TSTP Solution File: COM138+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM138+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 : n020.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 13.79s 2.59s
% Output : Proof 17.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM138+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 : n020.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 13:24:58 EDT 2023
% 0.13/0.34 % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.66/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.66/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.66/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.66/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.66/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.66/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.66/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.17/1.42 Prover 1: Preprocessing ...
% 5.17/1.46 Prover 2: Preprocessing ...
% 5.17/1.46 Prover 0: Preprocessing ...
% 5.17/1.46 Prover 3: Preprocessing ...
% 5.17/1.46 Prover 5: Preprocessing ...
% 5.17/1.47 Prover 6: Preprocessing ...
% 5.17/1.48 Prover 4: Preprocessing ...
% 11.83/2.30 Prover 3: Constructing countermodel ...
% 11.83/2.30 Prover 1: Constructing countermodel ...
% 11.83/2.32 Prover 6: Proving ...
% 12.05/2.34 Prover 4: Constructing countermodel ...
% 12.05/2.36 Prover 0: Proving ...
% 13.01/2.47 Prover 5: Proving ...
% 13.79/2.58 Prover 2: Proving ...
% 13.79/2.58 Prover 3: proved (1936ms)
% 13.79/2.58
% 13.79/2.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.79/2.59
% 13.79/2.59 Prover 2: stopped
% 13.79/2.59 Prover 6: stopped
% 13.79/2.60 Prover 0: stopped
% 13.79/2.61 Prover 5: stopped
% 13.79/2.62 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.79/2.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.79/2.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.79/2.62 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.25/2.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.48/2.70 Prover 1: Found proof (size 42)
% 14.48/2.70 Prover 1: proved (2056ms)
% 14.48/2.70 Prover 4: stopped
% 15.27/2.81 Prover 8: Preprocessing ...
% 15.79/2.84 Prover 11: Preprocessing ...
% 15.79/2.84 Prover 10: Preprocessing ...
% 15.79/2.85 Prover 13: Preprocessing ...
% 15.79/2.85 Prover 7: Preprocessing ...
% 16.58/2.98 Prover 10: stopped
% 17.10/3.04 Prover 11: stopped
% 17.10/3.04 Prover 7: stopped
% 17.10/3.04 Prover 13: stopped
% 17.10/3.08 Prover 8: Warning: ignoring some quantifiers
% 17.60/3.09 Prover 8: Constructing countermodel ...
% 17.60/3.10 Prover 8: stopped
% 17.60/3.10
% 17.60/3.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.60/3.11
% 17.60/3.11 % SZS output start Proof for theBenchmark
% 17.60/3.12 Assumptions after simplification:
% 17.60/3.12 ---------------------------------
% 17.60/3.12
% 17.60/3.12 (DIFF-var-abs)
% 17.80/3.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 17.80/3.14 (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 17.80/3.14 $i(v1) | ~ $i(v0))
% 17.80/3.14
% 17.80/3.14 (DIFF-var-app)
% 17.80/3.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vapp(v1, v2) =
% 17.80/3.14 v3) | ~ (vvar(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 17.80/3.14
% 17.80/3.14 (EQ-var)
% 17.80/3.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vvar(v1) = v2) | ~
% 17.80/3.14 (vvar(v0) = v2) | ~ $i(v1) | ~ $i(v0))
% 17.80/3.14
% 17.80/3.14 (T-Strong-var)
% 17.80/3.15 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 17.80/3.15 $i] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & ~ (v6 = 0)
% 17.80/3.15 & vtcheck(v7, v5, v4) = 0 & vtcheck(v2, v5, v4) = v8 & vbind(v0, v1, v2) =
% 17.80/3.15 v7 & visFreeVar(v0, v5) = v6 & vvar(v3) = v5 & $i(v7) & $i(v5) & $i(v4) &
% 17.80/3.15 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.80/3.15
% 17.80/3.15 (T-inv)
% 17.80/3.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vtcheck(v2, v0, v1) = 0) | ~
