TSTP Solution File: COM143+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM143+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 13.73s 2.61s
% Output : Proof 17.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : COM143+1 : TPTP v8.1.2. Released v6.4.0.
% 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 13:09:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.19/1.47 Prover 1: Preprocessing ...
% 5.19/1.49 Prover 4: Preprocessing ...
% 5.19/1.50 Prover 6: Preprocessing ...
% 5.19/1.50 Prover 5: Preprocessing ...
% 5.19/1.50 Prover 2: Preprocessing ...
% 5.19/1.50 Prover 0: Preprocessing ...
% 5.19/1.50 Prover 3: Preprocessing ...
% 11.58/2.27 Prover 1: Constructing countermodel ...
% 11.58/2.28 Prover 6: Proving ...
% 11.58/2.30 Prover 4: Constructing countermodel ...
% 11.58/2.31 Prover 3: Constructing countermodel ...
% 11.58/2.34 Prover 0: Proving ...
% 12.41/2.42 Prover 5: Proving ...
% 12.86/2.52 Prover 2: Proving ...
% 13.73/2.61 Prover 3: proved (1966ms)
% 13.73/2.61
% 13.73/2.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.73/2.61
% 13.73/2.61 Prover 5: stopped
% 13.73/2.61 Prover 6: stopped
% 13.73/2.61 Prover 0: stopped
% 13.73/2.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.73/2.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.73/2.61 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.73/2.61 Prover 2: stopped
% 13.73/2.61 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.73/2.61 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.29/2.69 Prover 1: Found proof (size 42)
% 14.29/2.69 Prover 1: proved (2053ms)
% 14.29/2.69 Prover 4: stopped
% 15.36/2.78 Prover 13: Preprocessing ...
% 15.36/2.80 Prover 11: Preprocessing ...
% 15.36/2.80 Prover 10: Preprocessing ...
% 15.36/2.80 Prover 7: Preprocessing ...
% 15.36/2.81 Prover 8: Preprocessing ...
% 16.07/2.87 Prover 11: stopped
% 16.07/2.87 Prover 7: stopped
% 16.07/2.87 Prover 10: stopped
% 16.07/2.89 Prover 13: stopped
% 16.45/2.97 Prover 8: Warning: ignoring some quantifiers
% 16.45/2.99 Prover 8: Constructing countermodel ...
% 16.45/3.00 Prover 8: stopped
% 16.45/3.00
% 16.45/3.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.45/3.00
% 16.45/3.00 % SZS output start Proof for theBenchmark
% 16.45/3.01 Assumptions after simplification:
% 16.45/3.01 ---------------------------------
% 16.45/3.01
% 16.45/3.01 (DIFF-noType-someType)
% 16.84/3.03 $i(vnoType) & ! [v0: $i] : ( ~ (vsomeType(v0) = vnoType) | ~ $i(v0))
% 16.84/3.03
% 16.84/3.03 (DIFF-var-abs)
% 16.84/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 16.84/3.03 (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 16.84/3.03 $i(v1) | ~ $i(v0))
% 16.84/3.03
% 16.84/3.03 (DIFF-var-app)
% 16.84/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vapp(v1, v2) =
% 16.84/3.03 v3) | ~ (vvar(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 16.84/3.03
% 16.84/3.03 (EQ-var)
% 16.84/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vvar(v1) = v2) | ~
% 16.84/3.03 (vvar(v0) = v2) | ~ $i(v1) | ~ $i(v0))
% 16.84/3.03
% 16.84/3.03 (T-Weak-var)
% 16.84/3.03 $i(vnoType) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 16.84/3.03 $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & vtcheck(v6,
% 16.84/3.03 v5, v4) = v7 & vtcheck(v2, v5, v4) = 0 & vlookup(v0, v2) = vnoType &
% 16.84/3.03 vbind(v0, v1, v2) = v6 & vvar(v3) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 16.84/3.03 $i(v2) & $i(v1) & $i(v0))
% 16.84/3.03
% 16.84/3.03 (T-inv)
% 16.84/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vtcheck(v2, v0, v1) = 0) | ~
% 16.84/3.04 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 16.84/3.04 ? [v6: $i] : ? [v7: $i] : (varrow(v5, v6) = v1 & vtcheck(v7, v4, v6) = 0 &
% 16.84/3.04 vbind(v3, v5, v2) = v7 & vabs(v3, v5, v4) = v0 & $i(v7) & $i(v6) & $i(v5)
