TSTP Solution File: NUM533+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM533+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 : n012.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 11:48:26 EDT 2023
% Result : Theorem 6.13s 1.63s
% Output : Proof 8.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM533+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34 % Computer : n012.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Fri Aug 25 11:12:11 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.20/0.64 ________ _____
% 0.20/0.64 ___ __ \_________(_)________________________________
% 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.64
% 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.64 (2023-06-19)
% 0.20/0.64
% 0.20/0.64 (c) Philipp Rümmer, 2009-2023
% 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.64 Amanda Stjerna.
% 0.20/0.64 Free software under BSD-3-Clause.
% 0.20/0.64
% 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.64
% 0.20/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.66 Running up to 7 provers in parallel.
% 0.20/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.43/1.05 Prover 4: Preprocessing ...
% 2.43/1.05 Prover 1: Preprocessing ...
% 2.60/1.09 Prover 2: Preprocessing ...
% 2.60/1.09 Prover 3: Preprocessing ...
% 2.60/1.09 Prover 6: Preprocessing ...
% 2.60/1.09 Prover 5: Preprocessing ...
% 2.60/1.09 Prover 0: Preprocessing ...
% 4.09/1.30 Prover 2: Constructing countermodel ...
% 4.09/1.30 Prover 5: Constructing countermodel ...
% 4.09/1.34 Prover 1: Constructing countermodel ...
% 4.09/1.37 Prover 3: Constructing countermodel ...
% 4.09/1.39 Prover 6: Proving ...
% 5.04/1.43 Prover 4: Constructing countermodel ...
% 5.25/1.52 Prover 0: Proving ...
% 6.13/1.63 Prover 3: proved (951ms)
% 6.13/1.63
% 6.13/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.13/1.63
% 6.13/1.63 Prover 2: stopped
% 6.13/1.63 Prover 5: stopped
% 6.61/1.65 Prover 0: stopped
% 6.83/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.83/1.67 Prover 6: stopped
% 6.83/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.83/1.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.83/1.67 Prover 7: Preprocessing ...
% 6.83/1.67 Prover 8: Preprocessing ...
% 6.83/1.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.83/1.68 Prover 10: Preprocessing ...
% 6.83/1.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.83/1.69 Prover 11: Preprocessing ...
% 6.83/1.71 Prover 13: Preprocessing ...
% 6.83/1.71 Prover 7: Constructing countermodel ...
% 7.28/1.74 Prover 10: Constructing countermodel ...
% 7.28/1.75 Prover 1: Found proof (size 40)
% 7.28/1.75 Prover 1: proved (1075ms)
% 7.28/1.75 Prover 10: stopped
% 7.28/1.75 Prover 7: stopped
% 7.28/1.75 Prover 4: stopped
% 7.28/1.76 Prover 13: Constructing countermodel ...
% 7.54/1.76 Prover 13: stopped
% 7.54/1.77 Prover 8: Warning: ignoring some quantifiers
% 7.54/1.77 Prover 8: Constructing countermodel ...
% 7.54/1.78 Prover 8: stopped
% 7.54/1.82 Prover 11: Constructing countermodel ...
% 7.54/1.82 Prover 11: stopped
% 7.54/1.82
% 7.54/1.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.54/1.82
% 7.54/1.83 % SZS output start Proof for theBenchmark
% 7.92/1.83 Assumptions after simplification:
% 7.92/1.83 ---------------------------------
% 7.92/1.83
% 7.92/1.83 (mDefSub)
% 7.92/1.86 ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: int] :
% 7.92/1.86 (v2 = 0 | ~ (aSubsetOf0(v1, v0) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4:
% 7.92/1.86 int] : ( ~ (v4 = 0) & aElementOf0(v3, v1) = 0 & aElementOf0(v3, v0) =
% 7.92/1.86 v4 & $i(v3)) | ? [v3: int] : ( ~ (v3 = 0) & aSet0(v1) = v3)) & !
% 7.92/1.86 [v1: $i] : ( ~ (aSubsetOf0(v1, v0) = 0) | ~ $i(v1) | (aSet0(v1) = 0 & !