% 17.80/3.15 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 17.80/3.15 ? [v6: $i] : ? [v7: $i] : (varrow(v5, v6) = v1 & vtcheck(v7, v4, v6) = 0 &
% 17.80/3.15 vbind(v3, v5, v2) = v7 & vabs(v3, v5, v4) = v0 & $i(v7) & $i(v6) & $i(v5)
% 17.80/3.15 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 17.80/3.15 : (varrow(v5, v1) = v6 & vtcheck(v2, v4, v5) = 0 & vtcheck(v2, v3, v6) = 0 &
% 17.80/3.15 vapp(v3, v4) = v0 & $i(v6) & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] :
% 17.80/3.15 (vsomeType(v1) = v3 & $i(v3) & ? [v4: $i] : (vlookup(v4, v2) = v3 &
% 17.80/3.15 vvar(v4) = v0 & $i(v4))))
% 17.80/3.15
% 17.80/3.15 (T-var)
% 17.80/3.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 17.80/3.15 | ~ (vtcheck(v0, v3, v2) = v4) | ~ (vvar(v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 17.80/3.15 | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & vlookup(v1, v0) =
% 17.80/3.15 v5 & vsomeType(v2) = v6 & $i(v6) & $i(v5)))
% 17.80/3.15
% 17.80/3.15 (isFreeVar0)
% 17.80/3.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (visFreeVar(v0,
% 17.80/3.15 v1) = v3) | ~ (vvar(v2) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ((
% 17.80/3.15 ~ (v3 = 0) | v2 = v0) & ( ~ (v2 = v0) | v3 = 0)))
% 17.80/3.15
% 17.80/3.15 (lookup2)
% 17.80/3.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.80/3.15 $i] : ! [v6: $i] : (v6 = v4 | v2 = v1 | ~ (vlookup(v2, v5) = v6) | ~
% 17.80/3.15 (vlookup(v2, v3) = v4) | ~ (vbind(v1, v0, v5) = v3) | ~ $i(v5) | ~ $i(v4)
% 17.80/3.15 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 17.80/3.15
% 17.80/3.15 (function-axioms)
% 17.80/3.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 17.80/3.16 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0:
% 17.80/3.16 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.80/3.16 : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3,
% 17.80/3.16 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 17.80/3.16 [v4: $i] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) =
% 17.80/3.16 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 17.80/3.16 : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & !
% 17.80/3.16 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3,
% 17.80/3.16 v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.80/3.16 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~
% 17.80/3.16 (vlookup(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.80/3.16 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.80/3.16 (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0: $i] : !
% 17.80/3.16 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~
% 17.80/3.16 (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 17.80/3.16 ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 17.80/3.16 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0))
% 17.80/3.16 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 17.80/3.16 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: $i] :
% 17.80/3.16 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~
% 17.80/3.16 (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 17.80/3.16 ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 17.80/3.16 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) =
% 17.80/3.16 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 17.80/3.16 $i] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & !
% 17.80/3.16 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~
% 17.80/3.16 (vsomeType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.80/3.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (visValue(v2) = v1) | ~
% 17.80/3.16 (visValue(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 17.80/3.16 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0))
% 17.80/3.16
% 17.80/3.16 Further assumptions not needed in the proof:
% 17.80/3.16 --------------------------------------------
% 17.80/3.16 DIFF-abs-app, DIFF-empty-bind, DIFF-noExp-someExp, DIFF-noType-someType, EQ-abs,
% 17.80/3.16 EQ-app, EQ-arrow, EQ-bind, EQ-empty, EQ-noExp, EQ-noType, EQ-someExp,
