TSTP Solution File: NUM460+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM460+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 : n011.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 11:47:53 EDT 2023
% Result : Theorem 7.73s 2.70s
% Output : Proof 11.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM460+1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 14:27:53 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.59 ________ _____
% 0.18/0.59 ___ __ \_________(_)________________________________
% 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.59
% 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.59 (2023-06-19)
% 0.18/0.59
% 0.18/0.59 (c) Philipp Rümmer, 2009-2023
% 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.59 Amanda Stjerna.
% 0.18/0.59 Free software under BSD-3-Clause.
% 0.18/0.59
% 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.60 Running up to 7 provers in parallel.
% 0.18/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.97/1.26 Prover 1: Preprocessing ...
% 1.97/1.26 Prover 4: Preprocessing ...
% 2.72/1.43 Prover 6: Preprocessing ...
% 2.72/1.43 Prover 5: Preprocessing ...
% 2.72/1.43 Prover 2: Preprocessing ...
% 2.72/1.43 Prover 3: Preprocessing ...
% 2.72/1.43 Prover 0: Preprocessing ...
% 5.70/2.21 Prover 1: Constructing countermodel ...
% 5.70/2.22 Prover 6: Proving ...
% 5.90/2.24 Prover 3: Constructing countermodel ...
% 6.59/2.38 Prover 5: Constructing countermodel ...
% 7.41/2.65 Prover 2: Proving ...
% 7.73/2.70 Prover 4: Constructing countermodel ...
% 7.73/2.70 Prover 3: proved (2078ms)
% 7.73/2.70
% 7.73/2.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.73/2.70
% 7.73/2.72 Prover 2: stopped
% 7.73/2.73 Prover 5: stopped
% 8.08/2.75 Prover 6: stopped
% 8.08/2.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.08/2.77 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.08/2.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.08/2.77 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.39/2.83 Prover 7: Preprocessing ...
% 8.39/2.85 Prover 8: Preprocessing ...
% 8.39/2.85 Prover 10: Preprocessing ...
% 8.53/2.87 Prover 11: Preprocessing ...
% 9.07/3.00 Prover 0: Proving ...
% 9.07/3.01 Prover 0: stopped
% 9.07/3.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.40/3.06 Prover 8: Warning: ignoring some quantifiers
% 9.55/3.08 Prover 8: Constructing countermodel ...
% 9.55/3.08 Prover 10: Constructing countermodel ...
% 9.55/3.09 Prover 13: Preprocessing ...
% 9.80/3.19 Prover 7: Constructing countermodel ...
% 10.76/3.36 Prover 13: Constructing countermodel ...
% 11.08/3.45 Prover 11: Constructing countermodel ...
% 11.08/3.48 Prover 1: Found proof (size 139)
% 11.08/3.48 Prover 1: proved (2856ms)
% 11.08/3.48 Prover 8: stopped
% 11.08/3.48 Prover 4: stopped
% 11.08/3.48 Prover 10: stopped
% 11.08/3.48 Prover 7: stopped
% 11.08/3.49 Prover 13: stopped
% 11.08/3.49 Prover 11: stopped
% 11.08/3.49
% 11.08/3.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.08/3.49
% 11.08/3.52 % SZS output start Proof for theBenchmark
% 11.08/3.52 Assumptions after simplification:
% 11.08/3.52 ---------------------------------
% 11.08/3.52
% 11.08/3.52 (mAddAsso)
% 11.45/3.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 11.45/3.56 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 11.45/3.56 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ?
