TSTP Solution File: NUM466+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM466+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 : n019.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 9.37s 2.13s
% Output : Proof 14.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM466+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 14:13:43 EDT 2023
% 0.12/0.34 % 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
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 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
% 2.61/1.14 Prover 1: Preprocessing ...
% 2.61/1.14 Prover 4: Preprocessing ...
% 3.19/1.18 Prover 2: Preprocessing ...
% 3.19/1.18 Prover 0: Preprocessing ...
% 3.19/1.18 Prover 6: Preprocessing ...
% 3.19/1.18 Prover 3: Preprocessing ...
% 3.48/1.19 Prover 5: Preprocessing ...
% 7.66/1.77 Prover 1: Constructing countermodel ...
% 7.66/1.78 Prover 3: Constructing countermodel ...
% 8.24/1.87 Prover 6: Proving ...
% 8.44/1.89 Prover 5: Constructing countermodel ...
% 9.37/2.05 Prover 2: Proving ...
% 9.37/2.13 Prover 3: proved (1502ms)
% 9.37/2.13
% 9.37/2.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.37/2.13
% 9.37/2.14 Prover 4: Constructing countermodel ...
% 9.37/2.14 Prover 5: stopped
% 9.37/2.15 Prover 6: stopped
% 9.37/2.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.37/2.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.37/2.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.37/2.19 Prover 2: stopped
% 9.37/2.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.61/2.25 Prover 7: Preprocessing ...
% 10.61/2.25 Prover 10: Preprocessing ...
% 10.61/2.26 Prover 11: Preprocessing ...
% 10.61/2.27 Prover 8: Preprocessing ...
% 10.61/2.28 Prover 0: Proving ...
% 10.61/2.28 Prover 0: stopped
% 10.61/2.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.52/2.33 Prover 13: Preprocessing ...
% 11.75/2.38 Prover 10: Constructing countermodel ...
% 11.75/2.38 Prover 8: Warning: ignoring some quantifiers
% 11.75/2.39 Prover 8: Constructing countermodel ...
% 12.89/2.55 Prover 7: Constructing countermodel ...
% 13.45/2.56 Prover 13: Constructing countermodel ...
% 13.54/2.58 Prover 1: Found proof (size 133)
% 13.54/2.58 Prover 1: proved (1959ms)
% 13.54/2.58 Prover 4: stopped
% 13.54/2.58 Prover 8: stopped
% 13.54/2.59 Prover 7: stopped
% 13.54/2.59 Prover 10: stopped
% 13.54/2.60 Prover 13: stopped
% 13.90/2.66 Prover 11: Constructing countermodel ...
% 13.90/2.67 Prover 11: stopped
% 13.90/2.67
% 13.90/2.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.90/2.67
% 13.90/2.69 % SZS output start Proof for theBenchmark
% 13.90/2.69 Assumptions after simplification:
% 13.90/2.69 ---------------------------------
% 13.90/2.69
% 13.90/2.69 (mDefDiv)
% 13.90/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (doDivides0(v0, v1) = v2) | ~
% 13.90/2.72 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aNaturalNumber0(v1) = v4
% 13.90/2.72 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (( ~ (v2 = 0)
% 13.90/2.72 | ? [v3: $i] : (sdtasdt0(v0, v3) = v1 & aNaturalNumber0(v3) = 0 &
% 13.90/2.72 $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = v1) | ~
% 13.90/2.72 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)))))
% 13.90/2.72
% 13.90/2.72 (mMulAsso)
% 13.90/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 13.90/2.72 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 13.90/2.72 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ?
% 13.90/2.72 [v9: $i] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 &
% 13.90/2.72 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0)
% 13.90/2.72 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 =
% 13.90/2.72 v4)))
% 13.90/2.72
% 13.90/2.72 (mMulComm)
% 13.90/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 13.90/2.72 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 13.90/2.72 (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3
% 13.90/2.72 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 13.90/2.72
% 13.90/2.72 (mSortsB_02)
% 14.31/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 14.31/2.72 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 14.31/2.72 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 14.31/2.72 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 14.31/2.72
% 14.31/2.72 (m__)
% 14.31/2.72 $i(xn) & $i(xm) & $i(xl) & ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xm, xn) =
% 14.31/2.72 0 & doDivides0(xl, xn) = v0 & doDivides0(xl, xm) = 0)
% 14.31/2.72
% 14.31/2.72 (m__1218)
% 14.31/2.73 aNaturalNumber0(xn) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xl) = 0 &
% 14.31/2.73 $i(xn) & $i(xm) & $i(xl)
% 14.31/2.73
% 14.31/2.73 (function-axioms)
% 14.31/2.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.31/2.73 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0:
% 14.31/2.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.31/2.73 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & !
% 14.31/2.73 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 14.31/2.73 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & !
% 14.31/2.73 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.31/2.73 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0:
% 14.31/2.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.31/2.73 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 14.31/2.73 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.31/2.73 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 14.31/2.73 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 14.31/2.73 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.31/2.73 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1)
% 14.31/2.73 | ~ (aNaturalNumber0(v2) = v0))
% 14.31/2.73
% 14.31/2.73 Further assumptions not needed in the proof:
% 14.31/2.73 --------------------------------------------
% 14.31/2.73 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefLE, mDefQuot, mIH, mIH_03,
% 14.31/2.73 mLEAsym, mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2,
% 14.31/2.73 mMulCanc, mNatSort, mSortsB, mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero,
% 14.31/2.73 m_MulUnit, m_MulZero
% 14.31/2.73
% 14.31/2.73 Those formulas are unsatisfiable:
% 14.31/2.73 ---------------------------------
% 14.31/2.73
% 14.31/2.73 Begin of proof
% 14.31/2.73 |
% 14.31/2.73 | ALPHA: (m__1218) implies:
% 14.31/2.73 | (1) aNaturalNumber0(xl) = 0
% 14.31/2.73 | (2) aNaturalNumber0(xm) = 0
% 14.31/2.73 | (3) aNaturalNumber0(xn) = 0
% 14.31/2.73 |
% 14.31/2.73 | ALPHA: (m__) implies:
% 14.31/2.73 | (4) $i(xl)
% 14.31/2.73 | (5) $i(xm)
% 14.31/2.73 | (6) $i(xn)
% 14.31/2.73 | (7) ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xm, xn) = 0 & doDivides0(xl,
% 14.31/2.73 | xn) = v0 & doDivides0(xl, xm) = 0)
% 14.31/2.73 |
% 14.31/2.73 | ALPHA: (function-axioms) implies:
% 14.31/2.74 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.31/2.74 | (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) =
% 14.31/2.74 | v0))
% 14.31/2.74 |
% 14.31/2.74 | DELTA: instantiating (7) with fresh symbol all_31_0 gives:
% 14.31/2.74 | (9) ~ (all_31_0 = 0) & doDivides0(xm, xn) = 0 & doDivides0(xl, xn) =
% 14.31/2.74 | all_31_0 & doDivides0(xl, xm) = 0
% 14.31/2.74 |
% 14.31/2.74 | ALPHA: (9) implies:
% 14.31/2.74 | (10) ~ (all_31_0 = 0)
% 14.31/2.74 | (11) doDivides0(xl, xm) = 0
% 14.31/2.74 | (12) doDivides0(xl, xn) = all_31_0
% 14.31/2.74 | (13) doDivides0(xm, xn) = 0
% 14.31/2.74 |
% 14.31/2.74 | GROUND_INST: instantiating (mDefDiv) with xl, xm, 0, simplifying with (4),
% 14.31/2.74 | (5), (11) gives:
% 14.31/2.74 | (14) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xm) = v1 &
% 14.31/2.74 | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0:
% 14.31/2.74 | $i] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0) = 0 & $i(v0))
% 14.31/2.74 |
% 14.31/2.74 | GROUND_INST: instantiating (mDefDiv) with xl, xn, all_31_0, simplifying with
% 14.31/2.74 | (4), (6), (12) gives:
% 14.31/2.74 | (15) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = v1 &
% 14.31/2.74 | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (( ~
% 14.31/2.74 | (all_31_0 = 0) | ? [v0: $i] : (sdtasdt0(xl, v0) = xn &
% 14.31/2.74 | aNaturalNumber0(v0) = 0 & $i(v0))) & (all_31_0 = 0 | ! [v0: $i]
% 14.31/2.74 | : ( ~ (sdtasdt0(xl, v0) = xn) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 14.31/2.74 | = 0) & aNaturalNumber0(v0) = v1))))
% 14.31/2.74 |
% 14.31/2.74 | GROUND_INST: instantiating (mDefDiv) with xm, xn, 0, simplifying with (5),
% 14.31/2.74 | (6), (13) gives:
% 14.31/2.74 | (16) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = v1 &
% 14.31/2.74 | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0:
% 14.31/2.74 | $i] : (sdtasdt0(xm, v0) = xn & aNaturalNumber0(v0) = 0 & $i(v0))
% 14.31/2.74 |
% 14.31/2.74 | BETA: splitting (16) gives:
% 14.31/2.74 |
% 14.31/2.74 | Case 1:
% 14.31/2.74 | |
% 14.31/2.74 | | (17) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = v1 &
% 14.31/2.74 | | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.31/2.74 | |
% 14.31/2.74 | | DELTA: instantiating (17) with fresh symbols all_39_0, all_39_1 gives:
% 14.31/2.74 | | (18) aNaturalNumber0(xn) = all_39_0 & aNaturalNumber0(xm) = all_39_1 & (
% 14.31/2.74 | | ~ (all_39_0 = 0) | ~ (all_39_1 = 0))
% 14.31/2.74 | |
% 14.31/2.74 | | ALPHA: (18) implies:
% 14.31/2.74 | | (19) aNaturalNumber0(xm) = all_39_1
% 14.31/2.74 | | (20) aNaturalNumber0(xn) = all_39_0
% 14.31/2.74 | | (21) ~ (all_39_0 = 0) | ~ (all_39_1 = 0)
% 14.31/2.74 | |
% 14.31/2.75 | | GROUND_INST: instantiating (8) with 0, all_39_1, xm, simplifying with (2),
% 14.31/2.75 | | (19) gives:
% 14.31/2.75 | | (22) all_39_1 = 0
% 14.31/2.75 | |
% 14.31/2.75 | | GROUND_INST: instantiating (8) with 0, all_39_0, xn, simplifying with (3),
% 14.31/2.75 | | (20) gives:
% 14.31/2.75 | | (23) all_39_0 = 0
% 14.31/2.75 | |
% 14.31/2.75 | | BETA: splitting (21) gives:
% 14.31/2.75 | |
% 14.31/2.75 | | Case 1:
% 14.31/2.75 | | |
% 14.31/2.75 | | | (24) ~ (all_39_0 = 0)
% 14.31/2.75 | | |
% 14.31/2.75 | | | REDUCE: (23), (24) imply:
% 14.31/2.75 | | | (25) $false
% 14.31/2.75 | | |
% 14.31/2.75 | | | CLOSE: (25) is inconsistent.
% 14.31/2.75 | | |
% 14.31/2.75 | | Case 2:
% 14.31/2.75 | | |
% 14.31/2.75 | | | (26) ~ (all_39_1 = 0)
% 14.31/2.75 | | |
% 14.31/2.75 | | | REDUCE: (22), (26) imply:
% 14.31/2.75 | | | (27) $false
% 14.31/2.75 | | |
% 14.31/2.75 | | | CLOSE: (27) is inconsistent.