% 17.80/3.16 EQ-someType, T-Context-Duplicate, T-Context-Swap, T-Weak, T-abs, T-app,
% 17.80/3.16 gensym-is-fresh, getSomeExp0, getSomeType0, isFreeVar1, isFreeVar2, isSomeExp0,
% 17.80/3.16 isSomeExp1, isSomeType0, isSomeType1, isValue0, isValue1, isValue2, lookup-INV,
% 17.80/3.16 lookup0, lookup1, reduce-INV, reduce0, reduce1, reduce2, reduce3, reduce4,
% 17.80/3.16 reduce5, reduce6, subst-INV, subst0, subst1, subst2, subst3, subst4, subst5
% 17.80/3.16
% 17.80/3.16 Those formulas are unsatisfiable:
% 17.80/3.16 ---------------------------------
% 17.80/3.16
% 17.80/3.16 Begin of proof
% 17.80/3.16 |
% 17.80/3.16 | ALPHA: (function-axioms) implies:
% 17.80/3.16 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2)
% 17.80/3.16 | = v1) | ~ (vsomeType(v2) = v0))
% 17.80/3.16 |
% 17.80/3.16 | DELTA: instantiating (T-Strong-var) with fresh symbols all_54_0, all_54_1,
% 17.80/3.16 | all_54_2, all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8
% 17.80/3.16 | gives:
% 17.80/3.16 | (2) ~ (all_54_0 = 0) & ~ (all_54_2 = 0) & vtcheck(all_54_1, all_54_3,
% 17.80/3.16 | all_54_4) = 0 & vtcheck(all_54_6, all_54_3, all_54_4) = all_54_0 &
% 17.80/3.16 | vbind(all_54_8, all_54_7, all_54_6) = all_54_1 & visFreeVar(all_54_8,
% 17.80/3.16 | all_54_3) = all_54_2 & vvar(all_54_5) = all_54_3 & $i(all_54_1) &
% 17.80/3.16 | $i(all_54_3) & $i(all_54_4) & $i(all_54_5) & $i(all_54_6) &
% 17.80/3.16 | $i(all_54_7) & $i(all_54_8)
% 17.80/3.16 |
% 17.80/3.16 | ALPHA: (2) implies:
% 17.80/3.16 | (3) ~ (all_54_2 = 0)
% 17.80/3.16 | (4) ~ (all_54_0 = 0)
% 17.80/3.17 | (5) $i(all_54_8)
% 17.80/3.17 | (6) $i(all_54_7)
% 17.80/3.17 | (7) $i(all_54_6)
% 17.80/3.17 | (8) $i(all_54_5)
% 17.80/3.17 | (9) $i(all_54_4)
% 17.80/3.17 | (10) $i(all_54_3)
% 17.80/3.17 | (11) $i(all_54_1)
% 17.80/3.17 | (12) vvar(all_54_5) = all_54_3
% 17.80/3.17 | (13) visFreeVar(all_54_8, all_54_3) = all_54_2
% 17.80/3.17 | (14) vbind(all_54_8, all_54_7, all_54_6) = all_54_1
% 17.80/3.17 | (15) vtcheck(all_54_6, all_54_3, all_54_4) = all_54_0
% 17.80/3.17 | (16) vtcheck(all_54_1, all_54_3, all_54_4) = 0
% 17.80/3.17 |
% 17.80/3.17 | GROUND_INST: instantiating (isFreeVar0) with all_54_8, all_54_3, all_54_5,
% 17.80/3.17 | all_54_2, simplifying with (5), (8), (10), (12), (13) gives:
% 17.80/3.17 | (17) ( ~ (all_54_2 = 0) | all_54_5 = all_54_8) & ( ~ (all_54_5 = all_54_8)
% 17.80/3.17 | | all_54_2 = 0)
% 17.80/3.17 |
% 17.80/3.17 | ALPHA: (17) implies:
% 17.80/3.17 | (18) ~ (all_54_5 = all_54_8) | all_54_2 = 0
% 17.80/3.17 |
% 17.80/3.17 | GROUND_INST: instantiating (T-var) with all_54_6, all_54_5, all_54_4,
% 17.80/3.17 | all_54_3, all_54_0, simplifying with (7), (8), (9), (12), (15)
% 17.80/3.17 | gives:
% 17.80/3.17 | (19) all_54_0 = 0 | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 17.80/3.17 | vlookup(all_54_5, all_54_6) = v0 & vsomeType(all_54_4) = v1 & $i(v1)
% 17.80/3.17 | & $i(v0))
% 17.80/3.17 |
% 17.80/3.17 | GROUND_INST: instantiating (T-inv) with all_54_3, all_54_4, all_54_1,
% 17.80/3.17 | simplifying with (9), (10), (11), (16) gives:
% 17.80/3.17 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 17.80/3.17 | (varrow(v2, v3) = all_54_4 & vtcheck(v4, v1, v3) = 0 & vbind(v0, v2,
% 17.80/3.17 | all_54_1) = v4 & vabs(v0, v2, v1) = all_54_3 & $i(v4) & $i(v3) &
% 17.80/3.17 | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 17.80/3.17 | : ? [v3: $i] : (varrow(v2, all_54_4) = v3 & vtcheck(all_54_1, v1, v2)
% 17.80/3.17 | = 0 & vtcheck(all_54_1, v0, v3) = 0 & vapp(v0, v1) = all_54_3 &
% 17.80/3.17 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] :
% 17.80/3.17 | (vsomeType(all_54_4) = v0 & $i(v0) & ? [v1: $i] : (vlookup(v1,
% 17.80/3.17 | all_54_1) = v0 & vvar(v1) = all_54_3 & $i(v1)))
% 17.80/3.17 |
% 17.80/3.17 | BETA: splitting (19) gives:
% 17.80/3.17 |
% 17.80/3.17 | Case 1:
% 17.80/3.17 | |
% 17.80/3.17 | | (21) all_54_0 = 0
% 17.80/3.17 | |
% 17.80/3.17 | | REDUCE: (4), (21) imply:
% 17.80/3.17 | | (22) $false
% 17.80/3.17 | |
% 17.80/3.17 | | CLOSE: (22) is inconsistent.
