TSTP Solution File: NUM467+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM467+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n015.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 11:47:56 EDT 2023
% Result : Theorem 11.86s 2.41s
% Output : Proof 18.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM467+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.34 % Computer : n015.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Fri Aug 25 15:48:22 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.49/1.23 Prover 4: Preprocessing ...
% 3.49/1.23 Prover 1: Preprocessing ...
% 3.80/1.27 Prover 3: Preprocessing ...
% 3.80/1.27 Prover 6: Preprocessing ...
% 3.80/1.27 Prover 2: Preprocessing ...
% 3.80/1.27 Prover 0: Preprocessing ...
% 3.80/1.28 Prover 5: Preprocessing ...
% 8.70/1.95 Prover 1: Constructing countermodel ...
% 8.98/1.99 Prover 3: Constructing countermodel ...
% 8.98/2.04 Prover 6: Proving ...
% 9.52/2.05 Prover 5: Constructing countermodel ...
% 9.74/2.26 Prover 2: Proving ...
% 11.34/2.34 Prover 4: Constructing countermodel ...
% 11.86/2.41 Prover 3: proved (1768ms)
% 11.86/2.41
% 11.86/2.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.86/2.41
% 11.86/2.41 Prover 5: stopped
% 11.86/2.42 Prover 6: stopped
% 11.86/2.42 Prover 2: stopped
% 11.86/2.43 Prover 0: Proving ...
% 11.86/2.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.86/2.43 Prover 0: stopped
% 11.86/2.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.86/2.45 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.86/2.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.86/2.45 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.92/2.52 Prover 8: Preprocessing ...
% 13.00/2.53 Prover 10: Preprocessing ...
% 13.00/2.53 Prover 13: Preprocessing ...
% 13.00/2.54 Prover 7: Preprocessing ...
% 13.00/2.56 Prover 11: Preprocessing ...
% 14.18/2.71 Prover 10: Constructing countermodel ...
% 14.18/2.74 Prover 8: Warning: ignoring some quantifiers
% 14.18/2.74 Prover 8: Constructing countermodel ...
% 14.18/2.76 Prover 7: Constructing countermodel ...
% 14.95/2.80 Prover 13: Constructing countermodel ...
% 17.07/3.08 Prover 11: Constructing countermodel ...
% 17.58/3.16 Prover 1: Found proof (size 200)
% 17.58/3.16 Prover 1: proved (2527ms)
% 17.58/3.16 Prover 11: stopped
% 17.58/3.16 Prover 4: stopped
% 17.58/3.16 Prover 8: stopped
% 17.58/3.16 Prover 13: stopped
% 17.58/3.16 Prover 10: stopped
% 17.58/3.16 Prover 7: stopped
% 17.58/3.16
% 17.58/3.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.58/3.16
% 17.58/3.19 % SZS output start Proof for theBenchmark
% 17.58/3.19 Assumptions after simplification:
% 17.58/3.19 ---------------------------------
% 17.58/3.19
% 17.58/3.19 (mAMDistr)
% 17.94/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.94/3.22 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~
% 17.94/3.22 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] :
% 17.94/3.22 ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ?
% 17.94/3.22 [v12: $i] : ? [v13: $i] : ? [v14: $i] : (sdtasdt0(v9, v0) = v11 &
% 17.94/3.22 sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v9) = v10 &
% 17.94/3.22 sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9 & aNaturalNumber0(v2) =
% 17.94/3.22 v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & $i(v14) &
% 17.94/3.22 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & ( ~ (v8 = 0) | ~ (v7 =
% 17.94/3.22 0) | ~ (v6 = 0) | (v14 = v11 & v10 = v5))))
% 17.94/3.22
% 17.94/3.22 (mAddComm)
% 17.94/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 17.94/3.22 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 17.94/3.22 (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3
% 17.94/3.22 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 17.94/3.22
% 17.94/3.22 (mDivTrans)
% 17.94/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 17.94/3.22 (doDivides0(v0, v2) = v3) | ~ (doDivides0(v0, v1) = 0) | ~ $i(v2) | ~
% 17.94/3.22 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7:
% 17.94/3.22 any] : (doDivides0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 &
% 17.94/3.22 aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~
% 17.94/3.22 (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 17.94/3.22
% 17.94/3.22 (mMulComm)
% 17.94/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 17.94/3.22 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 17.94/3.22 (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3
% 17.94/3.22 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 17.94/3.22
% 17.94/3.22 (mSortsB)
% 17.94/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 17.94/3.22 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 17.94/3.22 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 17.94/3.22 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 17.94/3.22
% 17.94/3.22 (mSortsB_02)
% 17.94/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 17.94/3.23 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 17.94/3.23 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 17.94/3.23 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 17.94/3.23
% 17.94/3.23 (m__)
% 17.94/3.23 $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 17.94/3.23 doDivides0(xl, v0) = v1 & sdtpldt0(xm, xn) = v0 & $i(v0) & ! [v2: $i] : ( ~
% 17.94/3.23 (sdtasdt0(xl, v2) = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 17.94/3.23 aNaturalNumber0(v2) = v3)))
% 17.94/3.23
% 17.94/3.23 (m__1240)
% 17.94/3.23 aNaturalNumber0(xn) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xl) = 0 &
% 17.94/3.23 $i(xn) & $i(xm) & $i(xl)
% 17.94/3.23
% 17.94/3.23 (m__1240_04)
% 17.94/3.23 doDivides0(xl, xn) = 0 & doDivides0(xl, xm) = 0 & $i(xn) & $i(xm) & $i(xl) &
% 17.94/3.23 ? [v0: $i] : (sdtasdt0(xl, v0) = xn & aNaturalNumber0(v0) = 0 & $i(v0)) & ?
% 17.94/3.23 [v0: $i] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0) = 0 & $i(v0))
% 17.94/3.23
% 17.94/3.23 (function-axioms)
% 17.94/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.94/3.23 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0:
% 17.94/3.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.94/3.23 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & !
% 17.94/3.23 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 17.94/3.23 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & !
% 17.94/3.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.94/3.23 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0:
% 17.94/3.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.94/3.23 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 17.94/3.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.94/3.23 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 17.94/3.23 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 17.94/3.23 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.94/3.23 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1)
% 17.94/3.23 | ~ (aNaturalNumber0(v2) = v0))
% 17.94/3.23
% 17.94/3.23 Further assumptions not needed in the proof:
% 17.94/3.23 --------------------------------------------
% 17.94/3.23 mAddAsso, mAddCanc, mDefDiff, mDefDiv, mDefLE, mDefQuot, mIH, mIH_03, mLEAsym,
% 17.94/3.23 mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso,
% 17.94/3.23 mMulCanc, mNatSort, mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero,
% 17.94/3.23 m_MulUnit, m_MulZero
% 17.94/3.23
% 17.94/3.23 Those formulas are unsatisfiable:
% 17.94/3.23 ---------------------------------
% 17.94/3.23
% 17.94/3.23 Begin of proof
% 17.94/3.23 |
% 17.94/3.23 | ALPHA: (m__1240) implies:
% 17.94/3.24 | (1) aNaturalNumber0(xl) = 0
% 17.94/3.24 | (2) aNaturalNumber0(xm) = 0
% 17.94/3.24 | (3) aNaturalNumber0(xn) = 0
% 17.94/3.24 |
% 17.94/3.24 | ALPHA: (m__1240_04) implies:
% 17.94/3.24 | (4) doDivides0(xl, xm) = 0
% 17.94/3.24 | (5) doDivides0(xl, xn) = 0
% 17.94/3.24 | (6) ? [v0: $i] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0) = 0 &
% 17.94/3.24 | $i(v0))
% 17.94/3.24 | (7) ? [v0: $i] : (sdtasdt0(xl, v0) = xn & aNaturalNumber0(v0) = 0 &
% 17.94/3.24 | $i(v0))
% 17.94/3.24 |
% 17.94/3.24 | ALPHA: (m__) implies:
% 17.94/3.24 | (8) $i(xl)
% 17.94/3.24 | (9) $i(xm)
% 17.94/3.24 | (10) $i(xn)
% 17.94/3.24 | (11) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & doDivides0(xl, v0) = v1 &
% 17.94/3.24 | sdtpldt0(xm, xn) = v0 & $i(v0) & ! [v2: $i] : ( ~ (sdtasdt0(xl, v2)
% 17.94/3.24 | = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 17.94/3.24 | aNaturalNumber0(v2) = v3)))
% 17.94/3.24 |
% 17.94/3.24 | ALPHA: (function-axioms) implies:
% 17.94/3.24 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 17.94/3.24 | : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) =
% 17.94/3.24 | v0))
% 17.94/3.24 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.94/3.24 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 17.94/3.24 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.94/3.24 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 17.94/3.24 |