% 14.31/2.75 | | |
% 14.31/2.75 | | End of split
% 14.31/2.75 | |
% 14.31/2.75 | Case 2:
% 14.31/2.75 | |
% 14.31/2.75 | | (28) ? [v0: $i] : (sdtasdt0(xm, v0) = xn & aNaturalNumber0(v0) = 0 &
% 14.31/2.75 | | $i(v0))
% 14.31/2.75 | |
% 14.31/2.75 | | DELTA: instantiating (28) with fresh symbol all_39_0 gives:
% 14.31/2.75 | | (29) sdtasdt0(xm, all_39_0) = xn & aNaturalNumber0(all_39_0) = 0 &
% 14.31/2.75 | | $i(all_39_0)
% 14.31/2.75 | |
% 14.31/2.75 | | ALPHA: (29) implies:
% 14.31/2.75 | | (30) $i(all_39_0)
% 14.31/2.75 | | (31) aNaturalNumber0(all_39_0) = 0
% 14.31/2.75 | | (32) sdtasdt0(xm, all_39_0) = xn
% 14.31/2.75 | |
% 14.31/2.75 | | BETA: splitting (15) gives:
% 14.31/2.75 | |
% 14.31/2.75 | | Case 1:
% 14.31/2.75 | | |
% 14.31/2.75 | | | (33) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = v1 &
% 14.31/2.75 | | | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.31/2.75 | | |
% 14.31/2.75 | | | DELTA: instantiating (33) with fresh symbols all_47_0, all_47_1 gives:
% 14.31/2.75 | | | (34) aNaturalNumber0(xn) = all_47_0 & aNaturalNumber0(xl) = all_47_1 &
% 14.31/2.75 | | | ( ~ (all_47_0 = 0) | ~ (all_47_1 = 0))
% 14.31/2.75 | | |
% 14.31/2.75 | | | ALPHA: (34) implies:
% 14.31/2.75 | | | (35) aNaturalNumber0(xl) = all_47_1
% 14.31/2.75 | | | (36) aNaturalNumber0(xn) = all_47_0
% 14.31/2.75 | | | (37) ~ (all_47_0 = 0) | ~ (all_47_1 = 0)
% 14.31/2.75 | | |
% 14.31/2.75 | | | GROUND_INST: instantiating (8) with 0, all_47_1, xl, simplifying with (1),
% 14.31/2.75 | | | (35) gives:
% 14.31/2.75 | | | (38) all_47_1 = 0
% 14.31/2.75 | | |
% 14.31/2.75 | | | GROUND_INST: instantiating (8) with 0, all_47_0, xn, simplifying with (3),
% 14.31/2.75 | | | (36) gives:
% 14.31/2.75 | | | (39) all_47_0 = 0
% 14.31/2.75 | | |
% 14.31/2.75 | | | BETA: splitting (37) gives:
% 14.31/2.75 | | |
% 14.31/2.75 | | | Case 1:
% 14.31/2.75 | | | |
% 14.31/2.75 | | | | (40) ~ (all_47_0 = 0)
% 14.31/2.75 | | | |
% 14.31/2.75 | | | | REDUCE: (39), (40) imply:
% 14.31/2.75 | | | | (41) $false
% 14.31/2.75 | | | |
% 14.31/2.75 | | | | CLOSE: (41) is inconsistent.
% 14.31/2.75 | | | |
% 14.31/2.75 | | | Case 2:
% 14.31/2.75 | | | |
% 14.31/2.75 | | | | (42) ~ (all_47_1 = 0)
% 14.31/2.75 | | | |
% 14.31/2.75 | | | | REDUCE: (38), (42) imply:
% 14.31/2.75 | | | | (43) $false
% 14.31/2.75 | | | |
% 14.31/2.75 | | | | CLOSE: (43) is inconsistent.
% 14.31/2.75 | | | |
% 14.31/2.75 | | | End of split
% 14.31/2.75 | | |
% 14.31/2.75 | | Case 2:
% 14.31/2.75 | | |
% 14.31/2.75 | | | (44) ( ~ (all_31_0 = 0) | ? [v0: $i] : (sdtasdt0(xl, v0) = xn &
% 14.31/2.75 | | | aNaturalNumber0(v0) = 0 & $i(v0))) & (all_31_0 = 0 | ! [v0:
% 14.31/2.75 | | | $i] : ( ~ (sdtasdt0(xl, v0) = xn) | ~ $i(v0) | ? [v1: int] :
% 14.31/2.75 | | | ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)))
% 14.31/2.75 | | |
% 14.31/2.75 | | | ALPHA: (44) implies:
% 14.31/2.75 | | | (45) all_31_0 = 0 | ! [v0: $i] : ( ~ (sdtasdt0(xl, v0) = xn) | ~
% 14.31/2.75 | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) =
% 14.31/2.75 | | | v1))
% 14.31/2.75 | | |
% 14.31/2.75 | | | BETA: splitting (14) gives:
% 14.31/2.75 | | |
% 14.31/2.75 | | | Case 1:
% 14.31/2.75 | | | |
% 14.31/2.76 | | | | (46) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xm) = v1 &
% 14.31/2.76 | | | | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.31/2.76 | | | |
% 14.31/2.76 | | | | DELTA: instantiating (46) with fresh symbols all_49_0, all_49_1 gives:
% 14.31/2.76 | | | | (47) aNaturalNumber0(xm) = all_49_0 & aNaturalNumber0(xl) = all_49_1
% 14.31/2.76 | | | | & ( ~ (all_49_0 = 0) | ~ (all_49_1 = 0))
% 14.31/2.76 | | | |
% 14.31/2.76 | | | | ALPHA: (47) implies:
% 14.31/2.76 | | | | (48) aNaturalNumber0(xl) = all_49_1
% 14.31/2.76 | | | | (49) aNaturalNumber0(xm) = all_49_0
% 14.31/2.76 | | | | (50) ~ (all_49_0 = 0) | ~ (all_49_1 = 0)
% 14.31/2.76 | | | |
% 14.31/2.76 | | | | GROUND_INST: instantiating (8) with 0, all_49_1, xl, simplifying with
% 14.31/2.76 | | | | (1), (48) gives:
% 14.31/2.76 | | | | (51) all_49_1 = 0
% 14.31/2.76 | | | |
% 14.31/2.76 | | | | GROUND_INST: instantiating (8) with 0, all_49_0, xm, simplifying with
% 14.31/2.76 | | | | (2), (49) gives:
% 14.31/2.76 | | | | (52) all_49_0 = 0
% 14.31/2.76 | | | |
% 14.31/2.76 | | | | BETA: splitting (50) gives:
% 14.31/2.76 | | | |
% 14.31/2.76 | | | | Case 1:
% 14.31/2.76 | | | | |
% 14.31/2.76 | | | | | (53) ~ (all_49_0 = 0)
% 14.31/2.76 | | | | |
% 14.31/2.76 | | | | | REDUCE: (52), (53) imply:
% 14.31/2.76 | | | | | (54) $false
% 14.31/2.76 | | | | |
% 14.31/2.76 | | | | | CLOSE: (54) is inconsistent.
