TSTP Solution File: RNG114+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG114+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 : n005.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 13:57:57 EDT 2023
% Result : Theorem 39.04s 5.87s
% Output : Proof 102.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : RNG114+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 02:20:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 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 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 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 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
% 3.41/1.14 Prover 4: Preprocessing ...
% 3.41/1.14 Prover 1: Preprocessing ...
% 3.51/1.18 Prover 6: Preprocessing ...
% 3.51/1.18 Prover 2: Preprocessing ...
% 3.51/1.19 Prover 0: Preprocessing ...
% 3.51/1.19 Prover 5: Preprocessing ...
% 3.51/1.19 Prover 3: Preprocessing ...
% 8.67/1.93 Prover 3: Constructing countermodel ...
% 8.67/1.93 Prover 1: Constructing countermodel ...
% 8.67/1.95 Prover 6: Proving ...
% 9.33/2.01 Prover 5: Proving ...
% 9.81/2.09 Prover 2: Proving ...
% 10.51/2.14 Prover 4: Constructing countermodel ...
% 11.15/2.24 Prover 0: Proving ...
% 39.04/5.85 Prover 3: proved (5215ms)
% 39.04/5.87
% 39.04/5.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 39.04/5.87
% 39.04/5.87 Prover 2: stopped
% 39.04/5.87 Prover 5: stopped
% 39.04/5.88 Prover 6: stopped
% 39.04/5.89 Prover 0: stopped
% 39.04/5.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 39.04/5.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 39.04/5.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 39.89/5.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 39.89/5.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 40.17/5.95 Prover 7: Preprocessing ...
% 40.17/5.97 Prover 8: Preprocessing ...
% 40.51/5.99 Prover 11: Preprocessing ...
% 40.51/6.03 Prover 10: Preprocessing ...
% 41.12/6.07 Prover 13: Preprocessing ...
% 41.12/6.07 Prover 7: Constructing countermodel ...
% 41.12/6.08 Prover 8: Warning: ignoring some quantifiers
% 41.12/6.09 Prover 8: Constructing countermodel ...
% 41.57/6.14 Prover 10: Constructing countermodel ...
% 42.49/6.28 Prover 13: Warning: ignoring some quantifiers
% 42.85/6.29 Prover 13: Constructing countermodel ...
% 43.32/6.35 Prover 11: Constructing countermodel ...
% 77.25/10.74 Prover 13: stopped
% 77.25/10.75 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 77.71/10.79 Prover 16: Preprocessing ...
% 78.50/10.89 Prover 16: Warning: ignoring some quantifiers
% 78.50/10.90 Prover 16: Constructing countermodel ...
% 102.51/13.94 Prover 10: Found proof (size 47)
% 102.51/13.94 Prover 10: proved (8023ms)
% 102.51/13.94 Prover 7: stopped
% 102.51/13.94 Prover 16: stopped
% 102.51/13.95 Prover 1: stopped
% 102.51/13.95 Prover 4: stopped
% 102.51/13.95 Prover 8: stopped
% 102.51/13.95 Prover 11: stopped
% 102.51/13.95
% 102.51/13.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 102.51/13.95
% 102.51/13.96 % SZS output start Proof for theBenchmark
% 102.51/13.96 Assumptions after simplification:
% 102.51/13.96 ---------------------------------
% 102.51/13.96
% 102.51/13.96 (mDefPrIdeal)
% 102.51/13.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (slsdtgt0(v0) =
% 102.51/13.99 v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 102.51/13.99 $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) | aElementOf0(v2, v1)) & !
% 102.51/13.99 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slsdtgt0(v0) = v1) | ~
% 102.51/13.99 $i(v2) | ~ $i(v0) | ~ aSet0(v2) | ~ aElement0(v0) | ? [v3: $i] : ? [v4:
% 102.51/13.99 $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ aElementOf0(v3, v2) | ! [v6:
% 102.51/13.99 $i] : ( ~ (sdtasdt0(v0, v6) = v3) | ~ $i(v6) | ~ aElement0(v6))) &
% 102.51/13.99 (aElementOf0(v3, v2) | (v5 = v3 & sdtasdt0(v0, v4) = v3 &
% 102.51/13.99 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 102.51/13.99 (slsdtgt0(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2,
% 102.51/13.99 v1) | ~ aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 102.51/13.99 aElement0(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~
% 102.51/13.99 $i(v1) | ~ $i(v0) | ~ aElement0(v0) | aSet0(v1))
% 102.51/13.99
% 102.51/13.99 (mDefSSum)
% 102.51/14.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 102.51/14.00 $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | ~ $i(v5) |
% 102.51/14.00 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 102.51/14.00 aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ aSet0(v0) |
% 102.51/14.00 aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 102.51/14.00 : (v3 = v2 | ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 102.51/14.00 ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4: $i] : ? [v5: $i] : ?
