TSTP Solution File: RNG106+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG106+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 : n001.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 13:57:55 EDT 2023
% Result : Theorem 41.29s 6.27s
% Output : Proof 51.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG106+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 : n001.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 : Sun Aug 27 02:41:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.15/1.11 Prover 4: Preprocessing ...
% 3.15/1.11 Prover 1: Preprocessing ...
% 3.15/1.15 Prover 2: Preprocessing ...
% 3.15/1.15 Prover 0: Preprocessing ...
% 3.15/1.15 Prover 5: Preprocessing ...
% 3.15/1.15 Prover 3: Preprocessing ...
% 3.15/1.15 Prover 6: Preprocessing ...
% 8.98/1.89 Prover 1: Constructing countermodel ...
% 9.08/1.95 Prover 3: Constructing countermodel ...
% 9.08/1.97 Prover 2: Proving ...
% 9.08/1.98 Prover 6: Proving ...
% 9.08/1.99 Prover 5: Proving ...
% 10.07/2.24 Prover 4: Constructing countermodel ...
% 12.68/2.40 Prover 0: Proving ...
% 41.29/6.27 Prover 3: proved (5639ms)
% 41.29/6.27
% 41.29/6.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 41.29/6.27
% 41.29/6.27 Prover 6: stopped
% 41.29/6.27 Prover 2: stopped
% 41.90/6.28 Prover 5: stopped
% 41.90/6.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 41.90/6.29 Prover 0: stopped
% 41.90/6.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 41.90/6.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 41.90/6.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 41.90/6.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 41.90/6.35 Prover 7: Preprocessing ...
% 41.90/6.37 Prover 8: Preprocessing ...
% 42.86/6.41 Prover 11: Preprocessing ...
% 43.03/6.45 Prover 13: Preprocessing ...
% 43.03/6.46 Prover 10: Preprocessing ...
% 43.03/6.47 Prover 7: Constructing countermodel ...
% 43.82/6.57 Prover 8: Warning: ignoring some quantifiers
% 43.82/6.58 Prover 13: Warning: ignoring some quantifiers
% 43.82/6.58 Prover 8: Constructing countermodel ...
% 43.82/6.61 Prover 13: Constructing countermodel ...
% 43.82/6.61 Prover 10: Constructing countermodel ...
% 46.16/6.87 Prover 11: Constructing countermodel ...
% 50.28/7.45 Prover 10: Found proof (size 136)
% 50.28/7.46 Prover 10: proved (1149ms)
% 50.28/7.46 Prover 11: stopped
% 50.28/7.46 Prover 7: stopped
% 50.28/7.46 Prover 13: stopped
% 50.28/7.46 Prover 8: stopped
% 50.28/7.47 Prover 1: stopped
% 50.28/7.47 Prover 4: stopped
% 50.28/7.47
% 50.28/7.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.28/7.47
% 50.28/7.48 % SZS output start Proof for theBenchmark
% 50.28/7.48 Assumptions after simplification:
% 50.28/7.48 ---------------------------------
% 50.28/7.48
% 50.28/7.48 (mAMDistr)
% 50.28/7.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 50.28/7.51 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~
% 50.28/7.51 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 50.28/7.51 aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6: $i] : ? [v7:
% 50.28/7.51 $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2,
% 50.28/7.51 v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8,
% 50.28/7.51 v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 50.28/7.51 $i(v5)))
% 50.28/7.51
% 50.28/7.51 (mAddComm)
% 50.28/7.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 50.28/7.51 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtpldt0(v1, v0)
% 50.28/7.51 = v2 & $i(v2)))
% 50.28/7.51
% 50.28/7.51 (mDefDiv)
% 50.28/7.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | ~
% 50.28/7.51 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~
% 50.28/7.51 aElement0(v0) | doDivides0(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1)
% 50.28/7.51 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aElement0(v1) | ~ aElement0(v0) |
% 50.28/7.51 ? [v2: $i] : (sdtasdt0(v0, v2) = v1 & $i(v2) & aElement0(v2)))
% 50.28/7.51
% 50.28/7.51 (mDefIdeal)
% 50.28/7.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v1)
% 50.28/7.52 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~
% 50.28/7.52 aElementOf0(v1, v0) | ~ aElement0(v2) | aElementOf0(v3, v0)) & ! [v0: $i]
% 50.28/7.52 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v1, v2) = v3) | ~
% 50.28/7.52 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ aElementOf0(v2, v0) |
% 50.28/7.52 ~ aElementOf0(v1, v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 50.28/7.52 aIdeal0(v0) | aSet0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aSet0(v0) |
% 50.28/7.52 aIdeal0(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ?
% 50.28/7.52 [v5: $i] : ($i(v4) & $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2,
% 50.28/7.52 v1) = v3 & $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) |
% 50.28/7.52 (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~
% 50.28/7.52 aElementOf0(v5, v0)))))
% 50.28/7.52
% 50.28/7.52 (mDefPrIdeal)
% 50.28/7.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (slsdtgt0(v0) =
% 50.28/7.52 v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 50.28/7.52 $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) | aElementOf0(v2, v1)) & !
% 50.28/7.52 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slsdtgt0(v0) = v1) | ~
% 50.28/7.52 $i(v2) | ~ $i(v0) | ~ aSet0(v2) | ~ aElement0(v0) | ? [v3: $i] : ? [v4:
% 50.28/7.52 $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ aElementOf0(v3, v2) | ! [v6:
% 50.28/7.52 $i] : ( ~ (sdtasdt0(v0, v6) = v3) | ~ $i(v6) | ~ aElement0(v6))) &
% 50.28/7.52 (aElementOf0(v3, v2) | (v5 = v3 & sdtasdt0(v0, v4) = v3 &
% 50.28/7.52 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 50.28/7.52 (slsdtgt0(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2,
% 50.28/7.52 v1) | ~ aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 50.28/7.52 aElement0(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~
% 50.28/7.52 $i(v1) | ~ $i(v0) | ~ aElement0(v0) | aSet0(v1))
% 50.28/7.52
% 50.28/7.52 (mEOfElem)
% 50.28/7.52 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) |
% 50.28/7.52 ~ aSet0(v0) | aElement0(v1))
% 50.28/7.52
% 50.28/7.52 (mMulAsso)
% 50.28/7.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 50.28/7.52 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 50.28/7.52 | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ?