% 11.45/3.56 [v9: $i] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 &
% 11.45/3.56 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0)
% 11.45/3.56 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 =
% 11.45/3.56 v4)))
% 11.45/3.56
% 11.45/3.56 (mAddComm)
% 11.45/3.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 11.45/3.57 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 11.45/3.57 (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3
% 11.45/3.57 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 11.45/3.57
% 11.45/3.57 (mDefLE)
% 11.45/3.57 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (sdtlseqdt0(v0, v1) = v2) | ~
% 11.45/3.57 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aNaturalNumber0(v1) = v4
% 11.45/3.57 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (( ~ (v2 = 0)
% 11.45/3.57 | ? [v3: $i] : (sdtpldt0(v0, v3) = v1 & aNaturalNumber0(v3) = 0 &
% 11.45/3.57 $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (sdtpldt0(v0, v3) = v1) | ~
% 11.45/3.57 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)))))
% 11.45/3.57
% 11.45/3.57 (mSortsB)
% 11.45/3.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 11.45/3.59 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 11.45/3.59 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 11.45/3.59 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 11.45/3.59
% 11.45/3.59 (m__)
% 11.45/3.59 $i(xl) & $i(xn) & $i(xm) & ? [v0: int] : ( ~ (v0 = 0) & sdtlseqdt0(xn, xl) =
% 11.45/3.59 0 & sdtlseqdt0(xm, xl) = v0 & sdtlseqdt0(xm, xn) = 0)
% 11.45/3.59
% 11.45/3.59 (m__773)
% 11.45/3.59 aNaturalNumber0(xl) = 0 & aNaturalNumber0(xn) = 0 & aNaturalNumber0(xm) = 0 &
% 11.45/3.59 $i(xl) & $i(xn) & $i(xm)
% 11.45/3.59
% 11.45/3.59 (function-axioms)
% 11.65/3.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.65/3.60 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0:
% 11.65/3.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.65/3.60 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 11.65/3.60 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.65/3.60 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 11.65/3.60 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 11.65/3.60 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.65/3.60 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1)
% 11.65/3.60 | ~ (aNaturalNumber0(v2) = v0))
% 11.65/3.60
% 11.65/3.60 Further assumptions not needed in the proof:
% 11.65/3.60 --------------------------------------------
% 11.65/3.61 mAMDistr, mAddCanc, mDefDiff, mLEAsym, mLERefl, mMulAsso, mMulCanc, mMulComm,
% 11.65/3.61 mNatSort, mSortsB_02, mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero,
% 11.65/3.61 m_MulUnit, m_MulZero
% 11.65/3.61
% 11.65/3.61 Those formulas are unsatisfiable:
% 11.65/3.61 ---------------------------------
% 11.65/3.61
% 11.65/3.61 Begin of proof
% 11.65/3.61 |
% 11.65/3.61 | ALPHA: (m__773) implies:
% 11.65/3.61 | (1) aNaturalNumber0(xm) = 0
% 11.65/3.61 | (2) aNaturalNumber0(xn) = 0
% 11.65/3.61 | (3) aNaturalNumber0(xl) = 0
% 11.65/3.61 |
% 11.65/3.61 | ALPHA: (m__) implies:
% 11.65/3.61 | (4) $i(xm)
% 11.65/3.61 | (5) $i(xn)
% 11.65/3.61 | (6) $i(xl)
% 11.65/3.61 | (7) ? [v0: int] : ( ~ (v0 = 0) & sdtlseqdt0(xn, xl) = 0 & sdtlseqdt0(xm,
% 11.65/3.61 | xl) = v0 & sdtlseqdt0(xm, xn) = 0)
% 11.65/3.61 |
% 11.65/3.61 | ALPHA: (function-axioms) implies:
% 11.65/3.62 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.65/3.62 | (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) =