% 17.94/3.24 | DELTA: instantiating (6) with fresh symbol all_32_0 gives:
% 17.94/3.24 | (15) sdtasdt0(xl, all_32_0) = xm & aNaturalNumber0(all_32_0) = 0 &
% 17.94/3.24 | $i(all_32_0)
% 17.94/3.24 |
% 17.94/3.24 | ALPHA: (15) implies:
% 17.94/3.24 | (16) $i(all_32_0)
% 17.94/3.24 | (17) aNaturalNumber0(all_32_0) = 0
% 17.94/3.24 | (18) sdtasdt0(xl, all_32_0) = xm
% 17.94/3.24 |
% 17.94/3.24 | DELTA: instantiating (7) with fresh symbol all_34_0 gives:
% 17.94/3.24 | (19) sdtasdt0(xl, all_34_0) = xn & aNaturalNumber0(all_34_0) = 0 &
% 17.94/3.24 | $i(all_34_0)
% 17.94/3.24 |
% 17.94/3.24 | ALPHA: (19) implies:
% 17.94/3.24 | (20) $i(all_34_0)
% 17.94/3.24 | (21) aNaturalNumber0(all_34_0) = 0
% 17.94/3.24 | (22) sdtasdt0(xl, all_34_0) = xn
% 17.94/3.24 |
% 17.94/3.24 | DELTA: instantiating (11) with fresh symbols all_36_0, all_36_1 gives:
% 17.94/3.24 | (23) ~ (all_36_0 = 0) & doDivides0(xl, all_36_1) = all_36_0 & sdtpldt0(xm,
% 17.94/3.24 | xn) = all_36_1 & $i(all_36_1) & ! [v0: $i] : ( ~ (sdtasdt0(xl, v0)
% 17.94/3.24 | = all_36_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 17.94/3.24 | aNaturalNumber0(v0) = v1))
% 17.94/3.24 |
% 17.94/3.24 | ALPHA: (23) implies:
% 17.94/3.24 | (24) ~ (all_36_0 = 0)
% 17.94/3.24 | (25) $i(all_36_1)
% 17.94/3.24 | (26) sdtpldt0(xm, xn) = all_36_1
% 17.94/3.24 | (27) doDivides0(xl, all_36_1) = all_36_0
% 17.94/3.25 | (28) ! [v0: $i] : ( ~ (sdtasdt0(xl, v0) = all_36_1) | ~ $i(v0) | ? [v1:
% 17.94/3.25 | int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))
% 17.94/3.25 |
% 17.94/3.25 | GROUND_INST: instantiating (mAddComm) with xm, xn, all_36_1, simplifying with
% 17.94/3.25 | (9), (10), (26) gives:
% 17.94/3.25 | (29) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xn, xm) = v2 &
% 17.94/3.25 | aNaturalNumber0(xn) = v1 & aNaturalNumber0(xm) = v0 & $i(v2) & ( ~
% 17.94/3.25 | (v1 = 0) | ~ (v0 = 0) | v2 = all_36_1))
% 17.94/3.25 |
% 17.94/3.25 | GROUND_INST: instantiating (mSortsB) with xm, xn, all_36_1, simplifying with
% 17.94/3.25 | (9), (10), (26) gives:
% 17.94/3.25 | (30) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.94/3.25 | (aNaturalNumber0(all_36_1) = v2 & aNaturalNumber0(xn) = v1 &
% 17.94/3.25 | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 17.94/3.25 |
% 17.94/3.25 | GROUND_INST: instantiating (mMulComm) with xl, all_32_0, xm, simplifying with
% 17.94/3.25 | (8), (16), (18) gives:
% 17.94/3.25 | (31) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_32_0, xl) =
% 17.94/3.25 | v2 & aNaturalNumber0(all_32_0) = v1 & aNaturalNumber0(xl) = v0 &
% 17.94/3.25 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xm))
% 17.94/3.25 |
% 17.94/3.25 | GROUND_INST: instantiating (mAMDistr) with xl, all_32_0, all_34_0, xm, xn,
% 17.94/3.25 | all_36_1, simplifying with (8), (16), (18), (20), (22), (26)
% 17.94/3.25 | gives:
% 17.94/3.25 | (32) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i]
% 17.94/3.25 | : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 17.94/3.25 | (sdtasdt0(v3, xl) = v5 & sdtasdt0(all_34_0, xl) = v7 &
% 17.94/3.25 | sdtasdt0(all_32_0, xl) = v6 & sdtasdt0(xl, v3) = v4 & sdtpldt0(v6,
% 17.94/3.25 | v7) = v8 & sdtpldt0(all_32_0, all_34_0) = v3 &
% 17.94/3.25 | aNaturalNumber0(all_34_0) = v2 & aNaturalNumber0(all_32_0) = v1 &
% 17.94/3.25 | aNaturalNumber0(xl) = v0 & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 17.94/3.25 | $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v8 =
% 17.94/3.25 | v5 & v4 = all_36_1)))
% 17.94/3.25 |
% 17.94/3.25 | GROUND_INST: instantiating (mMulComm) with xl, all_34_0, xn, simplifying with
% 17.94/3.25 | (8), (20), (22) gives:
% 17.94/3.25 | (33) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_34_0, xl) =
% 17.94/3.25 | v2 & aNaturalNumber0(all_34_0) = v1 & aNaturalNumber0(xl) = v0 &
% 17.94/3.25 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xn))
% 17.94/3.25 |
% 17.94/3.25 | GROUND_INST: instantiating (mDivTrans) with xl, xn, all_36_1, all_36_0,
% 17.94/3.25 | simplifying with (5), (8), (10), (25), (27) gives:
% 17.94/3.25 | (34) all_36_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 17.94/3.25 | any] : (doDivides0(xn, all_36_1) = v3 & aNaturalNumber0(all_36_1) =
% 17.94/3.25 | v2 & aNaturalNumber0(xn) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v3 =
% 17.94/3.25 | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 17.94/3.25 |
% 17.94/3.26 | GROUND_INST: instantiating (mDivTrans) with xl, xm, all_36_1, all_36_0,
% 17.94/3.26 | simplifying with (4), (8), (9), (25), (27) gives:
% 17.94/3.26 | (35) all_36_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 17.94/3.26 | any] : (doDivides0(xm, all_36_1) = v3 & aNaturalNumber0(all_36_1) =
% 17.94/3.26 | v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v3 =
% 17.94/3.26 | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 17.94/3.26 |
% 17.94/3.26 | DELTA: instantiating (30) with fresh symbols all_44_0, all_44_1, all_44_2
% 17.94/3.26 | gives:
% 17.94/3.26 | (36) aNaturalNumber0(all_36_1) = all_44_0 & aNaturalNumber0(xn) = all_44_1
% 17.94/3.26 | & aNaturalNumber0(xm) = all_44_2 & ( ~ (all_44_1 = 0) | ~ (all_44_2 =
% 17.94/3.26 | 0) | all_44_0 = 0)
% 17.94/3.26 |
% 17.94/3.26 | ALPHA: (36) implies:
% 17.94/3.26 | (37) aNaturalNumber0(xm) = all_44_2
% 17.94/3.26 |
% 17.94/3.26 | DELTA: instantiating (33) with fresh symbols all_46_0, all_46_1, all_46_2
% 17.94/3.26 | gives:
% 17.94/3.26 | (38) sdtasdt0(all_34_0, xl) = all_46_0 & aNaturalNumber0(all_34_0) =
% 17.94/3.26 | all_46_1 & aNaturalNumber0(xl) = all_46_2 & $i(all_46_0) & ( ~
% 17.94/3.26 | (all_46_1 = 0) | ~ (all_46_2 = 0) | all_46_0 = xn)
% 17.94/3.26 |
% 17.94/3.26 | ALPHA: (38) implies:
% 17.94/3.26 | (39) aNaturalNumber0(xl) = all_46_2
% 17.94/3.26 | (40) aNaturalNumber0(all_34_0) = all_46_1
% 17.94/3.26 | (41) sdtasdt0(all_34_0, xl) = all_46_0
% 17.94/3.26 | (42) ~ (all_46_1 = 0) | ~ (all_46_2 = 0) | all_46_0 = xn
% 17.94/3.26 |
% 17.94/3.26 | DELTA: instantiating (29) with fresh symbols all_48_0, all_48_1, all_48_2
% 17.94/3.26 | gives:
% 17.94/3.26 | (43) sdtpldt0(xn, xm) = all_48_0 & aNaturalNumber0(xn) = all_48_1 &
% 17.94/3.26 | aNaturalNumber0(xm) = all_48_2 & $i(all_48_0) & ( ~ (all_48_1 = 0) |
% 17.94/3.26 | ~ (all_48_2 = 0) | all_48_0 = all_36_1)
% 17.94/3.26 |
% 17.94/3.26 | ALPHA: (43) implies:
% 17.94/3.26 | (44) aNaturalNumber0(xm) = all_48_2
% 17.94/3.26 | (45) aNaturalNumber0(xn) = all_48_1
% 17.94/3.26 | (46) sdtpldt0(xn, xm) = all_48_0
% 17.94/3.26 | (47) ~ (all_48_1 = 0) | ~ (all_48_2 = 0) | all_48_0 = all_36_1
% 17.94/3.26 |
% 17.94/3.26 | DELTA: instantiating (31) with fresh symbols all_50_0, all_50_1, all_50_2
% 17.94/3.26 | gives:
% 17.94/3.26 | (48) sdtasdt0(all_32_0, xl) = all_50_0 & aNaturalNumber0(all_32_0) =
% 17.94/3.26 | all_50_1 & aNaturalNumber0(xl) = all_50_2 & $i(all_50_0) & ( ~
% 17.94/3.26 | (all_50_1 = 0) | ~ (all_50_2 = 0) | all_50_0 = xm)
% 17.94/3.26 |
% 17.94/3.26 | ALPHA: (48) implies:
% 17.94/3.26 | (49) aNaturalNumber0(xl) = all_50_2
% 17.94/3.26 | (50) aNaturalNumber0(all_32_0) = all_50_1
% 17.94/3.26 | (51) sdtasdt0(all_32_0, xl) = all_50_0
% 17.94/3.26 | (52) ~ (all_50_1 = 0) | ~ (all_50_2 = 0) | all_50_0 = xm
% 17.94/3.26 |
% 17.94/3.26 | DELTA: instantiating (32) with fresh symbols all_52_0, all_52_1, all_52_2,
% 17.94/3.26 | all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8 gives:
% 17.94/3.26 | (53) sdtasdt0(all_52_5, xl) = all_52_3 & sdtasdt0(all_34_0, xl) = all_52_1
% 17.94/3.26 | & sdtasdt0(all_32_0, xl) = all_52_2 & sdtasdt0(xl, all_52_5) =
% 17.94/3.26 | all_52_4 & sdtpldt0(all_52_2, all_52_1) = all_52_0 &
% 17.94/3.26 | sdtpldt0(all_32_0, all_34_0) = all_52_5 & aNaturalNumber0(all_34_0) =
% 17.94/3.26 | all_52_6 & aNaturalNumber0(all_32_0) = all_52_7 & aNaturalNumber0(xl)
% 17.94/3.26 | = all_52_8 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3)
% 17.94/3.26 | & $i(all_52_4) & $i(all_52_5) & ( ~ (all_52_6 = 0) | ~ (all_52_7 = 0)
% 17.94/3.26 | | ~ (all_52_8 = 0) | (all_52_0 = all_52_3 & all_52_4 = all_36_1))
% 17.94/3.26 |
% 17.94/3.26 | ALPHA: (53) implies:
% 17.94/3.26 | (54) $i(all_52_5)
% 17.94/3.26 | (55) aNaturalNumber0(xl) = all_52_8
% 17.94/3.26 | (56) aNaturalNumber0(all_32_0) = all_52_7
% 17.94/3.26 | (57) aNaturalNumber0(all_34_0) = all_52_6
% 17.94/3.26 | (58) sdtpldt0(all_32_0, all_34_0) = all_52_5
% 17.94/3.26 | (59) sdtpldt0(all_52_2, all_52_1) = all_52_0
% 17.94/3.27 | (60) sdtasdt0(xl, all_52_5) = all_52_4
% 17.94/3.27 | (61) sdtasdt0(all_32_0, xl) = all_52_2
% 17.94/3.27 | (62) sdtasdt0(all_34_0, xl) = all_52_1
% 17.94/3.27 | (63) sdtasdt0(all_52_5, xl) = all_52_3
% 17.94/3.27 | (64) ~ (all_52_6 = 0) | ~ (all_52_7 = 0) | ~ (all_52_8 = 0) | (all_52_0
% 17.94/3.27 | = all_52_3 & all_52_4 = all_36_1)
% 17.94/3.27 |
% 17.94/3.27 | BETA: splitting (35) gives:
% 17.94/3.27 |
% 17.94/3.27 | Case 1:
% 17.94/3.27 | |
% 18.19/3.27 | | (65) all_36_0 = 0
% 18.19/3.27 | |
% 18.19/3.27 | | REDUCE: (24), (65) imply:
% 18.19/3.27 | | (66) $false
% 18.19/3.27 | |
% 18.19/3.27 | | CLOSE: (66) is inconsistent.
