TSTP Solution File: COM135+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM135+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 : n014.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 18:44:34 EDT 2023
% Result : Theorem 15.32s 3.01s
% Output : Proof 19.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : COM135+1 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 13:05:00 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.66 ________ _____
% 0.21/0.66 ___ __ \_________(_)________________________________
% 0.21/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.66
% 0.21/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.66 (2023-06-19)
% 0.21/0.66
% 0.21/0.66 (c) Philipp Rümmer, 2009-2023
% 0.21/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.66 Amanda Stjerna.
% 0.21/0.66 Free software under BSD-3-Clause.
% 0.21/0.66
% 0.21/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.66
% 0.21/0.66 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.69 Running up to 7 provers in parallel.
% 0.21/0.71 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.71 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.71 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.71 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.71 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.85/1.51 Prover 1: Preprocessing ...
% 4.85/1.51 Prover 4: Preprocessing ...
% 4.85/1.55 Prover 5: Preprocessing ...
% 4.85/1.55 Prover 0: Preprocessing ...
% 4.85/1.55 Prover 3: Preprocessing ...
% 4.85/1.55 Prover 6: Preprocessing ...
% 4.85/1.55 Prover 2: Preprocessing ...
% 11.68/2.44 Prover 6: Proving ...
% 11.68/2.44 Prover 1: Constructing countermodel ...
% 11.68/2.45 Prover 4: Constructing countermodel ...
% 11.68/2.46 Prover 3: Constructing countermodel ...
% 11.96/2.49 Prover 0: Proving ...
% 12.75/2.62 Prover 5: Proving ...
% 14.82/2.88 Prover 2: Proving ...
% 15.32/3.01 Prover 3: proved (2310ms)
% 15.32/3.01
% 15.32/3.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.32/3.01
% 15.32/3.01 Prover 6: stopped
% 15.32/3.02 Prover 0: stopped
% 15.99/3.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.99/3.02 Prover 2: stopped
% 15.99/3.03 Prover 5: stopped
% 15.99/3.03 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.99/3.03 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.99/3.03 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.99/3.03 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.46/3.16 Prover 13: Preprocessing ...
% 17.06/3.16 Prover 7: Preprocessing ...
% 17.15/3.18 Prover 8: Preprocessing ...
% 17.15/3.20 Prover 10: Preprocessing ...
% 17.44/3.21 Prover 11: Preprocessing ...
% 18.27/3.36 Prover 1: Found proof (size 79)
% 18.27/3.36 Prover 1: proved (2671ms)
% 18.27/3.37 Prover 10: stopped
% 18.27/3.37 Prover 4: stopped
% 18.27/3.37 Prover 7: stopped
% 18.27/3.39 Prover 11: stopped
% 18.27/3.39 Prover 13: stopped
% 18.27/3.44 Prover 8: Warning: ignoring some quantifiers
% 18.27/3.45 Prover 8: Constructing countermodel ...
% 18.27/3.46 Prover 8: stopped
% 18.27/3.46
% 18.27/3.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.27/3.46
% 18.27/3.47 % SZS output start Proof for theBenchmark
% 18.27/3.48 Assumptions after simplification:
% 18.27/3.48 ---------------------------------
% 18.27/3.48
% 18.27/3.48 (DIFF-var-abs)
% 18.27/3.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 18.27/3.50 (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 18.27/3.50 $i(v1) | ~ $i(v0))
% 18.27/3.50
% 18.27/3.50 (DIFF-var-app)
% 18.27/3.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vapp(v1, v2) =
% 18.27/3.50 v3) | ~ (vvar(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 18.27/3.50
% 18.27/3.50 (EQ-someType)
% 18.27/3.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v1) = v2) |
% 18.27/3.50 ~ (vsomeType(v0) = v2) | ~ $i(v1) | ~ $i(v0))
% 18.27/3.50
% 18.27/3.50 (EQ-var)
% 18.27/3.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vvar(v1) = v2) | ~
% 18.27/3.50 (vvar(v0) = v2) | ~ $i(v1) | ~ $i(v0))
% 18.27/3.50
% 18.27/3.50 (T-Strong)
% 18.27/3.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 18.27/3.51 $i] : ( ~ (vtcheck(v5, v3, v4) = 0) | ~ (vbind(v0, v1, v2) = v5) | ~
