TSTP Solution File: RNG104+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG104+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 : 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 13:57:54 EDT 2023
% Result : Theorem 15.63s 2.92s
% Output : Proof 22.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG104+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 02:14:40 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.11/1.12 Prover 1: Preprocessing ...
% 3.11/1.12 Prover 4: Preprocessing ...
% 3.57/1.16 Prover 3: Preprocessing ...
% 3.57/1.16 Prover 6: Preprocessing ...
% 3.57/1.16 Prover 5: Preprocessing ...
% 3.57/1.16 Prover 2: Preprocessing ...
% 3.57/1.17 Prover 0: Preprocessing ...
% 8.90/2.02 Prover 3: Constructing countermodel ...
% 8.90/2.02 Prover 6: Proving ...
% 8.90/2.05 Prover 1: Constructing countermodel ...
% 8.90/2.11 Prover 5: Proving ...
% 11.13/2.30 Prover 2: Proving ...
% 11.62/2.40 Prover 4: Constructing countermodel ...
% 12.25/2.47 Prover 0: Proving ...
% 15.63/2.92 Prover 0: proved (2306ms)
% 15.63/2.92
% 15.63/2.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.63/2.92
% 15.63/2.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.63/2.92 Prover 5: stopped
% 15.63/2.92 Prover 3: stopped
% 16.09/2.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 16.09/2.93 Prover 2: stopped
% 16.09/2.95 Prover 6: stopped
% 16.09/2.95 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 16.09/2.95 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 16.09/2.96 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.30/3.01 Prover 8: Preprocessing ...
% 16.30/3.02 Prover 7: Preprocessing ...
% 16.79/3.03 Prover 10: Preprocessing ...
% 17.07/3.06 Prover 13: Preprocessing ...
% 17.07/3.07 Prover 11: Preprocessing ...
% 18.43/3.24 Prover 7: Constructing countermodel ...
% 18.64/3.26 Prover 10: Constructing countermodel ...
% 19.07/3.33 Prover 8: Warning: ignoring some quantifiers
% 19.07/3.34 Prover 8: Constructing countermodel ...
% 19.07/3.35 Prover 13: Warning: ignoring some quantifiers
% 19.07/3.36 Prover 13: Constructing countermodel ...
% 21.05/3.62 Prover 11: Constructing countermodel ...
% 21.87/3.70 Prover 10: Found proof (size 60)
% 21.87/3.70 Prover 10: proved (768ms)
% 21.87/3.70 Prover 13: stopped
% 21.87/3.70 Prover 1: stopped
% 21.87/3.70 Prover 7: stopped
% 21.87/3.70 Prover 4: stopped
% 21.87/3.70 Prover 11: stopped
% 21.87/3.70 Prover 8: stopped
% 21.87/3.70
% 21.87/3.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.87/3.70
% 21.87/3.72 % SZS output start Proof for theBenchmark
% 21.87/3.72 Assumptions after simplification:
% 21.87/3.72 ---------------------------------
% 21.87/3.72
% 21.87/3.72 (mAMDistr)
% 21.87/3.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 21.87/3.74 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~
% 21.87/3.75 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 21.87/3.75 aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6: $i] : ? [v7:
% 21.87/3.75 $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2,
% 21.87/3.75 v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8,
% 21.87/3.75 v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 21.87/3.75 $i(v5)))
% 21.87/3.75
% 21.87/3.75 (mAddComm)
% 21.87/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 21.87/3.75 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtpldt0(v1, v0)
% 21.87/3.75 = v2 & $i(v2)))
% 21.87/3.75
% 21.87/3.75 (mDefPrIdeal)
% 21.87/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (slsdtgt0(v0) =
% 21.87/3.75 v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 21.87/3.75 $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) | aElementOf0(v2, v1)) & !