% 11.65/3.62 | v0))
% 11.65/3.62 |
% 11.65/3.62 | DELTA: instantiating (7) with fresh symbol all_22_0 gives:
% 11.65/3.62 | (9) ~ (all_22_0 = 0) & sdtlseqdt0(xn, xl) = 0 & sdtlseqdt0(xm, xl) =
% 11.65/3.62 | all_22_0 & sdtlseqdt0(xm, xn) = 0
% 11.65/3.62 |
% 11.65/3.62 | ALPHA: (9) implies:
% 11.65/3.62 | (10) ~ (all_22_0 = 0)
% 11.65/3.62 | (11) sdtlseqdt0(xm, xn) = 0
% 11.65/3.62 | (12) sdtlseqdt0(xm, xl) = all_22_0
% 11.65/3.62 | (13) sdtlseqdt0(xn, xl) = 0
% 11.65/3.62 |
% 11.65/3.62 | GROUND_INST: instantiating (mDefLE) with xm, xn, 0, simplifying with (4), (5),
% 11.65/3.62 | (11) gives:
% 11.65/3.62 | (14) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = v1 &
% 11.65/3.62 | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0:
% 11.65/3.62 | $i] : (sdtpldt0(xm, v0) = xn & aNaturalNumber0(v0) = 0 & $i(v0))
% 11.65/3.62 |
% 11.65/3.62 | GROUND_INST: instantiating (mDefLE) with xm, xl, all_22_0, simplifying with
% 11.65/3.62 | (4), (6), (12) gives:
% 11.65/3.62 | (15) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xl) = v1 &
% 11.65/3.62 | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (( ~
% 11.65/3.62 | (all_22_0 = 0) | ? [v0: $i] : (sdtpldt0(xm, v0) = xl &
% 11.65/3.62 | aNaturalNumber0(v0) = 0 & $i(v0))) & (all_22_0 = 0 | ! [v0: $i]
% 11.65/3.62 | : ( ~ (sdtpldt0(xm, v0) = xl) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 11.65/3.63 | = 0) & aNaturalNumber0(v0) = v1))))
% 11.65/3.63 |
% 11.65/3.63 | GROUND_INST: instantiating (mDefLE) with xn, xl, 0, simplifying with (5), (6),
% 11.65/3.63 | (13) gives:
% 11.65/3.63 | (16) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xl) = v1 &
% 11.65/3.63 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0:
% 11.65/3.63 | $i] : (sdtpldt0(xn, v0) = xl & aNaturalNumber0(v0) = 0 & $i(v0))
% 11.65/3.63 |
% 11.65/3.63 | BETA: splitting (16) gives:
% 11.65/3.63 |
% 11.65/3.63 | Case 1:
% 11.65/3.63 | |
% 11.65/3.63 | | (17) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xl) = v1 &
% 11.65/3.63 | | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 11.65/3.63 | |
% 11.65/3.63 | | DELTA: instantiating (17) with fresh symbols all_30_0, all_30_1 gives:
% 11.65/3.63 | | (18) aNaturalNumber0(xl) = all_30_0 & aNaturalNumber0(xn) = all_30_1 & (
% 11.65/3.63 | | ~ (all_30_0 = 0) | ~ (all_30_1 = 0))
% 11.65/3.63 | |
% 11.65/3.63 | | ALPHA: (18) implies:
% 11.65/3.63 | | (19) aNaturalNumber0(xn) = all_30_1
% 11.65/3.63 | | (20) aNaturalNumber0(xl) = all_30_0
% 11.65/3.63 | | (21) ~ (all_30_0 = 0) | ~ (all_30_1 = 0)
% 11.65/3.63 | |
% 11.65/3.63 | | GROUND_INST: instantiating (8) with 0, all_30_1, xn, simplifying with (2),
% 11.65/3.63 | | (19) gives:
% 11.65/3.63 | | (22) all_30_1 = 0
% 11.65/3.63 | |
% 11.65/3.63 | | GROUND_INST: instantiating (8) with 0, all_30_0, xl, simplifying with (3),
% 11.65/3.63 | | (20) gives:
% 11.65/3.63 | | (23) all_30_0 = 0
% 11.65/3.63 | |
% 11.65/3.63 | | BETA: splitting (21) gives:
% 11.65/3.63 | |
% 11.65/3.63 | | Case 1:
% 11.65/3.63 | | |
% 11.65/3.63 | | | (24) ~ (all_30_0 = 0)
% 11.65/3.63 | | |
% 11.65/3.63 | | | REDUCE: (23), (24) imply:
% 11.65/3.63 | | | (25) $false
% 11.65/3.63 | | |
% 11.65/3.63 | | | CLOSE: (25) is inconsistent.
% 11.65/3.63 | | |
% 11.65/3.63 | | Case 2:
% 11.65/3.63 | | |
% 11.65/3.63 | | | (26) ~ (all_30_1 = 0)
% 11.65/3.63 | | |
% 11.65/3.64 | | | REDUCE: (22), (26) imply:
% 11.65/3.64 | | | (27) $false
% 11.65/3.64 | | |
% 11.65/3.64 | | | CLOSE: (27) is inconsistent.
