TSTP Solution File: COM139+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM139+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 : n025.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 18:44:35 EDT 2023
% Result : Theorem 13.13s 2.54s
% Output : Proof 16.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : COM139+1 : TPTP v8.1.2. Released v6.4.0.
% 0.09/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.39 % Computer : n025.cluster.edu
% 0.15/0.39 % Model : x86_64 x86_64
% 0.15/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.39 % Memory : 8042.1875MB
% 0.15/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.39 % CPULimit : 300
% 0.15/0.39 % WCLimit : 300
% 0.15/0.39 % DateTime : Tue Aug 29 12:58:40 EDT 2023
% 0.15/0.39 % CPUTime :
% 0.24/0.66 ________ _____
% 0.24/0.66 ___ __ \_________(_)________________________________
% 0.24/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.24/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.24/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.24/0.66
% 0.24/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.24/0.66 (2023-06-19)
% 0.24/0.66
% 0.24/0.66 (c) Philipp Rümmer, 2009-2023
% 0.24/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.24/0.66 Amanda Stjerna.
% 0.24/0.66 Free software under BSD-3-Clause.
% 0.24/0.66
% 0.24/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.24/0.66
% 0.24/0.66 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.24/0.68 Running up to 7 provers in parallel.
% 0.24/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.24/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.24/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.24/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.24/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.24/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.24/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.04/1.39 Prover 1: Preprocessing ...
% 4.04/1.39 Prover 4: Preprocessing ...
% 5.01/1.43 Prover 5: Preprocessing ...
% 5.01/1.43 Prover 2: Preprocessing ...
% 5.01/1.43 Prover 3: Preprocessing ...
% 5.01/1.43 Prover 0: Preprocessing ...
% 5.01/1.43 Prover 6: Preprocessing ...
% 10.25/2.21 Prover 6: Proving ...
% 10.25/2.21 Prover 3: Constructing countermodel ...
% 10.25/2.22 Prover 1: Constructing countermodel ...
% 11.01/2.24 Prover 4: Constructing countermodel ...
% 11.53/2.33 Prover 5: Proving ...
% 11.53/2.33 Prover 0: Proving ...
% 12.44/2.45 Prover 2: Proving ...
% 13.13/2.54 Prover 3: proved (1843ms)
% 13.13/2.54
% 13.13/2.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.13/2.54
% 13.13/2.54 Prover 6: stopped
% 13.13/2.54 Prover 2: stopped
% 13.13/2.56 Prover 5: stopped
% 13.13/2.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.13/2.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.13/2.56 Prover 0: stopped
% 13.13/2.56 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.13/2.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.13/2.56 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.64/2.75 Prover 8: Preprocessing ...
% 13.64/2.76 Prover 11: Preprocessing ...
% 13.64/2.79 Prover 1: Found proof (size 67)
% 13.64/2.79 Prover 1: proved (2104ms)
% 13.64/2.80 Prover 13: Preprocessing ...
% 13.64/2.80 Prover 7: Preprocessing ...
% 13.64/2.82 Prover 4: stopped
% 15.29/2.82 Prover 11: stopped
% 15.29/2.83 Prover 10: Preprocessing ...
% 15.47/2.86 Prover 7: stopped
% 15.47/2.88 Prover 10: stopped
% 15.47/2.90 Prover 13: stopped
% 15.95/2.93 Prover 8: Warning: ignoring some quantifiers
% 15.95/2.94 Prover 8: Constructing countermodel ...
% 15.95/2.95 Prover 8: stopped
% 15.95/2.95
% 15.95/2.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.95/2.95
% 15.95/2.96 % SZS output start Proof for theBenchmark
% 15.95/2.97 Assumptions after simplification:
% 15.95/2.97 ---------------------------------
% 15.95/2.97
% 15.95/2.97 (DIFF-abs-app)
% 16.20/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.20/2.99 $i] : ( ~ (vapp(v3, v4) = v5) | ~ (vabs(v0, v1, v2) = v5) | ~ $i(v4) | ~
% 16.20/2.99 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 16.20/2.99
% 16.20/2.99 (DIFF-var-abs)
% 16.20/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 16.20/2.99 (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 16.20/2.99 $i(v1) | ~ $i(v0))
% 16.20/2.99
% 16.20/2.99 (EQ-abs)
% 16.20/3.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.20/3.00 $i] : ! [v6: $i] : ( ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6)
% 16.20/3.00 | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 16.20/3.00 (v5 = v2 & v4 = v1 & v3 = v0))
% 16.20/3.00
% 16.20/3.00 (T-Context-Swap)
% 16.20/3.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.20/3.00 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: int] : (v9 = 0 | v2