% 21.87/3.75 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slsdtgt0(v0) = v1) | ~
% 21.87/3.75 $i(v2) | ~ $i(v0) | ~ aSet0(v2) | ~ aElement0(v0) | ? [v3: $i] : ? [v4:
% 21.87/3.75 $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ aElementOf0(v3, v2) | ! [v6:
% 21.87/3.75 $i] : ( ~ (sdtasdt0(v0, v6) = v3) | ~ $i(v6) | ~ aElement0(v6))) &
% 21.87/3.75 (aElementOf0(v3, v2) | (v5 = v3 & sdtasdt0(v0, v4) = v3 &
% 21.87/3.75 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 21.87/3.75 (slsdtgt0(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2,
% 21.87/3.75 v1) | ~ aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 21.87/3.75 aElement0(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~
% 21.87/3.75 $i(v1) | ~ $i(v0) | ~ aElement0(v0) | aSet0(v1))
% 21.87/3.75
% 21.87/3.75 (mMulAsso)
% 21.87/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 21.87/3.75 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 21.87/3.75 | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ?
% 21.87/3.75 [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4 & $i(v5) &
% 21.87/3.75 $i(v4)))
% 21.87/3.75
% 21.87/3.75 (mMulComm)
% 21.87/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 21.87/3.75 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtasdt0(v1, v0)
% 21.87/3.75 = v2 & $i(v2)))
% 21.87/3.75
% 21.87/3.76 (mSortsB_02)
% 21.87/3.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 21.87/3.76 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2))
% 21.87/3.76
% 21.87/3.76 (m__)
% 21.87/3.76 $i(xu) & $i(xz) & $i(xx) & $i(xc) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 21.87/3.76 ( ~ (v2 = v0) & sdtasdt0(xu, xz) = v1 & sdtasdt0(xz, xx) = v0 & sdtasdt0(xc,
% 21.87/3.76 v1) = v2 & $i(v2) & $i(v1) & $i(v0))
% 21.87/3.76
% 21.87/3.76 (m__1905)
% 21.87/3.76 $i(xc) & aElement0(xc)
% 21.87/3.76
% 21.87/3.76 (m__1933)
% 21.87/3.76 $i(xz) & $i(xy) & $i(xx) & $i(xc) & ? [v0: $i] : (slsdtgt0(xc) = v0 & $i(v0)
% 21.87/3.76 & aElementOf0(xy, v0) & aElementOf0(xx, v0) & aElement0(xz))
% 21.87/3.76
% 21.87/3.76 (m__1956)
% 22.17/3.76 sdtasdt0(xc, xu) = xx & $i(xu) & $i(xx) & $i(xc) & aElement0(xu)
% 22.17/3.76
% 22.17/3.76 (m__1979)
% 22.17/3.76 sdtasdt0(xc, xv) = xy & $i(xv) & $i(xy) & $i(xc) & aElement0(xv)
% 22.17/3.76
% 22.17/3.76 (m__2010)
% 22.17/3.76 $i(xv) & $i(xu) & $i(xy) & $i(xx) & $i(xc) & ? [v0: $i] : ? [v1: $i] :
% 22.17/3.76 (sdtasdt0(xc, v1) = v0 & sdtpldt0(xu, xv) = v1 & sdtpldt0(xx, xy) = v0 &
% 22.17/3.76 $i(v1) & $i(v0))
% 22.17/3.76
% 22.17/3.76 (function-axioms)
% 22.17/3.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.17/3.76 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 22.17/3.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) |
