TSTP Solution File: COM125+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM125+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 : n016.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 18:44:32 EDT 2023
% Result : Theorem 18.12s 3.12s
% Output : Proof 24.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM125+1 : TPTP v8.1.2. Released v6.4.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n016.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 13:35:01 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.61/0.60 ________ _____
% 0.61/0.60 ___ __ \_________(_)________________________________
% 0.61/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.61/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.61/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.61/0.60
% 0.61/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.61/0.60 (2023-06-19)
% 0.61/0.60
% 0.61/0.60 (c) Philipp Rümmer, 2009-2023
% 0.61/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.61/0.60 Amanda Stjerna.
% 0.61/0.60 Free software under BSD-3-Clause.
% 0.61/0.60
% 0.61/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.61/0.60
% 0.61/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.61/0.61 Running up to 7 provers in parallel.
% 0.61/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.61/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.61/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.61/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.61/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.61/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.61/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.47/1.46 Prover 4: Preprocessing ...
% 5.96/1.47 Prover 1: Preprocessing ...
% 6.19/1.52 Prover 3: Preprocessing ...
% 6.19/1.52 Prover 0: Preprocessing ...
% 6.19/1.52 Prover 2: Preprocessing ...
% 6.19/1.52 Prover 5: Preprocessing ...
% 6.19/1.52 Prover 6: Preprocessing ...
% 15.09/2.75 Prover 3: Constructing countermodel ...
% 15.09/2.76 Prover 1: Constructing countermodel ...
% 15.09/2.78 Prover 6: Proving ...
% 16.08/2.86 Prover 4: Constructing countermodel ...
% 16.08/2.90 Prover 0: Proving ...
% 17.31/3.02 Prover 5: Proving ...
% 18.12/3.11 Prover 6: proved (2485ms)
% 18.12/3.12
% 18.12/3.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.12/3.12
% 18.12/3.12 Prover 3: stopped
% 18.32/3.14 Prover 5: stopped
% 18.32/3.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 18.32/3.15 Prover 0: stopped
% 18.32/3.16 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 18.32/3.16 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 18.32/3.16 Prover 2: Proving ...
% 18.32/3.16 Prover 2: stopped
% 18.32/3.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 18.32/3.19 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 19.07/3.26 Prover 1: Found proof (size 40)
% 19.07/3.26 Prover 1: proved (2641ms)
% 19.07/3.27 Prover 4: stopped
% 20.77/3.47 Prover 8: Preprocessing ...
% 20.77/3.52 Prover 13: Preprocessing ...
% 20.77/3.52 Prover 10: Preprocessing ...
% 20.77/3.52 Prover 11: Preprocessing ...
% 21.45/3.52 Prover 7: Preprocessing ...
% 21.90/3.61 Prover 10: stopped
% 21.90/3.62 Prover 11: stopped
% 21.90/3.64 Prover 7: stopped
% 22.53/3.70 Prover 13: stopped
% 22.90/3.79 Prover 8: Warning: ignoring some quantifiers
% 22.90/3.82 Prover 8: Constructing countermodel ...
% 23.30/3.83 Prover 8: stopped
% 23.30/3.83
% 23.30/3.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.30/3.84
% 23.30/3.85 % SZS output start Proof for theBenchmark
% 23.30/3.85 Assumptions after simplification:
% 23.30/3.85 ---------------------------------
% 23.30/3.85
% 23.30/3.86 (T-Weak-FreeVar-abs)
% 23.57/3.89 $i(veabs) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 23.57/3.89 $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int]
% 23.57/3.89 : ( ~ (v9 = 0) & ~ (v7 = 0) & vtcheck(v8, v6, v5) = v9 & vtcheck(v2, v6, v5)
% 23.57/3.89 = 0 & vbind(v0, v1, v2) = v8 & visFreeVar(v0, v6) = v7 & vabs(v3, v4, veabs)
% 23.57/3.89 = v6 & $i(v8) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 23.57/3.90 $i(v0))
% 23.57/3.90
% 23.57/3.90 (T-Weak-FreeVar-abs-1)
% 23.57/3.90 $i(veabs) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 23.57/3.90 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : (v8 = 0 | v3
% 23.57/3.90 = v0 | ~ (vtcheck(v7, v6, v5) = v8) | ~ (vbind(v0, v1, v2) = v7) | ~
% 23.57/3.90 (vabs(v3, v4, veabs) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 23.57/3.90 ~ $i(v1) | ~ $i(v0) | ? [v9: any] : ? [v10: any] : (vtcheck(v2, v6, v5)
% 23.57/3.90 = v10 & visFreeVar(v0, v6) = v9 & ( ~ (v10 = 0) | v9 = 0)))
% 23.57/3.90
% 23.57/3.90 (T-Weak-FreeVar-abs-2)
% 23.57/3.91 $i(veabs) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 23.57/3.91 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (vtcheck(v6,
% 23.57/3.91 v5, v4) = v7) | ~ (vbind(v0, v1, v2) = v6) | ~ (vabs(v0, v3, veabs) =
% 23.57/3.91 v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8:
% 23.57/3.91 any] : ? [v9: any] : (vtcheck(v2, v5, v4) = v9 & visFreeVar(v0, v5) = v8
% 23.57/3.91 & ( ~ (v9 = 0) | v8 = 0)))
% 23.57/3.91
% 23.57/3.91 (function-axioms)
% 23.57/3.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 23.57/3.92 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0:
% 23.57/3.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 23.57/3.92 : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3,
% 23.57/3.92 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 23.57/3.92 [v4: $i] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) =
% 23.57/3.92 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 23.57/3.92 : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & !
% 23.57/3.92 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3,
% 23.57/3.92 v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 23.57/3.92 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~
% 23.57/3.92 (vlookup(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 23.57/3.92 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.57/3.92 (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0: $i] : !
% 23.57/3.92 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~
% 23.57/3.92 (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 23.57/3.92 ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 23.57/3.92 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0))
% 23.57/3.92 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 23.57/3.92 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: $i] :
% 23.57/3.92 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~
% 23.57/3.92 (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 23.57/3.92 ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 23.57/3.92 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) =
% 23.57/3.92 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 23.57/3.92 $i] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & !
% 23.57/3.92 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~
% 23.57/3.92 (vsomeType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 23.57/3.92 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (visValue(v2) = v1) | ~
% 23.57/3.92 (visValue(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 23.57/3.92 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0))
% 23.57/3.92
% 23.57/3.92 Further assumptions not needed in the proof:
% 23.57/3.92 --------------------------------------------
% 23.57/3.93 DIFF-abs-app, DIFF-empty-bind, DIFF-noExp-someExp, DIFF-noType-someType,
% 23.57/3.93 DIFF-var-abs, DIFF-var-app, EQ-abs, EQ-app, EQ-arrow, EQ-bind, EQ-empty,
% 23.57/3.93 EQ-noExp, EQ-noType, EQ-someExp, EQ-someType, EQ-var, T-Context-Duplicate,
% 23.57/3.93 T-Context-Swap, T-Strong, T-Weak, T-Weak-FreeVar-abs-IH, T-abs, T-app, T-inv,
% 23.57/3.93 T-var, gensym-is-fresh, getSomeExp0, getSomeType0, isFreeVar0, isFreeVar1,
% 23.57/3.93 isFreeVar2, isSomeExp0, isSomeExp1, isSomeType0, isSomeType1, isValue0,
% 23.57/3.93 isValue1, isValue2, lookup-INV, lookup0, lookup1, lookup2, reduce-INV, reduce0,
% 23.57/3.93 reduce1, reduce2, reduce3, reduce4, reduce5, reduce6, subst-INV, subst0, subst1,
% 23.57/3.93 subst2, subst3, subst4, subst5
% 23.57/3.93
% 23.57/3.93 Those formulas are unsatisfiable:
% 23.57/3.93 ---------------------------------
% 23.57/3.93
% 23.57/3.93 Begin of proof
% 23.57/3.93 |
% 23.57/3.93 | ALPHA: (T-Weak-FreeVar-abs-1) implies:
% 23.57/3.93 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 23.57/3.93 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : (v8 = 0 | v3 =
% 23.57/3.93 | v0 | ~ (vtcheck(v7, v6, v5) = v8) | ~ (vbind(v0, v1, v2) = v7) | ~
% 23.57/3.93 | (vabs(v3, v4, veabs) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 23.57/3.93 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: any] : ? [v10: any] :
% 23.57/3.93 | (vtcheck(v2, v6, v5) = v10 & visFreeVar(v0, v6) = v9 & ( ~ (v10 = 0)
% 23.57/3.93 | | v9 = 0)))
% 23.57/3.93 |
% 23.57/3.93 | ALPHA: (T-Weak-FreeVar-abs-2) implies:
% 23.57/3.94 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 23.57/3.94 | ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (vtcheck(v6, v5,