% 7.92/1.86 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, v0) = v3) | ~
% 7.92/1.86 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v2, v1) =
% 7.92/1.86 v4))))))
% 7.92/1.86
% 7.92/1.86 (m__)
% 7.92/1.87 $i(xC) & $i(xB) & $i(xA) & ? [v0: int] : ( ~ (v0 = 0) & aSubsetOf0(xB, xC) =
% 7.92/1.87 0 & aSubsetOf0(xA, xC) = v0 & aSubsetOf0(xA, xB) = 0 & ! [v1: $i] : ! [v2:
% 7.92/1.87 int] : (v2 = 0 | ~ (aElementOf0(v1, xC) = v2) | ~ $i(v1) | ? [v3: int]
% 7.92/1.87 : ( ~ (v3 = 0) & aElementOf0(v1, xB) = v3)) & ! [v1: $i] : ! [v2: int] :
% 7.92/1.87 (v2 = 0 | ~ (aElementOf0(v1, xB) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3
% 7.92/1.87 = 0) & aElementOf0(v1, xA) = v3)) & ? [v1: $i] : ? [v2: int] : ( ~
% 7.92/1.87 (v2 = 0) & aElementOf0(v1, xC) = v2 & aElementOf0(v1, xA) = 0 & $i(v1)))
% 7.92/1.87
% 7.92/1.87 (m__522)
% 7.92/1.87 aSet0(xC) = 0 & aSet0(xB) = 0 & aSet0(xA) = 0 & $i(xC) & $i(xB) & $i(xA)
% 7.92/1.87
% 7.92/1.87 (function-axioms)
% 8.10/1.87 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.10/1.87 [v3: $i] : (v1 = v0 | ~ (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) =
% 8.10/1.87 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.10/1.87 $i] : ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~
% 8.10/1.87 (aElementOf0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.10/1.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) |
% 8.10/1.87 ~ (isCountable0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.10/1.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isFinite0(v2) = v1) | ~
% 8.10/1.87 (isFinite0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.10/1.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~
% 8.10/1.87 (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 8.10/1.87 : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0))
% 8.10/1.87
% 8.10/1.87 Further assumptions not needed in the proof:
% 8.10/1.87 --------------------------------------------
% 8.10/1.87 mCntRel, mCountNFin, mCountNFin_01, mDefEmp, mEOfElem, mElmSort, mEmpFin,
% 8.10/1.87 mFinRel, mSetSort, mSubASymm, mSubFSet, mSubRefl
% 8.10/1.87
% 8.10/1.87 Those formulas are unsatisfiable:
% 8.10/1.87 ---------------------------------
% 8.10/1.87
% 8.10/1.87 Begin of proof
% 8.10/1.88 |
% 8.10/1.88 | ALPHA: (m__522) implies:
% 8.10/1.88 | (1) aSet0(xB) = 0
% 8.10/1.88 | (2) aSet0(xC) = 0
% 8.10/1.88 |
% 8.10/1.88 | ALPHA: (m__) implies:
% 8.10/1.88 | (3) $i(xA)
% 8.10/1.88 | (4) $i(xB)
% 8.10/1.88 | (5) $i(xC)
% 8.10/1.88 | (6) ? [v0: int] : ( ~ (v0 = 0) & aSubsetOf0(xB, xC) = 0 & aSubsetOf0(xA,
% 8.10/1.88 | xC) = v0 & aSubsetOf0(xA, xB) = 0 & ! [v1: $i] : ! [v2: int] :
% 8.10/1.88 | (v2 = 0 | ~ (aElementOf0(v1, xC) = v2) | ~ $i(v1) | ? [v3: int] :
% 8.10/1.88 | ( ~ (v3 = 0) & aElementOf0(v1, xB) = v3)) & ! [v1: $i] : ! [v2:
% 8.10/1.88 | int] : (v2 = 0 | ~ (aElementOf0(v1, xB) = v2) | ~ $i(v1) | ?
