TSTP Solution File: RNG116+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG116+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 : n016.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 13:57:58 EDT 2023
% Result : Theorem 42.55s 6.44s
% Output : Proof 46.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG116+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.34 % Computer : n016.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sun Aug 27 02:44:28 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.57 ________ _____
% 0.19/0.57 ___ __ \_________(_)________________________________
% 0.19/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.57
% 0.19/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.57 (2023-06-19)
% 0.19/0.57
% 0.19/0.57 (c) Philipp Rümmer, 2009-2023
% 0.19/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.57 Amanda Stjerna.
% 0.19/0.57 Free software under BSD-3-Clause.
% 0.19/0.57
% 0.19/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.57
% 0.19/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.58 Running up to 7 provers in parallel.
% 0.19/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.31/1.15 Prover 4: Preprocessing ...
% 3.31/1.15 Prover 1: Preprocessing ...
% 3.31/1.19 Prover 3: Preprocessing ...
% 3.31/1.19 Prover 5: Preprocessing ...
% 3.31/1.19 Prover 0: Preprocessing ...
% 3.31/1.19 Prover 6: Preprocessing ...
% 3.31/1.19 Prover 2: Preprocessing ...
% 9.46/2.04 Prover 6: Proving ...
% 9.46/2.04 Prover 1: Constructing countermodel ...
% 9.46/2.04 Prover 3: Constructing countermodel ...
% 9.46/2.11 Prover 5: Proving ...
% 11.23/2.29 Prover 2: Proving ...
% 11.86/2.38 Prover 4: Constructing countermodel ...
% 12.64/2.49 Prover 0: Proving ...
% 42.55/6.44 Prover 3: proved (5842ms)
% 42.55/6.44
% 42.55/6.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 42.55/6.44
% 42.55/6.44 Prover 0: stopped
% 42.79/6.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 42.79/6.45 Prover 6: stopped
% 42.79/6.45 Prover 5: stopped
% 42.79/6.46 Prover 2: stopped
% 42.79/6.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 42.79/6.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 42.79/6.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 42.79/6.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 43.43/6.54 Prover 7: Preprocessing ...
% 43.43/6.54 Prover 8: Preprocessing ...
% 43.43/6.57 Prover 13: Preprocessing ...
% 43.43/6.58 Prover 11: Preprocessing ...
% 43.85/6.59 Prover 10: Preprocessing ...
% 43.85/6.68 Prover 10: Constructing countermodel ...
% 43.85/6.70 Prover 7: Constructing countermodel ...
% 43.85/6.74 Prover 8: Warning: ignoring some quantifiers
% 43.85/6.75 Prover 8: Constructing countermodel ...
% 43.85/6.77 Prover 13: Warning: ignoring some quantifiers
% 43.85/6.80 Prover 13: Constructing countermodel ...
% 46.07/6.89 Prover 11: Constructing countermodel ...
% 46.56/6.95 Prover 10: Found proof (size 44)
% 46.56/6.95 Prover 10: proved (504ms)
% 46.56/6.95 Prover 7: stopped
% 46.56/6.95 Prover 13: stopped
% 46.56/6.95 Prover 11: stopped
% 46.56/6.95 Prover 1: stopped
% 46.56/6.95 Prover 4: stopped
% 46.56/6.96 Prover 8: stopped
% 46.56/6.96
% 46.56/6.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.56/6.96
% 46.65/6.96 % SZS output start Proof for theBenchmark
% 46.65/6.97 Assumptions after simplification:
% 46.65/6.97 ---------------------------------
% 46.65/6.97
% 46.65/6.97 (mDefPrIdeal)
% 46.65/7.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (slsdtgt0(v0) =
% 46.65/7.00 v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 46.65/7.00 $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) | aElementOf0(v2, v1)) & !
