TSTP Solution File: NUM535+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM535+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n018.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 : Thu Aug 31 11:48:27 EDT 2023
% Result : Theorem 20.94s 3.75s
% Output : Proof 22.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM535+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n018.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 : Fri Aug 25 13:44:28 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.55/1.08 Prover 4: Preprocessing ...
% 2.55/1.08 Prover 1: Preprocessing ...
% 2.55/1.12 Prover 0: Preprocessing ...
% 2.55/1.12 Prover 5: Preprocessing ...
% 2.55/1.12 Prover 3: Preprocessing ...
% 3.20/1.12 Prover 6: Preprocessing ...
% 3.20/1.13 Prover 2: Preprocessing ...
% 7.22/1.79 Prover 1: Constructing countermodel ...
% 7.22/1.79 Prover 5: Constructing countermodel ...
% 7.80/1.80 Prover 2: Proving ...
% 7.80/1.80 Prover 3: Constructing countermodel ...
% 7.80/1.82 Prover 6: Proving ...
% 9.36/2.07 Prover 4: Constructing countermodel ...
% 10.58/2.24 Prover 0: Proving ...
% 20.94/3.74 Prover 1: Found proof (size 113)
% 20.94/3.74 Prover 1: proved (3127ms)
% 20.94/3.74 Prover 5: stopped
% 20.94/3.74 Prover 4: stopped
% 20.94/3.74 Prover 0: stopped
% 20.94/3.74 Prover 6: stopped
% 20.94/3.75 Prover 3: stopped
% 20.94/3.75 Prover 2: stopped
% 20.94/3.75
% 20.94/3.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.94/3.75
% 20.94/3.77 % SZS output start Proof for theBenchmark
% 20.94/3.77 Assumptions after simplification:
% 20.94/3.77 ---------------------------------
% 20.94/3.77
% 20.94/3.77 (mDefDiff)
% 20.94/3.82 ! [v0: $i] : ! [v1: $i] : ( ~ (aSet0(v0) = 0) | ~ (aElement0(v1) = 0) | ~
% 20.94/3.82 $i(v1) | ~ $i(v0) | ? [v2: $i] : (sdtmndt0(v0, v1) = v2 & $i(v2) & ! [v3:
% 20.94/3.82 $i] : (v3 = v2 | ~ (aSet0(v3) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5:
% 20.94/3.82 any] : ? [v6: any] : ? [v7: any] : (aElement0(v4) = v6 &
% 20.94/3.82 aElementOf0(v4, v3) = v5 & aElementOf0(v4, v0) = v7 & $i(v4) & ( ~ (v7
% 20.94/3.82 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v4 = v1) & (v5 = 0 | (v7 = 0 &
% 20.94/3.82 v6 = 0 & ~ (v4 = v1))))) & ! [v3: any] : ( ~ (aSet0(v2) = v3) |
% 20.94/3.82 (v3 = 0 & ! [v4: $i] : ! [v5: any] : ( ~ (aElement0(v4) = v5) | ~
% 20.94/3.83 $i(v4) | ? [v6: any] : ? [v7: any] : (aElementOf0(v4, v2) = v6 &
% 21.91/3.83 aElementOf0(v4, v0) = v7 & ( ~ (v6 = 0) | (v7 = 0 & v5 = 0 & ~
% 21.91/3.83 (v4 = v1))))) & ! [v4: $i] : (v4 = v1 | ~ (aElement0(v4) =
% 21.91/3.83 0) | ~ $i(v4) | ? [v5: any] : ? [v6: any] : (aElementOf0(v4,
% 21.91/3.83 v2) = v6 & aElementOf0(v4, v0) = v5 & ( ~ (v5 = 0) | v6 =
% 21.91/3.83 0)))))))
% 21.91/3.83
% 21.91/3.83 (mDefSub)
% 21.91/3.83 ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: int] :
% 21.91/3.83 (v2 = 0 | ~ (aSubsetOf0(v1, v0) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4:
% 21.91/3.83 int] : ( ~ (v4 = 0) & aElementOf0(v3, v1) = 0 & aElementOf0(v3, v0) =
% 21.91/3.83 v4 & $i(v3)) | ? [v3: int] : ( ~ (v3 = 0) & aSet0(v1) = v3)) & !
% 21.91/3.83 [v1: $i] : ( ~ (aSubsetOf0(v1, v0) = 0) | ~ $i(v1) | (aSet0(v1) = 0 & !
% 21.91/3.83 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, v0) = v3) | ~
% 21.91/3.83 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v2, v1) =
% 21.91/3.83 v4))))))
% 21.91/3.83
% 21.91/3.83 (mEOfElem)
% 21.91/3.84 ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: int] :
% 21.91/3.84 (v2 = 0 | ~ (aElement0(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0)
% 21.91/3.84 & aElementOf0(v1, v0) = v3)))
% 21.91/3.84
% 21.91/3.84 (m__)
% 21.91/3.85 $i(xx) & $i(xS) & ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] :
% 21.91/3.85 (sdtmndt0(xS, xx) = v0 & sdtpldt0(v0, xx) = v1 & aSubsetOf0(v1, xS) = v3 &
% 21.91/3.85 aSubsetOf0(xS, v1) = v2 & aSet0(v1) = 0 & aSet0(v0) = 0 & $i(v1) & $i(v0) &
% 21.91/3.85 ! [v4: $i] : ! [v5: int] : (v5 = 0 | v4 = xx | ~ (aElementOf0(v4, v0) =
% 21.91/3.85 v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] : (aElement0(v4) = v6 &
% 21.91/3.85 aElementOf0(v4, xS) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v4: $i] :
% 21.91/3.85 ! [v5: int] : (v5 = 0 | ~ (aElementOf0(v4, v1) = v5) | ~ $i(v4) | ? [v6:
% 21.91/3.85 any] : ? [v7: any] : (aElement0(v4) = v6 & aElementOf0(v4, v0) = v7 & (
% 21.91/3.85 ~ (v6 = 0) | ( ~ (v7 = 0) & ~ (v4 = xx))))) & ! [v4: $i] : ( ~
% 21.91/3.85 (aElementOf0(v4, v1) = 0) | ~ $i(v4) | ? [v5: any] : (aElement0(v4) = 0
% 21.91/3.85 & aElementOf0(v4, v0) = v5 & (v5 = 0 | v4 = xx))) & ! [v4: $i] : ( ~
% 21.91/3.85 (aElementOf0(v4, v0) = 0) | ~ $i(v4) | ( ~ (v4 = xx) & aElement0(v4) = 0
% 21.91/3.85 & aElementOf0(v4, xS) = 0)) & (( ~ (v3 = 0) & ? [v4: $i] : ? [v5: int]
% 21.91/3.85 : ( ~ (v5 = 0) & aElementOf0(v4, v1) = 0 & aElementOf0(v4, xS) = v5 &
% 21.91/3.85 $i(v4))) | ( ~ (v2 = 0) & ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 21.91/3.85 aElementOf0(v4, v1) = v5 & aElementOf0(v4, xS) = 0 & $i(v4)))))
% 21.91/3.85
% 21.91/3.85 (m__617)
% 21.91/3.85 aSet0(xS) = 0 & $i(xS)
% 21.91/3.85
% 21.91/3.85 (m__617_02)
% 21.91/3.85 aElementOf0(xx, xS) = 0 & $i(xx) & $i(xS)
% 21.91/3.85
% 21.91/3.85 (function-axioms)
% 21.91/3.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 21.91/3.86 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : !
% 21.91/3.86 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 21.91/3.86 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 21.91/3.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 21.91/3.86 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0:
% 21.91/3.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 21.91/3.86 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) &
% 21.91/3.86 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 21.91/3.86 v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) & ! [v0:
% 21.91/3.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 21.91/3.86 ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0:
% 21.91/3.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 21.91/3.86 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 21.91/3.86 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) |
% 21.91/3.86 ~ (aElement0(v2) = v0))
% 21.91/3.86
% 21.91/3.86 Further assumptions not needed in the proof:
% 21.91/3.86 --------------------------------------------
% 21.91/3.86 mCntRel, mCountNFin, mCountNFin_01, mDefCons, mDefEmp, mElmSort, mEmpFin,
% 21.91/3.86 mFinRel, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans
% 21.91/3.86
% 21.91/3.86 Those formulas are unsatisfiable:
% 21.91/3.86 ---------------------------------
% 21.91/3.86
% 21.91/3.86 Begin of proof
% 21.91/3.86 |
% 21.91/3.86 | ALPHA: (m__617) implies:
% 21.91/3.86 | (1) aSet0(xS) = 0
% 21.91/3.86 |
% 21.91/3.86 | ALPHA: (m__617_02) implies:
% 21.91/3.87 | (2) aElementOf0(xx, xS) = 0
% 21.91/3.87 |
% 21.91/3.87 | ALPHA: (m__) implies:
% 21.91/3.87 | (3) $i(xS)
% 21.91/3.88 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : (sdtmndt0(xS,
% 21.91/3.88 | xx) = v0 & sdtpldt0(v0, xx) = v1 & aSubsetOf0(v1, xS) = v3 &
% 21.91/3.88 | aSubsetOf0(xS, v1) = v2 & aSet0(v1) = 0 & aSet0(v0) = 0 & $i(v1) &
% 21.91/3.88 | $i(v0) & ! [v4: $i] : ! [v5: int] : (v5 = 0 | v4 = xx | ~
% 21.91/3.88 | (aElementOf0(v4, v0) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7:
% 21.91/3.88 | any] : (aElement0(v4) = v6 & aElementOf0(v4, xS) = v7 & ( ~ (v7 =
% 21.91/3.88 | 0) | ~ (v6 = 0)))) & ! [v4: $i] : ! [v5: int] : (v5 = 0 |
% 21.91/3.88 | ~ (aElementOf0(v4, v1) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7:
% 21.91/3.88 | any] : (aElement0(v4) = v6 & aElementOf0(v4, v0) = v7 & ( ~ (v6 =
% 21.91/3.88 | 0) | ( ~ (v7 = 0) & ~ (v4 = xx))))) & ! [v4: $i] : ( ~
% 21.91/3.88 | (aElementOf0(v4, v1) = 0) | ~ $i(v4) | ? [v5: any] :
% 21.91/3.88 | (aElement0(v4) = 0 & aElementOf0(v4, v0) = v5 & (v5 = 0 | v4 =
% 21.91/3.88 | xx))) & ! [v4: $i] : ( ~ (aElementOf0(v4, v0) = 0) | ~ $i(v4)
% 21.91/3.88 | | ( ~ (v4 = xx) & aElement0(v4) = 0 & aElementOf0(v4, xS) = 0)) &
% 21.91/3.88 | (( ~ (v3 = 0) & ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 21.91/3.88 | aElementOf0(v4, v1) = 0 & aElementOf0(v4, xS) = v5 & $i(v4))) |
% 21.91/3.88 | ( ~ (v2 = 0) & ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 21.91/3.88 | aElementOf0(v4, v1) = v5 & aElementOf0(v4, xS) = 0 & $i(v4)))))
% 21.91/3.88 |
% 21.91/3.88 | ALPHA: (function-axioms) implies:
% 21.91/3.88 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 21.91/3.88 | (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0))
% 21.91/3.88 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 21.91/3.88 | (v1 = v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0))
% 21.91/3.88 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 21.91/3.88 | ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~
% 21.91/3.88 | (aElementOf0(v3, v2) = v0))
% 21.91/3.88 |
% 21.91/3.88 | DELTA: instantiating (4) with fresh symbols all_14_0, all_14_1, all_14_2,
% 21.91/3.88 | all_14_3 gives:
% 21.91/3.89 | (8) sdtmndt0(xS, xx) = all_14_3 & sdtpldt0(all_14_3, xx) = all_14_2 &
% 21.91/3.89 | aSubsetOf0(all_14_2, xS) = all_14_0 & aSubsetOf0(xS, all_14_2) =
% 21.91/3.89 | all_14_1 & aSet0(all_14_2) = 0 & aSet0(all_14_3) = 0 & $i(all_14_2) &
% 21.91/3.89 | $i(all_14_3) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | v0 = xx | ~
% 21.91/3.89 | (aElementOf0(v0, all_14_3) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 21.91/3.89 | any] : (aElement0(v0) = v2 & aElementOf0(v0, xS) = v3 & ( ~ (v3 =
% 21.91/3.89 | 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 21.91/3.89 | (aElementOf0(v0, all_14_2) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 21.91/3.89 | any] : (aElement0(v0) = v2 & aElementOf0(v0, all_14_3) = v3 & ( ~
% 21.91/3.89 | (v2 = 0) | ( ~ (v3 = 0) & ~ (v0 = xx))))) & ! [v0: $i] : ( ~
% 21.91/3.89 | (aElementOf0(v0, all_14_2) = 0) | ~ $i(v0) | ? [v1: any] :
% 21.91/3.89 | (aElement0(v0) = 0 & aElementOf0(v0, all_14_3) = v1 & (v1 = 0 | v0 =
% 21.91/3.89 | xx))) & ! [v0: $i] : ( ~ (aElementOf0(v0, all_14_3) = 0) | ~
% 21.91/3.89 | $i(v0) | ( ~ (v0 = xx) & aElement0(v0) = 0 & aElementOf0(v0, xS) =
% 21.91/3.89 | 0)) & (( ~ (all_14_0 = 0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 =
% 21.91/3.89 | 0) & aElementOf0(v0, all_14_2) = 0 & aElementOf0(v0, xS) = v1 &
% 21.91/3.89 | $i(v0))) | ( ~ (all_14_1 = 0) & ? [v0: $i] : ? [v1: int] : ( ~
% 21.91/3.89 | (v1 = 0) & aElementOf0(v0, all_14_2) = v1 & aElementOf0(v0, xS) =
% 21.91/3.89 | 0 & $i(v0))))
% 21.91/3.89 |
% 21.91/3.89 | ALPHA: (8) implies:
% 21.91/3.89 | (9) $i(all_14_2)
% 21.91/3.89 | (10) aSet0(all_14_2) = 0
% 21.91/3.89 | (11) aSubsetOf0(xS, all_14_2) = all_14_1
% 21.91/3.89 | (12) aSubsetOf0(all_14_2, xS) = all_14_0
% 22.51/3.90 | (13) ( ~ (all_14_0 = 0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 22.51/3.90 | aElementOf0(v0, all_14_2) = 0 & aElementOf0(v0, xS) = v1 &
% 22.51/3.90 | $i(v0))) | ( ~ (all_14_1 = 0) & ? [v0: $i] : ? [v1: int] : ( ~
% 22.51/3.90 | (v1 = 0) & aElementOf0(v0, all_14_2) = v1 & aElementOf0(v0, xS) =
% 22.51/3.90 | 0 & $i(v0)))
% 22.51/3.90 | (14) ! [v0: $i] : ( ~ (aElementOf0(v0, all_14_3) = 0) | ~ $i(v0) | ( ~
% 22.51/3.90 | (v0 = xx) & aElement0(v0) = 0 & aElementOf0(v0, xS) = 0))
% 22.51/3.90 | (15) ! [v0: $i] : ( ~ (aElementOf0(v0, all_14_2) = 0) | ~ $i(v0) | ?