% 23.57/3.94 | v4) = v7) | ~ (vbind(v0, v1, v2) = v6) | ~ (vabs(v0, v3, veabs)
% 23.57/3.94 | = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 23.57/3.94 | ? [v8: any] : ? [v9: any] : (vtcheck(v2, v5, v4) = v9 &
% 23.57/3.94 | visFreeVar(v0, v5) = v8 & ( ~ (v9 = 0) | v8 = 0)))
% 23.57/3.94 |
% 23.57/3.94 | ALPHA: (T-Weak-FreeVar-abs) implies:
% 23.57/3.94 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 23.57/3.94 | ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int] :
% 23.57/3.94 | ( ~ (v9 = 0) & ~ (v7 = 0) & vtcheck(v8, v6, v5) = v9 & vtcheck(v2, v6,
% 23.57/3.94 | v5) = 0 & vbind(v0, v1, v2) = v8 & visFreeVar(v0, v6) = v7 &
% 23.57/3.94 | vabs(v3, v4, veabs) = v6 & $i(v8) & $i(v6) & $i(v5) & $i(v4) & $i(v3)
% 23.57/3.94 | & $i(v2) & $i(v1) & $i(v0))
% 23.57/3.94 |
% 23.57/3.94 | ALPHA: (function-axioms) implies:
% 23.57/3.94 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 23.57/3.94 | ! [v3: $i] : (v1 = v0 | ~ (visFreeVar(v3, v2) = v1) | ~
% 23.57/3.94 | (visFreeVar(v3, v2) = v0))
% 23.57/3.95 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 23.57/3.95 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) |
% 23.57/3.95 | ~ (vtcheck(v4, v3, v2) = v0))
% 23.57/3.95 |
% 23.57/3.95 | DELTA: instantiating (3) with fresh symbols all_58_0, all_58_1, all_58_2,
% 23.57/3.95 | all_58_3, all_58_4, all_58_5, all_58_6, all_58_7, all_58_8, all_58_9
% 23.57/3.95 | gives:
% 23.57/3.95 | (6) ~ (all_58_0 = 0) & ~ (all_58_2 = 0) & vtcheck(all_58_1, all_58_3,
% 23.57/3.95 | all_58_4) = all_58_0 & vtcheck(all_58_7, all_58_3, all_58_4) = 0 &
% 23.57/3.95 | vbind(all_58_9, all_58_8, all_58_7) = all_58_1 & visFreeVar(all_58_9,
% 23.57/3.95 | all_58_3) = all_58_2 & vabs(all_58_6, all_58_5, veabs) = all_58_3 &
% 23.57/3.95 | $i(all_58_1) & $i(all_58_3) & $i(all_58_4) & $i(all_58_5) &
% 23.57/3.95 | $i(all_58_6) & $i(all_58_7) & $i(all_58_8) & $i(all_58_9)
% 23.57/3.95 |
% 23.57/3.95 | ALPHA: (6) implies:
% 23.57/3.95 | (7) ~ (all_58_2 = 0)
% 23.57/3.95 | (8) ~ (all_58_0 = 0)
% 23.57/3.95 | (9) $i(all_58_9)
% 23.57/3.95 | (10) $i(all_58_8)
% 23.57/3.95 | (11) $i(all_58_7)
% 23.57/3.95 | (12) $i(all_58_6)
% 23.57/3.95 | (13) $i(all_58_5)
% 23.57/3.95 | (14) $i(all_58_4)
% 23.57/3.95 | (15) vabs(all_58_6, all_58_5, veabs) = all_58_3
% 23.57/3.95 | (16) visFreeVar(all_58_9, all_58_3) = all_58_2
% 23.57/3.95 | (17) vbind(all_58_9, all_58_8, all_58_7) = all_58_1
% 23.57/3.95 | (18) vtcheck(all_58_7, all_58_3, all_58_4) = 0
% 23.57/3.96 | (19) vtcheck(all_58_1, all_58_3, all_58_4) = all_58_0
% 23.57/3.96 |
% 23.57/3.96 | GROUND_INST: instantiating (1) with all_58_9, all_58_8, all_58_7, all_58_6,
% 23.57/3.96 | all_58_5, all_58_4, all_58_3, all_58_1, all_58_0, simplifying
% 23.57/3.96 | with (9), (10), (11), (12), (13), (14), (15), (17), (19) gives:
% 23.57/3.96 | (20) all_58_0 = 0 | all_58_6 = all_58_9 | ? [v0: any] : ? [v1: any] :
% 23.57/3.96 | (vtcheck(all_58_7, all_58_3, all_58_4) = v1 & visFreeVar(all_58_9,
% 23.57/3.96 | all_58_3) = v0 & ( ~ (v1 = 0) | v0 = 0))
% 23.57/3.96 |
% 23.57/3.96 | BETA: splitting (20) gives:
% 23.57/3.96 |
% 23.57/3.96 | Case 1:
% 23.57/3.96 | |
% 23.57/3.96 | | (21) all_58_0 = 0
% 23.57/3.96 | |
% 23.57/3.96 | | REDUCE: (8), (21) imply:
% 23.57/3.96 | | (22) $false
% 23.57/3.96 | |
% 23.57/3.96 | | CLOSE: (22) is inconsistent.