% 102.51/14.00 [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v5) & $i(v4) & ( ~ aElementOf0(v4, v3)
% 102.51/14.00 | ! [v8: $i] : ! [v9: $i] : ( ~ (sdtpldt0(v8, v9) = v4) | ~ $i(v9) |
% 102.51/14.00 ~ $i(v8) | ~ aElementOf0(v9, v1) | ~ aElementOf0(v8, v0))) &
% 102.51/14.00 (aElementOf0(v4, v3) | (v7 = v4 & sdtpldt0(v5, v6) = v4 & aElementOf0(v6,
% 102.51/14.00 v1) & aElementOf0(v5, v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 102.51/14.00 $i] : ! [v3: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 102.51/14.00 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) |
% 102.51/14.00 ? [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) &
% 102.51/14.00 aElementOf0(v5, v1) & aElementOf0(v4, v0))) & ! [v0: $i] : ! [v1: $i] :
% 102.51/14.00 ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 102.51/14.00 ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2))
% 102.51/14.00
% 102.51/14.00 (m__)
% 102.51/14.00 $i(xu) & $i(xb) & $i(xa) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 102.51/14.00 $i] : ( ~ (sdtasdt0(xb, v1) = v3) | ~ (sdtasdt0(xa, v0) = v2) | ~
% 102.51/14.00 (sdtpldt0(v2, v3) = xu) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~
% 102.51/14.00 aElement0(v0))
% 102.51/14.00
% 102.51/14.00 (m__2091)
% 102.51/14.00 $i(xb) & $i(xa) & aElement0(xb) & aElement0(xa)
% 102.51/14.00
% 102.51/14.00 (m__2174)
% 102.51/14.01 $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 &
% 102.51/14.01 slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = xI & $i(v1) & $i(v0) & aIdeal0(xI))
% 102.51/14.01
% 102.51/14.01 (m__2203)
% 102.51/14.01 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 &
% 102.51/14.01 slsdtgt0(xa) = v0 & $i(v1) & $i(v0) & aElementOf0(xb, v1) & aElementOf0(xa,
% 102.51/14.01 v0) & aElementOf0(sz00, v1) & aElementOf0(sz00, v0))
% 102.51/14.01
% 102.51/14.01 (m__2228)
% 102.51/14.01 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 102.51/14.01 $i] : ( ~ (v3 = sz00) & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sdtpldt1(v0,
% 102.51/14.01 v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v2))
% 102.51/14.01
% 102.51/14.01 (m__2273)
% 102.51/14.01 $i(xu) & $i(xI) & $i(sz00) & ? [v0: $i] : ( ~ (xu = sz00) & sbrdtbr0(xu) = v0
% 102.51/14.01 & $i(v0) & aElementOf0(xu, xI) & ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~
% 102.51/14.01 (sbrdtbr0(v1) = v2) | ~ $i(v1) | ~ iLess0(v2, v0) | ~ aElementOf0(v1,
% 102.51/14.01 xI)))
% 102.51/14.01
% 102.51/14.01 (function-axioms)
% 102.51/14.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 102.51/14.01 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 102.51/14.01 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) |
% 102.51/14.01 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 102.51/14.01 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 102.51/14.01 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 102.51/14.01 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 102.51/14.01 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) | ~ (slsdtgt0(v2)
% 102.51/14.01 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 102.51/14.01 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 102.51/14.01 ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0))
% 102.51/14.01
% 102.51/14.01 Further assumptions not needed in the proof:
% 102.51/14.01 --------------------------------------------
% 102.51/14.01 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder,
% 102.51/14.01 mDefDiv, mDefDvs, mDefGCD, mDefIdeal, mDefMod, mDefRel, mDefSInt, mDivision,
% 102.51/14.01 mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso, mMulComm, mMulMnOne,
% 102.51/14.01 mMulUnit, mMulZero, mNatLess, mNatSort, mPrIdeal, mSetEq, mSetSort, mSortsB,
% 102.51/14.01 mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__2110, m__2129, m__2383
% 102.51/14.01
% 102.51/14.01 Those formulas are unsatisfiable:
% 102.51/14.01 ---------------------------------
% 102.51/14.01
% 102.51/14.01 Begin of proof
% 102.51/14.01 |
% 102.51/14.02 | ALPHA: (mDefSSum) implies:
% 102.51/14.02 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 102.51/14.02 | (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 102.51/14.02 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | ?