% 22.51/3.90 | [v1: any] : (aElement0(v0) = 0 & aElementOf0(v0, all_14_3) = v1 &
% 22.51/3.90 | (v1 = 0 | v0 = xx)))
% 22.51/3.90 | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_14_2) =
% 22.51/3.90 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (aElement0(v0) =
% 22.51/3.90 | v2 & aElementOf0(v0, all_14_3) = v3 & ( ~ (v2 = 0) | ( ~ (v3 = 0)
% 22.51/3.90 | & ~ (v0 = xx)))))
% 22.51/3.90 | (17) ! [v0: $i] : ! [v1: int] : (v1 = 0 | v0 = xx | ~ (aElementOf0(v0,
% 22.51/3.90 | all_14_3) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 22.51/3.90 | (aElement0(v0) = v2 & aElementOf0(v0, xS) = v3 & ( ~ (v3 = 0) | ~
% 22.51/3.90 | (v2 = 0))))
% 22.51/3.90 |
% 22.51/3.90 | GROUND_INST: instantiating (mEOfElem) with xS, simplifying with (1), (3)
% 22.51/3.90 | gives:
% 22.51/3.90 | (18) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElement0(v0) = v1) | ~
% 22.51/3.90 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, xS) = v2))
% 22.51/3.90 |
% 22.51/3.90 | GROUND_INST: instantiating (mDefSub) with xS, simplifying with (1), (3) gives:
% 22.51/3.91 | (19) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xS) = v1) |
% 22.51/3.91 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 22.51/3.91 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xS) = v3 & $i(v2)) | ?
% 22.51/3.91 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~
% 22.51/3.91 | (aSubsetOf0(v0, xS) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i]
% 22.51/3.91 | : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xS) = v2) | ~
% 22.51/3.91 | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, v0) =
% 22.51/3.91 | v3))))
% 22.51/3.91 |
% 22.51/3.91 | ALPHA: (19) implies:
% 22.51/3.91 | (20) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xS) = v1) |
% 22.51/3.91 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 22.51/3.91 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xS) = v3 & $i(v2)) | ?
% 22.51/3.91 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2))
% 22.51/3.91 |
% 22.51/3.91 | GROUND_INST: instantiating (mDefSub) with all_14_2, simplifying with (9), (10)
% 22.51/3.91 | gives:
% 22.58/3.91 | (21) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, all_14_2) =
% 22.58/3.91 | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 22.58/3.91 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, all_14_2) = v3 & $i(v2))
% 22.58/3.91 | | ? [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~
% 22.58/3.91 | (aSubsetOf0(v0, all_14_2) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & !
% 22.58/3.91 | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, all_14_2)
% 22.58/3.91 | = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 22.58/3.91 | aElementOf0(v1, v0) = v3))))
% 22.58/3.91 |
% 22.58/3.91 | ALPHA: (21) implies:
% 22.60/3.91 | (22) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, all_14_2) =
% 22.60/3.91 | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 22.60/3.91 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, all_14_2) = v3 & $i(v2))
% 22.60/3.91 | | ? [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2))
% 22.60/3.91 |
% 22.60/3.91 | GROUND_INST: instantiating (22) with xS, all_14_1, simplifying with (3), (11)
% 22.60/3.91 | gives:
% 22.60/3.91 | (23) all_14_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 22.60/3.91 | aElementOf0(v0, all_14_2) = v1 & aElementOf0(v0, xS) = 0 & $i(v0)) |
% 22.60/3.91 | ? [v0: int] : ( ~ (v0 = 0) & aSet0(xS) = v0)
% 22.60/3.91 |
% 22.60/3.91 | GROUND_INST: instantiating (20) with all_14_2, all_14_0, simplifying with (9),
% 22.60/3.91 | (12) gives:
% 22.60/3.91 | (24) all_14_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 22.60/3.91 | aElementOf0(v0, all_14_2) = 0 & aElementOf0(v0, xS) = v1 & $i(v0)) |
% 22.60/3.91 | ? [v0: int] : ( ~ (v0 = 0) & aSet0(all_14_2) = v0)
% 22.60/3.91 |
% 22.60/3.91 | BETA: splitting (13) gives:
% 22.60/3.91 |
% 22.60/3.92 | Case 1:
% 22.60/3.92 | |
% 22.60/3.92 | | (25) ~ (all_14_0 = 0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 22.60/3.92 | | aElementOf0(v0, all_14_2) = 0 & aElementOf0(v0, xS) = v1 & $i(v0))
% 22.60/3.92 | |
% 22.60/3.92 | | ALPHA: (25) implies:
% 22.60/3.92 | | (26) ~ (all_14_0 = 0)
% 22.60/3.92 | | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0,
% 22.60/3.92 | | all_14_2) = 0 & aElementOf0(v0, xS) = v1 & $i(v0))
% 22.60/3.92 | |
% 22.60/3.92 | | DELTA: instantiating (27) with fresh symbols all_40_0, all_40_1 gives:
% 22.60/3.92 | | (28) ~ (all_40_0 = 0) & aElementOf0(all_40_1, all_14_2) = 0 &
% 22.60/3.92 | | aElementOf0(all_40_1, xS) = all_40_0 & $i(all_40_1)
% 22.60/3.92 | |
% 22.60/3.92 | | ALPHA: (28) implies:
% 22.60/3.92 | | (29) ~ (all_40_0 = 0)
% 22.60/3.92 | | (30) $i(all_40_1)
% 22.60/3.92 | | (31) aElementOf0(all_40_1, xS) = all_40_0
% 22.60/3.92 | | (32) aElementOf0(all_40_1, all_14_2) = 0
% 22.60/3.92 | |
% 22.60/3.92 | | BETA: splitting (24) gives:
% 22.60/3.92 | |
% 22.60/3.92 | | Case 1:
% 22.60/3.92 | | |
% 22.60/3.92 | | | (33) all_14_0 = 0
% 22.60/3.92 | | |
% 22.60/3.92 | | | REDUCE: (26), (33) imply:
% 22.60/3.92 | | | (34) $false
% 22.60/3.92 | | |
% 22.60/3.92 | | | CLOSE: (34) is inconsistent.