% 46.65/7.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slsdtgt0(v0) = v1) | ~
% 46.65/7.00 $i(v2) | ~ $i(v0) | ~ aSet0(v2) | ~ aElement0(v0) | ? [v3: $i] : ? [v4:
% 46.65/7.00 $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ aElementOf0(v3, v2) | ! [v6:
% 46.65/7.00 $i] : ( ~ (sdtasdt0(v0, v6) = v3) | ~ $i(v6) | ~ aElement0(v6))) &
% 46.65/7.00 (aElementOf0(v3, v2) | (v5 = v3 & sdtasdt0(v0, v4) = v3 &
% 46.65/7.00 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 46.65/7.00 (slsdtgt0(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2,
% 46.65/7.00 v1) | ~ aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 46.65/7.00 aElement0(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~
% 46.65/7.00 $i(v1) | ~ $i(v0) | ~ aElement0(v0) | aSet0(v1))
% 46.65/7.00
% 46.65/7.00 (m__)
% 46.65/7.00 $i(xu) & $i(xb) & $i(xa) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 46.65/7.00 $i] : ( ~ (sdtasdt0(xb, v1) = v3) | ~ (sdtasdt0(xa, v0) = v2) | ~
% 46.65/7.00 (sdtpldt0(v2, v3) = xu) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~
% 46.65/7.00 aElement0(v0))
% 46.65/7.00
% 46.65/7.00 (m__2091)
% 46.65/7.00 $i(xb) & $i(xa) & aElement0(xb) & aElement0(xa)
% 46.65/7.00
% 46.65/7.00 (m__2174)
% 46.65/7.00 $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 &
% 46.65/7.00 slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = xI & $i(v1) & $i(v0) & aIdeal0(xI))
% 46.65/7.00
% 46.65/7.00 (m__2203)
% 46.65/7.00 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 &
% 46.65/7.00 slsdtgt0(xa) = v0 & $i(v1) & $i(v0) & aElementOf0(xb, v1) & aElementOf0(xa,
% 46.65/7.00 v0) & aElementOf0(sz00, v1) & aElementOf0(sz00, v0))
% 46.65/7.00
% 46.65/7.00 (m__2228)
% 46.65/7.01 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 46.65/7.01 $i] : ( ~ (v3 = sz00) & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sdtpldt1(v0,
% 46.65/7.01 v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v2))
% 46.65/7.01
% 46.65/7.01 (m__2456)
% 46.65/7.01 $i(xl) & $i(xk) & $i(xu) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] :
% 46.65/7.01 (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sdtpldt0(xk, xl) = xu & $i(v1) &
% 46.65/7.01 $i(v0) & aElementOf0(xl, v1) & aElementOf0(xk, v0))
% 46.65/7.01
% 46.65/7.01 (function-axioms)
% 46.65/7.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 46.65/7.01 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 46.65/7.01 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) |
% 46.65/7.01 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 46.65/7.01 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 46.65/7.01 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 46.91/7.01 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 46.91/7.01 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) | ~ (slsdtgt0(v2)
% 46.91/7.01 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 46.91/7.01 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 46.91/7.01 ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0))