% 18.27/3.51 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 18.27/3.51 [v7: any] : (vtcheck(v2, v3, v4) = v7 & visFreeVar(v0, v3) = v6 & (v7 = 0 |
% 18.27/3.51 v6 = 0)))
% 18.27/3.51
% 18.27/3.51 (T-inv)
% 18.27/3.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vtcheck(v2, v0, v1) = 0) | ~
% 18.27/3.51 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 18.27/3.51 ? [v6: $i] : ? [v7: $i] : (varrow(v5, v6) = v1 & vtcheck(v7, v4, v6) = 0 &
% 18.27/3.51 vbind(v3, v5, v2) = v7 & vabs(v3, v5, v4) = v0 & $i(v7) & $i(v6) & $i(v5)
% 18.27/3.51 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 18.27/3.51 : (varrow(v5, v1) = v6 & vtcheck(v2, v4, v5) = 0 & vtcheck(v2, v3, v6) = 0 &
% 18.27/3.51 vapp(v3, v4) = v0 & $i(v6) & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] :
% 18.27/3.51 (vsomeType(v1) = v3 & $i(v3) & ? [v4: $i] : (vlookup(v4, v2) = v3 &
% 18.27/3.51 vvar(v4) = v0 & $i(v4))))
% 18.27/3.51
% 18.27/3.51 (T-subst-var)
% 18.27/3.51 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 18.27/3.51 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ( ~ (v9 = 0)
% 18.27/3.51 & vsubst(v2, v3, v7) = v8 & vtcheck(v6, v7, v5) = 0 & vtcheck(v1, v8, v5) =
% 18.27/3.51 v9 & vtcheck(v1, v3, v0) = 0 & vbind(v2, v0, v1) = v6 & vvar(v4) = v7 &
% 18.27/3.51 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 18.27/3.51 $i(v0))
% 18.27/3.51
% 18.27/3.51 (isFreeVar0)
% 18.27/3.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (visFreeVar(v0,
% 18.27/3.51 v1) = v3) | ~ (vvar(v2) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ((
% 18.27/3.52 ~ (v3 = 0) | v2 = v0) & ( ~ (v2 = v0) | v3 = 0)))
% 18.27/3.52
% 18.27/3.52 (lookup1)
% 18.27/3.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 18.27/3.52 (vlookup(v1, v2) = v3) | ~ (vbind(v1, v4, v0) = v2) | ~ $i(v4) | ~ $i(v3)
% 18.27/3.52 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | vsomeType(v4) = v3)
% 18.27/3.52
% 18.27/3.52 (subst0)
% 18.27/3.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 18.27/3.52 (vsubst(v0, v1, v2) = v3) | ~ (vvar(v0) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 18.27/3.52 $i(v1) | ~ $i(v0))
% 18.27/3.52
% 18.27/3.52 (subst1)
% 18.27/3.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1
% 18.27/3.52 | v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vvar(v4) = v2) | ~ $i(v4) |
% 18.27/3.52 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 18.27/3.52
% 18.27/3.52 (function-axioms)
% 18.27/3.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 18.27/3.53 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0:
% 18.27/3.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.27/3.53 : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3,
% 18.27/3.53 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 18.27/3.53 [v4: $i] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) =
% 18.27/3.53 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 18.27/3.53 : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & !
% 18.27/3.53 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3,
% 18.27/3.53 v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 18.27/3.53 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~
% 18.27/3.53 (vlookup(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.27/3.53 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.27/3.53 (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0: $i] : !
% 18.27/3.53 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~
% 18.27/3.53 (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 18.27/3.53 ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 18.27/3.53 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0))
% 18.27/3.53 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 18.27/3.53 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: $i] :
% 18.27/3.53 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~
% 18.27/3.53 (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 18.27/3.53 ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 18.27/3.53 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) =
% 18.27/3.53 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 18.27/3.53 $i] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & !
% 18.27/3.53 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~
% 18.27/3.53 (vsomeType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.27/3.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (visValue(v2) = v1) | ~
% 18.27/3.53 (visValue(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 18.27/3.53 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0))
% 18.27/3.53
% 18.27/3.53 Further assumptions not needed in the proof:
% 18.27/3.53 --------------------------------------------
% 18.27/3.53 DIFF-abs-app, DIFF-empty-bind, DIFF-noExp-someExp, DIFF-noType-someType, EQ-abs,
% 18.27/3.53 EQ-app, EQ-arrow, EQ-bind, EQ-empty, EQ-noExp, EQ-noType, EQ-someExp,
% 18.27/3.53 T-Context-Duplicate, T-Context-Swap, T-Weak, T-Weak-FreeVar, T-abs, T-app,
% 18.27/3.53 T-var, gensym-is-fresh, getSomeExp0, getSomeType0, isFreeVar1, isFreeVar2,
% 18.27/3.53 isSomeExp0, isSomeExp1, isSomeType0, isSomeType1, isValue0, isValue1, isValue2,
% 18.27/3.53 lookup-INV, lookup0, lookup2, reduce-INV, reduce0, reduce1, reduce2, reduce3,
% 18.27/3.53 reduce4, reduce5, reduce6, subst-INV, subst2, subst3, subst4, subst5
% 18.27/3.53
% 18.27/3.53 Those formulas are unsatisfiable:
% 18.27/3.53 ---------------------------------
% 18.27/3.53
% 18.27/3.53 Begin of proof
% 18.27/3.53 |
% 18.27/3.53 | ALPHA: (function-axioms) implies:
% 19.11/3.53 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 19.11/3.53 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) |
% 19.11/3.53 | ~ (vtcheck(v4, v3, v2) = v0))
% 19.11/3.53 |
% 19.11/3.53 | DELTA: instantiating (T-subst-var) with fresh symbols all_56_0, all_56_1,
% 19.11/3.53 | all_56_2, all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8,
% 19.11/3.53 | all_56_9 gives:
% 19.11/3.53 | (2) ~ (all_56_0 = 0) & vsubst(all_56_7, all_56_6, all_56_2) = all_56_1 &
% 19.11/3.53 | vtcheck(all_56_3, all_56_2, all_56_4) = 0 & vtcheck(all_56_8, all_56_1,
% 19.11/3.53 | all_56_4) = all_56_0 & vtcheck(all_56_8, all_56_6, all_56_9) = 0 &
% 19.11/3.53 | vbind(all_56_7, all_56_9, all_56_8) = all_56_3 & vvar(all_56_5) =
% 19.11/3.53 | all_56_2 & $i(all_56_1) & $i(all_56_2) & $i(all_56_3) & $i(all_56_4) &
% 19.11/3.53 | $i(all_56_5) & $i(all_56_6) & $i(all_56_7) & $i(all_56_8) &
% 19.11/3.53 | $i(all_56_9)
% 19.11/3.53 |
% 19.11/3.53 | ALPHA: (2) implies:
% 19.11/3.53 | (3) ~ (all_56_0 = 0)
% 19.11/3.53 | (4) $i(all_56_9)
% 19.11/3.53 | (5) $i(all_56_8)
% 19.11/3.53 | (6) $i(all_56_7)
% 19.11/3.53 | (7) $i(all_56_6)
% 19.11/3.53 | (8) $i(all_56_5)
% 19.11/3.53 | (9) $i(all_56_4)
% 19.11/3.53 | (10) $i(all_56_3)
% 19.11/3.53 | (11) $i(all_56_2)
% 19.11/3.53 | (12) $i(all_56_1)
% 19.11/3.53 | (13) vvar(all_56_5) = all_56_2
% 19.11/3.53 | (14) vbind(all_56_7, all_56_9, all_56_8) = all_56_3
% 19.11/3.53 | (15) vtcheck(all_56_8, all_56_6, all_56_9) = 0
% 19.11/3.53 | (16) vtcheck(all_56_8, all_56_1, all_56_4) = all_56_0
% 19.11/3.53 | (17) vtcheck(all_56_3, all_56_2, all_56_4) = 0
% 19.11/3.53 | (18) vsubst(all_56_7, all_56_6, all_56_2) = all_56_1
% 19.11/3.53 |
% 19.11/3.54 | GROUND_INST: instantiating (T-Strong) with all_56_7, all_56_9, all_56_8,
% 19.11/3.54 | all_56_2, all_56_4, all_56_3, simplifying with (4), (5), (6),