% 22.60/3.92 | | |
% 22.60/3.92 | | Case 2:
% 22.60/3.92 | | |
% 22.60/3.92 | | | (35) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0,
% 22.60/3.92 | | | all_14_2) = 0 & aElementOf0(v0, xS) = v1 & $i(v0)) | ? [v0:
% 22.60/3.92 | | | int] : ( ~ (v0 = 0) & aSet0(all_14_2) = v0)
% 22.60/3.92 | | |
% 22.60/3.92 | | | BETA: splitting (35) gives:
% 22.60/3.92 | | |
% 22.60/3.92 | | | Case 1:
% 22.60/3.92 | | | |
% 22.60/3.92 | | | |
% 22.60/3.92 | | | | GROUND_INST: instantiating (15) with all_40_1, simplifying with (30),
% 22.60/3.92 | | | | (32) gives:
% 22.60/3.92 | | | | (36) ? [v0: any] : (aElement0(all_40_1) = 0 & aElementOf0(all_40_1,
% 22.60/3.92 | | | | all_14_3) = v0 & (v0 = 0 | all_40_1 = xx))
% 22.60/3.92 | | | |
% 22.60/3.92 | | | | DELTA: instantiating (36) with fresh symbol all_58_0 gives:
% 22.60/3.92 | | | | (37) aElement0(all_40_1) = 0 & aElementOf0(all_40_1, all_14_3) =
% 22.60/3.92 | | | | all_58_0 & (all_58_0 = 0 | all_40_1 = xx)
% 22.60/3.92 | | | |
% 22.60/3.92 | | | | ALPHA: (37) implies:
% 22.60/3.93 | | | | (38) aElementOf0(all_40_1, all_14_3) = all_58_0
% 22.60/3.93 | | | | (39) aElement0(all_40_1) = 0
% 22.60/3.93 | | | | (40) all_58_0 = 0 | all_40_1 = xx
% 22.60/3.93 | | | |
% 22.60/3.93 | | | | GROUND_INST: instantiating (mDefDiff) with xS, all_40_1, simplifying
% 22.60/3.93 | | | | with (1), (3), (30), (39) gives:
% 22.60/3.93 | | | | (41) ? [v0: $i] : (sdtmndt0(xS, all_40_1) = v0 & $i(v0) & ! [v1:
% 22.60/3.93 | | | | $i] : (v1 = v0 | ~ (aSet0(v1) = 0) | ~ $i(v1) | ? [v2:
% 22.60/3.93 | | | | $i] : ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 22.60/3.93 | | | | (aElement0(v2) = v4 & aElementOf0(v2, v1) = v3 &
% 22.60/3.93 | | | | aElementOf0(v2, xS) = v5 & $i(v2) & ( ~ (v5 = 0) | ~ (v4
% 22.60/3.93 | | | | = 0) | ~ (v3 = 0) | v2 = all_40_1) & (v3 = 0 | (v5 =
% 22.60/3.93 | | | | 0 & v4 = 0 & ~ (v2 = all_40_1))))) & ! [v1: any] : (
% 22.60/3.93 | | | | ~ (aSet0(v0) = v1) | (v1 = 0 & ! [v2: $i] : ! [v3: any] :
% 22.60/3.93 | | | | ( ~ (aElement0(v2) = v3) | ~ $i(v2) | ? [v4: any] : ?
% 22.60/3.93 | | | | [v5: any] : (aElementOf0(v2, v0) = v4 & aElementOf0(v2,
% 22.60/3.93 | | | | xS) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0 & ~ (v2
% 22.60/3.93 | | | | = all_40_1))))) & ! [v2: any] : (v2 = all_40_1
% 22.60/3.93 | | | | | ~ (aElement0(v2) = 0) | ~ $i(v2) | ? [v3: any] : ?
% 22.60/3.93 | | | | [v4: any] : (aElementOf0(v2, v0) = v4 & aElementOf0(v2,
% 22.60/3.93 | | | | xS) = v3 & ( ~ (v3 = 0) | v4 = 0))))))
% 22.60/3.93 | | | |
% 22.60/3.93 | | | | DELTA: instantiating (41) with fresh symbol all_71_0 gives:
% 22.60/3.93 | | | | (42) sdtmndt0(xS, all_40_1) = all_71_0 & $i(all_71_0) & ! [v0: any]
% 22.60/3.94 | | | | : (v0 = all_71_0 | ~ (aSet0(v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 22.60/3.94 | | | | : ? [v2: any] : ? [v3: any] : ? [v4: any] : (aElement0(v1)
% 22.60/3.94 | | | | = v3 & aElementOf0(v1, v0) = v2 & aElementOf0(v1, xS) = v4 &
% 22.60/3.94 | | | | $i(v1) & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 =
% 22.60/3.94 | | | | all_40_1) & (v2 = 0 | (v4 = 0 & v3 = 0 & ~ (v1 =
% 22.60/3.94 | | | | all_40_1))))) & ! [v0: any] : ( ~ (aSet0(all_71_0) =
% 22.60/3.94 | | | | v0) | (v0 = 0 & ! [v1: $i] : ! [v2: any] : ( ~
% 22.60/3.94 | | | | (aElement0(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4:
% 22.60/3.94 | | | | any] : (aElementOf0(v1, all_71_0) = v3 & aElementOf0(v1,
% 22.60/3.94 | | | | xS) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0 & ~ (v1 =
% 22.60/3.94 | | | | all_40_1))))) & ! [v1: any] : (v1 = all_40_1 | ~
% 22.60/3.94 | | | | (aElement0(v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3:
% 22.60/3.94 | | | | any] : (aElementOf0(v1, all_71_0) = v3 & aElementOf0(v1,
% 22.60/3.94 | | | | xS) = v2 & ( ~ (v2 = 0) | v3 = 0)))))
% 22.60/3.94 | | | |
% 22.60/3.94 | | | | ALPHA: (42) implies:
% 22.60/3.94 | | | | (43) ! [v0: any] : (v0 = all_71_0 | ~ (aSet0(v0) = 0) | ~ $i(v0) |
% 22.60/3.94 | | | | ? [v1: $i] : ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 22.60/3.94 | | | | (aElement0(v1) = v3 & aElementOf0(v1, v0) = v2 &
% 22.60/3.94 | | | | aElementOf0(v1, xS) = v4 & $i(v1) & ( ~ (v4 = 0) | ~ (v3 =
% 22.60/3.94 | | | | 0) | ~ (v2 = 0) | v1 = all_40_1) & (v2 = 0 | (v4 = 0 &
% 22.60/3.94 | | | | v3 = 0 & ~ (v1 = all_40_1)))))
% 22.60/3.94 | | | |
% 22.60/3.94 | | | | GROUND_INST: instantiating (43) with xS, simplifying with (1), (3)
% 22.60/3.94 | | | | gives:
% 22.60/3.94 | | | | (44) all_71_0 = xS | ? [v0: $i] : ? [v1: any] : ? [v2: any] : ?