% 16.20/3.00 = v0 | ~ (vtcheck(v8, v5, v6) = v9) | ~ (vbind(v2, v3, v4) = v7) | ~
% 16.20/3.00 (vbind(v0, v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) |
% 16.20/3.00 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: $i] : ? [v11: $i] : ? [v12:
% 16.20/3.00 int] : ( ~ (v12 = 0) & vtcheck(v11, v5, v6) = v12 & vbind(v2, v3, v10) =
% 16.20/3.00 v11 & vbind(v0, v1, v4) = v10 & $i(v11) & $i(v10)))
% 16.20/3.00
% 16.20/3.00 (T-Weak-abs-1)
% 16.20/3.00 $i(veabs) & $i(vnoType) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 16.20/3.00 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] :
% 16.20/3.00 ( ~ (v8 = 0) & ~ (v3 = v0) & vtcheck(v7, v6, v5) = v8 & vtcheck(v2, v6, v5) =
% 16.20/3.00 0 & vlookup(v0, v2) = vnoType & vbind(v0, v1, v2) = v7 & vabs(v3, v4, veabs)
% 16.20/3.00 = v6 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 16.20/3.00 $i(v0))
% 16.20/3.00
% 16.20/3.00 (T-Weak-abs-IH)
% 16.20/3.00 $i(veabs) & $i(vnoType) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 16.20/3.00 $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (vtcheck(v4, veabs, v3) =
% 16.20/3.00 v5) | ~ (vbind(v0, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.20/3.00 $i(v0) | ? [v6: $i] : ? [v7: any] : (vtcheck(v2, veabs, v3) = v7 &
% 16.20/3.00 vlookup(v0, v2) = v6 & $i(v6) & ( ~ (v7 = 0) | ~ (v6 = vnoType))))
% 16.20/3.00
% 16.20/3.00 (T-abs)
% 16.20/3.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.20/3.01 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (varrow(v3, v4) = v6) | ~
% 16.20/3.01 (vtcheck(v0, v5, v6) = v7) | ~ (vabs(v1, v3, v2) = v5) | ~ $i(v4) | ~
% 16.20/3.01 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: int] : (
% 16.20/3.01 ~ (v9 = 0) & vtcheck(v8, v2, v4) = v9 & vbind(v1, v3, v0) = v8 & $i(v8)))
% 16.20/3.01
% 16.20/3.01 (T-inv)
% 16.20/3.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vtcheck(v2, v0, v1) = 0) | ~
% 16.20/3.01 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 16.20/3.01 ? [v6: $i] : ? [v7: $i] : (varrow(v5, v6) = v1 & vtcheck(v7, v4, v6) = 0 &
% 16.20/3.01 vbind(v3, v5, v2) = v7 & vabs(v3, v5, v4) = v0 & $i(v7) & $i(v6) & $i(v5)
% 16.20/3.01 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 16.20/3.01 : (varrow(v5, v1) = v6 & vtcheck(v2, v4, v5) = 0 & vtcheck(v2, v3, v6) = 0 &
% 16.20/3.01 vapp(v3, v4) = v0 & $i(v6) & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] :
% 16.20/3.01 (vsomeType(v1) = v3 & $i(v3) & ? [v4: $i] : (vlookup(v4, v2) = v3 &
% 16.20/3.01 vvar(v4) = v0 & $i(v4))))
% 16.20/3.01
% 16.20/3.01 (lookup2)
% 16.20/3.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.20/3.01 $i] : ! [v6: $i] : (v6 = v4 | v2 = v1 | ~ (vlookup(v2, v5) = v6) | ~
% 16.20/3.01 (vlookup(v2, v3) = v4) | ~ (vbind(v1, v0, v5) = v3) | ~ $i(v5) | ~ $i(v4)
% 16.20/3.01 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 16.20/3.01
% 16.20/3.01 (function-axioms)
% 16.20/3.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 16.20/3.02 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0:
% 16.20/3.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 16.20/3.02 : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3,
% 16.20/3.02 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 16.20/3.02 [v4: $i] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) =
% 16.20/3.02 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 16.20/3.02 : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & !
% 16.20/3.02 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3,
% 16.20/3.02 v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 16.20/3.02 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~
% 16.20/3.02 (vlookup(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.20/3.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.20/3.02 (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0: $i] : !
% 16.20/3.02 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~
% 16.20/3.02 (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 16.20/3.02 ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 16.20/3.02 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0))
% 16.20/3.02 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 16.20/3.02 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: $i] :
% 16.20/3.02 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~
% 16.20/3.02 (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 16.20/3.02 ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 16.20/3.02 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) =
% 16.20/3.02 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 16.20/3.02 $i] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & !
% 16.20/3.02 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~
% 16.20/3.02 (vsomeType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.20/3.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (visValue(v2) = v1) | ~
% 16.20/3.02 (visValue(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 16.20/3.02 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0))
% 16.20/3.02
% 16.20/3.02 Further assumptions not needed in the proof:
% 16.20/3.02 --------------------------------------------
% 16.20/3.02 DIFF-empty-bind, DIFF-noExp-someExp, DIFF-noType-someType, DIFF-var-app, EQ-app,
% 16.20/3.02 EQ-arrow, EQ-bind, EQ-empty, EQ-noExp, EQ-noType, EQ-someExp, EQ-someType,
% 16.20/3.02 EQ-var, T-Context-Duplicate, T-app, T-var, gensym-is-fresh, getSomeExp0,
% 16.20/3.02 getSomeType0, isFreeVar0, isFreeVar1, isFreeVar2, isSomeExp0, isSomeExp1,
% 16.20/3.02 isSomeType0, isSomeType1, isValue0, isValue1, isValue2, lookup-INV, lookup0,
% 16.20/3.02 lookup1, reduce-INV, reduce0, reduce1, reduce2, reduce3, reduce4, reduce5,
% 16.20/3.02 reduce6, subst-INV, subst0, subst1, subst2, subst3, subst4, subst5
% 16.20/3.02
% 16.20/3.02 Those formulas are unsatisfiable:
% 16.20/3.02 ---------------------------------
% 16.20/3.02
% 16.20/3.02 Begin of proof
% 16.20/3.02 |
% 16.20/3.02 | ALPHA: (T-Weak-abs-IH) implies:
% 16.20/3.02 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 16.20/3.02 | ! [v5: int] : (v5 = 0 | ~ (vtcheck(v4, veabs, v3) = v5) | ~
% 16.20/3.02 | (vbind(v0, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.20/3.02 | $i(v0) | ? [v6: $i] : ? [v7: any] : (vtcheck(v2, veabs, v3) = v7 &
% 16.20/3.02 | vlookup(v0, v2) = v6 & $i(v6) & ( ~ (v7 = 0) | ~ (v6 = vnoType))))
% 16.20/3.02 |
% 16.20/3.02 | ALPHA: (T-Weak-abs-1) implies:
% 16.20/3.02 | (2) $i(veabs)
% 16.20/3.02 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 16.20/3.02 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) &
% 16.20/3.02 | ~ (v3 = v0) & vtcheck(v7, v6, v5) = v8 & vtcheck(v2, v6, v5) = 0 &
% 16.20/3.02 | vlookup(v0, v2) = vnoType & vbind(v0, v1, v2) = v7 & vabs(v3, v4,
% 16.20/3.02 | veabs) = v6 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 16.20/3.02 | $i(v1) & $i(v0))
% 16.20/3.02 |
% 16.20/3.02 | ALPHA: (function-axioms) implies:
% 16.20/3.02 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 16.20/3.02 | (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = v0))
% 16.20/3.02 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 16.20/3.02 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) |
% 16.20/3.02 | ~ (vtcheck(v4, v3, v2) = v0))
% 16.20/3.02 |
% 16.20/3.03 | DELTA: instantiating (3) with fresh symbols all_54_0, all_54_1, all_54_2,
% 16.20/3.03 | all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8 gives:
% 16.20/3.03 | (6) ~ (all_54_0 = 0) & ~ (all_54_5 = all_54_8) & vtcheck(all_54_1,
% 16.20/3.03 | all_54_2, all_54_3) = all_54_0 & vtcheck(all_54_6, all_54_2,
% 16.20/3.03 | all_54_3) = 0 & vlookup(all_54_8, all_54_6) = vnoType &
% 16.20/3.03 | vbind(all_54_8, all_54_7, all_54_6) = all_54_1 & vabs(all_54_5,
% 16.20/3.03 | all_54_4, veabs) = all_54_2 & $i(all_54_1) & $i(all_54_2) &
% 16.20/3.03 | $i(all_54_3) & $i(all_54_4) & $i(all_54_5) & $i(all_54_6) &
% 16.20/3.03 | $i(all_54_7) & $i(all_54_8)
% 16.20/3.03 |
% 16.20/3.03 | ALPHA: (6) implies:
% 16.20/3.03 | (7) ~ (all_54_5 = all_54_8)
% 16.20/3.03 | (8) ~ (all_54_0 = 0)
% 16.20/3.03 | (9) $i(all_54_8)
% 16.20/3.03 | (10) $i(all_54_7)
% 16.20/3.03 | (11) $i(all_54_6)
% 16.20/3.03 | (12) $i(all_54_5)
% 16.20/3.03 | (13) $i(all_54_4)
% 16.20/3.03 | (14) $i(all_54_3)
% 16.20/3.03 | (15) $i(all_54_2)
% 16.20/3.03 | (16) $i(all_54_1)
% 16.20/3.03 | (17) vabs(all_54_5, all_54_4, veabs) = all_54_2
% 16.20/3.03 | (18) vbind(all_54_8, all_54_7, all_54_6) = all_54_1
% 16.20/3.03 | (19) vlookup(all_54_8, all_54_6) = vnoType