% 17.80/3.17 | |
% 17.80/3.17 | Case 2:
% 17.80/3.17 | |
% 17.80/3.17 | | (23) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & vlookup(all_54_5,
% 17.80/3.17 | | all_54_6) = v0 & vsomeType(all_54_4) = v1 & $i(v1) & $i(v0))
% 17.80/3.17 | |
% 17.80/3.17 | | DELTA: instantiating (23) with fresh symbols all_63_0, all_63_1 gives:
% 17.80/3.17 | | (24) ~ (all_63_0 = all_63_1) & vlookup(all_54_5, all_54_6) = all_63_1 &
% 17.80/3.17 | | vsomeType(all_54_4) = all_63_0 & $i(all_63_0) & $i(all_63_1)
% 17.80/3.17 | |
% 17.80/3.17 | | ALPHA: (24) implies:
% 17.80/3.17 | | (25) ~ (all_63_0 = all_63_1)
% 17.80/3.18 | | (26) vsomeType(all_54_4) = all_63_0
% 17.80/3.18 | | (27) vlookup(all_54_5, all_54_6) = all_63_1
% 17.80/3.18 | |
% 17.80/3.18 | | BETA: splitting (18) gives:
% 17.80/3.18 | |
% 17.80/3.18 | | Case 1:
% 17.80/3.18 | | |
% 17.80/3.18 | | | (28) ~ (all_54_5 = all_54_8)
% 17.80/3.18 | | |
% 17.80/3.18 | | | BETA: splitting (20) gives:
% 17.80/3.18 | | |
% 17.80/3.18 | | | Case 1:
% 17.80/3.18 | | | |
% 17.80/3.18 | | | | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 17.80/3.18 | | | | $i] : (varrow(v2, v3) = all_54_4 & vtcheck(v4, v1, v3) = 0 &
% 17.80/3.18 | | | | vbind(v0, v2, all_54_1) = v4 & vabs(v0, v2, v1) = all_54_3 &
% 17.80/3.18 | | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.80/3.18 | | | |
% 17.80/3.18 | | | | DELTA: instantiating (29) with fresh symbols all_75_0, all_75_1,
% 17.80/3.18 | | | | all_75_2, all_75_3, all_75_4 gives:
% 17.80/3.18 | | | | (30) varrow(all_75_2, all_75_1) = all_54_4 & vtcheck(all_75_0,
% 17.80/3.18 | | | | all_75_3, all_75_1) = 0 & vbind(all_75_4, all_75_2, all_54_1)
% 17.80/3.18 | | | | = all_75_0 & vabs(all_75_4, all_75_2, all_75_3) = all_54_3 &
% 17.80/3.18 | | | | $i(all_75_0) & $i(all_75_1) & $i(all_75_2) & $i(all_75_3) &
% 17.80/3.18 | | | | $i(all_75_4)
% 17.80/3.18 | | | |
% 17.80/3.18 | | | | ALPHA: (30) implies:
% 17.80/3.18 | | | | (31) $i(all_75_4)
% 17.80/3.18 | | | | (32) $i(all_75_3)
% 17.80/3.18 | | | | (33) $i(all_75_2)
% 17.80/3.18 | | | | (34) vabs(all_75_4, all_75_2, all_75_3) = all_54_3
% 17.80/3.18 | | | |
% 17.80/3.18 | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_54_5, all_75_4,
% 17.80/3.18 | | | | all_75_2, all_75_3, all_54_3, simplifying with (8), (12),
% 17.80/3.18 | | | | (31), (32), (33), (34) gives:
% 17.80/3.18 | | | | (35) $false
% 17.80/3.18 | | | |
% 17.80/3.18 | | | | CLOSE: (35) is inconsistent.