% 11.65/3.64 | | |
% 11.65/3.64 | | End of split
% 11.65/3.64 | |
% 11.65/3.64 | Case 2:
% 11.65/3.64 | |
% 11.65/3.64 | | (28) ? [v0: $i] : (sdtpldt0(xn, v0) = xl & aNaturalNumber0(v0) = 0 &
% 11.65/3.64 | | $i(v0))
% 11.65/3.64 | |
% 11.65/3.64 | | DELTA: instantiating (28) with fresh symbol all_30_0 gives:
% 11.65/3.64 | | (29) sdtpldt0(xn, all_30_0) = xl & aNaturalNumber0(all_30_0) = 0 &
% 11.65/3.64 | | $i(all_30_0)
% 11.65/3.64 | |
% 11.65/3.64 | | ALPHA: (29) implies:
% 11.65/3.64 | | (30) $i(all_30_0)
% 11.65/3.64 | | (31) aNaturalNumber0(all_30_0) = 0
% 11.65/3.64 | | (32) sdtpldt0(xn, all_30_0) = xl
% 11.65/3.64 | |
% 11.65/3.64 | | BETA: splitting (15) gives:
% 11.65/3.64 | |
% 11.65/3.64 | | Case 1:
% 11.65/3.64 | | |
% 11.65/3.64 | | | (33) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xl) = v1 &
% 11.65/3.64 | | | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 11.65/3.64 | | |
% 11.65/3.64 | | | DELTA: instantiating (33) with fresh symbols all_38_0, all_38_1 gives:
% 11.65/3.64 | | | (34) aNaturalNumber0(xl) = all_38_0 & aNaturalNumber0(xm) = all_38_1 &
% 11.65/3.64 | | | ( ~ (all_38_0 = 0) | ~ (all_38_1 = 0))
% 11.65/3.64 | | |
% 11.65/3.64 | | | ALPHA: (34) implies:
% 11.65/3.64 | | | (35) aNaturalNumber0(xm) = all_38_1
% 11.65/3.64 | | | (36) aNaturalNumber0(xl) = all_38_0
% 11.65/3.64 | | | (37) ~ (all_38_0 = 0) | ~ (all_38_1 = 0)
% 11.65/3.64 | | |
% 11.65/3.64 | | | GROUND_INST: instantiating (8) with 0, all_38_1, xm, simplifying with (1),
% 11.65/3.64 | | | (35) gives:
% 11.65/3.64 | | | (38) all_38_1 = 0
% 11.65/3.64 | | |
% 11.65/3.64 | | | GROUND_INST: instantiating (8) with 0, all_38_0, xl, simplifying with (3),
% 11.65/3.64 | | | (36) gives:
% 11.65/3.64 | | | (39) all_38_0 = 0
% 11.65/3.64 | | |
% 11.65/3.64 | | | BETA: splitting (37) gives:
% 11.65/3.64 | | |
% 11.65/3.64 | | | Case 1:
% 11.65/3.64 | | | |
% 11.65/3.64 | | | | (40) ~ (all_38_0 = 0)
% 11.65/3.64 | | | |
% 11.65/3.64 | | | | REDUCE: (39), (40) imply:
% 11.65/3.64 | | | | (41) $false
% 11.65/3.64 | | | |
% 11.65/3.64 | | | | CLOSE: (41) is inconsistent.
% 11.65/3.64 | | | |
% 11.65/3.64 | | | Case 2:
% 11.65/3.64 | | | |
% 11.65/3.64 | | | | (42) ~ (all_38_1 = 0)
% 11.65/3.64 | | | |
% 11.65/3.64 | | | | REDUCE: (38), (42) imply:
% 11.65/3.64 | | | | (43) $false
% 11.65/3.64 | | | |
% 11.65/3.64 | | | | CLOSE: (43) is inconsistent.
% 11.65/3.64 | | | |
% 11.65/3.64 | | | End of split
% 11.65/3.64 | | |
% 11.65/3.64 | | Case 2:
% 11.65/3.64 | | |
% 11.65/3.64 | | | (44) ( ~ (all_22_0 = 0) | ? [v0: $i] : (sdtpldt0(xm, v0) = xl &
% 11.65/3.64 | | | aNaturalNumber0(v0) = 0 & $i(v0))) & (all_22_0 = 0 | ! [v0:
% 11.65/3.64 | | | $i] : ( ~ (sdtpldt0(xm, v0) = xl) | ~ $i(v0) | ? [v1: int] :
% 11.65/3.64 | | | ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)))
% 11.65/3.64 | | |
% 11.65/3.64 | | | ALPHA: (44) implies:
% 11.65/3.65 | | | (45) all_22_0 = 0 | ! [v0: $i] : ( ~ (sdtpldt0(xm, v0) = xl) | ~
% 11.65/3.65 | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) =
% 11.65/3.65 | | | v1))