% 102.51/14.02 | [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) &
% 102.51/14.02 | aElementOf0(v5, v1) & aElementOf0(v4, v0)))
% 102.51/14.02 |
% 102.51/14.02 | ALPHA: (mDefPrIdeal) implies:
% 102.51/14.02 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~ $i(v1) | ~
% 102.51/14.02 | $i(v0) | ~ aElement0(v0) | aSet0(v1))
% 102.51/14.02 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slsdtgt0(v0) = v1) | ~
% 102.51/14.02 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 102.51/14.02 | aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 102.51/14.02 | aElement0(v3)))
% 102.51/14.02 |
% 102.51/14.02 | ALPHA: (m__2091) implies:
% 102.51/14.02 | (4) aElement0(xa)
% 102.51/14.02 | (5) aElement0(xb)
% 102.51/14.02 |
% 102.51/14.02 | ALPHA: (m__2174) implies:
% 102.51/14.02 | (6) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 102.51/14.02 | sdtpldt1(v0, v1) = xI & $i(v1) & $i(v0) & aIdeal0(xI))
% 102.51/14.02 |
% 102.51/14.02 | ALPHA: (m__2203) implies:
% 102.51/14.02 | (7) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 102.51/14.02 | $i(v1) & $i(v0) & aElementOf0(xb, v1) & aElementOf0(xa, v0) &
% 102.51/14.02 | aElementOf0(sz00, v1) & aElementOf0(sz00, v0))
% 102.51/14.02 |
% 102.51/14.02 | ALPHA: (m__2228) implies:
% 102.51/14.02 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = sz00)
% 102.51/14.02 | & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = v2 &
% 102.51/14.02 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v2))
% 102.51/14.02 |
% 102.51/14.02 | ALPHA: (m__2273) implies:
% 102.51/14.02 | (9) ? [v0: $i] : ( ~ (xu = sz00) & sbrdtbr0(xu) = v0 & $i(v0) &
% 102.51/14.02 | aElementOf0(xu, xI) & ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~
% 102.51/14.02 | (sbrdtbr0(v1) = v2) | ~ $i(v1) | ~ iLess0(v2, v0) | ~
% 102.51/14.02 | aElementOf0(v1, xI)))
% 102.51/14.02 |
% 102.51/14.02 | ALPHA: (m__) implies:
% 102.51/14.02 | (10) $i(xa)
% 102.51/14.02 | (11) $i(xb)
% 102.51/14.02 | (12) $i(xu)
% 102.51/14.03 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 102.51/14.03 | (sdtasdt0(xb, v1) = v3) | ~ (sdtasdt0(xa, v0) = v2) | ~
% 102.51/14.03 | (sdtpldt0(v2, v3) = xu) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) |
% 102.51/14.03 | ~ aElement0(v0))
% 102.51/14.03 |
% 102.51/14.03 | ALPHA: (function-axioms) implies:
% 102.51/14.03 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2)
% 102.51/14.03 | = v1) | ~ (slsdtgt0(v2) = v0))
% 102.51/14.03 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 102.51/14.03 | (sdtpldt1(v3, v2) = v1) | ~ (sdtpldt1(v3, v2) = v0))
% 102.51/14.03 |
% 102.51/14.03 | DELTA: instantiating (6) with fresh symbols all_35_0, all_35_1 gives:
% 102.51/14.03 | (16) slsdtgt0(xb) = all_35_0 & slsdtgt0(xa) = all_35_1 & sdtpldt1(all_35_1,
% 102.51/14.03 | all_35_0) = xI & $i(all_35_0) & $i(all_35_1) & aIdeal0(xI)
% 102.51/14.03 |
% 102.51/14.03 | ALPHA: (16) implies:
% 102.51/14.03 | (17) sdtpldt1(all_35_1, all_35_0) = xI
% 102.51/14.03 | (18) slsdtgt0(xa) = all_35_1
% 102.51/14.03 | (19) slsdtgt0(xb) = all_35_0
% 102.51/14.03 |
% 102.51/14.03 | DELTA: instantiating (7) with fresh symbols all_37_0, all_37_1 gives:
% 102.51/14.03 | (20) slsdtgt0(xb) = all_37_0 & slsdtgt0(xa) = all_37_1 & $i(all_37_0) &