% 16.84/3.04 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 16.84/3.04 : (varrow(v5, v1) = v6 & vtcheck(v2, v4, v5) = 0 & vtcheck(v2, v3, v6) = 0 &
% 16.84/3.04 vapp(v3, v4) = v0 & $i(v6) & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] :
% 16.84/3.04 (vsomeType(v1) = v3 & $i(v3) & ? [v4: $i] : (vlookup(v4, v2) = v3 &
% 16.84/3.04 vvar(v4) = v0 & $i(v4))))
% 16.84/3.04
% 16.84/3.04 (T-var)
% 16.84/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 16.84/3.04 | ~ (vtcheck(v0, v3, v2) = v4) | ~ (vvar(v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 16.84/3.04 | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & vlookup(v1, v0) =
% 16.84/3.04 v5 & vsomeType(v2) = v6 & $i(v6) & $i(v5)))
% 16.84/3.04
% 16.84/3.04 (lookup2)
% 16.84/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.84/3.04 $i] : ! [v6: $i] : (v6 = v4 | v2 = v1 | ~ (vlookup(v2, v5) = v6) | ~
% 16.84/3.04 (vlookup(v2, v3) = v4) | ~ (vbind(v1, v0, v5) = v3) | ~ $i(v5) | ~ $i(v4)
% 16.84/3.04 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 16.84/3.04
% 16.84/3.04 (function-axioms)
% 16.84/3.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 16.84/3.05 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0:
% 16.84/3.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 16.84/3.05 : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3,
% 16.84/3.05 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 16.84/3.05 [v4: $i] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) =
% 16.84/3.05 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 16.84/3.05 : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & !
% 16.84/3.05 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3,
% 16.84/3.05 v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 16.84/3.05 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~
% 16.84/3.05 (vlookup(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.84/3.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.84/3.05 (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0: $i] : !
% 16.84/3.05 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~
% 16.84/3.05 (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 16.84/3.05 ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 16.84/3.05 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0))
% 16.84/3.05 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 16.84/3.05 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: $i] :
% 16.84/3.05 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~
% 16.84/3.05 (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 16.84/3.05 ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 16.84/3.05 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) =
% 16.84/3.05 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 16.84/3.05 $i] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & !
% 16.84/3.05 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~
% 16.84/3.05 (vsomeType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.84/3.05 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (visValue(v2) = v1) | ~
% 16.84/3.05 (visValue(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 16.84/3.05 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0))
% 16.84/3.05
% 16.84/3.05 Further assumptions not needed in the proof:
% 16.84/3.05 --------------------------------------------
% 16.84/3.05 DIFF-abs-app, DIFF-empty-bind, DIFF-noExp-someExp, EQ-abs, EQ-app, EQ-arrow,
% 16.84/3.05 EQ-bind, EQ-empty, EQ-noExp, EQ-noType, EQ-someExp, EQ-someType,
% 16.84/3.05 T-Context-Duplicate, T-Context-Swap, T-abs, T-app, gensym-is-fresh, getSomeExp0,
% 16.84/3.05 getSomeType0, isFreeVar0, isFreeVar1, isFreeVar2, isSomeExp0, isSomeExp1,
% 16.84/3.05 isSomeType0, isSomeType1, isValue0, isValue1, isValue2, lookup-INV, lookup0,
% 16.84/3.05 lookup1, reduce-INV, reduce0, reduce1, reduce2, reduce3, reduce4, reduce5,