% 50.28/7.52 [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4 & $i(v5) &
% 50.28/7.52 $i(v4)))
% 50.28/7.52
% 50.28/7.52 (mMulComm)
% 50.28/7.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 50.28/7.52 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtasdt0(v1, v0)
% 50.28/7.52 = v2 & $i(v2)))
% 50.28/7.52
% 50.28/7.52 (mSortsB)
% 50.28/7.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 50.28/7.52 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2))
% 50.28/7.52
% 50.28/7.52 (mSortsB_02)
% 50.28/7.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 50.28/7.52 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2))
% 50.28/7.52
% 50.28/7.52 (m__)
% 50.28/7.53 $i(xc) & ? [v0: $i] : (slsdtgt0(xc) = v0 & $i(v0) & ~ aIdeal0(v0) & ! [v1:
% 50.28/7.53 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 50.28/7.53 (sdtasdt0(v3, v1) = v5) | ~ (sdtpldt0(v1, v2) = v4) | ~ $i(v3) | ~
% 50.28/7.53 $i(v2) | ~ $i(v1) | ~ aElementOf0(v2, v0) | ~ aElementOf0(v1, v0) | ~
% 50.28/7.53 aElement0(v3) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 50.28/7.53 (sdtasdt0(v6, v3) = v7 & sdtasdt0(xc, v9) = v4 & sdtasdt0(xc, v8) = v2 &
% 50.28/7.53 sdtasdt0(xc, v7) = v5 & sdtasdt0(xc, v6) = v1 & sdtpldt0(v6, v8) = v9 &
% 50.28/7.53 $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & aElementOf0(v5,
% 50.28/7.53 v0) & aElementOf0(v4, v0) & aElement0(v8) & aElement0(v6))))
% 50.28/7.53
% 50.28/7.53 (m__1905)
% 50.28/7.53 $i(xc) & aElement0(xc)
% 50.28/7.53
% 50.28/7.53 (function-axioms)
% 50.28/7.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.28/7.53 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 50.28/7.53 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) |
% 50.28/7.53 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 50.28/7.53 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 50.28/7.53 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.28/7.53 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 50.28/7.53 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) | ~ (slsdtgt0(v2)
% 50.28/7.53 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 50.28/7.53 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 50.28/7.53 ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0))
% 50.28/7.53
% 50.28/7.53 Further assumptions not needed in the proof:
% 50.28/7.53 --------------------------------------------
% 50.28/7.53 mAddAsso, mAddInvr, mAddZero, mCancel, mChineseRemainder, mDefDvs, mDefGCD,
% 50.28/7.53 mDefMod, mDefRel, mDefSInt, mDefSSum, mDivision, mElmSort, mEucSort, mIdeInt,
% 50.28/7.53 mIdeSum, mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mSetEq, mSetSort,
% 50.28/7.53 mSortsC, mSortsC_01, mSortsU, mUnNeZr
% 50.28/7.53
% 50.28/7.53 Those formulas are unsatisfiable:
% 50.28/7.53 ---------------------------------
% 50.28/7.53
% 50.28/7.53 Begin of proof
% 50.28/7.53 |
% 50.28/7.53 | ALPHA: (mDefIdeal) implies:
% 50.28/7.53 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ aSet0(v0) | aIdeal0(v0) | ? [v1: $i] :
% 50.28/7.53 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) &
% 50.28/7.53 | $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2, v1) = v3 &
% 50.28/7.53 | $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) |
% 50.28/7.53 | (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~
% 50.28/7.53 | aElementOf0(v5, v0)))))
% 50.28/7.53 |
% 50.28/7.53 | ALPHA: (mDefDiv) implies:
% 50.28/7.53 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0,
% 50.28/7.53 | v1) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v2: $i] :
% 50.28/7.53 | (sdtasdt0(v0, v2) = v1 & $i(v2) & aElement0(v2)))
% 50.28/7.53 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) |
% 50.28/7.53 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v2) | ~
% 50.28/7.53 | aElement0(v1) | ~ aElement0(v0) | doDivides0(v0, v1))
% 50.28/7.53 |
% 50.28/7.53 | ALPHA: (mDefPrIdeal) implies:
% 50.28/7.53 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~ $i(v1) | ~
% 50.28/7.53 | $i(v0) | ~ aElement0(v0) | aSet0(v1))
% 50.28/7.54 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slsdtgt0(v0) = v1) | ~
% 50.28/7.54 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 50.28/7.54 | aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 50.28/7.54 | aElement0(v3)))
% 50.28/7.54 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 50.28/7.54 | (slsdtgt0(v0) = v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~
% 50.28/7.54 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v3) | ~ aElement0(v0)
% 50.28/7.54 | | aElementOf0(v2, v1))
% 50.28/7.54 |
% 50.28/7.54 | ALPHA: (m__1905) implies:
% 50.28/7.54 | (7) aElement0(xc)
% 50.28/7.54 |
% 50.28/7.54 | ALPHA: (m__) implies:
% 50.28/7.54 | (8) $i(xc)
% 50.28/7.54 | (9) ? [v0: $i] : (slsdtgt0(xc) = v0 & $i(v0) & ~ aIdeal0(v0) & ! [v1:
% 50.28/7.54 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 50.28/7.54 | (sdtasdt0(v3, v1) = v5) | ~ (sdtpldt0(v1, v2) = v4) | ~ $i(v3) |
% 50.28/7.54 | ~ $i(v2) | ~ $i(v1) | ~ aElementOf0(v2, v0) | ~ aElementOf0(v1,
% 50.28/7.54 | v0) | ~ aElement0(v3) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 50.28/7.54 | : ? [v9: $i] : (sdtasdt0(v6, v3) = v7 & sdtasdt0(xc, v9) = v4 &
% 50.28/7.54 | sdtasdt0(xc, v8) = v2 & sdtasdt0(xc, v7) = v5 & sdtasdt0(xc, v6)
% 50.28/7.54 | = v1 & sdtpldt0(v6, v8) = v9 & $i(v9) & $i(v8) & $i(v7) & $i(v6)
% 50.28/7.54 | & $i(v5) & $i(v4) & aElementOf0(v5, v0) & aElementOf0(v4, v0) &
% 50.28/7.54 | aElement0(v8) & aElement0(v6))))
% 50.28/7.54 |
% 50.28/7.54 | ALPHA: (function-axioms) implies:
% 50.28/7.54 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.28/7.54 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 50.28/7.54 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.28/7.54 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 50.28/7.54 |
% 50.28/7.54 | DELTA: instantiating (9) with fresh symbol all_36_0 gives:
% 50.28/7.54 | (12) slsdtgt0(xc) = all_36_0 & $i(all_36_0) & ~ aIdeal0(all_36_0) & !
