TSTP Solution File: LAT388+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LAT388+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 06:25:19 EDT 2023
% Result : Theorem 11.92s 2.36s
% Output : Proof 14.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT388+4 : 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 : n014.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 : Thu Aug 24 06:25:19 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.58/1.19 Prover 4: Preprocessing ...
% 3.58/1.19 Prover 1: Preprocessing ...
% 3.58/1.24 Prover 6: Preprocessing ...
% 3.58/1.24 Prover 3: Preprocessing ...
% 3.58/1.24 Prover 5: Preprocessing ...
% 3.58/1.24 Prover 0: Preprocessing ...
% 3.58/1.24 Prover 2: Preprocessing ...
% 8.88/2.01 Prover 5: Proving ...
% 8.88/2.02 Prover 2: Proving ...
% 8.88/2.05 Prover 1: Constructing countermodel ...
% 9.59/2.07 Prover 3: Constructing countermodel ...
% 9.59/2.08 Prover 6: Proving ...
% 11.92/2.35 Prover 3: proved (1716ms)
% 11.92/2.35
% 11.92/2.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.92/2.36
% 11.92/2.38 Prover 2: stopped
% 11.92/2.38 Prover 6: stopped
% 11.92/2.40 Prover 5: stopped
% 11.92/2.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.92/2.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.92/2.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.92/2.42 Prover 1: Found proof (size 12)
% 11.92/2.42 Prover 1: proved (1790ms)
% 11.92/2.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.54/2.47 Prover 4: Constructing countermodel ...
% 12.91/2.50 Prover 4: stopped
% 12.91/2.51 Prover 0: Proving ...
% 12.91/2.51 Prover 0: stopped
% 12.91/2.52 Prover 7: Preprocessing ...
% 12.91/2.54 Prover 10: Preprocessing ...
% 12.91/2.54 Prover 8: Preprocessing ...
% 13.40/2.55 Prover 11: Preprocessing ...
% 13.51/2.58 Prover 7: stopped
% 13.51/2.58 Prover 10: stopped
% 13.51/2.65 Prover 11: stopped
% 13.51/2.70 Prover 8: Warning: ignoring some quantifiers
% 13.51/2.71 Prover 8: Constructing countermodel ...
% 13.51/2.72 Prover 8: stopped
% 13.51/2.72
% 13.51/2.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.51/2.72
% 13.51/2.72 % SZS output start Proof for theBenchmark
% 13.51/2.72 Assumptions after simplification:
% 13.51/2.72 ---------------------------------
% 13.51/2.72
% 13.51/2.72 (m__)
% 14.26/2.75 $i(xT) & $i(xS) & ! [v0: $i] : ! [v1: any] : ( ~ (aUpperBoundOfIn0(v0, xT,
% 14.26/2.75 xS) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 14.26/2.75 aUpperBoundOfIn0(v2, xT, xS) = 0 & sdtlseqdt0(v0, v2) = v3 &
% 14.26/2.75 aElementOf0(v2, xS) = 0 & $i(v2) & ! [v4: $i] : ( ~ (aElementOf0(v4, xT)
% 14.26/2.75 = 0) | ~ $i(v4) | sdtlseqdt0(v4, v2) = 0)) | ? [v2: any] :
% 14.26/2.75 (aElementOf0(v0, xS) = v2 & ( ~ (v2 = 0) | ( ~ (v1 = 0) & ? [v3: $i] : ?