% 16.84/3.05 reduce6, subst-INV, subst0, subst1, subst2, subst3, subst4, subst5
% 16.84/3.05
% 16.84/3.05 Those formulas are unsatisfiable:
% 16.84/3.05 ---------------------------------
% 16.84/3.05
% 16.84/3.05 Begin of proof
% 16.84/3.05 |
% 16.84/3.05 | ALPHA: (DIFF-noType-someType) implies:
% 16.84/3.05 | (1) ! [v0: $i] : ( ~ (vsomeType(v0) = vnoType) | ~ $i(v0))
% 16.84/3.05 |
% 16.84/3.05 | ALPHA: (T-Weak-var) implies:
% 16.84/3.05 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 16.84/3.05 | ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & vtcheck(v6,
% 16.84/3.05 | v5, v4) = v7 & vtcheck(v2, v5, v4) = 0 & vlookup(v0, v2) = vnoType
% 16.84/3.05 | & vbind(v0, v1, v2) = v6 & vvar(v3) = v5 & $i(v6) & $i(v5) & $i(v4) &
% 16.84/3.05 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 16.84/3.05 |
% 16.84/3.05 | ALPHA: (function-axioms) implies:
% 16.84/3.05 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2)
% 16.84/3.05 | = v1) | ~ (vsomeType(v2) = v0))
% 16.84/3.05 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.84/3.05 | (vlookup(v3, v2) = v1) | ~ (vlookup(v3, v2) = v0))
% 16.84/3.05 |
% 16.84/3.05 | DELTA: instantiating (2) with fresh symbols all_53_0, all_53_1, all_53_2,
% 16.84/3.05 | all_53_3, all_53_4, all_53_5, all_53_6, all_53_7 gives:
% 16.84/3.05 | (5) ~ (all_53_0 = 0) & vtcheck(all_53_1, all_53_2, all_53_3) = all_53_0 &
% 16.84/3.05 | vtcheck(all_53_5, all_53_2, all_53_3) = 0 & vlookup(all_53_7, all_53_5)
% 16.84/3.05 | = vnoType & vbind(all_53_7, all_53_6, all_53_5) = all_53_1 &
% 16.84/3.05 | vvar(all_53_4) = all_53_2 & $i(all_53_1) & $i(all_53_2) & $i(all_53_3)
% 16.84/3.05 | & $i(all_53_4) & $i(all_53_5) & $i(all_53_6) & $i(all_53_7)
% 16.84/3.05 |
% 16.84/3.05 | ALPHA: (5) implies:
% 16.84/3.05 | (6) ~ (all_53_0 = 0)
% 16.84/3.05 | (7) $i(all_53_7)
% 16.84/3.05 | (8) $i(all_53_6)
% 16.84/3.05 | (9) $i(all_53_5)
% 16.84/3.05 | (10) $i(all_53_4)
% 16.84/3.05 | (11) $i(all_53_3)
% 16.84/3.05 | (12) $i(all_53_2)
% 16.84/3.05 | (13) $i(all_53_1)
% 16.84/3.05 | (14) vvar(all_53_4) = all_53_2
% 16.84/3.05 | (15) vbind(all_53_7, all_53_6, all_53_5) = all_53_1
% 16.84/3.05 | (16) vlookup(all_53_7, all_53_5) = vnoType
% 16.84/3.06 | (17) vtcheck(all_53_5, all_53_2, all_53_3) = 0
% 16.84/3.06 | (18) vtcheck(all_53_1, all_53_2, all_53_3) = all_53_0
% 16.84/3.06 |
% 16.84/3.06 | GROUND_INST: instantiating (T-inv) with all_53_2, all_53_3, all_53_5,
% 16.84/3.06 | simplifying with (9), (11), (12), (17) gives:
% 16.84/3.06 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 16.84/3.06 | (varrow(v2, v3) = all_53_3 & vtcheck(v4, v1, v3) = 0 & vbind(v0, v2,
% 16.84/3.06 | all_53_5) = v4 & vabs(v0, v2, v1) = all_53_2 & $i(v4) & $i(v3) &
% 16.84/3.06 | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 16.84/3.06 | : ? [v3: $i] : (varrow(v2, all_53_3) = v3 & vtcheck(all_53_5, v1, v2)
% 16.84/3.06 | = 0 & vtcheck(all_53_5, v0, v3) = 0 & vapp(v0, v1) = all_53_2 &
% 16.84/3.06 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] :
% 16.84/3.06 | (vsomeType(all_53_3) = v0 & $i(v0) & ? [v1: $i] : (vlookup(v1,
% 16.84/3.06 | all_53_5) = v0 & vvar(v1) = all_53_2 & $i(v1)))
% 16.84/3.06 |
% 16.84/3.06 | GROUND_INST: instantiating (T-var) with all_53_1, all_53_4, all_53_3,
% 16.84/3.06 | all_53_2, all_53_0, simplifying with (10), (11), (13), (14), (18)
% 16.84/3.06 | gives:
% 16.84/3.06 | (20) all_53_0 = 0 | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 16.84/3.06 | vlookup(all_53_4, all_53_1) = v0 & vsomeType(all_53_3) = v1 & $i(v1)
% 16.84/3.06 | & $i(v0))
% 16.84/3.06 |
% 16.84/3.06 | BETA: splitting (20) gives:
% 16.84/3.06 |
% 16.84/3.06 | Case 1:
% 16.84/3.06 | |
% 16.84/3.06 | | (21) all_53_0 = 0
% 16.84/3.06 | |
% 16.84/3.06 | | REDUCE: (6), (21) imply:
% 16.84/3.06 | | (22) $false
% 16.84/3.06 | |
% 16.84/3.06 | | CLOSE: (22) is inconsistent.