% 50.28/7.54 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 50.28/7.54 | (sdtasdt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) |
% 50.28/7.54 | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_36_0) | ~
% 50.28/7.54 | aElementOf0(v0, all_36_0) | ~ aElement0(v2) | ? [v5: $i] : ? [v6:
% 50.28/7.54 | $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v5, v2) = v6 &
% 50.28/7.54 | sdtasdt0(xc, v8) = v3 & sdtasdt0(xc, v7) = v1 & sdtasdt0(xc, v6) =
% 50.28/7.54 | v4 & sdtasdt0(xc, v5) = v0 & sdtpldt0(v5, v7) = v8 & $i(v8) &
% 50.28/7.54 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & aElementOf0(v4,
% 50.28/7.54 | all_36_0) & aElementOf0(v3, all_36_0) & aElement0(v7) &
% 50.28/7.54 | aElement0(v5)))
% 50.28/7.54 |
% 50.28/7.54 | ALPHA: (12) implies:
% 50.28/7.54 | (13) ~ aIdeal0(all_36_0)
% 50.28/7.54 | (14) $i(all_36_0)
% 50.28/7.54 | (15) slsdtgt0(xc) = all_36_0
% 50.28/7.54 |
% 50.28/7.54 | GROUND_INST: instantiating (4) with xc, all_36_0, simplifying with (7), (8),
% 50.28/7.54 | (14), (15) gives:
% 50.28/7.54 | (16) aSet0(all_36_0)
% 50.28/7.54 |
% 50.28/7.54 | GROUND_INST: instantiating (1) with all_36_0, simplifying with (13), (14),
% 50.28/7.54 | (16) gives:
% 50.28/7.55 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 50.28/7.55 | ($i(v3) & $i(v1) & $i(v0) & aElementOf0(v0, all_36_0) & ((sdtasdt0(v1,
% 50.28/7.55 | v0) = v2 & $i(v2) & aElement0(v1) & ~ aElementOf0(v2,
% 50.28/7.55 | all_36_0)) | (sdtpldt0(v0, v3) = v4 & $i(v4) & aElementOf0(v3,
% 50.28/7.55 | all_36_0) & ~ aElementOf0(v4, all_36_0))))
% 50.28/7.55 |
% 50.28/7.55 | DELTA: instantiating (17) with fresh symbols all_50_0, all_50_1, all_50_2,
% 50.28/7.55 | all_50_3, all_50_4 gives:
% 50.28/7.55 | (18) $i(all_50_1) & $i(all_50_3) & $i(all_50_4) & aElementOf0(all_50_4,
% 50.28/7.55 | all_36_0) & ((sdtasdt0(all_50_3, all_50_4) = all_50_2 & $i(all_50_2)
% 50.28/7.55 | & aElement0(all_50_3) & ~ aElementOf0(all_50_2, all_36_0)) |
% 50.28/7.55 | (sdtpldt0(all_50_4, all_50_1) = all_50_0 & $i(all_50_0) &
% 50.28/7.55 | aElementOf0(all_50_1, all_36_0) & ~ aElementOf0(all_50_0,
% 50.28/7.55 | all_36_0)))
% 50.28/7.55 |
% 50.28/7.55 | ALPHA: (18) implies:
% 50.28/7.55 | (19) aElementOf0(all_50_4, all_36_0)
% 50.28/7.55 | (20) $i(all_50_4)
% 50.28/7.55 | (21) $i(all_50_3)
% 50.28/7.55 | (22) $i(all_50_1)
% 50.28/7.55 | (23) (sdtasdt0(all_50_3, all_50_4) = all_50_2 & $i(all_50_2) &
% 50.28/7.55 | aElement0(all_50_3) & ~ aElementOf0(all_50_2, all_36_0)) |
% 50.28/7.55 | (sdtpldt0(all_50_4, all_50_1) = all_50_0 & $i(all_50_0) &
% 50.28/7.55 | aElementOf0(all_50_1, all_36_0) & ~ aElementOf0(all_50_0,
% 50.28/7.55 | all_36_0))
% 50.28/7.55 |
% 50.28/7.55 | GROUND_INST: instantiating (5) with xc, all_36_0, all_50_4, simplifying with
% 50.28/7.55 | (7), (8), (14), (15), (19), (20) gives:
% 50.28/7.55 | (24) ? [v0: $i] : (sdtasdt0(xc, v0) = all_50_4 & $i(v0) & aElement0(v0))
% 50.28/7.55 |
% 50.28/7.55 | GROUND_INST: instantiating (mEOfElem) with all_36_0, all_50_4, simplifying
% 50.28/7.55 | with (14), (16), (19), (20) gives:
% 50.28/7.55 | (25) aElement0(all_50_4)
% 50.28/7.55 |
% 50.28/7.55 | DELTA: instantiating (24) with fresh symbol all_58_0 gives:
% 50.28/7.55 | (26) sdtasdt0(xc, all_58_0) = all_50_4 & $i(all_58_0) & aElement0(all_58_0)
% 50.28/7.55 |
% 50.28/7.55 | ALPHA: (26) implies:
% 50.28/7.55 | (27) aElement0(all_58_0)
% 50.28/7.55 | (28) $i(all_58_0)
% 50.28/7.55 | (29) sdtasdt0(xc, all_58_0) = all_50_4
% 50.28/7.55 |
% 50.28/7.55 | GROUND_INST: instantiating (mMulComm) with xc, all_58_0, all_50_4, simplifying
% 50.28/7.55 | with (7), (8), (27), (28), (29) gives:
% 50.28/7.55 | (30) sdtasdt0(all_58_0, xc) = all_50_4 & $i(all_50_4)
% 50.28/7.55 |
% 50.28/7.55 | ALPHA: (30) implies:
% 50.28/7.55 | (31) sdtasdt0(all_58_0, xc) = all_50_4
% 50.28/7.55 |
% 50.28/7.55 | GROUND_INST: instantiating (3) with xc, all_50_4, all_58_0, simplifying with
% 50.28/7.55 | (7), (8), (20), (25), (27), (28), (29) gives:
% 50.28/7.55 | (32) doDivides0(xc, all_50_4)
% 50.28/7.55 |
% 50.28/7.55 | GROUND_INST: instantiating (3) with all_58_0, all_50_4, xc, simplifying with
% 50.28/7.55 | (7), (8), (20), (25), (27), (28), (31) gives:
% 50.28/7.55 | (33) doDivides0(all_58_0, all_50_4)
% 50.28/7.55 |
% 50.28/7.55 | DELTA: instantiating (24) with fresh symbol all_72_0 gives:
% 50.28/7.55 | (34) sdtasdt0(xc, all_72_0) = all_50_4 & $i(all_72_0) & aElement0(all_72_0)
% 50.28/7.55 |
% 50.28/7.55 | ALPHA: (34) implies:
% 50.28/7.55 | (35) aElement0(all_72_0)
% 50.28/7.55 | (36) $i(all_72_0)
% 50.28/7.55 | (37) sdtasdt0(xc, all_72_0) = all_50_4
% 50.28/7.55 |
% 50.28/7.55 | GROUND_INST: instantiating (2) with all_58_0, all_50_4, simplifying with (20),
% 50.28/7.55 | (25), (27), (28), (33) gives:
% 50.28/7.55 | (38) ? [v0: $i] : (sdtasdt0(all_58_0, v0) = all_50_4 & $i(v0) &
% 50.28/7.55 | aElement0(v0))
% 50.28/7.55 |