% 16.20/3.03 | (20) vtcheck(all_54_6, all_54_2, all_54_3) = 0
% 16.20/3.03 | (21) vtcheck(all_54_1, all_54_2, all_54_3) = all_54_0
% 16.20/3.03 |
% 16.20/3.03 | GROUND_INST: instantiating (T-inv) with all_54_2, all_54_3, all_54_6,
% 16.20/3.03 | simplifying with (11), (14), (15), (20) gives:
% 16.20/3.03 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 16.20/3.03 | (varrow(v2, v3) = all_54_3 & vtcheck(v4, v1, v3) = 0 & vbind(v0, v2,
% 16.20/3.03 | all_54_6) = v4 & vabs(v0, v2, v1) = all_54_2 & $i(v4) & $i(v3) &
% 16.20/3.03 | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 16.20/3.03 | : ? [v3: $i] : (varrow(v2, all_54_3) = v3 & vtcheck(all_54_6, v1, v2)
% 16.20/3.03 | = 0 & vtcheck(all_54_6, v0, v3) = 0 & vapp(v0, v1) = all_54_2 &
% 16.20/3.03 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] :
% 16.20/3.03 | (vsomeType(all_54_3) = v0 & $i(v0) & ? [v1: $i] : (vlookup(v1,
% 16.20/3.03 | all_54_6) = v0 & vvar(v1) = all_54_2 & $i(v1)))
% 16.20/3.03 |
% 16.20/3.03 | BETA: splitting (22) gives:
% 16.20/3.03 |
% 16.20/3.03 | Case 1:
% 16.20/3.03 | |
% 16.20/3.03 | | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 16.20/3.03 | | : (varrow(v2, v3) = all_54_3 & vtcheck(v4, v1, v3) = 0 & vbind(v0,
% 16.20/3.03 | | v2, all_54_6) = v4 & vabs(v0, v2, v1) = all_54_2 & $i(v4) &
% 16.20/3.03 | | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 16.20/3.03 | |
% 16.20/3.03 | | DELTA: instantiating (23) with fresh symbols all_62_0, all_62_1, all_62_2,
% 16.20/3.03 | | all_62_3, all_62_4 gives:
% 16.20/3.03 | | (24) varrow(all_62_2, all_62_1) = all_54_3 & vtcheck(all_62_0, all_62_3,
% 16.20/3.03 | | all_62_1) = 0 & vbind(all_62_4, all_62_2, all_54_6) = all_62_0 &
% 16.20/3.03 | | vabs(all_62_4, all_62_2, all_62_3) = all_54_2 & $i(all_62_0) &
% 16.20/3.03 | | $i(all_62_1) & $i(all_62_2) & $i(all_62_3) & $i(all_62_4)
% 16.20/3.03 | |
% 16.20/3.03 | | ALPHA: (24) implies:
% 16.20/3.04 | | (25) $i(all_62_4)
% 16.20/3.04 | | (26) $i(all_62_3)
% 16.20/3.04 | | (27) $i(all_62_2)
% 16.20/3.04 | | (28) $i(all_62_1)
% 16.20/3.04 | | (29) vabs(all_62_4, all_62_2, all_62_3) = all_54_2
% 16.20/3.04 | | (30) vbind(all_62_4, all_62_2, all_54_6) = all_62_0
% 16.20/3.04 | | (31) vtcheck(all_62_0, all_62_3, all_62_1) = 0
% 16.20/3.04 | | (32) varrow(all_62_2, all_62_1) = all_54_3
% 16.20/3.04 | |
% 16.20/3.04 | | GROUND_INST: instantiating (EQ-abs) with all_54_5, all_54_4, veabs,
% 16.20/3.04 | | all_62_4, all_62_2, all_62_3, all_54_2, simplifying with (2),
% 16.20/3.04 | | (12), (13), (17), (25), (26), (27), (29) gives:
% 16.20/3.04 | | (33) all_62_2 = all_54_4 & all_62_3 = veabs & all_62_4 = all_54_5
% 16.20/3.04 | |
% 16.20/3.04 | | ALPHA: (33) implies:
% 16.20/3.04 | | (34) all_62_4 = all_54_5
% 16.20/3.04 | | (35) all_62_3 = veabs
% 16.20/3.04 | | (36) all_62_2 = all_54_4
% 16.20/3.04 | |
% 16.20/3.04 | | GROUND_INST: instantiating (T-abs) with all_54_1, all_62_4, all_62_3,
% 16.20/3.04 | | all_62_2, all_62_1, all_54_2, all_54_3, all_54_0, simplifying
% 16.20/3.04 | | with (16), (21), (25), (26), (27), (28), (29), (32) gives:
% 16.20/3.04 | | (37) all_54_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 16.20/3.04 | | vtcheck(v0, all_62_3, all_62_1) = v1 & vbind(all_62_4, all_62_2,
% 16.20/3.04 | | all_54_1) = v0 & $i(v0))
% 16.20/3.04 | |
% 16.20/3.04 | | REDUCE: (31), (35) imply:
% 16.20/3.04 | | (38) vtcheck(all_62_0, veabs, all_62_1) = 0
% 16.20/3.04 | |
% 16.20/3.04 | | REDUCE: (30), (34), (36) imply:
% 16.20/3.04 | | (39) vbind(all_54_5, all_54_4, all_54_6) = all_62_0
% 16.20/3.04 | |
% 16.20/3.04 | | BETA: splitting (37) gives:
% 16.20/3.04 | |
% 16.20/3.04 | | Case 1:
% 16.20/3.04 | | |
% 16.20/3.04 | | | (40) all_54_0 = 0
% 16.20/3.04 | | |
% 16.20/3.04 | | | REDUCE: (8), (40) imply:
% 16.20/3.04 | | | (41) $false
% 16.20/3.04 | | |
% 16.20/3.04 | | | CLOSE: (41) is inconsistent.