% 18.19/3.27 | |
% 18.19/3.27 | Case 2:
% 18.19/3.27 | |
% 18.19/3.27 | | (67) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 18.19/3.27 | | (doDivides0(xm, all_36_1) = v3 & aNaturalNumber0(all_36_1) = v2 &
% 18.19/3.27 | | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v3 = 0)
% 18.19/3.27 | | | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 18.19/3.27 | |
% 18.19/3.27 | | DELTA: instantiating (67) with fresh symbols all_62_0, all_62_1, all_62_2,
% 18.19/3.27 | | all_62_3 gives:
% 18.19/3.27 | | (68) doDivides0(xm, all_36_1) = all_62_0 & aNaturalNumber0(all_36_1) =
% 18.19/3.27 | | all_62_1 & aNaturalNumber0(xm) = all_62_2 & aNaturalNumber0(xl) =
% 18.19/3.27 | | all_62_3 & ( ~ (all_62_0 = 0) | ~ (all_62_1 = 0) | ~ (all_62_2 =
% 18.19/3.27 | | 0) | ~ (all_62_3 = 0))
% 18.19/3.27 | |
% 18.19/3.27 | | ALPHA: (68) implies:
% 18.19/3.27 | | (69) aNaturalNumber0(xl) = all_62_3
% 18.19/3.27 | | (70) aNaturalNumber0(xm) = all_62_2
% 18.19/3.27 | |
% 18.19/3.27 | | BETA: splitting (34) gives:
% 18.19/3.27 | |
% 18.19/3.27 | | Case 1:
% 18.19/3.27 | | |
% 18.19/3.27 | | | (71) all_36_0 = 0
% 18.19/3.27 | | |
% 18.19/3.27 | | | REDUCE: (24), (71) imply:
% 18.19/3.27 | | | (72) $false
% 18.19/3.27 | | |
% 18.19/3.27 | | | CLOSE: (72) is inconsistent.
% 18.19/3.27 | | |
% 18.19/3.27 | | Case 2:
% 18.19/3.27 | | |
% 18.19/3.27 | | | (73) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 18.19/3.27 | | | (doDivides0(xn, all_36_1) = v3 & aNaturalNumber0(all_36_1) = v2 &
% 18.19/3.27 | | | aNaturalNumber0(xn) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v3 =
% 18.19/3.27 | | | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 18.19/3.27 | | |
% 18.19/3.27 | | | DELTA: instantiating (73) with fresh symbols all_67_0, all_67_1, all_67_2,
% 18.19/3.27 | | | all_67_3 gives:
% 18.19/3.27 | | | (74) doDivides0(xn, all_36_1) = all_67_0 & aNaturalNumber0(all_36_1) =
% 18.19/3.27 | | | all_67_1 & aNaturalNumber0(xn) = all_67_2 & aNaturalNumber0(xl) =
% 18.19/3.27 | | | all_67_3 & ( ~ (all_67_0 = 0) | ~ (all_67_1 = 0) | ~ (all_67_2 =
% 18.19/3.27 | | | 0) | ~ (all_67_3 = 0))
% 18.19/3.27 | | |
% 18.19/3.27 | | | ALPHA: (74) implies:
% 18.19/3.27 | | | (75) aNaturalNumber0(xl) = all_67_3
% 18.19/3.27 | | | (76) aNaturalNumber0(xn) = all_67_2
% 18.19/3.27 | | |
% 18.19/3.27 | | | GROUND_INST: instantiating (12) with all_50_2, all_52_8, xl, simplifying
% 18.19/3.27 | | | with (49), (55) gives:
% 18.19/3.27 | | | (77) all_52_8 = all_50_2
% 18.19/3.27 | | |
% 18.19/3.27 | | | GROUND_INST: instantiating (12) with 0, all_62_3, xl, simplifying with
% 18.19/3.27 | | | (1), (69) gives:
% 18.19/3.27 | | | (78) all_62_3 = 0
% 18.19/3.27 | | |
% 18.19/3.27 | | | GROUND_INST: instantiating (12) with all_52_8, all_62_3, xl, simplifying
% 18.19/3.27 | | | with (55), (69) gives:
% 18.19/3.27 | | | (79) all_62_3 = all_52_8
% 18.19/3.27 | | |
% 18.19/3.27 | | | GROUND_INST: instantiating (12) with all_52_8, all_67_3, xl, simplifying
% 18.19/3.27 | | | with (55), (75) gives:
% 18.19/3.27 | | | (80) all_67_3 = all_52_8
% 18.19/3.27 | | |
% 18.19/3.27 | | | GROUND_INST: instantiating (12) with all_46_2, all_67_3, xl, simplifying
% 18.19/3.27 | | | with (39), (75) gives:
% 18.19/3.27 | | | (81) all_67_3 = all_46_2
% 18.19/3.28 | | |
% 18.19/3.28 | | | GROUND_INST: instantiating (12) with 0, all_48_2, xm, simplifying with
% 18.19/3.28 | | | (2), (44) gives:
% 18.19/3.28 | | | (82) all_48_2 = 0
% 18.19/3.28 | | |
% 18.19/3.28 | | | GROUND_INST: instantiating (12) with all_48_2, all_62_2, xm, simplifying
% 18.19/3.28 | | | with (44), (70) gives:
% 18.19/3.28 | | | (83) all_62_2 = all_48_2
% 18.19/3.28 | | |
% 18.19/3.28 | | | GROUND_INST: instantiating (12) with all_44_2, all_62_2, xm, simplifying
% 18.19/3.28 | | | with (37), (70) gives:
% 18.19/3.28 | | | (84) all_62_2 = all_44_2
% 18.19/3.28 | | |
% 18.19/3.28 | | | GROUND_INST: instantiating (12) with 0, all_67_2, xn, simplifying with
% 18.19/3.28 | | | (3), (76) gives:
% 18.19/3.28 | | | (85) all_67_2 = 0
% 18.19/3.28 | | |
% 18.19/3.28 | | | GROUND_INST: instantiating (12) with all_48_1, all_67_2, xn, simplifying
% 18.19/3.28 | | | with (45), (76) gives:
% 18.19/3.28 | | | (86) all_67_2 = all_48_1
% 18.19/3.28 | | |
% 18.19/3.28 | | | GROUND_INST: instantiating (12) with 0, all_52_7, all_32_0, simplifying
% 18.19/3.28 | | | with (17), (56) gives:
% 18.19/3.28 | | | (87) all_52_7 = 0
% 18.19/3.28 | | |
% 18.19/3.28 | | | GROUND_INST: instantiating (12) with all_50_1, all_52_7, all_32_0,
% 18.19/3.28 | | | simplifying with (50), (56) gives:
% 18.19/3.28 | | | (88) all_52_7 = all_50_1
% 18.19/3.28 | | |
% 18.19/3.28 | | | GROUND_INST: instantiating (12) with 0, all_52_6, all_34_0, simplifying
% 18.19/3.28 | | | with (21), (57) gives:
% 18.19/3.28 | | | (89) all_52_6 = 0
% 18.19/3.28 | | |
% 18.19/3.28 | | | GROUND_INST: instantiating (12) with all_46_1, all_52_6, all_34_0,
% 18.19/3.28 | | | simplifying with (40), (57) gives:
% 18.19/3.28 | | | (90) all_52_6 = all_46_1
% 18.19/3.28 | | |
% 18.19/3.28 | | | GROUND_INST: instantiating (14) with all_50_0, all_52_2, xl, all_32_0,
% 18.19/3.28 | | | simplifying with (51), (61) gives:
% 18.19/3.28 | | | (91) all_52_2 = all_50_0
% 18.19/3.28 | | |
% 18.19/3.28 | | | GROUND_INST: instantiating (14) with all_46_0, all_52_1, xl, all_34_0,
% 18.19/3.28 | | | simplifying with (41), (62) gives:
% 18.19/3.28 | | | (92) all_52_1 = all_46_0
% 18.19/3.28 | | |
% 18.19/3.28 | | | COMBINE_EQS: (85), (86) imply:
% 18.19/3.28 | | | (93) all_48_1 = 0
% 18.19/3.28 | | |
% 18.19/3.28 | | | SIMP: (93) implies:
% 18.19/3.28 | | | (94) all_48_1 = 0
% 18.19/3.28 | | |
% 18.19/3.28 | | | COMBINE_EQS: (80), (81) imply:
% 18.19/3.28 | | | (95) all_52_8 = all_46_2
% 18.19/3.28 | | |
% 18.19/3.28 | | | SIMP: (95) implies:
% 18.19/3.28 | | | (96) all_52_8 = all_46_2
% 18.19/3.28 | | |
% 18.19/3.28 | | | COMBINE_EQS: (83), (84) imply:
% 18.19/3.28 | | | (97) all_48_2 = all_44_2
% 18.19/3.28 | | |
% 18.19/3.28 | | | SIMP: (97) implies:
% 18.19/3.28 | | | (98) all_48_2 = all_44_2
% 18.19/3.28 | | |
% 18.19/3.28 | | | COMBINE_EQS: (78), (79) imply:
% 18.19/3.28 | | | (99) all_52_8 = 0
% 18.19/3.28 | | |
% 18.19/3.28 | | | SIMP: (99) implies:
% 18.19/3.28 | | | (100) all_52_8 = 0
% 18.19/3.28 | | |
% 18.19/3.28 | | | COMBINE_EQS: (89), (90) imply:
% 18.19/3.28 | | | (101) all_46_1 = 0
% 18.19/3.28 | | |
% 18.19/3.28 | | | COMBINE_EQS: (87), (88) imply:
% 18.19/3.28 | | | (102) all_50_1 = 0
% 18.19/3.28 | | |
% 18.19/3.28 | | | SIMP: (102) implies:
% 18.19/3.28 | | | (103) all_50_1 = 0
% 18.19/3.28 | | |
% 18.19/3.28 | | | COMBINE_EQS: (77), (96) imply:
% 18.19/3.28 | | | (104) all_50_2 = all_46_2
% 18.19/3.28 | | |
% 18.19/3.28 | | | COMBINE_EQS: (77), (100) imply:
% 18.19/3.28 | | | (105) all_50_2 = 0
% 18.19/3.28 | | |
% 18.19/3.28 | | | COMBINE_EQS: (104), (105) imply:
% 18.19/3.28 | | | (106) all_46_2 = 0
% 18.19/3.28 | | |
% 18.19/3.28 | | | COMBINE_EQS: (82), (98) imply:
% 18.19/3.28 | | | (107) all_44_2 = 0
% 18.19/3.28 | | |
% 18.19/3.28 | | | REDUCE: (59), (91), (92) imply:
% 18.19/3.28 | | | (108) sdtpldt0(all_50_0, all_46_0) = all_52_0
% 18.19/3.28 | | |
% 18.19/3.28 | | | BETA: splitting (42) gives:
% 18.19/3.28 | | |
% 18.19/3.28 | | | Case 1:
% 18.19/3.28 | | | |
% 18.19/3.28 | | | | (109) ~ (all_46_1 = 0)
% 18.19/3.28 | | | |
% 18.19/3.28 | | | | REDUCE: (101), (109) imply:
% 18.19/3.28 | | | | (110) $false
% 18.19/3.28 | | | |
% 18.19/3.28 | | | | CLOSE: (110) is inconsistent.