% 22.60/3.94 | | | | [v3: any] : (aElement0(v0) = v2 & aElementOf0(v0, xS) = v3 &
% 22.60/3.94 | | | | aElementOf0(v0, xS) = v1 & $i(v0) & ( ~ (v3 = 0) | ~ (v2 = 0)
% 22.60/3.94 | | | | | ~ (v1 = 0) | v0 = all_40_1) & (v1 = 0 | (v3 = 0 & v2 = 0
% 22.60/3.94 | | | | & ~ (v0 = all_40_1))))
% 22.60/3.94 | | | |
% 22.60/3.94 | | | | BETA: splitting (40) gives:
% 22.60/3.94 | | | |
% 22.60/3.94 | | | | Case 1:
% 22.60/3.94 | | | | |
% 22.60/3.94 | | | | | (45) all_40_1 = xx
% 22.60/3.94 | | | | |
% 22.60/3.94 | | | | | REDUCE: (31), (45) imply:
% 22.60/3.94 | | | | | (46) aElementOf0(xx, xS) = all_40_0
% 22.60/3.94 | | | | |
% 22.60/3.94 | | | | | GROUND_INST: instantiating (7) with 0, all_40_0, xS, xx, simplifying
% 22.60/3.94 | | | | | with (2), (46) gives:
% 22.60/3.94 | | | | | (47) all_40_0 = 0
% 22.60/3.94 | | | | |
% 22.60/3.94 | | | | | REDUCE: (29), (47) imply:
% 22.60/3.94 | | | | | (48) $false
% 22.60/3.94 | | | | |
% 22.60/3.94 | | | | | CLOSE: (48) is inconsistent.
% 22.60/3.94 | | | | |
% 22.60/3.94 | | | | Case 2:
% 22.60/3.94 | | | | |
% 22.60/3.94 | | | | | (49) all_58_0 = 0
% 22.60/3.94 | | | | |
% 22.60/3.94 | | | | | REDUCE: (38), (49) imply:
% 22.60/3.94 | | | | | (50) aElementOf0(all_40_1, all_14_3) = 0
% 22.60/3.94 | | | | |
% 22.60/3.94 | | | | | BETA: splitting (44) gives:
% 22.60/3.94 | | | | |
% 22.60/3.94 | | | | | Case 1:
% 22.60/3.94 | | | | | |
% 22.60/3.94 | | | | | |
% 22.60/3.94 | | | | | | GROUND_INST: instantiating (14) with all_40_1, simplifying with
% 22.60/3.94 | | | | | | (30), (50) gives:
% 22.60/3.94 | | | | | | (51) ~ (all_40_1 = xx) & aElement0(all_40_1) = 0 &
% 22.60/3.94 | | | | | | aElementOf0(all_40_1, xS) = 0
% 22.60/3.94 | | | | | |
% 22.60/3.94 | | | | | | REF_CLOSE: (7), (29), (31), (51) are inconsistent by sub-proof #1.
% 22.60/3.94 | | | | | |
% 22.60/3.94 | | | | | Case 2:
% 22.60/3.94 | | | | | |
% 22.60/3.95 | | | | | | (52) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 22.60/3.95 | | | | | | (aElement0(v0) = v2 & aElementOf0(v0, xS) = v3 &
% 22.60/3.95 | | | | | | aElementOf0(v0, xS) = v1 & $i(v0) & ( ~ (v3 = 0) | ~ (v2
% 22.60/3.95 | | | | | | = 0) | ~ (v1 = 0) | v0 = all_40_1) & (v1 = 0 | (v3 =
% 22.60/3.95 | | | | | | 0 & v2 = 0 & ~ (v0 = all_40_1))))
% 22.60/3.95 | | | | | |
% 22.60/3.95 | | | | | | DELTA: instantiating (52) with fresh symbols all_310_0, all_310_1,
% 22.60/3.95 | | | | | | all_310_2, all_310_3 gives:
% 22.60/3.95 | | | | | | (53) aElement0(all_310_3) = all_310_1 & aElementOf0(all_310_3,
% 22.60/3.95 | | | | | | xS) = all_310_0 & aElementOf0(all_310_3, xS) = all_310_2 &
% 22.60/3.95 | | | | | | $i(all_310_3) & ( ~ (all_310_0 = 0) | ~ (all_310_1 = 0) |
% 22.60/3.95 | | | | | | ~ (all_310_2 = 0) | all_310_3 = all_40_1) & (all_310_2 = 0
% 22.60/3.95 | | | | | | | (all_310_0 = 0 & all_310_1 = 0 & ~ (all_310_3 =
% 22.60/3.95 | | | | | | all_40_1)))
% 22.60/3.95 | | | | | |
% 22.60/3.95 | | | | | | ALPHA: (53) implies:
% 22.60/3.95 | | | | | | (54) aElementOf0(all_310_3, xS) = all_310_2
% 22.60/3.95 | | | | | | (55) aElementOf0(all_310_3, xS) = all_310_0
% 22.60/3.95 | | | | | | (56) all_310_2 = 0 | (all_310_0 = 0 & all_310_1 = 0 & ~
% 22.60/3.95 | | | | | | (all_310_3 = all_40_1))
% 22.60/3.95 | | | | | |
% 22.60/3.95 | | | | | | GROUND_INST: instantiating (7) with all_310_2, all_310_0, xS,
% 22.60/3.95 | | | | | | all_310_3, simplifying with (54), (55) gives:
% 22.60/3.95 | | | | | | (57) all_310_0 = all_310_2
% 22.60/3.95 | | | | | |
% 22.60/3.95 | | | | | | BETA: splitting (56) gives:
% 22.60/3.95 | | | | | |
% 22.60/3.95 | | | | | | Case 1:
% 22.60/3.95 | | | | | | |
% 22.60/3.95 | | | | | | |
% 22.60/3.95 | | | | | | | GROUND_INST: instantiating (14) with all_40_1, simplifying with
% 22.60/3.95 | | | | | | | (30), (50) gives:
% 22.60/3.95 | | | | | | | (58) ~ (all_40_1 = xx) & aElement0(all_40_1) = 0 &
% 22.60/3.95 | | | | | | | aElementOf0(all_40_1, xS) = 0
% 22.60/3.95 | | | | | | |
% 22.60/3.95 | | | | | | | REF_CLOSE: (7), (29), (31), (58) are inconsistent by sub-proof #1.