% 22.17/3.76 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 22.17/3.76 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 22.17/3.76 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.17/3.76 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 22.17/3.76 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) | ~ (slsdtgt0(v2)
% 22.17/3.76 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 22.17/3.76 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 22.17/3.76 ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0))
% 22.17/3.76
% 22.17/3.76 Further assumptions not needed in the proof:
% 22.17/3.76 --------------------------------------------
% 22.17/3.76 mAddAsso, mAddInvr, mAddZero, mCancel, mChineseRemainder, mDefDiv, mDefDvs,
% 22.17/3.76 mDefGCD, mDefIdeal, mDefMod, mDefRel, mDefSInt, mDefSSum, mDivision, mEOfElem,
% 22.17/3.76 mElmSort, mEucSort, mIdeInt, mIdeSum, mMulMnOne, mMulUnit, mMulZero, mNatLess,
% 22.17/3.76 mNatSort, mSetEq, mSetSort, mSortsB, mSortsC, mSortsC_01, mSortsU, mUnNeZr
% 22.17/3.76
% 22.17/3.76 Those formulas are unsatisfiable:
% 22.17/3.76 ---------------------------------
% 22.17/3.76
% 22.17/3.76 Begin of proof
% 22.17/3.76 |
% 22.17/3.76 | ALPHA: (mDefPrIdeal) implies:
% 22.17/3.77 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slsdtgt0(v0) = v1) | ~
% 22.17/3.77 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 22.17/3.77 | aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 22.17/3.77 | aElement0(v3)))
% 22.17/3.77 |
% 22.17/3.77 | ALPHA: (m__1905) implies:
% 22.17/3.77 | (2) aElement0(xc)
% 22.17/3.77 |
% 22.17/3.77 | ALPHA: (m__1933) implies:
% 22.17/3.77 | (3) ? [v0: $i] : (slsdtgt0(xc) = v0 & $i(v0) & aElementOf0(xy, v0) &
% 22.17/3.77 | aElementOf0(xx, v0) & aElement0(xz))
% 22.17/3.77 |
% 22.17/3.77 | ALPHA: (m__1956) implies:
% 22.17/3.77 | (4) aElement0(xu)
% 22.17/3.77 | (5) sdtasdt0(xc, xu) = xx
% 22.17/3.77 |
% 22.17/3.77 | ALPHA: (m__1979) implies:
% 22.17/3.77 | (6) aElement0(xv)
% 22.17/3.77 | (7) sdtasdt0(xc, xv) = xy
% 22.17/3.77 |
% 22.17/3.77 | ALPHA: (m__2010) implies:
% 22.17/3.77 | (8) $i(xv)
% 22.17/3.77 | (9) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xc, v1) = v0 & sdtpldt0(xu, xv) =
% 22.17/3.77 | v1 & sdtpldt0(xx, xy) = v0 & $i(v1) & $i(v0))
% 22.17/3.77 |
% 22.17/3.77 | ALPHA: (m__) implies:
% 22.17/3.77 | (10) $i(xc)
% 22.17/3.77 | (11) $i(xz)
% 22.17/3.77 | (12) $i(xu)
% 22.17/3.77 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v0) & sdtasdt0(xu,
% 22.17/3.77 | xz) = v1 & sdtasdt0(xz, xx) = v0 & sdtasdt0(xc, v1) = v2 & $i(v2)
% 22.17/3.77 | & $i(v1) & $i(v0))
% 22.17/3.77 |
% 22.17/3.77 | ALPHA: (function-axioms) implies:
% 22.17/3.77 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.17/3.77 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 22.17/3.77 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.17/3.77 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 22.17/3.77 |
% 22.17/3.77 | DELTA: instantiating (3) with fresh symbol all_33_0 gives:
% 22.17/3.77 | (16) slsdtgt0(xc) = all_33_0 & $i(all_33_0) & aElementOf0(xy, all_33_0) &
% 22.17/3.77 | aElementOf0(xx, all_33_0) & aElement0(xz)
% 22.17/3.77 |
% 22.17/3.77 | ALPHA: (16) implies:
% 22.17/3.77 | (17) aElement0(xz)
% 22.17/3.77 | (18) aElementOf0(xy, all_33_0)
% 22.17/3.77 | (19) $i(all_33_0)
% 22.17/3.77 | (20) slsdtgt0(xc) = all_33_0
% 22.17/3.77 |
% 22.17/3.77 | DELTA: instantiating (9) with fresh symbols all_35_0, all_35_1 gives:
% 22.17/3.77 | (21) sdtasdt0(xc, all_35_0) = all_35_1 & sdtpldt0(xu, xv) = all_35_0 &
% 22.17/3.77 | sdtpldt0(xx, xy) = all_35_1 & $i(all_35_0) & $i(all_35_1)
% 22.17/3.77 |
% 22.17/3.77 | ALPHA: (21) implies:
% 22.17/3.77 | (22) sdtpldt0(xx, xy) = all_35_1
% 22.17/3.77 |
% 22.17/3.77 | DELTA: instantiating (13) with fresh symbols all_37_0, all_37_1, all_37_2
% 22.17/3.77 | gives:
% 22.17/3.77 | (23) ~ (all_37_0 = all_37_2) & sdtasdt0(xu, xz) = all_37_1 & sdtasdt0(xz,
% 22.17/3.77 | xx) = all_37_2 & sdtasdt0(xc, all_37_1) = all_37_0 & $i(all_37_0) &
% 22.17/3.77 | $i(all_37_1) & $i(all_37_2)
% 22.17/3.77 |
% 22.17/3.77 | ALPHA: (23) implies:
% 22.17/3.77 | (24) ~ (all_37_0 = all_37_2)
% 22.17/3.77 | (25) sdtasdt0(xc, all_37_1) = all_37_0
% 22.17/3.77 | (26) sdtasdt0(xz, xx) = all_37_2
% 22.17/3.77 | (27) sdtasdt0(xu, xz) = all_37_1
% 22.17/3.78 |
% 22.17/3.78 | GROUND_INST: instantiating (mSortsB_02) with xc, xu, xx, simplifying with (2),
% 22.17/3.78 | (4), (5), (10), (12) gives:
% 22.17/3.78 | (28) aElement0(xx)
% 22.17/3.78 |
% 22.17/3.78 | GROUND_INST: instantiating (mMulComm) with xc, xu, xx, simplifying with (2),
% 22.17/3.78 | (4), (5), (10), (12) gives:
% 22.17/3.78 | (29) sdtasdt0(xu, xc) = xx & $i(xx)
% 22.17/3.78 |
% 22.17/3.78 | ALPHA: (29) implies:
% 22.17/3.78 | (30) sdtasdt0(xu, xc) = xx
% 22.17/3.78 |
% 22.17/3.78 | GROUND_INST: instantiating (mAMDistr) with xc, xu, xv, xx, xy, all_35_1,
% 22.17/3.78 | simplifying with (2), (4), (5), (6), (7), (8), (10), (12), (22)
% 22.17/3.78 | gives:
% 22.17/3.78 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0,
% 22.17/3.78 | xc) = v1 & sdtasdt0(xv, xc) = v3 & sdtasdt0(xu, xc) = v2 &
% 22.17/3.78 | sdtasdt0(xc, v0) = all_35_1 & sdtpldt0(v2, v3) = v1 & sdtpldt0(xu,
% 22.17/3.78 | xv) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_35_1))
% 22.17/3.78 |
% 22.17/3.78 | GROUND_INST: instantiating (mSortsB_02) with xc, xv, xy, simplifying with (2),