% 11.65/3.65 | | |
% 11.65/3.65 | | | BETA: splitting (14) gives:
% 11.65/3.65 | | |
% 11.65/3.65 | | | Case 1:
% 11.65/3.65 | | | |
% 11.65/3.65 | | | | (46) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = v1 &
% 11.65/3.65 | | | | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 11.65/3.65 | | | |
% 11.65/3.65 | | | | DELTA: instantiating (46) with fresh symbols all_40_0, all_40_1 gives:
% 11.65/3.65 | | | | (47) aNaturalNumber0(xn) = all_40_0 & aNaturalNumber0(xm) = all_40_1
% 11.65/3.65 | | | | & ( ~ (all_40_0 = 0) | ~ (all_40_1 = 0))
% 11.65/3.65 | | | |
% 11.65/3.65 | | | | ALPHA: (47) implies:
% 11.65/3.65 | | | | (48) aNaturalNumber0(xm) = all_40_1
% 11.65/3.65 | | | | (49) aNaturalNumber0(xn) = all_40_0
% 11.65/3.65 | | | | (50) ~ (all_40_0 = 0) | ~ (all_40_1 = 0)
% 11.65/3.65 | | | |
% 11.65/3.65 | | | | GROUND_INST: instantiating (8) with 0, all_40_1, xm, simplifying with
% 11.65/3.65 | | | | (1), (48) gives:
% 11.65/3.65 | | | | (51) all_40_1 = 0
% 11.65/3.65 | | | |
% 11.65/3.65 | | | | GROUND_INST: instantiating (8) with 0, all_40_0, xn, simplifying with
% 11.65/3.65 | | | | (2), (49) gives:
% 11.65/3.65 | | | | (52) all_40_0 = 0
% 11.65/3.65 | | | |
% 11.65/3.65 | | | | BETA: splitting (50) gives:
% 11.65/3.65 | | | |
% 11.65/3.65 | | | | Case 1:
% 11.65/3.65 | | | | |
% 11.65/3.65 | | | | | (53) ~ (all_40_0 = 0)
% 11.65/3.65 | | | | |
% 11.65/3.65 | | | | | REDUCE: (52), (53) imply:
% 11.65/3.65 | | | | | (54) $false
% 11.65/3.65 | | | | |
% 11.65/3.65 | | | | | CLOSE: (54) is inconsistent.
% 11.65/3.65 | | | | |
% 11.65/3.65 | | | | Case 2:
% 11.65/3.65 | | | | |
% 11.65/3.65 | | | | | (55) ~ (all_40_1 = 0)
% 11.65/3.65 | | | | |
% 11.65/3.65 | | | | | REDUCE: (51), (55) imply:
% 11.65/3.65 | | | | | (56) $false
% 11.65/3.65 | | | | |
% 11.65/3.65 | | | | | CLOSE: (56) is inconsistent.
% 11.65/3.65 | | | | |
% 11.65/3.65 | | | | End of split
% 11.65/3.65 | | | |
% 11.82/3.65 | | | Case 2:
% 11.82/3.65 | | | |
% 11.82/3.65 | | | | (57) ? [v0: $i] : (sdtpldt0(xm, v0) = xn & aNaturalNumber0(v0) = 0 &
% 11.82/3.65 | | | | $i(v0))
% 11.82/3.65 | | | |
% 11.82/3.65 | | | | DELTA: instantiating (57) with fresh symbol all_40_0 gives:
% 11.82/3.65 | | | | (58) sdtpldt0(xm, all_40_0) = xn & aNaturalNumber0(all_40_0) = 0 &
% 11.82/3.65 | | | | $i(all_40_0)
% 11.82/3.65 | | | |
% 11.82/3.65 | | | | ALPHA: (58) implies:
% 11.82/3.65 | | | | (59) $i(all_40_0)
% 11.82/3.65 | | | | (60) aNaturalNumber0(all_40_0) = 0
% 11.82/3.65 | | | | (61) sdtpldt0(xm, all_40_0) = xn
% 11.82/3.65 | | | |
% 11.82/3.65 | | | | BETA: splitting (45) gives:
% 11.82/3.65 | | | |
% 11.82/3.65 | | | | Case 1:
% 11.83/3.65 | | | | |
% 11.83/3.65 | | | | | (62) all_22_0 = 0
% 11.83/3.65 | | | | |
% 11.83/3.65 | | | | | REDUCE: (10), (62) imply:
% 11.83/3.65 | | | | | (63) $false
% 11.83/3.65 | | | | |
% 11.83/3.65 | | | | | CLOSE: (63) is inconsistent.
% 11.83/3.65 | | | | |
% 11.83/3.65 | | | | Case 2:
% 11.83/3.65 | | | | |
% 11.83/3.65 | | | | | (64) ! [v0: $i] : ( ~ (sdtpldt0(xm, v0) = xl) | ~ $i(v0) | ?