% 102.51/14.03 | $i(all_37_1) & aElementOf0(xb, all_37_0) & aElementOf0(xa, all_37_1) &
% 102.51/14.03 | aElementOf0(sz00, all_37_0) & aElementOf0(sz00, all_37_1)
% 102.51/14.03 |
% 102.51/14.03 | ALPHA: (20) implies:
% 102.51/14.03 | (21) $i(all_37_1)
% 102.51/14.03 | (22) $i(all_37_0)
% 102.51/14.03 | (23) slsdtgt0(xa) = all_37_1
% 102.51/14.03 | (24) slsdtgt0(xb) = all_37_0
% 102.51/14.03 |
% 102.51/14.03 | DELTA: instantiating (9) with fresh symbol all_42_0 gives:
% 102.51/14.03 | (25) ~ (xu = sz00) & sbrdtbr0(xu) = all_42_0 & $i(all_42_0) &
% 102.51/14.03 | aElementOf0(xu, xI) & ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~
% 102.51/14.03 | (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ iLess0(v1, all_42_0) | ~
% 102.51/14.03 | aElementOf0(v0, xI))
% 102.51/14.03 |
% 102.51/14.03 | ALPHA: (25) implies:
% 102.51/14.03 | (26) aElementOf0(xu, xI)
% 102.51/14.03 |
% 102.51/14.03 | DELTA: instantiating (8) with fresh symbols all_45_0, all_45_1, all_45_2,
% 102.51/14.03 | all_45_3 gives:
% 102.51/14.03 | (27) ~ (all_45_0 = sz00) & slsdtgt0(xb) = all_45_2 & slsdtgt0(xa) =
% 102.51/14.03 | all_45_3 & sdtpldt1(all_45_3, all_45_2) = all_45_1 & $i(all_45_0) &
% 102.51/14.03 | $i(all_45_1) & $i(all_45_2) & $i(all_45_3) & aElementOf0(all_45_0,
% 102.51/14.03 | all_45_1)
% 102.51/14.03 |
% 102.51/14.03 | ALPHA: (27) implies:
% 102.51/14.03 | (28) $i(all_45_1)
% 102.51/14.03 | (29) sdtpldt1(all_45_3, all_45_2) = all_45_1
% 102.51/14.03 | (30) slsdtgt0(xa) = all_45_3
% 102.51/14.03 | (31) slsdtgt0(xb) = all_45_2
% 102.51/14.03 |
% 102.51/14.03 | GROUND_INST: instantiating (14) with all_37_1, all_45_3, xa, simplifying with
% 102.51/14.03 | (23), (30) gives:
% 102.51/14.03 | (32) all_45_3 = all_37_1
% 102.51/14.03 |
% 102.51/14.03 | GROUND_INST: instantiating (14) with all_35_1, all_45_3, xa, simplifying with
% 102.51/14.03 | (18), (30) gives:
% 102.51/14.03 | (33) all_45_3 = all_35_1
% 102.51/14.03 |
% 102.51/14.03 | GROUND_INST: instantiating (14) with all_37_0, all_45_2, xb, simplifying with
% 102.51/14.03 | (24), (31) gives:
% 102.51/14.03 | (34) all_45_2 = all_37_0
% 102.51/14.03 |
% 102.51/14.03 | GROUND_INST: instantiating (14) with all_35_0, all_45_2, xb, simplifying with
% 102.51/14.03 | (19), (31) gives:
% 102.51/14.04 | (35) all_45_2 = all_35_0
% 102.51/14.04 |
% 102.51/14.04 | COMBINE_EQS: (34), (35) imply:
% 102.51/14.04 | (36) all_37_0 = all_35_0
% 102.51/14.04 |
% 102.51/14.04 | SIMP: (36) implies:
% 102.51/14.04 | (37) all_37_0 = all_35_0
% 102.51/14.04 |
% 102.51/14.04 | COMBINE_EQS: (32), (33) imply:
% 102.51/14.04 | (38) all_37_1 = all_35_1
% 102.51/14.04 |
% 102.51/14.04 | SIMP: (38) implies:
% 102.51/14.04 | (39) all_37_1 = all_35_1
% 102.51/14.04 |
% 102.51/14.04 | REDUCE: (29), (33), (35) imply:
% 102.51/14.04 | (40) sdtpldt1(all_35_1, all_35_0) = all_45_1
% 102.51/14.04 |
% 102.51/14.04 | REDUCE: (22), (37) imply:
% 102.51/14.04 | (41) $i(all_35_0)
% 102.51/14.04 |
% 102.51/14.04 | REDUCE: (21), (39) imply:
% 102.51/14.04 | (42) $i(all_35_1)
% 102.51/14.04 |
% 102.51/14.04 | GROUND_INST: instantiating (15) with xI, all_45_1, all_35_0, all_35_1,
% 102.51/14.04 | simplifying with (17), (40) gives:
% 102.51/14.04 | (43) all_45_1 = xI