% 14.31/2.76 | | | | |
% 14.31/2.76 | | | | Case 2:
% 14.31/2.76 | | | | |
% 14.31/2.76 | | | | | (55) ~ (all_49_1 = 0)
% 14.31/2.76 | | | | |
% 14.31/2.76 | | | | | REDUCE: (51), (55) imply:
% 14.31/2.76 | | | | | (56) $false
% 14.31/2.76 | | | | |
% 14.31/2.76 | | | | | CLOSE: (56) is inconsistent.
% 14.31/2.76 | | | | |
% 14.31/2.76 | | | | End of split
% 14.31/2.76 | | | |
% 14.31/2.76 | | | Case 2:
% 14.31/2.76 | | | |
% 14.31/2.76 | | | | (57) ? [v0: $i] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0) = 0 &
% 14.31/2.76 | | | | $i(v0))
% 14.31/2.76 | | | |
% 14.31/2.76 | | | | DELTA: instantiating (57) with fresh symbol all_49_0 gives:
% 14.31/2.76 | | | | (58) sdtasdt0(xl, all_49_0) = xm & aNaturalNumber0(all_49_0) = 0 &
% 14.31/2.76 | | | | $i(all_49_0)
% 14.31/2.76 | | | |
% 14.31/2.76 | | | | ALPHA: (58) implies:
% 14.31/2.76 | | | | (59) $i(all_49_0)
% 14.31/2.76 | | | | (60) aNaturalNumber0(all_49_0) = 0
% 14.31/2.76 | | | | (61) sdtasdt0(xl, all_49_0) = xm
% 14.31/2.76 | | | |
% 14.31/2.76 | | | | BETA: splitting (45) gives:
% 14.31/2.76 | | | |
% 14.31/2.76 | | | | Case 1:
% 14.31/2.76 | | | | |
% 14.31/2.76 | | | | | (62) all_31_0 = 0
% 14.31/2.76 | | | | |
% 14.31/2.76 | | | | | REDUCE: (10), (62) imply:
% 14.31/2.76 | | | | | (63) $false
% 14.31/2.76 | | | | |
% 14.31/2.76 | | | | | CLOSE: (63) is inconsistent.
% 14.31/2.76 | | | | |
% 14.31/2.76 | | | | Case 2:
% 14.31/2.76 | | | | |
% 14.31/2.76 | | | | | (64) ! [v0: $i] : ( ~ (sdtasdt0(xl, v0) = xn) | ~ $i(v0) | ?
% 14.31/2.76 | | | | | [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))
% 14.31/2.76 | | | | |
% 14.31/2.76 | | | | | GROUND_INST: instantiating (mMulComm) with xl, all_49_0, xm,
% 14.31/2.76 | | | | | simplifying with (4), (59), (61) gives:
% 14.31/2.76 | | | | | (65) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 14.31/2.76 | | | | | (sdtasdt0(all_49_0, xl) = v2 & aNaturalNumber0(all_49_0) = v1
% 14.31/2.76 | | | | | & aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0
% 14.31/2.76 | | | | | = 0) | v2 = xm))
% 14.31/2.76 | | | | |
% 14.31/2.76 | | | | | GROUND_INST: instantiating (mMulAsso) with xl, all_49_0, all_39_0, xm,
% 14.31/2.76 | | | | | xn, simplifying with (4), (30), (32), (59), (61) gives:
% 14.31/2.77 | | | | | (66) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ?
% 14.31/2.77 | | | | | [v4: $i] : (sdtasdt0(all_49_0, all_39_0) = v3 & sdtasdt0(xl,
% 14.31/2.77 | | | | | v3) = v4 & aNaturalNumber0(all_49_0) = v1 &
% 14.31/2.77 | | | | | aNaturalNumber0(all_39_0) = v2 & aNaturalNumber0(xl) = v0 &
% 14.31/2.77 | | | | | $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) |
% 14.31/2.77 | | | | | v4 = xn))
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | GROUND_INST: instantiating (mMulComm) with xm, all_39_0, xn,
% 14.31/2.77 | | | | | simplifying with (5), (30), (32) gives:
% 14.31/2.77 | | | | | (67) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 14.31/2.77 | | | | | (sdtasdt0(all_39_0, xm) = v2 & aNaturalNumber0(all_39_0) = v1
% 14.31/2.77 | | | | | & aNaturalNumber0(xm) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0
% 14.31/2.77 | | | | | = 0) | v2 = xn))
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | DELTA: instantiating (67) with fresh symbols all_61_0, all_61_1,
% 14.31/2.77 | | | | | all_61_2 gives:
% 14.31/2.77 | | | | | (68) sdtasdt0(all_39_0, xm) = all_61_0 & aNaturalNumber0(all_39_0)
% 14.31/2.77 | | | | | = all_61_1 & aNaturalNumber0(xm) = all_61_2 & $i(all_61_0) & (
% 14.31/2.77 | | | | | ~ (all_61_1 = 0) | ~ (all_61_2 = 0) | all_61_0 = xn)
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | ALPHA: (68) implies:
% 14.31/2.77 | | | | | (69) aNaturalNumber0(all_39_0) = all_61_1
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | DELTA: instantiating (65) with fresh symbols all_63_0, all_63_1,
% 14.31/2.77 | | | | | all_63_2 gives:
% 14.31/2.77 | | | | | (70) sdtasdt0(all_49_0, xl) = all_63_0 & aNaturalNumber0(all_49_0)
% 14.31/2.77 | | | | | = all_63_1 & aNaturalNumber0(xl) = all_63_2 & $i(all_63_0) & (
% 14.31/2.77 | | | | | ~ (all_63_1 = 0) | ~ (all_63_2 = 0) | all_63_0 = xm)
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | ALPHA: (70) implies:
% 14.31/2.77 | | | | | (71) aNaturalNumber0(xl) = all_63_2
% 14.31/2.77 | | | | | (72) aNaturalNumber0(all_49_0) = all_63_1