% 22.17/3.78 | (6), (7), (8), (10) gives:
% 22.17/3.78 | (32) aElement0(xy)
% 22.17/3.78 |
% 22.17/3.78 | GROUND_INST: instantiating (mMulComm) with xc, xv, xy, simplifying with (2),
% 22.17/3.78 | (6), (7), (8), (10) gives:
% 22.17/3.78 | (33) sdtasdt0(xv, xc) = xy & $i(xy)
% 22.17/3.78 |
% 22.17/3.78 | ALPHA: (33) implies:
% 22.17/3.78 | (34) $i(xy)
% 22.17/3.78 | (35) sdtasdt0(xv, xc) = xy
% 22.17/3.78 |
% 22.17/3.78 | GROUND_INST: instantiating (mSortsB_02) with xu, xz, all_37_1, simplifying
% 22.17/3.78 | with (4), (11), (12), (17), (27) gives:
% 22.17/3.78 | (36) aElement0(all_37_1)
% 22.17/3.78 |
% 22.17/3.78 | GROUND_INST: instantiating (mMulComm) with xu, xz, all_37_1, simplifying with
% 22.17/3.78 | (4), (11), (12), (17), (27) gives:
% 22.17/3.78 | (37) sdtasdt0(xz, xu) = all_37_1 & $i(all_37_1)
% 22.17/3.78 |
% 22.17/3.78 | ALPHA: (37) implies:
% 22.17/3.78 | (38) $i(all_37_1)
% 22.17/3.78 | (39) sdtasdt0(xz, xu) = all_37_1
% 22.17/3.78 |
% 22.17/3.78 | GROUND_INST: instantiating (1) with xc, all_33_0, xy, simplifying with (2),
% 22.17/3.78 | (10), (18), (19), (20), (34) gives:
% 22.17/3.78 | (40) ? [v0: $i] : (sdtasdt0(xc, v0) = xy & $i(v0) & aElement0(v0))
% 22.17/3.78 |
% 22.17/3.78 | DELTA: instantiating (40) with fresh symbol all_50_0 gives:
% 22.17/3.78 | (41) sdtasdt0(xc, all_50_0) = xy & $i(all_50_0) & aElement0(all_50_0)
% 22.17/3.78 |
% 22.17/3.78 | ALPHA: (41) implies:
% 22.17/3.78 | (42) aElement0(all_50_0)
% 22.17/3.78 | (43) $i(all_50_0)
% 22.17/3.79 | (44) sdtasdt0(xc, all_50_0) = xy
% 22.17/3.79 |
% 22.17/3.79 | DELTA: instantiating (31) with fresh symbols all_52_0, all_52_1, all_52_2,
% 22.17/3.79 | all_52_3 gives:
% 22.17/3.79 | (45) sdtasdt0(all_52_3, xc) = all_52_2 & sdtasdt0(xv, xc) = all_52_0 &
% 22.17/3.79 | sdtasdt0(xu, xc) = all_52_1 & sdtasdt0(xc, all_52_3) = all_35_1 &
% 22.17/3.79 | sdtpldt0(all_52_1, all_52_0) = all_52_2 & sdtpldt0(xu, xv) = all_52_3
% 22.17/3.79 | & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3) &
% 22.17/3.79 | $i(all_35_1)
% 22.17/3.79 |
% 22.17/3.79 | ALPHA: (45) implies:
% 22.17/3.79 | (46) $i(all_52_1)
% 22.17/3.79 | (47) $i(all_52_0)
% 22.17/3.79 | (48) sdtpldt0(all_52_1, all_52_0) = all_52_2
% 22.17/3.79 | (49) sdtasdt0(xu, xc) = all_52_1
% 22.17/3.79 | (50) sdtasdt0(xv, xc) = all_52_0
% 22.17/3.79 |
% 22.17/3.79 | GROUND_INST: instantiating (15) with xx, all_52_1, xc, xu, simplifying with
% 22.17/3.79 | (30), (49) gives:
% 22.17/3.79 | (51) all_52_1 = xx
% 22.17/3.79 |
% 22.17/3.79 | GROUND_INST: instantiating (15) with xy, all_52_0, xc, xv, simplifying with
% 22.17/3.79 | (35), (50) gives:
% 22.17/3.79 | (52) all_52_0 = xy
% 22.17/3.79 |