% 50.28/7.55 | GROUND_INST: instantiating (mMulComm) with xc, all_72_0, all_50_4, simplifying
% 50.28/7.55 | with (7), (8), (35), (36), (37) gives:
% 50.28/7.55 | (39) sdtasdt0(all_72_0, xc) = all_50_4 & $i(all_50_4)
% 50.28/7.55 |
% 50.28/7.56 | ALPHA: (39) implies:
% 50.28/7.56 | (40) sdtasdt0(all_72_0, xc) = all_50_4
% 50.28/7.56 |
% 50.28/7.56 | DELTA: instantiating (38) with fresh symbol all_80_0 gives:
% 50.28/7.56 | (41) sdtasdt0(all_58_0, all_80_0) = all_50_4 & $i(all_80_0) &
% 50.28/7.56 | aElement0(all_80_0)
% 50.28/7.56 |
% 50.28/7.56 | ALPHA: (41) implies:
% 50.28/7.56 | (42) aElement0(all_80_0)
% 50.28/7.56 | (43) $i(all_80_0)
% 50.28/7.56 | (44) sdtasdt0(all_58_0, all_80_0) = all_50_4
% 50.28/7.56 |
% 50.28/7.56 | GROUND_INST: instantiating (mMulComm) with all_58_0, all_80_0, all_50_4,
% 50.28/7.56 | simplifying with (27), (28), (42), (43), (44) gives:
% 50.28/7.56 | (45) sdtasdt0(all_80_0, all_58_0) = all_50_4 & $i(all_50_4)
% 50.28/7.56 |
% 50.28/7.56 | ALPHA: (45) implies:
% 50.28/7.56 | (46) sdtasdt0(all_80_0, all_58_0) = all_50_4
% 50.28/7.56 |
% 50.28/7.56 | GROUND_INST: instantiating (3) with all_72_0, all_50_4, xc, simplifying with
% 50.28/7.56 | (7), (8), (20), (25), (35), (36), (40) gives:
% 50.28/7.56 | (47) doDivides0(all_72_0, all_50_4)
% 50.28/7.56 |
% 50.28/7.56 | GROUND_INST: instantiating (2) with all_72_0, all_50_4, simplifying with (20),
% 50.28/7.56 | (25), (35), (36), (47) gives:
% 50.28/7.56 | (48) ? [v0: $i] : (sdtasdt0(all_72_0, v0) = all_50_4 & $i(v0) &
% 50.28/7.56 | aElement0(v0))
% 50.28/7.56 |
% 50.28/7.56 | GROUND_INST: instantiating (3) with all_80_0, all_50_4, all_58_0, simplifying
% 50.28/7.56 | with (20), (25), (27), (28), (42), (43), (46) gives:
% 50.28/7.56 | (49) doDivides0(all_80_0, all_50_4)
% 50.28/7.56 |
% 50.28/7.56 | DELTA: instantiating (48) with fresh symbol all_94_0 gives:
% 50.28/7.56 | (50) sdtasdt0(all_72_0, all_94_0) = all_50_4 & $i(all_94_0) &
% 50.28/7.56 | aElement0(all_94_0)
% 50.28/7.56 |
% 50.28/7.56 | ALPHA: (50) implies:
% 50.28/7.56 | (51) aElement0(all_94_0)
% 50.28/7.56 | (52) $i(all_94_0)
% 50.28/7.56 | (53) sdtasdt0(all_72_0, all_94_0) = all_50_4
% 50.28/7.56 |
% 50.28/7.56 | GROUND_INST: instantiating (2) with all_80_0, all_50_4, simplifying with (20),
% 50.28/7.56 | (25), (42), (43), (49) gives:
% 50.28/7.56 | (54) ? [v0: $i] : (sdtasdt0(all_80_0, v0) = all_50_4 & $i(v0) &
% 50.28/7.56 | aElement0(v0))
% 50.28/7.56 |
% 50.28/7.56 | GROUND_INST: instantiating (mMulComm) with all_72_0, all_94_0, all_50_4,
% 50.28/7.56 | simplifying with (35), (36), (51), (52), (53) gives:
% 50.28/7.56 | (55) sdtasdt0(all_94_0, all_72_0) = all_50_4 & $i(all_50_4)
% 50.28/7.56 |
% 50.28/7.56 | ALPHA: (55) implies:
% 50.28/7.56 | (56) sdtasdt0(all_94_0, all_72_0) = all_50_4
% 50.28/7.56 |
% 50.28/7.56 | DELTA: instantiating (54) with fresh symbol all_102_0 gives:
% 50.28/7.56 | (57) sdtasdt0(all_80_0, all_102_0) = all_50_4 & $i(all_102_0) &
% 50.28/7.56 | aElement0(all_102_0)
% 50.28/7.56 |
% 50.28/7.56 | ALPHA: (57) implies:
% 50.28/7.56 | (58) aElement0(all_102_0)
% 50.28/7.56 | (59) $i(all_102_0)
% 50.28/7.56 | (60) sdtasdt0(all_80_0, all_102_0) = all_50_4
% 50.28/7.56 |
% 50.28/7.56 | GROUND_INST: instantiating (mMulComm) with all_80_0, all_102_0, all_50_4,
% 50.28/7.56 | simplifying with (42), (43), (58), (59), (60) gives:
% 50.28/7.56 | (61) sdtasdt0(all_102_0, all_80_0) = all_50_4 & $i(all_50_4)
% 50.28/7.56 |
% 50.28/7.56 | ALPHA: (61) implies:
% 50.28/7.56 | (62) sdtasdt0(all_102_0, all_80_0) = all_50_4
% 50.28/7.56 |
% 50.28/7.56 | GROUND_INST: instantiating (3) with all_102_0, all_50_4, all_80_0, simplifying
% 50.28/7.56 | with (20), (25), (42), (43), (58), (59), (62) gives:
% 50.28/7.57 | (63) doDivides0(all_102_0, all_50_4)
% 50.28/7.57 |
% 51.17/7.57 | GROUND_INST: instantiating (2) with all_102_0, all_50_4, simplifying with
% 51.17/7.57 | (20), (25), (58), (59), (63) gives:
% 51.17/7.57 | (64) ? [v0: $i] : (sdtasdt0(all_102_0, v0) = all_50_4 & $i(v0) &
% 51.17/7.57 | aElement0(v0))
% 51.17/7.57 |
% 51.17/7.57 | DELTA: instantiating (64) with fresh symbol all_124_0 gives:
% 51.17/7.57 | (65) sdtasdt0(all_102_0, all_124_0) = all_50_4 & $i(all_124_0) &
% 51.17/7.57 | aElement0(all_124_0)
% 51.17/7.57 |
% 51.17/7.57 | ALPHA: (65) implies:
% 51.17/7.57 | (66) aElement0(all_124_0)
% 51.17/7.57 | (67) $i(all_124_0)
% 51.17/7.57 | (68) sdtasdt0(all_102_0, all_124_0) = all_50_4
% 51.17/7.57 |
% 51.17/7.57 | GROUND_INST: instantiating (mMulComm) with all_102_0, all_124_0, all_50_4,
% 51.17/7.57 | simplifying with (58), (59), (66), (67), (68) gives:
% 51.17/7.57 | (69) sdtasdt0(all_124_0, all_102_0) = all_50_4 & $i(all_50_4)
% 51.17/7.57 |
% 51.17/7.57 | ALPHA: (69) implies:
% 51.17/7.57 | (70) sdtasdt0(all_124_0, all_102_0) = all_50_4
% 51.17/7.57 |
% 51.17/7.57 | GROUND_INST: instantiating (3) with all_124_0, all_50_4, all_102_0,