% 14.31/2.77 | | | | | (73) sdtasdt0(all_49_0, xl) = all_63_0
% 14.31/2.77 | | | | | (74) ~ (all_63_1 = 0) | ~ (all_63_2 = 0) | all_63_0 = xm
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | DELTA: instantiating (66) with fresh symbols all_65_0, all_65_1,
% 14.31/2.77 | | | | | all_65_2, all_65_3, all_65_4 gives:
% 14.31/2.77 | | | | | (75) sdtasdt0(all_49_0, all_39_0) = all_65_1 & sdtasdt0(xl,
% 14.31/2.77 | | | | | all_65_1) = all_65_0 & aNaturalNumber0(all_49_0) = all_65_3
% 14.31/2.77 | | | | | & aNaturalNumber0(all_39_0) = all_65_2 & aNaturalNumber0(xl) =
% 14.31/2.77 | | | | | all_65_4 & $i(all_65_0) & $i(all_65_1) & ( ~ (all_65_2 = 0) |
% 14.31/2.77 | | | | | ~ (all_65_3 = 0) | ~ (all_65_4 = 0) | all_65_0 = xn)
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | ALPHA: (75) implies:
% 14.31/2.77 | | | | | (76) $i(all_65_1)
% 14.31/2.77 | | | | | (77) aNaturalNumber0(xl) = all_65_4
% 14.31/2.77 | | | | | (78) aNaturalNumber0(all_39_0) = all_65_2
% 14.31/2.77 | | | | | (79) aNaturalNumber0(all_49_0) = all_65_3
% 14.31/2.77 | | | | | (80) sdtasdt0(xl, all_65_1) = all_65_0
% 14.31/2.77 | | | | | (81) sdtasdt0(all_49_0, all_39_0) = all_65_1
% 14.31/2.77 | | | | | (82) ~ (all_65_2 = 0) | ~ (all_65_3 = 0) | ~ (all_65_4 = 0) |
% 14.31/2.77 | | | | | all_65_0 = xn
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | GROUND_INST: instantiating (8) with 0, all_65_4, xl, simplifying with
% 14.31/2.77 | | | | | (1), (77) gives:
% 14.31/2.77 | | | | | (83) all_65_4 = 0
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | GROUND_INST: instantiating (8) with all_63_2, all_65_4, xl,
% 14.31/2.77 | | | | | simplifying with (71), (77) gives:
% 14.31/2.77 | | | | | (84) all_65_4 = all_63_2
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | GROUND_INST: instantiating (8) with 0, all_65_2, all_39_0, simplifying
% 14.31/2.77 | | | | | with (31), (78) gives:
% 14.31/2.77 | | | | | (85) all_65_2 = 0
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | GROUND_INST: instantiating (8) with all_61_1, all_65_2, all_39_0,
% 14.31/2.77 | | | | | simplifying with (69), (78) gives:
% 14.31/2.77 | | | | | (86) all_65_2 = all_61_1
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | GROUND_INST: instantiating (8) with 0, all_65_3, all_49_0, simplifying
% 14.31/2.77 | | | | | with (60), (79) gives:
% 14.31/2.77 | | | | | (87) all_65_3 = 0
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | GROUND_INST: instantiating (8) with all_63_1, all_65_3, all_49_0,
% 14.31/2.77 | | | | | simplifying with (72), (79) gives:
% 14.31/2.77 | | | | | (88) all_65_3 = all_63_1
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | COMBINE_EQS: (85), (86) imply:
% 14.31/2.77 | | | | | (89) all_61_1 = 0
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | SIMP: (89) implies:
% 14.31/2.77 | | | | | (90) all_61_1 = 0
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | COMBINE_EQS: (87), (88) imply:
% 14.31/2.77 | | | | | (91) all_63_1 = 0
% 14.31/2.77 | | | | |
% 14.31/2.77 | | | | | SIMP: (91) implies:
% 14.31/2.78 | | | | | (92) all_63_1 = 0
% 14.31/2.78 | | | | |
% 14.31/2.78 | | | | | COMBINE_EQS: (83), (84) imply:
% 14.31/2.78 | | | | | (93) all_63_2 = 0
% 14.31/2.78 | | | | |
% 14.31/2.78 | | | | | SIMP: (93) implies:
% 14.31/2.78 | | | | | (94) all_63_2 = 0
% 14.31/2.78 | | | | |
% 14.31/2.78 | | | | | BETA: splitting (82) gives:
% 14.31/2.78 | | | | |
% 14.31/2.78 | | | | | Case 1:
% 14.31/2.78 | | | | | |
% 14.31/2.78 | | | | | | (95) ~ (all_65_2 = 0)
% 14.31/2.78 | | | | | |
% 14.31/2.78 | | | | | | REDUCE: (85), (95) imply:
% 14.31/2.78 | | | | | | (96) $false
% 14.31/2.78 | | | | | |
% 14.31/2.78 | | | | | | CLOSE: (96) is inconsistent.
% 14.31/2.78 | | | | | |
% 14.31/2.78 | | | | | Case 2:
% 14.31/2.78 | | | | | |
% 14.31/2.78 | | | | | | (97) ~ (all_65_3 = 0) | ~ (all_65_4 = 0) | all_65_0 = xn
% 14.31/2.78 | | | | | |
% 14.31/2.78 | | | | | | BETA: splitting (97) gives:
% 14.31/2.78 | | | | | |
% 14.31/2.78 | | | | | | Case 1:
% 14.31/2.78 | | | | | | |
% 14.31/2.78 | | | | | | | (98) ~ (all_65_3 = 0)
% 14.31/2.78 | | | | | | |
% 14.31/2.78 | | | | | | | REDUCE: (87), (98) imply:
% 14.31/2.78 | | | | | | | (99) $false
% 14.31/2.78 | | | | | | |
% 14.31/2.78 | | | | | | | CLOSE: (99) is inconsistent.