% 46.91/7.01
% 46.91/7.01 Further assumptions not needed in the proof:
% 46.91/7.01 --------------------------------------------
% 46.91/7.01 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder,
% 46.91/7.01 mDefDiv, mDefDvs, mDefGCD, mDefIdeal, mDefMod, mDefRel, mDefSInt, mDefSSum,
% 46.91/7.01 mDivision, mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso, mMulComm,
% 46.91/7.01 mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mPrIdeal, mSetEq, mSetSort,
% 46.91/7.01 mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__2110, m__2129,
% 46.91/7.01 m__2273, m__2383
% 46.91/7.01
% 46.91/7.01 Those formulas are unsatisfiable:
% 46.91/7.01 ---------------------------------
% 46.91/7.01
% 46.91/7.01 Begin of proof
% 46.91/7.01 |
% 46.91/7.01 | ALPHA: (mDefPrIdeal) implies:
% 46.91/7.02 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slsdtgt0(v0) = v1) | ~
% 46.91/7.02 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 46.91/7.02 | aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 46.91/7.02 | aElement0(v3)))
% 46.91/7.02 |
% 46.91/7.02 | ALPHA: (m__2091) implies:
% 46.91/7.02 | (2) aElement0(xa)
% 46.91/7.02 | (3) aElement0(xb)
% 46.91/7.02 |
% 46.91/7.02 | ALPHA: (m__2174) implies:
% 46.91/7.02 | (4) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 46.91/7.02 | sdtpldt1(v0, v1) = xI & $i(v1) & $i(v0) & aIdeal0(xI))
% 46.91/7.02 |
% 46.91/7.02 | ALPHA: (m__2203) implies:
% 46.91/7.02 | (5) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 46.91/7.02 | $i(v1) & $i(v0) & aElementOf0(xb, v1) & aElementOf0(xa, v0) &
% 46.91/7.02 | aElementOf0(sz00, v1) & aElementOf0(sz00, v0))
% 46.91/7.02 |
% 46.91/7.02 | ALPHA: (m__2228) implies:
% 46.91/7.02 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = sz00)
% 46.91/7.02 | & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = v2 &
% 46.91/7.02 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v2))
% 46.91/7.02 |
% 46.91/7.02 | ALPHA: (m__2456) implies:
% 46.91/7.02 | (7) $i(xk)
% 46.91/7.02 | (8) $i(xl)
% 46.91/7.02 | (9) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 46.91/7.02 | sdtpldt0(xk, xl) = xu & $i(v1) & $i(v0) & aElementOf0(xl, v1) &
% 46.91/7.02 | aElementOf0(xk, v0))
% 46.91/7.02 |
% 46.91/7.02 | ALPHA: (m__) implies:
% 46.91/7.02 | (10) $i(xa)
% 46.91/7.02 | (11) $i(xb)
% 46.91/7.02 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 46.91/7.02 | (sdtasdt0(xb, v1) = v3) | ~ (sdtasdt0(xa, v0) = v2) | ~
% 46.91/7.02 | (sdtpldt0(v2, v3) = xu) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) |
% 46.91/7.02 | ~ aElement0(v0))
% 46.91/7.02 |
% 46.91/7.02 | ALPHA: (function-axioms) implies:
% 46.91/7.02 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2)
% 46.91/7.02 | = v1) | ~ (slsdtgt0(v2) = v0))
% 46.91/7.02 |
% 46.91/7.03 | DELTA: instantiating (4) with fresh symbols all_35_0, all_35_1 gives:
% 46.91/7.03 | (14) slsdtgt0(xb) = all_35_0 & slsdtgt0(xa) = all_35_1 & sdtpldt1(all_35_1,
% 46.91/7.03 | all_35_0) = xI & $i(all_35_0) & $i(all_35_1) & aIdeal0(xI)
% 46.91/7.03 |
% 46.91/7.03 | ALPHA: (14) implies:
% 46.91/7.03 | (15) slsdtgt0(xa) = all_35_1
% 46.91/7.03 | (16) slsdtgt0(xb) = all_35_0
% 46.91/7.03 |
% 46.91/7.03 | DELTA: instantiating (9) with fresh symbols all_37_0, all_37_1 gives:
% 46.91/7.03 | (17) slsdtgt0(xb) = all_37_0 & slsdtgt0(xa) = all_37_1 & sdtpldt0(xk, xl) =
% 46.91/7.03 | xu & $i(all_37_0) & $i(all_37_1) & aElementOf0(xl, all_37_0) &
% 46.91/7.03 | aElementOf0(xk, all_37_1)
% 46.91/7.03 |
% 46.91/7.03 | ALPHA: (17) implies:
% 46.91/7.03 | (18) aElementOf0(xk, all_37_1)
% 46.91/7.03 | (19) aElementOf0(xl, all_37_0)
% 46.91/7.03 | (20) $i(all_37_1)
% 46.91/7.03 | (21) $i(all_37_0)
% 46.91/7.03 | (22) sdtpldt0(xk, xl) = xu
% 46.91/7.03 | (23) slsdtgt0(xa) = all_37_1
% 46.91/7.03 | (24) slsdtgt0(xb) = all_37_0
% 46.91/7.03 |
% 46.91/7.03 | DELTA: instantiating (5) with fresh symbols all_42_0, all_42_1 gives:
% 46.91/7.03 | (25) slsdtgt0(xb) = all_42_0 & slsdtgt0(xa) = all_42_1 & $i(all_42_0) &
% 46.91/7.03 | $i(all_42_1) & aElementOf0(xb, all_42_0) & aElementOf0(xa, all_42_1) &
% 46.91/7.03 | aElementOf0(sz00, all_42_0) & aElementOf0(sz00, all_42_1)
% 46.91/7.03 |
% 46.91/7.03 | ALPHA: (25) implies:
% 46.91/7.03 | (26) slsdtgt0(xa) = all_42_1
% 46.91/7.03 | (27) slsdtgt0(xb) = all_42_0
% 46.91/7.03 |
% 46.91/7.03 | DELTA: instantiating (6) with fresh symbols all_47_0, all_47_1, all_47_2,
% 46.91/7.03 | all_47_3 gives:
% 46.91/7.03 | (28) ~ (all_47_0 = sz00) & slsdtgt0(xb) = all_47_2 & slsdtgt0(xa) =
% 46.91/7.03 | all_47_3 & sdtpldt1(all_47_3, all_47_2) = all_47_1 & $i(all_47_0) &
% 46.91/7.03 | $i(all_47_1) & $i(all_47_2) & $i(all_47_3) & aElementOf0(all_47_0,
% 46.91/7.03 | all_47_1)
% 46.91/7.03 |
% 46.91/7.03 | ALPHA: (28) implies:
% 46.91/7.03 | (29) slsdtgt0(xa) = all_47_3
% 46.91/7.03 | (30) slsdtgt0(xb) = all_47_2
% 46.91/7.03 |
% 46.91/7.03 | GROUND_INST: instantiating (13) with all_37_1, all_42_1, xa, simplifying with
% 46.91/7.03 | (23), (26) gives:
% 46.91/7.03 | (31) all_42_1 = all_37_1
% 46.91/7.03 |
% 46.91/7.03 | GROUND_INST: instantiating (13) with all_42_1, all_47_3, xa, simplifying with
% 46.91/7.03 | (26), (29) gives:
% 46.91/7.03 | (32) all_47_3 = all_42_1
% 46.91/7.03 |
% 46.91/7.03 | GROUND_INST: instantiating (13) with all_35_1, all_47_3, xa, simplifying with
% 46.91/7.03 | (15), (29) gives:
% 46.91/7.03 | (33) all_47_3 = all_35_1
% 46.91/7.03 |
% 46.91/7.03 | GROUND_INST: instantiating (13) with all_37_0, all_42_0, xb, simplifying with
% 46.91/7.03 | (24), (27) gives:
% 46.91/7.03 | (34) all_42_0 = all_37_0
% 46.91/7.03 |
% 46.91/7.03 | GROUND_INST: instantiating (13) with all_42_0, all_47_2, xb, simplifying with
% 46.91/7.03 | (27), (30) gives:
% 46.91/7.03 | (35) all_47_2 = all_42_0
% 46.91/7.03 |