% 51.17/7.57 | simplifying with (20), (25), (58), (59), (66), (67), (70) gives:
% 51.17/7.57 | (71) doDivides0(all_124_0, all_50_4)
% 51.17/7.57 |
% 51.17/7.57 | GROUND_INST: instantiating (2) with all_124_0, all_50_4, simplifying with
% 51.17/7.57 | (20), (25), (66), (67), (71) gives:
% 51.17/7.57 | (72) ? [v0: $i] : (sdtasdt0(all_124_0, v0) = all_50_4 & $i(v0) &
% 51.17/7.57 | aElement0(v0))
% 51.17/7.57 |
% 51.17/7.57 | DELTA: instantiating (72) with fresh symbol all_146_0 gives:
% 51.17/7.57 | (73) sdtasdt0(all_124_0, all_146_0) = all_50_4 & $i(all_146_0) &
% 51.17/7.57 | aElement0(all_146_0)
% 51.17/7.57 |
% 51.17/7.57 | ALPHA: (73) implies:
% 51.17/7.57 | (74) aElement0(all_146_0)
% 51.17/7.57 | (75) $i(all_146_0)
% 51.17/7.57 | (76) sdtasdt0(all_124_0, all_146_0) = all_50_4
% 51.17/7.57 |
% 51.17/7.57 | GROUND_INST: instantiating (mMulComm) with all_124_0, all_146_0, all_50_4,
% 51.17/7.57 | simplifying with (66), (67), (74), (75), (76) gives:
% 51.17/7.57 | (77) sdtasdt0(all_146_0, all_124_0) = all_50_4 & $i(all_50_4)
% 51.17/7.57 |
% 51.17/7.57 | BETA: splitting (23) gives:
% 51.17/7.57 |
% 51.17/7.57 | Case 1:
% 51.17/7.57 | |
% 51.17/7.57 | | (78) sdtasdt0(all_50_3, all_50_4) = all_50_2 & $i(all_50_2) &
% 51.17/7.57 | | aElement0(all_50_3) & ~ aElementOf0(all_50_2, all_36_0)
% 51.17/7.57 | |
% 51.17/7.57 | | ALPHA: (78) implies:
% 51.17/7.57 | | (79) ~ aElementOf0(all_50_2, all_36_0)
% 51.17/7.57 | | (80) aElement0(all_50_3)
% 51.17/7.57 | | (81) sdtasdt0(all_50_3, all_50_4) = all_50_2
% 51.17/7.57 | |
% 51.17/7.57 | | GROUND_INST: instantiating (mMulComm) with all_50_3, all_50_4, all_50_2,
% 51.17/7.57 | | simplifying with (20), (21), (25), (80), (81) gives:
% 51.17/7.57 | | (82) sdtasdt0(all_50_4, all_50_3) = all_50_2 & $i(all_50_2)
% 51.17/7.57 | |
% 51.17/7.57 | | ALPHA: (82) implies:
% 51.17/7.57 | | (83) sdtasdt0(all_50_4, all_50_3) = all_50_2
% 51.17/7.57 | |
% 51.17/7.57 | | GROUND_INST: instantiating (mMulAsso) with all_94_0, all_72_0, all_50_3,
% 51.17/7.57 | | all_50_4, all_50_2, simplifying with (21), (35), (36), (51),
% 51.17/7.57 | | (52), (56), (80), (83) gives:
% 51.17/7.57 | | (84) ? [v0: $i] : (sdtasdt0(all_94_0, v0) = all_50_2 &
% 51.17/7.57 | | sdtasdt0(all_72_0, all_50_3) = v0 & $i(v0) & $i(all_50_2))
% 51.17/7.57 | |
% 51.17/7.57 | | GROUND_INST: instantiating (mMulAsso) with xc, all_72_0, all_50_3, all_50_4,
% 51.17/7.57 | | all_50_2, simplifying with (7), (8), (21), (35), (36), (37),
% 51.17/7.57 | | (80), (83) gives:
% 51.17/7.57 | | (85) ? [v0: $i] : (sdtasdt0(all_72_0, all_50_3) = v0 & sdtasdt0(xc, v0)
% 51.17/7.57 | | = all_50_2 & $i(v0) & $i(all_50_2))
% 51.17/7.57 | |
% 51.17/7.57 | | DELTA: instantiating (85) with fresh symbol all_180_0 gives:
% 51.17/7.57 | | (86) sdtasdt0(all_72_0, all_50_3) = all_180_0 & sdtasdt0(xc, all_180_0) =
% 51.17/7.57 | | all_50_2 & $i(all_180_0) & $i(all_50_2)
% 51.17/7.57 | |
% 51.17/7.57 | | ALPHA: (86) implies:
% 51.17/7.57 | | (87) sdtasdt0(xc, all_180_0) = all_50_2
% 51.17/7.57 | | (88) sdtasdt0(all_72_0, all_50_3) = all_180_0
% 51.17/7.57 | |
% 51.17/7.57 | | DELTA: instantiating (84) with fresh symbol all_200_0 gives:
% 51.17/7.57 | | (89) sdtasdt0(all_94_0, all_200_0) = all_50_2 & sdtasdt0(all_72_0,
% 51.17/7.57 | | all_50_3) = all_200_0 & $i(all_200_0) & $i(all_50_2)
% 51.17/7.57 | |
% 51.17/7.58 | | ALPHA: (89) implies:
% 51.17/7.58 | | (90) sdtasdt0(all_72_0, all_50_3) = all_200_0
% 51.17/7.58 | |
% 51.17/7.58 | | GROUND_INST: instantiating (11) with all_180_0, all_200_0, all_50_3,
% 51.17/7.58 | | all_72_0, simplifying with (88), (90) gives:
% 51.17/7.58 | | (91) all_200_0 = all_180_0
% 51.17/7.58 | |
% 51.17/7.58 | | GROUND_INST: instantiating (mSortsB_02) with all_72_0, all_50_3, all_180_0,
% 51.17/7.58 | | simplifying with (21), (35), (36), (80), (88) gives:
% 51.17/7.58 | | (92) aElement0(all_180_0)
% 51.17/7.58 | |
% 51.17/7.58 | | GROUND_INST: instantiating (mMulComm) with all_72_0, all_50_3, all_180_0,
% 51.17/7.58 | | simplifying with (21), (35), (36), (80), (88) gives:
% 51.17/7.58 | | (93) sdtasdt0(all_50_3, all_72_0) = all_180_0 & $i(all_180_0)
% 51.17/7.58 | |
% 51.17/7.58 | | ALPHA: (93) implies:
% 51.17/7.58 | | (94) $i(all_180_0)
% 51.17/7.58 | |
% 51.17/7.58 | | GROUND_INST: instantiating (mMulComm) with xc, all_180_0, all_50_2,
% 51.17/7.58 | | simplifying with (7), (8), (87), (92), (94) gives:
% 51.17/7.58 | | (95) sdtasdt0(all_180_0, xc) = all_50_2 & $i(all_50_2)
% 51.17/7.58 | |
% 51.17/7.58 | | ALPHA: (95) implies:
% 51.17/7.58 | | (96) $i(all_50_2)
% 51.17/7.58 | |
% 51.17/7.58 | | GROUND_INST: instantiating (6) with xc, all_36_0, all_50_2, all_180_0,
% 51.17/7.58 | | simplifying with (7), (8), (14), (15), (79), (87), (92), (94),
% 51.17/7.58 | | (96) gives:
% 51.17/7.58 | | (97) $false
% 51.17/7.58 | |
% 51.17/7.58 | | CLOSE: (97) is inconsistent.