% 102.51/14.04 |
% 102.51/14.04 | REDUCE: (28), (43) imply:
% 102.51/14.04 | (44) $i(xI)
% 102.51/14.04 |
% 102.51/14.04 | GROUND_INST: instantiating (2) with xa, all_35_1, simplifying with (4), (10),
% 102.51/14.04 | (18), (42) gives:
% 102.51/14.04 | (45) aSet0(all_35_1)
% 102.51/14.04 |
% 102.51/14.04 | GROUND_INST: instantiating (2) with xb, all_35_0, simplifying with (5), (11),
% 102.51/14.04 | (19), (41) gives:
% 102.51/14.04 | (46) aSet0(all_35_0)
% 102.51/14.04 |
% 102.51/14.04 | GROUND_INST: instantiating (1) with all_35_1, all_35_0, xI, xu, simplifying
% 102.51/14.04 | with (12), (17), (26), (41), (42), (44), (45), (46) gives:
% 102.51/14.04 | (47) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, v1) = xu & $i(v1) & $i(v0) &
% 102.51/14.04 | aElementOf0(v1, all_35_0) & aElementOf0(v0, all_35_1))
% 102.51/14.04 |
% 102.51/14.04 | DELTA: instantiating (47) with fresh symbols all_83_0, all_83_1 gives:
% 102.51/14.04 | (48) sdtpldt0(all_83_1, all_83_0) = xu & $i(all_83_0) & $i(all_83_1) &
% 102.51/14.04 | aElementOf0(all_83_0, all_35_0) & aElementOf0(all_83_1, all_35_1)
% 102.51/14.04 |
% 102.51/14.04 | ALPHA: (48) implies:
% 102.51/14.04 | (49) aElementOf0(all_83_1, all_35_1)
% 102.51/14.04 | (50) aElementOf0(all_83_0, all_35_0)
% 102.51/14.04 | (51) $i(all_83_1)
% 102.51/14.04 | (52) $i(all_83_0)
% 102.51/14.04 | (53) sdtpldt0(all_83_1, all_83_0) = xu
% 102.51/14.04 |
% 102.51/14.04 | GROUND_INST: instantiating (3) with xa, all_35_1, all_83_1, simplifying with
% 102.51/14.04 | (4), (10), (18), (42), (49), (51) gives:
% 102.51/14.04 | (54) ? [v0: $i] : (sdtasdt0(xa, v0) = all_83_1 & $i(v0) & aElement0(v0))
% 102.51/14.04 |
% 102.51/14.04 | GROUND_INST: instantiating (3) with xb, all_35_0, all_83_0, simplifying with
% 102.51/14.04 | (5), (11), (19), (41), (50), (52) gives:
% 102.51/14.04 | (55) ? [v0: $i] : (sdtasdt0(xb, v0) = all_83_0 & $i(v0) & aElement0(v0))
% 102.51/14.04 |
% 102.51/14.04 | DELTA: instantiating (55) with fresh symbol all_263_0 gives:
% 102.51/14.04 | (56) sdtasdt0(xb, all_263_0) = all_83_0 & $i(all_263_0) &
% 102.51/14.04 | aElement0(all_263_0)
% 102.51/14.04 |
% 102.51/14.04 | ALPHA: (56) implies:
% 102.51/14.04 | (57) aElement0(all_263_0)
% 102.51/14.04 | (58) $i(all_263_0)
% 102.51/14.04 | (59) sdtasdt0(xb, all_263_0) = all_83_0
% 102.51/14.04 |
% 102.51/14.04 | DELTA: instantiating (54) with fresh symbol all_267_0 gives:
% 102.51/14.05 | (60) sdtasdt0(xa, all_267_0) = all_83_1 & $i(all_267_0) &
% 102.51/14.05 | aElement0(all_267_0)
% 102.51/14.05 |
% 102.51/14.05 | ALPHA: (60) implies:
% 102.51/14.05 | (61) aElement0(all_267_0)
% 102.51/14.05 | (62) $i(all_267_0)
% 102.51/14.05 | (63) sdtasdt0(xa, all_267_0) = all_83_1
% 102.51/14.05 |
% 102.51/14.05 | GROUND_INST: instantiating (13) with all_267_0, all_263_0, all_83_1, all_83_0,
% 102.51/14.05 | simplifying with (53), (57), (58), (59), (61), (62), (63) gives:
% 102.51/14.05 | (64) $false
% 102.51/14.05 |
% 102.51/14.05 | CLOSE: (64) is inconsistent.
% 102.51/14.05 |
% 102.51/14.05 End of proof
% 102.51/14.05 % SZS output end Proof for theBenchmark
% 102.51/14.05
% 102.51/14.05 13429ms
%------------------------------------------------------------------------------