | | | | | | | | | | | | | | | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | ALPHA: (288) implies: % 32.11/5.12 | | | | | | | | | | | | | | | | (289) vsomeExp(all_166_0) = all_60_0 % 32.11/5.12 | | | | | | | | | | | | | | | | (290) $i(all_166_0) % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (getSomeExp0) with all_60_0, % 32.11/5.12 | | | | | | | | | | | | | | | | all_122_1, all_166_0, simplifying with (19), % 32.11/5.12 | | | | | | | | | | | | | | | | (191), (208), (289), (290) gives: % 32.11/5.12 | | | | | | | | | | | | | | | | (291) all_166_0 = all_122_1 % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_65_3, all_166_0, % 32.11/5.12 | | | | | | | | | | | | | | | | all_73_1, simplifying with (30), (52), (63), % 32.11/5.12 | | | | | | | | | | | | | | | | (289), (290) gives: % 32.11/5.12 | | | | | | | | | | | | | | | | (292) vtcheck(all_65_3, all_166_0, all_73_1) = 0 % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | REDUCE: (291), (292) imply: % 32.11/5.12 | | | | | | | | | | | | | | | | (293) vtcheck(all_65_3, all_122_1, all_73_1) = 0 % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (219), (220), (293) are inconsistent by % 32.11/5.12 | | | | | | | | | | | | | | | | sub-proof #2. % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | Case 2: % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | (294) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.12 | | | | | | | | | | | | | | | | int] : (all_60_0 = vnoExp & ~ (v3 = 0) & % 32.11/5.12 | | | | | | | | | | | | | | | | vreduce(v1) = v2 & visSomeExp(v2) = v3 & % 32.11/5.12 | | | | | | | | | | | | | | | | vapp(v1, v0) = ve2 & $i(v2) & $i(v1) & $i(v0) & % 32.11/5.12 | | | | | | | | | | | | | | | | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 32.11/5.12 | | | | | | | | | | | | | | | | (vabs(v4, v5, v6) = v1) | ~ $i(v6) | ~ % 32.11/5.12 | | | | | | | | | | | | | | | | $i(v5) | ~ $i(v4))) % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | DELTA: instantiating (294) with fresh symbols all_166_0, % 32.11/5.12 | | | | | | | | | | | | | | | | all_166_1, all_166_2, all_166_3 gives: % 32.11/5.12 | | | | | | | | | | | | | | | | (295) all_60_0 = vnoExp & ~ (all_166_0 = 0) & % 32.11/5.12 | | | | | | | | | | | | | | | | vreduce(all_166_2) = all_166_1 & % 32.11/5.12 | | | | | | | | | | | | | | | | visSomeExp(all_166_1) = all_166_0 & % 32.11/5.12 | | | | | | | | | | | | | | | | vapp(all_166_2, all_166_3) = ve2 & $i(all_166_1) & % 32.11/5.12 | | | | | | | | | | | | | | | | $i(all_166_2) & $i(all_166_3) & ! [v0: $i] : ! % 32.11/5.12 | | | | | | | | | | | | | | | | [v1: $i] : ! [v2: $i] : ( ~ (vabs(v0, v1, v2) = % 32.11/5.12 | | | | | | | | | | | | | | | | all_166_2) | ~ $i(v2) | ~ $i(v1) | ~ % 32.11/5.12 | | | | | | | | | | | | | | | | $i(v0)) % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | ALPHA: (295) implies: % 32.11/5.12 | | | | | | | | | | | | | | | | (296) all_60_0 = vnoExp % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | REDUCE: (209), (296) imply: % 32.11/5.12 | | | | | | | | | | | | | | | | (297) visSomeExp(vnoExp) = 0 % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | PRED_UNIFY: (2), (297) imply: % 32.11/5.12 | | | | | | | | | | | | | | | | (298) $false % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | CLOSE: (298) is inconsistent. % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | End of split % 32.11/5.12 | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | Case 2: % 32.11/5.12 | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | (299) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 32.11/5.12 | | | | | | | | | | | | | | | (all_60_0 = vnoExp & vabs(v0, v1, v2) = ve2 & % 32.11/5.12 | | | | | | | | | | | | | | | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 32.11/5.12 | | | | | | | | | | | | | | | (all_60_0 = vnoExp & vvar(v0) = ve2 & $i(v0)) % 32.11/5.12 | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 32.11/5.12 | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | Case 1: % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | (300) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 32.11/5.12 | | | | | | | | | | | | | | | | (all_60_0 = vnoExp & vabs(v0, v1, v2) = ve2 & % 32.11/5.12 | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & $i(v0)) % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | DELTA: instantiating (300) with fresh symbols all_166_0, % 32.11/5.12 | | | | | | | | | | | | | | | | all_166_1, all_166_2 gives: % 32.11/5.12 | | | | | | | | | | | | | | | | (301) all_60_0 = vnoExp & vabs(all_166_2, all_166_1, % 32.11/5.12 | | | | | | | | | | | | | | | | all_166_0) = ve2 & $i(all_166_0) & $i(all_166_1) % 32.11/5.12 | | | | | | | | | | | | | | | | & $i(all_166_2) % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | ALPHA: (301) implies: % 32.11/5.12 | | | | | | | | | | | | | | | | (302) all_60_0 = vnoExp % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | REDUCE: (209), (302) imply: % 32.11/5.12 | | | | | | | | | | | | | | | | (303) visSomeExp(vnoExp) = 0 % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | PRED_UNIFY: (2), (303) imply: % 32.11/5.12 | | | | | | | | | | | | | | | | (304) $false % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | CLOSE: (304) is inconsistent. % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | Case 2: % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | (305) ? [v0: $i] : (all_60_0 = vnoExp & vvar(v0) = ve2 % 32.11/5.12 | | | | | | | | | | | | | | | | & $i(v0)) % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | DELTA: instantiating (305) with fresh symbol all_166_0 % 32.11/5.12 | | | | | | | | | | | | | | | | gives: % 32.11/5.12 | | | | | | | | | | | | | | | | (306) all_60_0 = vnoExp & vvar(all_166_0) = ve2 & % 32.11/5.12 | | | | | | | | | | | | | | | | $i(all_166_0) % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | ALPHA: (306) implies: % 32.11/5.12 | | | | | | | | | | | | | | | | (307) all_60_0 = vnoExp % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | REDUCE: (209), (307) imply: % 32.11/5.12 | | | | | | | | | | | | | | | | (308) visSomeExp(vnoExp) = 0 % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | PRED_UNIFY: (2), (308) imply: % 32.11/5.12 | | | | | | | | | | | | | | | | (309) $false % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | | CLOSE: (309) is inconsistent. % 32.11/5.12 | | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | | End of split % 32.11/5.12 | | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | | End of split % 32.11/5.12 | | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | End of split % 32.11/5.12 | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | Case 2: % 32.11/5.12 | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | (310) ? [v0: $i] : (all_57_0 = vnoExp & vvar(v0) = ve1 % 32.11/5.12 | | | | | | | | | | | | | & $i(v0)) % 32.11/5.12 | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | DELTA: instantiating (310) with fresh symbol all_152_0 % 32.11/5.12 | | | | | | | | | | | | | gives: % 32.11/5.12 | | | | | | | | | | | | | (311) all_57_0 = vnoExp & vvar(all_152_0) = ve1 & % 32.11/5.12 | | | | | | | | | | | | | $i(all_152_0) % 32.11/5.12 | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | ALPHA: (311) implies: % 32.11/5.12 | | | | | | | | | | | | | (312) $i(all_152_0) % 32.11/5.12 | | | | | | | | | | | | | (313) vvar(all_152_0) = ve1 % 32.11/5.12 | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_152_0, % 32.11/5.12 | | | | | | | | | | | | | all_87_4, all_73_1, all_87_3, ve1, simplifying % 32.11/5.12 | | | | | | | | | | | | | with (52), (67), (68), (82), (312), (313) gives: % 32.11/5.12 | | | | | | | | | | | | | (314) $false % 32.11/5.12 | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | | CLOSE: (314) is inconsistent. % 32.11/5.12 | | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | | End of split % 32.11/5.12 | | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | | End of split % 32.11/5.12 | | | | | | | | | | | % 32.11/5.12 | | | | | | | | | | End of split % 32.11/5.12 | | | | | | | | | | % 32.11/5.12 | | | | | | | | | End of split % 32.11/5.12 | | | | | | | | | % 32.11/5.12 | | | | | | | | End of split % 32.11/5.12 | | | | | | | | % 32.11/5.12 | | | | | | | End of split % 32.11/5.12 | | | | | | | % 32.11/5.12 | | | | | | Case 2: % 32.11/5.12 | | | | | | | % 32.11/5.13 | | | | | | | (315) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.11/5.13 | | | | | | | ? [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & % 32.11/5.13 | | | | | | | visSomeExp(v1) = 0 & vsomeExp(v4) = all_63_0 & vapp(v3, % 32.11/5.13 | | | | | | | v2) = v4 & vapp(v0, v2) = all_63_1 & $i(v4) & $i(v3) % 32.11/5.13 | | | | | | | & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] % 32.11/5.13 | | | | | | | : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ $i(v7) % 32.11/5.13 | | | | | | | | ~ $i(v6) | ~ $i(v5))) | ? [v0: $i] : ? [v1: $i] % 32.11/5.13 | | | | | | | : ? [v2: $i] : ? [v3: int] : (all_63_0 = vnoExp & ~ % 32.11/5.13 | | | | | | | (v3 = 0) & vreduce(v1) = v2 & visSomeExp(v2) = v3 & % 32.11/5.13 | | | | | | | vapp(v1, v0) = all_63_1 & $i(v2) & $i(v1) & $i(v0) & ! % 32.11/5.13 | | | | | | | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (vabs(v4, % 32.11/5.13 | | | | | | | v5, v6) = v1) | ~ $i(v6) | ~ $i(v5) | ~ % 32.11/5.13 | | | | | | | $i(v4))) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 32.11/5.13 | | | | | | | (all_63_0 = vnoExp & vabs(v0, v1, v2) = all_63_1 & $i(v2) % 32.11/5.13 | | | | | | | & $i(v1) & $i(v0)) | ? [v0: $i] : (all_63_0 = vnoExp & % 32.11/5.13 | | | | | | | vvar(v0) = all_63_1 & $i(v0)) % 32.11/5.13 | | | | | | | % 32.11/5.13 | | | | | | | BETA: splitting (315) gives: % 32.11/5.13 | | | | | | | % 32.11/5.13 | | | | | | | Case 1: % 32.11/5.13 | | | | | | | | % 32.11/5.13 | | | | | | | | (316) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.11/5.13 | | | | | | | | ? [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 % 32.11/5.13 | | | | | | | | & visSomeExp(v1) = 0 & vsomeExp(v4) = all_63_0 & % 32.11/5.13 | | | | | | | | vapp(v3, v2) = v4 & vapp(v0, v2) = all_63_1 & $i(v4) % 32.11/5.13 | | | | | | | | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : % 32.11/5.13 | | | | | | | | ! [v6: $i] : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = % 32.11/5.13 | | | | | | | | v0) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5))) | ? % 32.11/5.13 | | | | | | | | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : % 32.11/5.13 | | | | | | | | (all_63_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) = v2 & % 32.11/5.13 | | | | | | | | visSomeExp(v2) = v3 & vapp(v1, v0) = all_63_1 & % 32.11/5.13 | | | | | | | | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] % 32.11/5.13 | | | | | | | | : ! [v6: $i] : ( ~ (vabs(v4, v5, v6) = v1) | ~ % 32.11/5.13 | | | | | | | | $i(v6) | ~ $i(v5) | ~ $i(v4))) % 32.11/5.13 | | | | | | | | % 32.11/5.13 | | | | | | | | BETA: splitting (316) gives: % 32.11/5.13 | | | | | | | | % 32.11/5.13 | | | | | | | | Case 1: % 32.11/5.13 | | | | | | | | | % 32.11/5.13 | | | | | | | | | (317) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 32.11/5.13 | | | | | | | | | : ? [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = % 32.11/5.13 | | | | | | | | | v3 & visSomeExp(v1) = 0 & vsomeExp(v4) = all_63_0 & % 32.11/5.13 | | | | | | | | | vapp(v3, v2) = v4 & vapp(v0, v2) = all_63_1 & % 32.11/5.13 | | | | | | | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! % 32.11/5.13 | | | | | | | | | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 32.11/5.13 | | | | | | | | | (vabs(v5, v6, v7) = v0) | ~ $i(v7) | ~ $i(v6) | % 32.11/5.13 | | | | | | | | | ~ $i(v5))) % 32.11/5.13 | | | | | | | | | % 32.11/5.13 | | | | | | | | | DELTA: instantiating (317) with fresh symbols all_111_0, % 32.11/5.13 | | | | | | | | | all_111_1, all_111_2, all_111_3, all_111_4 gives: % 32.11/5.13 | | | | | | | | | (318) vreduce(all_111_4) = all_111_3 & % 32.11/5.13 | | | | | | | | | vgetSomeExp(all_111_3) = all_111_1 & % 32.11/5.13 | | | | | | | | | visSomeExp(all_111_3) = 0 & vsomeExp(all_111_0) = % 32.11/5.13 | | | | | | | | | all_63_0 & vapp(all_111_1, all_111_2) = all_111_0 & % 32.11/5.13 | | | | | | | | | vapp(all_111_4, all_111_2) = all_63_1 & $i(all_111_0) % 32.11/5.13 | | | | | | | | | & $i(all_111_1) & $i(all_111_2) & $i(all_111_3) & % 32.11/5.13 | | | | | | | | | $i(all_111_4) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 32.11/5.13 | | | | | | | | | $i] : ( ~ (vabs(v0, v1, v2) = all_111_4) | ~ % 32.11/5.13 | | | | | | | | | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 32.11/5.13 | | | | | | | | | % 32.11/5.13 | | | | | | | | | REF_CLOSE: (2), (8), (9), (12), (13), (16), (17), (25), (29), % 32.11/5.13 | | | | | | | | | (30), (31), (32), (34), (35), (37), (52), (53), % 32.11/5.13 | | | | | | | | | (57), (63), (64), (318), (EQ-app), (EQ-someExp), % 32.11/5.13 | | | | | | | | | (T-app), (getSomeExp0) are inconsistent by % 32.11/5.13 | | | | | | | | | sub-proof #6. % 32.11/5.13 | | | | | | | | | % 32.11/5.13 | | | | | | | | Case 2: % 32.11/5.13 | | | | | | | | | % 32.11/5.13 | | | | | | | | | (319) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.11/5.13 | | | | | | | | | int] : (all_63_0 = vnoExp & ~ (v3 = 0) & % 32.11/5.13 | | | | | | | | | vreduce(v1) = v2 & visSomeExp(v2) = v3 & vapp(v1, % 32.11/5.13 | | | | | | | | | v0) = all_63_1 & $i(v2) & $i(v1) & $i(v0) & ! % 32.11/5.13 | | | | | | | | | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 32.11/5.13 | | | | | | | | | (vabs(v4, v5, v6) = v1) | ~ $i(v6) | ~ $i(v5) | % 32.11/5.13 | | | | | | | | | ~ $i(v4))) % 32.11/5.13 | | | | | | | | | % 32.11/5.13 | | | | | | | | | DELTA: instantiating (319) with fresh symbols all_111_0, % 32.11/5.13 | | | | | | | | | all_111_1, all_111_2, all_111_3 gives: % 32.11/5.13 | | | | | | | | | (320) all_63_0 = vnoExp & ~ (all_111_0 = 0) & % 32.11/5.13 | | | | | | | | | vreduce(all_111_2) = all_111_1 & % 32.11/5.13 | | | | | | | | | visSomeExp(all_111_1) = all_111_0 & vapp(all_111_2, % 32.11/5.13 | | | | | | | | | all_111_3) = all_63_1 & $i(all_111_1) & % 32.11/5.13 | | | | | | | | | $i(all_111_2) & $i(all_111_3) & ! [v0: $i] : ! [v1: % 32.11/5.13 | | | | | | | | | $i] : ! [v2: $i] : ( ~ (vabs(v0, v1, v2) = % 32.11/5.13 | | | | | | | | | all_111_2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 32.11/5.13 | | | | | | | | | % 32.11/5.13 | | | | | | | | | REF_CLOSE: (1), (31), (35), (320) are inconsistent by % 32.11/5.13 | | | | | | | | | sub-proof #5. % 32.11/5.13 | | | | | | | | | % 32.11/5.13 | | | | | | | | End of split % 32.11/5.13 | | | | | | | | % 32.11/5.13 | | | | | | | Case 2: % 32.11/5.13 | | | | | | | | % 32.11/5.13 | | | | | | | | (321) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_63_0 = % 32.11/5.13 | | | | | | | | vnoExp & vabs(v0, v1, v2) = all_63_1 & $i(v2) & % 32.11/5.13 | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (all_63_0 = vnoExp & % 32.11/5.13 | | | | | | | | vvar(v0) = all_63_1 & $i(v0)) % 32.11/5.13 | | | | | | | | % 32.11/5.13 | | | | | | | | BETA: splitting (321) gives: % 32.11/5.13 | | | | | | | | % 32.11/5.13 | | | | | | | | Case 1: % 32.11/5.13 | | | | | | | | | % 32.11/5.13 | | | | | | | | | (322) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_63_0 = % 32.11/5.13 | | | | | | | | | vnoExp & vabs(v0, v1, v2) = all_63_1 & $i(v2) & % 32.11/5.13 | | | | | | | | | $i(v1) & $i(v0)) % 32.11/5.13 | | | | | | | | | % 32.11/5.13 | | | | | | | | | DELTA: instantiating (322) with fresh symbols all_111_0, % 32.11/5.13 | | | | | | | | | all_111_1, all_111_2 gives: % 32.11/5.13 | | | | | | | | | (323) all_63_0 = vnoExp & vabs(all_111_2, all_111_1, % 32.11/5.13 | | | | | | | | | all_111_0) = all_63_1 & $i(all_111_0) & % 32.11/5.13 | | | | | | | | | $i(all_111_1) & $i(all_111_2) % 32.11/5.13 | | | | | | | | | % 32.11/5.13 | | | | | | | | | REF_CLOSE: (1), (31), (35), (323) are inconsistent by % 32.11/5.13 | | | | | | | | | sub-proof #4. % 32.11/5.13 | | | | | | | | | % 32.11/5.13 | | | | | | | | Case 2: % 32.11/5.13 | | | | | | | | | % 32.11/5.13 | | | | | | | | | (324) ? [v0: $i] : (all_63_0 = vnoExp & vvar(v0) = % 32.11/5.13 | | | | | | | | | all_63_1 & $i(v0)) % 32.11/5.13 | | | | | | | | | % 32.11/5.13 | | | | | | | | | DELTA: instantiating (324) with fresh symbol all_111_0 gives: % 32.11/5.13 | | | | | | | | | (325) all_63_0 = vnoExp & vvar(all_111_0) = all_63_1 & % 32.11/5.13 | | | | | | | | | $i(all_111_0) % 32.11/5.13 | | | | | | | | | % 32.11/5.13 | | | | | | | | | REF_CLOSE: (1), (31), (35), (325) are inconsistent by % 32.11/5.13 | | | | | | | | | sub-proof #3. % 32.11/5.13 | | | | | | | | | % 32.11/5.13 | | | | | | | | End of split % 32.11/5.13 | | | | | | | | % 32.11/5.13 | | | | | | | End of split % 32.11/5.13 | | | | | | | % 32.11/5.13 | | | | | | End of split % 32.11/5.13 | | | | | | % 32.11/5.13 | | | | | Case 2: % 32.11/5.13 | | | | | | % 32.11/5.13 | | | | | | (326) ? [v0: $i] : (vsomeType(all_73_1) = v0 & $i(v0) & ? [v1: % 32.11/5.13 | | | | | | $i] : (vlookup(v1, all_65_3) = v0 & vvar(v1) = all_73_2 % 32.11/5.13 | | | | | | & $i(v1))) % 32.11/5.13 | | | | | | % 32.11/5.13 | | | | | | REF_CLOSE: (1), (2), (3), (8), (9), (12), (13), (16), (17), (19), % 32.11/5.13 | | | | | | (20), (25), (29), (30), (31), (32), (34), (35), (37), % 32.11/5.13 | | | | | | (39), (52), (53), (57), (60), (63), (64), (326), % 32.11/5.13 | | | | | | (EQ-app), (EQ-someExp), (T-app), (getSomeExp0), % 32.11/5.13 | | | | | | (isValue1) are inconsistent by sub-proof #1. % 32.11/5.13 | | | | | | % 32.11/5.13 | | | | | End of split % 32.11/5.13 | | | | | % 32.11/5.13 | | | | End of split % 32.11/5.13 | | | | % 32.11/5.13 | | | Case 2: % 32.11/5.13 | | | | % 32.11/5.13 | | | | (327) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.11/5.13 | | | | (varrow(v2, all_73_0) = v3 & vtcheck(all_65_3, v1, v2) = 0 & % 32.11/5.13 | | | | vtcheck(all_65_3, v0, v3) = 0 & vapp(v0, v1) = all_73_3 & % 32.11/5.13 | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 32.11/5.13 | | | | (vsomeType(all_73_0) = v0 & $i(v0) & ? [v1: $i] : (vlookup(v1, % 32.11/5.13 | | | | all_65_3) = v0 & vvar(v1) = all_73_3 & $i(v1))) % 32.11/5.13 | | | | % 32.11/5.13 | | | | BETA: splitting (327) gives: % 32.11/5.13 | | | | % 32.11/5.13 | | | | Case 1: % 32.11/5.13 | | | | | % 32.11/5.13 | | | | | (328) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.11/5.13 | | | | | (varrow(v2, all_73_0) = v3 & vtcheck(all_65_3, v1, v2) = 0 & % 32.11/5.13 | | | | | vtcheck(all_65_3, v0, v3) = 0 & vapp(v0, v1) = all_73_3 & % 32.11/5.13 | | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.11/5.13 | | | | | % 32.11/5.13 | | | | | DELTA: instantiating (328) with fresh symbols all_87_0, all_87_1, % 32.11/5.13 | | | | | all_87_2, all_87_3 gives: % 32.11/5.13 | | | | | (329) varrow(all_87_1, all_73_0) = all_87_0 & vtcheck(all_65_3, % 32.11/5.13 | | | | | all_87_2, all_87_1) = 0 & vtcheck(all_65_3, all_87_3, % 32.11/5.13 | | | | | all_87_0) = 0 & vapp(all_87_3, all_87_2) = all_73_3 & % 32.11/5.13 | | | | | $i(all_87_0) & $i(all_87_1) & $i(all_87_2) & $i(all_87_3) % 32.11/5.13 | | | | | % 32.11/5.13 | | | | | ALPHA: (329) implies: % 32.11/5.13 | | | | | (330) $i(all_87_3) % 32.11/5.13 | | | | | (331) $i(all_87_2) % 32.11/5.13 | | | | | (332) vapp(all_87_3, all_87_2) = all_73_3 % 32.11/5.13 | | | | | % 32.11/5.13 | | | | | REDUCE: (59), (332) imply: % 32.11/5.13 | | | | | (333) vapp(all_87_3, all_87_2) = ve1 % 32.11/5.13 | | | | | % 32.11/5.13 | | | | | BETA: splitting (39) gives: % 32.11/5.13 | | | | | % 32.11/5.13 | | | | | Case 1: % 32.11/5.13 | | | | | | % 32.11/5.13 | | | | | | (334) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 32.11/5.13 | | | | | | [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : % 32.11/5.13 | | | | | | (all_63_0 = vnoExp & ~ (v7 = 0) & ~ (v6 = 0) & % 32.11/5.13 | | | | | | vreduce(v4) = v3 & visSomeExp(v3) = v6 & visValue(v4) = % 32.11/5.13 | | | | | | v7 & vapp(v5, v4) = all_63_1 & vabs(v0, v1, v2) = v5 & % 32.11/5.13 | | | | | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? % 32.11/5.13 | | | | | | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 32.11/5.13 | | | | | | [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ( ~ % 32.11/5.13 | | | | | | (v6 = 0) & vreduce(v3) = v1 & visSomeExp(v1) = v6 & % 32.11/5.13 | | | | | | vsomeExp(v7) = all_63_0 & vsubst(v2, v3, v4) = v7 & % 32.11/5.13 | | | | | | visValue(v3) = 0 & vapp(v5, v3) = all_63_1 & vabs(v2, v0, % 32.11/5.13 | | | | | | v4) = v5 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 32.11/5.13 | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: % 32.11/5.13 | | | | | | $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 32.11/5.13 | | | | | | $i] : ? [v7: $i] : (vreduce(v0) = v4 & vgetSomeExp(v4) = % 32.11/5.13 | | | | | | v6 & visSomeExp(v4) = 0 & vsomeExp(v7) = all_63_0 & % 32.11/5.13 | | | | | | vapp(v5, v6) = v7 & vapp(v5, v0) = all_63_1 & vabs(v1, % 32.11/5.13 | | | | | | v2, v3) = v5 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 32.11/5.13 | | | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.11/5.13 | | | | | | % 32.11/5.13 | | | | | | BETA: splitting (334) gives: % 32.11/5.13 | | | | | | % 32.11/5.13 | | | | | | Case 1: % 32.11/5.13 | | | | | | | % 32.11/5.13 | | | | | | | (335) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.11/5.13 | | | | | | | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : % 32.11/5.13 | | | | | | | (all_63_0 = vnoExp & ~ (v7 = 0) & ~ (v6 = 0) & % 32.11/5.13 | | | | | | | vreduce(v4) = v3 & visSomeExp(v3) = v6 & visValue(v4) = % 32.11/5.13 | | | | | | | v7 & vapp(v5, v4) = all_63_1 & vabs(v0, v1, v2) = v5 & % 32.11/5.13 | | | | | | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.11/5.13 | | | | | | | % 32.11/5.13 | | | | | | | DELTA: instantiating (335) with fresh symbols all_111_0, % 32.11/5.13 | | | | | | | all_111_1, all_111_2, all_111_3, all_111_4, all_111_5, % 32.11/5.13 | | | | | | | all_111_6, all_111_7 gives: % 32.11/5.13 | | | | | | | (336) all_63_0 = vnoExp & ~ (all_111_0 = 0) & ~ (all_111_1 = % 32.11/5.13 | | | | | | | 0) & vreduce(all_111_3) = all_111_4 & % 32.11/5.13 | | | | | | | visSomeExp(all_111_4) = all_111_1 & visValue(all_111_3) = % 32.11/5.13 | | | | | | | all_111_0 & vapp(all_111_2, all_111_3) = all_63_1 & % 32.11/5.13 | | | | | | | vabs(all_111_7, all_111_6, all_111_5) = all_111_2 & % 32.11/5.13 | | | | | | | $i(all_111_2) & $i(all_111_3) & $i(all_111_4) & % 32.11/5.13 | | | | | | | $i(all_111_5) & $i(all_111_6) & $i(all_111_7) % 32.11/5.13 | | | | | | | % 32.11/5.13 | | | | | | | REF_CLOSE: (1), (31), (35), (336) are inconsistent by sub-proof % 32.11/5.13 | | | | | | | #9. % 32.11/5.13 | | | | | | | % 32.11/5.13 | | | | | | Case 2: % 32.11/5.13 | | | | | | | % 32.11/5.14 | | | | | | | (337) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.11/5.14 | | | | | | | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ( % 32.11/5.14 | | | | | | | ~ (v6 = 0) & vreduce(v3) = v1 & visSomeExp(v1) = v6 & % 32.11/5.14 | | | | | | | vsomeExp(v7) = all_63_0 & vsubst(v2, v3, v4) = v7 & % 32.11/5.14 | | | | | | | visValue(v3) = 0 & vapp(v5, v3) = all_63_1 & vabs(v2, % 32.11/5.14 | | | | | | | v0, v4) = v5 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & % 32.11/5.14 | | | | | | | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : % 32.11/5.14 | | | | | | | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 32.11/5.14 | | | | | | | ? [v6: $i] : ? [v7: $i] : (vreduce(v0) = v4 & % 32.11/5.14 | | | | | | | vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & % 32.11/5.14 | | | | | | | vsomeExp(v7) = all_63_0 & vapp(v5, v6) = v7 & vapp(v5, % 32.11/5.14 | | | | | | | v0) = all_63_1 & vabs(v1, v2, v3) = v5 & $i(v7) & % 32.11/5.14 | | | | | | | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 32.11/5.14 | | | | | | | $i(v0)) % 32.11/5.14 | | | | | | | % 32.11/5.14 | | | | | | | BETA: splitting (337) gives: % 32.11/5.14 | | | | | | | % 32.11/5.14 | | | | | | | Case 1: % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | (338) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.11/5.14 | | | | | | | | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] % 32.11/5.14 | | | | | | | | : ( ~ (v6 = 0) & vreduce(v3) = v1 & visSomeExp(v1) = v6 % 32.11/5.14 | | | | | | | | & vsomeExp(v7) = all_63_0 & vsubst(v2, v3, v4) = v7 & % 32.11/5.14 | | | | | | | | visValue(v3) = 0 & vapp(v5, v3) = all_63_1 & vabs(v2, % 32.11/5.14 | | | | | | | | v0, v4) = v5 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & % 32.11/5.14 | | | | | | | | $i(v2) & $i(v1) & $i(v0)) % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | DELTA: instantiating (338) with fresh symbols all_111_0, % 32.11/5.14 | | | | | | | | all_111_1, all_111_2, all_111_3, all_111_4, all_111_5, % 32.11/5.14 | | | | | | | | all_111_6, all_111_7 gives: % 32.11/5.14 | | | | | | | | (339) ~ (all_111_1 = 0) & vreduce(all_111_4) = all_111_6 & % 32.11/5.14 | | | | | | | | visSomeExp(all_111_6) = all_111_1 & vsomeExp(all_111_0) % 32.11/5.14 | | | | | | | | = all_63_0 & vsubst(all_111_5, all_111_4, all_111_3) = % 32.11/5.14 | | | | | | | | all_111_0 & visValue(all_111_4) = 0 & vapp(all_111_2, % 32.11/5.14 | | | | | | | | all_111_4) = all_63_1 & vabs(all_111_5, all_111_7, % 32.11/5.14 | | | | | | | | all_111_3) = all_111_2 & $i(all_111_0) & % 32.11/5.14 | | | | | | | | $i(all_111_2) & $i(all_111_3) & $i(all_111_4) & % 32.11/5.14 | | | | | | | | $i(all_111_5) & $i(all_111_6) & $i(all_111_7) % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | ALPHA: (339) implies: % 32.11/5.14 | | | | | | | | (340) $i(all_111_7) % 32.11/5.14 | | | | | | | | (341) $i(all_111_5) % 32.11/5.14 | | | | | | | | (342) $i(all_111_4) % 32.11/5.14 | | | | | | | | (343) $i(all_111_3) % 32.11/5.14 | | | | | | | | (344) $i(all_111_2) % 32.11/5.14 | | | | | | | | (345) vabs(all_111_5, all_111_7, all_111_3) = all_111_2 % 32.11/5.14 | | | | | | | | (346) vapp(all_111_2, all_111_4) = all_63_1 % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | GROUND_INST: instantiating (EQ-app) with ve1, ve2, all_111_2, % 32.11/5.14 | | | | | | | | all_111_4, all_63_1, simplifying with (8), (9), % 32.11/5.14 | | | | | | | | (25), (342), (344), (346) gives: % 32.11/5.14 | | | | | | | | (347) all_111_2 = ve1 & all_111_4 = ve2 % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | ALPHA: (347) implies: % 32.11/5.14 | | | | | | | | (348) all_111_2 = ve1 % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | REDUCE: (345), (348) imply: % 32.11/5.14 | | | | | | | | (349) vabs(all_111_5, all_111_7, all_111_3) = ve1 % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | GROUND_INST: instantiating (DIFF-abs-app) with all_111_5, % 32.11/5.14 | | | | | | | | all_111_7, all_111_3, all_87_3, all_87_2, ve1, % 32.11/5.14 | | | | | | | | simplifying with (330), (331), (333), (340), (341), % 32.11/5.14 | | | | | | | | (343), (349) gives: % 32.11/5.14 | | | | | | | | (350) $false % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | CLOSE: (350) is inconsistent. % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | Case 2: % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | (351) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.11/5.14 | | | | | | | | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 32.11/5.14 | | | | | | | | (vreduce(v0) = v4 & vgetSomeExp(v4) = v6 & % 32.11/5.14 | | | | | | | | visSomeExp(v4) = 0 & vsomeExp(v7) = all_63_0 & % 32.11/5.14 | | | | | | | | vapp(v5, v6) = v7 & vapp(v5, v0) = all_63_1 & % 32.11/5.14 | | | | | | | | vabs(v1, v2, v3) = v5 & $i(v7) & $i(v6) & $i(v5) & % 32.11/5.14 | | | | | | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | DELTA: instantiating (351) with fresh symbols all_103_0, % 32.11/5.14 | | | | | | | | all_103_1, all_103_2, all_103_3, all_103_4, all_103_5, % 32.11/5.14 | | | | | | | | all_103_6, all_103_7 gives: % 32.11/5.14 | | | | | | | | (352) vreduce(all_103_7) = all_103_3 & vgetSomeExp(all_103_3) % 32.11/5.14 | | | | | | | | = all_103_1 & visSomeExp(all_103_3) = 0 & % 32.11/5.14 | | | | | | | | vsomeExp(all_103_0) = all_63_0 & vapp(all_103_2, % 32.11/5.14 | | | | | | | | all_103_1) = all_103_0 & vapp(all_103_2, all_103_7) = % 32.11/5.14 | | | | | | | | all_63_1 & vabs(all_103_6, all_103_5, all_103_4) = % 32.11/5.14 | | | | | | | | all_103_2 & $i(all_103_0) & $i(all_103_1) & % 32.11/5.14 | | | | | | | | $i(all_103_2) & $i(all_103_3) & $i(all_103_4) & % 32.11/5.14 | | | | | | | | $i(all_103_5) & $i(all_103_6) & $i(all_103_7) % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | ALPHA: (352) implies: % 32.11/5.14 | | | | | | | | (353) $i(all_103_7) % 32.11/5.14 | | | | | | | | (354) $i(all_103_6) % 32.11/5.14 | | | | | | | | (355) $i(all_103_5) % 32.11/5.14 | | | | | | | | (356) $i(all_103_4) % 32.11/5.14 | | | | | | | | (357) $i(all_103_2) % 32.11/5.14 | | | | | | | | (358) vabs(all_103_6, all_103_5, all_103_4) = all_103_2 % 32.11/5.14 | | | | | | | | (359) vapp(all_103_2, all_103_7) = all_63_1 % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | GROUND_INST: instantiating (EQ-app) with ve1, ve2, all_103_2, % 32.11/5.14 | | | | | | | | all_103_7, all_63_1, simplifying with (8), (9), % 32.11/5.14 | | | | | | | | (25), (353), (357), (359) gives: % 32.11/5.14 | | | | | | | | (360) all_103_2 = ve1 & all_103_7 = ve2 % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | ALPHA: (360) implies: % 32.11/5.14 | | | | | | | | (361) all_103_2 = ve1 % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | REDUCE: (358), (361) imply: % 32.11/5.14 | | | | | | | | (362) vabs(all_103_6, all_103_5, all_103_4) = ve1 % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | GROUND_INST: instantiating (DIFF-abs-app) with all_103_6, % 32.11/5.14 | | | | | | | | all_103_5, all_103_4, all_87_3, all_87_2, ve1, % 32.11/5.14 | | | | | | | | simplifying with (330), (331), (333), (354), (355), % 32.11/5.14 | | | | | | | | (356), (362) gives: % 32.11/5.14 | | | | | | | | (363) $false % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | CLOSE: (363) is inconsistent. % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | End of split % 32.11/5.14 | | | | | | | % 32.11/5.14 | | | | | | End of split % 32.11/5.14 | | | | | | % 32.11/5.14 | | | | | Case 2: % 32.11/5.14 | | | | | | % 32.11/5.14 | | | | | | (364) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 32.11/5.14 | | | | | | [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & % 32.11/5.14 | | | | | | visSomeExp(v1) = 0 & vsomeExp(v4) = all_63_0 & vapp(v3, % 32.11/5.14 | | | | | | v2) = v4 & vapp(v0, v2) = all_63_1 & $i(v4) & $i(v3) & % 32.11/5.14 | | | | | | $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! % 32.11/5.14 | | | | | | [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ $i(v7) | ~ % 32.11/5.14 | | | | | | $i(v6) | ~ $i(v5))) | ? [v0: $i] : ? [v1: $i] : ? % 32.11/5.14 | | | | | | [v2: $i] : ? [v3: int] : (all_63_0 = vnoExp & ~ (v3 = 0) % 32.11/5.14 | | | | | | & vreduce(v1) = v2 & visSomeExp(v2) = v3 & vapp(v1, v0) = % 32.11/5.14 | | | | | | all_63_1 & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! % 32.11/5.14 | | | | | | [v5: $i] : ! [v6: $i] : ( ~ (vabs(v4, v5, v6) = v1) | ~ % 32.11/5.14 | | | | | | $i(v6) | ~ $i(v5) | ~ $i(v4))) | ? [v0: $i] : ? % 32.11/5.14 | | | | | | [v1: $i] : ? [v2: $i] : (all_63_0 = vnoExp & vabs(v0, v1, % 32.11/5.14 | | | | | | v2) = all_63_1 & $i(v2) & $i(v1) & $i(v0)) | ? [v0: % 32.11/5.14 | | | | | | $i] : (all_63_0 = vnoExp & vvar(v0) = all_63_1 & $i(v0)) % 32.11/5.14 | | | | | | % 32.11/5.14 | | | | | | BETA: splitting (364) gives: % 32.11/5.14 | | | | | | % 32.11/5.14 | | | | | | Case 1: % 32.11/5.14 | | | | | | | % 32.11/5.14 | | | | | | | (365) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.11/5.14 | | | | | | | ? [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & % 32.11/5.14 | | | | | | | visSomeExp(v1) = 0 & vsomeExp(v4) = all_63_0 & vapp(v3, % 32.11/5.14 | | | | | | | v2) = v4 & vapp(v0, v2) = all_63_1 & $i(v4) & $i(v3) % 32.11/5.14 | | | | | | | & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] % 32.11/5.14 | | | | | | | : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ $i(v7) % 32.11/5.14 | | | | | | | | ~ $i(v6) | ~ $i(v5))) | ? [v0: $i] : ? [v1: $i] % 32.11/5.14 | | | | | | | : ? [v2: $i] : ? [v3: int] : (all_63_0 = vnoExp & ~ % 32.11/5.14 | | | | | | | (v3 = 0) & vreduce(v1) = v2 & visSomeExp(v2) = v3 & % 32.11/5.14 | | | | | | | vapp(v1, v0) = all_63_1 & $i(v2) & $i(v1) & $i(v0) & ! % 32.11/5.14 | | | | | | | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (vabs(v4, % 32.11/5.14 | | | | | | | v5, v6) = v1) | ~ $i(v6) | ~ $i(v5) | ~ % 32.11/5.14 | | | | | | | $i(v4))) % 32.11/5.14 | | | | | | | % 32.11/5.14 | | | | | | | BETA: splitting (365) gives: % 32.11/5.14 | | | | | | | % 32.11/5.14 | | | | | | | Case 1: % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | (366) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.11/5.14 | | | | | | | | ? [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 % 32.11/5.14 | | | | | | | | & visSomeExp(v1) = 0 & vsomeExp(v4) = all_63_0 & % 32.11/5.14 | | | | | | | | vapp(v3, v2) = v4 & vapp(v0, v2) = all_63_1 & $i(v4) % 32.11/5.14 | | | | | | | | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : % 32.11/5.14 | | | | | | | | ! [v6: $i] : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = % 32.11/5.14 | | | | | | | | v0) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5))) % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | DELTA: instantiating (366) with fresh symbols all_111_0, % 32.11/5.14 | | | | | | | | all_111_1, all_111_2, all_111_3, all_111_4 gives: % 32.11/5.14 | | | | | | | | (367) vreduce(all_111_4) = all_111_3 & vgetSomeExp(all_111_3) % 32.11/5.14 | | | | | | | | = all_111_1 & visSomeExp(all_111_3) = 0 & % 32.11/5.14 | | | | | | | | vsomeExp(all_111_0) = all_63_0 & vapp(all_111_1, % 32.11/5.14 | | | | | | | | all_111_2) = all_111_0 & vapp(all_111_4, all_111_2) = % 32.11/5.14 | | | | | | | | all_63_1 & $i(all_111_0) & $i(all_111_1) & % 32.11/5.14 | | | | | | | | $i(all_111_2) & $i(all_111_3) & $i(all_111_4) & ! [v0: % 32.11/5.14 | | | | | | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vabs(v0, v1, % 32.11/5.14 | | | | | | | | v2) = all_111_4) | ~ $i(v2) | ~ $i(v1) | ~ % 32.11/5.14 | | | | | | | | $i(v0)) % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | REF_CLOSE: (2), (8), (9), (12), (13), (16), (17), (25), (29), % 32.11/5.14 | | | | | | | | (30), (31), (32), (34), (35), (37), (52), (53), (57), % 32.11/5.14 | | | | | | | | (63), (64), (367), (EQ-app), (EQ-someExp), (T-app), % 32.11/5.14 | | | | | | | | (getSomeExp0) are inconsistent by sub-proof #6. % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | Case 2: % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | (368) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] % 32.11/5.14 | | | | | | | | : (all_63_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) = v2 & % 32.11/5.14 | | | | | | | | visSomeExp(v2) = v3 & vapp(v1, v0) = all_63_1 & % 32.11/5.14 | | | | | | | | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] % 32.11/5.14 | | | | | | | | : ! [v6: $i] : ( ~ (vabs(v4, v5, v6) = v1) | ~ % 32.11/5.14 | | | | | | | | $i(v6) | ~ $i(v5) | ~ $i(v4))) % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | DELTA: instantiating (368) with fresh symbols all_111_0, % 32.11/5.14 | | | | | | | | all_111_1, all_111_2, all_111_3 gives: % 32.11/5.14 | | | | | | | | (369) all_63_0 = vnoExp & ~ (all_111_0 = 0) & % 32.11/5.14 | | | | | | | | vreduce(all_111_2) = all_111_1 & visSomeExp(all_111_1) % 32.11/5.14 | | | | | | | | = all_111_0 & vapp(all_111_2, all_111_3) = all_63_1 & % 32.11/5.14 | | | | | | | | $i(all_111_1) & $i(all_111_2) & $i(all_111_3) & ! [v0: % 32.11/5.14 | | | | | | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vabs(v0, v1, % 32.11/5.14 | | | | | | | | v2) = all_111_2) | ~ $i(v2) | ~ $i(v1) | ~ % 32.11/5.14 | | | | | | | | $i(v0)) % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | REF_CLOSE: (1), (31), (35), (369) are inconsistent by sub-proof % 32.11/5.14 | | | | | | | | #5. % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | End of split % 32.11/5.14 | | | | | | | % 32.11/5.14 | | | | | | Case 2: % 32.11/5.14 | | | | | | | % 32.11/5.14 | | | | | | | (370) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_63_0 = % 32.11/5.14 | | | | | | | vnoExp & vabs(v0, v1, v2) = all_63_1 & $i(v2) & $i(v1) % 32.11/5.14 | | | | | | | & $i(v0)) | ? [v0: $i] : (all_63_0 = vnoExp & vvar(v0) % 32.11/5.14 | | | | | | | = all_63_1 & $i(v0)) % 32.11/5.14 | | | | | | | % 32.11/5.14 | | | | | | | BETA: splitting (370) gives: % 32.11/5.14 | | | | | | | % 32.11/5.14 | | | | | | | Case 1: % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | (371) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_63_0 = % 32.11/5.14 | | | | | | | | vnoExp & vabs(v0, v1, v2) = all_63_1 & $i(v2) & % 32.11/5.14 | | | | | | | | $i(v1) & $i(v0)) % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | DELTA: instantiating (371) with fresh symbols all_111_0, % 32.11/5.14 | | | | | | | | all_111_1, all_111_2 gives: % 32.11/5.14 | | | | | | | | (372) all_63_0 = vnoExp & vabs(all_111_2, all_111_1, % 32.11/5.14 | | | | | | | | all_111_0) = all_63_1 & $i(all_111_0) & $i(all_111_1) % 32.11/5.14 | | | | | | | | & $i(all_111_2) % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | REF_CLOSE: (1), (31), (35), (372) are inconsistent by sub-proof % 32.11/5.14 | | | | | | | | #4. % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | Case 2: % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | (373) ? [v0: $i] : (all_63_0 = vnoExp & vvar(v0) = all_63_1 % 32.11/5.14 | | | | | | | | & $i(v0)) % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | DELTA: instantiating (373) with fresh symbol all_111_0 gives: % 32.11/5.14 | | | | | | | | (374) all_63_0 = vnoExp & vvar(all_111_0) = all_63_1 & % 32.11/5.14 | | | | | | | | $i(all_111_0) % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | | REF_CLOSE: (1), (31), (35), (374) are inconsistent by sub-proof % 32.11/5.14 | | | | | | | | #3. % 32.11/5.14 | | | | | | | | % 32.11/5.14 | | | | | | | End of split % 32.11/5.14 | | | | | | | % 32.11/5.15 | | | | | | End of split % 32.11/5.15 | | | | | | % 32.11/5.15 | | | | | End of split % 32.11/5.15 | | | | | % 32.11/5.15 | | | | Case 2: % 32.11/5.15 | | | | | % 32.11/5.15 | | | | | (375) ? [v0: $i] : (vsomeType(all_73_0) = v0 & $i(v0) & ? [v1: % 32.11/5.15 | | | | | $i] : (vlookup(v1, all_65_3) = v0 & vvar(v1) = all_73_3 & % 32.11/5.15 | | | | | $i(v1))) % 32.11/5.15 | | | | | % 32.11/5.15 | | | | | DELTA: instantiating (375) with fresh symbol all_87_0 gives: % 32.11/5.15 | | | | | (376) vsomeType(all_73_0) = all_87_0 & $i(all_87_0) & ? [v0: $i] : % 32.11/5.15 | | | | | (vlookup(v0, all_65_3) = all_87_0 & vvar(v0) = all_73_3 & % 32.11/5.15 | | | | | $i(v0)) % 32.11/5.15 | | | | | % 32.11/5.15 | | | | | ALPHA: (376) implies: % 32.11/5.15 | | | | | (377) ? [v0: $i] : (vlookup(v0, all_65_3) = all_87_0 & vvar(v0) = % 32.11/5.15 | | | | | all_73_3 & $i(v0)) % 32.11/5.15 | | | | | % 32.11/5.15 | | | | | DELTA: instantiating (377) with fresh symbol all_89_0 gives: % 32.11/5.15 | | | | | (378) vlookup(all_89_0, all_65_3) = all_87_0 & vvar(all_89_0) = % 32.11/5.15 | | | | | all_73_3 & $i(all_89_0) % 32.11/5.15 | | | | | % 32.11/5.15 | | | | | ALPHA: (378) implies: % 32.11/5.15 | | | | | (379) $i(all_89_0) % 32.11/5.15 | | | | | (380) vvar(all_89_0) = all_73_3 % 32.11/5.15 | | | | | % 32.11/5.15 | | | | | REDUCE: (59), (380) imply: % 32.11/5.15 | | | | | (381) vvar(all_89_0) = ve1 % 32.11/5.15 | | | | | % 32.11/5.15 | | | | | BETA: splitting (62) gives: % 32.11/5.15 | | | | | % 32.11/5.15 | | | | | Case 1: % 32.11/5.15 | | | | | | % 32.11/5.15 | | | | | | (382) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 32.11/5.15 | | | | | | [v4: $i] : (varrow(v2, v3) = all_73_1 & vtcheck(v4, v1, v3) % 32.11/5.15 | | | | | | = 0 & vbind(v0, v2, all_65_3) = v4 & vabs(v0, v2, v1) = % 32.11/5.15 | | | | | | all_73_2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.11/5.15 | | | | | | % 32.11/5.15 | | | | | | DELTA: instantiating (382) with fresh symbols all_103_0, all_103_1, % 32.11/5.15 | | | | | | all_103_2, all_103_3, all_103_4 gives: % 32.11/5.15 | | | | | | (383) varrow(all_103_2, all_103_1) = all_73_1 & % 32.11/5.15 | | | | | | vtcheck(all_103_0, all_103_3, all_103_1) = 0 & % 32.11/5.15 | | | | | | vbind(all_103_4, all_103_2, all_65_3) = all_103_0 & % 32.11/5.15 | | | | | | vabs(all_103_4, all_103_2, all_103_3) = all_73_2 & % 32.11/5.15 | | | | | | $i(all_103_0) & $i(all_103_1) & $i(all_103_2) & % 32.11/5.15 | | | | | | $i(all_103_3) & $i(all_103_4) % 32.11/5.15 | | | | | | % 32.11/5.15 | | | | | | ALPHA: (383) implies: % 32.11/5.15 | | | | | | (384) $i(all_103_4) % 32.11/5.15 | | | | | | (385) $i(all_103_3) % 32.11/5.15 | | | | | | (386) $i(all_103_2) % 32.11/5.15 | | | | | | (387) vabs(all_103_4, all_103_2, all_103_3) = all_73_2 % 32.11/5.15 | | | | | | % 32.11/5.15 | | | | | | REDUCE: (60), (387) imply: % 32.11/5.15 | | | | | | (388) vabs(all_103_4, all_103_2, all_103_3) = ve2 % 32.11/5.15 | | | | | | % 32.11/5.15 | | | | | | GROUND_INST: instantiating (4) with all_103_4, all_103_2, all_103_3, % 32.11/5.15 | | | | | | ve2, all_60_0, simplifying with (9), (19), (20), (384), % 32.11/5.15 | | | | | | (385), (386), (388) gives: % 32.11/5.15 | | | | | | (389) all_60_0 = vnoExp % 32.11/5.15 | | | | | | % 32.11/5.15 | | | | | | REDUCE: (20), (389) imply: % 32.11/5.15 | | | | | | (390) vreduce(ve2) = vnoExp % 32.11/5.15 | | | | | | % 32.11/5.15 | | | | | | BETA: splitting (39) gives: % 32.11/5.15 | | | | | | % 32.11/5.15 | | | | | | Case 1: % 32.11/5.15 | | | | | | | % 32.11/5.15 | | | | | | | (391) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.11/5.15 | | | | | | | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : % 32.11/5.15 | | | | | | | (all_63_0 = vnoExp & ~ (v7 = 0) & ~ (v6 = 0) & % 32.11/5.15 | | | | | | | vreduce(v4) = v3 & visSomeExp(v3) = v6 & visValue(v4) = % 32.11/5.15 | | | | | | | v7 & vapp(v5, v4) = all_63_1 & vabs(v0, v1, v2) = v5 & % 32.11/5.15 | | | | | | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | % 32.11/5.15 | | | | | | | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 32.11/5.15 | | | | | | | [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ( ~ % 32.11/5.15 | | | | | | | (v6 = 0) & vreduce(v3) = v1 & visSomeExp(v1) = v6 & % 32.11/5.15 | | | | | | | vsomeExp(v7) = all_63_0 & vsubst(v2, v3, v4) = v7 & % 32.11/5.15 | | | | | | | visValue(v3) = 0 & vapp(v5, v3) = all_63_1 & vabs(v2, % 32.11/5.15 | | | | | | | v0, v4) = v5 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & % 32.11/5.15 | | | | | | | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : % 32.11/5.15 | | | | | | | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 32.11/5.15 | | | | | | | ? [v6: $i] : ? [v7: $i] : (vreduce(v0) = v4 & % 32.11/5.15 | | | | | | | vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & % 32.11/5.15 | | | | | | | vsomeExp(v7) = all_63_0 & vapp(v5, v6) = v7 & vapp(v5, % 32.11/5.15 | | | | | | | v0) = all_63_1 & vabs(v1, v2, v3) = v5 & $i(v7) & % 32.11/5.15 | | | | | | | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 32.11/5.15 | | | | | | | $i(v0)) % 32.11/5.15 | | | | | | | % 32.11/5.15 | | | | | | | BETA: splitting (391) gives: % 32.11/5.15 | | | | | | | % 32.11/5.15 | | | | | | | Case 1: % 32.11/5.15 | | | | | | | | % 32.34/5.15 | | | | | | | | (392) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.34/5.15 | | | | | | | | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] % 32.34/5.15 | | | | | | | | : (all_63_0 = vnoExp & ~ (v7 = 0) & ~ (v6 = 0) & % 32.34/5.15 | | | | | | | | vreduce(v4) = v3 & visSomeExp(v3) = v6 & visValue(v4) % 32.34/5.15 | | | | | | | | = v7 & vapp(v5, v4) = all_63_1 & vabs(v0, v1, v2) = % 32.34/5.15 | | | | | | | | v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 32.34/5.15 | | | | | | | | $i(v0)) % 32.34/5.15 | | | | | | | | % 32.34/5.15 | | | | | | | | DELTA: instantiating (392) with fresh symbols all_111_0, % 32.34/5.15 | | | | | | | | all_111_1, all_111_2, all_111_3, all_111_4, all_111_5, % 32.34/5.15 | | | | | | | | all_111_6, all_111_7 gives: % 32.34/5.15 | | | | | | | | (393) all_63_0 = vnoExp & ~ (all_111_0 = 0) & ~ (all_111_1 % 32.34/5.15 | | | | | | | | = 0) & vreduce(all_111_3) = all_111_4 & % 32.34/5.15 | | | | | | | | visSomeExp(all_111_4) = all_111_1 & visValue(all_111_3) % 32.34/5.15 | | | | | | | | = all_111_0 & vapp(all_111_2, all_111_3) = all_63_1 & % 32.34/5.15 | | | | | | | | vabs(all_111_7, all_111_6, all_111_5) = all_111_2 & % 32.34/5.15 | | | | | | | | $i(all_111_2) & $i(all_111_3) & $i(all_111_4) & % 32.34/5.15 | | | | | | | | $i(all_111_5) & $i(all_111_6) & $i(all_111_7) % 32.34/5.15 | | | | | | | | % 32.34/5.15 | | | | | | | | REF_CLOSE: (1), (31), (35), (393) are inconsistent by sub-proof % 32.34/5.15 | | | | | | | | #9. % 32.34/5.15 | | | | | | | | % 32.34/5.15 | | | | | | | Case 2: % 32.34/5.15 | | | | | | | | % 32.34/5.15 | | | | | | | | (394) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.34/5.15 | | | | | | | | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] % 32.34/5.15 | | | | | | | | : ( ~ (v6 = 0) & vreduce(v3) = v1 & visSomeExp(v1) = v6 % 32.34/5.15 | | | | | | | | & vsomeExp(v7) = all_63_0 & vsubst(v2, v3, v4) = v7 & % 32.34/5.15 | | | | | | | | visValue(v3) = 0 & vapp(v5, v3) = all_63_1 & vabs(v2, % 32.34/5.15 | | | | | | | | v0, v4) = v5 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & % 32.34/5.15 | | | | | | | | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] % 32.34/5.15 | | | | | | | | : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] % 32.34/5.15 | | | | | | | | : ? [v6: $i] : ? [v7: $i] : (vreduce(v0) = v4 & % 32.34/5.15 | | | | | | | | vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & % 32.34/5.15 | | | | | | | | vsomeExp(v7) = all_63_0 & vapp(v5, v6) = v7 & % 32.34/5.15 | | | | | | | | vapp(v5, v0) = all_63_1 & vabs(v1, v2, v3) = v5 & % 32.34/5.15 | | | | | | | | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 32.34/5.15 | | | | | | | | $i(v1) & $i(v0)) % 32.34/5.15 | | | | | | | | % 32.34/5.15 | | | | | | | | BETA: splitting (394) gives: % 32.34/5.15 | | | | | | | | % 32.34/5.15 | | | | | | | | Case 1: % 32.34/5.15 | | | | | | | | | % 32.34/5.15 | | | | | | | | | (395) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 32.34/5.15 | | | | | | | | | : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: % 32.34/5.15 | | | | | | | | | $i] : ( ~ (v6 = 0) & vreduce(v3) = v1 & % 32.34/5.15 | | | | | | | | | visSomeExp(v1) = v6 & vsomeExp(v7) = all_63_0 & % 32.34/5.15 | | | | | | | | | vsubst(v2, v3, v4) = v7 & visValue(v3) = 0 & % 32.34/5.15 | | | | | | | | | vapp(v5, v3) = all_63_1 & vabs(v2, v0, v4) = v5 & % 32.34/5.15 | | | | | | | | | $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 32.34/5.15 | | | | | | | | | & $i(v0)) % 32.34/5.15 | | | | | | | | | % 32.34/5.15 | | | | | | | | | DELTA: instantiating (395) with fresh symbols all_119_0, % 32.34/5.15 | | | | | | | | | all_119_1, all_119_2, all_119_3, all_119_4, all_119_5, % 32.34/5.15 | | | | | | | | | all_119_6, all_119_7 gives: % 32.34/5.15 | | | | | | | | | (396) ~ (all_119_1 = 0) & vreduce(all_119_4) = all_119_6 & % 32.34/5.15 | | | | | | | | | visSomeExp(all_119_6) = all_119_1 & % 32.34/5.15 | | | | | | | | | vsomeExp(all_119_0) = all_63_0 & vsubst(all_119_5, % 32.34/5.15 | | | | | | | | | all_119_4, all_119_3) = all_119_0 & % 32.34/5.15 | | | | | | | | | visValue(all_119_4) = 0 & vapp(all_119_2, all_119_4) % 32.34/5.15 | | | | | | | | | = all_63_1 & vabs(all_119_5, all_119_7, all_119_3) = % 32.34/5.15 | | | | | | | | | all_119_2 & $i(all_119_0) & $i(all_119_2) & % 32.34/5.15 | | | | | | | | | $i(all_119_3) & $i(all_119_4) & $i(all_119_5) & % 32.34/5.15 | | | | | | | | | $i(all_119_6) & $i(all_119_7) % 32.34/5.15 | | | | | | | | | % 32.34/5.15 | | | | | | | | | ALPHA: (396) implies: % 32.34/5.15 | | | | | | | | | (397) $i(all_119_7) % 32.34/5.15 | | | | | | | | | (398) $i(all_119_5) % 32.34/5.15 | | | | | | | | | (399) $i(all_119_4) % 32.34/5.15 | | | | | | | | | (400) $i(all_119_3) % 32.34/5.15 | | | | | | | | | (401) $i(all_119_2) % 32.34/5.15 | | | | | | | | | (402) vabs(all_119_5, all_119_7, all_119_3) = all_119_2 % 32.34/5.15 | | | | | | | | | (403) vapp(all_119_2, all_119_4) = all_63_1 % 32.34/5.15 | | | | | | | | | % 32.34/5.15 | | | | | | | | | GROUND_INST: instantiating (EQ-app) with ve1, ve2, all_119_2, % 32.34/5.15 | | | | | | | | | all_119_4, all_63_1, simplifying with (8), (9), % 32.34/5.15 | | | | | | | | | (25), (399), (401), (403) gives: % 32.34/5.15 | | | | | | | | | (404) all_119_2 = ve1 & all_119_4 = ve2 % 32.34/5.15 | | | | | | | | | % 32.34/5.15 | | | | | | | | | ALPHA: (404) implies: % 32.34/5.15 | | | | | | | | | (405) all_119_2 = ve1 % 32.34/5.15 | | | | | | | | | % 32.34/5.15 | | | | | | | | | REDUCE: (402), (405) imply: % 32.34/5.15 | | | | | | | | | (406) vabs(all_119_5, all_119_7, all_119_3) = ve1 % 32.34/5.15 | | | | | | | | | % 32.34/5.15 | | | | | | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_89_0, % 32.34/5.15 | | | | | | | | | all_119_5, all_119_7, all_119_3, ve1, simplifying % 32.34/5.15 | | | | | | | | | with (379), (381), (397), (398), (400), (406) % 32.34/5.15 | | | | | | | | | gives: % 32.34/5.15 | | | | | | | | | (407) $false % 32.34/5.15 | | | | | | | | | % 32.34/5.15 | | | | | | | | | CLOSE: (407) is inconsistent. % 32.34/5.15 | | | | | | | | | % 32.34/5.15 | | | | | | | | Case 2: % 32.34/5.15 | | | | | | | | | % 32.34/5.15 | | | | | | | | | (408) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 32.34/5.15 | | | | | | | | | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 32.34/5.15 | | | | | | | | | $i] : (vreduce(v0) = v4 & vgetSomeExp(v4) = v6 & % 32.34/5.15 | | | | | | | | | visSomeExp(v4) = 0 & vsomeExp(v7) = all_63_0 & % 32.34/5.15 | | | | | | | | | vapp(v5, v6) = v7 & vapp(v5, v0) = all_63_1 & % 32.34/5.15 | | | | | | | | | vabs(v1, v2, v3) = v5 & $i(v7) & $i(v6) & $i(v5) & % 32.34/5.15 | | | | | | | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.34/5.15 | | | | | | | | | % 32.34/5.15 | | | | | | | | | DELTA: instantiating (408) with fresh symbols all_111_0, % 32.34/5.15 | | | | | | | | | all_111_1, all_111_2, all_111_3, all_111_4, all_111_5, % 32.34/5.15 | | | | | | | | | all_111_6, all_111_7 gives: % 32.34/5.15 | | | | | | | | | (409) vreduce(all_111_7) = all_111_3 & % 32.34/5.15 | | | | | | | | | vgetSomeExp(all_111_3) = all_111_1 & % 32.34/5.15 | | | | | | | | | visSomeExp(all_111_3) = 0 & vsomeExp(all_111_0) = % 32.34/5.15 | | | | | | | | | all_63_0 & vapp(all_111_2, all_111_1) = all_111_0 & % 32.34/5.15 | | | | | | | | | vapp(all_111_2, all_111_7) = all_63_1 & % 32.34/5.15 | | | | | | | | | vabs(all_111_6, all_111_5, all_111_4) = all_111_2 & % 32.34/5.15 | | | | | | | | | $i(all_111_0) & $i(all_111_1) & $i(all_111_2) & % 32.34/5.15 | | | | | | | | | $i(all_111_3) & $i(all_111_4) & $i(all_111_5) & % 32.34/5.15 | | | | | | | | | $i(all_111_6) & $i(all_111_7) % 32.34/5.15 | | | | | | | | | % 32.34/5.15 | | | | | | | | | REF_CLOSE: (2), (8), (9), (12), (25), (390), (409), (EQ-app) % 32.34/5.15 | | | | | | | | | are inconsistent by sub-proof #7. % 32.34/5.15 | | | | | | | | | % 32.34/5.15 | | | | | | | | End of split % 32.34/5.15 | | | | | | | | % 32.34/5.15 | | | | | | | End of split % 32.34/5.15 | | | | | | | % 32.34/5.15 | | | | | | Case 2: % 32.34/5.15 | | | | | | | % 32.34/5.15 | | | | | | | (410) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.34/5.15 | | | | | | | ? [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & % 32.34/5.15 | | | | | | | visSomeExp(v1) = 0 & vsomeExp(v4) = all_63_0 & vapp(v3, % 32.34/5.15 | | | | | | | v2) = v4 & vapp(v0, v2) = all_63_1 & $i(v4) & $i(v3) % 32.34/5.15 | | | | | | | & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] % 32.34/5.15 | | | | | | | : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ $i(v7) % 32.34/5.15 | | | | | | | | ~ $i(v6) | ~ $i(v5))) | ? [v0: $i] : ? [v1: $i] % 32.34/5.15 | | | | | | | : ? [v2: $i] : ? [v3: int] : (all_63_0 = vnoExp & ~ % 32.34/5.15 | | | | | | | (v3 = 0) & vreduce(v1) = v2 & visSomeExp(v2) = v3 & % 32.34/5.15 | | | | | | | vapp(v1, v0) = all_63_1 & $i(v2) & $i(v1) & $i(v0) & ! % 32.34/5.15 | | | | | | | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (vabs(v4, % 32.34/5.15 | | | | | | | v5, v6) = v1) | ~ $i(v6) | ~ $i(v5) | ~ % 32.34/5.15 | | | | | | | $i(v4))) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 32.34/5.15 | | | | | | | (all_63_0 = vnoExp & vabs(v0, v1, v2) = all_63_1 & $i(v2) % 32.34/5.15 | | | | | | | & $i(v1) & $i(v0)) | ? [v0: $i] : (all_63_0 = vnoExp & % 32.34/5.15 | | | | | | | vvar(v0) = all_63_1 & $i(v0)) % 32.34/5.15 | | | | | | | % 32.34/5.15 | | | | | | | BETA: splitting (410) gives: % 32.34/5.15 | | | | | | | % 32.34/5.15 | | | | | | | Case 1: % 32.34/5.15 | | | | | | | | % 32.34/5.16 | | | | | | | | (411) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.34/5.16 | | | | | | | | ? [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 % 32.34/5.16 | | | | | | | | & visSomeExp(v1) = 0 & vsomeExp(v4) = all_63_0 & % 32.34/5.16 | | | | | | | | vapp(v3, v2) = v4 & vapp(v0, v2) = all_63_1 & $i(v4) % 32.34/5.16 | | | | | | | | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : % 32.34/5.16 | | | | | | | | ! [v6: $i] : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = % 32.34/5.16 | | | | | | | | v0) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5))) | ? % 32.34/5.16 | | | | | | | | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : % 32.34/5.16 | | | | | | | | (all_63_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) = v2 & % 32.34/5.16 | | | | | | | | visSomeExp(v2) = v3 & vapp(v1, v0) = all_63_1 & % 32.34/5.16 | | | | | | | | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] % 32.34/5.16 | | | | | | | | : ! [v6: $i] : ( ~ (vabs(v4, v5, v6) = v1) | ~ % 32.34/5.16 | | | | | | | | $i(v6) | ~ $i(v5) | ~ $i(v4))) % 32.34/5.16 | | | | | | | | % 32.34/5.16 | | | | | | | | BETA: splitting (411) gives: % 32.34/5.16 | | | | | | | | % 32.34/5.16 | | | | | | | | Case 1: % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | (412) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 32.34/5.16 | | | | | | | | | : ? [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = % 32.34/5.16 | | | | | | | | | v3 & visSomeExp(v1) = 0 & vsomeExp(v4) = all_63_0 & % 32.34/5.16 | | | | | | | | | vapp(v3, v2) = v4 & vapp(v0, v2) = all_63_1 & % 32.34/5.16 | | | | | | | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! % 32.34/5.16 | | | | | | | | | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 32.34/5.16 | | | | | | | | | (vabs(v5, v6, v7) = v0) | ~ $i(v7) | ~ $i(v6) | % 32.34/5.16 | | | | | | | | | ~ $i(v5))) % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | DELTA: instantiating (412) with fresh symbols all_111_0, % 32.34/5.16 | | | | | | | | | all_111_1, all_111_2, all_111_3, all_111_4 gives: % 32.34/5.16 | | | | | | | | | (413) vreduce(all_111_4) = all_111_3 & % 32.34/5.16 | | | | | | | | | vgetSomeExp(all_111_3) = all_111_1 & % 32.34/5.16 | | | | | | | | | visSomeExp(all_111_3) = 0 & vsomeExp(all_111_0) = % 32.34/5.16 | | | | | | | | | all_63_0 & vapp(all_111_1, all_111_2) = all_111_0 & % 32.34/5.16 | | | | | | | | | vapp(all_111_4, all_111_2) = all_63_1 & $i(all_111_0) % 32.34/5.16 | | | | | | | | | & $i(all_111_1) & $i(all_111_2) & $i(all_111_3) & % 32.34/5.16 | | | | | | | | | $i(all_111_4) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 32.34/5.16 | | | | | | | | | $i] : ( ~ (vabs(v0, v1, v2) = all_111_4) | ~ % 32.34/5.16 | | | | | | | | | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | REF_CLOSE: (2), (8), (9), (12), (13), (16), (17), (25), (29), % 32.34/5.16 | | | | | | | | | (30), (31), (32), (34), (35), (37), (52), (53), % 32.34/5.16 | | | | | | | | | (57), (63), (64), (413), (EQ-app), (EQ-someExp), % 32.34/5.16 | | | | | | | | | (T-app), (getSomeExp0) are inconsistent by % 32.34/5.16 | | | | | | | | | sub-proof #6. % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | Case 2: % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | (414) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.34/5.16 | | | | | | | | | int] : (all_63_0 = vnoExp & ~ (v3 = 0) & % 32.34/5.16 | | | | | | | | | vreduce(v1) = v2 & visSomeExp(v2) = v3 & vapp(v1, % 32.34/5.16 | | | | | | | | | v0) = all_63_1 & $i(v2) & $i(v1) & $i(v0) & ! % 32.34/5.16 | | | | | | | | | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 32.34/5.16 | | | | | | | | | (vabs(v4, v5, v6) = v1) | ~ $i(v6) | ~ $i(v5) | % 32.34/5.16 | | | | | | | | | ~ $i(v4))) % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | DELTA: instantiating (414) with fresh symbols all_111_0, % 32.34/5.16 | | | | | | | | | all_111_1, all_111_2, all_111_3 gives: % 32.34/5.16 | | | | | | | | | (415) all_63_0 = vnoExp & ~ (all_111_0 = 0) & % 32.34/5.16 | | | | | | | | | vreduce(all_111_2) = all_111_1 & % 32.34/5.16 | | | | | | | | | visSomeExp(all_111_1) = all_111_0 & vapp(all_111_2, % 32.34/5.16 | | | | | | | | | all_111_3) = all_63_1 & $i(all_111_1) & % 32.34/5.16 | | | | | | | | | $i(all_111_2) & $i(all_111_3) & ! [v0: $i] : ! [v1: % 32.34/5.16 | | | | | | | | | $i] : ! [v2: $i] : ( ~ (vabs(v0, v1, v2) = % 32.34/5.16 | | | | | | | | | all_111_2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | REF_CLOSE: (1), (31), (35), (415) are inconsistent by % 32.34/5.16 | | | | | | | | | sub-proof #5. % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | End of split % 32.34/5.16 | | | | | | | | % 32.34/5.16 | | | | | | | Case 2: % 32.34/5.16 | | | | | | | | % 32.34/5.16 | | | | | | | | (416) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_63_0 = % 32.34/5.16 | | | | | | | | vnoExp & vabs(v0, v1, v2) = all_63_1 & $i(v2) & % 32.34/5.16 | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (all_63_0 = vnoExp & % 32.34/5.16 | | | | | | | | vvar(v0) = all_63_1 & $i(v0)) % 32.34/5.16 | | | | | | | | % 32.34/5.16 | | | | | | | | BETA: splitting (416) gives: % 32.34/5.16 | | | | | | | | % 32.34/5.16 | | | | | | | | Case 1: % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | (417) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_63_0 = % 32.34/5.16 | | | | | | | | | vnoExp & vabs(v0, v1, v2) = all_63_1 & $i(v2) & % 32.34/5.16 | | | | | | | | | $i(v1) & $i(v0)) % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | DELTA: instantiating (417) with fresh symbols all_111_0, % 32.34/5.16 | | | | | | | | | all_111_1, all_111_2 gives: % 32.34/5.16 | | | | | | | | | (418) all_63_0 = vnoExp & vabs(all_111_2, all_111_1, % 32.34/5.16 | | | | | | | | | all_111_0) = all_63_1 & $i(all_111_0) & % 32.34/5.16 | | | | | | | | | $i(all_111_1) & $i(all_111_2) % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | REF_CLOSE: (1), (31), (35), (418) are inconsistent by % 32.34/5.16 | | | | | | | | | sub-proof #4. % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | Case 2: % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | (419) ? [v0: $i] : (all_63_0 = vnoExp & vvar(v0) = % 32.34/5.16 | | | | | | | | | all_63_1 & $i(v0)) % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | DELTA: instantiating (419) with fresh symbol all_111_0 gives: % 32.34/5.16 | | | | | | | | | (420) all_63_0 = vnoExp & vvar(all_111_0) = all_63_1 & % 32.34/5.16 | | | | | | | | | $i(all_111_0) % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | REF_CLOSE: (1), (31), (35), (420) are inconsistent by % 32.34/5.16 | | | | | | | | | sub-proof #3. % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | End of split % 32.34/5.16 | | | | | | | | % 32.34/5.16 | | | | | | | End of split % 32.34/5.16 | | | | | | | % 32.34/5.16 | | | | | | End of split % 32.34/5.16 | | | | | | % 32.34/5.16 | | | | | Case 2: % 32.34/5.16 | | | | | | % 32.34/5.16 | | | | | | (421) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.34/5.16 | | | | | | (varrow(v2, all_73_1) = v3 & vtcheck(all_65_3, v1, v2) = 0 % 32.34/5.16 | | | | | | & vtcheck(all_65_3, v0, v3) = 0 & vapp(v0, v1) = all_73_2 % 32.34/5.16 | | | | | | & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 32.34/5.16 | | | | | | (vsomeType(all_73_1) = v0 & $i(v0) & ? [v1: $i] : % 32.34/5.16 | | | | | | (vlookup(v1, all_65_3) = v0 & vvar(v1) = all_73_2 & % 32.34/5.16 | | | | | | $i(v1))) % 32.34/5.16 | | | | | | % 32.34/5.16 | | | | | | BETA: splitting (421) gives: % 32.34/5.16 | | | | | | % 32.34/5.16 | | | | | | Case 1: % 32.34/5.16 | | | | | | | % 32.34/5.16 | | | | | | | (422) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.34/5.16 | | | | | | | (varrow(v2, all_73_1) = v3 & vtcheck(all_65_3, v1, v2) = % 32.34/5.16 | | | | | | | 0 & vtcheck(all_65_3, v0, v3) = 0 & vapp(v0, v1) = % 32.34/5.16 | | | | | | | all_73_2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.34/5.16 | | | | | | | % 32.34/5.16 | | | | | | | DELTA: instantiating (422) with fresh symbols all_103_0, % 32.34/5.16 | | | | | | | all_103_1, all_103_2, all_103_3 gives: % 32.34/5.16 | | | | | | | (423) varrow(all_103_1, all_73_1) = all_103_0 & % 32.34/5.16 | | | | | | | vtcheck(all_65_3, all_103_2, all_103_1) = 0 & % 32.34/5.16 | | | | | | | vtcheck(all_65_3, all_103_3, all_103_0) = 0 & % 32.34/5.16 | | | | | | | vapp(all_103_3, all_103_2) = all_73_2 & $i(all_103_0) & % 32.34/5.16 | | | | | | | $i(all_103_1) & $i(all_103_2) & $i(all_103_3) % 32.34/5.16 | | | | | | | % 32.34/5.16 | | | | | | | ALPHA: (423) implies: % 32.34/5.16 | | | | | | | (424) $i(all_103_3) % 32.34/5.16 | | | | | | | (425) $i(all_103_2) % 32.34/5.16 | | | | | | | (426) vapp(all_103_3, all_103_2) = all_73_2 % 32.34/5.16 | | | | | | | % 32.34/5.16 | | | | | | | REDUCE: (60), (426) imply: % 32.34/5.16 | | | | | | | (427) vapp(all_103_3, all_103_2) = ve2 % 32.34/5.16 | | | | | | | % 32.34/5.16 | | | | | | | BETA: splitting (39) gives: % 32.34/5.16 | | | | | | | % 32.34/5.16 | | | | | | | Case 1: % 32.34/5.16 | | | | | | | | % 32.34/5.16 | | | | | | | | (428) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.34/5.16 | | | | | | | | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] % 32.34/5.16 | | | | | | | | : (all_63_0 = vnoExp & ~ (v7 = 0) & ~ (v6 = 0) & % 32.34/5.16 | | | | | | | | vreduce(v4) = v3 & visSomeExp(v3) = v6 & visValue(v4) % 32.34/5.16 | | | | | | | | = v7 & vapp(v5, v4) = all_63_1 & vabs(v0, v1, v2) = % 32.34/5.16 | | | | | | | | v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 32.34/5.16 | | | | | | | | $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 32.34/5.16 | | | | | | | | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : % 32.34/5.16 | | | | | | | | ? [v7: $i] : ( ~ (v6 = 0) & vreduce(v3) = v1 & % 32.34/5.16 | | | | | | | | visSomeExp(v1) = v6 & vsomeExp(v7) = all_63_0 & % 32.34/5.16 | | | | | | | | vsubst(v2, v3, v4) = v7 & visValue(v3) = 0 & vapp(v5, % 32.34/5.16 | | | | | | | | v3) = all_63_1 & vabs(v2, v0, v4) = v5 & $i(v7) & % 32.34/5.16 | | | | | | | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.34/5.16 | | | | | | | | | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 32.34/5.16 | | | | | | | | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 32.34/5.16 | | | | | | | | : (vreduce(v0) = v4 & vgetSomeExp(v4) = v6 & % 32.34/5.16 | | | | | | | | visSomeExp(v4) = 0 & vsomeExp(v7) = all_63_0 & % 32.34/5.16 | | | | | | | | vapp(v5, v6) = v7 & vapp(v5, v0) = all_63_1 & % 32.34/5.16 | | | | | | | | vabs(v1, v2, v3) = v5 & $i(v7) & $i(v6) & $i(v5) & % 32.34/5.16 | | | | | | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.34/5.16 | | | | | | | | % 32.34/5.16 | | | | | | | | BETA: splitting (428) gives: % 32.34/5.16 | | | | | | | | % 32.34/5.16 | | | | | | | | Case 1: % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | (429) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 32.34/5.16 | | | | | | | | | : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: % 32.34/5.16 | | | | | | | | | int] : (all_63_0 = vnoExp & ~ (v7 = 0) & ~ (v6 = % 32.34/5.16 | | | | | | | | | 0) & vreduce(v4) = v3 & visSomeExp(v3) = v6 & % 32.34/5.16 | | | | | | | | | visValue(v4) = v7 & vapp(v5, v4) = all_63_1 & % 32.34/5.16 | | | | | | | | | vabs(v0, v1, v2) = v5 & $i(v5) & $i(v4) & $i(v3) & % 32.34/5.16 | | | | | | | | | $i(v2) & $i(v1) & $i(v0)) % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | DELTA: instantiating (429) with fresh symbols all_111_0, % 32.34/5.16 | | | | | | | | | all_111_1, all_111_2, all_111_3, all_111_4, all_111_5, % 32.34/5.16 | | | | | | | | | all_111_6, all_111_7 gives: % 32.34/5.16 | | | | | | | | | (430) all_63_0 = vnoExp & ~ (all_111_0 = 0) & ~ % 32.34/5.16 | | | | | | | | | (all_111_1 = 0) & vreduce(all_111_3) = all_111_4 & % 32.34/5.16 | | | | | | | | | visSomeExp(all_111_4) = all_111_1 & % 32.34/5.16 | | | | | | | | | visValue(all_111_3) = all_111_0 & vapp(all_111_2, % 32.34/5.16 | | | | | | | | | all_111_3) = all_63_1 & vabs(all_111_7, all_111_6, % 32.34/5.16 | | | | | | | | | all_111_5) = all_111_2 & $i(all_111_2) & % 32.34/5.16 | | | | | | | | | $i(all_111_3) & $i(all_111_4) & $i(all_111_5) & % 32.34/5.16 | | | | | | | | | $i(all_111_6) & $i(all_111_7) % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | REF_CLOSE: (1), (31), (35), (430) are inconsistent by % 32.34/5.16 | | | | | | | | | sub-proof #9. % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | Case 2: % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | (431) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 32.34/5.16 | | | | | | | | | : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: % 32.34/5.16 | | | | | | | | | $i] : ( ~ (v6 = 0) & vreduce(v3) = v1 & % 32.34/5.16 | | | | | | | | | visSomeExp(v1) = v6 & vsomeExp(v7) = all_63_0 & % 32.34/5.16 | | | | | | | | | vsubst(v2, v3, v4) = v7 & visValue(v3) = 0 & % 32.34/5.16 | | | | | | | | | vapp(v5, v3) = all_63_1 & vabs(v2, v0, v4) = v5 & % 32.34/5.16 | | | | | | | | | $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 32.34/5.16 | | | | | | | | | & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 32.34/5.16 | | | | | | | | | : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 32.34/5.16 | | | | | | | | | $i] : ? [v7: $i] : (vreduce(v0) = v4 & % 32.34/5.16 | | | | | | | | | vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & % 32.34/5.16 | | | | | | | | | vsomeExp(v7) = all_63_0 & vapp(v5, v6) = v7 & % 32.34/5.16 | | | | | | | | | vapp(v5, v0) = all_63_1 & vabs(v1, v2, v3) = v5 & % 32.34/5.16 | | | | | | | | | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) % 32.34/5.16 | | | | | | | | | & $i(v1) & $i(v0)) % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | BETA: splitting (431) gives: % 32.34/5.16 | | | | | | | | | % 32.34/5.16 | | | | | | | | | Case 1: % 32.34/5.16 | | | | | | | | | | % 32.34/5.16 | | | | | | | | | | (432) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.34/5.16 | | | | | | | | | | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : % 32.34/5.16 | | | | | | | | | | ? [v7: $i] : ( ~ (v6 = 0) & vreduce(v3) = v1 & % 32.34/5.16 | | | | | | | | | | visSomeExp(v1) = v6 & vsomeExp(v7) = all_63_0 & % 32.34/5.16 | | | | | | | | | | vsubst(v2, v3, v4) = v7 & visValue(v3) = 0 & % 32.34/5.16 | | | | | | | | | | vapp(v5, v3) = all_63_1 & vabs(v2, v0, v4) = v5 & % 32.34/5.16 | | | | | | | | | | $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 32.34/5.16 | | | | | | | | | | $i(v1) & $i(v0)) % 32.34/5.16 | | | | | | | | | | % 32.34/5.16 | | | | | | | | | | DELTA: instantiating (432) with fresh symbols all_111_0, % 32.34/5.16 | | | | | | | | | | all_111_1, all_111_2, all_111_3, all_111_4, % 32.34/5.16 | | | | | | | | | | all_111_5, all_111_6, all_111_7 gives: % 32.34/5.16 | | | | | | | | | | (433) ~ (all_111_1 = 0) & vreduce(all_111_4) = all_111_6 % 32.34/5.16 | | | | | | | | | | & visSomeExp(all_111_6) = all_111_1 & % 32.34/5.16 | | | | | | | | | | vsomeExp(all_111_0) = all_63_0 & vsubst(all_111_5, % 32.34/5.16 | | | | | | | | | | all_111_4, all_111_3) = all_111_0 & % 32.34/5.16 | | | | | | | | | | visValue(all_111_4) = 0 & vapp(all_111_2, % 32.34/5.16 | | | | | | | | | | all_111_4) = all_63_1 & vabs(all_111_5, % 32.34/5.16 | | | | | | | | | | all_111_7, all_111_3) = all_111_2 & $i(all_111_0) % 32.34/5.16 | | | | | | | | | | & $i(all_111_2) & $i(all_111_3) & $i(all_111_4) & % 32.34/5.16 | | | | | | | | | | $i(all_111_5) & $i(all_111_6) & $i(all_111_7) % 32.34/5.16 | | | | | | | | | | % 32.34/5.16 | | | | | | | | | | ALPHA: (433) implies: % 32.34/5.16 | | | | | | | | | | (434) $i(all_111_4) % 32.34/5.16 | | | | | | | | | | (435) $i(all_111_2) % 32.34/5.16 | | | | | | | | | | (436) vapp(all_111_2, all_111_4) = all_63_1 % 32.34/5.16 | | | | | | | | | | (437) visValue(all_111_4) = 0 % 32.34/5.16 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | GROUND_INST: instantiating (EQ-app) with ve1, ve2, all_111_2, % 32.34/5.17 | | | | | | | | | | all_111_4, all_63_1, simplifying with (8), (9), % 32.34/5.17 | | | | | | | | | | (25), (434), (435), (436) gives: % 32.34/5.17 | | | | | | | | | | (438) all_111_2 = ve1 & all_111_4 = ve2 % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | ALPHA: (438) implies: % 32.34/5.17 | | | | | | | | | | (439) all_111_4 = ve2 % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | REDUCE: (437), (439) imply: % 32.34/5.17 | | | | | | | | | | (440) visValue(ve2) = 0 % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | GROUND_INST: instantiating (isValue2) with all_103_3, % 32.34/5.17 | | | | | | | | | | all_103_2, ve2, simplifying with (9), (424), % 32.34/5.17 | | | | | | | | | | (425), (427), (440) gives: % 32.34/5.17 | | | | | | | | | | (441) $false % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | CLOSE: (441) is inconsistent. % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | Case 2: % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | (442) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.34/5.17 | | | | | | | | | | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 32.34/5.17 | | | | | | | | | | ? [v7: $i] : (vreduce(v0) = v4 & vgetSomeExp(v4) = % 32.34/5.17 | | | | | | | | | | v6 & visSomeExp(v4) = 0 & vsomeExp(v7) = all_63_0 % 32.34/5.17 | | | | | | | | | | & vapp(v5, v6) = v7 & vapp(v5, v0) = all_63_1 & % 32.34/5.17 | | | | | | | | | | vabs(v1, v2, v3) = v5 & $i(v7) & $i(v6) & $i(v5) % 32.34/5.17 | | | | | | | | | | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | DELTA: instantiating (442) with fresh symbols all_111_0, % 32.34/5.17 | | | | | | | | | | all_111_1, all_111_2, all_111_3, all_111_4, % 32.34/5.17 | | | | | | | | | | all_111_5, all_111_6, all_111_7 gives: % 32.34/5.17 | | | | | | | | | | (443) vreduce(all_111_7) = all_111_3 & % 32.34/5.17 | | | | | | | | | | vgetSomeExp(all_111_3) = all_111_1 & % 32.34/5.17 | | | | | | | | | | visSomeExp(all_111_3) = 0 & vsomeExp(all_111_0) = % 32.34/5.17 | | | | | | | | | | all_63_0 & vapp(all_111_2, all_111_1) = all_111_0 & % 32.34/5.17 | | | | | | | | | | vapp(all_111_2, all_111_7) = all_63_1 & % 32.34/5.17 | | | | | | | | | | vabs(all_111_6, all_111_5, all_111_4) = all_111_2 & % 32.34/5.17 | | | | | | | | | | $i(all_111_0) & $i(all_111_1) & $i(all_111_2) & % 32.34/5.17 | | | | | | | | | | $i(all_111_3) & $i(all_111_4) & $i(all_111_5) & % 32.34/5.17 | | | | | | | | | | $i(all_111_6) & $i(all_111_7) % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | ALPHA: (443) implies: % 32.34/5.17 | | | | | | | | | | (444) $i(all_111_7) % 32.34/5.17 | | | | | | | | | | (445) $i(all_111_6) % 32.34/5.17 | | | | | | | | | | (446) $i(all_111_5) % 32.34/5.17 | | | | | | | | | | (447) $i(all_111_4) % 32.34/5.17 | | | | | | | | | | (448) $i(all_111_2) % 32.34/5.17 | | | | | | | | | | (449) vabs(all_111_6, all_111_5, all_111_4) = all_111_2 % 32.34/5.17 | | | | | | | | | | (450) vapp(all_111_2, all_111_7) = all_63_1 % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | GROUND_INST: instantiating (EQ-app) with ve1, ve2, all_111_2, % 32.34/5.17 | | | | | | | | | | all_111_7, all_63_1, simplifying with (8), (9), % 32.34/5.17 | | | | | | | | | | (25), (444), (448), (450) gives: % 32.34/5.17 | | | | | | | | | | (451) all_111_2 = ve1 & all_111_7 = ve2 % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | ALPHA: (451) implies: % 32.34/5.17 | | | | | | | | | | (452) all_111_2 = ve1 % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | REDUCE: (449), (452) imply: % 32.34/5.17 | | | | | | | | | | (453) vabs(all_111_6, all_111_5, all_111_4) = ve1 % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_89_0, % 32.34/5.17 | | | | | | | | | | all_111_6, all_111_5, all_111_4, ve1, simplifying % 32.34/5.17 | | | | | | | | | | with (379), (381), (445), (446), (447), (453) % 32.34/5.17 | | | | | | | | | | gives: % 32.34/5.17 | | | | | | | | | | (454) $false % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | CLOSE: (454) is inconsistent. % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | End of split % 32.34/5.17 | | | | | | | | | % 32.34/5.17 | | | | | | | | End of split % 32.34/5.17 | | | | | | | | % 32.34/5.17 | | | | | | | Case 2: % 32.34/5.17 | | | | | | | | % 32.34/5.17 | | | | | | | | (455) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.34/5.17 | | | | | | | | ? [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 % 32.34/5.17 | | | | | | | | & visSomeExp(v1) = 0 & vsomeExp(v4) = all_63_0 & % 32.34/5.17 | | | | | | | | vapp(v3, v2) = v4 & vapp(v0, v2) = all_63_1 & $i(v4) % 32.34/5.17 | | | | | | | | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : % 32.34/5.17 | | | | | | | | ! [v6: $i] : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = % 32.34/5.17 | | | | | | | | v0) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5))) | ? % 32.34/5.17 | | | | | | | | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : % 32.34/5.17 | | | | | | | | (all_63_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) = v2 & % 32.34/5.17 | | | | | | | | visSomeExp(v2) = v3 & vapp(v1, v0) = all_63_1 & % 32.34/5.17 | | | | | | | | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] % 32.34/5.17 | | | | | | | | : ! [v6: $i] : ( ~ (vabs(v4, v5, v6) = v1) | ~ % 32.34/5.17 | | | | | | | | $i(v6) | ~ $i(v5) | ~ $i(v4))) | ? [v0: $i] : ? % 32.34/5.17 | | | | | | | | [v1: $i] : ? [v2: $i] : (all_63_0 = vnoExp & vabs(v0, % 32.34/5.17 | | | | | | | | v1, v2) = all_63_1 & $i(v2) & $i(v1) & $i(v0)) | ? % 32.34/5.17 | | | | | | | | [v0: $i] : (all_63_0 = vnoExp & vvar(v0) = all_63_1 & % 32.34/5.17 | | | | | | | | $i(v0)) % 32.34/5.17 | | | | | | | | % 32.34/5.17 | | | | | | | | BETA: splitting (455) gives: % 32.34/5.17 | | | | | | | | % 32.34/5.17 | | | | | | | | Case 1: % 32.34/5.17 | | | | | | | | | % 32.34/5.17 | | | | | | | | | (456) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 32.34/5.17 | | | | | | | | | : ? [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = % 32.34/5.17 | | | | | | | | | v3 & visSomeExp(v1) = 0 & vsomeExp(v4) = all_63_0 & % 32.34/5.17 | | | | | | | | | vapp(v3, v2) = v4 & vapp(v0, v2) = all_63_1 & % 32.34/5.17 | | | | | | | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! % 32.34/5.17 | | | | | | | | | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 32.34/5.17 | | | | | | | | | (vabs(v5, v6, v7) = v0) | ~ $i(v7) | ~ $i(v6) | % 32.34/5.17 | | | | | | | | | ~ $i(v5))) | ? [v0: $i] : ? [v1: $i] : ? [v2: % 32.34/5.17 | | | | | | | | | $i] : ? [v3: int] : (all_63_0 = vnoExp & ~ (v3 = % 32.34/5.17 | | | | | | | | | 0) & vreduce(v1) = v2 & visSomeExp(v2) = v3 & % 32.34/5.17 | | | | | | | | | vapp(v1, v0) = all_63_1 & $i(v2) & $i(v1) & $i(v0) % 32.34/5.17 | | | | | | | | | & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 32.34/5.17 | | | | | | | | | (vabs(v4, v5, v6) = v1) | ~ $i(v6) | ~ $i(v5) | % 32.34/5.17 | | | | | | | | | ~ $i(v4))) % 32.34/5.17 | | | | | | | | | % 32.34/5.17 | | | | | | | | | BETA: splitting (456) gives: % 32.34/5.17 | | | | | | | | | % 32.34/5.17 | | | | | | | | | Case 1: % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | (457) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.34/5.17 | | | | | | | | | | $i] : ? [v4: $i] : (vreduce(v0) = v1 & % 32.34/5.17 | | | | | | | | | | vgetSomeExp(v1) = v3 & visSomeExp(v1) = 0 & % 32.34/5.17 | | | | | | | | | | vsomeExp(v4) = all_63_0 & vapp(v3, v2) = v4 & % 32.34/5.17 | | | | | | | | | | vapp(v0, v2) = all_63_1 & $i(v4) & $i(v3) & % 32.34/5.17 | | | | | | | | | | $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: % 32.34/5.17 | | | | | | | | | | $i] : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) % 32.34/5.17 | | | | | | | | | | | ~ $i(v7) | ~ $i(v6) | ~ $i(v5))) % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | DELTA: instantiating (457) with fresh symbols all_111_0, % 32.34/5.17 | | | | | | | | | | all_111_1, all_111_2, all_111_3, all_111_4 gives: % 32.34/5.17 | | | | | | | | | | (458) vreduce(all_111_4) = all_111_3 & % 32.34/5.17 | | | | | | | | | | vgetSomeExp(all_111_3) = all_111_1 & % 32.34/5.17 | | | | | | | | | | visSomeExp(all_111_3) = 0 & vsomeExp(all_111_0) = % 32.34/5.17 | | | | | | | | | | all_63_0 & vapp(all_111_1, all_111_2) = all_111_0 & % 32.34/5.17 | | | | | | | | | | vapp(all_111_4, all_111_2) = all_63_1 & % 32.34/5.17 | | | | | | | | | | $i(all_111_0) & $i(all_111_1) & $i(all_111_2) & % 32.34/5.17 | | | | | | | | | | $i(all_111_3) & $i(all_111_4) & ! [v0: $i] : ! % 32.34/5.17 | | | | | | | | | | [v1: $i] : ! [v2: $i] : ( ~ (vabs(v0, v1, v2) = % 32.34/5.17 | | | | | | | | | | all_111_4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | REF_CLOSE: (2), (8), (9), (12), (13), (16), (17), (25), (29), % 32.34/5.17 | | | | | | | | | | (30), (31), (32), (34), (35), (37), (52), (53), % 32.34/5.17 | | | | | | | | | | (57), (63), (64), (458), (EQ-app), (EQ-someExp), % 32.34/5.17 | | | | | | | | | | (T-app), (getSomeExp0) are inconsistent by % 32.34/5.17 | | | | | | | | | | sub-proof #6. % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | Case 2: % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | (459) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 32.34/5.17 | | | | | | | | | | int] : (all_63_0 = vnoExp & ~ (v3 = 0) & % 32.34/5.17 | | | | | | | | | | vreduce(v1) = v2 & visSomeExp(v2) = v3 & vapp(v1, % 32.34/5.17 | | | | | | | | | | v0) = all_63_1 & $i(v2) & $i(v1) & $i(v0) & ! % 32.34/5.17 | | | | | | | | | | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 32.34/5.17 | | | | | | | | | | (vabs(v4, v5, v6) = v1) | ~ $i(v6) | ~ $i(v5) % 32.34/5.17 | | | | | | | | | | | ~ $i(v4))) % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | DELTA: instantiating (459) with fresh symbols all_111_0, % 32.34/5.17 | | | | | | | | | | all_111_1, all_111_2, all_111_3 gives: % 32.34/5.17 | | | | | | | | | | (460) all_63_0 = vnoExp & ~ (all_111_0 = 0) & % 32.34/5.17 | | | | | | | | | | vreduce(all_111_2) = all_111_1 & % 32.34/5.17 | | | | | | | | | | visSomeExp(all_111_1) = all_111_0 & vapp(all_111_2, % 32.34/5.17 | | | | | | | | | | all_111_3) = all_63_1 & $i(all_111_1) & % 32.34/5.17 | | | | | | | | | | $i(all_111_2) & $i(all_111_3) & ! [v0: $i] : ! % 32.34/5.17 | | | | | | | | | | [v1: $i] : ! [v2: $i] : ( ~ (vabs(v0, v1, v2) = % 32.34/5.17 | | | | | | | | | | all_111_2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | REF_CLOSE: (1), (31), (35), (460) are inconsistent by % 32.34/5.17 | | | | | | | | | | sub-proof #5. % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | End of split % 32.34/5.17 | | | | | | | | | % 32.34/5.17 | | | | | | | | Case 2: % 32.34/5.17 | | | | | | | | | % 32.34/5.17 | | | | | | | | | (461) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_63_0 = % 32.34/5.17 | | | | | | | | | vnoExp & vabs(v0, v1, v2) = all_63_1 & $i(v2) & % 32.34/5.17 | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (all_63_0 = vnoExp % 32.34/5.17 | | | | | | | | | & vvar(v0) = all_63_1 & $i(v0)) % 32.34/5.17 | | | | | | | | | % 32.34/5.17 | | | | | | | | | BETA: splitting (461) gives: % 32.34/5.17 | | | | | | | | | % 32.34/5.17 | | | | | | | | | Case 1: % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | (462) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_63_0 % 32.34/5.17 | | | | | | | | | | = vnoExp & vabs(v0, v1, v2) = all_63_1 & $i(v2) & % 32.34/5.17 | | | | | | | | | | $i(v1) & $i(v0)) % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | DELTA: instantiating (462) with fresh symbols all_111_0, % 32.34/5.17 | | | | | | | | | | all_111_1, all_111_2 gives: % 32.34/5.17 | | | | | | | | | | (463) all_63_0 = vnoExp & vabs(all_111_2, all_111_1, % 32.34/5.17 | | | | | | | | | | all_111_0) = all_63_1 & $i(all_111_0) & % 32.34/5.17 | | | | | | | | | | $i(all_111_1) & $i(all_111_2) % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | REF_CLOSE: (1), (31), (35), (463) are inconsistent by % 32.34/5.17 | | | | | | | | | | sub-proof #4. % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | Case 2: % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | (464) ? [v0: $i] : (all_63_0 = vnoExp & vvar(v0) = % 32.34/5.17 | | | | | | | | | | all_63_1 & $i(v0)) % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | DELTA: instantiating (464) with fresh symbol all_111_0 % 32.34/5.17 | | | | | | | | | | gives: % 32.34/5.17 | | | | | | | | | | (465) all_63_0 = vnoExp & vvar(all_111_0) = all_63_1 & % 32.34/5.17 | | | | | | | | | | $i(all_111_0) % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | | REF_CLOSE: (1), (31), (35), (465) are inconsistent by % 32.34/5.17 | | | | | | | | | | sub-proof #3. % 32.34/5.17 | | | | | | | | | | % 32.34/5.17 | | | | | | | | | End of split % 32.34/5.17 | | | | | | | | | % 32.34/5.17 | | | | | | | | End of split % 32.34/5.17 | | | | | | | | % 32.34/5.17 | | | | | | | End of split % 32.34/5.17 | | | | | | | % 32.34/5.17 | | | | | | Case 2: % 32.34/5.17 | | | | | | | % 32.34/5.17 | | | | | | | (466) ? [v0: $i] : (vsomeType(all_73_1) = v0 & $i(v0) & ? % 32.34/5.17 | | | | | | | [v1: $i] : (vlookup(v1, all_65_3) = v0 & vvar(v1) = % 32.34/5.17 | | | | | | | all_73_2 & $i(v1))) % 32.34/5.17 | | | | | | | % 32.34/5.17 | | | | | | | REF_CLOSE: (1), (2), (3), (8), (9), (12), (13), (16), (17), (19), % 32.34/5.17 | | | | | | | (20), (25), (29), (30), (31), (32), (34), (35), (37), % 32.34/5.17 | | | | | | | (39), (52), (53), (57), (60), (63), (64), (466), % 32.34/5.17 | | | | | | | (EQ-app), (EQ-someExp), (T-app), (getSomeExp0), % 32.34/5.17 | | | | | | | (isValue1) are inconsistent by sub-proof #1. % 32.34/5.17 | | | | | | | % 32.34/5.17 | | | | | | End of split % 32.34/5.17 | | | | | | % 32.34/5.17 | | | | | End of split % 32.34/5.17 | | | | | % 32.34/5.17 | | | | End of split % 32.34/5.17 | | | | % 32.34/5.17 | | | End of split % 32.34/5.17 | | | % 32.34/5.17 | | Case 2: % 32.34/5.17 | | | % 32.34/5.17 | | | (467) ? [v0: $i] : (vsomeType(all_65_1) = v0 & $i(v0) & ? [v1: $i] : % 32.34/5.17 | | | (vlookup(v1, all_65_3) = v0 & vvar(v1) = all_63_1 & $i(v1))) % 32.34/5.17 | | | % 32.34/5.17 | | | DELTA: instantiating (467) with fresh symbol all_73_0 gives: % 32.34/5.17 | | | (468) vsomeType(all_65_1) = all_73_0 & $i(all_73_0) & ? [v0: $i] : % 32.34/5.17 | | | (vlookup(v0, all_65_3) = all_73_0 & vvar(v0) = all_63_1 & $i(v0)) % 32.34/5.17 | | | % 32.34/5.17 | | | ALPHA: (468) implies: % 32.34/5.17 | | | (469) ? [v0: $i] : (vlookup(v0, all_65_3) = all_73_0 & vvar(v0) = % 32.34/5.17 | | | all_63_1 & $i(v0)) % 32.34/5.17 | | | % 32.34/5.17 | | | DELTA: instantiating (469) with fresh symbol all_75_0 gives: % 32.34/5.17 | | | (470) vlookup(all_75_0, all_65_3) = all_73_0 & vvar(all_75_0) = % 32.34/5.17 | | | all_63_1 & $i(all_75_0) % 32.34/5.17 | | | % 32.34/5.17 | | | ALPHA: (470) implies: % 32.34/5.17 | | | (471) $i(all_75_0) % 32.34/5.18 | | | (472) vvar(all_75_0) = all_63_1 % 32.34/5.18 | | | % 32.34/5.18 | | | GROUND_INST: instantiating (DIFF-var-app) with all_75_0, ve1, ve2, % 32.34/5.18 | | | all_63_1, simplifying with (8), (9), (25), (471), (472) % 32.34/5.18 | | | gives: % 32.34/5.18 | | | (473) $false % 32.34/5.18 | | | % 32.34/5.18 | | | CLOSE: (473) is inconsistent. % 32.34/5.18 | | | % 32.34/5.18 | | End of split % 32.34/5.18 | | % 32.34/5.18 | End of split % 32.34/5.18 | % 32.34/5.18 End of proof % 32.34/5.18 % 32.34/5.18 Sub-proof #1 shows that the following formulas are inconsistent: % 32.34/5.18 ---------------------------------------------------------------- % 32.34/5.18 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v1) = % 32.34/5.18 v2) | ~ (vsomeExp(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 32.34/5.18 (2) $i(all_73_1) % 32.34/5.18 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = vnoExp | ~ (vreduce(v1) % 32.34/5.18 = v2) | ~ (vvar(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 32.34/5.18 (4) vreduce(ve2) = all_60_0 % 32.34/5.18 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vreduce(v2) = % 32.34/5.18 v1) | ~ (vreduce(v2) = v0)) % 32.34/5.18 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 32.34/5.18 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ % 32.34/5.18 (vtcheck(v4, v3, v2) = v0)) % 32.34/5.18 (7) $i(all_65_3) % 32.34/5.18 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (vgetSomeExp(v0) % 32.34/5.18 = v1) | ~ (vsomeExp(v2) = v0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 32.34/5.18 (9) vapp(ve1, ve2) = all_63_1 % 32.34/5.18 (10) $i(all_60_0) % 32.34/5.18 (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 32.34/5.18 [v5: $i] : ? [v6: int] : ? [v7: int] : (all_57_0 = vnoExp & ~ (v7 = % 32.34/5.18 0) & ~ (v6 = 0) & vreduce(v4) = v3 & visSomeExp(v3) = v6 & % 32.34/5.18 visValue(v4) = v7 & vapp(v5, v4) = ve1 & vabs(v0, v1, v2) = v5 & % 32.34/5.18 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 32.34/5.18 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 32.34/5.18 [v6: int] : ? [v7: $i] : ( ~ (v6 = 0) & vreduce(v3) = v1 & % 32.34/5.18 visSomeExp(v1) = v6 & vsomeExp(v7) = all_57_0 & vsubst(v2, v3, v4) = % 32.34/5.18 v7 & visValue(v3) = 0 & vapp(v5, v3) = ve1 & vabs(v2, v0, v4) = v5 & % 32.34/5.18 $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? % 32.34/5.18 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 32.34/5.18 [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vreduce(v0) = v4 & % 32.34/5.18 vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & vsomeExp(v7) = all_57_0 & % 32.34/5.18 vapp(v5, v6) = v7 & vapp(v5, v0) = ve1 & vabs(v1, v2, v3) = v5 & % 32.34/5.18 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.34/5.18 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 32.34/5.18 (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & visSomeExp(v1) = 0 & % 32.34/5.18 vsomeExp(v4) = all_57_0 & vapp(v3, v2) = v4 & vapp(v0, v2) = ve1 & % 32.34/5.18 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] % 32.34/5.18 : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ $i(v7) | ~ $i(v6) | % 32.34/5.18 ~ $i(v5))) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] % 32.34/5.18 : (all_57_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) = v2 & visSomeExp(v2) = % 32.34/5.18 v3 & vapp(v1, v0) = ve1 & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! % 32.34/5.18 [v5: $i] : ! [v6: $i] : ( ~ (vabs(v4, v5, v6) = v1) | ~ $i(v6) | ~ % 32.34/5.18 $i(v5) | ~ $i(v4))) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 32.34/5.18 (all_57_0 = vnoExp & vabs(v0, v1, v2) = ve1 & $i(v2) & $i(v1) & $i(v0)) % 32.34/5.18 | ? [v0: $i] : (all_57_0 = vnoExp & vvar(v0) = ve1 & $i(v0)) % 32.34/5.18 (12) $i(all_73_0) % 32.34/5.18 (13) ~ (visSomeExp(vnoExp) = 0) % 32.34/5.18 (14) $i(ve2) % 32.34/5.18 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vsomeExp(v1) = all_57_0) % 32.34/5.18 | ~ (vtcheck(v0, ve1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 32.34/5.18 vtcheck(v0, v1, v2) = 0) % 32.34/5.18 (16) vreduce(ve1) = all_57_0 % 32.34/5.18 (17) ! [v0: $i] : ! [v1: $i] : ( ~ (visValue(v1) = 0) | ~ (vvar(v0) = v1) % 32.34/5.18 | ~ $i(v1) | ~ $i(v0)) % 32.34/5.18 (18) ! [v0: $i] : ( ~ (vsomeExp(v0) = vnoExp) | ~ $i(v0)) % 