TSTP Solution File: NUM533+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM533+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n026.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 6.33s 1.73s
% Output : Proof 8.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM533+1 : 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 : n026.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 13:15:32 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.10/1.07 Prover 1: Preprocessing ...
% 2.42/1.07 Prover 4: Preprocessing ...
% 2.42/1.11 Prover 0: Preprocessing ...
% 2.42/1.11 Prover 2: Preprocessing ...
% 2.42/1.11 Prover 6: Preprocessing ...
% 2.42/1.11 Prover 5: Preprocessing ...
% 2.42/1.11 Prover 3: Preprocessing ...
% 4.14/1.33 Prover 2: Constructing countermodel ...
% 4.14/1.34 Prover 5: Constructing countermodel ...
% 4.41/1.41 Prover 1: Constructing countermodel ...
% 4.41/1.44 Prover 6: Proving ...
% 4.41/1.46 Prover 3: Constructing countermodel ...
% 4.41/1.54 Prover 4: Constructing countermodel ...
% 5.94/1.66 Prover 0: Proving ...
% 6.33/1.73 Prover 3: proved (1090ms)
% 6.33/1.73
% 6.33/1.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.33/1.73
% 6.33/1.73 Prover 2: stopped
% 6.33/1.73 Prover 0: stopped
% 6.33/1.73 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.33/1.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.33/1.74 Prover 6: stopped
% 6.33/1.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.33/1.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.33/1.74 Prover 5: stopped
% 6.33/1.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.92/1.78 Prover 10: Preprocessing ...
% 6.92/1.78 Prover 8: Preprocessing ...
% 6.92/1.80 Prover 11: Preprocessing ...
% 6.92/1.80 Prover 13: Preprocessing ...
% 6.92/1.80 Prover 7: Preprocessing ...
% 7.26/1.83 Prover 10: Constructing countermodel ...
% 7.50/1.86 Prover 7: Constructing countermodel ...
% 7.50/1.90 Prover 13: Constructing countermodel ...
% 7.50/1.92 Prover 1: Found proof (size 42)
% 7.50/1.92 Prover 1: proved (1290ms)
% 7.50/1.92 Prover 7: stopped
% 7.50/1.92 Prover 13: stopped
% 7.50/1.93 Prover 4: stopped
% 7.50/1.93 Prover 10: stopped
% 7.50/1.93 Prover 8: Warning: ignoring some quantifiers
% 8.10/1.94 Prover 8: Constructing countermodel ...
% 8.10/1.95 Prover 8: stopped
% 8.35/2.00 Prover 11: Constructing countermodel ...
% 8.35/2.01 Prover 11: stopped
% 8.35/2.01
% 8.35/2.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.35/2.01
% 8.35/2.01 % SZS output start Proof for theBenchmark
% 8.35/2.02 Assumptions after simplification:
% 8.35/2.02 ---------------------------------
% 8.35/2.02
% 8.35/2.02 (mDefSub)
% 8.65/2.05 ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: int] :
% 8.65/2.05 (v2 = 0 | ~ (aSubsetOf0(v1, v0) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4:
% 8.65/2.05 int] : ( ~ (v4 = 0) & aElementOf0(v3, v1) = 0 & aElementOf0(v3, v0) =
% 8.65/2.05 v4 & $i(v3)) | ? [v3: int] : ( ~ (v3 = 0) & aSet0(v1) = v3)) & !
% 8.65/2.05 [v1: $i] : ( ~ (aSubsetOf0(v1, v0) = 0) | ~ $i(v1) | (aSet0(v1) = 0 & !