% 8.10/1.88 | [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, xA) = v3)) & ? [v1: $i]
% 8.10/1.88 | : ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v1, xC) = v2 &
% 8.10/1.88 | aElementOf0(v1, xA) = 0 & $i(v1)))
% 8.10/1.88 |
% 8.10/1.88 | ALPHA: (function-axioms) implies:
% 8.10/1.88 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.10/1.88 | (v1 = v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0))
% 8.10/1.89 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.10/1.89 | ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~
% 8.10/1.89 | (aElementOf0(v3, v2) = v0))
% 8.10/1.89 |
% 8.10/1.89 | DELTA: instantiating (6) with fresh symbol all_11_0 gives:
% 8.10/1.89 | (9) ~ (all_11_0 = 0) & aSubsetOf0(xB, xC) = 0 & aSubsetOf0(xA, xC) =
% 8.10/1.89 | all_11_0 & aSubsetOf0(xA, xB) = 0 & ! [v0: $i] : ! [v1: int] : (v1 =
% 8.10/1.89 | 0 | ~ (aElementOf0(v0, xC) = v1) | ~ $i(v0) | ? [v2: int] : ( ~
% 8.10/1.89 | (v2 = 0) & aElementOf0(v0, xB) = v2)) & ! [v0: $i] : ! [v1: int]
% 8.10/1.89 | : (v1 = 0 | ~ (aElementOf0(v0, xB) = v1) | ~ $i(v0) | ? [v2: int] :
% 8.10/1.89 | ( ~ (v2 = 0) & aElementOf0(v0, xA) = v2)) & ? [v0: $i] : ? [v1:
% 8.10/1.89 | int] : ( ~ (v1 = 0) & aElementOf0(v0, xC) = v1 & aElementOf0(v0, xA)
% 8.10/1.89 | = 0 & $i(v0))
% 8.10/1.89 |
% 8.10/1.89 | ALPHA: (9) implies:
% 8.10/1.89 | (10) ~ (all_11_0 = 0)
% 8.10/1.89 | (11) aSubsetOf0(xA, xB) = 0
% 8.10/1.89 | (12) aSubsetOf0(xA, xC) = all_11_0
% 8.10/1.89 | (13) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, xC) = v1) |
% 8.10/1.89 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, xB) = v2))
% 8.10/1.89 | (14) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0, xC) = v1 &
% 8.10/1.89 | aElementOf0(v0, xA) = 0 & $i(v0))
% 8.10/1.89 |
% 8.10/1.89 | DELTA: instantiating (14) with fresh symbols all_14_0, all_14_1 gives:
% 8.10/1.89 | (15) ~ (all_14_0 = 0) & aElementOf0(all_14_1, xC) = all_14_0 &
% 8.10/1.89 | aElementOf0(all_14_1, xA) = 0 & $i(all_14_1)
% 8.10/1.89 |
% 8.10/1.89 | ALPHA: (15) implies:
% 8.10/1.89 | (16) ~ (all_14_0 = 0)
% 8.10/1.89 | (17) $i(all_14_1)
% 8.10/1.89 | (18) aElementOf0(all_14_1, xA) = 0
% 8.10/1.89 | (19) aElementOf0(all_14_1, xC) = all_14_0
% 8.10/1.89 |
% 8.10/1.89 | GROUND_INST: instantiating (13) with all_14_1, all_14_0, simplifying with
% 8.10/1.89 | (17), (19) gives:
% 8.10/1.89 | (20) all_14_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_14_1, xB)
% 8.10/1.90 | = v0)
% 8.10/1.90 |
% 8.10/1.90 | GROUND_INST: instantiating (mDefSub) with xB, simplifying with (1), (4) gives:
% 8.10/1.90 | (21) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xB) = v1) |
% 8.10/1.90 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 8.10/1.90 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xB) = v3 & $i(v2)) | ?
% 8.10/1.90 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~
% 8.10/1.90 | (aSubsetOf0(v0, xB) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i]
% 8.10/1.90 | : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xB) = v2) | ~
% 8.10/1.90 | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, v0) =
% 8.10/1.90 | v3))))
% 8.10/1.90 |
% 8.10/1.90 | ALPHA: (21) implies:
% 8.10/1.90 | (22) ! [v0: $i] : ( ~ (aSubsetOf0(v0, xB) = 0) | ~ $i(v0) | (aSet0(v0) =
% 8.10/1.90 | 0 & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xB)
% 8.10/1.90 | = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 8.10/1.90 | aElementOf0(v1, v0) = v3))))
% 8.10/1.90 |
% 8.10/1.90 | GROUND_INST: instantiating (mDefSub) with xC, simplifying with (2), (5) gives:
% 8.10/1.90 | (23) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xC) = v1) |
% 8.10/1.90 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 8.10/1.90 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xC) = v3 & $i(v2)) | ?