% 17.80/3.18 | | | |
% 17.80/3.18 | | | Case 2:
% 17.80/3.18 | | | |
% 17.80/3.18 | | | | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 17.80/3.18 | | | | (varrow(v2, all_54_4) = v3 & vtcheck(all_54_1, v1, v2) = 0 &
% 17.80/3.18 | | | | vtcheck(all_54_1, v0, v3) = 0 & vapp(v0, v1) = all_54_3 &
% 17.80/3.18 | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] :
% 17.80/3.18 | | | | (vsomeType(all_54_4) = v0 & $i(v0) & ? [v1: $i] : (vlookup(v1,
% 17.80/3.18 | | | | all_54_1) = v0 & vvar(v1) = all_54_3 & $i(v1)))
% 17.80/3.18 | | | |
% 17.80/3.18 | | | | BETA: splitting (36) gives:
% 17.80/3.18 | | | |
% 17.80/3.18 | | | | Case 1:
% 17.80/3.18 | | | | |
% 17.80/3.18 | | | | | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 17.80/3.18 | | | | | (varrow(v2, all_54_4) = v3 & vtcheck(all_54_1, v1, v2) = 0 &
% 17.80/3.18 | | | | | vtcheck(all_54_1, v0, v3) = 0 & vapp(v0, v1) = all_54_3 &
% 17.80/3.18 | | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.80/3.18 | | | | |
% 17.80/3.18 | | | | | DELTA: instantiating (37) with fresh symbols all_75_0, all_75_1,
% 17.80/3.18 | | | | | all_75_2, all_75_3 gives:
% 17.80/3.18 | | | | | (38) varrow(all_75_1, all_54_4) = all_75_0 & vtcheck(all_54_1,
% 17.80/3.18 | | | | | all_75_2, all_75_1) = 0 & vtcheck(all_54_1, all_75_3,
% 17.80/3.18 | | | | | all_75_0) = 0 & vapp(all_75_3, all_75_2) = all_54_3 &
% 17.80/3.18 | | | | | $i(all_75_0) & $i(all_75_1) & $i(all_75_2) & $i(all_75_3)
% 17.80/3.18 | | | | |
% 17.80/3.18 | | | | | ALPHA: (38) implies:
% 17.80/3.18 | | | | | (39) $i(all_75_3)
% 17.80/3.18 | | | | | (40) $i(all_75_2)
% 17.80/3.18 | | | | | (41) vapp(all_75_3, all_75_2) = all_54_3
% 17.80/3.18 | | | | |
% 17.80/3.18 | | | | | GROUND_INST: instantiating (DIFF-var-app) with all_54_5, all_75_3,
% 17.80/3.18 | | | | | all_75_2, all_54_3, simplifying with (8), (12), (39),
% 17.80/3.18 | | | | | (40), (41) gives:
% 17.80/3.18 | | | | | (42) $false
% 17.80/3.18 | | | | |
% 17.80/3.18 | | | | | CLOSE: (42) is inconsistent.
% 17.80/3.18 | | | | |
% 17.80/3.18 | | | | Case 2:
% 17.80/3.18 | | | | |
% 17.80/3.18 | | | | | (43) ? [v0: $i] : (vsomeType(all_54_4) = v0 & $i(v0) & ? [v1: $i]
% 17.80/3.18 | | | | | : (vlookup(v1, all_54_1) = v0 & vvar(v1) = all_54_3 &
% 17.80/3.18 | | | | | $i(v1)))
% 17.80/3.18 | | | | |
% 17.80/3.18 | | | | | DELTA: instantiating (43) with fresh symbol all_75_0 gives:
% 17.80/3.18 | | | | | (44) vsomeType(all_54_4) = all_75_0 & $i(all_75_0) & ? [v0: $i] :
% 17.80/3.18 | | | | | (vlookup(v0, all_54_1) = all_75_0 & vvar(v0) = all_54_3 &
% 17.80/3.18 | | | | | $i(v0))
% 17.80/3.18 | | | | |
% 17.80/3.18 | | | | | ALPHA: (44) implies:
% 17.80/3.18 | | | | | (45) $i(all_75_0)
% 17.80/3.19 | | | | | (46) vsomeType(all_54_4) = all_75_0
% 17.80/3.19 | | | | | (47) ? [v0: $i] : (vlookup(v0, all_54_1) = all_75_0 & vvar(v0) =
% 17.80/3.19 | | | | | all_54_3 & $i(v0))
% 17.80/3.19 | | | | |
% 17.80/3.19 | | | | | DELTA: instantiating (47) with fresh symbol all_77_0 gives:
% 17.80/3.19 | | | | | (48) vlookup(all_77_0, all_54_1) = all_75_0 & vvar(all_77_0) =
% 17.80/3.19 | | | | | all_54_3 & $i(all_77_0)
% 17.80/3.19 | | | | |
% 17.80/3.19 | | | | | ALPHA: (48) implies:
% 17.80/3.19 | | | | | (49) $i(all_77_0)
% 17.80/3.19 | | | | | (50) vvar(all_77_0) = all_54_3
% 17.80/3.19 | | | | | (51) vlookup(all_77_0, all_54_1) = all_75_0
% 17.80/3.19 | | | | |
% 17.80/3.19 | | | | | GROUND_INST: instantiating (1) with all_63_0, all_75_0, all_54_4,
% 17.80/3.19 | | | | | simplifying with (26), (46) gives:
% 17.80/3.19 | | | | | (52) all_75_0 = all_63_0
% 17.80/3.19 | | | | |
% 17.80/3.19 | | | | | REDUCE: (51), (52) imply:
% 17.80/3.19 | | | | | (53) vlookup(all_77_0, all_54_1) = all_63_0
% 17.80/3.19 | | | | |
% 17.80/3.19 | | | | | REDUCE: (45), (52) imply:
% 17.80/3.19 | | | | | (54) $i(all_63_0)
% 17.80/3.19 | | | | |
% 17.80/3.19 | | | | | GROUND_INST: instantiating (EQ-var) with all_54_5, all_77_0, all_54_3,
% 17.80/3.19 | | | | | simplifying with (8), (12), (49), (50) gives:
% 17.80/3.19 | | | | | (55) all_77_0 = all_54_5
% 17.80/3.19 | | | | |
% 17.80/3.19 | | | | | REDUCE: (53), (55) imply:
% 17.80/3.19 | | | | | (56) vlookup(all_54_5, all_54_1) = all_63_0
% 17.80/3.19 | | | | |
% 17.80/3.19 | | | | | GROUND_INST: instantiating (lookup2) with all_54_7, all_54_8,
% 17.80/3.19 | | | | | all_54_5, all_54_1, all_63_0, all_54_6, all_63_1,
% 17.80/3.19 | | | | | simplifying with (5), (6), (7), (8), (11), (14), (27),
% 17.80/3.19 | | | | | (54), (56) gives:
% 17.80/3.19 | | | | | (57) all_63_0 = all_63_1 | all_54_5 = all_54_8
% 17.80/3.19 | | | | |
% 17.80/3.19 | | | | | BETA: splitting (57) gives:
% 17.80/3.19 | | | | |
% 17.80/3.19 | | | | | Case 1:
% 17.80/3.19 | | | | | |
% 17.80/3.19 | | | | | | (58) all_63_0 = all_63_1
% 17.80/3.19 | | | | | |
% 17.80/3.19 | | | | | | REDUCE: (25), (58) imply:
% 17.80/3.19 | | | | | | (59) $false
% 17.80/3.19 | | | | | |
% 17.80/3.19 | | | | | | CLOSE: (59) is inconsistent.
% 17.80/3.19 | | | | | |
% 17.80/3.19 | | | | | Case 2:
% 17.80/3.19 | | | | | |
% 17.80/3.19 | | | | | | (60) all_54_5 = all_54_8
% 17.80/3.19 | | | | | |
% 17.80/3.19 | | | | | | REDUCE: (28), (60) imply:
% 17.80/3.19 | | | | | | (61) $false
% 17.80/3.19 | | | | | |
% 17.80/3.19 | | | | | | CLOSE: (61) is inconsistent.
% 17.80/3.19 | | | | | |
% 17.80/3.19 | | | | | End of split
% 17.80/3.19 | | | | |
% 17.80/3.19 | | | | End of split
% 17.80/3.19 | | | |
% 17.80/3.19 | | | End of split
% 17.80/3.19 | | |
% 17.80/3.19 | | Case 2:
% 17.80/3.19 | | |
% 17.80/3.19 | | | (62) all_54_2 = 0
% 17.80/3.19 | | |
% 17.80/3.19 | | | REDUCE: (3), (62) imply:
% 17.80/3.19 | | | (63) $false
% 17.80/3.19 | | |
% 17.80/3.19 | | | CLOSE: (63) is inconsistent.
% 17.80/3.19 | | |
% 17.80/3.19 | | End of split
% 17.80/3.19 | |
% 17.80/3.19 | End of split
% 17.80/3.19 |
% 17.80/3.19 End of proof
% 17.80/3.19 % SZS output end Proof for theBenchmark
% 17.80/3.19
% 17.80/3.19 2570ms
%------------------------------------------------------------------------------