% 16.20/3.04 | | |
% 16.20/3.04 | | Case 2:
% 16.20/3.04 | | |
% 16.20/3.04 | | | (42) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & vtcheck(v0, all_62_3,
% 16.20/3.04 | | | all_62_1) = v1 & vbind(all_62_4, all_62_2, all_54_1) = v0 &
% 16.20/3.04 | | | $i(v0))
% 16.20/3.04 | | |
% 16.20/3.04 | | | DELTA: instantiating (42) with fresh symbols all_74_0, all_74_1 gives:
% 16.20/3.04 | | | (43) ~ (all_74_0 = 0) & vtcheck(all_74_1, all_62_3, all_62_1) =
% 16.20/3.04 | | | all_74_0 & vbind(all_62_4, all_62_2, all_54_1) = all_74_1 &
% 16.20/3.04 | | | $i(all_74_1)
% 16.20/3.04 | | |
% 16.20/3.04 | | | ALPHA: (43) implies:
% 16.20/3.04 | | | (44) ~ (all_74_0 = 0)
% 16.20/3.04 | | | (45) vbind(all_62_4, all_62_2, all_54_1) = all_74_1
% 16.20/3.04 | | | (46) vtcheck(all_74_1, all_62_3, all_62_1) = all_74_0
% 16.20/3.04 | | |
% 16.20/3.04 | | | REDUCE: (35), (46) imply:
% 16.20/3.05 | | | (47) vtcheck(all_74_1, veabs, all_62_1) = all_74_0
% 16.20/3.05 | | |
% 16.20/3.05 | | | REDUCE: (34), (36), (45) imply:
% 16.20/3.05 | | | (48) vbind(all_54_5, all_54_4, all_54_1) = all_74_1
% 16.20/3.05 | | |
% 16.55/3.05 | | | GROUND_INST: instantiating (T-Context-Swap) with all_54_5, all_54_4,
% 16.55/3.05 | | | all_54_8, all_54_7, all_54_6, veabs, all_62_1, all_54_1,
% 16.55/3.05 | | | all_74_1, all_74_0, simplifying with (2), (9), (10), (11),
% 16.55/3.05 | | | (12), (13), (18), (28), (47), (48) gives:
% 16.55/3.05 | | | (49) all_74_0 = 0 | all_54_5 = all_54_8 | ? [v0: $i] : ? [v1: $i] :
% 16.55/3.05 | | | ? [v2: int] : ( ~ (v2 = 0) & vtcheck(v1, veabs, all_62_1) = v2 &
% 16.55/3.05 | | | vbind(all_54_5, all_54_4, all_54_6) = v0 & vbind(all_54_8,
% 16.55/3.05 | | | all_54_7, v0) = v1 & $i(v1) & $i(v0))
% 16.55/3.05 | | |
% 16.55/3.05 | | | BETA: splitting (49) gives:
% 16.55/3.05 | | |
% 16.55/3.05 | | | Case 1:
% 16.55/3.05 | | | |
% 16.55/3.05 | | | | (50) all_74_0 = 0
% 16.55/3.05 | | | |
% 16.55/3.05 | | | | REDUCE: (44), (50) imply:
% 16.55/3.05 | | | | (51) $false
% 16.55/3.05 | | | |
% 16.55/3.05 | | | | CLOSE: (51) is inconsistent.
% 16.55/3.05 | | | |
% 16.55/3.05 | | | Case 2:
% 16.55/3.05 | | | |
% 16.55/3.05 | | | | (52) all_54_5 = all_54_8 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] :
% 16.55/3.05 | | | | ( ~ (v2 = 0) & vtcheck(v1, veabs, all_62_1) = v2 &
% 16.55/3.05 | | | | vbind(all_54_5, all_54_4, all_54_6) = v0 & vbind(all_54_8,
% 16.55/3.05 | | | | all_54_7, v0) = v1 & $i(v1) & $i(v0))
% 16.55/3.05 | | | |
% 16.55/3.05 | | | | BETA: splitting (52) gives:
% 16.55/3.05 | | | |
% 16.55/3.05 | | | | Case 1:
% 16.55/3.05 | | | | |
% 16.55/3.05 | | | | | (53) all_54_5 = all_54_8
% 16.55/3.05 | | | | |
% 16.55/3.05 | | | | | REDUCE: (7), (53) imply:
% 16.55/3.05 | | | | | (54) $false
% 16.55/3.05 | | | | |
% 16.55/3.05 | | | | | CLOSE: (54) is inconsistent.