% 51.17/7.58 | |
% 51.17/7.58 | Case 2:
% 51.17/7.58 | |
% 51.17/7.58 | | (98) sdtpldt0(all_50_4, all_50_1) = all_50_0 & $i(all_50_0) &
% 51.17/7.58 | | aElementOf0(all_50_1, all_36_0) & ~ aElementOf0(all_50_0, all_36_0)
% 51.17/7.58 | |
% 51.17/7.58 | | ALPHA: (98) implies:
% 51.17/7.58 | | (99) ~ aElementOf0(all_50_0, all_36_0)
% 51.17/7.58 | | (100) aElementOf0(all_50_1, all_36_0)
% 51.17/7.58 | | (101) sdtpldt0(all_50_4, all_50_1) = all_50_0
% 51.17/7.58 | |
% 51.17/7.58 | | GROUND_INST: instantiating (5) with xc, all_36_0, all_50_1, simplifying with
% 51.17/7.58 | | (7), (8), (14), (15), (22), (100) gives:
% 51.17/7.58 | | (102) ? [v0: $i] : (sdtasdt0(xc, v0) = all_50_1 & $i(v0) &
% 51.17/7.58 | | aElement0(v0))
% 51.17/7.58 | |
% 51.17/7.58 | | GROUND_INST: instantiating (mEOfElem) with all_36_0, all_50_1, simplifying
% 51.17/7.58 | | with (14), (16), (22), (100) gives:
% 51.17/7.58 | | (103) aElement0(all_50_1)
% 51.17/7.58 | |
% 51.17/7.58 | | DELTA: instantiating (102) with fresh symbol all_168_0 gives:
% 51.17/7.58 | | (104) sdtasdt0(xc, all_168_0) = all_50_1 & $i(all_168_0) &
% 51.17/7.58 | | aElement0(all_168_0)
% 51.17/7.58 | |
% 51.17/7.58 | | ALPHA: (104) implies:
% 51.17/7.58 | | (105) aElement0(all_168_0)
% 51.17/7.58 | | (106) $i(all_168_0)
% 51.17/7.58 | | (107) sdtasdt0(xc, all_168_0) = all_50_1
% 51.17/7.58 | |
% 51.17/7.58 | | GROUND_INST: instantiating (mAddComm) with all_50_4, all_50_1, all_50_0,
% 51.17/7.58 | | simplifying with (20), (22), (25), (101), (103) gives:
% 51.17/7.58 | | (108) sdtpldt0(all_50_1, all_50_4) = all_50_0 & $i(all_50_0)
% 51.17/7.58 | |
% 51.17/7.58 | | ALPHA: (108) implies:
% 51.17/7.58 | | (109) sdtpldt0(all_50_1, all_50_4) = all_50_0
% 51.17/7.58 | |
% 51.17/7.58 | | GROUND_INST: instantiating (mAMDistr) with xc, all_72_0, all_168_0,
% 51.17/7.58 | | all_50_4, all_50_1, all_50_0, simplifying with (7), (8), (35),
% 51.17/7.58 | | (36), (37), (101), (105), (106), (107) gives:
% 51.17/7.58 | | (110) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 51.17/7.58 | | (sdtasdt0(v0, xc) = v1 & sdtasdt0(all_168_0, xc) = v3 &
% 51.17/7.58 | | sdtasdt0(all_72_0, xc) = v2 & sdtasdt0(xc, v0) = all_50_0 &
% 51.17/7.58 | | sdtpldt0(v2, v3) = v1 & sdtpldt0(all_72_0, all_168_0) = v0 &
% 51.17/7.58 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_50_0))
% 51.17/7.58 | |
% 51.17/7.58 | | GROUND_INST: instantiating (mAMDistr) with xc, all_58_0, all_168_0,
% 51.17/7.58 | | all_50_4, all_50_1, all_50_0, simplifying with (7), (8), (27),
% 51.17/7.58 | | (28), (29), (101), (105), (106), (107) gives:
% 51.17/7.58 | | (111) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 51.17/7.58 | | (sdtasdt0(v0, xc) = v1 & sdtasdt0(all_168_0, xc) = v3 &
% 51.17/7.58 | | sdtasdt0(all_58_0, xc) = v2 & sdtasdt0(xc, v0) = all_50_0 &
% 51.17/7.58 | | sdtpldt0(v2, v3) = v1 & sdtpldt0(all_58_0, all_168_0) = v0 &
% 51.17/7.58 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_50_0))
% 51.17/7.58 | |
% 51.17/7.58 | | GROUND_INST: instantiating (mMulComm) with xc, all_168_0, all_50_1,
% 51.17/7.58 | | simplifying with (7), (8), (105), (106), (107) gives:
% 51.17/7.58 | | (112) sdtasdt0(all_168_0, xc) = all_50_1 & $i(all_50_1)
% 51.17/7.58 | |
% 51.17/7.58 | | ALPHA: (112) implies:
% 51.17/7.58 | | (113) sdtasdt0(all_168_0, xc) = all_50_1
% 51.17/7.58 | |
% 51.17/7.58 | | DELTA: instantiating (110) with fresh symbols all_178_0, all_178_1,
% 51.17/7.58 | | all_178_2, all_178_3 gives:
% 51.17/7.58 | | (114) sdtasdt0(all_178_3, xc) = all_178_2 & sdtasdt0(all_168_0, xc) =
% 51.17/7.58 | | all_178_0 & sdtasdt0(all_72_0, xc) = all_178_1 & sdtasdt0(xc,
% 51.17/7.58 | | all_178_3) = all_50_0 & sdtpldt0(all_178_1, all_178_0) =
% 51.17/7.58 | | all_178_2 & sdtpldt0(all_72_0, all_168_0) = all_178_3 &
% 51.17/7.58 | | $i(all_178_0) & $i(all_178_1) & $i(all_178_2) & $i(all_178_3) &
% 51.17/7.58 | | $i(all_50_0)
% 51.17/7.58 | |
% 51.17/7.58 | | ALPHA: (114) implies:
% 51.17/7.58 | | (115) sdtpldt0(all_72_0, all_168_0) = all_178_3
% 51.17/7.58 | | (116) sdtpldt0(all_178_1, all_178_0) = all_178_2
% 51.17/7.58 | | (117) sdtasdt0(all_72_0, xc) = all_178_1
% 51.17/7.59 | | (118) sdtasdt0(all_168_0, xc) = all_178_0
% 51.17/7.59 | | (119) sdtasdt0(all_178_3, xc) = all_178_2
% 51.17/7.59 | |
% 51.17/7.59 | | DELTA: instantiating (111) with fresh symbols all_180_0, all_180_1,
% 51.17/7.59 | | all_180_2, all_180_3 gives:
% 51.17/7.59 | | (120) sdtasdt0(all_180_3, xc) = all_180_2 & sdtasdt0(all_168_0, xc) =
% 51.17/7.59 | | all_180_0 & sdtasdt0(all_58_0, xc) = all_180_1 & sdtasdt0(xc,
% 51.17/7.59 | | all_180_3) = all_50_0 & sdtpldt0(all_180_1, all_180_0) =
% 51.17/7.59 | | all_180_2 & sdtpldt0(all_58_0, all_168_0) = all_180_3 &
% 51.17/7.59 | | $i(all_180_0) & $i(all_180_1) & $i(all_180_2) & $i(all_180_3) &
% 51.17/7.59 | | $i(all_50_0)
% 51.17/7.59 | |