% 16.84/3.06 | |
% 16.84/3.06 | Case 2:
% 16.84/3.06 | |
% 16.84/3.06 | | (23) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & vlookup(all_53_4,
% 16.84/3.06 | | all_53_1) = v0 & vsomeType(all_53_3) = v1 & $i(v1) & $i(v0))
% 16.84/3.06 | |
% 16.84/3.06 | | DELTA: instantiating (23) with fresh symbols all_62_0, all_62_1 gives:
% 16.84/3.06 | | (24) ~ (all_62_0 = all_62_1) & vlookup(all_53_4, all_53_1) = all_62_1 &
% 16.84/3.06 | | vsomeType(all_53_3) = all_62_0 & $i(all_62_0) & $i(all_62_1)
% 16.84/3.06 | |
% 16.84/3.06 | | ALPHA: (24) implies:
% 16.84/3.06 | | (25) ~ (all_62_0 = all_62_1)
% 16.84/3.06 | | (26) $i(all_62_1)
% 16.84/3.06 | | (27) vsomeType(all_53_3) = all_62_0
% 16.84/3.06 | | (28) vlookup(all_53_4, all_53_1) = all_62_1
% 16.84/3.06 | |
% 16.84/3.06 | | BETA: splitting (19) gives:
% 16.84/3.06 | |
% 16.84/3.06 | | Case 1:
% 16.84/3.06 | | |
% 16.84/3.06 | | | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 16.84/3.06 | | | $i] : (varrow(v2, v3) = all_53_3 & vtcheck(v4, v1, v3) = 0 &
% 16.84/3.06 | | | vbind(v0, v2, all_53_5) = v4 & vabs(v0, v2, v1) = all_53_2 &
% 16.84/3.06 | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 16.84/3.06 | | |
% 16.84/3.06 | | | DELTA: instantiating (29) with fresh symbols all_70_0, all_70_1, all_70_2,
% 16.84/3.06 | | | all_70_3, all_70_4 gives:
% 16.84/3.06 | | | (30) varrow(all_70_2, all_70_1) = all_53_3 & vtcheck(all_70_0,
% 16.84/3.06 | | | all_70_3, all_70_1) = 0 & vbind(all_70_4, all_70_2, all_53_5) =
% 16.84/3.06 | | | all_70_0 & vabs(all_70_4, all_70_2, all_70_3) = all_53_2 &
% 16.84/3.06 | | | $i(all_70_0) & $i(all_70_1) & $i(all_70_2) & $i(all_70_3) &
% 16.84/3.06 | | | $i(all_70_4)
% 16.84/3.06 | | |
% 16.84/3.06 | | | ALPHA: (30) implies:
% 16.84/3.06 | | | (31) $i(all_70_4)
% 16.84/3.06 | | | (32) $i(all_70_3)
% 16.84/3.07 | | | (33) $i(all_70_2)
% 16.84/3.07 | | | (34) vabs(all_70_4, all_70_2, all_70_3) = all_53_2
% 16.84/3.07 | | |
% 16.84/3.07 | | | GROUND_INST: instantiating (DIFF-var-abs) with all_53_4, all_70_4,
% 16.84/3.07 | | | all_70_2, all_70_3, all_53_2, simplifying with (10), (14),
% 16.84/3.07 | | | (31), (32), (33), (34) gives:
% 16.84/3.07 | | | (35) $false
% 16.84/3.07 | | |
% 16.84/3.07 | | | CLOSE: (35) is inconsistent.