% 16.55/3.05 | | | | |
% 16.55/3.05 | | | | Case 2:
% 16.55/3.05 | | | | |
% 16.55/3.05 | | | | | (55) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 16.55/3.05 | | | | | vtcheck(v1, veabs, all_62_1) = v2 & vbind(all_54_5,
% 16.55/3.05 | | | | | all_54_4, all_54_6) = v0 & vbind(all_54_8, all_54_7, v0) =
% 16.55/3.05 | | | | | v1 & $i(v1) & $i(v0))
% 16.55/3.05 | | | | |
% 16.55/3.05 | | | | | DELTA: instantiating (55) with fresh symbols all_96_0, all_96_1,
% 16.55/3.05 | | | | | all_96_2 gives:
% 16.55/3.05 | | | | | (56) ~ (all_96_0 = 0) & vtcheck(all_96_1, veabs, all_62_1) =
% 16.55/3.05 | | | | | all_96_0 & vbind(all_54_5, all_54_4, all_54_6) = all_96_2 &
% 16.55/3.05 | | | | | vbind(all_54_8, all_54_7, all_96_2) = all_96_1 & $i(all_96_1)
% 16.55/3.05 | | | | | & $i(all_96_2)
% 16.55/3.05 | | | | |
% 16.55/3.05 | | | | | ALPHA: (56) implies:
% 16.55/3.05 | | | | | (57) ~ (all_96_0 = 0)
% 16.55/3.05 | | | | | (58) $i(all_96_2)
% 16.55/3.05 | | | | | (59) vbind(all_54_8, all_54_7, all_96_2) = all_96_1
% 16.55/3.05 | | | | | (60) vbind(all_54_5, all_54_4, all_54_6) = all_96_2
% 16.55/3.05 | | | | | (61) vtcheck(all_96_1, veabs, all_62_1) = all_96_0
% 16.55/3.05 | | | | |
% 16.55/3.05 | | | | | GROUND_INST: instantiating (4) with all_62_0, all_96_2, all_54_6,
% 16.55/3.05 | | | | | all_54_4, all_54_5, simplifying with (39), (60) gives:
% 16.55/3.05 | | | | | (62) all_96_2 = all_62_0
% 16.55/3.05 | | | | |
% 16.55/3.05 | | | | | REDUCE: (59), (62) imply:
% 16.55/3.05 | | | | | (63) vbind(all_54_8, all_54_7, all_62_0) = all_96_1
% 16.55/3.05 | | | | |
% 16.55/3.05 | | | | | REDUCE: (58), (62) imply:
% 16.55/3.05 | | | | | (64) $i(all_62_0)
% 16.55/3.05 | | | | |
% 16.55/3.05 | | | | | GROUND_INST: instantiating (1) with all_54_8, all_54_7, all_62_0,
% 16.55/3.05 | | | | | all_62_1, all_96_1, all_96_0, simplifying with (9), (10),
% 16.55/3.05 | | | | | (28), (61), (63), (64) gives:
% 16.55/3.05 | | | | | (65) all_96_0 = 0 | ? [v0: $i] : ? [v1: any] : (vtcheck(all_62_0,
% 16.55/3.05 | | | | | veabs, all_62_1) = v1 & vlookup(all_54_8, all_62_0) = v0 &
% 16.55/3.06 | | | | | $i(v0) & ( ~ (v1 = 0) | ~ (v0 = vnoType)))
% 16.55/3.06 | | | | |
% 16.55/3.06 | | | | | BETA: splitting (65) gives:
% 16.55/3.06 | | | | |
% 16.55/3.06 | | | | | Case 1:
% 16.55/3.06 | | | | | |
% 16.55/3.06 | | | | | | (66) all_96_0 = 0
% 16.55/3.06 | | | | | |
% 16.55/3.06 | | | | | | REDUCE: (57), (66) imply:
% 16.55/3.06 | | | | | | (67) $false
% 16.55/3.06 | | | | | |
% 16.55/3.06 | | | | | | CLOSE: (67) is inconsistent.