% 19.11/3.54 | (9), (11), (14), (17) gives:
% 19.11/3.54 | (19) ? [v0: any] : ? [v1: any] : (vtcheck(all_56_8, all_56_2, all_56_4) =
% 19.11/3.54 | v1 & visFreeVar(all_56_7, all_56_2) = v0 & (v1 = 0 | v0 = 0))
% 19.11/3.54 |
% 19.11/3.54 | GROUND_INST: instantiating (T-inv) with all_56_2, all_56_4, all_56_3,
% 19.11/3.54 | simplifying with (9), (10), (11), (17) gives:
% 19.11/3.54 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 19.11/3.54 | (varrow(v2, v3) = all_56_4 & vtcheck(v4, v1, v3) = 0 & vbind(v0, v2,
% 19.11/3.54 | all_56_3) = v4 & vabs(v0, v2, v1) = all_56_2 & $i(v4) & $i(v3) &
% 19.11/3.54 | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 19.11/3.54 | : ? [v3: $i] : (varrow(v2, all_56_4) = v3 & vtcheck(all_56_3, v1, v2)
% 19.11/3.54 | = 0 & vtcheck(all_56_3, v0, v3) = 0 & vapp(v0, v1) = all_56_2 &
% 19.11/3.54 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] :
% 19.11/3.54 | (vsomeType(all_56_4) = v0 & $i(v0) & ? [v1: $i] : (vlookup(v1,
% 19.11/3.54 | all_56_3) = v0 & vvar(v1) = all_56_2 & $i(v1)))
% 19.11/3.54 |
% 19.11/3.54 | GROUND_INST: instantiating (subst1) with all_56_6, all_56_7, all_56_2,
% 19.11/3.54 | all_56_1, all_56_5, simplifying with (6), (7), (8), (11), (12),
% 19.11/3.54 | (13), (18) gives:
% 19.11/3.54 | (21) all_56_1 = all_56_2 | all_56_5 = all_56_7
% 19.11/3.54 |
% 19.11/3.54 | DELTA: instantiating (19) with fresh symbols all_63_0, all_63_1 gives:
% 19.11/3.54 | (22) vtcheck(all_56_8, all_56_2, all_56_4) = all_63_0 &
% 19.11/3.54 | visFreeVar(all_56_7, all_56_2) = all_63_1 & (all_63_0 = 0 | all_63_1 =
% 19.11/3.54 | 0)
% 19.11/3.54 |
% 19.11/3.54 | ALPHA: (22) implies:
% 19.11/3.54 | (23) visFreeVar(all_56_7, all_56_2) = all_63_1
% 19.11/3.54 | (24) vtcheck(all_56_8, all_56_2, all_56_4) = all_63_0
% 19.11/3.54 | (25) all_63_0 = 0 | all_63_1 = 0
% 19.11/3.54 |
% 19.11/3.54 | GROUND_INST: instantiating (isFreeVar0) with all_56_7, all_56_2, all_56_5,
% 19.11/3.54 | all_63_1, simplifying with (6), (8), (11), (13), (23) gives:
% 19.11/3.54 | (26) ( ~ (all_63_1 = 0) | all_56_5 = all_56_7) & ( ~ (all_56_5 = all_56_7)
% 19.11/3.54 | | all_63_1 = 0)
% 19.11/3.54 |
% 19.11/3.54 | ALPHA: (26) implies:
% 19.11/3.54 | (27) ~ (all_63_1 = 0) | all_56_5 = all_56_7
% 19.11/3.54 |
% 19.11/3.54 | BETA: splitting (21) gives:
% 19.11/3.54 |
% 19.11/3.54 | Case 1:
% 19.11/3.54 | |
% 19.11/3.54 | | (28) all_56_1 = all_56_2
% 19.11/3.54 | |
% 19.11/3.54 | | REDUCE: (16), (28) imply:
% 19.11/3.54 | | (29) vtcheck(all_56_8, all_56_2, all_56_4) = all_56_0
% 19.11/3.54 | |
% 19.11/3.54 | | GROUND_INST: instantiating (1) with all_63_0, all_56_0, all_56_4, all_56_2,
% 19.11/3.54 | | all_56_8, simplifying with (24), (29) gives:
% 19.11/3.54 | | (30) all_63_0 = all_56_0
% 19.11/3.54 | |
% 19.11/3.54 | | BETA: splitting (25) gives:
% 19.11/3.54 | |
% 19.11/3.54 | | Case 1:
% 19.11/3.54 | | |
% 19.11/3.54 | | | (31) all_63_0 = 0
% 19.11/3.54 | | |
% 19.11/3.54 | | | COMBINE_EQS: (30), (31) imply:
% 19.11/3.54 | | | (32) all_56_0 = 0
% 19.11/3.54 | | |
% 19.11/3.54 | | | REDUCE: (3), (32) imply:
% 19.11/3.54 | | | (33) $false
% 19.11/3.55 | | |
% 19.11/3.55 | | | CLOSE: (33) is inconsistent.