% 51.17/7.59 | | ALPHA: (120) implies:
% 51.17/7.59 | | (121) sdtpldt0(all_58_0, all_168_0) = all_180_3
% 51.17/7.59 | | (122) sdtpldt0(all_180_1, all_180_0) = all_180_2
% 51.17/7.59 | | (123) sdtasdt0(all_58_0, xc) = all_180_1
% 51.17/7.59 | | (124) sdtasdt0(all_168_0, xc) = all_180_0
% 51.17/7.59 | |
% 51.17/7.59 | | GROUND_INST: instantiating (11) with all_50_4, all_180_1, xc, all_58_0,
% 51.17/7.59 | | simplifying with (31), (123) gives:
% 51.17/7.59 | | (125) all_180_1 = all_50_4
% 51.17/7.59 | |
% 51.17/7.59 | | GROUND_INST: instantiating (11) with all_50_4, all_178_1, xc, all_72_0,
% 51.17/7.59 | | simplifying with (40), (117) gives:
% 51.17/7.59 | | (126) all_178_1 = all_50_4
% 51.17/7.59 | |
% 51.17/7.59 | | GROUND_INST: instantiating (11) with all_178_0, all_180_0, xc, all_168_0,
% 51.17/7.59 | | simplifying with (118), (124) gives:
% 51.17/7.59 | | (127) all_180_0 = all_178_0
% 51.17/7.59 | |
% 51.17/7.59 | | GROUND_INST: instantiating (11) with all_50_1, all_180_0, xc, all_168_0,
% 51.17/7.59 | | simplifying with (113), (124) gives:
% 51.17/7.59 | | (128) all_180_0 = all_50_1
% 51.17/7.59 | |
% 51.17/7.59 | | COMBINE_EQS: (127), (128) imply:
% 51.17/7.59 | | (129) all_178_0 = all_50_1
% 51.17/7.59 | |
% 51.17/7.59 | | SIMP: (129) implies:
% 51.17/7.59 | | (130) all_178_0 = all_50_1
% 51.17/7.59 | |
% 51.17/7.59 | | REDUCE: (122), (125), (128) imply:
% 51.17/7.59 | | (131) sdtpldt0(all_50_4, all_50_1) = all_180_2
% 51.17/7.59 | |
% 51.17/7.59 | | REDUCE: (116), (126), (130) imply:
% 51.17/7.59 | | (132) sdtpldt0(all_50_4, all_50_1) = all_178_2
% 51.17/7.59 | |
% 51.17/7.59 | | GROUND_INST: instantiating (10) with all_50_0, all_180_2, all_50_1,
% 51.17/7.59 | | all_50_4, simplifying with (101), (131) gives:
% 51.17/7.59 | | (133) all_180_2 = all_50_0
% 51.17/7.59 | |
% 51.17/7.59 | | GROUND_INST: instantiating (10) with all_178_2, all_180_2, all_50_1,
% 51.17/7.59 | | all_50_4, simplifying with (131), (132) gives:
% 51.17/7.59 | | (134) all_180_2 = all_178_2
% 51.17/7.59 | |
% 51.17/7.59 | | COMBINE_EQS: (133), (134) imply:
% 51.17/7.59 | | (135) all_178_2 = all_50_0
% 51.17/7.59 | |
% 51.17/7.59 | | REDUCE: (119), (135) imply:
% 51.17/7.59 | | (136) sdtasdt0(all_178_3, xc) = all_50_0
% 51.17/7.59 | |
% 51.17/7.59 | | GROUND_INST: instantiating (mAMDistr) with xc, all_168_0, all_72_0,
% 51.17/7.59 | | all_50_1, all_50_4, all_50_0, simplifying with (7), (8), (35),
% 51.17/7.59 | | (36), (37), (105), (106), (107), (109) gives:
% 51.17/7.59 | | (137) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 51.17/7.59 | | (sdtasdt0(v0, xc) = v1 & sdtasdt0(all_168_0, xc) = v2 &
% 51.17/7.59 | | sdtasdt0(all_72_0, xc) = v3 & sdtasdt0(xc, v0) = all_50_0 &
% 51.17/7.59 | | sdtpldt0(v2, v3) = v1 & sdtpldt0(all_168_0, all_72_0) = v0 &
% 51.17/7.59 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_50_0))
% 51.17/7.59 | |
% 51.17/7.59 | | GROUND_INST: instantiating (mAMDistr) with xc, all_168_0, all_58_0,
% 51.17/7.59 | | all_50_1, all_50_4, all_50_0, simplifying with (7), (8), (27),
% 51.17/7.59 | | (28), (29), (105), (106), (107), (109) gives:
% 51.17/7.59 | | (138) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 51.17/7.59 | | (sdtasdt0(v0, xc) = v1 & sdtasdt0(all_168_0, xc) = v2 &
% 51.17/7.59 | | sdtasdt0(all_58_0, xc) = v3 & sdtasdt0(xc, v0) = all_50_0 &
% 51.17/7.59 | | sdtpldt0(v2, v3) = v1 & sdtpldt0(all_168_0, all_58_0) = v0 &
% 51.17/7.59 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_50_0))
% 51.17/7.59 | |
% 51.17/7.59 | | GROUND_INST: instantiating (mSortsB) with all_58_0, all_168_0, all_180_3,
% 51.17/7.59 | | simplifying with (27), (28), (105), (106), (121) gives:
% 51.17/7.59 | | (139) aElement0(all_180_3)
% 51.17/7.59 | |
% 51.17/7.59 | | GROUND_INST: instantiating (mAddComm) with all_58_0, all_168_0, all_180_3,
% 51.17/7.59 | | simplifying with (27), (28), (105), (106), (121) gives:
% 51.17/7.59 | | (140) sdtpldt0(all_168_0, all_58_0) = all_180_3 & $i(all_180_3)
% 51.17/7.59 | |
% 51.17/7.59 | | ALPHA: (140) implies:
% 51.17/7.59 | | (141) sdtpldt0(all_168_0, all_58_0) = all_180_3
% 51.17/7.59 | |
% 51.17/7.59 | | GROUND_INST: instantiating (mAddComm) with all_72_0, all_168_0, all_178_3,
% 51.17/7.59 | | simplifying with (35), (36), (105), (106), (115) gives:
% 51.17/7.59 | | (142) sdtpldt0(all_168_0, all_72_0) = all_178_3 & $i(all_178_3)
% 51.17/7.59 | |
% 51.17/7.59 | | ALPHA: (142) implies:
% 51.17/7.59 | | (143) sdtpldt0(all_168_0, all_72_0) = all_178_3
% 51.17/7.59 | |
% 51.17/7.59 | | DELTA: instantiating (138) with fresh symbols all_206_0, all_206_1,
% 51.17/7.59 | | all_206_2, all_206_3 gives:
% 51.17/7.59 | | (144) sdtasdt0(all_206_3, xc) = all_206_2 & sdtasdt0(all_168_0, xc) =
% 51.17/7.59 | | all_206_1 & sdtasdt0(all_58_0, xc) = all_206_0 & sdtasdt0(xc,
% 51.17/7.59 | | all_206_3) = all_50_0 & sdtpldt0(all_206_1, all_206_0) =