% 18.19/3.28 | | | |
% 18.19/3.28 | | | Case 2:
% 18.19/3.28 | | | |
% 18.19/3.28 | | | | (111) ~ (all_46_2 = 0) | all_46_0 = xn
% 18.19/3.28 | | | |
% 18.19/3.28 | | | | DELTA: instantiating (7) with fresh symbol all_79_0 gives:
% 18.19/3.28 | | | | (112) sdtasdt0(xl, all_79_0) = xn & aNaturalNumber0(all_79_0) = 0 &
% 18.19/3.28 | | | | $i(all_79_0)
% 18.19/3.28 | | | |
% 18.19/3.28 | | | | ALPHA: (112) implies:
% 18.19/3.28 | | | | (113) $i(all_79_0)
% 18.19/3.28 | | | | (114) sdtasdt0(xl, all_79_0) = xn
% 18.19/3.28 | | | |
% 18.19/3.28 | | | | BETA: splitting (47) gives:
% 18.19/3.28 | | | |
% 18.19/3.28 | | | | Case 1:
% 18.19/3.28 | | | | |
% 18.19/3.28 | | | | | (115) ~ (all_48_1 = 0)
% 18.19/3.28 | | | | |
% 18.19/3.28 | | | | | REDUCE: (94), (115) imply:
% 18.19/3.28 | | | | | (116) $false
% 18.19/3.29 | | | | |
% 18.19/3.29 | | | | | CLOSE: (116) is inconsistent.
% 18.19/3.29 | | | | |
% 18.19/3.29 | | | | Case 2:
% 18.19/3.29 | | | | |
% 18.19/3.29 | | | | | (117) ~ (all_48_2 = 0) | all_48_0 = all_36_1
% 18.19/3.29 | | | | |
% 18.19/3.29 | | | | | BETA: splitting (117) gives:
% 18.19/3.29 | | | | |
% 18.19/3.29 | | | | | Case 1:
% 18.19/3.29 | | | | | |
% 18.19/3.29 | | | | | | (118) ~ (all_48_2 = 0)
% 18.19/3.29 | | | | | |
% 18.19/3.29 | | | | | | REDUCE: (82), (118) imply:
% 18.19/3.29 | | | | | | (119) $false
% 18.19/3.29 | | | | | |
% 18.19/3.29 | | | | | | CLOSE: (119) is inconsistent.
% 18.19/3.29 | | | | | |
% 18.19/3.29 | | | | | Case 2:
% 18.19/3.29 | | | | | |
% 18.19/3.29 | | | | | | (120) all_48_0 = all_36_1
% 18.19/3.29 | | | | | |
% 18.19/3.29 | | | | | | REDUCE: (46), (120) imply:
% 18.19/3.29 | | | | | | (121) sdtpldt0(xn, xm) = all_36_1
% 18.19/3.29 | | | | | |
% 18.19/3.29 | | | | | | DELTA: instantiating (6) with fresh symbol all_95_0 gives:
% 18.19/3.29 | | | | | | (122) sdtasdt0(xl, all_95_0) = xm & aNaturalNumber0(all_95_0) = 0
% 18.19/3.29 | | | | | | & $i(all_95_0)
% 18.19/3.29 | | | | | |
% 18.19/3.29 | | | | | | ALPHA: (122) implies:
% 18.19/3.29 | | | | | | (123) $i(all_95_0)
% 18.19/3.29 | | | | | | (124) sdtasdt0(xl, all_95_0) = xm
% 18.19/3.29 | | | | | |
% 18.19/3.29 | | | | | | BETA: splitting (52) gives:
% 18.19/3.29 | | | | | |
% 18.19/3.29 | | | | | | Case 1:
% 18.19/3.29 | | | | | | |
% 18.19/3.29 | | | | | | | (125) ~ (all_50_1 = 0)
% 18.19/3.29 | | | | | | |
% 18.19/3.29 | | | | | | | REDUCE: (103), (125) imply:
% 18.19/3.29 | | | | | | | (126) $false
% 18.19/3.29 | | | | | | |
% 18.19/3.29 | | | | | | | CLOSE: (126) is inconsistent.
% 18.19/3.29 | | | | | | |
% 18.19/3.29 | | | | | | Case 2:
% 18.19/3.29 | | | | | | |
% 18.19/3.29 | | | | | | | (127) ~ (all_50_2 = 0) | all_50_0 = xm
% 18.19/3.29 | | | | | | |
% 18.19/3.29 | | | | | | | BETA: splitting (127) gives:
% 18.19/3.29 | | | | | | |
% 18.19/3.29 | | | | | | | Case 1:
% 18.19/3.29 | | | | | | | |
% 18.19/3.29 | | | | | | | | (128) ~ (all_50_2 = 0)
% 18.19/3.29 | | | | | | | |
% 18.19/3.29 | | | | | | | | REDUCE: (105), (128) imply:
% 18.19/3.29 | | | | | | | | (129) $false
% 18.19/3.29 | | | | | | | |
% 18.19/3.29 | | | | | | | | CLOSE: (129) is inconsistent.
% 18.19/3.29 | | | | | | | |
% 18.19/3.29 | | | | | | | Case 2:
% 18.19/3.29 | | | | | | | |
% 18.19/3.29 | | | | | | | | (130) all_50_0 = xm
% 18.19/3.29 | | | | | | | |
% 18.19/3.29 | | | | | | | | REDUCE: (108), (130) imply:
% 18.19/3.29 | | | | | | | | (131) sdtpldt0(xm, all_46_0) = all_52_0
% 18.19/3.29 | | | | | | | |
% 18.19/3.29 | | | | | | | | BETA: splitting (111) gives:
% 18.19/3.29 | | | | | | | |
% 18.19/3.29 | | | | | | | | Case 1:
% 18.19/3.29 | | | | | | | | |
% 18.19/3.29 | | | | | | | | | (132) ~ (all_46_2 = 0)
% 18.19/3.29 | | | | | | | | |
% 18.19/3.29 | | | | | | | | | REDUCE: (106), (132) imply:
% 18.19/3.29 | | | | | | | | | (133) $false
% 18.19/3.29 | | | | | | | | |
% 18.19/3.29 | | | | | | | | | CLOSE: (133) is inconsistent.
% 18.19/3.29 | | | | | | | | |
% 18.19/3.29 | | | | | | | | Case 2:
% 18.19/3.29 | | | | | | | | |
% 18.19/3.29 | | | | | | | | | (134) all_46_0 = xn
% 18.19/3.29 | | | | | | | | |
% 18.19/3.29 | | | | | | | | | REDUCE: (131), (134) imply:
% 18.19/3.29 | | | | | | | | | (135) sdtpldt0(xm, xn) = all_52_0
% 18.19/3.29 | | | | | | | | |
% 18.19/3.29 | | | | | | | | | BETA: splitting (64) gives:
% 18.19/3.29 | | | | | | | | |
% 18.19/3.29 | | | | | | | | | Case 1:
% 18.19/3.29 | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | (136) ~ (all_52_6 = 0)
% 18.19/3.29 | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | REDUCE: (89), (136) imply:
% 18.19/3.29 | | | | | | | | | | (137) $false
% 18.19/3.29 | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | CLOSE: (137) is inconsistent.