% 14.26/2.75 [v4: int] : ( ~ (v4 = 0) & sdtlseqdt0(v3, v0) = v4 & aElementOf0(v3,
% 14.26/2.75 xT) = 0 & $i(v3)))))) & ! [v0: $i] : ( ~ (aSupremumOfIn0(v0, xT,
% 14.26/2.75 xS) = 0) | ~ $i(v0))
% 14.26/2.75
% 14.26/2.75 (m__1299)
% 14.26/2.75 $i(xp) & $i(xP) & $i(xT) & $i(xf) & $i(xU) & ? [v0: $i] : (sdtlpdtrp0(xf, xp)
% 14.26/2.75 = v0 & aUpperBoundOfIn0(v0, xT, xU) = 0 & aLowerBoundOfIn0(v0, xP, xU) = 0 &
% 14.26/2.75 $i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (sdtlseqdt0(v1, v0) = v2)
% 14.26/2.75 | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, xT) = v3)) &
% 14.26/2.75 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~
% 14.26/2.75 $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, xP) = v3)))
% 14.26/2.75
% 14.26/2.75 (m__1330)
% 14.26/2.75 $i(xp) & $i(xT) & $i(xS) & $i(xf) & ? [v0: $i] : (aFixedPointOf0(xp, xf) = 0
% 14.26/2.75 & sdtlpdtrp0(xf, xp) = xp & szDzozmdt0(xf) = v0 & aSupremumOfIn0(xp, xT, xS)
% 14.26/2.75 = 0 & aUpperBoundOfIn0(xp, xT, xS) = 0 & aElementOf0(xp, v0) = 0 & $i(v0) &
% 14.26/2.75 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (sdtlseqdt0(v1, xp) = v2) | ~
% 14.26/2.75 $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, xT) = v3)) & !
% 14.26/2.75 [v1: $i] : ! [v2: any] : ( ~ (aUpperBoundOfIn0(v1, xT, xS) = v2) | ~
% 14.26/2.75 $i(v1) | ? [v3: any] : ? [v4: any] : (sdtlseqdt0(xp, v1) = v4 &
% 14.26/2.75 aElementOf0(v1, xS) = v3 & (v4 = 0 | ( ~ (v2 = 0) & ( ~ (v3 = 0) | ?
% 14.26/2.75 [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & sdtlseqdt0(v5, v1) = v6 &
% 14.26/2.75 aElementOf0(v5, xT) = 0 & $i(v5))))))))
% 14.26/2.75
% 14.26/2.75 (function-axioms)
% 14.59/2.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 14.59/2.76 | ~ (cS1241(v4, v3, v2) = v1) | ~ (cS1241(v4, v3, v2) = v0)) & ! [v0:
% 14.59/2.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.59/2.76 : ! [v4: $i] : (v1 = v0 | ~ (aSupremumOfIn0(v4, v3, v2) = v1) | ~
% 14.59/2.76 (aSupremumOfIn0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.59/2.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 14.59/2.76 (aInfimumOfIn0(v4, v3, v2) = v1) | ~ (aInfimumOfIn0(v4, v3, v2) = v0)) & !
% 14.59/2.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 14.59/2.76 $i] : ! [v4: $i] : (v1 = v0 | ~ (aUpperBoundOfIn0(v4, v3, v2) = v1) | ~
% 14.59/2.76 (aUpperBoundOfIn0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.59/2.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 14.59/2.76 (aLowerBoundOfIn0(v4, v3, v2) = v1) | ~ (aLowerBoundOfIn0(v4, v3, v2) =
% 14.59/2.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.59/2.76 $i] : ! [v3: $i] : (v1 = v0 | ~ (aFixedPointOf0(v3, v2) = v1) | ~
% 14.59/2.76 (aFixedPointOf0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.59/2.76 ! [v3: $i] : (v1 = v0 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2)
% 14.59/2.76 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.59/2.76 $i] : ! [v3: $i] : (v1 = v0 | ~ (isOn0(v3, v2) = v1) | ~ (isOn0(v3, v2) =
% 14.59/2.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.59/2.76 $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~