% 8.10/1.90 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~
% 8.10/1.90 | (aSubsetOf0(v0, xC) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i]
% 8.10/1.90 | : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xC) = v2) | ~
% 8.10/1.90 | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, v0) =
% 8.10/1.90 | v3))))
% 8.10/1.90 |
% 8.10/1.90 | ALPHA: (23) implies:
% 8.10/1.90 | (24) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xC) = v1) |
% 8.10/1.90 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 8.10/1.90 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xC) = v3 & $i(v2)) | ?
% 8.10/1.90 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2))
% 8.10/1.90 |
% 8.10/1.90 | GROUND_INST: instantiating (24) with xA, all_11_0, simplifying with (3), (12)
% 8.10/1.90 | gives:
% 8.10/1.90 | (25) all_11_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 8.10/1.90 | aElementOf0(v0, xC) = v1 & aElementOf0(v0, xA) = 0 & $i(v0)) | ?
% 8.10/1.90 | [v0: int] : ( ~ (v0 = 0) & aSet0(xA) = v0)
% 8.10/1.90 |
% 8.10/1.90 | GROUND_INST: instantiating (22) with xA, simplifying with (3), (11) gives:
% 8.10/1.91 | (26) aSet0(xA) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 8.10/1.91 | (aElementOf0(v0, xB) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0)
% 8.10/1.91 | & aElementOf0(v0, xA) = v2))
% 8.10/1.91 |
% 8.10/1.91 | ALPHA: (26) implies:
% 8.10/1.91 | (27) aSet0(xA) = 0
% 8.10/1.91 | (28) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, xB) = v1) |
% 8.10/1.91 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, xA) = v2))
% 8.10/1.91 |
% 8.10/1.91 | BETA: splitting (20) gives:
% 8.10/1.91 |
% 8.10/1.91 | Case 1:
% 8.10/1.91 | |
% 8.10/1.91 | | (29) all_14_0 = 0
% 8.10/1.91 | |
% 8.10/1.91 | | REDUCE: (16), (29) imply:
% 8.10/1.91 | | (30) $false
% 8.10/1.91 | |
% 8.10/1.91 | | CLOSE: (30) is inconsistent.
% 8.10/1.91 | |
% 8.10/1.91 | Case 2:
% 8.10/1.91 | |
% 8.10/1.91 | | (31) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_14_1, xB) = v0)
% 8.10/1.91 | |
% 8.10/1.91 | | DELTA: instantiating (31) with fresh symbol all_35_0 gives:
% 8.10/1.91 | | (32) ~ (all_35_0 = 0) & aElementOf0(all_14_1, xB) = all_35_0
% 8.10/1.91 | |
% 8.10/1.91 | | ALPHA: (32) implies:
% 8.10/1.91 | | (33) ~ (all_35_0 = 0)
% 8.10/1.91 | | (34) aElementOf0(all_14_1, xB) = all_35_0
% 8.10/1.91 | |
% 8.10/1.91 | | BETA: splitting (25) gives:
% 8.10/1.91 | |
% 8.10/1.91 | | Case 1:
% 8.10/1.91 | | |
% 8.10/1.91 | | | (35) all_11_0 = 0
% 8.10/1.91 | | |
% 8.10/1.91 | | | REDUCE: (10), (35) imply:
% 8.10/1.91 | | | (36) $false
% 8.10/1.91 | | |
% 8.10/1.91 | | | CLOSE: (36) is inconsistent.