% 18.19/3.29 | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | Case 2:
% 18.19/3.29 | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | (138) ~ (all_52_7 = 0) | ~ (all_52_8 = 0) | (all_52_0 =
% 18.19/3.29 | | | | | | | | | | all_52_3 & all_52_4 = all_36_1)
% 18.19/3.29 | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | BETA: splitting (138) gives:
% 18.19/3.29 | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | Case 1:
% 18.19/3.29 | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | (139) ~ (all_52_7 = 0)
% 18.19/3.29 | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | REDUCE: (87), (139) imply:
% 18.19/3.29 | | | | | | | | | | | (140) $false
% 18.19/3.29 | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | CLOSE: (140) is inconsistent.
% 18.19/3.29 | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | Case 2:
% 18.19/3.29 | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | (141) ~ (all_52_8 = 0) | (all_52_0 = all_52_3 &
% 18.19/3.29 | | | | | | | | | | | all_52_4 = all_36_1)
% 18.19/3.29 | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | BETA: splitting (141) gives:
% 18.19/3.29 | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | Case 1:
% 18.19/3.29 | | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | | (142) ~ (all_52_8 = 0)
% 18.19/3.29 | | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | | REDUCE: (100), (142) imply:
% 18.19/3.29 | | | | | | | | | | | | (143) $false
% 18.19/3.29 | | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | | CLOSE: (143) is inconsistent.
% 18.19/3.29 | | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | Case 2:
% 18.19/3.29 | | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | | (144) all_52_0 = all_52_3 & all_52_4 = all_36_1
% 18.19/3.29 | | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | | ALPHA: (144) implies:
% 18.19/3.29 | | | | | | | | | | | | (145) all_52_4 = all_36_1
% 18.19/3.29 | | | | | | | | | | | | (146) all_52_0 = all_52_3
% 18.19/3.29 | | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | | REDUCE: (60), (145) imply:
% 18.19/3.29 | | | | | | | | | | | | (147) sdtasdt0(xl, all_52_5) = all_36_1
% 18.19/3.29 | | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | | REDUCE: (135), (146) imply:
% 18.19/3.29 | | | | | | | | | | | | (148) sdtpldt0(xm, xn) = all_52_3
% 18.19/3.29 | | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_36_1, all_52_3, xn,
% 18.19/3.29 | | | | | | | | | | | | xm, simplifying with (26), (148) gives:
% 18.19/3.29 | | | | | | | | | | | | (149) all_52_3 = all_36_1
% 18.19/3.29 | | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | | REDUCE: (63), (149) imply:
% 18.19/3.29 | | | | | | | | | | | | (150) sdtasdt0(all_52_5, xl) = all_36_1
% 18.19/3.29 | | | | | | | | | | | |
% 18.19/3.29 | | | | | | | | | | | | GROUND_INST: instantiating (mAMDistr) with xl, all_34_0,
% 18.19/3.29 | | | | | | | | | | | | all_32_0, xn, xm, all_36_1, simplifying with (8),
% 18.19/3.29 | | | | | | | | | | | | (16), (18), (20), (22), (121) gives:
% 18.19/3.30 | | | | | | | | | | | | (151) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 18.19/3.30 | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 18.19/3.30 | | | | | | | | | | | | : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v3, xl) =
% 18.19/3.30 | | | | | | | | | | | | v5 & sdtasdt0(all_34_0, xl) = v6 &
% 18.19/3.30 | | | | | | | | | | | | sdtasdt0(all_32_0, xl) = v7 & sdtasdt0(xl, v3) =
% 18.19/3.30 | | | | | | | | | | | | v4 & sdtpldt0(v6, v7) = v8 & sdtpldt0(all_34_0,
% 18.19/3.30 | | | | | | | | | | | | all_32_0) = v3 & aNaturalNumber0(all_34_0) =
% 18.19/3.30 | | | | | | | | | | | | v1 & aNaturalNumber0(all_32_0) = v2 &
% 18.19/3.30 | | | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v8) & $i(v7) &
% 18.19/3.30 | | | | | | | | | | | | $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0)
% 18.19/3.30 | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0) | (v8 = v5 & v4 =
% 18.19/3.30 | | | | | | | | | | | | all_36_1)))
% 18.19/3.30 | | | | | | | | | | | |
% 18.19/3.30 | | | | | | | | | | | | GROUND_INST: instantiating (mAddComm) with all_32_0, all_34_0,
% 18.19/3.30 | | | | | | | | | | | | all_52_5, simplifying with (16), (20), (58) gives:
% 18.19/3.30 | | | | | | | | | | | | (152) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 18.19/3.30 | | | | | | | | | | | | (sdtpldt0(all_34_0, all_32_0) = v2 &
% 18.19/3.30 | | | | | | | | | | | | aNaturalNumber0(all_34_0) = v1 &
% 18.19/3.30 | | | | | | | | | | | | aNaturalNumber0(all_32_0) = v0 & $i(v2) & ( ~
% 18.19/3.30 | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v2 = all_52_5))
% 18.19/3.30 | | | | | | | | | | | |
% 18.19/3.30 | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB) with all_32_0, all_34_0,
% 18.19/3.30 | | | | | | | | | | | | all_52_5, simplifying with (16), (20), (58) gives:
% 18.19/3.30 | | | | | | | | | | | | (153) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 18.19/3.30 | | | | | | | | | | | | (aNaturalNumber0(all_52_5) = v2 &
% 18.19/3.30 | | | | | | | | | | | | aNaturalNumber0(all_34_0) = v1 &
% 18.19/3.30 | | | | | | | | | | | | aNaturalNumber0(all_32_0) = v0 & ( ~ (v1 = 0) |
% 18.19/3.30 | | | | | | | | | | | | ~ (v0 = 0) | v2 = 0))
% 18.19/3.30 | | | | | | | | | | | |
% 18.19/3.30 | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_52_5, simplifying with
% 18.19/3.30 | | | | | | | | | | | | (54), (147) gives:
% 18.19/3.30 | | | | | | | | | | | | (154) ? [v0: int] : ( ~ (v0 = 0) &
% 18.19/3.30 | | | | | | | | | | | | aNaturalNumber0(all_52_5) = v0)
% 18.19/3.30 | | | | | | | | | | | |
% 18.19/3.30 | | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xl, all_52_5,
% 18.19/3.30 | | | | | | | | | | | | all_36_1, simplifying with (8), (54), (147) gives:
% 18.19/3.30 | | | | | | | | | | | | (155) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 18.19/3.30 | | | | | | | | | | | | (sdtasdt0(all_52_5, xl) = v2 &
% 18.19/3.30 | | | | | | | | | | | | aNaturalNumber0(all_52_5) = v1 &
% 18.19/3.30 | | | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ (v1 = 0)
% 18.19/3.30 | | | | | | | | | | | | | ~ (v0 = 0) | v2 = all_36_1))
% 18.19/3.30 | | | | | | | | | | | |
% 18.19/3.30 | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with xl, all_52_5,
% 18.19/3.30 | | | | | | | | | | | | all_36_1, simplifying with (8), (54), (147) gives:
% 18.19/3.30 | | | | | | | | | | | | (156) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 18.19/3.30 | | | | | | | | | | | | (aNaturalNumber0(all_52_5) = v1 &
% 18.19/3.30 | | | | | | | | | | | | aNaturalNumber0(all_36_1) = v2 &
% 18.19/3.30 | | | | | | | | | | | | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0
% 18.19/3.30 | | | | | | | | | | | | = 0) | v2 = 0))
% 18.19/3.30 | | | | | | | | | | | |
% 18.19/3.30 | | | | | | | | | | | | GROUND_INST: instantiating (mAMDistr) with xl, all_32_0,
% 18.19/3.30 | | | | | | | | | | | | all_79_0, xm, xn, all_36_1, simplifying with (8),
% 18.19/3.30 | | | | | | | | | | | | (16), (18), (26), (113), (114) gives:
% 18.19/3.30 | | | | | | | | | | | | (157) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 18.19/3.30 | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 18.19/3.30 | | | | | | | | | | | | : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v3, xl) =
% 18.19/3.30 | | | | | | | | | | | | v5 & sdtasdt0(all_79_0, xl) = v7 &
% 18.19/3.30 | | | | | | | | | | | | sdtasdt0(all_32_0, xl) = v6 & sdtasdt0(xl, v3) =
% 18.19/3.30 | | | | | | | | | | | | v4 & sdtpldt0(v6, v7) = v8 & sdtpldt0(all_32_0,
% 18.19/3.30 | | | | | | | | | | | | all_79_0) = v3 & aNaturalNumber0(all_79_0) =
% 18.19/3.30 | | | | | | | | | | | | v2 & aNaturalNumber0(all_32_0) = v1 &
% 18.19/3.30 | | | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v8) & $i(v7) &
% 18.19/3.30 | | | | | | | | | | | | $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0)
% 18.19/3.30 | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0) | (v8 = v5 & v4 =
% 18.19/3.30 | | | | | | | | | | | | all_36_1)))
% 18.19/3.30 | | | | | | | | | | | |
% 18.19/3.30 | | | | | | | | | | | | GROUND_INST: instantiating (mAMDistr) with xl, all_79_0,
% 18.19/3.30 | | | | | | | | | | | | all_32_0, xn, xm, all_36_1, simplifying with (8),
% 18.19/3.30 | | | | | | | | | | | | (16), (18), (113), (114), (121) gives:
% 18.19/3.30 | | | | | | | | | | | | (158) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 18.19/3.30 | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 18.19/3.30 | | | | | | | | | | | | : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v3, xl) =