32.34/5.18 (19) $i(ve1) % 32.34/5.18 (20) vsomeExp(all_65_2) = all_63_0 % 32.34/5.18 (21) ~ (all_65_0 = 0) % 32.34/5.18 (22) all_73_2 = ve2 % 32.34/5.18 (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 32.34/5.18 [v5: $i] : ? [v6: int] : ? [v7: int] : (all_63_0 = vnoExp & ~ (v7 = % 32.34/5.18 0) & ~ (v6 = 0) & vreduce(v4) = v3 & visSomeExp(v3) = v6 & % 32.34/5.18 visValue(v4) = v7 & vapp(v5, v4) = all_63_1 & vabs(v0, v1, v2) = v5 & % 32.34/5.18 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 32.34/5.18 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 32.34/5.18 [v6: int] : ? [v7: $i] : ( ~ (v6 = 0) & vreduce(v3) = v1 & % 32.34/5.18 visSomeExp(v1) = v6 & vsomeExp(v7) = all_63_0 & vsubst(v2, v3, v4) = % 32.34/5.18 v7 & visValue(v3) = 0 & vapp(v5, v3) = all_63_1 & vabs(v2, v0, v4) = % 32.34/5.18 v5 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | % 32.34/5.18 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 32.34/5.18 [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vreduce(v0) = v4 & % 32.34/5.18 vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & vsomeExp(v7) = all_63_0 & % 32.34/5.18 vapp(v5, v6) = v7 & vapp(v5, v0) = all_63_1 & vabs(v1, v2, v3) = v5 & % 32.34/5.18 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.34/5.18 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 32.34/5.18 (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & visSomeExp(v1) = 0 & % 32.34/5.18 vsomeExp(v4) = all_63_0 & vapp(v3, v2) = v4 & vapp(v0, v2) = all_63_1 % 32.34/5.18 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: % 32.34/5.18 $i] : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ $i(v7) | ~ % 32.34/5.18 $i(v6) | ~ $i(v5))) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 32.34/5.18 [v3: int] : (all_63_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) = v2 & % 32.34/5.18 visSomeExp(v2) = v3 & vapp(v1, v0) = all_63_1 & $i(v2) & $i(v1) & % 32.34/5.18 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (vabs(v4, v5, % 32.34/5.18 v6) = v1) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4))) | ? [v0: $i] : % 32.34/5.18 ? [v1: $i] : ? [v2: $i] : (all_63_0 = vnoExp & vabs(v0, v1, v2) = % 32.34/5.18 all_63_1 & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : (all_63_0 = % 32.34/5.18 vnoExp & vvar(v0) = all_63_1 & $i(v0)) % 32.34/5.18 (24) $i(all_65_1) % 32.34/5.18 (25) vtcheck(all_65_3, all_65_2, all_65_1) = all_65_0 % 32.34/5.18 (26) vtcheck(all_65_3, ve1, all_73_0) = 0 % 32.34/5.18 (27) $i(all_65_2) % 32.34/5.18 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 32.34/5.18 ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) % 32.34/5.18 | ~ $i(v1) | ~ $i(v0) | (v3 = v1 & v2 = v0)) % 32.34/5.18 (29) vtcheck(all_65_3, ve2, all_73_1) = 0 % 32.34/5.18 (30) ? [v0: $i] : (vsomeType(all_73_1) = v0 & $i(v0) & ? [v1: $i] : % 32.34/5.18 (vlookup(v1, all_65_3) = v0 & vvar(v1) = all_73_2 & $i(v1))) % 32.34/5.18 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 32.34/5.18 [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (varrow(v0, v4) = % 32.34/5.18 v5) | ~ (vtcheck(v1, v6, v4) = v7) | ~ (vtcheck(v1, v2, v5) = 0) | % 32.34/5.18 ~ (vapp(v2, v3) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 32.34/5.18 | ~ $i(v0) | ? [v8: int] : ( ~ (v8 = 0) & vtcheck(v1, v3, v0) = v8)) % 32.34/5.18 (32) varrow(all_73_1, all_65_1) = all_73_0 % 32.34/5.18 % 32.34/5.18 Begin of proof % 32.34/5.18 | % 32.34/5.18 | DELTA: instantiating (30) with fresh symbol all_95_0 gives: % 32.34/5.18 | (33) vsomeType(all_73_1) = all_95_0 & $i(all_95_0) & ? [v0: $i] : % 32.34/5.18 | (vlookup(v0, all_65_3) = all_95_0 & vvar(v0) = all_73_2 & $i(v0)) % 32.34/5.18 | % 32.34/5.18 | ALPHA: (33) implies: % 32.34/5.18 | (34) ? [v0: $i] : (vlookup(v0, all_65_3) = all_95_0 & vvar(v0) = all_73_2 % 32.34/5.18 | & $i(v0)) % 32.34/5.18 | % 32.34/5.18 | DELTA: instantiating (34) with fresh symbol all_97_0 gives: % 32.34/5.18 | (35) vlookup(all_97_0, all_65_3) = all_95_0 & vvar(all_97_0) = all_73_2 & % 32.34/5.18 | $i(all_97_0) % 32.34/5.18 | % 32.34/5.18 | ALPHA: (35) implies: % 32.34/5.18 | (36) $i(all_97_0) % 32.34/5.18 | (37) vvar(all_97_0) = all_73_2 % 32.34/5.18 | % 32.34/5.18 | REDUCE: (22), (37) imply: % 32.34/5.18 | (38) vvar(all_97_0) = ve2 % 32.34/5.18 | % 32.34/5.18 | GROUND_INST: instantiating (3) with all_97_0, ve2, all_60_0, simplifying with % 32.34/5.18 | (4), (10), (14), (36), (38) gives: % 32.34/5.18 | (39) all_60_0 = vnoExp % 32.34/5.18 | % 32.34/5.18 | REDUCE: (4), (39) imply: % 32.34/5.18 | (40) vreduce(ve2) = vnoExp % 32.34/5.18 | % 32.34/5.18 | BETA: splitting (23) gives: % 32.34/5.18 | % 32.34/5.18 | Case 1: % 32.34/5.18 | | % 32.34/5.18 | | (41) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 32.34/5.18 | | : ? [v5: $i] : ? [v6: int] : ? [v7: int] : (all_63_0 = vnoExp & % 32.34/5.18 | | ~ (v7 = 0) & ~ (v6 = 0) & vreduce(v4) = v3 & visSomeExp(v3) = v6 % 32.34/5.18 | | & visValue(v4) = v7 & vapp(v5, v4) = all_63_1 & vabs(v0, v1, v2) = % 32.34/5.18 | | v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? % 32.34/5.18 | | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 32.34/5.18 | | ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ( ~ (v6 = 0) & vreduce(v3) % 32.34/5.18 | | = v1 & visSomeExp(v1) = v6 & vsomeExp(v7) = all_63_0 & vsubst(v2, % 32.34/5.18 | | v3, v4) = v7 & visValue(v3) = 0 & vapp(v5, v3) = all_63_1 & % 32.34/5.18 | | vabs(v2, v0, v4) = v5 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) % 32.34/5.18 | | & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 32.34/5.18 | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 32.34/5.18 | | (vreduce(v0) = v4 & vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & % 32.34/5.18 | | vsomeExp(v7) = all_63_0 & vapp(v5, v6) = v7 & vapp(v5, v0) = % 32.34/5.18 | | all_63_1 & vabs(v1, v2, v3) = v5 & $i(v7) & $i(v6) & $i(v5) & % 32.34/5.18 | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.34/5.18 | | % 32.34/5.18 | | BETA: splitting (41) gives: % 32.34/5.18 | | % 32.34/5.18 | | Case 1: % 32.34/5.18 | | | % 32.34/5.19 | | | (42) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 32.34/5.19 | | | $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : (all_63_0 = % 32.34/5.19 | | | vnoExp & ~ (v7 = 0) & ~ (v6 = 0) & vreduce(v4) = v3 & % 32.34/5.19 | | | visSomeExp(v3) = v6 & visValue(v4) = v7 & vapp(v5, v4) = % 32.34/5.19 | | | all_63_1 & vabs(v0, v1, v2) = v5 & $i(v5) & $i(v4) & $i(v3) & % 32.34/5.19 | | | $i(v2) & $i(v1) & $i(v0)) % 32.34/5.19 | | | % 32.34/5.19 | | | DELTA: instantiating (42) with fresh symbols all_111_0, all_111_1, % 32.34/5.19 | | | all_111_2, all_111_3, all_111_4, all_111_5, all_111_6, all_111_7 % 32.34/5.19 | | | gives: % 32.34/5.19 | | | (43) all_63_0 = vnoExp & ~ (all_111_0 = 0) & ~ (all_111_1 = 0) & % 32.34/5.19 | | | vreduce(all_111_3) = all_111_4 & visSomeExp(all_111_4) = all_111_1 % 32.34/5.19 | | | & visValue(all_111_3) = all_111_0 & vapp(all_111_2, all_111_3) = % 32.34/5.19 | | | all_63_1 & vabs(all_111_7, all_111_6, all_111_5) = all_111_2 & % 32.34/5.19 | | | $i(all_111_2) & $i(all_111_3) & $i(all_111_4) & $i(all_111_5) & % 32.34/5.19 | | | $i(all_111_6) & $i(all_111_7) % 32.34/5.19 | | | % 32.34/5.19 | | | REF_CLOSE: (18), (20), (27), (43) are inconsistent by sub-proof #9. % 32.34/5.19 | | | % 32.34/5.19 | | Case 2: % 32.34/5.19 | | | % 32.34/5.19 | | | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 32.34/5.19 | | | $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ( ~ (v6 = 0) & % 32.34/5.19 | | | vreduce(v3) = v1 & visSomeExp(v1) = v6 & vsomeExp(v7) = all_63_0 % 32.34/5.19 | | | & vsubst(v2, v3, v4) = v7 & visValue(v3) = 0 & vapp(v5, v3) = % 32.34/5.19 | | | all_63_1 & vabs(v2, v0, v4) = v5 & $i(v7) & $i(v5) & $i(v4) & % 32.34/5.19 | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : % 32.34/5.19 | | | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 32.34/5.19 | | | $i] : ? [v7: $i] : (vreduce(v0) = v4 & vgetSomeExp(v4) = v6 & % 32.34/5.19 | | | visSomeExp(v4) = 0 & vsomeExp(v7) = all_63_0 & vapp(v5, v6) = v7 % 32.34/5.19 | | | & vapp(v5, v0) = all_63_1 & vabs(v1, v2, v3) = v5 & $i(v7) & % 32.34/5.19 | | | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.34/5.19 | | | % 32.34/5.19 | | | BETA: splitting (44) gives: % 32.34/5.19 | | | % 32.34/5.19 | | | Case 1: % 32.34/5.19 | | | | % 32.34/5.19 | | | | (45) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 32.34/5.19 | | | | $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ( ~ (v6 = 0) % 32.34/5.19 | | | | & vreduce(v3) = v1 & visSomeExp(v1) = v6 & vsomeExp(v7) = % 32.34/5.19 | | | | all_63_0 & vsubst(v2, v3, v4) = v7 & visValue(v3) = 0 & % 32.34/5.19 | | | | vapp(v5, v3) = all_63_1 & vabs(v2, v0, v4) = v5 & $i(v7) & % 32.34/5.19 | | | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.34/5.19 | | | | % 32.34/5.19 | | | | DELTA: instantiating (45) with fresh symbols all_111_0, all_111_1, % 32.34/5.19 | | | | all_111_2, all_111_3, all_111_4, all_111_5, all_111_6, all_111_7 % 32.34/5.19 | | | | gives: % 32.34/5.19 | | | | (46) ~ (all_111_1 = 0) & vreduce(all_111_4) = all_111_6 & % 32.34/5.19 | | | | visSomeExp(all_111_6) = all_111_1 & vsomeExp(all_111_0) = % 32.34/5.19 | | | | all_63_0 & vsubst(all_111_5, all_111_4, all_111_3) = all_111_0 & % 32.34/5.19 | | | | visValue(all_111_4) = 0 & vapp(all_111_2, all_111_4) = all_63_1 % 32.34/5.19 | | | | & vabs(all_111_5, all_111_7, all_111_3) = all_111_2 & % 32.34/5.19 | | | | $i(all_111_0) & $i(all_111_2) & $i(all_111_3) & $i(all_111_4) & % 32.34/5.19 | | | | $i(all_111_5) & $i(all_111_6) & $i(all_111_7) % 32.34/5.19 | | | | % 32.34/5.19 | | | | ALPHA: (46) implies: % 32.34/5.19 | | | | (47) $i(all_111_4) % 32.34/5.19 | | | | (48) $i(all_111_2) % 32.34/5.19 | | | | (49) vapp(all_111_2, all_111_4) = all_63_1 % 32.34/5.19 | | | | (50) visValue(all_111_4) = 0 % 32.34/5.19 | | | | % 32.34/5.19 | | | | GROUND_INST: instantiating (28) with ve1, ve2, all_111_2, all_111_4, % 32.34/5.19 | | | | all_63_1, simplifying with (9), (14), (19), (47), (48), % 32.34/5.19 | | | | (49) gives: % 32.34/5.19 | | | | (51) all_111_2 = ve1 & all_111_4 = ve2 % 32.34/5.19 | | | | % 32.34/5.19 | | | | ALPHA: (51) implies: % 32.34/5.19 | | | | (52) all_111_4 = ve2 % 32.34/5.19 | | | | % 32.34/5.19 | | | | REDUCE: (50), (52) imply: % 32.34/5.19 | | | | (53) visValue(ve2) = 0 % 32.34/5.19 | | | | % 32.34/5.19 | | | | GROUND_INST: instantiating (17) with all_97_0, ve2, simplifying with % 32.34/5.19 | | | | (14), (36), (38), (53) gives: % 32.34/5.19 | | | | (54) $false % 32.34/5.19 | | | | % 32.34/5.19 | | | | CLOSE: (54) is inconsistent. % 32.34/5.19 | | | | % 32.34/5.19 | | | Case 2: % 32.34/5.19 | | | | % 32.34/5.19 | | | | (55) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 32.34/5.19 | | | | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vreduce(v0) = % 32.34/5.19 | | | | v4 & vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & vsomeExp(v7) % 32.34/5.19 | | | | = all_63_0 & vapp(v5, v6) = v7 & vapp(v5, v0) = all_63_1 & % 32.34/5.19 | | | | vabs(v1, v2, v3) = v5 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 32.34/5.19 | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.34/5.19 | | | | % 32.34/5.19 | | | | DELTA: instantiating (55) with fresh symbols all_111_0, all_111_1, % 32.34/5.19 | | | | all_111_2, all_111_3, all_111_4, all_111_5, all_111_6, all_111_7 % 32.34/5.19 | | | | gives: % 32.34/5.19 | | | | (56) vreduce(all_111_7) = all_111_3 & vgetSomeExp(all_111_3) = % 32.34/5.19 | | | | all_111_1 & visSomeExp(all_111_3) = 0 & vsomeExp(all_111_0) = % 32.34/5.19 | | | | all_63_0 & vapp(all_111_2, all_111_1) = all_111_0 & % 32.34/5.19 | | | | vapp(all_111_2, all_111_7) = all_63_1 & vabs(all_111_6, % 32.34/5.19 | | | | all_111_5, all_111_4) = all_111_2 & $i(all_111_0) & % 32.34/5.19 | | | | $i(all_111_1) & $i(all_111_2) & $i(all_111_3) & $i(all_111_4) & % 32.34/5.19 | | | | $i(all_111_5) & $i(all_111_6) & $i(all_111_7) % 32.34/5.19 | | | | % 32.34/5.19 | | | | REF_CLOSE: (5), (9), (13), (14), (19), (28), (40), (56) are inconsistent % 32.34/5.19 | | | | by sub-proof #7. % 32.34/5.19 | | | | % 32.34/5.19 | | | End of split % 32.34/5.19 | | | % 32.34/5.19 | | End of split % 32.34/5.19 | | % 32.34/5.19 | Case 2: % 32.34/5.19 | | % 32.34/5.19 | | (57) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 32.34/5.19 | | : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & visSomeExp(v1) = 0 & % 32.34/5.19 | | vsomeExp(v4) = all_63_0 & vapp(v3, v2) = v4 & vapp(v0, v2) = % 32.34/5.19 | | all_63_1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: % 32.34/5.19 | | $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | % 32.34/5.19 | | ~ $i(v7) | ~ $i(v6) | ~ $i(v5))) | ? [v0: $i] : ? [v1: $i] : % 32.34/5.19 | | ? [v2: $i] : ? [v3: int] : (all_63_0 = vnoExp & ~ (v3 = 0) & % 32.34/5.19 | | vreduce(v1) = v2 & visSomeExp(v2) = v3 & vapp(v1, v0) = all_63_1 & % 32.34/5.19 | | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 32.34/5.19 | | : ( ~ (vabs(v4, v5, v6) = v1) | ~ $i(v6) | ~ $i(v5) | ~ % 32.34/5.19 | | $i(v4))) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_63_0 = % 32.34/5.19 | | vnoExp & vabs(v0, v1, v2) = all_63_1 & $i(v2) & $i(v1) & $i(v0)) | % 32.34/5.19 | | ? [v0: $i] : (all_63_0 = vnoExp & vvar(v0) = all_63_1 & $i(v0)) % 32.34/5.19 | | % 32.34/5.19 | | BETA: splitting (57) gives: % 32.34/5.19 | | % 32.34/5.19 | | Case 1: % 32.34/5.19 | | | % 32.34/5.19 | | | (58) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 32.34/5.19 | | | $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & visSomeExp(v1) % 32.34/5.19 | | | = 0 & vsomeExp(v4) = all_63_0 & vapp(v3, v2) = v4 & vapp(v0, v2) % 32.34/5.19 | | | = all_63_1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! % 32.34/5.19 | | | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = % 32.34/5.19 | | | v0) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5))) | ? [v0: $i] : ? % 32.34/5.19 | | | [v1: $i] : ? [v2: $i] : ? [v3: int] : (all_63_0 = vnoExp & ~ % 32.34/5.19 | | | (v3 = 0) & vreduce(v1) = v2 & visSomeExp(v2) = v3 & vapp(v1, v0) % 32.34/5.19 | | | = all_63_1 & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: % 32.34/5.19 | | | $i] : ! [v6: $i] : ( ~ (vabs(v4, v5, v6) = v1) | ~ $i(v6) | % 32.34/5.19 | | | ~ $i(v5) | ~ $i(v4))) % 32.34/5.19 | | | % 32.34/5.19 | | | BETA: splitting (58) gives: % 32.34/5.19 | | | % 32.34/5.19 | | | Case 1: % 32.34/5.19 | | | | % 32.34/5.19 | | | | (59) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 32.34/5.19 | | | | $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & % 32.34/5.19 | | | | visSomeExp(v1) = 0 & vsomeExp(v4) = all_63_0 & vapp(v3, v2) = % 32.34/5.19 | | | | v4 & vapp(v0, v2) = all_63_1 & $i(v4) & $i(v3) & $i(v2) & % 32.34/5.19 | | | | $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( % 32.34/5.19 | | | | ~ (vabs(v5, v6, v7) = v0) | ~ $i(v7) | ~ $i(v6) | ~ % 32.34/5.19 | | | | $i(v5))) % 32.34/5.19 | | | | % 32.34/5.19 | | | | DELTA: instantiating (59) with fresh symbols all_111_0, all_111_1, % 32.34/5.19 | | | | all_111_2, all_111_3, all_111_4 gives: % 32.34/5.19 | | | | (60) vreduce(all_111_4) = all_111_3 & vgetSomeExp(all_111_3) = % 32.34/5.19 | | | | all_111_1 & visSomeExp(all_111_3) = 0 & vsomeExp(all_111_0) = % 32.34/5.19 | | | | all_63_0 & vapp(all_111_1, all_111_2) = all_111_0 & % 32.34/5.19 | | | | vapp(all_111_4, all_111_2) = all_63_1 & $i(all_111_0) & % 32.34/5.19 | | | | $i(all_111_1) & $i(all_111_2) & $i(all_111_3) & $i(all_111_4) & % 32.34/5.19 | | | | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vabs(v0, v1, v2) = % 32.34/5.19 | | | | all_111_4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 32.34/5.19 | | | | % 32.34/5.19 | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (12), (13), (14), % 32.34/5.19 | | | | (15), (16), (19), (20), (21), (24), (25), (26), (27), (28), % 32.34/5.19 | | | | (29), (31), (32), (60) are inconsistent by sub-proof #6. % 32.34/5.19 | | | | % 32.34/5.19 | | | Case 2: % 32.34/5.19 | | | | % 32.34/5.19 | | | | (61) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : % 32.34/5.19 | | | | (all_63_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) = v2 & % 32.34/5.19 | | | | visSomeExp(v2) = v3 & vapp(v1, v0) = all_63_1 & $i(v2) & % 32.34/5.19 | | | | $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 32.34/5.19 | | | | ~ (vabs(v4, v5, v6) = v1) | ~ $i(v6) | ~ $i(v5) | ~ % 32.34/5.19 | | | | $i(v4))) % 32.34/5.19 | | | | % 32.34/5.19 | | | | DELTA: instantiating (61) with fresh symbols all_111_0, all_111_1, % 32.34/5.19 | | | | all_111_2, all_111_3 gives: % 32.34/5.19 | | | | (62) all_63_0 = vnoExp & ~ (all_111_0 = 0) & vreduce(all_111_2) = % 32.34/5.19 | | | | all_111_1 & visSomeExp(all_111_1) = all_111_0 & vapp(all_111_2, % 32.34/5.19 | | | | all_111_3) = all_63_1 & $i(all_111_1) & $i(all_111_2) & % 32.34/5.19 | | | | $i(all_111_3) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 32.34/5.19 | | | | (vabs(v0, v1, v2) = all_111_2) | ~ $i(v2) | ~ $i(v1) | ~ % 32.34/5.19 | | | | $i(v0)) % 32.34/5.19 | | | | % 32.34/5.19 | | | | REF_CLOSE: (18), (20), (27), (62) are inconsistent by sub-proof #5. % 32.34/5.19 | | | | % 32.34/5.19 | | | End of split % 32.34/5.19 | | | % 32.34/5.19 | | Case 2: % 32.34/5.19 | | | % 32.34/5.19 | | | (63) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_63_0 = vnoExp & % 32.34/5.19 | | | vabs(v0, v1, v2) = all_63_1 & $i(v2) & $i(v1) & $i(v0)) | ? % 32.34/5.19 | | | [v0: $i] : (all_63_0 = vnoExp & vvar(v0) = all_63_1 & $i(v0)) % 32.34/5.19 | | | % 32.34/5.19 | | | BETA: splitting (63) gives: % 32.34/5.19 | | | % 32.34/5.19 | | | Case 1: % 32.34/5.19 | | | | % 32.34/5.19 | | | | (64) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_63_0 = vnoExp & % 32.34/5.19 | | | | vabs(v0, v1, v2) = all_63_1 & $i(v2) & $i(v1) & $i(v0)) % 32.34/5.19 | | | | % 32.34/5.19 | | | | DELTA: instantiating (64) with fresh symbols all_111_0, all_111_1, % 32.34/5.19 | | | | all_111_2 gives: % 32.34/5.19 | | | | (65) all_63_0 = vnoExp & vabs(all_111_2, all_111_1, all_111_0) = % 32.34/5.19 | | | | all_63_1 & $i(all_111_0) & $i(all_111_1) & $i(all_111_2) % 32.34/5.19 | | | | % 32.34/5.19 | | | | REF_CLOSE: (18), (20), (27), (65) are inconsistent by sub-proof #4. % 32.34/5.19 | | | | % 32.34/5.19 | | | Case 2: % 32.34/5.19 | | | | % 32.34/5.19 | | | | (66) ? [v0: $i] : (all_63_0 = vnoExp & vvar(v0) = all_63_1 & $i(v0)) % 32.34/5.19 | | | | % 32.34/5.19 | | | | DELTA: instantiating (66) with fresh symbol all_111_0 gives: % 32.34/5.19 | | | | (67) all_63_0 = vnoExp & vvar(all_111_0) = all_63_1 & $i(all_111_0) % 32.34/5.19 | | | | % 32.34/5.19 | | | | REF_CLOSE: (18), (20), (27), (67) are inconsistent by sub-proof #3. % 32.34/5.19 | | | | % 32.34/5.19 | | | End of split % 32.34/5.19 | | | % 32.34/5.19 | | End of split % 32.34/5.19 | | % 32.34/5.19 | End of split % 32.34/5.19 | % 32.34/5.19 End of proof % 32.34/5.19 % 32.34/5.19 Sub-proof #2 shows that the following formulas are inconsistent: % 32.34/5.19 ---------------------------------------------------------------- % 32.34/5.19 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 32.34/5.19 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ % 32.34/5.19 (vtcheck(v4, v3, v2) = v0)) % 32.34/5.19 (2) vtcheck(all_65_3, all_122_1, all_73_1) = all_144_0 % 32.34/5.19 (3) vtcheck(all_65_3, all_122_1, all_73_1) = 0 % 32.34/5.19 (4) ~ (all_144_0 = 0) % 32.34/5.19 % 32.34/5.19 Begin of proof % 32.34/5.19 | % 32.34/5.19 | GROUND_INST: instantiating (1) with all_144_0, 0, all_73_1, all_122_1, % 32.34/5.19 | all_65_3, simplifying with (2), (3) gives: % 32.34/5.19 | (5) all_144_0 = 0 % 32.34/5.19 | % 32.34/5.19 | REDUCE: (4), (5) imply: % 32.34/5.19 | (6) $false % 32.34/5.19 | % 32.34/5.19 | CLOSE: (6) is inconsistent. % 32.34/5.19 | % 32.34/5.19 End of proof % 32.34/5.19 % 32.34/5.19 Sub-proof #3 shows that the following formulas are inconsistent: % 32.34/5.19 ---------------------------------------------------------------- % 32.34/5.19 (1) all_63_0 = vnoExp & vvar(all_111_0) = all_63_1 & $i(all_111_0) % 32.34/5.19 (2) vsomeExp(all_65_2) = all_63_0 % 32.34/5.19 (3) ! [v0: $i] : ( ~ (vsomeExp(v0) = vnoExp) | ~ $i(v0)) % 32.34/5.19 (4) $i(all_65_2) % 32.34/5.19 % 32.34/5.19 Begin of proof % 32.34/5.19 | % 32.34/5.19 | ALPHA: (1) implies: % 32.34/5.19 | (5) all_63_0 = vnoExp % 32.34/5.19 | % 32.34/5.19 | REDUCE: (2), (5) imply: % 32.34/5.19 | (6) vsomeExp(all_65_2) = vnoExp % 32.34/5.19 | % 32.34/5.19 | GROUND_INST: instantiating (3) with all_65_2, simplifying with (4), (6) gives: % 32.34/5.19 | (7) $false % 32.34/5.19 | % 32.34/5.19 | CLOSE: (7) is inconsistent. % 32.34/5.19 | % 32.34/5.19 End of proof % 32.34/5.19 % 32.34/5.19 Sub-proof #4 shows that the following formulas are inconsistent: % 32.34/5.19 ---------------------------------------------------------------- % 32.34/5.19 (1) all_63_0 = vnoExp & vabs(all_111_2, all_111_1, all_111_0) = all_63_1 & % 32.34/5.19 $i(all_111_0) & $i(all_111_1) & $i(all_111_2) % 32.34/5.20 (2) vsomeExp(all_65_2) = all_63_0 % 32.34/5.20 (3) ! [v0: $i] : ( ~ (vsomeExp(v0) = vnoExp) | ~ $i(v0)) % 32.34/5.20 (4) $i(all_65_2) % 32.34/5.20 % 32.34/5.20 Begin of proof % 32.34/5.20 | % 32.34/5.20 | ALPHA: (1) implies: % 32.34/5.20 | (5) all_63_0 = vnoExp % 32.34/5.20 | % 32.34/5.20 | REDUCE: (2), (5) imply: % 32.34/5.20 | (6) vsomeExp(all_65_2) = vnoExp % 32.34/5.20 | % 32.34/5.20 | GROUND_INST: instantiating (3) with all_65_2, simplifying with (4), (6) gives: % 32.34/5.20 | (7) $false % 32.34/5.20 | % 32.34/5.20 | CLOSE: (7) is inconsistent. % 32.34/5.20 | % 32.34/5.20 End of proof % 32.34/5.20 % 32.34/5.20 Sub-proof #5 shows that the following formulas are inconsistent: % 32.34/5.20 ---------------------------------------------------------------- % 32.34/5.20 (1) all_63_0 = vnoExp & ~ (all_111_0 = 0) & vreduce(all_111_2) = all_111_1 & % 32.34/5.20 visSomeExp(all_111_1) = all_111_0 & vapp(all_111_2, all_111_3) = all_63_1 % 32.34/5.20 & $i(all_111_1) & $i(all_111_2) & $i(all_111_3) & ! [v0: $i] : ! [v1: % 32.34/5.20 $i] : ! [v2: $i] : ( ~ (vabs(v0, v1, v2) = all_111_2) | ~ $i(v2) | ~ % 32.34/5.20 $i(v1) | ~ $i(v0)) % 32.34/5.20 (2) vsomeExp(all_65_2) = all_63_0 % 32.34/5.20 (3) ! [v0: $i] : ( ~ (vsomeExp(v0) = vnoExp) | ~ $i(v0)) % 32.34/5.20 (4) $i(all_65_2) % 32.34/5.20 % 32.34/5.20 Begin of proof % 32.34/5.20 | % 32.34/5.20 | ALPHA: (1) implies: % 32.34/5.20 | (5) all_63_0 = vnoExp % 32.34/5.20 | % 32.34/5.20 | REDUCE: (2), (5) imply: % 32.34/5.20 | (6) vsomeExp(all_65_2) = vnoExp % 32.34/5.20 | % 32.34/5.20 | GROUND_INST: instantiating (3) with all_65_2, simplifying with (4), (6) gives: % 32.34/5.20 | (7) $false % 32.34/5.20 | % 32.34/5.20 | CLOSE: (7) is inconsistent. % 32.34/5.20 | % 32.34/5.20 End of proof % 32.34/5.20 % 32.34/5.20 Sub-proof #6 shows that the following formulas are inconsistent: % 32.34/5.20 ---------------------------------------------------------------- % 32.34/5.20 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v1) = % 32.34/5.20 v2) | ~ (vsomeExp(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 32.34/5.20 (2) $i(all_73_1) % 32.34/5.20 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vreduce(v2) = % 32.34/5.20 v1) | ~ (vreduce(v2) = v0)) % 32.34/5.20 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 32.34/5.20 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ % 32.34/5.20 (vtcheck(v4, v3, v2) = v0)) % 32.34/5.20 (5) $i(all_65_3) % 32.34/5.20 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (vgetSomeExp(v0) % 32.34/5.20 = v1) | ~ (vsomeExp(v2) = v0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 32.34/5.20 (7) vapp(ve1, ve2) = all_63_1 % 32.34/5.20 (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 32.34/5.20 [v5: $i] : ? [v6: int] : ? [v7: int] : (all_57_0 = vnoExp & ~ (v7 = 0) % 32.34/5.20 & ~ (v6 = 0) & vreduce(v4) = v3 & visSomeExp(v3) = v6 & visValue(v4) = % 32.34/5.20 v7 & vapp(v5, v4) = ve1 & vabs(v0, v1, v2) = v5 & $i(v5) & $i(v4) & % 32.34/5.20 $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? % 32.34/5.20 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? % 32.34/5.20 [v7: $i] : ( ~ (v6 = 0) & vreduce(v3) = v1 & visSomeExp(v1) = v6 & % 32.34/5.20 vsomeExp(v7) = all_57_0 & vsubst(v2, v3, v4) = v7 & visValue(v3) = 0 & % 32.34/5.20 vapp(v5, v3) = ve1 & vabs(v2, v0, v4) = v5 & $i(v7) & $i(v5) & $i(v4) & % 32.34/5.20 $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? % 32.34/5.20 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? % 32.34/5.20 [v7: $i] : (vreduce(v0) = v4 & vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 % 32.34/5.20 & vsomeExp(v7) = all_57_0 & vapp(v5, v6) = v7 & vapp(v5, v0) = ve1 & % 32.34/5.20 vabs(v1, v2, v3) = v5 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 32.34/5.20 $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 32.34/5.20 ? [v3: $i] : ? [v4: $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & % 32.34/5.20 visSomeExp(v1) = 0 & vsomeExp(v4) = all_57_0 & vapp(v3, v2) = v4 & % 32.34/5.20 vapp(v0, v2) = ve1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! % 32.34/5.20 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ % 32.34/5.20 $i(v7) | ~ $i(v6) | ~ $i(v5))) | ? [v0: $i] : ? [v1: $i] : ? % 32.34/5.20 [v2: $i] : ? [v3: int] : (all_57_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) % 32.34/5.20 = v2 & visSomeExp(v2) = v3 & vapp(v1, v0) = ve1 & $i(v2) & $i(v1) & % 32.34/5.20 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (vabs(v4, v5, % 32.34/5.20 v6) = v1) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4))) | ? [v0: $i] : % 32.34/5.20 ? [v1: $i] : ? [v2: $i] : (all_57_0 = vnoExp & vabs(v0, v1, v2) = ve1 & % 32.34/5.20 $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : (all_57_0 = vnoExp & vvar(v0) % 32.34/5.20 = ve1 & $i(v0)) % 32.34/5.20 (9) $i(all_73_0) % 32.34/5.20 (10) ~ (visSomeExp(vnoExp) = 0) % 32.34/5.20 (11) $i(ve2) % 32.34/5.20 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vsomeExp(v1) = all_57_0) % 32.34/5.20 | ~ (vtcheck(v0, ve1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 32.34/5.20 vtcheck(v0, v1, v2) = 0) % 32.34/5.20 (13) vreduce(ve1) = all_57_0 % 32.34/5.20 (14) vreduce(all_111_4) = all_111_3 & vgetSomeExp(all_111_3) = all_111_1 & % 32.34/5.20 visSomeExp(all_111_3) = 0 & vsomeExp(all_111_0) = all_63_0 & % 32.34/5.20 vapp(all_111_1, all_111_2) = all_111_0 & vapp(all_111_4, all_111_2) = % 32.34/5.20 all_63_1 & $i(all_111_0) & $i(all_111_1) & $i(all_111_2) & $i(all_111_3) % 32.34/5.20 & $i(all_111_4) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 32.34/5.20 (vabs(v0, v1, v2) = all_111_4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 32.34/5.20 (15) $i(ve1) % 32.34/5.20 (16) vsomeExp(all_65_2) = all_63_0 % 32.34/5.20 (17) ~ (all_65_0 = 0) % 32.34/5.20 (18) $i(all_65_1) % 32.34/5.20 (19) vtcheck(all_65_3, all_65_2, all_65_1) = all_65_0 % 32.34/5.20 (20) vtcheck(all_65_3, ve1, all_73_0) = 0 % 32.34/5.20 (21) $i(all_65_2) % 32.34/5.20 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 32.34/5.20 ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) % 32.34/5.20 | ~ $i(v1) | ~ $i(v0) | (v3 = v1 & v2 = v0)) % 32.34/5.20 (23) vtcheck(all_65_3, ve2, all_73_1) = 0 % 32.34/5.20 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 32.34/5.20 [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (varrow(v0, v4) = % 32.34/5.20 v5) | ~ (vtcheck(v1, v6, v4) = v7) | ~ (vtcheck(v1, v2, v5) = 0) | % 32.34/5.20 ~ (vapp(v2, v3) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 32.34/5.20 | ~ $i(v0) | ? [v8: int] : ( ~ (v8 = 0) & vtcheck(v1, v3, v0) = v8)) % 32.34/5.20 (25) varrow(all_73_1, all_65_1) = all_73_0 % 32.34/5.20 % 32.34/5.20 Begin of proof % 32.34/5.20 | % 32.34/5.20 | ALPHA: (14) implies: % 32.34/5.20 | (26) $i(all_111_4) % 32.34/5.20 | (27) $i(all_111_3) % 32.34/5.20 | (28) $i(all_111_2) % 32.34/5.20 | (29) $i(all_111_1) % 32.34/5.20 | (30) $i(all_111_0) % 32.34/5.20 | (31) vapp(all_111_4, all_111_2) = all_63_1 % 32.34/5.20 | (32) vapp(all_111_1, all_111_2) = all_111_0 % 32.34/5.20 | (33) vsomeExp(all_111_0) = all_63_0 % 32.34/5.20 | (34) visSomeExp(all_111_3) = 0 % 32.34/5.20 | (35) vgetSomeExp(all_111_3) = all_111_1 % 32.34/5.20 | (36) vreduce(all_111_4) = all_111_3 % 32.34/5.20 | % 32.34/5.20 | GROUND_INST: instantiating (22) with ve1, ve2, all_111_4, all_111_2, all_63_1, % 32.34/5.20 | simplifying with (7), (11), (15), (26), (28), (31) gives: % 32.34/5.20 | (37) all_111_2 = ve2 & all_111_4 = ve1 % 32.34/5.20 | % 32.34/5.20 | ALPHA: (37) implies: % 32.34/5.20 | (38) all_111_4 = ve1 % 32.34/5.20 | (39) all_111_2 = ve2 % 32.34/5.20 | % 32.34/5.20 | GROUND_INST: instantiating (1) with all_65_2, all_111_0, all_63_0, simplifying % 32.34/5.20 | with (16), (21), (30), (33) gives: % 32.34/5.20 | (40) all_111_0 = all_65_2 % 32.34/5.20 | % 32.34/5.20 | REDUCE: (36), (38) imply: % 32.34/5.20 | (41) vreduce(ve1) = all_111_3 % 32.34/5.20 | % 32.34/5.20 | REDUCE: (32), (39), (40) imply: % 32.34/5.20 | (42) vapp(all_111_1, ve2) = all_65_2 % 32.34/5.20 | % 32.34/5.20 | GROUND_INST: instantiating (3) with all_57_0, all_111_3, ve1, simplifying with % 32.34/5.20 | (13), (41) gives: % 32.34/5.20 | (43) all_111_3 = all_57_0 % 32.34/5.20 | % 32.34/5.20 | REDUCE: (35), (43) imply: % 32.34/5.20 | (44) vgetSomeExp(all_57_0) = all_111_1 % 32.34/5.20 | % 32.34/5.20 | REDUCE: (34), (43) imply: % 32.34/5.20 | (45) visSomeExp(all_57_0) = 0 % 32.34/5.20 | % 32.34/5.20 | REDUCE: (27), (43) imply: % 32.34/5.20 | (46) $i(all_57_0) % 32.34/5.20 | % 32.34/5.20 | BETA: splitting (8) gives: % 32.34/5.20 | % 32.34/5.20 | Case 1: % 32.34/5.20 | | % 32.34/5.20 | | (47) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 32.34/5.20 | | : ? [v5: $i] : ? [v6: int] : ? [v7: int] : (all_57_0 = vnoExp & % 32.34/5.20 | | ~ (v7 = 0) & ~ (v6 = 0) & vreduce(v4) = v3 & visSomeExp(v3) = v6 % 32.34/5.20 | | & visValue(v4) = v7 & vapp(v5, v4) = ve1 & vabs(v0, v1, v2) = v5 & % 32.34/5.20 | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] % 32.34/5.20 | | : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 32.34/5.20 | | $i] : ? [v6: int] : ? [v7: $i] : ( ~ (v6 = 0) & vreduce(v3) = v1 % 32.34/5.20 | | & visSomeExp(v1) = v6 & vsomeExp(v7) = all_57_0 & vsubst(v2, v3, % 32.34/5.20 | | v4) = v7 & visValue(v3) = 0 & vapp(v5, v3) = ve1 & vabs(v2, v0, % 32.34/5.20 | | v4) = v5 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 32.34/5.20 | | $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 32.34/5.20 | | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vreduce(v0) % 32.34/5.20 | | = v4 & vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & vsomeExp(v7) = % 32.34/5.20 | | all_57_0 & vapp(v5, v6) = v7 & vapp(v5, v0) = ve1 & vabs(v1, v2, % 32.34/5.20 | | v3) = v5 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 32.34/5.20 | | $i(v1) & $i(v0)) % 32.34/5.20 | | % 32.34/5.20 | | BETA: splitting (47) gives: % 32.34/5.20 | | % 32.34/5.20 | | Case 1: % 32.34/5.20 | | | % 32.34/5.20 | | | (48) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 32.34/5.20 | | | $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : (all_57_0 = % 32.34/5.20 | | | vnoExp & ~ (v7 = 0) & ~ (v6 = 0) & vreduce(v4) = v3 & % 32.34/5.20 | | | visSomeExp(v3) = v6 & visValue(v4) = v7 & vapp(v5, v4) = ve1 & % 32.34/5.20 | | | vabs(v0, v1, v2) = v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 32.34/5.20 | | | $i(v1) & $i(v0)) % 32.34/5.20 | | | % 32.34/5.20 | | | DELTA: instantiating (48) with fresh symbols all_130_0, all_130_1, % 32.34/5.20 | | | all_130_2, all_130_3, all_130_4, all_130_5, all_130_6, all_130_7 % 32.34/5.20 | | | gives: % 32.34/5.20 | | | (49) all_57_0 = vnoExp & ~ (all_130_0 = 0) & ~ (all_130_1 = 0) & % 32.34/5.20 | | | vreduce(all_130_3) = all_130_4 & visSomeExp(all_130_4) = all_130_1 % 32.34/5.20 | | | & visValue(all_130_3) = all_130_0 & vapp(all_130_2, all_130_3) = % 32.34/5.20 | | | ve1 & vabs(all_130_7, all_130_6, all_130_5) = all_130_2 & % 32.34/5.20 | | | $i(all_130_2) & $i(all_130_3) & $i(all_130_4) & $i(all_130_5) & % 32.34/5.20 | | | $i(all_130_6) & $i(all_130_7) % 32.34/5.20 | | | % 32.34/5.20 | | | ALPHA: (49) implies: % 32.34/5.20 | | | (50) all_57_0 = vnoExp % 32.34/5.20 | | | % 32.34/5.20 | | | REDUCE: (45), (50) imply: % 32.34/5.20 | | | (51) visSomeExp(vnoExp) = 0 % 32.34/5.20 | | | % 32.34/5.20 | | | PRED_UNIFY: (10), (51) imply: % 32.34/5.20 | | | (52) $false % 32.34/5.20 | | | % 32.34/5.20 | | | CLOSE: (52) is inconsistent. % 32.34/5.20 | | | % 32.34/5.20 | | Case 2: % 32.34/5.20 | | | % 32.34/5.21 | | | (53) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 32.34/5.21 | | | $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ( ~ (v6 = 0) & % 32.34/5.21 | | | vreduce(v3) = v1 & visSomeExp(v1) = v6 & vsomeExp(v7) = all_57_0 % 32.34/5.21 | | | & vsubst(v2, v3, v4) = v7 & visValue(v3) = 0 & vapp(v5, v3) = % 32.34/5.21 | | | ve1 & vabs(v2, v0, v4) = v5 & $i(v7) & $i(v5) & $i(v4) & $i(v3) % 32.34/5.21 | | | & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? % 32.34/5.21 | | | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 32.34/5.21 | | | ? [v7: $i] : (vreduce(v0) = v4 & vgetSomeExp(v4) = v6 & % 32.34/5.21 | | | visSomeExp(v4) = 0 & vsomeExp(v7) = all_57_0 & vapp(v5, v6) = v7 % 32.34/5.21 | | | & vapp(v5, v0) = ve1 & vabs(v1, v2, v3) = v5 & $i(v7) & $i(v6) & % 32.34/5.21 | | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.34/5.21 | | | % 32.34/5.21 | | | BETA: splitting (53) gives: % 32.34/5.21 | | | % 32.34/5.21 | | | Case 1: % 32.34/5.21 | | | | % 32.34/5.21 | | | | (54) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 32.34/5.21 | | | | $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ( ~ (v6 = 0) % 32.34/5.21 | | | | & vreduce(v3) = v1 & visSomeExp(v1) = v6 & vsomeExp(v7) = % 32.34/5.21 | | | | all_57_0 & vsubst(v2, v3, v4) = v7 & visValue(v3) = 0 & % 32.34/5.21 | | | | vapp(v5, v3) = ve1 & vabs(v2, v0, v4) = v5 & $i(v7) & $i(v5) & % 32.34/5.21 | | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 32.34/5.21 | | | | % 32.34/5.21 | | | | DELTA: instantiating (54) with fresh symbols all_130_0, all_130_1, % 32.34/5.21 | | | | all_130_2, all_130_3, all_130_4, all_130_5, all_130_6, all_130_7 % 32.34/5.21 | | | | gives: % 32.34/5.21 | | | | (55) ~ (all_130_1 = 0) & vreduce(all_130_4) = all_130_6 & % 32.34/5.21 | | | | visSomeExp(all_130_6) = all_130_1 & vsomeExp(all_130_0) = % 32.34/5.21 | | | | all_57_0 & vsubst(all_130_5, all_130_4, all_130_3) = all_130_0 & % 32.34/5.21 | | | | visValue(all_130_4) = 0 & vapp(all_130_2, all_130_4) = ve1 & % 32.34/5.21 | | | | vabs(all_130_5, all_130_7, all_130_3) = all_130_2 & % 32.34/5.21 | | | | $i(all_130_0) & $i(all_130_2) & $i(all_130_3) & $i(all_130_4) & % 32.34/5.21 | | | | $i(all_130_5) & $i(all_130_6) & $i(all_130_7) % 32.34/5.21 | | | | % 32.34/5.21 | | | | ALPHA: (55) implies: % 32.34/5.21 | | | | (56) vsomeExp(all_130_0) = all_57_0 % 32.34/5.21 | | | | (57) $i(all_130_0) % 32.34/5.21 | | | | % 32.34/5.21 | | | | GROUND_INST: instantiating (6) with all_57_0, all_111_1, all_130_0, % 32.34/5.21 | | | | simplifying with (29), (44), (46), (56), (57) gives: % 32.34/5.21 | | | | (58) all_130_0 = all_111_1 % 32.34/5.21 | | | | % 32.34/5.21 | | | | GROUND_INST: instantiating (12) with all_65_3, all_130_0, all_73_0, % 