% 16.55/3.06 | | | | | |
% 16.55/3.06 | | | | | Case 2:
% 16.55/3.06 | | | | | |
% 16.55/3.06 | | | | | | (68) ? [v0: $i] : ? [v1: any] : (vtcheck(all_62_0, veabs,
% 16.55/3.06 | | | | | | all_62_1) = v1 & vlookup(all_54_8, all_62_0) = v0 &
% 16.55/3.06 | | | | | | $i(v0) & ( ~ (v1 = 0) | ~ (v0 = vnoType)))
% 16.55/3.06 | | | | | |
% 16.55/3.06 | | | | | | DELTA: instantiating (68) with fresh symbols all_116_0, all_116_1
% 16.55/3.06 | | | | | | gives:
% 16.55/3.06 | | | | | | (69) vtcheck(all_62_0, veabs, all_62_1) = all_116_0 &
% 16.55/3.06 | | | | | | vlookup(all_54_8, all_62_0) = all_116_1 & $i(all_116_1) & (
% 16.55/3.06 | | | | | | ~ (all_116_0 = 0) | ~ (all_116_1 = vnoType))
% 16.55/3.06 | | | | | |
% 16.55/3.06 | | | | | | ALPHA: (69) implies:
% 16.55/3.06 | | | | | | (70) $i(all_116_1)
% 16.55/3.06 | | | | | | (71) vlookup(all_54_8, all_62_0) = all_116_1
% 16.55/3.06 | | | | | | (72) vtcheck(all_62_0, veabs, all_62_1) = all_116_0
% 16.55/3.06 | | | | | | (73) ~ (all_116_0 = 0) | ~ (all_116_1 = vnoType)
% 16.55/3.06 | | | | | |
% 16.55/3.06 | | | | | | GROUND_INST: instantiating (5) with 0, all_116_0, all_62_1, veabs,
% 16.55/3.06 | | | | | | all_62_0, simplifying with (38), (72) gives:
% 16.55/3.06 | | | | | | (74) all_116_0 = 0
% 16.55/3.06 | | | | | |
% 16.55/3.06 | | | | | | BETA: splitting (73) gives:
% 16.55/3.06 | | | | | |
% 16.55/3.06 | | | | | | Case 1:
% 16.55/3.06 | | | | | | |
% 16.55/3.06 | | | | | | | (75) ~ (all_116_1 = vnoType)
% 16.55/3.06 | | | | | | |
% 16.55/3.06 | | | | | | | GROUND_INST: instantiating (lookup2) with all_54_4, all_54_5,
% 16.55/3.06 | | | | | | | all_54_8, all_62_0, all_116_1, all_54_6, vnoType,
% 16.55/3.06 | | | | | | | simplifying with (9), (11), (12), (13), (19), (39),
% 16.55/3.06 | | | | | | | (64), (70), (71) gives:
% 16.55/3.06 | | | | | | | (76) all_116_1 = vnoType | all_54_5 = all_54_8
% 16.55/3.06 | | | | | | |
% 16.55/3.06 | | | | | | | BETA: splitting (76) gives:
% 16.55/3.06 | | | | | | |
% 16.55/3.06 | | | | | | | Case 1:
% 16.55/3.06 | | | | | | | |
% 16.55/3.06 | | | | | | | | (77) all_116_1 = vnoType
% 16.55/3.06 | | | | | | | |
% 16.55/3.06 | | | | | | | | REDUCE: (75), (77) imply:
% 16.55/3.06 | | | | | | | | (78) $false
% 16.55/3.06 | | | | | | | |
% 16.55/3.06 | | | | | | | | CLOSE: (78) is inconsistent.
% 16.55/3.06 | | | | | | | |
% 16.55/3.06 | | | | | | | Case 2:
% 16.55/3.06 | | | | | | | |
% 16.55/3.06 | | | | | | | | (79) all_54_5 = all_54_8
% 16.55/3.06 | | | | | | | |
% 16.55/3.06 | | | | | | | | REDUCE: (7), (79) imply:
% 16.55/3.06 | | | | | | | | (80) $false
% 16.55/3.06 | | | | | | | |
% 16.55/3.06 | | | | | | | | CLOSE: (80) is inconsistent.
% 16.55/3.06 | | | | | | | |
% 16.55/3.06 | | | | | | | End of split
% 16.55/3.06 | | | | | | |
% 16.55/3.06 | | | | | | Case 2:
% 16.55/3.06 | | | | | | |
% 16.55/3.06 | | | | | | | (81) ~ (all_116_0 = 0)
% 16.55/3.06 | | | | | | |
% 16.55/3.06 | | | | | | | REDUCE: (74), (81) imply:
% 16.55/3.06 | | | | | | | (82) $false
% 16.55/3.06 | | | | | | |
% 16.55/3.06 | | | | | | | CLOSE: (82) is inconsistent.