% 8.65/2.05 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, v0) = v3) | ~
% 8.65/2.05 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v2, v1) =
% 8.65/2.05 v4))))))
% 8.65/2.05
% 8.65/2.06 (m__)
% 8.65/2.06 $i(xC) & $i(xB) & $i(xA) & ? [v0: int] : ( ~ (v0 = 0) & aSubsetOf0(xB, xC) =
% 8.65/2.06 0 & aSubsetOf0(xA, xC) = v0 & aSubsetOf0(xA, xB) = 0)
% 8.65/2.06
% 8.65/2.06 (m__522)
% 8.72/2.06 aSet0(xC) = 0 & aSet0(xB) = 0 & aSet0(xA) = 0 & $i(xC) & $i(xB) & $i(xA)
% 8.72/2.06
% 8.72/2.06 (function-axioms)
% 8.72/2.06 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.72/2.06 [v3: $i] : (v1 = v0 | ~ (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) =
% 8.72/2.06 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.72/2.06 $i] : ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~
% 8.72/2.06 (aElementOf0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.72/2.06 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) |
% 8.72/2.06 ~ (isCountable0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.72/2.06 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isFinite0(v2) = v1) | ~
% 8.72/2.06 (isFinite0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.72/2.06 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~
% 8.72/2.06 (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 8.72/2.06 : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0))
% 8.72/2.06
% 8.72/2.06 Further assumptions not needed in the proof:
% 8.72/2.06 --------------------------------------------
% 8.72/2.06 mCntRel, mCountNFin, mCountNFin_01, mDefEmp, mEOfElem, mElmSort, mEmpFin,
% 8.72/2.06 mFinRel, mSetSort, mSubASymm, mSubFSet, mSubRefl
% 8.72/2.06
% 8.72/2.06 Those formulas are unsatisfiable:
% 8.72/2.06 ---------------------------------
% 8.72/2.06
% 8.72/2.06 Begin of proof
% 8.72/2.07 |
% 8.72/2.07 | ALPHA: (m__522) implies:
% 8.72/2.07 | (1) aSet0(xB) = 0
% 8.72/2.07 | (2) aSet0(xC) = 0
% 8.72/2.07 |
% 8.72/2.07 | ALPHA: (m__) implies:
% 8.72/2.07 | (3) $i(xA)
% 8.72/2.07 | (4) $i(xB)
% 8.72/2.07 | (5) $i(xC)
% 8.72/2.07 | (6) ? [v0: int] : ( ~ (v0 = 0) & aSubsetOf0(xB, xC) = 0 & aSubsetOf0(xA,
% 8.72/2.07 | xC) = v0 & aSubsetOf0(xA, xB) = 0)
% 8.72/2.07 |
% 8.72/2.07 | ALPHA: (function-axioms) implies:
% 8.72/2.07 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.72/2.07 | (v1 = v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0))
% 8.72/2.07 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.72/2.07 | ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~
% 8.72/2.07 | (aElementOf0(v3, v2) = v0))
% 8.72/2.07 |
% 8.72/2.07 | DELTA: instantiating (6) with fresh symbol all_11_0 gives:
% 8.72/2.07 | (9) ~ (all_11_0 = 0) & aSubsetOf0(xB, xC) = 0 & aSubsetOf0(xA, xC) =
% 8.72/2.07 | all_11_0 & aSubsetOf0(xA, xB) = 0
% 8.72/2.07 |
% 8.72/2.07 | ALPHA: (9) implies:
% 8.72/2.07 | (10) ~ (all_11_0 = 0)
% 8.72/2.07 | (11) aSubsetOf0(xA, xB) = 0
% 8.72/2.07 | (12) aSubsetOf0(xA, xC) = all_11_0
% 8.72/2.07 | (13) aSubsetOf0(xB, xC) = 0
% 8.72/2.08 |
% 8.72/2.08 | GROUND_INST: instantiating (mDefSub) with xB, simplifying with (1), (4) gives:
% 8.72/2.08 | (14) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xB) = v1) |
% 8.72/2.08 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 8.72/2.08 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xB) = v3 & $i(v2)) | ?
% 8.72/2.08 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~
% 8.72/2.08 | (aSubsetOf0(v0, xB) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i]
% 8.72/2.08 | : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xB) = v2) | ~
% 8.72/2.08 | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, v0) =
% 8.72/2.08 | v3))))
% 8.72/2.08 |
% 8.72/2.08 | ALPHA: (14) implies:
% 8.72/2.08 | (15) ! [v0: $i] : ( ~ (aSubsetOf0(v0, xB) = 0) | ~ $i(v0) | (aSet0(v0) =
% 8.72/2.08 | 0 & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xB)
% 8.72/2.08 | = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 8.72/2.08 | aElementOf0(v1, v0) = v3))))
% 8.72/2.08 |
% 8.72/2.08 | GROUND_INST: instantiating (mDefSub) with xC, simplifying with (2), (5) gives:
% 8.72/2.08 | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xC) = v1) |
% 8.72/2.08 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 8.72/2.08 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xC) = v3 & $i(v2)) | ?
% 8.72/2.08 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~
% 8.72/2.08 | (aSubsetOf0(v0, xC) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i]
% 8.72/2.08 | : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xC) = v2) | ~
% 8.72/2.08 | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, v0) =
% 8.72/2.08 | v3))))
% 8.72/2.08 |
% 8.72/2.08 | ALPHA: (16) implies:
% 8.72/2.09 | (17) ! [v0: $i] : ( ~ (aSubsetOf0(v0, xC) = 0) | ~ $i(v0) | (aSet0(v0) =
% 8.72/2.09 | 0 & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xC)
% 8.72/2.09 | = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 8.72/2.09 | aElementOf0(v1, v0) = v3))))
% 8.72/2.09 | (18) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xC) = v1) |
% 8.72/2.09 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 8.72/2.09 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xC) = v3 & $i(v2)) | ?