% 14.31/2.78 | | | | | | |
% 14.31/2.78 | | | | | | Case 2:
% 14.31/2.78 | | | | | | |
% 14.31/2.78 | | | | | | | (100) ~ (all_65_4 = 0) | all_65_0 = xn
% 14.31/2.78 | | | | | | |
% 14.31/2.78 | | | | | | | BETA: splitting (74) gives:
% 14.31/2.78 | | | | | | |
% 14.31/2.78 | | | | | | | Case 1:
% 14.31/2.78 | | | | | | | |
% 14.31/2.78 | | | | | | | | (101) ~ (all_63_1 = 0)
% 14.31/2.78 | | | | | | | |
% 14.31/2.78 | | | | | | | | REDUCE: (92), (101) imply:
% 14.31/2.78 | | | | | | | | (102) $false
% 14.31/2.78 | | | | | | | |
% 14.31/2.78 | | | | | | | | CLOSE: (102) is inconsistent.
% 14.31/2.78 | | | | | | | |
% 14.31/2.78 | | | | | | | Case 2:
% 14.31/2.78 | | | | | | | |
% 14.31/2.78 | | | | | | | | (103) ~ (all_63_2 = 0) | all_63_0 = xm
% 14.31/2.78 | | | | | | | |
% 14.31/2.78 | | | | | | | | BETA: splitting (103) gives:
% 14.31/2.78 | | | | | | | |
% 14.31/2.78 | | | | | | | | Case 1:
% 14.31/2.78 | | | | | | | | |
% 14.31/2.78 | | | | | | | | | (104) ~ (all_63_2 = 0)
% 14.31/2.78 | | | | | | | | |
% 14.31/2.78 | | | | | | | | | REDUCE: (94), (104) imply:
% 14.31/2.78 | | | | | | | | | (105) $false
% 14.31/2.78 | | | | | | | | |
% 14.31/2.78 | | | | | | | | | CLOSE: (105) is inconsistent.
% 14.31/2.78 | | | | | | | | |
% 14.31/2.78 | | | | | | | | Case 2:
% 14.31/2.78 | | | | | | | | |
% 14.31/2.78 | | | | | | | | | (106) all_63_0 = xm
% 14.31/2.78 | | | | | | | | |
% 14.31/2.78 | | | | | | | | | REDUCE: (73), (106) imply:
% 14.31/2.78 | | | | | | | | | (107) sdtasdt0(all_49_0, xl) = xm
% 14.31/2.78 | | | | | | | | |
% 14.31/2.78 | | | | | | | | | BETA: splitting (100) gives:
% 14.31/2.78 | | | | | | | | |
% 14.31/2.78 | | | | | | | | | Case 1:
% 14.31/2.78 | | | | | | | | | |
% 14.31/2.78 | | | | | | | | | | (108) ~ (all_65_4 = 0)
% 14.31/2.78 | | | | | | | | | |
% 14.31/2.78 | | | | | | | | | | REDUCE: (83), (108) imply:
% 14.31/2.78 | | | | | | | | | | (109) $false
% 14.31/2.78 | | | | | | | | | |
% 14.31/2.78 | | | | | | | | | | CLOSE: (109) is inconsistent.
% 14.31/2.78 | | | | | | | | | |
% 14.31/2.78 | | | | | | | | | Case 2:
% 14.31/2.78 | | | | | | | | | |
% 14.31/2.78 | | | | | | | | | | (110) all_65_0 = xn
% 14.31/2.78 | | | | | | | | | |
% 14.31/2.78 | | | | | | | | | | REDUCE: (80), (110) imply:
% 14.31/2.78 | | | | | | | | | | (111) sdtasdt0(xl, all_65_1) = xn
% 14.31/2.78 | | | | | | | | | |
% 14.31/2.78 | | | | | | | | | | GROUND_INST: instantiating (64) with all_65_1, simplifying with
% 14.31/2.78 | | | | | | | | | | (76), (111) gives:
% 14.31/2.78 | | | | | | | | | | (112) ? [v0: int] : ( ~ (v0 = 0) &
% 14.31/2.78 | | | | | | | | | | aNaturalNumber0(all_65_1) = v0)
% 14.31/2.78 | | | | | | | | | |
% 14.31/2.78 | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xl, all_65_1, xn,
% 14.31/2.78 | | | | | | | | | | simplifying with (4), (76), (111) gives:
% 14.31/2.78 | | | | | | | | | | (113) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 14.31/2.78 | | | | | | | | | | (sdtasdt0(all_65_1, xl) = v2 &
% 14.31/2.78 | | | | | | | | | | aNaturalNumber0(all_65_1) = v1 &
% 14.31/2.78 | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ (v1 = 0)
% 14.31/2.78 | | | | | | | | | | | ~ (v0 = 0) | v2 = xn))
% 14.31/2.78 | | | | | | | | | |
% 14.31/2.78 | | | | | | | | | | GROUND_INST: instantiating (mMulAsso) with all_49_0, xl,
% 14.31/2.78 | | | | | | | | | | all_39_0, xm, xn, simplifying with (4), (30),
% 14.31/2.78 | | | | | | | | | | (32), (59), (107) gives:
% 14.60/2.78 | | | | | | | | | | (114) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 14.60/2.78 | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtasdt0(all_49_0, v3) =
% 14.60/2.78 | | | | | | | | | | v4 & sdtasdt0(xl, all_39_0) = v3 &
% 14.60/2.78 | | | | | | | | | | aNaturalNumber0(all_49_0) = v0 &
% 14.60/2.78 | | | | | | | | | | aNaturalNumber0(all_39_0) = v2 &
% 14.60/2.78 | | | | | | | | | | aNaturalNumber0(xl) = v1 & $i(v4) & $i(v3) & ( ~
% 14.60/2.78 | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 =
% 14.60/2.78 | | | | | | | | | | xn))
% 14.60/2.78 | | | | | | | | | |
% 14.60/2.78 | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with all_49_0, all_39_0,
% 14.60/2.78 | | | | | | | | | | all_65_1, simplifying with (30), (59), (81) gives:
% 14.60/2.78 | | | | | | | | | | (115) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 14.60/2.78 | | | | | | | | | | (sdtasdt0(all_39_0, all_49_0) = v2 &
% 14.60/2.78 | | | | | | | | | | aNaturalNumber0(all_49_0) = v0 &
% 14.60/2.78 | | | | | | | | | | aNaturalNumber0(all_39_0) = v1 & $i(v2) & ( ~ (v1
% 14.60/2.78 | | | | | | | | | | = 0) | ~ (v0 = 0) | v2 = all_65_1))
% 14.60/2.78 | | | | | | | | | |
% 14.60/2.78 | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with all_49_0,
% 14.60/2.78 | | | | | | | | | | all_39_0, all_65_1, simplifying with (30), (59),
% 14.60/2.78 | | | | | | | | | | (81) gives:
% 14.60/2.79 | | | | | | | | | | (116) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 14.60/2.79 | | | | | | | | | | (aNaturalNumber0(all_65_1) = v2 &