% 8.10/1.91 | | |
% 8.10/1.91 | | Case 2:
% 8.10/1.91 | | |
% 8.10/1.91 | | | (37) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0, xC) =
% 8.10/1.91 | | | v1 & aElementOf0(v0, xA) = 0 & $i(v0)) | ? [v0: int] : ( ~ (v0
% 8.10/1.91 | | | = 0) & aSet0(xA) = v0)
% 8.10/1.91 | | |
% 8.10/1.91 | | | BETA: splitting (37) gives:
% 8.10/1.91 | | |
% 8.10/1.91 | | | Case 1:
% 8.10/1.91 | | | |
% 8.10/1.91 | | | |
% 8.10/1.91 | | | | GROUND_INST: instantiating (28) with all_14_1, all_35_0, simplifying
% 8.10/1.91 | | | | with (17), (34) gives:
% 8.10/1.91 | | | | (38) all_35_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 8.10/1.91 | | | | aElementOf0(all_14_1, xA) = v0)
% 8.10/1.91 | | | |
% 8.10/1.91 | | | | BETA: splitting (38) gives:
% 8.10/1.91 | | | |
% 8.10/1.91 | | | | Case 1:
% 8.10/1.91 | | | | |
% 8.10/1.91 | | | | | (39) all_35_0 = 0
% 8.10/1.91 | | | | |
% 8.10/1.91 | | | | | REDUCE: (33), (39) imply:
% 8.10/1.91 | | | | | (40) $false
% 8.10/1.91 | | | | |
% 8.10/1.91 | | | | | CLOSE: (40) is inconsistent.
% 8.10/1.91 | | | | |
% 8.10/1.91 | | | | Case 2:
% 8.10/1.91 | | | | |
% 8.10/1.91 | | | | | (41) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_14_1, xA) = v0)
% 8.10/1.91 | | | | |
% 8.10/1.91 | | | | | DELTA: instantiating (41) with fresh symbol all_58_0 gives:
% 8.10/1.91 | | | | | (42) ~ (all_58_0 = 0) & aElementOf0(all_14_1, xA) = all_58_0
% 8.10/1.91 | | | | |
% 8.10/1.91 | | | | | ALPHA: (42) implies:
% 8.10/1.91 | | | | | (43) ~ (all_58_0 = 0)
% 8.10/1.92 | | | | | (44) aElementOf0(all_14_1, xA) = all_58_0
% 8.10/1.92 | | | | |
% 8.10/1.92 | | | | | GROUND_INST: instantiating (8) with 0, all_58_0, xA, all_14_1,
% 8.10/1.92 | | | | | simplifying with (18), (44) gives:
% 8.10/1.92 | | | | | (45) all_58_0 = 0
% 8.10/1.92 | | | | |
% 8.10/1.92 | | | | | REDUCE: (43), (45) imply:
% 8.10/1.92 | | | | | (46) $false
% 8.10/1.92 | | | | |
% 8.10/1.92 | | | | | CLOSE: (46) is inconsistent.
% 8.10/1.92 | | | | |
% 8.10/1.92 | | | | End of split
% 8.10/1.92 | | | |
% 8.10/1.92 | | | Case 2:
% 8.10/1.92 | | | |
% 8.10/1.92 | | | | (47) ? [v0: int] : ( ~ (v0 = 0) & aSet0(xA) = v0)
% 8.10/1.92 | | | |
% 8.10/1.92 | | | | DELTA: instantiating (47) with fresh symbol all_43_0 gives:
% 8.10/1.92 | | | | (48) ~ (all_43_0 = 0) & aSet0(xA) = all_43_0
% 8.10/1.92 | | | |
% 8.10/1.92 | | | | ALPHA: (48) implies:
% 8.10/1.92 | | | | (49) ~ (all_43_0 = 0)
% 8.10/1.92 | | | | (50) aSet0(xA) = all_43_0
% 8.10/1.92 | | | |
% 8.10/1.92 | | | | GROUND_INST: instantiating (7) with 0, all_43_0, xA, simplifying with
% 8.10/1.92 | | | | (27), (50) gives:
% 8.10/1.92 | | | | (51) all_43_0 = 0
% 8.10/1.92 | | | |
% 8.10/1.92 | | | | REDUCE: (49), (51) imply:
% 8.10/1.92 | | | | (52) $false
% 8.10/1.92 | | | |
% 8.10/1.92 | | | | CLOSE: (52) is inconsistent.
% 8.10/1.92 | | | |
% 8.10/1.92 | | | End of split
% 8.10/1.92 | | |
% 8.10/1.92 | | End of split
% 8.10/1.92 | |
% 8.10/1.92 | End of split
% 8.10/1.92 |
% 8.10/1.92 End of proof
% 8.10/1.92 % SZS output end Proof for theBenchmark
% 8.10/1.92
% 8.10/1.92 1272ms
%------------------------------------------------------------------------------