% 23.57/3.96 | |
% 23.57/3.96 | Case 2:
% 23.57/3.96 | |
% 23.57/3.96 | | (23) all_58_6 = all_58_9 | ? [v0: any] : ? [v1: any] :
% 23.57/3.97 | | (vtcheck(all_58_7, all_58_3, all_58_4) = v1 & visFreeVar(all_58_9,
% 23.57/3.97 | | all_58_3) = v0 & ( ~ (v1 = 0) | v0 = 0))
% 23.57/3.97 | |
% 23.57/3.97 | | BETA: splitting (23) gives:
% 23.57/3.97 | |
% 23.57/3.97 | | Case 1:
% 23.57/3.97 | | |
% 23.57/3.97 | | | (24) all_58_6 = all_58_9
% 23.57/3.97 | | |
% 23.57/3.97 | | | REDUCE: (15), (24) imply:
% 23.57/3.97 | | | (25) vabs(all_58_9, all_58_5, veabs) = all_58_3
% 23.57/3.97 | | |
% 23.99/3.97 | | | GROUND_INST: instantiating (2) with all_58_9, all_58_8, all_58_7,
% 23.99/3.97 | | | all_58_5, all_58_4, all_58_3, all_58_1, all_58_0, simplifying
% 23.99/3.97 | | | with (9), (10), (11), (13), (14), (17), (19), (25) gives:
% 23.99/3.97 | | | (26) all_58_0 = 0 | ? [v0: any] : ? [v1: any] : (vtcheck(all_58_7,
% 23.99/3.97 | | | all_58_3, all_58_4) = v1 & visFreeVar(all_58_9, all_58_3) = v0
% 23.99/3.97 | | | & ( ~ (v1 = 0) | v0 = 0))
% 23.99/3.97 | | |
% 23.99/3.97 | | | BETA: splitting (26) gives:
% 23.99/3.97 | | |
% 23.99/3.97 | | | Case 1:
% 23.99/3.97 | | | |
% 23.99/3.97 | | | | (27) all_58_0 = 0
% 23.99/3.97 | | | |
% 23.99/3.97 | | | | REDUCE: (8), (27) imply:
% 23.99/3.97 | | | | (28) $false
% 23.99/3.97 | | | |
% 23.99/3.97 | | | | CLOSE: (28) is inconsistent.
% 23.99/3.97 | | | |
% 23.99/3.97 | | | Case 2:
% 23.99/3.97 | | | |
% 23.99/3.97 | | | | (29) ? [v0: any] : ? [v1: any] : (vtcheck(all_58_7, all_58_3,
% 23.99/3.97 | | | | all_58_4) = v1 & visFreeVar(all_58_9, all_58_3) = v0 & ( ~
% 23.99/3.97 | | | | (v1 = 0) | v0 = 0))
% 23.99/3.97 | | | |
% 23.99/3.97 | | | | DELTA: instantiating (29) with fresh symbols all_85_0, all_85_1 gives:
% 23.99/3.97 | | | | (30) vtcheck(all_58_7, all_58_3, all_58_4) = all_85_0 &
% 23.99/3.97 | | | | visFreeVar(all_58_9, all_58_3) = all_85_1 & ( ~ (all_85_0 = 0) |
% 23.99/3.97 | | | | all_85_1 = 0)
% 23.99/3.97 | | | |
% 23.99/3.97 | | | | REF_CLOSE: (4), (5), (7), (16), (18), (30) are inconsistent by sub-proof
% 23.99/3.97 | | | | #1.