% 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_49_0) = v0 &
% 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_39_0) = v1 & ( ~ (v1 = 0) |
% 14.60/2.79 | | | | | | | | | | ~ (v0 = 0) | v2 = 0))
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | DELTA: instantiating (112) with fresh symbol all_104_0
% 14.60/2.79 | | | | | | | | | | gives:
% 14.60/2.79 | | | | | | | | | | (117) ~ (all_104_0 = 0) & aNaturalNumber0(all_65_1) =
% 14.60/2.79 | | | | | | | | | | all_104_0
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | ALPHA: (117) implies:
% 14.60/2.79 | | | | | | | | | | (118) ~ (all_104_0 = 0)
% 14.60/2.79 | | | | | | | | | | (119) aNaturalNumber0(all_65_1) = all_104_0
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | DELTA: instantiating (116) with fresh symbols all_108_0,
% 14.60/2.79 | | | | | | | | | | all_108_1, all_108_2 gives:
% 14.60/2.79 | | | | | | | | | | (120) aNaturalNumber0(all_65_1) = all_108_0 &
% 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_49_0) = all_108_2 &
% 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_39_0) = all_108_1 & ( ~
% 14.60/2.79 | | | | | | | | | | (all_108_1 = 0) | ~ (all_108_2 = 0) | all_108_0
% 14.60/2.79 | | | | | | | | | | = 0)
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | ALPHA: (120) implies:
% 14.60/2.79 | | | | | | | | | | (121) aNaturalNumber0(all_39_0) = all_108_1
% 14.60/2.79 | | | | | | | | | | (122) aNaturalNumber0(all_49_0) = all_108_2
% 14.60/2.79 | | | | | | | | | | (123) aNaturalNumber0(all_65_1) = all_108_0
% 14.60/2.79 | | | | | | | | | | (124) ~ (all_108_1 = 0) | ~ (all_108_2 = 0) | all_108_0
% 14.60/2.79 | | | | | | | | | | = 0
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | DELTA: instantiating (115) with fresh symbols all_110_0,
% 14.60/2.79 | | | | | | | | | | all_110_1, all_110_2 gives:
% 14.60/2.79 | | | | | | | | | | (125) sdtasdt0(all_39_0, all_49_0) = all_110_0 &
% 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_49_0) = all_110_2 &
% 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_39_0) = all_110_1 &
% 14.60/2.79 | | | | | | | | | | $i(all_110_0) & ( ~ (all_110_1 = 0) | ~ (all_110_2
% 14.60/2.79 | | | | | | | | | | = 0) | all_110_0 = all_65_1)
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | ALPHA: (125) implies:
% 14.60/2.79 | | | | | | | | | | (126) aNaturalNumber0(all_39_0) = all_110_1
% 14.60/2.79 | | | | | | | | | | (127) aNaturalNumber0(all_49_0) = all_110_2
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | DELTA: instantiating (113) with fresh symbols all_112_0,
% 14.60/2.79 | | | | | | | | | | all_112_1, all_112_2 gives:
% 14.60/2.79 | | | | | | | | | | (128) sdtasdt0(all_65_1, xl) = all_112_0 &
% 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_65_1) = all_112_1 &
% 14.60/2.79 | | | | | | | | | | aNaturalNumber0(xl) = all_112_2 & $i(all_112_0) & (
% 14.60/2.79 | | | | | | | | | | ~ (all_112_1 = 0) | ~ (all_112_2 = 0) |
% 14.60/2.79 | | | | | | | | | | all_112_0 = xn)
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | ALPHA: (128) implies:
% 14.60/2.79 | | | | | | | | | | (129) aNaturalNumber0(all_65_1) = all_112_1
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | DELTA: instantiating (114) with fresh symbols all_114_0,
% 14.60/2.79 | | | | | | | | | | all_114_1, all_114_2, all_114_3, all_114_4 gives:
% 14.60/2.79 | | | | | | | | | | (130) sdtasdt0(all_49_0, all_114_1) = all_114_0 &
% 14.60/2.79 | | | | | | | | | | sdtasdt0(xl, all_39_0) = all_114_1 &
% 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_49_0) = all_114_4 &
% 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_39_0) = all_114_2 &
% 14.60/2.79 | | | | | | | | | | aNaturalNumber0(xl) = all_114_3 & $i(all_114_0) &
% 14.60/2.79 | | | | | | | | | | $i(all_114_1) & ( ~ (all_114_2 = 0) | ~ (all_114_3
% 14.60/2.79 | | | | | | | | | | = 0) | ~ (all_114_4 = 0) | all_114_0 = xn)
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | ALPHA: (130) implies:
% 14.60/2.79 | | | | | | | | | | (131) aNaturalNumber0(all_39_0) = all_114_2
% 14.60/2.79 | | | | | | | | | | (132) aNaturalNumber0(all_49_0) = all_114_4
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_114_2, all_39_0,
% 14.60/2.79 | | | | | | | | | | simplifying with (31), (131) gives:
% 14.60/2.79 | | | | | | | | | | (133) all_114_2 = 0
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | GROUND_INST: instantiating (8) with all_110_1, all_114_2,
% 14.60/2.79 | | | | | | | | | | all_39_0, simplifying with (126), (131) gives:
% 14.60/2.79 | | | | | | | | | | (134) all_114_2 = all_110_1
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | GROUND_INST: instantiating (8) with all_108_1, all_114_2,
% 14.60/2.79 | | | | | | | | | | all_39_0, simplifying with (121), (131) gives:
% 14.60/2.79 | | | | | | | | | | (135) all_114_2 = all_108_1
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_114_4, all_49_0,
% 14.60/2.79 | | | | | | | | | | simplifying with (60), (132) gives:
% 14.60/2.79 | | | | | | | | | | (136) all_114_4 = 0