% 18.19/3.30 | | | | | | | | | | | | v5 & sdtasdt0(all_79_0, xl) = v6 &
% 18.19/3.30 | | | | | | | | | | | | sdtasdt0(all_32_0, xl) = v7 & sdtasdt0(xl, v3) =
% 18.19/3.30 | | | | | | | | | | | | v4 & sdtpldt0(v6, v7) = v8 & sdtpldt0(all_79_0,
% 18.19/3.30 | | | | | | | | | | | | all_32_0) = v3 & aNaturalNumber0(all_79_0) =
% 18.19/3.30 | | | | | | | | | | | | v1 & aNaturalNumber0(all_32_0) = v2 &
% 18.19/3.30 | | | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v8) & $i(v7) &
% 18.19/3.30 | | | | | | | | | | | | $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0)
% 18.19/3.30 | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0) | (v8 = v5 & v4 =
% 18.19/3.30 | | | | | | | | | | | | all_36_1)))
% 18.19/3.30 | | | | | | | | | | | |
% 18.19/3.31 | | | | | | | | | | | | GROUND_INST: instantiating (mAMDistr) with xl, all_95_0,
% 18.19/3.31 | | | | | | | | | | | | all_34_0, xm, xn, all_36_1, simplifying with (8),
% 18.19/3.31 | | | | | | | | | | | | (20), (22), (26), (123), (124) gives:
% 18.19/3.31 | | | | | | | | | | | | (159) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 18.19/3.31 | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 18.19/3.31 | | | | | | | | | | | | : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v3, xl) =
% 18.19/3.31 | | | | | | | | | | | | v5 & sdtasdt0(all_95_0, xl) = v6 &
% 18.19/3.31 | | | | | | | | | | | | sdtasdt0(all_34_0, xl) = v7 & sdtasdt0(xl, v3) =
% 18.19/3.31 | | | | | | | | | | | | v4 & sdtpldt0(v6, v7) = v8 & sdtpldt0(all_95_0,
% 18.19/3.31 | | | | | | | | | | | | all_34_0) = v3 & aNaturalNumber0(all_95_0) =
% 18.19/3.31 | | | | | | | | | | | | v1 & aNaturalNumber0(all_34_0) = v2 &
% 18.19/3.31 | | | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v8) & $i(v7) &
% 18.19/3.31 | | | | | | | | | | | | $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0)
% 18.19/3.31 | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0) | (v8 = v5 & v4 =
% 18.19/3.31 | | | | | | | | | | | | all_36_1)))
% 18.19/3.31 | | | | | | | | | | | |
% 18.19/3.31 | | | | | | | | | | | | GROUND_INST: instantiating (mAMDistr) with xl, all_34_0,
% 18.19/3.31 | | | | | | | | | | | | all_95_0, xn, xm, all_36_1, simplifying with (8),
% 18.19/3.31 | | | | | | | | | | | | (20), (22), (121), (123), (124) gives:
% 18.19/3.31 | | | | | | | | | | | | (160) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 18.19/3.31 | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 18.19/3.31 | | | | | | | | | | | | : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v3, xl) =
% 18.19/3.31 | | | | | | | | | | | | v5 & sdtasdt0(all_95_0, xl) = v7 &
% 18.19/3.31 | | | | | | | | | | | | sdtasdt0(all_34_0, xl) = v6 & sdtasdt0(xl, v3) =
% 18.19/3.31 | | | | | | | | | | | | v4 & sdtpldt0(v6, v7) = v8 & sdtpldt0(all_34_0,
% 18.19/3.31 | | | | | | | | | | | | all_95_0) = v3 & aNaturalNumber0(all_95_0) =
% 18.19/3.31 | | | | | | | | | | | | v2 & aNaturalNumber0(all_34_0) = v1 &
% 18.19/3.31 | | | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v8) & $i(v7) &
% 18.19/3.31 | | | | | | | | | | | | $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0)
% 18.19/3.31 | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0) | (v8 = v5 & v4 =
% 18.19/3.31 | | | | | | | | | | | | all_36_1)))
% 18.19/3.31 | | | | | | | | | | | |
% 18.19/3.31 | | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with all_52_5, xl,
% 18.19/3.31 | | | | | | | | | | | | all_36_1, simplifying with (8), (54), (150) gives:
% 18.19/3.31 | | | | | | | | | | | | (161) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 18.19/3.31 | | | | | | | | | | | | (sdtasdt0(xl, all_52_5) = v2 &
% 18.19/3.31 | | | | | | | | | | | | aNaturalNumber0(all_52_5) = v0 &
% 18.19/3.31 | | | | | | | | | | | | aNaturalNumber0(xl) = v1 & $i(v2) & ( ~ (v1 = 0)
% 18.19/3.31 | | | | | | | | | | | | | ~ (v0 = 0) | v2 = all_36_1))
% 18.19/3.31 | | | | | | | | | | | |
% 18.19/3.31 | | | | | | | | | | | | DELTA: instantiating (154) with fresh symbol all_147_0
% 18.19/3.31 | | | | | | | | | | | | gives:
% 18.19/3.31 | | | | | | | | | | | | (162) ~ (all_147_0 = 0) & aNaturalNumber0(all_52_5) =
% 18.19/3.31 | | | | | | | | | | | | all_147_0
% 18.19/3.31 | | | | | | | | | | | |
% 18.19/3.31 | | | | | | | | | | | | ALPHA: (162) implies:
% 18.19/3.31 | | | | | | | | | | | | (163) ~ (all_147_0 = 0)
% 18.19/3.31 | | | | | | | | | | | | (164) aNaturalNumber0(all_52_5) = all_147_0
% 18.19/3.31 | | | | | | | | | | | |
% 18.19/3.31 | | | | | | | | | | | | DELTA: instantiating (156) with fresh symbols all_151_0,
% 18.19/3.31 | | | | | | | | | | | | all_151_1, all_151_2 gives:
% 18.19/3.31 | | | | | | | | | | | | (165) aNaturalNumber0(all_52_5) = all_151_1 &
% 18.19/3.31 | | | | | | | | | | | | aNaturalNumber0(all_36_1) = all_151_0 &
% 18.19/3.31 | | | | | | | | | | | | aNaturalNumber0(xl) = all_151_2 & ( ~ (all_151_1 =
% 18.19/3.31 | | | | | | | | | | | | 0) | ~ (all_151_2 = 0) | all_151_0 = 0)
% 18.19/3.31 | | | | | | | | | | | |
% 18.19/3.31 | | | | | | | | | | | | ALPHA: (165) implies:
% 18.19/3.31 | | | | | | | | | | | | (166) aNaturalNumber0(all_52_5) = all_151_1
% 18.19/3.31 | | | | | | | | | | | |
% 18.19/3.31 | | | | | | | | | | | | DELTA: instantiating (153) with fresh symbols all_153_0,
% 18.19/3.31 | | | | | | | | | | | | all_153_1, all_153_2 gives:
% 18.19/3.31 | | | | | | | | | | | | (167) aNaturalNumber0(all_52_5) = all_153_0 &
% 18.19/3.31 | | | | | | | | | | | | aNaturalNumber0(all_34_0) = all_153_1 &
% 18.19/3.31 | | | | | | | | | | | | aNaturalNumber0(all_32_0) = all_153_2 & ( ~
% 18.19/3.31 | | | | | | | | | | | | (all_153_1 = 0) | ~ (all_153_2 = 0) | all_153_0
% 18.19/3.31 | | | | | | | | | | | | = 0)
% 18.19/3.31 | | | | | | | | | | | |
% 18.19/3.31 | | | | | | | | | | | | ALPHA: (167) implies:
% 18.19/3.31 | | | | | | | | | | | | (168) aNaturalNumber0(all_32_0) = all_153_2
% 18.19/3.31 | | | | | | | | | | | | (169) aNaturalNumber0(all_34_0) = all_153_1
% 18.19/3.31 | | | | | | | | | | | | (170) aNaturalNumber0(all_52_5) = all_153_0
% 18.19/3.31 | | | | | | | | | | | | (171) ~ (all_153_1 = 0) | ~ (all_153_2 = 0) |
% 18.19/3.31 | | | | | | | | | | | | all_153_0 = 0
% 18.19/3.31 | | | | | | | | | | | |
% 18.19/3.31 | | | | | | | | | | | | DELTA: instantiating (155) with fresh symbols all_155_0,
% 18.19/3.31 | | | | | | | | | | | | all_155_1, all_155_2 gives:
% 18.19/3.31 | | | | | | | | | | | | (172) sdtasdt0(all_52_5, xl) = all_155_0 &
% 18.19/3.31 | | | | | | | | | | | | aNaturalNumber0(all_52_5) = all_155_1 &
% 18.19/3.31 | | | | | | | | | | | | aNaturalNumber0(xl) = all_155_2 & $i(all_155_0) &
% 18.19/3.31 | | | | | | | | | | | | ( ~ (all_155_1 = 0) | ~ (all_155_2 = 0) |
% 18.19/3.31 | | | | | | | | | | | | all_155_0 = all_36_1)
% 18.19/3.31 | | | | | | | | | | | |
% 18.19/3.31 | | | | | | | | | | | | ALPHA: (172) implies:
% 18.19/3.31 | | | | | | | | | | | | (173) aNaturalNumber0(all_52_5) = all_155_1
% 18.19/3.31 | | | | | | | | | | | |
% 18.19/3.31 | | | | | | | | | | | | DELTA: instantiating (152) with fresh symbols all_157_0,
% 18.19/3.31 | | | | | | | | | | | | all_157_1, all_157_2 gives:
% 18.19/3.31 | | | | | | | | | | | | (174) sdtpldt0(all_34_0, all_32_0) = all_157_0 &
% 18.19/3.31 | | | | | | | | | | | | aNaturalNumber0(all_34_0) = all_157_1 &
% 18.19/3.31 | | | | | | | | | | | | aNaturalNumber0(all_32_0) = all_157_2 &
% 18.19/3.31 | | | | | | | | | | | | $i(all_157_0) & ( ~ (all_157_1 = 0) | ~
% 18.19/3.31 | | | | | | | | | | | | (all_157_2 = 0) | all_157_0 = all_52_5)
% 18.19/3.31 | | | | | | | | | | | |
% 18.19/3.31 | | | | | | | | | | | | ALPHA: (174) implies:
% 18.19/3.31 | | | | | | | | | | | | (175) aNaturalNumber0(all_32_0) = all_157_2
% 18.19/3.31 | | | | | | | | | | | | (176) aNaturalNumber0(all_34_0) = all_157_1
% 18.19/3.31 | | | | | | | | | | | |
% 18.19/3.31 | | | | | | | | | | | | DELTA: instantiating (161) with fresh symbols all_159_0,
% 18.19/3.31 | | | | | | | | | | | | all_159_1, all_159_2 gives:
% 18.19/3.31 | | | | | | | | | | | | (177) sdtasdt0(xl, all_52_5) = all_159_0 &
% 18.19/3.31 | | | | | | | | | | | | aNaturalNumber0(all_52_5) = all_159_2 &
% 18.19/3.31 | | | | | | | | | | | | aNaturalNumber0(xl) = all_159_1 & $i(all_159_0) &
% 18.19/3.31 | | | | | | | | | | | | ( ~ (all_159_1 = 0) | ~ (all_159_2 = 0) |
% 18.19/3.31 | | | | | | | | | | | | all_159_0 = all_36_1)
% 18.19/3.31 | | | | | | | | | | | |