% 16.84/3.07 | | |
% 16.84/3.07 | | Case 2:
% 16.84/3.07 | | |
% 16.84/3.07 | | | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 16.84/3.07 | | | (varrow(v2, all_53_3) = v3 & vtcheck(all_53_5, v1, v2) = 0 &
% 16.84/3.07 | | | vtcheck(all_53_5, v0, v3) = 0 & vapp(v0, v1) = all_53_2 & $i(v3)
% 16.84/3.07 | | | & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : (vsomeType(all_53_3)
% 16.84/3.07 | | | = v0 & $i(v0) & ? [v1: $i] : (vlookup(v1, all_53_5) = v0 &
% 16.84/3.07 | | | vvar(v1) = all_53_2 & $i(v1)))
% 16.84/3.07 | | |
% 16.84/3.07 | | | BETA: splitting (36) gives:
% 16.84/3.07 | | |
% 16.84/3.07 | | | Case 1:
% 16.84/3.07 | | | |
% 16.84/3.07 | | | | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 16.84/3.07 | | | | (varrow(v2, all_53_3) = v3 & vtcheck(all_53_5, v1, v2) = 0 &
% 16.84/3.07 | | | | vtcheck(all_53_5, v0, v3) = 0 & vapp(v0, v1) = all_53_2 &
% 16.84/3.07 | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 16.84/3.07 | | | |
% 16.84/3.07 | | | | DELTA: instantiating (37) with fresh symbols all_70_0, all_70_1,
% 16.84/3.07 | | | | all_70_2, all_70_3 gives:
% 16.84/3.07 | | | | (38) varrow(all_70_1, all_53_3) = all_70_0 & vtcheck(all_53_5,
% 16.84/3.07 | | | | all_70_2, all_70_1) = 0 & vtcheck(all_53_5, all_70_3,
% 16.84/3.07 | | | | all_70_0) = 0 & vapp(all_70_3, all_70_2) = all_53_2 &
% 16.84/3.07 | | | | $i(all_70_0) & $i(all_70_1) & $i(all_70_2) & $i(all_70_3)
% 16.84/3.07 | | | |
% 16.84/3.07 | | | | ALPHA: (38) implies:
% 16.84/3.07 | | | | (39) $i(all_70_3)
% 16.84/3.07 | | | | (40) $i(all_70_2)
% 16.84/3.07 | | | | (41) vapp(all_70_3, all_70_2) = all_53_2
% 16.84/3.07 | | | |
% 16.84/3.07 | | | | GROUND_INST: instantiating (DIFF-var-app) with all_53_4, all_70_3,
% 16.84/3.07 | | | | all_70_2, all_53_2, simplifying with (10), (14), (39),
% 16.84/3.07 | | | | (40), (41) gives:
% 16.84/3.07 | | | | (42) $false
% 16.84/3.07 | | | |
% 16.84/3.07 | | | | CLOSE: (42) is inconsistent.
% 16.84/3.07 | | | |
% 16.84/3.07 | | | Case 2:
% 16.84/3.07 | | | |
% 16.84/3.07 | | | | (43) ? [v0: $i] : (vsomeType(all_53_3) = v0 & $i(v0) & ? [v1: $i] :
% 16.84/3.07 | | | | (vlookup(v1, all_53_5) = v0 & vvar(v1) = all_53_2 & $i(v1)))
% 16.84/3.07 | | | |
% 16.84/3.07 | | | | DELTA: instantiating (43) with fresh symbol all_70_0 gives:
% 16.84/3.07 | | | | (44) vsomeType(all_53_3) = all_70_0 & $i(all_70_0) & ? [v0: $i] :
% 16.84/3.07 | | | | (vlookup(v0, all_53_5) = all_70_0 & vvar(v0) = all_53_2 &
% 16.84/3.07 | | | | $i(v0))
% 16.84/3.07 | | | |
% 16.84/3.07 | | | | ALPHA: (44) implies:
% 16.84/3.07 | | | | (45) vsomeType(all_53_3) = all_70_0
% 16.84/3.07 | | | | (46) ? [v0: $i] : (vlookup(v0, all_53_5) = all_70_0 & vvar(v0) =
% 16.84/3.07 | | | | all_53_2 & $i(v0))
% 16.84/3.07 | | | |
% 16.84/3.07 | | | | DELTA: instantiating (46) with fresh symbol all_72_0 gives:
% 16.84/3.07 | | | | (47) vlookup(all_72_0, all_53_5) = all_70_0 & vvar(all_72_0) =
% 16.84/3.07 | | | | all_53_2 & $i(all_72_0)