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | GROUND_INST: instantiating (8) with all_110_2, all_114_4,
% 14.60/2.79 | | | | | | | | | | all_49_0, simplifying with (127), (132) gives:
% 14.60/2.79 | | | | | | | | | | (137) all_114_4 = all_110_2
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | GROUND_INST: instantiating (8) with all_108_2, all_114_4,
% 14.60/2.79 | | | | | | | | | | all_49_0, simplifying with (122), (132) gives:
% 14.60/2.79 | | | | | | | | | | (138) all_114_4 = all_108_2
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | GROUND_INST: instantiating (8) with all_108_0, all_112_1,
% 14.60/2.79 | | | | | | | | | | all_65_1, simplifying with (123), (129) gives:
% 14.60/2.79 | | | | | | | | | | (139) all_112_1 = all_108_0
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | GROUND_INST: instantiating (8) with all_104_0, all_112_1,
% 14.60/2.79 | | | | | | | | | | all_65_1, simplifying with (119), (129) gives:
% 14.60/2.79 | | | | | | | | | | (140) all_112_1 = all_104_0
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | COMBINE_EQS: (134), (135) imply:
% 14.60/2.79 | | | | | | | | | | (141) all_110_1 = all_108_1
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | COMBINE_EQS: (133), (134) imply:
% 14.60/2.79 | | | | | | | | | | (142) all_110_1 = 0
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | COMBINE_EQS: (136), (137) imply:
% 14.60/2.79 | | | | | | | | | | (143) all_110_2 = 0
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | COMBINE_EQS: (137), (138) imply:
% 14.60/2.79 | | | | | | | | | | (144) all_110_2 = all_108_2
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | COMBINE_EQS: (139), (140) imply:
% 14.60/2.79 | | | | | | | | | | (145) all_108_0 = all_104_0
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | SIMP: (145) implies:
% 14.60/2.79 | | | | | | | | | | (146) all_108_0 = all_104_0
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | COMBINE_EQS: (141), (142) imply:
% 14.60/2.79 | | | | | | | | | | (147) all_108_1 = 0
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | COMBINE_EQS: (143), (144) imply:
% 14.60/2.79 | | | | | | | | | | (148) all_108_2 = 0
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | BETA: splitting (124) gives:
% 14.60/2.79 | | | | | | | | | |
% 14.60/2.79 | | | | | | | | | | Case 1:
% 14.60/2.79 | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | | (149) ~ (all_108_1 = 0)
% 14.60/2.80 | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | | REDUCE: (147), (149) imply:
% 14.60/2.80 | | | | | | | | | | | (150) $false
% 14.60/2.80 | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | | CLOSE: (150) is inconsistent.
% 14.60/2.80 | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | Case 2:
% 14.60/2.80 | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | | (151) ~ (all_108_2 = 0) | all_108_0 = 0
% 14.60/2.80 | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | | BETA: splitting (151) gives:
% 14.60/2.80 | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | | Case 1:
% 14.60/2.80 | | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | | | (152) ~ (all_108_2 = 0)
% 14.60/2.80 | | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | | | REDUCE: (148), (152) imply:
% 14.60/2.80 | | | | | | | | | | | | (153) $false
% 14.60/2.80 | | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | | | CLOSE: (153) is inconsistent.
% 14.60/2.80 | | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | | Case 2:
% 14.60/2.80 | | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | | | (154) all_108_0 = 0
% 14.60/2.80 | | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | | | COMBINE_EQS: (146), (154) imply:
% 14.60/2.80 | | | | | | | | | | | | (155) all_104_0 = 0
% 14.60/2.80 | | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | | | SIMP: (155) implies:
% 14.60/2.80 | | | | | | | | | | | | (156) all_104_0 = 0
% 14.60/2.80 | | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | | | REDUCE: (118), (156) imply:
% 14.60/2.80 | | | | | | | | | | | | (157) $false
% 14.60/2.80 | | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | | | CLOSE: (157) is inconsistent.
% 14.60/2.80 | | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | | End of split
% 14.60/2.80 | | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | | End of split
% 14.60/2.80 | | | | | | | | | |
% 14.60/2.80 | | | | | | | | | End of split
% 14.60/2.80 | | | | | | | | |
% 14.60/2.80 | | | | | | | | End of split
% 14.60/2.80 | | | | | | | |
% 14.60/2.80 | | | | | | | End of split
% 14.60/2.80 | | | | | | |
% 14.60/2.80 | | | | | | End of split
% 14.60/2.80 | | | | | |
% 14.60/2.80 | | | | | End of split
% 14.60/2.80 | | | | |
% 14.60/2.80 | | | | End of split
% 14.60/2.80 | | | |
% 14.60/2.80 | | | End of split
% 14.60/2.80 | | |
% 14.60/2.80 | | End of split
% 14.60/2.80 | |
% 14.60/2.80 | End of split
% 14.60/2.80 |
% 14.60/2.80 End of proof
% 14.60/2.80 % SZS output end Proof for theBenchmark
% 14.60/2.80
% 14.60/2.80 2191ms
%------------------------------------------------------------------------------