32.34/5.21 | | | | simplifying with (5), (9), (20), (56), (57) gives: % 32.34/5.21 | | | | (59) vtcheck(all_65_3, all_130_0, all_73_0) = 0 % 32.34/5.21 | | | | % 32.34/5.21 | | | | REDUCE: (58), (59) imply: % 32.34/5.21 | | | | (60) vtcheck(all_65_3, all_111_1, all_73_0) = 0 % 32.34/5.21 | | | | % 32.34/5.21 | | | | GROUND_INST: instantiating (24) with all_73_1, all_65_3, all_111_1, ve2, % 32.34/5.21 | | | | all_65_1, all_73_0, all_65_2, all_65_0, simplifying with % 32.34/5.21 | | | | (2), (5), (11), (18), (19), (25), (29), (42), (60) gives: % 32.34/5.21 | | | | (61) all_65_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & vtcheck(all_65_3, % 32.34/5.21 | | | | ve2, all_73_1) = v0) % 32.34/5.21 | | | | % 32.34/5.21 | | | | REF_CLOSE: (4), (17), (23), (61) are inconsistent by sub-proof #8. % 32.34/5.21 | | | | % 32.34/5.21 | | | Case 2: % 32.34/5.21 | | | | % 32.34/5.21 | | | | (62) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 32.34/5.21 | | | | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vreduce(v0) = % 32.34/5.21 | | | | v4 & vgetSomeExp(v4) = v6 & visSomeExp(v4) = 0 & vsomeExp(v7) % 32.34/5.21 | | | | = all_57_0 & vapp(v5, v6) = v7 & vapp(v5, v0) = ve1 & vabs(v1, % 32.34/5.21 | | | | v2, v3) = v5 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 32.34/5.21 | | | | $i(v2) & $i(v1) & $i(v0)) % 32.34/5.21 | | | | % 32.34/5.21 | | | | DELTA: instantiating (62) with fresh symbols all_130_0, all_130_1, % 32.34/5.21 | | | | all_130_2, all_130_3, all_130_4, all_130_5, all_130_6, all_130_7 % 32.34/5.21 | | | | gives: % 32.34/5.21 | | | | (63) vreduce(all_130_7) = all_130_3 & vgetSomeExp(all_130_3) = % 32.34/5.21 | | | | all_130_1 & visSomeExp(all_130_3) = 0 & vsomeExp(all_130_0) = % 32.34/5.21 | | | | all_57_0 & vapp(all_130_2, all_130_1) = all_130_0 & % 32.34/5.21 | | | | vapp(all_130_2, all_130_7) = ve1 & vabs(all_130_6, all_130_5, % 32.34/5.21 | | | | all_130_4) = all_130_2 & $i(all_130_0) & $i(all_130_1) & % 32.34/5.21 | | | | $i(all_130_2) & $i(all_130_3) & $i(all_130_4) & $i(all_130_5) & % 32.34/5.21 | | | | $i(all_130_6) & $i(all_130_7) % 32.34/5.21 | | | | % 32.34/5.21 | | | | ALPHA: (63) implies: % 32.34/5.21 | | | | (64) $i(all_130_0) % 32.34/5.21 | | | | (65) vsomeExp(all_130_0) = all_57_0 % 32.34/5.21 | | | | % 32.34/5.21 | | | | GROUND_INST: instantiating (6) with all_57_0, all_111_1, all_130_0, % 32.34/5.21 | | | | simplifying with (29), (44), (46), (64), (65) gives: % 32.34/5.21 | | | | (66) all_130_0 = all_111_1 % 32.34/5.21 | | | | % 32.34/5.21 | | | | GROUND_INST: instantiating (12) with all_65_3, all_130_0, all_73_0, % 32.34/5.21 | | | | simplifying with (5), (9), (20), (64), (65) gives: % 32.34/5.21 | | | | (67) vtcheck(all_65_3, all_130_0, all_73_0) = 0 % 32.34/5.21 | | | | % 32.34/5.21 | | | | REDUCE: (66), (67) imply: % 32.34/5.21 | | | | (68) vtcheck(all_65_3, all_111_1, all_73_0) = 0 % 32.34/5.21 | | | | % 32.34/5.21 | | | | GROUND_INST: instantiating (24) with all_73_1, all_65_3, all_111_1, ve2, % 32.34/5.21 | | | | all_65_1, all_73_0, all_65_2, all_65_0, simplifying with % 32.34/5.21 | | | | (2), (5), (11), (18), (19), (25), (29), (42), (68) gives: % 32.34/5.21 | | | | (69) all_65_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & vtcheck(all_65_3, % 32.34/5.21 | | | | ve2, all_73_1) = v0) % 32.34/5.21 | | | | % 32.34/5.21 | | | | REF_CLOSE: (4), (17), (23), (69) are inconsistent by sub-proof #8. % 32.34/5.21 | | | | % 32.34/5.21 | | | End of split % 32.34/5.21 | | | % 32.34/5.21 | | End of split % 32.34/5.21 | | % 32.34/5.21 | Case 2: % 32.34/5.21 | | % 32.34/5.21 | | (70) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 32.34/5.21 | | : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & visSomeExp(v1) = 0 & % 32.34/5.21 | | vsomeExp(v4) = all_57_0 & vapp(v3, v2) = v4 & vapp(v0, v2) = ve1 & % 32.34/5.21 | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: % 32.34/5.21 | | $i] : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ $i(v7) | ~ % 32.34/5.21 | | $i(v6) | ~ $i(v5))) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 32.34/5.21 | | ? [v3: int] : (all_57_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) = v2 & % 32.34/5.21 | | visSomeExp(v2) = v3 & vapp(v1, v0) = ve1 & $i(v2) & $i(v1) & % 32.34/5.21 | | $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (vabs(v4, % 32.34/5.21 | | v5, v6) = v1) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4))) | ? % 32.34/5.21 | | [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_57_0 = vnoExp & vabs(v0, % 32.34/5.21 | | v1, v2) = ve1 & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 32.34/5.21 | | (all_57_0 = vnoExp & vvar(v0) = ve1 & $i(v0)) % 32.34/5.21 | | % 32.34/5.21 | | BETA: splitting (70) gives: % 32.34/5.21 | | % 32.34/5.21 | | Case 1: % 32.34/5.21 | | | % 32.34/5.21 | | | (71) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 32.34/5.21 | | | $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & visSomeExp(v1) % 32.34/5.21 | | | = 0 & vsomeExp(v4) = all_57_0 & vapp(v3, v2) = v4 & vapp(v0, v2) % 32.34/5.21 | | | = ve1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] % 32.34/5.21 | | | : ! [v6: $i] : ! [v7: $i] : ( ~ (vabs(v5, v6, v7) = v0) | ~ % 32.34/5.21 | | | $i(v7) | ~ $i(v6) | ~ $i(v5))) | ? [v0: $i] : ? [v1: $i] : % 32.34/5.21 | | | ? [v2: $i] : ? [v3: int] : (all_57_0 = vnoExp & ~ (v3 = 0) & % 32.34/5.21 | | | vreduce(v1) = v2 & visSomeExp(v2) = v3 & vapp(v1, v0) = ve1 & % 32.34/5.21 | | | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: % 32.34/5.21 | | | $i] : ( ~ (vabs(v4, v5, v6) = v1) | ~ $i(v6) | ~ $i(v5) | ~ % 32.34/5.21 | | | $i(v4))) % 32.34/5.21 | | | % 32.34/5.21 | | | BETA: splitting (71) gives: % 32.34/5.21 | | | % 32.34/5.21 | | | Case 1: % 32.34/5.21 | | | | % 32.34/5.21 | | | | (72) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 32.34/5.21 | | | | $i] : (vreduce(v0) = v1 & vgetSomeExp(v1) = v3 & % 32.34/5.21 | | | | visSomeExp(v1) = 0 & vsomeExp(v4) = all_57_0 & vapp(v3, v2) = % 32.34/5.21 | | | | v4 & vapp(v0, v2) = ve1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 32.34/5.21 | | | | $i(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 32.34/5.21 | | | | (vabs(v5, v6, v7) = v0) | ~ $i(v7) | ~ $i(v6) | ~ % 32.34/5.21 | | | | $i(v5))) % 32.34/5.21 | | | | % 32.34/5.21 | | | | DELTA: instantiating (72) with fresh symbols all_130_0, all_130_1, % 32.34/5.21 | | | | all_130_2, all_130_3, all_130_4 gives: % 32.34/5.21 | | | | (73) vreduce(all_130_4) = all_130_3 & vgetSomeExp(all_130_3) = % 32.34/5.21 | | | | all_130_1 & visSomeExp(all_130_3) = 0 & vsomeExp(all_130_0) = % 32.34/5.21 | | | | all_57_0 & vapp(all_130_1, all_130_2) = all_130_0 & % 32.34/5.21 | | | | vapp(all_130_4, all_130_2) = ve1 & $i(all_130_0) & $i(all_130_1) % 32.34/5.21 | | | | & $i(all_130_2) & $i(all_130_3) & $i(all_130_4) & ! [v0: $i] : % 32.34/5.21 | | | | ! [v1: $i] : ! [v2: $i] : ( ~ (vabs(v0, v1, v2) = all_130_4) | % 32.34/5.21 | | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 32.34/5.21 | | | | % 32.34/5.21 | | | | ALPHA: (73) implies: % 32.34/5.21 | | | | (74) vsomeExp(all_130_0) = all_57_0 % 32.34/5.21 | | | | (75) $i(all_130_0) % 32.34/5.21 | | | | % 32.34/5.21 | | | | GROUND_INST: instantiating (6) with all_57_0, all_111_1, all_130_0, % 32.34/5.21 | | | | simplifying with (29), (44), (46), (74), (75) gives: % 32.34/5.21 | | | | (76) all_130_0 = all_111_1 % 32.34/5.21 | | | | % 32.34/5.21 | | | | GROUND_INST: instantiating (12) with all_65_3, all_130_0, all_73_0, % 32.34/5.21 | | | | simplifying with (5), (9), (20), (74), (75) gives: % 32.34/5.21 | | | | (77) vtcheck(all_65_3, all_130_0, all_73_0) = 0 % 32.34/5.21 | | | | % 32.34/5.21 | | | | REDUCE: (76), (77) imply: % 32.34/5.21 | | | | (78) vtcheck(all_65_3, all_111_1, all_73_0) = 0 % 32.34/5.21 | | | | % 32.34/5.21 | | | | GROUND_INST: instantiating (24) with all_73_1, all_65_3, all_111_1, ve2, % 32.34/5.21 | | | | all_65_1, all_73_0, all_65_2, all_65_0, simplifying with % 32.34/5.21 | | | | (2), (5), (11), (18), (19), (25), (29), (42), (78) gives: % 32.34/5.21 | | | | (79) all_65_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & vtcheck(all_65_3, % 32.34/5.21 | | | | ve2, all_73_1) = v0) % 32.34/5.21 | | | | % 32.34/5.21 | | | | REF_CLOSE: (4), (17), (23), (79) are inconsistent by sub-proof #8. % 32.34/5.21 | | | | % 32.34/5.21 | | | Case 2: % 32.34/5.21 | | | | % 32.34/5.21 | | | | (80) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : % 32.34/5.21 | | | | (all_57_0 = vnoExp & ~ (v3 = 0) & vreduce(v1) = v2 & % 32.34/5.21 | | | | visSomeExp(v2) = v3 & vapp(v1, v0) = ve1 & $i(v2) & $i(v1) & % 32.34/5.21 | | | | $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 32.34/5.21 | | | | (vabs(v4, v5, v6) = v1) | ~ $i(v6) | ~ $i(v5) | ~ % 32.34/5.21 | | | | $i(v4))) % 32.34/5.21 | | | | % 32.34/5.21 | | | | DELTA: instantiating (80) with fresh symbols all_130_0, all_130_1, % 32.34/5.21 | | | | all_130_2, all_130_3 gives: % 32.34/5.21 | | | | (81) all_57_0 = vnoExp & ~ (all_130_0 = 0) & vreduce(all_130_2) = % 32.34/5.21 | | | | all_130_1 & visSomeExp(all_130_1) = all_130_0 & vapp(all_130_2, % 32.34/5.21 | | | | all_130_3) = ve1 & $i(all_130_1) & $i(all_130_2) & % 32.34/5.21 | | | | $i(all_130_3) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 32.34/5.21 | | | | (vabs(v0, v1, v2) = all_130_2) | ~ $i(v2) | ~ $i(v1) | ~ % 32.34/5.21 | | | | $i(v0)) % 32.34/5.21 | | | | % 32.34/5.21 | | | | ALPHA: (81) implies: % 32.34/5.21 | | | | (82) all_57_0 = vnoExp % 32.34/5.21 | | | | % 32.34/5.21 | | | | REDUCE: (45), (82) imply: % 32.34/5.21 | | | | (83) visSomeExp(vnoExp) = 0 % 32.34/5.21 | | | | % 32.34/5.21 | | | | PRED_UNIFY: (10), (83) imply: % 32.34/5.21 | | | | (84) $false % 32.34/5.21 | | | | % 32.34/5.21 | | | | CLOSE: (84) is inconsistent. % 32.34/5.21 | | | | % 32.34/5.21 | | | End of split % 32.34/5.21 | | | % 32.34/5.21 | | Case 2: % 32.34/5.21 | | | % 32.34/5.21 | | | (85) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_57_0 = vnoExp & % 32.34/5.21 | | | vabs(v0, v1, v2) = ve1 & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] % 32.34/5.21 | | | : (all_57_0 = vnoExp & vvar(v0) = ve1 & $i(v0)) % 32.34/5.21 | | | % 32.34/5.21 | | | BETA: splitting (85) gives: % 32.34/5.21 | | | % 32.34/5.21 | | | Case 1: % 32.34/5.21 | | | | % 32.34/5.21 | | | | (86) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (all_57_0 = vnoExp & % 32.34/5.21 | | | | vabs(v0, v1, v2) = ve1 & $i(v2) & $i(v1) & $i(v0)) % 32.34/5.21 | | | | % 32.34/5.21 | | | | DELTA: instantiating (86) with fresh symbols all_130_0, all_130_1, % 32.34/5.21 | | | | all_130_2 gives: % 32.34/5.21 | | | | (87) all_57_0 = vnoExp & vabs(all_130_2, all_130_1, all_130_0) = ve1 % 32.34/5.21 | | | | & $i(all_130_0) & $i(all_130_1) & $i(all_130_2) % 32.34/5.22 | | | | % 32.34/5.22 | | | | ALPHA: (87) implies: % 32.34/5.22 | | | | (88) all_57_0 = vnoExp % 32.34/5.22 | | | | % 32.34/5.22 | | | | REDUCE: (45), (88) imply: % 32.34/5.22 | | | | (89) visSomeExp(vnoExp) = 0 % 32.34/5.22 | | | | % 32.34/5.22 | | | | PRED_UNIFY: (10), (89) imply: % 32.34/5.22 | | | | (90) $false % 32.34/5.22 | | | | % 32.34/5.22 | | | | CLOSE: (90) is inconsistent. % 32.34/5.22 | | | | % 32.34/5.22 | | | Case 2: % 32.34/5.22 | | | | % 32.34/5.22 | | | | (91) ? [v0: $i] : (all_57_0 = vnoExp & vvar(v0) = ve1 & $i(v0)) % 32.34/5.22 | | | | % 32.34/5.22 | | | | DELTA: instantiating (91) with fresh symbol all_130_0 gives: % 32.34/5.22 | | | | (92) all_57_0 = vnoExp & vvar(all_130_0) = ve1 & $i(all_130_0) % 32.34/5.22 | | | | % 32.34/5.22 | | | | ALPHA: (92) implies: % 32.34/5.22 | | | | (93) all_57_0 = vnoExp % 32.34/5.22 | | | | % 32.34/5.22 | | | | REDUCE: (45), (93) imply: % 32.34/5.22 | | | | (94) visSomeExp(vnoExp) = 0 % 32.34/5.22 | | | | % 32.34/5.22 | | | | PRED_UNIFY: (10), (94) imply: % 32.34/5.22 | | | | (95) $false % 32.34/5.22 | | | | % 32.34/5.22 | | | | CLOSE: (95) is inconsistent. % 32.34/5.22 | | | | % 32.34/5.22 | | | End of split % 32.34/5.22 | | | % 32.34/5.22 | | End of split % 32.34/5.22 | | % 32.34/5.22 | End of split % 32.34/5.22 | % 32.34/5.22 End of proof % 32.34/5.22 % 32.34/5.22 Sub-proof #7 shows that the following formulas are inconsistent: % 32.34/5.22 ---------------------------------------------------------------- % 32.34/5.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vreduce(v2) = % 32.34/5.22 v1) | ~ (vreduce(v2) = v0)) % 32.34/5.22 (2) vapp(ve1, ve2) = all_63_1 % 32.34/5.22 (3) ~ (visSomeExp(vnoExp) = 0) % 32.34/5.22 (4) $i(ve2) % 32.34/5.22 (5) $i(ve1) % 32.34/5.22 (6) vreduce(all_111_7) = all_111_3 & vgetSomeExp(all_111_3) = all_111_1 & % 32.34/5.22 visSomeExp(all_111_3) = 0 & vsomeExp(all_111_0) = all_63_0 & % 32.34/5.22 vapp(all_111_2, all_111_1) = all_111_0 & vapp(all_111_2, all_111_7) = % 32.34/5.22 all_63_1 & vabs(all_111_6, all_111_5, all_111_4) = all_111_2 & % 32.34/5.22 $i(all_111_0) & $i(all_111_1) & $i(all_111_2) & $i(all_111_3) & % 32.34/5.22 $i(all_111_4) & $i(all_111_5) & $i(all_111_6) & $i(all_111_7) % 32.34/5.22 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 32.34/5.22 (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 32.34/5.22 ~ $i(v1) | ~ $i(v0) | (v3 = v1 & v2 = v0)) % 32.34/5.22 (8) vreduce(ve2) = vnoExp % 32.34/5.22 % 32.34/5.22 Begin of proof % 32.34/5.22 | % 32.34/5.22 | ALPHA: (6) implies: % 32.34/5.22 | (9) $i(all_111_7) % 32.34/5.22 | (10) $i(all_111_2) % 32.34/5.22 | (11) vapp(all_111_2, all_111_7) = all_63_1 % 32.34/5.22 | (12) visSomeExp(all_111_3) = 0 % 32.34/5.22 | (13) vreduce(all_111_7) = all_111_3 % 32.34/5.22 | % 32.34/5.22 | GROUND_INST: instantiating (7) with ve1, ve2, all_111_2, all_111_7, all_63_1, % 32.34/5.22 | simplifying with (2), (4), (5), (9), (10), (11) gives: % 32.34/5.22 | (14) all_111_2 = ve1 & all_111_7 = ve2 % 32.34/5.22 | % 32.34/5.22 | ALPHA: (14) implies: % 32.34/5.22 | (15) all_111_7 = ve2 % 32.34/5.22 | % 32.34/5.22 | REDUCE: (13), (15) imply: % 32.34/5.22 | (16) vreduce(ve2) = all_111_3 % 32.34/5.22 | % 32.34/5.22 | GROUND_INST: instantiating (1) with vnoExp, all_111_3, ve2, simplifying with % 32.34/5.22 | (8), (16) gives: % 32.34/5.22 | (17) all_111_3 = vnoExp % 32.34/5.22 | % 32.34/5.22 | REDUCE: (12), (17) imply: % 32.34/5.22 | (18) visSomeExp(vnoExp) = 0 % 32.34/5.22 | % 32.34/5.22 | PRED_UNIFY: (3), (18) imply: % 32.34/5.22 | (19) $false % 32.34/5.22 | % 32.34/5.22 | CLOSE: (19) is inconsistent. % 32.34/5.22 | % 32.34/5.22 End of proof % 32.34/5.22 % 32.34/5.22 Sub-proof #8 shows that the following formulas are inconsistent: % 32.34/5.22 ---------------------------------------------------------------- % 32.34/5.22 (1) all_65_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & vtcheck(all_65_3, ve2, % 32.34/5.22 all_73_1) = v0) % 32.34/5.22 (2) ~ (all_65_0 = 0) % 32.34/5.22 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 32.34/5.22 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ % 32.34/5.22 (vtcheck(v4, v3, v2) = v0)) % 32.34/5.22 (4) vtcheck(all_65_3, ve2, all_73_1) = 0 % 32.34/5.22 % 32.34/5.22 Begin of proof % 32.34/5.22 | % 32.34/5.22 | BETA: splitting (1) gives: % 32.34/5.22 | % 32.34/5.22 | Case 1: % 32.34/5.22 | | % 32.34/5.22 | | (5) all_65_0 = 0 % 32.34/5.22 | | % 32.34/5.22 | | REDUCE: (2), (5) imply: % 32.34/5.22 | | (6) $false % 32.34/5.22 | | % 32.34/5.22 | | CLOSE: (6) is inconsistent. % 32.34/5.22 | | % 32.34/5.22 | Case 2: % 32.34/5.22 | | % 32.34/5.22 | | (7) ? [v0: int] : ( ~ (v0 = 0) & vtcheck(all_65_3, ve2, all_73_1) = v0) % 32.34/5.22 | | % 32.34/5.22 | | DELTA: instantiating (7) with fresh symbol all_150_0 gives: % 32.34/5.22 | | (8) ~ (all_150_0 = 0) & vtcheck(all_65_3, ve2, all_73_1) = all_150_0 % 32.34/5.22 | | % 32.34/5.22 | | ALPHA: (8) implies: % 32.34/5.22 | | (9) ~ (all_150_0 = 0) % 32.34/5.22 | | (10) vtcheck(all_65_3, ve2, all_73_1) = all_150_0 % 32.34/5.22 | | % 32.34/5.22 | | GROUND_INST: instantiating (3) with 0, all_150_0, all_73_1, ve2, all_65_3, % 32.34/5.22 | | simplifying with (4), (10) gives: % 32.34/5.22 | | (11) all_150_0 = 0 % 32.34/5.22 | | % 32.34/5.22 | | REDUCE: (9), (11) imply: % 32.34/5.22 | | (12) $false % 32.34/5.22 | | % 32.34/5.22 | | CLOSE: (12) is inconsistent. % 32.34/5.22 | | % 32.34/5.22 | End of split % 32.34/5.22 | % 32.34/5.22 End of proof % 32.34/5.22 % 32.34/5.22 Sub-proof #9 shows that the following formulas are inconsistent: % 32.34/5.22 ---------------------------------------------------------------- % 32.34/5.22 (1) all_63_0 = vnoExp & ~ (all_111_0 = 0) & ~ (all_111_1 = 0) & % 32.34/5.22 vreduce(all_111_3) = all_111_4 & visSomeExp(all_111_4) = all_111_1 & % 32.34/5.22 visValue(all_111_3) = all_111_0 & vapp(all_111_2, all_111_3) = all_63_1 & % 32.34/5.22 vabs(all_111_7, all_111_6, all_111_5) = all_111_2 & $i(all_111_2) & % 32.34/5.22 $i(all_111_3) & $i(all_111_4) & $i(all_111_5) & $i(all_111_6) & % 32.34/5.22 $i(all_111_7) % 32.34/5.22 (2) vsomeExp(all_65_2) = all_63_0 % 32.34/5.22 (3) ! [v0: $i] : ( ~ (vsomeExp(v0) = vnoExp) | ~ $i(v0)) % 32.34/5.22 (4) $i(all_65_2) % 32.34/5.22 % 32.34/5.22 Begin of proof % 32.34/5.22 | % 32.34/5.22 | ALPHA: (1) implies: % 32.34/5.22 | (5) all_63_0 = vnoExp % 32.34/5.22 | % 32.34/5.22 | REDUCE: (2), (5) imply: % 32.34/5.22 | (6) vsomeExp(all_65_2) = vnoExp % 32.34/5.22 | % 32.34/5.22 | GROUND_INST: instantiating (3) with all_65_2, simplifying with (4), (6) gives: % 32.34/5.22 | (7) $false % 32.34/5.22 | % 32.34/5.22 | CLOSE: (7) is inconsistent. % 32.34/5.22 | % 32.34/5.22 End of proof % 32.34/5.22 % SZS output end Proof for theBenchmark % 32.34/5.22 % 32.34/5.22 4551ms %------------------------------------------------------------------------------