% 22.60/3.95 | | | | | | |
% 22.60/3.95 | | | | | | Case 2:
% 22.60/3.95 | | | | | | |
% 22.60/3.95 | | | | | | | (59) ~ (all_310_2 = 0)
% 22.60/3.95 | | | | | | | (60) all_310_0 = 0 & all_310_1 = 0 & ~ (all_310_3 = all_40_1)
% 22.60/3.95 | | | | | | |
% 22.60/3.95 | | | | | | | ALPHA: (60) implies:
% 22.60/3.95 | | | | | | | (61) all_310_0 = 0
% 22.60/3.95 | | | | | | |
% 22.60/3.95 | | | | | | | COMBINE_EQS: (57), (61) imply:
% 22.60/3.95 | | | | | | | (62) all_310_2 = 0
% 22.60/3.95 | | | | | | |
% 22.60/3.95 | | | | | | | REDUCE: (59), (62) imply:
% 22.60/3.95 | | | | | | | (63) $false
% 22.60/3.95 | | | | | | |
% 22.60/3.95 | | | | | | | CLOSE: (63) is inconsistent.
% 22.60/3.95 | | | | | | |
% 22.60/3.95 | | | | | | End of split
% 22.60/3.95 | | | | | |
% 22.60/3.95 | | | | | End of split
% 22.60/3.95 | | | | |
% 22.60/3.95 | | | | End of split
% 22.60/3.95 | | | |
% 22.60/3.95 | | | Case 2:
% 22.60/3.95 | | | |
% 22.60/3.95 | | | | (64) ? [v0: int] : ( ~ (v0 = 0) & aSet0(all_14_2) = v0)
% 22.60/3.95 | | | |
% 22.60/3.95 | | | | DELTA: instantiating (64) with fresh symbol all_49_0 gives:
% 22.60/3.95 | | | | (65) ~ (all_49_0 = 0) & aSet0(all_14_2) = all_49_0
% 22.60/3.95 | | | |
% 22.60/3.95 | | | | ALPHA: (65) implies:
% 22.60/3.95 | | | | (66) ~ (all_49_0 = 0)
% 22.60/3.95 | | | | (67) aSet0(all_14_2) = all_49_0
% 22.60/3.95 | | | |
% 22.60/3.95 | | | | GROUND_INST: instantiating (6) with 0, all_49_0, all_14_2, simplifying
% 22.60/3.95 | | | | with (10), (67) gives:
% 22.60/3.95 | | | | (68) all_49_0 = 0
% 22.60/3.95 | | | |
% 22.60/3.95 | | | | REDUCE: (66), (68) imply:
% 22.60/3.95 | | | | (69) $false
% 22.60/3.95 | | | |
% 22.60/3.95 | | | | CLOSE: (69) is inconsistent.
% 22.60/3.95 | | | |
% 22.60/3.95 | | | End of split
% 22.60/3.95 | | |
% 22.60/3.95 | | End of split
% 22.60/3.95 | |
% 22.60/3.96 | Case 2:
% 22.60/3.96 | |
% 22.60/3.96 | | (70) ~ (all_14_1 = 0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 22.60/3.96 | | aElementOf0(v0, all_14_2) = v1 & aElementOf0(v0, xS) = 0 & $i(v0))
% 22.60/3.96 | |
% 22.60/3.96 | | ALPHA: (70) implies:
% 22.60/3.96 | | (71) ~ (all_14_1 = 0)
% 22.60/3.96 | | (72) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0,
% 22.60/3.96 | | all_14_2) = v1 & aElementOf0(v0, xS) = 0 & $i(v0))
% 22.60/3.96 | |
% 22.60/3.96 | | DELTA: instantiating (72) with fresh symbols all_40_0, all_40_1 gives:
% 22.60/3.96 | | (73) ~ (all_40_0 = 0) & aElementOf0(all_40_1, all_14_2) = all_40_0 &
% 22.60/3.96 | | aElementOf0(all_40_1, xS) = 0 & $i(all_40_1)
% 22.60/3.96 | |
% 22.60/3.96 | | ALPHA: (73) implies:
% 22.60/3.96 | | (74) ~ (all_40_0 = 0)
% 22.60/3.96 | | (75) $i(all_40_1)
% 22.60/3.96 | | (76) aElementOf0(all_40_1, xS) = 0
% 22.60/3.96 | | (77) aElementOf0(all_40_1, all_14_2) = all_40_0
% 22.60/3.96 | |
% 22.60/3.96 | | BETA: splitting (23) gives:
% 22.60/3.96 | |
% 22.60/3.96 | | Case 1:
% 22.60/3.96 | | |
% 22.60/3.96 | | | (78) all_14_1 = 0
% 22.60/3.96 | | |
% 22.60/3.96 | | | REDUCE: (71), (78) imply:
% 22.60/3.96 | | | (79) $false
% 22.60/3.96 | | |
% 22.60/3.96 | | | CLOSE: (79) is inconsistent.
% 22.60/3.96 | | |
% 22.60/3.96 | | Case 2:
% 22.60/3.96 | | |
% 22.60/3.96 | | | (80) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0,
% 22.60/3.96 | | | all_14_2) = v1 & aElementOf0(v0, xS) = 0 & $i(v0)) | ? [v0:
% 22.60/3.96 | | | int] : ( ~ (v0 = 0) & aSet0(xS) = v0)
% 22.60/3.96 | | |
% 22.60/3.96 | | | BETA: splitting (80) gives:
% 22.60/3.96 | | |
% 22.60/3.96 | | | Case 1:
% 22.60/3.96 | | | |
% 22.60/3.96 | | | |
% 22.60/3.96 | | | | GROUND_INST: instantiating (16) with all_40_1, all_40_0, simplifying
% 22.60/3.96 | | | | with (75), (77) gives:
% 22.60/3.96 | | | | (81) all_40_0 = 0 | ? [v0: any] : ? [v1: any] :
% 22.60/3.96 | | | | (aElement0(all_40_1) = v0 & aElementOf0(all_40_1, all_14_3) = v1
% 22.60/3.96 | | | | & ( ~ (v0 = 0) | ( ~ (v1 = 0) & ~ (all_40_1 = xx))))
% 22.60/3.96 | | | |
% 22.60/3.96 | | | | BETA: splitting (81) gives:
% 22.60/3.96 | | | |
% 22.60/3.96 | | | | Case 1:
% 22.60/3.96 | | | | |
% 22.60/3.96 | | | | | (82) all_40_0 = 0
% 22.60/3.96 | | | | |
% 22.60/3.96 | | | | | REDUCE: (74), (82) imply:
% 22.60/3.96 | | | | | (83) $false
% 22.60/3.96 | | | | |
% 22.60/3.96 | | | | | CLOSE: (83) is inconsistent.