% 8.72/2.09 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2))
% 8.72/2.09 |
% 8.72/2.09 | GROUND_INST: instantiating (18) with xA, all_11_0, simplifying with (3), (12)
% 8.72/2.09 | gives:
% 8.72/2.09 | (19) all_11_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 8.72/2.09 | aElementOf0(v0, xC) = v1 & aElementOf0(v0, xA) = 0 & $i(v0)) | ?
% 8.72/2.09 | [v0: int] : ( ~ (v0 = 0) & aSet0(xA) = v0)
% 8.72/2.09 |
% 8.72/2.09 | GROUND_INST: instantiating (17) with xB, simplifying with (4), (13) gives:
% 8.72/2.09 | (20) aSet0(xB) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 8.72/2.09 | (aElementOf0(v0, xC) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0)
% 8.72/2.09 | & aElementOf0(v0, xB) = v2))
% 8.72/2.09 |
% 8.72/2.09 | ALPHA: (20) implies:
% 8.72/2.09 | (21) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, xC) = v1) |
% 8.72/2.09 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, xB) = v2))
% 8.72/2.09 |
% 8.72/2.09 | GROUND_INST: instantiating (15) with xA, simplifying with (3), (11) gives:
% 8.72/2.09 | (22) aSet0(xA) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 8.72/2.09 | (aElementOf0(v0, xB) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0)
% 8.72/2.09 | & aElementOf0(v0, xA) = v2))
% 8.72/2.09 |
% 8.72/2.09 | ALPHA: (22) implies:
% 8.72/2.09 | (23) aSet0(xA) = 0
% 8.72/2.09 | (24) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, xB) = v1) |
% 8.72/2.09 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, xA) = v2))
% 8.72/2.09 |
% 8.72/2.09 | BETA: splitting (19) gives:
% 8.72/2.09 |
% 8.72/2.09 | Case 1:
% 8.72/2.09 | |
% 8.72/2.09 | | (25) all_11_0 = 0
% 8.72/2.09 | |
% 8.72/2.09 | | REDUCE: (10), (25) imply:
% 8.72/2.09 | | (26) $false
% 8.72/2.09 | |
% 8.72/2.09 | | CLOSE: (26) is inconsistent.
% 8.72/2.09 | |
% 8.72/2.09 | Case 2:
% 8.72/2.09 | |
% 8.72/2.10 | | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0, xC) = v1
% 8.72/2.10 | | & aElementOf0(v0, xA) = 0 & $i(v0)) | ? [v0: int] : ( ~ (v0 = 0)
% 8.72/2.10 | | & aSet0(xA) = v0)
% 8.72/2.10 | |
% 8.72/2.10 | | BETA: splitting (27) gives:
% 8.72/2.10 | |
% 8.72/2.10 | | Case 1:
% 8.72/2.10 | | |
% 8.72/2.10 | | | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0, xC) =
% 8.72/2.10 | | | v1 & aElementOf0(v0, xA) = 0 & $i(v0))
% 8.72/2.10 | | |
% 8.72/2.10 | | | DELTA: instantiating (28) with fresh symbols all_35_0, all_35_1 gives:
% 8.72/2.10 | | | (29) ~ (all_35_0 = 0) & aElementOf0(all_35_1, xC) = all_35_0 &
% 8.72/2.10 | | | aElementOf0(all_35_1, xA) = 0 & $i(all_35_1)
% 8.72/2.10 | | |
% 8.72/2.10 | | | ALPHA: (29) implies:
% 8.72/2.10 | | | (30) ~ (all_35_0 = 0)
% 8.72/2.10 | | | (31) $i(all_35_1)
% 8.72/2.10 | | | (32) aElementOf0(all_35_1, xA) = 0
% 8.72/2.10 | | | (33) aElementOf0(all_35_1, xC) = all_35_0
% 8.72/2.10 | | |
% 8.72/2.10 | | | GROUND_INST: instantiating (21) with all_35_1, all_35_0, simplifying with
% 8.72/2.10 | | | (31), (33) gives:
% 8.72/2.10 | | | (34) all_35_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_35_1,
% 8.72/2.10 | | | xB) = v0)
% 8.72/2.10 | | |
% 8.72/2.10 | | | BETA: splitting (34) gives:
% 8.72/2.10 | | |
% 8.72/2.10 | | | Case 1:
% 8.72/2.10 | | | |
% 8.72/2.10 | | | | (35) all_35_0 = 0
% 8.72/2.10 | | | |
% 8.72/2.10 | | | | REDUCE: (30), (35) imply:
% 8.72/2.10 | | | | (36) $false
% 8.72/2.10 | | | |
% 8.72/2.10 | | | | CLOSE: (36) is inconsistent.