% 18.19/3.31 | | | | | | | | | | | | ALPHA: (177) implies:
% 18.19/3.31 | | | | | | | | | | | | (178) aNaturalNumber0(all_52_5) = all_159_2
% 18.19/3.31 | | | | | | | | | | | |
% 18.19/3.31 | | | | | | | | | | | | DELTA: instantiating (158) with fresh symbols all_165_0,
% 18.19/3.31 | | | | | | | | | | | | all_165_1, all_165_2, all_165_3, all_165_4,
% 18.19/3.31 | | | | | | | | | | | | all_165_5, all_165_6, all_165_7, all_165_8 gives:
% 18.19/3.32 | | | | | | | | | | | | (179) sdtasdt0(all_165_5, xl) = all_165_3 &
% 18.19/3.32 | | | | | | | | | | | | sdtasdt0(all_79_0, xl) = all_165_2 &
% 18.19/3.32 | | | | | | | | | | | | sdtasdt0(all_32_0, xl) = all_165_1 & sdtasdt0(xl,
% 18.19/3.32 | | | | | | | | | | | | all_165_5) = all_165_4 & sdtpldt0(all_165_2,
% 18.19/3.32 | | | | | | | | | | | | all_165_1) = all_165_0 & sdtpldt0(all_79_0,
% 18.19/3.32 | | | | | | | | | | | | all_32_0) = all_165_5 &
% 18.19/3.32 | | | | | | | | | | | | aNaturalNumber0(all_79_0) = all_165_7 &
% 18.19/3.32 | | | | | | | | | | | | aNaturalNumber0(all_32_0) = all_165_6 &
% 18.19/3.32 | | | | | | | | | | | | aNaturalNumber0(xl) = all_165_8 & $i(all_165_0) &
% 18.19/3.32 | | | | | | | | | | | | $i(all_165_1) & $i(all_165_2) & $i(all_165_3) &
% 18.19/3.32 | | | | | | | | | | | | $i(all_165_4) & $i(all_165_5) & ( ~ (all_165_6 =
% 18.19/3.32 | | | | | | | | | | | | 0) | ~ (all_165_7 = 0) | ~ (all_165_8 = 0) |
% 18.19/3.32 | | | | | | | | | | | | (all_165_0 = all_165_3 & all_165_4 = all_36_1))
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | ALPHA: (179) implies:
% 18.19/3.32 | | | | | | | | | | | | (180) aNaturalNumber0(all_32_0) = all_165_6
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | DELTA: instantiating (160) with fresh symbols all_169_0,
% 18.19/3.32 | | | | | | | | | | | | all_169_1, all_169_2, all_169_3, all_169_4,
% 18.19/3.32 | | | | | | | | | | | | all_169_5, all_169_6, all_169_7, all_169_8 gives:
% 18.19/3.32 | | | | | | | | | | | | (181) sdtasdt0(all_169_5, xl) = all_169_3 &
% 18.19/3.32 | | | | | | | | | | | | sdtasdt0(all_95_0, xl) = all_169_1 &
% 18.19/3.32 | | | | | | | | | | | | sdtasdt0(all_34_0, xl) = all_169_2 & sdtasdt0(xl,
% 18.19/3.32 | | | | | | | | | | | | all_169_5) = all_169_4 & sdtpldt0(all_169_2,
% 18.19/3.32 | | | | | | | | | | | | all_169_1) = all_169_0 & sdtpldt0(all_34_0,
% 18.19/3.32 | | | | | | | | | | | | all_95_0) = all_169_5 &
% 18.19/3.32 | | | | | | | | | | | | aNaturalNumber0(all_95_0) = all_169_6 &
% 18.19/3.32 | | | | | | | | | | | | aNaturalNumber0(all_34_0) = all_169_7 &
% 18.19/3.32 | | | | | | | | | | | | aNaturalNumber0(xl) = all_169_8 & $i(all_169_0) &
% 18.19/3.32 | | | | | | | | | | | | $i(all_169_1) & $i(all_169_2) & $i(all_169_3) &
% 18.19/3.32 | | | | | | | | | | | | $i(all_169_4) & $i(all_169_5) & ( ~ (all_169_6 =
% 18.19/3.32 | | | | | | | | | | | | 0) | ~ (all_169_7 = 0) | ~ (all_169_8 = 0) |
% 18.19/3.32 | | | | | | | | | | | | (all_169_0 = all_169_3 & all_169_4 = all_36_1))
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | ALPHA: (181) implies:
% 18.19/3.32 | | | | | | | | | | | | (182) aNaturalNumber0(all_34_0) = all_169_7
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | DELTA: instantiating (159) with fresh symbols all_171_0,
% 18.19/3.32 | | | | | | | | | | | | all_171_1, all_171_2, all_171_3, all_171_4,
% 18.19/3.32 | | | | | | | | | | | | all_171_5, all_171_6, all_171_7, all_171_8 gives:
% 18.19/3.32 | | | | | | | | | | | | (183) sdtasdt0(all_171_5, xl) = all_171_3 &
% 18.19/3.32 | | | | | | | | | | | | sdtasdt0(all_95_0, xl) = all_171_2 &
% 18.19/3.32 | | | | | | | | | | | | sdtasdt0(all_34_0, xl) = all_171_1 & sdtasdt0(xl,
% 18.19/3.32 | | | | | | | | | | | | all_171_5) = all_171_4 & sdtpldt0(all_171_2,
% 18.19/3.32 | | | | | | | | | | | | all_171_1) = all_171_0 & sdtpldt0(all_95_0,
% 18.19/3.32 | | | | | | | | | | | | all_34_0) = all_171_5 &
% 18.19/3.32 | | | | | | | | | | | | aNaturalNumber0(all_95_0) = all_171_7 &
% 18.19/3.32 | | | | | | | | | | | | aNaturalNumber0(all_34_0) = all_171_6 &
% 18.19/3.32 | | | | | | | | | | | | aNaturalNumber0(xl) = all_171_8 & $i(all_171_0) &
% 18.19/3.32 | | | | | | | | | | | | $i(all_171_1) & $i(all_171_2) & $i(all_171_3) &
% 18.19/3.32 | | | | | | | | | | | | $i(all_171_4) & $i(all_171_5) & ( ~ (all_171_6 =
% 18.19/3.32 | | | | | | | | | | | | 0) | ~ (all_171_7 = 0) | ~ (all_171_8 = 0) |
% 18.19/3.32 | | | | | | | | | | | | (all_171_0 = all_171_3 & all_171_4 = all_36_1))
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | ALPHA: (183) implies:
% 18.19/3.32 | | | | | | | | | | | | (184) aNaturalNumber0(all_34_0) = all_171_6
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | DELTA: instantiating (157) with fresh symbols all_175_0,
% 18.19/3.32 | | | | | | | | | | | | all_175_1, all_175_2, all_175_3, all_175_4,
% 18.19/3.32 | | | | | | | | | | | | all_175_5, all_175_6, all_175_7, all_175_8 gives:
% 18.19/3.32 | | | | | | | | | | | | (185) sdtasdt0(all_175_5, xl) = all_175_3 &
% 18.19/3.32 | | | | | | | | | | | | sdtasdt0(all_79_0, xl) = all_175_1 &
% 18.19/3.32 | | | | | | | | | | | | sdtasdt0(all_32_0, xl) = all_175_2 & sdtasdt0(xl,
% 18.19/3.32 | | | | | | | | | | | | all_175_5) = all_175_4 & sdtpldt0(all_175_2,
% 18.19/3.32 | | | | | | | | | | | | all_175_1) = all_175_0 & sdtpldt0(all_32_0,
% 18.19/3.32 | | | | | | | | | | | | all_79_0) = all_175_5 &
% 18.19/3.32 | | | | | | | | | | | | aNaturalNumber0(all_79_0) = all_175_6 &
% 18.19/3.32 | | | | | | | | | | | | aNaturalNumber0(all_32_0) = all_175_7 &
% 18.19/3.32 | | | | | | | | | | | | aNaturalNumber0(xl) = all_175_8 & $i(all_175_0) &
% 18.19/3.32 | | | | | | | | | | | | $i(all_175_1) & $i(all_175_2) & $i(all_175_3) &
% 18.19/3.32 | | | | | | | | | | | | $i(all_175_4) & $i(all_175_5) & ( ~ (all_175_6 =
% 18.19/3.32 | | | | | | | | | | | | 0) | ~ (all_175_7 = 0) | ~ (all_175_8 = 0) |
% 18.19/3.32 | | | | | | | | | | | | (all_175_0 = all_175_3 & all_175_4 = all_36_1))
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | ALPHA: (185) implies:
% 18.19/3.32 | | | | | | | | | | | | (186) aNaturalNumber0(all_32_0) = all_175_7
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | DELTA: instantiating (151) with fresh symbols all_177_0,
% 18.19/3.32 | | | | | | | | | | | | all_177_1, all_177_2, all_177_3, all_177_4,
% 18.19/3.32 | | | | | | | | | | | | all_177_5, all_177_6, all_177_7, all_177_8 gives:
% 18.19/3.32 | | | | | | | | | | | | (187) sdtasdt0(all_177_5, xl) = all_177_3 &
% 18.19/3.32 | | | | | | | | | | | | sdtasdt0(all_34_0, xl) = all_177_2 &
% 18.19/3.32 | | | | | | | | | | | | sdtasdt0(all_32_0, xl) = all_177_1 & sdtasdt0(xl,
% 18.19/3.32 | | | | | | | | | | | | all_177_5) = all_177_4 & sdtpldt0(all_177_2,
% 18.19/3.32 | | | | | | | | | | | | all_177_1) = all_177_0 & sdtpldt0(all_34_0,
% 18.19/3.32 | | | | | | | | | | | | all_32_0) = all_177_5 &
% 18.19/3.32 | | | | | | | | | | | | aNaturalNumber0(all_34_0) = all_177_7 &
% 18.19/3.32 | | | | | | | | | | | | aNaturalNumber0(all_32_0) = all_177_6 &
% 18.19/3.32 | | | | | | | | | | | | aNaturalNumber0(xl) = all_177_8 & $i(all_177_0) &
% 18.19/3.32 | | | | | | | | | | | | $i(all_177_1) & $i(all_177_2) & $i(all_177_3) &
% 18.19/3.32 | | | | | | | | | | | | $i(all_177_4) & $i(all_177_5) & ( ~ (all_177_6 =
% 18.19/3.32 | | | | | | | | | | | | 0) | ~ (all_177_7 = 0) | ~ (all_177_8 = 0) |
% 18.19/3.32 | | | | | | | | | | | | (all_177_0 = all_177_3 & all_177_4 = all_36_1))
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | ALPHA: (187) implies:
% 18.19/3.32 | | | | | | | | | | | | (188) aNaturalNumber0(all_32_0) = all_177_6
% 18.19/3.32 | | | | | | | | | | | | (189) aNaturalNumber0(all_34_0) = all_177_7
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_157_2, all_32_0,
% 18.19/3.32 | | | | | | | | | | | | simplifying with (17), (175) gives:
% 18.19/3.32 | | | | | | | | | | | | (190) all_157_2 = 0
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_153_2, all_175_7,
% 18.19/3.32 | | | | | | | | | | | | all_32_0, simplifying with (168), (186) gives:
% 18.19/3.32 | | | | | | | | | | | | (191) all_175_7 = all_153_2
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_175_7, all_177_6,
% 18.19/3.32 | | | | | | | | | | | | all_32_0, simplifying with (186), (188) gives:
% 18.19/3.32 | | | | | | | | | | | | (192) all_177_6 = all_175_7
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_165_6, all_177_6,
% 18.19/3.32 | | | | | | | | | | | | all_32_0, simplifying with (180), (188) gives:
% 18.19/3.32 | | | | | | | | | | | | (193) all_177_6 = all_165_6
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_157_2, all_177_6,
% 18.19/3.32 | | | | | | | | | | | | all_32_0, simplifying with (175), (188) gives:
% 18.19/3.32 | | | | | | | | | | | | (194) all_177_6 = all_157_2
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_171_6, all_34_0,
% 18.19/3.32 | | | | | | | | | | | | simplifying with (21), (184) gives:
% 18.19/3.32 | | | | | | | | | | | | (195) all_171_6 = 0
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_169_7, all_171_6,
% 18.19/3.32 | | | | | | | | | | | | all_34_0, simplifying with (182), (184) gives:
% 18.19/3.32 | | | | | | | | | | | | (196) all_171_6 = all_169_7
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_169_7, all_177_7,
% 18.19/3.32 | | | | | | | | | | | | all_34_0, simplifying with (182), (189) gives:
% 18.19/3.32 | | | | | | | | | | | | (197) all_177_7 = all_169_7
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_157_1, all_177_7,
% 18.19/3.32 | | | | | | | | | | | | all_34_0, simplifying with (176), (189) gives:
% 18.19/3.32 | | | | | | | | | | | | (198) all_177_7 = all_157_1
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_153_1, all_177_7,
% 18.19/3.32 | | | | | | | | | | | | all_34_0, simplifying with (169), (189) gives:
% 18.19/3.32 | | | | | | | | | | | | (199) all_177_7 = all_153_1
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_147_0, all_153_0,
% 18.19/3.32 | | | | | | | | | | | | all_52_5, simplifying with (164), (170) gives:
% 18.19/3.32 | | | | | | | | | | | | (200) all_153_0 = all_147_0
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_155_1, all_159_2,
% 18.19/3.32 | | | | | | | | | | | | all_52_5, simplifying with (173), (178) gives:
% 18.19/3.32 | | | | | | | | | | | | (201) all_159_2 = all_155_1
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_153_0, all_159_2,
% 18.19/3.32 | | | | | | | | | | | | all_52_5, simplifying with (170), (178) gives:
% 18.19/3.32 | | | | | | | | | | | | (202) all_159_2 = all_153_0
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_151_1, all_159_2,
% 18.19/3.32 | | | | | | | | | | | | all_52_5, simplifying with (166), (178) gives:
% 18.19/3.32 | | | | | | | | | | | | (203) all_159_2 = all_151_1
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | COMBINE_EQS: (192), (193) imply:
% 18.19/3.32 | | | | | | | | | | | | (204) all_175_7 = all_165_6
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | SIMP: (204) implies:
% 18.19/3.32 | | | | | | | | | | | | (205) all_175_7 = all_165_6
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | COMBINE_EQS: (193), (194) imply:
% 18.19/3.32 | | | | | | | | | | | | (206) all_165_6 = all_157_2
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.32 | | | | | | | | | | | | COMBINE_EQS: (197), (198) imply:
% 18.19/3.32 | | | | | | | | | | | | (207) all_169_7 = all_157_1
% 18.19/3.32 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | SIMP: (207) implies:
% 18.19/3.33 | | | | | | | | | | | | (208) all_169_7 = all_157_1
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | COMBINE_EQS: (198), (199) imply:
% 18.19/3.33 | | | | | | | | | | | | (209) all_157_1 = all_153_1
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | COMBINE_EQS: (191), (205) imply:
% 18.19/3.33 | | | | | | | | | | | | (210) all_165_6 = all_153_2
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | SIMP: (210) implies:
% 18.19/3.33 | | | | | | | | | | | | (211) all_165_6 = all_153_2
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | COMBINE_EQS: (195), (196) imply:
% 18.19/3.33 | | | | | | | | | | | | (212) all_169_7 = 0
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | SIMP: (212) implies:
% 18.19/3.33 | | | | | | | | | | | | (213) all_169_7 = 0
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | COMBINE_EQS: (208), (213) imply:
% 18.19/3.33 | | | | | | | | | | | | (214) all_157_1 = 0
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | SIMP: (214) implies:
% 18.19/3.33 | | | | | | | | | | | | (215) all_157_1 = 0
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | COMBINE_EQS: (206), (211) imply:
% 18.19/3.33 | | | | | | | | | | | | (216) all_157_2 = all_153_2
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | SIMP: (216) implies:
% 18.19/3.33 | | | | | | | | | | | | (217) all_157_2 = all_153_2
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | COMBINE_EQS: (201), (203) imply:
% 18.19/3.33 | | | | | | | | | | | | (218) all_155_1 = all_151_1
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | COMBINE_EQS: (201), (202) imply:
% 18.19/3.33 | | | | | | | | | | | | (219) all_155_1 = all_153_0
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | COMBINE_EQS: (209), (215) imply:
% 18.19/3.33 | | | | | | | | | | | | (220) all_153_1 = 0
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | COMBINE_EQS: (190), (217) imply:
% 18.19/3.33 | | | | | | | | | | | | (221) all_153_2 = 0
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | COMBINE_EQS: (218), (219) imply:
% 18.19/3.33 | | | | | | | | | | | | (222) all_153_0 = all_151_1
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | SIMP: (222) implies:
% 18.19/3.33 | | | | | | | | | | | | (223) all_153_0 = all_151_1
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | COMBINE_EQS: (200), (223) imply:
% 18.19/3.33 | | | | | | | | | | | | (224) all_151_1 = all_147_0
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | BETA: splitting (171) gives:
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | Case 1:
% 18.19/3.33 | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | | (225) ~ (all_153_1 = 0)
% 18.19/3.33 | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | | REDUCE: (220), (225) imply:
% 18.19/3.33 | | | | | | | | | | | | | (226) $false
% 18.19/3.33 | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | | CLOSE: (226) is inconsistent.
% 18.19/3.33 | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | Case 2:
% 18.19/3.33 | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | | (227) ~ (all_153_2 = 0) | all_153_0 = 0
% 18.19/3.33 | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | | BETA: splitting (227) gives:
% 18.19/3.33 | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | | Case 1:
% 18.19/3.33 | | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | | | (228) ~ (all_153_2 = 0)
% 18.19/3.33 | | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | | | REDUCE: (221), (228) imply:
% 18.19/3.33 | | | | | | | | | | | | | | (229) $false
% 18.19/3.33 | | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | | | CLOSE: (229) is inconsistent.
% 18.19/3.33 | | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | | Case 2:
% 18.19/3.33 | | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | | | (230) all_153_0 = 0
% 18.19/3.33 | | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | | | COMBINE_EQS: (200), (230) imply:
% 18.19/3.33 | | | | | | | | | | | | | | (231) all_147_0 = 0
% 18.19/3.33 | | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | | | SIMP: (231) implies:
% 18.19/3.33 | | | | | | | | | | | | | | (232) all_147_0 = 0
% 18.19/3.33 | | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | | | REDUCE: (163), (232) imply:
% 18.19/3.33 | | | | | | | | | | | | | | (233) $false
% 18.19/3.33 | | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | | | CLOSE: (233) is inconsistent.
% 18.19/3.33 | | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | | End of split
% 18.19/3.33 | | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | | End of split
% 18.19/3.33 | | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | | End of split
% 18.19/3.33 | | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | | End of split
% 18.19/3.33 | | | | | | | | | |
% 18.19/3.33 | | | | | | | | | End of split
% 18.19/3.33 | | | | | | | | |
% 18.19/3.33 | | | | | | | | End of split
% 18.19/3.33 | | | | | | | |
% 18.19/3.33 | | | | | | | End of split
% 18.19/3.33 | | | | | | |
% 18.19/3.33 | | | | | | End of split
% 18.19/3.33 | | | | | |
% 18.19/3.33 | | | | | End of split
% 18.19/3.33 | | | | |
% 18.19/3.33 | | | | End of split
% 18.19/3.33 | | | |
% 18.19/3.33 | | | End of split
% 18.19/3.33 | | |
% 18.19/3.33 | | End of split
% 18.19/3.33 | |
% 18.19/3.33 | End of split
% 18.19/3.33 |
% 18.19/3.33 End of proof
% 18.19/3.33 % SZS output end Proof for theBenchmark
% 18.19/3.33
% 18.19/3.33 2719ms
%------------------------------------------------------------------------------