% 19.11/3.55 | | |
% 19.11/3.55 | | Case 2:
% 19.11/3.55 | | |
% 19.11/3.55 | | | (34) all_63_1 = 0
% 19.11/3.55 | | | (35) ~ (all_63_0 = 0)
% 19.11/3.55 | | |
% 19.11/3.55 | | | BETA: splitting (27) gives:
% 19.11/3.55 | | |
% 19.11/3.55 | | | Case 1:
% 19.11/3.55 | | | |
% 19.11/3.55 | | | | (36) ~ (all_63_1 = 0)
% 19.11/3.55 | | | |
% 19.11/3.55 | | | | REDUCE: (34), (36) imply:
% 19.11/3.55 | | | | (37) $false
% 19.11/3.55 | | | |
% 19.11/3.55 | | | | CLOSE: (37) is inconsistent.
% 19.11/3.55 | | | |
% 19.11/3.55 | | | Case 2:
% 19.11/3.55 | | | |
% 19.11/3.55 | | | | (38) all_56_5 = all_56_7
% 19.11/3.55 | | | |
% 19.11/3.55 | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 19.11/3.55 | | | | (14), (15), (16), (18), (20), (38), (DIFF-var-abs),
% 19.11/3.55 | | | | (DIFF-var-app), (EQ-someType), (EQ-var), (lookup1), (subst0)
% 19.11/3.55 | | | | are inconsistent by sub-proof #1.
% 19.11/3.55 | | | |
% 19.11/3.55 | | | End of split
% 19.11/3.55 | | |
% 19.11/3.55 | | End of split
% 19.11/3.55 | |
% 19.11/3.55 | Case 2:
% 19.11/3.55 | |
% 19.11/3.55 | | (39) all_56_5 = all_56_7
% 19.11/3.55 | |
% 19.11/3.55 | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 19.11/3.55 | | (15), (16), (18), (20), (39), (DIFF-var-abs), (DIFF-var-app),
% 19.11/3.55 | | (EQ-someType), (EQ-var), (lookup1), (subst0) are inconsistent by
% 19.11/3.55 | | sub-proof #1.
% 19.11/3.55 | |
% 19.11/3.55 | End of split
% 19.11/3.55 |
% 19.11/3.55 End of proof
% 19.11/3.55
% 19.11/3.55 Sub-proof #1 shows that the following formulas are inconsistent:
% 19.11/3.55 ----------------------------------------------------------------
% 19.11/3.55 (1) $i(all_56_6)
% 19.11/3.56 (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 19.11/3.56 (varrow(v2, v3) = all_56_4 & vtcheck(v4, v1, v3) = 0 & vbind(v0, v2,
% 19.11/3.56 all_56_3) = v4 & vabs(v0, v2, v1) = all_56_2 & $i(v4) & $i(v3) &
% 19.11/3.56 $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 19.11/3.56 ? [v3: $i] : (varrow(v2, all_56_4) = v3 & vtcheck(all_56_3, v1, v2) = 0 &
% 19.11/3.56 vtcheck(all_56_3, v0, v3) = 0 & vapp(v0, v1) = all_56_2 & $i(v3) &
% 19.11/3.56 $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : (vsomeType(all_56_4) = v0 &
% 19.11/3.56 $i(v0) & ? [v1: $i] : (vlookup(v1, all_56_3) = v0 & vvar(v1) =
% 19.11/3.56 all_56_2 & $i(v1)))
% 19.11/3.56 (3) all_56_5 = all_56_7
% 19.11/3.56 (4) vbind(all_56_7, all_56_9, all_56_8) = all_56_3
% 19.11/3.56 (5) $i(all_56_8)
% 19.11/3.56 (6) $i(all_56_3)
% 19.11/3.56 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 19.11/3.56 (vsubst(v0, v1, v2) = v3) | ~ (vvar(v0) = v2) | ~ $i(v3) | ~ $i(v2)
% 19.11/3.56 | ~ $i(v1) | ~ $i(v0))
% 19.11/3.56 (8) vtcheck(all_56_8, all_56_1, all_56_4) = all_56_0
% 19.11/3.56 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vapp(v1, v2)
% 19.11/3.56 = v3) | ~ (vvar(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 19.11/3.56 (10) $i(all_56_4)
% 19.11/3.56 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v1) =
% 19.11/3.56 v2) | ~ (vsomeType(v0) = v2) | ~ $i(v1) | ~ $i(v0))