% 14.59/2.76 (sdtlseqdt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.59/2.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.59/2.76 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0:
% 14.59/2.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.59/2.76 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) &
% 14.59/2.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cS1142(v2) = v1) | ~
% 14.59/2.76 (cS1142(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 14.59/2.76 : ! [v2: $i] : (v1 = v0 | ~ (isMonotone0(v2) = v1) | ~ (isMonotone0(v2) =
% 14.59/2.76 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.59/2.76 (szRzazndt0(v2) = v1) | ~ (szRzazndt0(v2) = v0)) & ! [v0:
% 14.59/2.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 14.59/2.76 ~ (aFunction0(v2) = v1) | ~ (aFunction0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 14.59/2.76 $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2)
% 14.59/2.76 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.59/2.76 $i] : (v1 = v0 | ~ (aCompleteLattice0(v2) = v1) | ~ (aCompleteLattice0(v2)
% 14.59/2.76 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.59/2.76 $i] : (v1 = v0 | ~ (isEmpty0(v2) = v1) | ~ (isEmpty0(v2) = v0)) & ! [v0:
% 14.59/2.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 14.59/2.76 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 14.59/2.76 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) |
% 14.59/2.76 ~ (aElement0(v2) = v0))
% 14.59/2.76
% 14.59/2.76 Further assumptions not needed in the proof:
% 14.59/2.76 --------------------------------------------
% 14.59/2.76 mARefl, mASymm, mConMap, mDefCLat, mDefDom, mDefEmpty, mDefFix, mDefInf, mDefLB,
% 14.59/2.76 mDefMonot, mDefSub, mDefSup, mDefUB, mDomSort, mEOfElem, mElmSort, mImgSort,
% 14.59/2.76 mInfUn, mLessRel, mRanSort, mSetSort, mSupUn, mTrans, m__1123, m__1144, m__1173,
% 14.59/2.76 m__1244, m__1261
% 14.59/2.76
% 14.59/2.76 Those formulas are unsatisfiable:
% 14.59/2.76 ---------------------------------
% 14.59/2.76
% 14.59/2.76 Begin of proof
% 14.59/2.76 |
% 14.59/2.76 | ALPHA: (m__1299) implies:
% 14.59/2.77 | (1) ? [v0: $i] : (sdtlpdtrp0(xf, xp) = v0 & aUpperBoundOfIn0(v0, xT, xU) =
% 14.59/2.77 | 0 & aLowerBoundOfIn0(v0, xP, xU) = 0 & $i(v0) & ! [v1: $i] : ! [v2:
% 14.59/2.77 | int] : (v2 = 0 | ~ (sdtlseqdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3:
% 14.59/2.77 | int] : ( ~ (v3 = 0) & aElementOf0(v1, xT) = v3)) & ! [v1: $i] :
% 14.59/2.77 | ! [v2: int] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ $i(v1) | ?
% 14.59/2.77 | [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, xP) = v3)))
% 14.59/2.77 |
% 14.59/2.77 | ALPHA: (m__1330) implies:
% 14.59/2.77 | (2) ? [v0: $i] : (aFixedPointOf0(xp, xf) = 0 & sdtlpdtrp0(xf, xp) = xp &
% 14.59/2.77 | szDzozmdt0(xf) = v0 & aSupremumOfIn0(xp, xT, xS) = 0 &
% 14.59/2.77 | aUpperBoundOfIn0(xp, xT, xS) = 0 & aElementOf0(xp, v0) = 0 & $i(v0) &
% 14.59/2.77 | ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (sdtlseqdt0(v1, xp) = v2) |
% 14.59/2.77 | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, xT) =