% 16.84/3.07 | | | |
% 16.84/3.07 | | | | ALPHA: (47) implies:
% 16.84/3.07 | | | | (48) $i(all_72_0)
% 16.84/3.07 | | | | (49) vvar(all_72_0) = all_53_2
% 16.84/3.07 | | | | (50) vlookup(all_72_0, all_53_5) = all_70_0
% 16.84/3.07 | | | |
% 16.84/3.07 | | | | GROUND_INST: instantiating (3) with all_62_0, all_70_0, all_53_3,
% 16.84/3.07 | | | | simplifying with (27), (45) gives:
% 16.84/3.07 | | | | (51) all_70_0 = all_62_0
% 16.84/3.07 | | | |
% 16.84/3.07 | | | | REDUCE: (50), (51) imply:
% 16.84/3.07 | | | | (52) vlookup(all_72_0, all_53_5) = all_62_0
% 16.84/3.07 | | | |
% 16.84/3.07 | | | | GROUND_INST: instantiating (EQ-var) with all_53_4, all_72_0, all_53_2,
% 16.84/3.07 | | | | simplifying with (10), (14), (48), (49) gives:
% 16.84/3.07 | | | | (53) all_72_0 = all_53_4
% 16.84/3.07 | | | |
% 16.84/3.08 | | | | REDUCE: (52), (53) imply:
% 16.84/3.08 | | | | (54) vlookup(all_53_4, all_53_5) = all_62_0
% 16.84/3.08 | | | |
% 16.84/3.08 | | | | GROUND_INST: instantiating (lookup2) with all_53_6, all_53_7, all_53_4,
% 16.84/3.08 | | | | all_53_1, all_62_1, all_53_5, all_62_0, simplifying with
% 16.84/3.08 | | | | (7), (8), (9), (10), (13), (15), (26), (28), (54) gives:
% 16.84/3.08 | | | | (55) all_62_0 = all_62_1 | all_53_4 = all_53_7
% 16.84/3.08 | | | |
% 16.84/3.08 | | | | BETA: splitting (55) gives:
% 16.84/3.08 | | | |
% 16.84/3.08 | | | | Case 1:
% 16.84/3.08 | | | | |
% 16.84/3.08 | | | | | (56) all_62_0 = all_62_1
% 16.84/3.08 | | | | |
% 16.84/3.08 | | | | | REDUCE: (25), (56) imply:
% 16.84/3.08 | | | | | (57) $false
% 16.84/3.08 | | | | |
% 16.84/3.08 | | | | | CLOSE: (57) is inconsistent.
% 16.84/3.08 | | | | |
% 16.84/3.08 | | | | Case 2:
% 16.84/3.08 | | | | |
% 16.84/3.08 | | | | | (58) all_53_4 = all_53_7
% 16.84/3.08 | | | | |
% 16.84/3.08 | | | | | REDUCE: (54), (58) imply:
% 16.84/3.08 | | | | | (59) vlookup(all_53_7, all_53_5) = all_62_0
% 16.84/3.08 | | | | |
% 16.84/3.08 | | | | | GROUND_INST: instantiating (4) with vnoType, all_62_0, all_53_5,
% 16.84/3.08 | | | | | all_53_7, simplifying with (16), (59) gives:
% 16.84/3.08 | | | | | (60) all_62_0 = vnoType
% 16.84/3.08 | | | | |
% 16.84/3.08 | | | | | REDUCE: (27), (60) imply:
% 16.84/3.08 | | | | | (61) vsomeType(all_53_3) = vnoType
% 16.84/3.08 | | | | |
% 16.84/3.08 | | | | | GROUND_INST: instantiating (1) with all_53_3, simplifying with (11),
% 16.84/3.08 | | | | | (61) gives:
% 16.84/3.08 | | | | | (62) $false
% 16.84/3.08 | | | | |
% 16.84/3.08 | | | | | CLOSE: (62) is inconsistent.
% 16.84/3.08 | | | | |
% 16.84/3.08 | | | | End of split
% 16.84/3.08 | | | |
% 17.13/3.08 | | | End of split
% 17.13/3.08 | | |
% 17.13/3.08 | | End of split
% 17.13/3.08 | |
% 17.13/3.08 | End of split
% 17.13/3.08 |
% 17.13/3.08 End of proof
% 17.13/3.08 % SZS output end Proof for theBenchmark
% 17.13/3.08
% 17.13/3.08 2460ms
%------------------------------------------------------------------------------