% 51.17/7.59 | | all_206_2 & sdtpldt0(all_168_0, all_58_0) = all_206_3 &
% 51.17/7.59 | | $i(all_206_0) & $i(all_206_1) & $i(all_206_2) & $i(all_206_3) &
% 51.17/7.59 | | $i(all_50_0)
% 51.17/7.59 | |
% 51.17/7.59 | | ALPHA: (144) implies:
% 51.17/7.59 | | (145) $i(all_206_3)
% 51.17/7.59 | | (146) $i(all_206_2)
% 51.17/7.59 | | (147) sdtpldt0(all_168_0, all_58_0) = all_206_3
% 51.17/7.59 | | (148) sdtpldt0(all_206_1, all_206_0) = all_206_2
% 51.17/7.59 | | (149) sdtasdt0(xc, all_206_3) = all_50_0
% 51.17/7.59 | | (150) sdtasdt0(all_58_0, xc) = all_206_0
% 51.17/7.59 | | (151) sdtasdt0(all_168_0, xc) = all_206_1
% 51.17/7.59 | |
% 51.17/7.59 | | DELTA: instantiating (137) with fresh symbols all_208_0, all_208_1,
% 51.17/7.59 | | all_208_2, all_208_3 gives:
% 51.17/7.59 | | (152) sdtasdt0(all_208_3, xc) = all_208_2 & sdtasdt0(all_168_0, xc) =
% 51.17/7.59 | | all_208_1 & sdtasdt0(all_72_0, xc) = all_208_0 & sdtasdt0(xc,
% 51.17/7.59 | | all_208_3) = all_50_0 & sdtpldt0(all_208_1, all_208_0) =
% 51.17/7.59 | | all_208_2 & sdtpldt0(all_168_0, all_72_0) = all_208_3 &
% 51.17/7.59 | | $i(all_208_0) & $i(all_208_1) & $i(all_208_2) & $i(all_208_3) &
% 51.17/7.59 | | $i(all_50_0)
% 51.17/7.59 | |
% 51.17/7.59 | | ALPHA: (152) implies:
% 51.17/7.59 | | (153) sdtpldt0(all_168_0, all_72_0) = all_208_3
% 51.17/7.59 | | (154) sdtpldt0(all_208_1, all_208_0) = all_208_2
% 51.17/7.59 | | (155) sdtasdt0(all_72_0, xc) = all_208_0
% 51.17/7.59 | | (156) sdtasdt0(all_168_0, xc) = all_208_1
% 51.17/7.59 | | (157) sdtasdt0(all_208_3, xc) = all_208_2
% 51.17/7.59 | |
% 51.17/7.59 | | GROUND_INST: instantiating (10) with all_180_3, all_206_3, all_58_0,
% 51.17/7.59 | | all_168_0, simplifying with (141), (147) gives:
% 51.17/7.59 | | (158) all_206_3 = all_180_3
% 51.17/7.59 | |
% 51.17/7.59 | | GROUND_INST: instantiating (10) with all_178_3, all_208_3, all_72_0,
% 51.17/7.59 | | all_168_0, simplifying with (143), (153) gives:
% 51.17/7.59 | | (159) all_208_3 = all_178_3
% 51.17/7.59 | |
% 51.17/7.59 | | GROUND_INST: instantiating (11) with all_50_4, all_206_0, xc, all_58_0,
% 51.17/7.59 | | simplifying with (31), (150) gives:
% 51.17/7.59 | | (160) all_206_0 = all_50_4
% 51.17/7.59 | |
% 51.17/7.59 | | GROUND_INST: instantiating (11) with all_50_4, all_208_0, xc, all_72_0,
% 51.17/7.59 | | simplifying with (40), (155) gives:
% 51.17/7.59 | | (161) all_208_0 = all_50_4
% 51.17/7.59 | |
% 51.17/7.59 | | GROUND_INST: instantiating (11) with all_50_1, all_208_1, xc, all_168_0,
% 51.17/7.59 | | simplifying with (113), (156) gives:
% 51.17/7.59 | | (162) all_208_1 = all_50_1
% 51.17/7.59 | |
% 51.17/7.60 | | GROUND_INST: instantiating (11) with all_206_1, all_208_1, xc, all_168_0,
% 51.17/7.60 | | simplifying with (151), (156) gives:
% 51.17/7.60 | | (163) all_208_1 = all_206_1
% 51.17/7.60 | |
% 51.17/7.60 | | COMBINE_EQS: (162), (163) imply:
% 51.17/7.60 | | (164) all_206_1 = all_50_1
% 51.17/7.60 | |
% 51.17/7.60 | | REDUCE: (157), (159) imply:
% 51.17/7.60 | | (165) sdtasdt0(all_178_3, xc) = all_208_2
% 51.17/7.60 | |
% 51.17/7.60 | | REDUCE: (149), (158) imply:
% 51.17/7.60 | | (166) sdtasdt0(xc, all_180_3) = all_50_0
% 51.17/7.60 | |
% 51.17/7.60 | | REDUCE: (154), (161), (162) imply:
% 51.17/7.60 | | (167) sdtpldt0(all_50_1, all_50_4) = all_208_2
% 51.17/7.60 | |
% 51.17/7.60 | | REDUCE: (148), (160), (164) imply:
% 51.17/7.60 | | (168) sdtpldt0(all_50_1, all_50_4) = all_206_2
% 51.17/7.60 | |
% 51.17/7.60 | | REDUCE: (145), (158) imply:
% 51.17/7.60 | | (169) $i(all_180_3)
% 51.17/7.60 | |
% 51.17/7.60 | | GROUND_INST: instantiating (10) with all_206_2, all_208_2, all_50_4,
% 51.17/7.60 | | all_50_1, simplifying with (167), (168) gives:
% 51.17/7.60 | | (170) all_208_2 = all_206_2
% 51.17/7.60 | |
% 51.17/7.60 | | GROUND_INST: instantiating (11) with all_50_0, all_208_2, xc, all_178_3,
% 51.17/7.60 | | simplifying with (136), (165) gives:
% 51.17/7.60 | | (171) all_208_2 = all_50_0
% 51.17/7.60 | |
% 51.17/7.60 | | COMBINE_EQS: (170), (171) imply:
% 51.17/7.60 | | (172) all_206_2 = all_50_0
% 51.17/7.60 | |
% 51.17/7.60 | | SIMP: (172) implies:
% 51.17/7.60 | | (173) all_206_2 = all_50_0
% 51.17/7.60 | |
% 51.17/7.60 | | REDUCE: (146), (173) imply:
% 51.17/7.60 | | (174) $i(all_50_0)
% 51.17/7.60 | |
% 51.17/7.60 | | GROUND_INST: instantiating (6) with xc, all_36_0, all_50_0, all_180_3,
% 51.17/7.60 | | simplifying with (7), (8), (14), (15), (99), (139), (166),
% 51.17/7.60 | | (169), (174) gives:
% 51.17/7.60 | | (175) $false
% 51.17/7.60 | |
% 51.17/7.60 | | CLOSE: (175) is inconsistent.
% 51.17/7.60 | |
% 51.17/7.60 | End of split
% 51.17/7.60 |
% 51.17/7.60 End of proof
% 51.17/7.60 % SZS output end Proof for theBenchmark
% 51.17/7.60
% 51.17/7.60 6995ms
%------------------------------------------------------------------------------