% 19.11/3.56 (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 19.11/3.56 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~
% 19.11/3.56 (vtcheck(v4, v3, v2) = v0))
% 19.11/3.56 (13) vtcheck(all_56_8, all_56_6, all_56_9) = 0
% 19.11/3.56 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vvar(v1) = v2)
% 19.11/3.56 | ~ (vvar(v0) = v2) | ~ $i(v1) | ~ $i(v0))
% 19.11/3.56 (15) $i(all_56_5)
% 19.11/3.56 (16) vvar(all_56_5) = all_56_2
% 19.11/3.56 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 19.11/3.56 ~ (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4) | ~ $i(v3) | ~ $i(v2)
% 19.11/3.56 | ~ $i(v1) | ~ $i(v0))
% 19.11/3.56 (18) $i(all_56_1)
% 19.11/3.56 (19) ~ (all_56_0 = 0)
% 19.11/3.56 (20) $i(all_56_2)
% 19.11/3.56 (21) $i(all_56_9)
% 19.11/3.56 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 19.11/3.56 ~ (vlookup(v1, v2) = v3) | ~ (vbind(v1, v4, v0) = v2) | ~ $i(v4) |
% 19.11/3.56 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | vsomeType(v4) = v3)
% 19.11/3.56 (23) vsubst(all_56_7, all_56_6, all_56_2) = all_56_1
% 19.11/3.56
% 19.11/3.56 Begin of proof
% 19.11/3.56 |
% 19.11/3.56 | REDUCE: (3), (16) imply:
% 19.11/3.56 | (24) vvar(all_56_7) = all_56_2
% 19.11/3.56 |
% 19.11/3.56 | REDUCE: (3), (15) imply:
% 19.11/3.56 | (25) $i(all_56_7)
% 19.11/3.56 |
% 19.11/3.56 | GROUND_INST: instantiating (7) with all_56_7, all_56_6, all_56_2, all_56_1,
% 19.11/3.56 | simplifying with (1), (18), (20), (23), (24), (25) gives:
% 19.11/3.56 | (26) all_56_1 = all_56_6
% 19.11/3.56 |
% 19.11/3.56 | REDUCE: (8), (26) imply:
% 19.11/3.56 | (27) vtcheck(all_56_8, all_56_6, all_56_4) = all_56_0
% 19.11/3.56 |
% 19.11/3.56 | BETA: splitting (2) gives:
% 19.11/3.56 |
% 19.11/3.56 | Case 1:
% 19.11/3.56 | |
% 19.11/3.57 | | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 19.11/3.57 | | : (varrow(v2, v3) = all_56_4 & vtcheck(v4, v1, v3) = 0 & vbind(v0,
% 19.11/3.57 | | v2, all_56_3) = v4 & vabs(v0, v2, v1) = all_56_2 & $i(v4) &
% 19.11/3.57 | | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 19.11/3.57 | |
% 19.11/3.57 | | DELTA: instantiating (28) with fresh symbols all_98_0, all_98_1, all_98_2,
% 19.11/3.57 | | all_98_3, all_98_4 gives:
% 19.11/3.57 | | (29) varrow(all_98_2, all_98_1) = all_56_4 & vtcheck(all_98_0, all_98_3,
% 19.11/3.57 | | all_98_1) = 0 & vbind(all_98_4, all_98_2, all_56_3) = all_98_0 &
% 19.11/3.57 | | vabs(all_98_4, all_98_2, all_98_3) = all_56_2 & $i(all_98_0) &
% 19.11/3.57 | | $i(all_98_1) & $i(all_98_2) & $i(all_98_3) & $i(all_98_4)
% 19.11/3.57 | |
% 19.11/3.57 | | ALPHA: (29) implies:
% 19.11/3.57 | | (30) $i(all_98_4)
% 19.11/3.57 | | (31) $i(all_98_3)
% 19.11/3.57 | | (32) $i(all_98_2)
% 19.11/3.57 | | (33) vabs(all_98_4, all_98_2, all_98_3) = all_56_2
% 19.11/3.57 | |
% 19.11/3.57 | | GROUND_INST: instantiating (17) with all_56_7, all_98_4, all_98_2, all_98_3,
% 19.11/3.57 | | all_56_2, simplifying with (24), (25), (30), (31), (32), (33)
% 19.11/3.57 | | gives:
% 19.11/3.57 | | (34) $false
% 19.11/3.57 | |
% 19.11/3.57 | | CLOSE: (34) is inconsistent.