% 14.59/2.77 | v3)) & ! [v1: $i] : ! [v2: any] : ( ~ (aUpperBoundOfIn0(v1, xT,
% 14.59/2.77 | xS) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] :
% 14.59/2.77 | (sdtlseqdt0(xp, v1) = v4 & aElementOf0(v1, xS) = v3 & (v4 = 0 | ( ~
% 14.59/2.77 | (v2 = 0) & ( ~ (v3 = 0) | ? [v5: $i] : ? [v6: int] : ( ~
% 14.59/2.77 | (v6 = 0) & sdtlseqdt0(v5, v1) = v6 & aElementOf0(v5, xT)
% 14.59/2.77 | = 0 & $i(v5))))))))
% 14.59/2.77 |
% 14.59/2.77 | ALPHA: (m__) implies:
% 14.59/2.77 | (3) ! [v0: $i] : ( ~ (aSupremumOfIn0(v0, xT, xS) = 0) | ~ $i(v0))
% 14.59/2.77 |
% 14.59/2.77 | ALPHA: (function-axioms) implies:
% 14.59/2.77 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.59/2.77 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 14.59/2.77 |
% 14.59/2.77 | DELTA: instantiating (1) with fresh symbol all_28_0 gives:
% 14.59/2.77 | (5) sdtlpdtrp0(xf, xp) = all_28_0 & aUpperBoundOfIn0(all_28_0, xT, xU) = 0
% 14.59/2.77 | & aLowerBoundOfIn0(all_28_0, xP, xU) = 0 & $i(all_28_0) & ! [v0: $i] :
% 14.59/2.77 | ! [v1: int] : (v1 = 0 | ~ (sdtlseqdt0(v0, all_28_0) = v1) | ~ $i(v0)
% 14.59/2.77 | | ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, xT) = v2)) & ! [v0:
% 14.59/2.77 | $i] : ! [v1: int] : (v1 = 0 | ~ (sdtlseqdt0(all_28_0, v0) = v1) |
% 14.59/2.77 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, xP) = v2))
% 14.59/2.77 |
% 14.59/2.77 | ALPHA: (5) implies:
% 14.59/2.77 | (6) $i(all_28_0)
% 14.59/2.77 | (7) sdtlpdtrp0(xf, xp) = all_28_0
% 14.59/2.77 |
% 14.59/2.77 | DELTA: instantiating (2) with fresh symbol all_31_0 gives:
% 14.59/2.77 | (8) aFixedPointOf0(xp, xf) = 0 & sdtlpdtrp0(xf, xp) = xp & szDzozmdt0(xf) =
% 14.59/2.77 | all_31_0 & aSupremumOfIn0(xp, xT, xS) = 0 & aUpperBoundOfIn0(xp, xT,
% 14.59/2.77 | xS) = 0 & aElementOf0(xp, all_31_0) = 0 & $i(all_31_0) & ! [v0: $i]
% 14.59/2.77 | : ! [v1: int] : (v1 = 0 | ~ (sdtlseqdt0(v0, xp) = v1) | ~ $i(v0) |
% 14.59/2.77 | ? [v2: int] : ( ~ (v2 = 0) & aElementOf0(v0, xT) = v2)) & ! [v0: $i]
% 14.59/2.77 | : ! [v1: any] : ( ~ (aUpperBoundOfIn0(v0, xT, xS) = v1) | ~ $i(v0) |
% 14.59/2.77 | ? [v2: any] : ? [v3: any] : (sdtlseqdt0(xp, v0) = v3 &
% 14.59/2.77 | aElementOf0(v0, xS) = v2 & (v3 = 0 | ( ~ (v1 = 0) & ( ~ (v2 = 0) |
% 14.59/2.77 | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & sdtlseqdt0(v4, v0)
% 14.59/2.77 | = v5 & aElementOf0(v4, xT) = 0 & $i(v4)))))))
% 14.59/2.77 |
% 14.59/2.77 | ALPHA: (8) implies:
% 14.59/2.78 | (9) aSupremumOfIn0(xp, xT, xS) = 0
% 14.59/2.78 | (10) sdtlpdtrp0(xf, xp) = xp
% 14.59/2.78 |
% 14.59/2.78 | GROUND_INST: instantiating (4) with xp, all_28_0, xp, xf, simplifying with
% 14.59/2.78 | (7), (10) gives:
% 14.59/2.78 | (11) all_28_0 = xp
% 14.59/2.78 |
% 14.59/2.78 | REDUCE: (6), (11) imply:
% 14.59/2.78 | (12) $i(xp)
% 14.59/2.78 |
% 14.59/2.78 | GROUND_INST: instantiating (3) with xp, simplifying with (9), (12) gives:
% 14.59/2.78 | (13) $false
% 14.59/2.78 |
% 14.59/2.78 | CLOSE: (13) is inconsistent.
% 14.59/2.78 |
% 14.59/2.78 End of proof
% 14.59/2.78 % SZS output end Proof for theBenchmark
% 14.59/2.78
% 14.59/2.78 2167ms
%------------------------------------------------------------------------------