% 22.17/3.79 | REDUCE: (48), (51), (52) imply:
% 22.17/3.79 | (53) sdtpldt0(xx, xy) = all_52_2
% 22.17/3.79 |
% 22.17/3.79 | REDUCE: (46), (51) imply:
% 22.17/3.79 | (54) $i(xx)
% 22.17/3.79 |
% 22.17/3.79 | GROUND_INST: instantiating (14) with all_35_1, all_52_2, xy, xx, simplifying
% 22.17/3.79 | with (22), (53) gives:
% 22.17/3.79 | (55) all_52_2 = all_35_1
% 22.17/3.79 |
% 22.17/3.79 | GROUND_INST: instantiating (mAddComm) with xx, xy, all_35_1, simplifying with
% 22.17/3.79 | (22), (28), (32), (34), (54) gives:
% 22.17/3.79 | (56) sdtpldt0(xy, xx) = all_35_1 & $i(all_35_1)
% 22.17/3.79 |
% 22.17/3.79 | ALPHA: (56) implies:
% 22.17/3.79 | (57) sdtpldt0(xy, xx) = all_35_1
% 22.17/3.79 |
% 22.17/3.79 | GROUND_INST: instantiating (mMulComm) with xc, all_37_1, all_37_0, simplifying
% 22.17/3.79 | with (2), (10), (25), (36), (38) gives:
% 22.17/3.79 | (58) sdtasdt0(all_37_1, xc) = all_37_0 & $i(all_37_0)
% 22.17/3.79 |
% 22.17/3.79 | ALPHA: (58) implies:
% 22.17/3.79 | (59) sdtasdt0(all_37_1, xc) = all_37_0
% 22.17/3.79 |
% 22.17/3.79 | GROUND_INST: instantiating (mAMDistr) with xc, xu, all_50_0, xx, xy, all_35_1,
% 22.17/3.79 | simplifying with (2), (4), (5), (10), (12), (22), (42), (43),
% 22.17/3.79 | (44) gives:
% 22.17/3.79 | (60) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0,
% 22.17/3.79 | xc) = v1 & sdtasdt0(all_50_0, xc) = v3 & sdtasdt0(xu, xc) = v2 &
% 22.17/3.79 | sdtasdt0(xc, v0) = all_35_1 & sdtpldt0(v2, v3) = v1 & sdtpldt0(xu,
% 22.17/3.79 | all_50_0) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_35_1))
% 22.17/3.79 |
% 22.17/3.79 | DELTA: instantiating (60) with fresh symbols all_70_0, all_70_1, all_70_2,
% 22.17/3.79 | all_70_3 gives:
% 22.17/3.79 | (61) sdtasdt0(all_70_3, xc) = all_70_2 & sdtasdt0(all_50_0, xc) = all_70_0
% 22.17/3.79 | & sdtasdt0(xu, xc) = all_70_1 & sdtasdt0(xc, all_70_3) = all_35_1 &
% 22.17/3.79 | sdtpldt0(all_70_1, all_70_0) = all_70_2 & sdtpldt0(xu, all_50_0) =
% 22.17/3.79 | all_70_3 & $i(all_70_0) & $i(all_70_1) & $i(all_70_2) & $i(all_70_3) &
% 22.17/3.79 | $i(all_35_1)
% 22.17/3.79 |
% 22.17/3.79 | ALPHA: (61) implies:
% 22.17/3.79 | (62) sdtasdt0(xu, xc) = all_70_1
% 22.17/3.79 |
% 22.17/3.79 | GROUND_INST: instantiating (15) with xx, all_70_1, xc, xu, simplifying with
% 22.17/3.79 | (30), (62) gives:
% 22.17/3.79 | (63) all_70_1 = xx
% 22.17/3.79 |
% 22.17/3.80 | GROUND_INST: instantiating (mAMDistr) with xc, all_50_0, xu, xy, xx, all_35_1,
% 22.17/3.80 | simplifying with (2), (4), (5), (10), (12), (42), (43), (44),
% 22.17/3.80 | (57) gives:
% 22.17/3.80 | (64) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0,
% 22.17/3.80 | xc) = v1 & sdtasdt0(all_50_0, xc) = v2 & sdtasdt0(xu, xc) = v3 &