% 46.91/7.03 | GROUND_INST: instantiating (13) with all_35_0, all_47_2, xb, simplifying with
% 46.91/7.03 | (16), (30) gives:
% 46.91/7.03 | (36) all_47_2 = all_35_0
% 46.91/7.03 |
% 46.91/7.03 | COMBINE_EQS: (35), (36) imply:
% 46.91/7.03 | (37) all_42_0 = all_35_0
% 46.91/7.03 |
% 46.91/7.03 | SIMP: (37) implies:
% 46.91/7.03 | (38) all_42_0 = all_35_0
% 46.91/7.03 |
% 46.91/7.03 | COMBINE_EQS: (32), (33) imply:
% 46.91/7.03 | (39) all_42_1 = all_35_1
% 46.91/7.03 |
% 46.91/7.03 | SIMP: (39) implies:
% 46.91/7.03 | (40) all_42_1 = all_35_1
% 46.91/7.03 |
% 46.91/7.03 | COMBINE_EQS: (34), (38) imply:
% 46.91/7.03 | (41) all_37_0 = all_35_0
% 46.91/7.03 |
% 46.91/7.03 | SIMP: (41) implies:
% 46.91/7.04 | (42) all_37_0 = all_35_0
% 46.91/7.04 |
% 46.91/7.04 | COMBINE_EQS: (31), (40) imply:
% 46.91/7.04 | (43) all_37_1 = all_35_1
% 46.91/7.04 |
% 46.91/7.04 | SIMP: (43) implies:
% 46.91/7.04 | (44) all_37_1 = all_35_1
% 46.91/7.04 |
% 46.91/7.04 | REDUCE: (21), (42) imply:
% 46.91/7.04 | (45) $i(all_35_0)
% 46.91/7.04 |
% 46.91/7.04 | REDUCE: (20), (44) imply:
% 46.91/7.04 | (46) $i(all_35_1)
% 46.91/7.04 |
% 46.91/7.04 | REDUCE: (19), (42) imply:
% 46.91/7.04 | (47) aElementOf0(xl, all_35_0)
% 46.91/7.04 |
% 46.91/7.04 | REDUCE: (18), (44) imply:
% 46.91/7.04 | (48) aElementOf0(xk, all_35_1)
% 46.91/7.04 |
% 46.91/7.04 | GROUND_INST: instantiating (1) with xa, all_35_1, xk, simplifying with (2),
% 46.91/7.04 | (7), (10), (15), (46), (48) gives:
% 46.91/7.04 | (49) ? [v0: $i] : (sdtasdt0(xa, v0) = xk & $i(v0) & aElement0(v0))
% 46.91/7.04 |
% 46.91/7.04 | GROUND_INST: instantiating (1) with xb, all_35_0, xl, simplifying with (3),
% 46.91/7.04 | (8), (11), (16), (45), (47) gives:
% 46.91/7.04 | (50) ? [v0: $i] : (sdtasdt0(xb, v0) = xl & $i(v0) & aElement0(v0))
% 46.91/7.04 |
% 46.91/7.04 | DELTA: instantiating (49) with fresh symbol all_67_0 gives:
% 46.91/7.04 | (51) sdtasdt0(xa, all_67_0) = xk & $i(all_67_0) & aElement0(all_67_0)
% 46.91/7.04 |
% 46.91/7.04 | ALPHA: (51) implies:
% 46.91/7.04 | (52) aElement0(all_67_0)
% 46.91/7.04 | (53) $i(all_67_0)
% 46.91/7.04 | (54) sdtasdt0(xa, all_67_0) = xk
% 46.91/7.04 |
% 46.91/7.04 | DELTA: instantiating (50) with fresh symbol all_71_0 gives:
% 46.91/7.04 | (55) sdtasdt0(xb, all_71_0) = xl & $i(all_71_0) & aElement0(all_71_0)
% 46.91/7.04 |
% 46.91/7.04 | ALPHA: (55) implies:
% 46.91/7.04 | (56) aElement0(all_71_0)
% 46.91/7.04 | (57) $i(all_71_0)
% 46.91/7.04 | (58) sdtasdt0(xb, all_71_0) = xl
% 46.91/7.04 |
% 46.91/7.04 | GROUND_INST: instantiating (12) with all_67_0, all_71_0, xk, xl, simplifying
% 46.91/7.04 | with (22), (52), (53), (54), (56), (57), (58) gives:
% 46.91/7.04 | (59) $false
% 46.91/7.04 |
% 46.91/7.04 | CLOSE: (59) is inconsistent.
% 46.91/7.04 |
% 46.91/7.04 End of proof
% 46.91/7.04 % SZS output end Proof for theBenchmark
% 46.91/7.04
% 46.91/7.04 6469ms
%------------------------------------------------------------------------------