% 19.11/3.57 | |
% 19.11/3.57 | Case 2:
% 19.11/3.57 | |
% 19.11/3.57 | | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (varrow(v2,
% 19.11/3.57 | | all_56_4) = v3 & vtcheck(all_56_3, v1, v2) = 0 &
% 19.11/3.57 | | vtcheck(all_56_3, v0, v3) = 0 & vapp(v0, v1) = all_56_2 & $i(v3) &
% 19.11/3.57 | | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : (vsomeType(all_56_4) =
% 19.11/3.57 | | v0 & $i(v0) & ? [v1: $i] : (vlookup(v1, all_56_3) = v0 & vvar(v1)
% 19.11/3.57 | | = all_56_2 & $i(v1)))
% 19.11/3.57 | |
% 19.11/3.57 | | BETA: splitting (35) gives:
% 19.11/3.57 | |
% 19.11/3.57 | | Case 1:
% 19.11/3.57 | | |
% 19.11/3.57 | | | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 19.11/3.57 | | | (varrow(v2, all_56_4) = v3 & vtcheck(all_56_3, v1, v2) = 0 &
% 19.11/3.57 | | | vtcheck(all_56_3, v0, v3) = 0 & vapp(v0, v1) = all_56_2 & $i(v3)
% 19.11/3.57 | | | & $i(v2) & $i(v1) & $i(v0))
% 19.11/3.57 | | |
% 19.11/3.57 | | | DELTA: instantiating (36) with fresh symbols all_98_0, all_98_1, all_98_2,
% 19.11/3.57 | | | all_98_3 gives:
% 19.11/3.57 | | | (37) varrow(all_98_1, all_56_4) = all_98_0 & vtcheck(all_56_3,
% 19.11/3.57 | | | all_98_2, all_98_1) = 0 & vtcheck(all_56_3, all_98_3, all_98_0)
% 19.11/3.57 | | | = 0 & vapp(all_98_3, all_98_2) = all_56_2 & $i(all_98_0) &
% 19.11/3.57 | | | $i(all_98_1) & $i(all_98_2) & $i(all_98_3)
% 19.11/3.57 | | |
% 19.11/3.57 | | | ALPHA: (37) implies:
% 19.11/3.57 | | | (38) $i(all_98_3)
% 19.11/3.57 | | | (39) $i(all_98_2)
% 19.11/3.57 | | | (40) vapp(all_98_3, all_98_2) = all_56_2
% 19.11/3.57 | | |
% 19.11/3.57 | | | GROUND_INST: instantiating (9) with all_56_7, all_98_3, all_98_2,
% 19.11/3.57 | | | all_56_2, simplifying with (24), (25), (38), (39), (40)
% 19.11/3.57 | | | gives:
% 19.11/3.57 | | | (41) $false
% 19.11/3.57 | | |
% 19.11/3.57 | | | CLOSE: (41) is inconsistent.