% 16.55/3.06 | | | | | | |
% 16.55/3.06 | | | | | | End of split
% 16.55/3.06 | | | | | |
% 16.55/3.06 | | | | | End of split
% 16.55/3.06 | | | | |
% 16.55/3.06 | | | | End of split
% 16.55/3.06 | | | |
% 16.55/3.06 | | | End of split
% 16.55/3.06 | | |
% 16.55/3.06 | | End of split
% 16.55/3.06 | |
% 16.55/3.06 | Case 2:
% 16.55/3.06 | |
% 16.55/3.06 | | (83) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (varrow(v2,
% 16.55/3.06 | | all_54_3) = v3 & vtcheck(all_54_6, v1, v2) = 0 &
% 16.55/3.06 | | vtcheck(all_54_6, v0, v3) = 0 & vapp(v0, v1) = all_54_2 & $i(v3) &
% 16.55/3.06 | | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : (vsomeType(all_54_3) =
% 16.55/3.06 | | v0 & $i(v0) & ? [v1: $i] : (vlookup(v1, all_54_6) = v0 & vvar(v1)
% 16.55/3.06 | | = all_54_2 & $i(v1)))
% 16.55/3.06 | |
% 16.55/3.06 | | BETA: splitting (83) gives:
% 16.55/3.06 | |
% 16.55/3.06 | | Case 1:
% 16.55/3.06 | | |
% 16.55/3.06 | | | (84) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 16.55/3.06 | | | (varrow(v2, all_54_3) = v3 & vtcheck(all_54_6, v1, v2) = 0 &
% 16.55/3.06 | | | vtcheck(all_54_6, v0, v3) = 0 & vapp(v0, v1) = all_54_2 & $i(v3)
% 16.55/3.06 | | | & $i(v2) & $i(v1) & $i(v0))
% 16.55/3.06 | | |
% 16.55/3.06 | | | DELTA: instantiating (84) with fresh symbols all_62_0, all_62_1, all_62_2,
% 16.55/3.06 | | | all_62_3 gives:
% 16.55/3.06 | | | (85) varrow(all_62_1, all_54_3) = all_62_0 & vtcheck(all_54_6,
% 16.55/3.06 | | | all_62_2, all_62_1) = 0 & vtcheck(all_54_6, all_62_3, all_62_0)
% 16.55/3.06 | | | = 0 & vapp(all_62_3, all_62_2) = all_54_2 & $i(all_62_0) &
% 16.55/3.06 | | | $i(all_62_1) & $i(all_62_2) & $i(all_62_3)
% 16.55/3.06 | | |
% 16.55/3.06 | | | ALPHA: (85) implies:
% 16.55/3.06 | | | (86) $i(all_62_3)
% 16.55/3.07 | | | (87) $i(all_62_2)
% 16.55/3.07 | | | (88) vapp(all_62_3, all_62_2) = all_54_2
% 16.55/3.07 | | |
% 16.55/3.07 | | | GROUND_INST: instantiating (DIFF-abs-app) with all_54_5, all_54_4, veabs,
% 16.55/3.07 | | | all_62_3, all_62_2, all_54_2, simplifying with (2), (12),
% 16.55/3.07 | | | (13), (17), (86), (87), (88) gives:
% 16.55/3.07 | | | (89) $false
% 16.55/3.07 | | |
% 16.55/3.07 | | | CLOSE: (89) is inconsistent.
% 16.55/3.07 | | |
% 16.55/3.07 | | Case 2:
% 16.55/3.07 | | |
% 16.55/3.07 | | | (90) ? [v0: $i] : (vsomeType(all_54_3) = v0 & $i(v0) & ? [v1: $i] :
% 16.55/3.07 | | | (vlookup(v1, all_54_6) = v0 & vvar(v1) = all_54_2 & $i(v1)))
% 16.55/3.07 | | |
% 16.55/3.07 | | | DELTA: instantiating (90) with fresh symbol all_62_0 gives:
% 16.55/3.07 | | | (91) vsomeType(all_54_3) = all_62_0 & $i(all_62_0) & ? [v0: $i] :
% 16.55/3.07 | | | (vlookup(v0, all_54_6) = all_62_0 & vvar(v0) = all_54_2 & $i(v0))
% 16.55/3.07 | | |
% 16.55/3.07 | | | ALPHA: (91) implies:
% 16.55/3.07 | | | (92) ? [v0: $i] : (vlookup(v0, all_54_6) = all_62_0 & vvar(v0) =
% 16.55/3.07 | | | all_54_2 & $i(v0))
% 16.55/3.07 | | |
% 16.55/3.07 | | | DELTA: instantiating (92) with fresh symbol all_64_0 gives:
% 16.55/3.07 | | | (93) vlookup(all_64_0, all_54_6) = all_62_0 & vvar(all_64_0) = all_54_2
% 16.55/3.07 | | | & $i(all_64_0)
% 16.55/3.07 | | |
% 16.55/3.07 | | | ALPHA: (93) implies:
% 16.55/3.07 | | | (94) $i(all_64_0)
% 16.55/3.07 | | | (95) vvar(all_64_0) = all_54_2
% 16.55/3.07 | | |
% 16.55/3.07 | | | GROUND_INST: instantiating (DIFF-var-abs) with all_64_0, all_54_5,
% 16.55/3.07 | | | all_54_4, veabs, all_54_2, simplifying with (2), (12), (13),
% 16.55/3.07 | | | (17), (94), (95) gives:
% 16.55/3.07 | | | (96) $false
% 16.55/3.07 | | |
% 16.55/3.07 | | | CLOSE: (96) is inconsistent.
% 16.55/3.07 | | |
% 16.55/3.07 | | End of split
% 16.55/3.07 | |
% 16.55/3.07 | End of split
% 16.55/3.07 |
% 16.55/3.07 End of proof
% 16.55/3.07 % SZS output end Proof for theBenchmark
% 16.55/3.07
% 16.55/3.07 2409ms
%------------------------------------------------------------------------------