% 22.60/3.96 | | | | |
% 22.60/3.96 | | | | Case 2:
% 22.60/3.96 | | | | |
% 22.60/3.96 | | | | | (84) ? [v0: any] : ? [v1: any] : (aElement0(all_40_1) = v0 &
% 22.60/3.96 | | | | | aElementOf0(all_40_1, all_14_3) = v1 & ( ~ (v0 = 0) | ( ~
% 22.60/3.96 | | | | | (v1 = 0) & ~ (all_40_1 = xx))))
% 22.60/3.96 | | | | |
% 22.60/3.96 | | | | | DELTA: instantiating (84) with fresh symbols all_67_0, all_67_1 gives:
% 22.60/3.96 | | | | | (85) aElement0(all_40_1) = all_67_1 & aElementOf0(all_40_1,
% 22.60/3.96 | | | | | all_14_3) = all_67_0 & ( ~ (all_67_1 = 0) | ( ~ (all_67_0 =
% 22.60/3.96 | | | | | 0) & ~ (all_40_1 = xx)))
% 22.60/3.96 | | | | |
% 22.60/3.96 | | | | | ALPHA: (85) implies:
% 22.60/3.97 | | | | | (86) aElementOf0(all_40_1, all_14_3) = all_67_0
% 22.60/3.97 | | | | | (87) aElement0(all_40_1) = all_67_1
% 22.60/3.97 | | | | | (88) ~ (all_67_1 = 0) | ( ~ (all_67_0 = 0) & ~ (all_40_1 = xx))
% 22.60/3.97 | | | | |
% 22.60/3.97 | | | | | GROUND_INST: instantiating (17) with all_40_1, all_67_0, simplifying
% 22.60/3.97 | | | | | with (75), (86) gives:
% 22.60/3.97 | | | | | (89) all_67_0 = 0 | all_40_1 = xx | ? [v0: any] : ? [v1: any] :
% 22.60/3.97 | | | | | (aElement0(all_40_1) = v0 & aElementOf0(all_40_1, xS) = v1 & (
% 22.60/3.97 | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 22.60/3.97 | | | | |
% 22.60/3.97 | | | | | GROUND_INST: instantiating (18) with all_40_1, all_67_1, simplifying
% 22.60/3.97 | | | | | with (75), (87) gives:
% 22.60/3.97 | | | | | (90) all_67_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 22.60/3.97 | | | | | aElementOf0(all_40_1, xS) = v0)
% 22.60/3.97 | | | | |
% 22.60/3.97 | | | | | BETA: splitting (90) gives:
% 22.60/3.97 | | | | |
% 22.60/3.97 | | | | | Case 1:
% 22.60/3.97 | | | | | |
% 22.60/3.97 | | | | | | (91) all_67_1 = 0
% 22.60/3.97 | | | | | |
% 22.60/3.97 | | | | | | REDUCE: (87), (91) imply:
% 22.60/3.97 | | | | | | (92) aElement0(all_40_1) = 0
% 22.60/3.97 | | | | | |
% 22.60/3.97 | | | | | | BETA: splitting (88) gives:
% 22.60/3.97 | | | | | |
% 22.60/3.97 | | | | | | Case 1:
% 22.60/3.97 | | | | | | |
% 22.60/3.97 | | | | | | | (93) ~ (all_67_1 = 0)
% 22.60/3.97 | | | | | | |
% 22.60/3.97 | | | | | | | REDUCE: (91), (93) imply:
% 22.60/3.97 | | | | | | | (94) $false
% 22.60/3.97 | | | | | | |
% 22.60/3.97 | | | | | | | CLOSE: (94) is inconsistent.
% 22.60/3.97 | | | | | | |
% 22.60/3.97 | | | | | | Case 2:
% 22.60/3.97 | | | | | | |
% 22.60/3.97 | | | | | | | (95) ~ (all_67_0 = 0) & ~ (all_40_1 = xx)
% 22.60/3.97 | | | | | | |
% 22.60/3.97 | | | | | | | ALPHA: (95) implies:
% 22.60/3.97 | | | | | | | (96) ~ (all_40_1 = xx)
% 22.60/3.97 | | | | | | | (97) ~ (all_67_0 = 0)
% 22.60/3.97 | | | | | | |
% 22.60/3.97 | | | | | | | BETA: splitting (89) gives:
% 22.60/3.97 | | | | | | |
% 22.60/3.97 | | | | | | | Case 1:
% 22.60/3.97 | | | | | | | |
% 22.60/3.97 | | | | | | | | (98) all_40_1 = xx
% 22.60/3.97 | | | | | | | |
% 22.60/3.97 | | | | | | | | REDUCE: (96), (98) imply:
% 22.60/3.97 | | | | | | | | (99) $false
% 22.60/3.97 | | | | | | | |
% 22.60/3.97 | | | | | | | | CLOSE: (99) is inconsistent.
% 22.60/3.97 | | | | | | | |
% 22.60/3.97 | | | | | | | Case 2:
% 22.60/3.97 | | | | | | | |
% 22.60/3.97 | | | | | | | | (100) all_67_0 = 0 | ? [v0: any] : ? [v1: any] :
% 22.60/3.97 | | | | | | | | (aElement0(all_40_1) = v0 & aElementOf0(all_40_1, xS) =
% 22.60/3.97 | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.60/3.97 | | | | | | | |
% 22.60/3.97 | | | | | | | | BETA: splitting (100) gives:
% 22.60/3.97 | | | | | | | |
% 22.60/3.97 | | | | | | | | Case 1:
% 22.60/3.97 | | | | | | | | |
% 22.60/3.97 | | | | | | | | | (101) all_67_0 = 0
% 22.60/3.97 | | | | | | | | |
% 22.60/3.97 | | | | | | | | | REDUCE: (97), (101) imply:
% 22.60/3.97 | | | | | | | | | (102) $false
% 22.60/3.97 | | | | | | | | |
% 22.60/3.97 | | | | | | | | | CLOSE: (102) is inconsistent.
% 22.60/3.97 | | | | | | | | |
% 22.60/3.97 | | | | | | | | Case 2:
% 22.60/3.97 | | | | | | | | |
% 22.60/3.97 | | | | | | | | | (103) ? [v0: any] : ? [v1: any] : (aElement0(all_40_1) =
% 22.60/3.97 | | | | | | | | | v0 & aElementOf0(all_40_1, xS) = v1 & ( ~ (v1 = 0)
% 22.60/3.97 | | | | | | | | | | ~ (v0 = 0)))
% 22.60/3.97 | | | | | | | | |
% 22.60/3.97 | | | | | | | | | DELTA: instantiating (103) with fresh symbols all_112_0,
% 22.60/3.97 | | | | | | | | | all_112_1 gives:
% 22.60/3.97 | | | | | | | | | (104) aElement0(all_40_1) = all_112_1 &
% 22.60/3.97 | | | | | | | | | aElementOf0(all_40_1, xS) = all_112_0 & ( ~
% 22.60/3.97 | | | | | | | | | (all_112_0 = 0) | ~ (all_112_1 = 0))
% 22.60/3.97 | | | | | | | | |
% 22.60/3.97 | | | | | | | | | ALPHA: (104) implies:
% 22.60/3.97 | | | | | | | | | (105) aElementOf0(all_40_1, xS) = all_112_0
% 22.60/3.97 | | | | | | | | | (106) aElement0(all_40_1) = all_112_1
% 22.60/3.97 | | | | | | | | | (107) ~ (all_112_0 = 0) | ~ (all_112_1 = 0)
% 22.60/3.97 | | | | | | | | |
% 22.60/3.97 | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_112_0, xS, all_40_1,
% 22.60/3.97 | | | | | | | | | simplifying with (76), (105) gives:
% 22.60/3.97 | | | | | | | | | (108) all_112_0 = 0
% 22.60/3.97 | | | | | | | | |
% 22.60/3.98 | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_112_1, all_40_1,
% 22.60/3.98 | | | | | | | | | simplifying with (92), (106) gives:
% 22.60/3.98 | | | | | | | | | (109) all_112_1 = 0
% 22.60/3.98 | | | | | | | | |
% 22.60/3.98 | | | | | | | | | BETA: splitting (107) gives:
% 22.60/3.98 | | | | | | | | |
% 22.60/3.98 | | | | | | | | | Case 1:
% 22.60/3.98 | | | | | | | | | |
% 22.60/3.98 | | | | | | | | | | (110) ~ (all_112_0 = 0)
% 22.60/3.98 | | | | | | | | | |
% 22.60/3.98 | | | | | | | | | | REDUCE: (108), (110) imply:
% 22.60/3.98 | | | | | | | | | | (111) $false
% 22.60/3.98 | | | | | | | | | |
% 22.60/3.98 | | | | | | | | | | CLOSE: (111) is inconsistent.