% 19.11/3.57 | | |
% 19.11/3.57 | | Case 2:
% 19.11/3.57 | | |
% 19.11/3.57 | | | (42) ? [v0: $i] : (vsomeType(all_56_4) = v0 & $i(v0) & ? [v1: $i] :
% 19.11/3.57 | | | (vlookup(v1, all_56_3) = v0 & vvar(v1) = all_56_2 & $i(v1)))
% 19.11/3.57 | | |
% 19.11/3.57 | | | DELTA: instantiating (42) with fresh symbol all_98_0 gives:
% 19.11/3.57 | | | (43) vsomeType(all_56_4) = all_98_0 & $i(all_98_0) & ? [v0: $i] :
% 19.11/3.57 | | | (vlookup(v0, all_56_3) = all_98_0 & vvar(v0) = all_56_2 & $i(v0))
% 19.11/3.57 | | |
% 19.11/3.57 | | | ALPHA: (43) implies:
% 19.11/3.57 | | | (44) $i(all_98_0)
% 19.11/3.57 | | | (45) vsomeType(all_56_4) = all_98_0
% 19.11/3.57 | | | (46) ? [v0: $i] : (vlookup(v0, all_56_3) = all_98_0 & vvar(v0) =
% 19.11/3.57 | | | all_56_2 & $i(v0))
% 19.11/3.57 | | |
% 19.11/3.57 | | | DELTA: instantiating (46) with fresh symbol all_100_0 gives:
% 19.11/3.58 | | | (47) vlookup(all_100_0, all_56_3) = all_98_0 & vvar(all_100_0) =
% 19.11/3.58 | | | all_56_2 & $i(all_100_0)
% 19.11/3.58 | | |
% 19.11/3.58 | | | ALPHA: (47) implies:
% 19.11/3.58 | | | (48) $i(all_100_0)
% 19.11/3.58 | | | (49) vvar(all_100_0) = all_56_2
% 19.11/3.58 | | | (50) vlookup(all_100_0, all_56_3) = all_98_0
% 19.11/3.58 | | |
% 19.11/3.58 | | | GROUND_INST: instantiating (14) with all_56_7, all_100_0, all_56_2,
% 19.11/3.58 | | | simplifying with (24), (25), (48), (49) gives:
% 19.11/3.58 | | | (51) all_100_0 = all_56_7
% 19.11/3.58 | | |
% 19.11/3.58 | | | REDUCE: (50), (51) imply:
% 19.11/3.58 | | | (52) vlookup(all_56_7, all_56_3) = all_98_0
% 19.11/3.58 | | |
% 19.11/3.58 | | | GROUND_INST: instantiating (22) with all_56_8, all_56_7, all_56_3,
% 19.11/3.58 | | | all_98_0, all_56_9, simplifying with (4), (5), (6), (21),
% 19.11/3.58 | | | (25), (44), (52) gives:
% 19.11/3.58 | | | (53) vsomeType(all_56_9) = all_98_0
% 19.11/3.58 | | |
% 19.11/3.58 | | | GROUND_INST: instantiating (11) with all_56_4, all_56_9, all_98_0,
% 19.11/3.58 | | | simplifying with (10), (21), (45), (53) gives:
% 19.11/3.58 | | | (54) all_56_4 = all_56_9
% 19.11/3.58 | | |
% 19.11/3.58 | | | REDUCE: (27), (54) imply:
% 19.11/3.58 | | | (55) vtcheck(all_56_8, all_56_6, all_56_9) = all_56_0
% 19.11/3.58 | | |
% 19.11/3.58 | | | GROUND_INST: instantiating (12) with 0, all_56_0, all_56_9, all_56_6,
% 19.11/3.58 | | | all_56_8, simplifying with (13), (55) gives:
% 19.11/3.58 | | | (56) all_56_0 = 0
% 19.11/3.58 | | |
% 19.11/3.58 | | | REDUCE: (19), (56) imply:
% 19.11/3.58 | | | (57) $false
% 19.11/3.58 | | |
% 19.11/3.58 | | | CLOSE: (57) is inconsistent.
% 19.11/3.58 | | |
% 19.11/3.58 | | End of split
% 19.11/3.58 | |
% 19.11/3.58 | End of split
% 19.11/3.58 |
% 19.11/3.58 End of proof
% 19.11/3.58 % SZS output end Proof for theBenchmark
% 19.11/3.58
% 19.11/3.58 2915ms
%------------------------------------------------------------------------------