% 8.72/2.10 | | | |
% 8.72/2.10 | | | Case 2:
% 8.72/2.10 | | | |
% 8.72/2.10 | | | | (37) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_35_1, xB) = v0)
% 8.72/2.10 | | | |
% 8.72/2.10 | | | | DELTA: instantiating (37) with fresh symbol all_48_0 gives:
% 8.72/2.10 | | | | (38) ~ (all_48_0 = 0) & aElementOf0(all_35_1, xB) = all_48_0
% 8.72/2.10 | | | |
% 8.72/2.10 | | | | ALPHA: (38) implies:
% 8.72/2.10 | | | | (39) ~ (all_48_0 = 0)
% 8.72/2.10 | | | | (40) aElementOf0(all_35_1, xB) = all_48_0
% 8.72/2.10 | | | |
% 8.72/2.10 | | | | GROUND_INST: instantiating (24) with all_35_1, all_48_0, simplifying
% 8.72/2.10 | | | | with (31), (40) gives:
% 8.72/2.10 | | | | (41) all_48_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 8.72/2.10 | | | | aElementOf0(all_35_1, xA) = v0)
% 8.72/2.10 | | | |
% 8.72/2.10 | | | | BETA: splitting (41) gives:
% 8.72/2.10 | | | |
% 8.72/2.10 | | | | Case 1:
% 8.72/2.10 | | | | |
% 8.72/2.10 | | | | | (42) all_48_0 = 0
% 8.72/2.10 | | | | |
% 8.72/2.10 | | | | | REDUCE: (39), (42) imply:
% 8.72/2.10 | | | | | (43) $false
% 8.72/2.10 | | | | |
% 8.72/2.10 | | | | | CLOSE: (43) is inconsistent.
% 8.72/2.10 | | | | |
% 8.72/2.10 | | | | Case 2:
% 8.72/2.10 | | | | |
% 8.72/2.10 | | | | | (44) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_35_1, xA) = v0)
% 8.72/2.10 | | | | |
% 8.72/2.10 | | | | | DELTA: instantiating (44) with fresh symbol all_63_0 gives:
% 8.72/2.10 | | | | | (45) ~ (all_63_0 = 0) & aElementOf0(all_35_1, xA) = all_63_0
% 8.72/2.10 | | | | |
% 8.72/2.10 | | | | | ALPHA: (45) implies:
% 8.72/2.10 | | | | | (46) ~ (all_63_0 = 0)
% 8.72/2.10 | | | | | (47) aElementOf0(all_35_1, xA) = all_63_0
% 8.72/2.10 | | | | |
% 8.72/2.11 | | | | | GROUND_INST: instantiating (8) with 0, all_63_0, xA, all_35_1,
% 8.72/2.11 | | | | | simplifying with (32), (47) gives:
% 8.72/2.11 | | | | | (48) all_63_0 = 0
% 8.72/2.11 | | | | |
% 8.72/2.11 | | | | | REDUCE: (46), (48) imply:
% 8.72/2.11 | | | | | (49) $false
% 8.72/2.11 | | | | |
% 8.72/2.11 | | | | | CLOSE: (49) is inconsistent.
% 8.72/2.11 | | | | |
% 8.72/2.11 | | | | End of split
% 8.72/2.11 | | | |
% 8.72/2.11 | | | End of split
% 8.72/2.11 | | |
% 8.72/2.11 | | Case 2:
% 8.72/2.11 | | |
% 8.72/2.11 | | | (50) ? [v0: int] : ( ~ (v0 = 0) & aSet0(xA) = v0)
% 8.72/2.11 | | |
% 8.72/2.11 | | | DELTA: instantiating (50) with fresh symbol all_35_0 gives:
% 8.72/2.11 | | | (51) ~ (all_35_0 = 0) & aSet0(xA) = all_35_0
% 8.72/2.11 | | |
% 8.72/2.11 | | | ALPHA: (51) implies:
% 8.72/2.11 | | | (52) ~ (all_35_0 = 0)
% 8.72/2.11 | | | (53) aSet0(xA) = all_35_0
% 8.72/2.11 | | |
% 8.72/2.11 | | | GROUND_INST: instantiating (7) with 0, all_35_0, xA, simplifying with
% 8.72/2.11 | | | (23), (53) gives:
% 8.72/2.11 | | | (54) all_35_0 = 0
% 8.72/2.11 | | |
% 8.72/2.11 | | | REDUCE: (52), (54) imply:
% 8.72/2.11 | | | (55) $false
% 8.72/2.11 | | |
% 8.72/2.11 | | | CLOSE: (55) is inconsistent.
% 8.72/2.11 | | |
% 8.72/2.11 | | End of split
% 8.72/2.11 | |
% 8.72/2.11 | End of split
% 8.72/2.11 |
% 8.72/2.11 End of proof
% 8.72/2.11 % SZS output end Proof for theBenchmark
% 8.72/2.11
% 8.72/2.11 1493ms
%------------------------------------------------------------------------------