% 23.99/3.97 | | | |
% 23.99/3.97 | | | End of split
% 23.99/3.98 | | |
% 23.99/3.98 | | Case 2:
% 23.99/3.98 | | |
% 23.99/3.98 | | | (31) ? [v0: any] : ? [v1: any] : (vtcheck(all_58_7, all_58_3,
% 23.99/3.98 | | | all_58_4) = v1 & visFreeVar(all_58_9, all_58_3) = v0 & ( ~ (v1
% 23.99/3.98 | | | = 0) | v0 = 0))
% 23.99/3.98 | | |
% 23.99/3.98 | | | DELTA: instantiating (31) with fresh symbols all_85_0, all_85_1 gives:
% 23.99/3.98 | | | (32) vtcheck(all_58_7, all_58_3, all_58_4) = all_85_0 &
% 23.99/3.98 | | | visFreeVar(all_58_9, all_58_3) = all_85_1 & ( ~ (all_85_0 = 0) |
% 23.99/3.98 | | | all_85_1 = 0)
% 23.99/3.98 | | |
% 23.99/3.98 | | | REF_CLOSE: (4), (5), (7), (16), (18), (32) are inconsistent by sub-proof
% 23.99/3.98 | | | #1.
% 23.99/3.98 | | |
% 23.99/3.98 | | End of split
% 23.99/3.98 | |
% 23.99/3.98 | End of split
% 23.99/3.98 |
% 23.99/3.98 End of proof
% 23.99/3.98
% 23.99/3.98 Sub-proof #1 shows that the following formulas are inconsistent:
% 23.99/3.98 ----------------------------------------------------------------
% 23.99/3.98 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 23.99/3.98 ! [v3: $i] : (v1 = v0 | ~ (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3,
% 23.99/3.98 v2) = v0))
% 23.99/3.98 (2) vtcheck(all_58_7, all_58_3, all_58_4) = 0
% 23.99/3.98 (3) visFreeVar(all_58_9, all_58_3) = all_58_2
% 23.99/3.98 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 23.99/3.98 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~
% 23.99/3.98 (vtcheck(v4, v3, v2) = v0))
% 23.99/3.98 (5) vtcheck(all_58_7, all_58_3, all_58_4) = all_85_0 & visFreeVar(all_58_9,
% 23.99/3.98 all_58_3) = all_85_1 & ( ~ (all_85_0 = 0) | all_85_1 = 0)
% 23.99/3.98 (6) ~ (all_58_2 = 0)
% 23.99/3.98
% 23.99/3.98 Begin of proof
% 23.99/3.98 |
% 23.99/3.98 | ALPHA: (5) implies:
% 23.99/3.98 | (7) visFreeVar(all_58_9, all_58_3) = all_85_1
% 23.99/3.98 | (8) vtcheck(all_58_7, all_58_3, all_58_4) = all_85_0
% 23.99/3.98 | (9) ~ (all_85_0 = 0) | all_85_1 = 0
% 23.99/3.98 |
% 23.99/3.98 | GROUND_INST: instantiating (1) with all_58_2, all_85_1, all_58_3, all_58_9,
% 23.99/3.98 | simplifying with (3), (7) gives:
% 23.99/3.98 | (10) all_85_1 = all_58_2
% 23.99/3.98 |
% 23.99/3.99 | GROUND_INST: instantiating (4) with 0, all_85_0, all_58_4, all_58_3, all_58_7,
% 23.99/3.99 | simplifying with (2), (8) gives:
% 24.08/3.99 | (11) all_85_0 = 0
% 24.08/3.99 |
% 24.08/3.99 | BETA: splitting (9) gives:
% 24.08/3.99 |
% 24.08/3.99 | Case 1:
% 24.08/3.99 | |
% 24.08/3.99 | | (12) ~ (all_85_0 = 0)
% 24.08/3.99 | |
% 24.08/3.99 | | REDUCE: (11), (12) imply:
% 24.08/3.99 | | (13) $false
% 24.08/3.99 | |
% 24.08/3.99 | | CLOSE: (13) is inconsistent.
% 24.08/3.99 | |
% 24.08/3.99 | Case 2:
% 24.08/3.99 | |
% 24.08/3.99 | | (14) all_85_1 = 0
% 24.08/3.99 | |
% 24.08/3.99 | | COMBINE_EQS: (10), (14) imply:
% 24.08/3.99 | | (15) all_58_2 = 0
% 24.08/3.99 | |
% 24.08/3.99 | | REDUCE: (6), (15) imply:
% 24.08/3.99 | | (16) $false
% 24.08/3.99 | |
% 24.08/3.99 | | CLOSE: (16) is inconsistent.
% 24.08/3.99 | |
% 24.08/3.99 | End of split
% 24.08/3.99 |
% 24.08/3.99 End of proof
% 24.08/3.99 % SZS output end Proof for theBenchmark
% 24.08/3.99
% 24.08/3.99 3385ms
%------------------------------------------------------------------------------