% 22.60/3.98 | | | | | | | | | |
% 22.60/3.98 | | | | | | | | | Case 2:
% 22.60/3.98 | | | | | | | | | |
% 22.60/3.98 | | | | | | | | | | (112) ~ (all_112_1 = 0)
% 22.60/3.98 | | | | | | | | | |
% 22.60/3.98 | | | | | | | | | | REDUCE: (109), (112) imply:
% 22.60/3.98 | | | | | | | | | | (113) $false
% 22.60/3.98 | | | | | | | | | |
% 22.60/3.98 | | | | | | | | | | CLOSE: (113) is inconsistent.
% 22.60/3.98 | | | | | | | | | |
% 22.60/3.98 | | | | | | | | | End of split
% 22.60/3.98 | | | | | | | | |
% 22.60/3.98 | | | | | | | | End of split
% 22.60/3.98 | | | | | | | |
% 22.60/3.98 | | | | | | | End of split
% 22.60/3.98 | | | | | | |
% 22.60/3.98 | | | | | | End of split
% 22.60/3.98 | | | | | |
% 22.60/3.98 | | | | | Case 2:
% 22.60/3.98 | | | | | |
% 22.60/3.98 | | | | | | (114) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_40_1, xS) =
% 22.60/3.98 | | | | | | v0)
% 22.60/3.98 | | | | | |
% 22.60/3.98 | | | | | | DELTA: instantiating (114) with fresh symbol all_86_0 gives:
% 22.60/3.98 | | | | | | (115) ~ (all_86_0 = 0) & aElementOf0(all_40_1, xS) = all_86_0
% 22.60/3.98 | | | | | |
% 22.60/3.98 | | | | | | ALPHA: (115) implies:
% 22.60/3.98 | | | | | | (116) ~ (all_86_0 = 0)
% 22.60/3.98 | | | | | | (117) aElementOf0(all_40_1, xS) = all_86_0
% 22.60/3.98 | | | | | |
% 22.60/3.98 | | | | | | GROUND_INST: instantiating (7) with 0, all_86_0, xS, all_40_1,
% 22.60/3.98 | | | | | | simplifying with (76), (117) gives:
% 22.60/3.98 | | | | | | (118) all_86_0 = 0
% 22.60/3.98 | | | | | |
% 22.60/3.98 | | | | | | REDUCE: (116), (118) imply:
% 22.60/3.98 | | | | | | (119) $false
% 22.60/3.98 | | | | | |
% 22.60/3.98 | | | | | | CLOSE: (119) is inconsistent.
% 22.60/3.98 | | | | | |
% 22.60/3.98 | | | | | End of split
% 22.60/3.98 | | | | |
% 22.60/3.98 | | | | End of split
% 22.60/3.98 | | | |
% 22.60/3.98 | | | Case 2:
% 22.60/3.98 | | | |
% 22.60/3.98 | | | | (120) ? [v0: int] : ( ~ (v0 = 0) & aSet0(xS) = v0)
% 22.60/3.98 | | | |
% 22.60/3.98 | | | | DELTA: instantiating (120) with fresh symbol all_49_0 gives:
% 22.60/3.98 | | | | (121) ~ (all_49_0 = 0) & aSet0(xS) = all_49_0
% 22.60/3.98 | | | |
% 22.60/3.98 | | | | ALPHA: (121) implies:
% 22.60/3.98 | | | | (122) ~ (all_49_0 = 0)
% 22.60/3.98 | | | | (123) aSet0(xS) = all_49_0
% 22.60/3.98 | | | |
% 22.60/3.98 | | | | GROUND_INST: instantiating (6) with 0, all_49_0, xS, simplifying with
% 22.60/3.98 | | | | (1), (123) gives:
% 22.60/3.98 | | | | (124) all_49_0 = 0
% 22.60/3.98 | | | |
% 22.60/3.98 | | | | REDUCE: (122), (124) imply:
% 22.60/3.98 | | | | (125) $false
% 22.60/3.98 | | | |
% 22.60/3.98 | | | | CLOSE: (125) is inconsistent.
% 22.60/3.98 | | | |
% 22.60/3.98 | | | End of split
% 22.60/3.98 | | |
% 22.60/3.98 | | End of split
% 22.60/3.98 | |
% 22.60/3.98 | End of split
% 22.60/3.98 |
% 22.60/3.98 End of proof
% 22.60/3.98
% 22.60/3.98 Sub-proof #1 shows that the following formulas are inconsistent:
% 22.60/3.98 ----------------------------------------------------------------
% 22.60/3.98 (1) ~ (all_40_1 = xx) & aElement0(all_40_1) = 0 & aElementOf0(all_40_1, xS)
% 22.60/3.98 = 0
% 22.60/3.98 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 22.60/3.98 ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~
% 22.60/3.98 (aElementOf0(v3, v2) = v0))
% 22.60/3.98 (3) aElementOf0(all_40_1, xS) = all_40_0
% 22.60/3.98 (4) ~ (all_40_0 = 0)
% 22.60/3.98
% 22.60/3.98 Begin of proof
% 22.60/3.98 |
% 22.60/3.98 | ALPHA: (1) implies:
% 22.60/3.98 | (5) aElementOf0(all_40_1, xS) = 0
% 22.60/3.98 |
% 22.60/3.98 | GROUND_INST: instantiating (2) with all_40_0, 0, xS, all_40_1, simplifying
% 22.60/3.98 | with (3), (5) gives:
% 22.60/3.98 | (6) all_40_0 = 0
% 22.60/3.98 |
% 22.60/3.98 | REDUCE: (4), (6) imply:
% 22.60/3.98 | (7) $false
% 22.60/3.98 |
% 22.60/3.98 | CLOSE: (7) is inconsistent.
% 22.60/3.98 |
% 22.60/3.98 End of proof
% 22.60/3.98 % SZS output end Proof for theBenchmark
% 22.60/3.99
% 22.60/3.99 3392ms
%------------------------------------------------------------------------------