% 22.17/3.80 | sdtasdt0(xc, v0) = all_35_1 & sdtpldt0(v2, v3) = v1 &
% 22.17/3.80 | sdtpldt0(all_50_0, xu) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 22.17/3.80 | $i(all_35_1))
% 22.17/3.80 |
% 22.17/3.80 | GROUND_INST: instantiating (mMulAsso) with xz, xu, xc, all_37_1, all_37_0,
% 22.17/3.80 | simplifying with (2), (4), (10), (11), (12), (17), (39), (59)
% 22.17/3.80 | gives:
% 22.17/3.80 | (65) ? [v0: $i] : (sdtasdt0(xu, xc) = v0 & sdtasdt0(xz, v0) = all_37_0 &
% 22.17/3.80 | $i(v0) & $i(all_37_0))
% 22.17/3.80 |
% 22.17/3.80 | DELTA: instantiating (65) with fresh symbol all_108_0 gives:
% 22.17/3.80 | (66) sdtasdt0(xu, xc) = all_108_0 & sdtasdt0(xz, all_108_0) = all_37_0 &
% 22.17/3.80 | $i(all_108_0) & $i(all_37_0)
% 22.17/3.80 |
% 22.17/3.80 | ALPHA: (66) implies:
% 22.17/3.80 | (67) sdtasdt0(xz, all_108_0) = all_37_0
% 22.17/3.80 | (68) sdtasdt0(xu, xc) = all_108_0
% 22.17/3.80 |
% 22.17/3.80 | DELTA: instantiating (64) with fresh symbols all_116_0, all_116_1, all_116_2,
% 22.17/3.80 | all_116_3 gives:
% 22.17/3.80 | (69) sdtasdt0(all_116_3, xc) = all_116_2 & sdtasdt0(all_50_0, xc) =
% 22.17/3.80 | all_116_1 & sdtasdt0(xu, xc) = all_116_0 & sdtasdt0(xc, all_116_3) =
% 22.17/3.80 | all_35_1 & sdtpldt0(all_116_1, all_116_0) = all_116_2 &
% 22.17/3.80 | sdtpldt0(all_50_0, xu) = all_116_3 & $i(all_116_0) & $i(all_116_1) &
% 22.17/3.80 | $i(all_116_2) & $i(all_116_3) & $i(all_35_1)
% 22.17/3.80 |
% 22.17/3.80 | ALPHA: (69) implies:
% 22.17/3.80 | (70) sdtasdt0(xu, xc) = all_116_0
% 22.17/3.80 |
% 22.17/3.80 | GROUND_INST: instantiating (15) with xx, all_116_0, xc, xu, simplifying with
% 22.17/3.80 | (30), (70) gives:
% 22.17/3.80 | (71) all_116_0 = xx
% 22.17/3.80 |
% 22.17/3.80 | GROUND_INST: instantiating (15) with all_108_0, all_116_0, xc, xu, simplifying
% 22.17/3.80 | with (68), (70) gives:
% 22.17/3.80 | (72) all_116_0 = all_108_0
% 22.17/3.80 |
% 22.17/3.80 | COMBINE_EQS: (71), (72) imply:
% 22.17/3.80 | (73) all_108_0 = xx
% 22.17/3.80 |
% 22.17/3.80 | SIMP: (73) implies:
% 22.17/3.80 | (74) all_108_0 = xx
% 22.17/3.80 |
% 22.17/3.80 | REDUCE: (67), (74) imply:
% 22.17/3.80 | (75) sdtasdt0(xz, xx) = all_37_0
% 22.17/3.80 |
% 22.17/3.80 | GROUND_INST: instantiating (15) with all_37_2, all_37_0, xx, xz, simplifying
% 22.17/3.80 | with (26), (75) gives:
% 22.17/3.80 | (76) all_37_0 = all_37_2
% 22.17/3.80 |
% 22.17/3.80 | REDUCE: (24), (76) imply:
% 22.17/3.80 | (77) $false
% 22.17/3.80 |
% 22.17/3.80 | CLOSE: (77) is inconsistent.
% 22.17/3.80 |
% 22.17/3.80 End of proof
% 22.17/3.80 % SZS output end Proof for theBenchmark
% 22.17/3.80
% 22.17/3.80 3212ms
%------------------------------------------------------------------------------