% 11.83/3.65 | | | | | [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))
% 11.83/3.65 | | | | |
% 11.83/3.66 | | | | | GROUND_INST: instantiating (mAddComm) with xm, all_40_0, xn,
% 11.83/3.66 | | | | | simplifying with (4), (59), (61) gives:
% 11.83/3.66 | | | | | (65) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 11.83/3.66 | | | | | (sdtpldt0(all_40_0, xm) = v2 & aNaturalNumber0(all_40_0) = v1
% 11.83/3.66 | | | | | & aNaturalNumber0(xm) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0
% 11.83/3.66 | | | | | = 0) | v2 = xn))
% 11.83/3.66 | | | | |
% 11.83/3.66 | | | | | GROUND_INST: instantiating (mAddAsso) with xm, all_40_0, all_30_0, xn,
% 11.83/3.66 | | | | | xl, simplifying with (4), (30), (32), (59), (61) gives:
% 11.83/3.66 | | | | | (66) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ?
% 11.83/3.66 | | | | | [v4: $i] : (sdtpldt0(all_40_0, all_30_0) = v3 & sdtpldt0(xm,
% 11.83/3.66 | | | | | v3) = v4 & aNaturalNumber0(all_40_0) = v1 &
% 11.83/3.66 | | | | | aNaturalNumber0(all_30_0) = v2 & aNaturalNumber0(xm) = v0 &
% 11.83/3.66 | | | | | $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) |
% 11.83/3.66 | | | | | v4 = xl))
% 11.83/3.66 | | | | |
% 11.83/3.66 | | | | | GROUND_INST: instantiating (mAddComm) with xn, all_30_0, xl,
% 11.83/3.66 | | | | | simplifying with (5), (30), (32) gives:
% 11.83/3.66 | | | | | (67) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 11.83/3.66 | | | | | (sdtpldt0(all_30_0, xn) = v2 & aNaturalNumber0(all_30_0) = v1
% 11.83/3.66 | | | | | & aNaturalNumber0(xn) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0
% 11.83/3.66 | | | | | = 0) | v2 = xl))
% 11.83/3.66 | | | | |
% 11.83/3.66 | | | | | DELTA: instantiating (67) with fresh symbols all_52_0, all_52_1,
% 11.83/3.66 | | | | | all_52_2 gives:
% 11.83/3.66 | | | | | (68) sdtpldt0(all_30_0, xn) = all_52_0 & aNaturalNumber0(all_30_0)
% 11.83/3.66 | | | | | = all_52_1 & aNaturalNumber0(xn) = all_52_2 & $i(all_52_0) & (
% 11.83/3.66 | | | | | ~ (all_52_1 = 0) | ~ (all_52_2 = 0) | all_52_0 = xl)
% 11.83/3.66 | | | | |
% 11.83/3.66 | | | | | ALPHA: (68) implies:
% 11.83/3.66 | | | | | (69) aNaturalNumber0(all_30_0) = all_52_1
% 11.83/3.66 | | | | |
% 11.83/3.66 | | | | | DELTA: instantiating (65) with fresh symbols all_54_0, all_54_1,
% 11.83/3.66 | | | | | all_54_2 gives:
% 11.83/3.66 | | | | | (70) sdtpldt0(all_40_0, xm) = all_54_0 & aNaturalNumber0(all_40_0)
% 11.83/3.66 | | | | | = all_54_1 & aNaturalNumber0(xm) = all_54_2 & $i(all_54_0) & (
% 11.83/3.66 | | | | | ~ (all_54_1 = 0) | ~ (all_54_2 = 0) | all_54_0 = xn)
% 11.83/3.66 | | | | |
% 11.83/3.66 | | | | | ALPHA: (70) implies:
% 11.83/3.66 | | | | | (71) aNaturalNumber0(xm) = all_54_2
% 11.83/3.66 | | | | | (72) aNaturalNumber0(all_40_0) = all_54_1
% 11.83/3.66 | | | | | (73) sdtpldt0(all_40_0, xm) = all_54_0
% 11.83/3.66 | | | | | (74) ~ (all_54_1 = 0) | ~ (all_54_2 = 0) | all_54_0 = xn
% 11.83/3.66 | | | | |
% 11.83/3.66 | | | | | DELTA: instantiating (66) with fresh symbols all_56_0, all_56_1,
% 11.83/3.66 | | | | | all_56_2, all_56_3, all_56_4 gives:
% 11.83/3.66 | | | | | (75) sdtpldt0(all_40_0, all_30_0) = all_56_1 & sdtpldt0(xm,
% 11.83/3.67 | | | | | all_56_1) = all_56_0 & aNaturalNumber0(all_40_0) = all_56_3
% 11.83/3.67 | | | | | & aNaturalNumber0(all_30_0) = all_56_2 & aNaturalNumber0(xm) =
% 11.83/3.67 | | | | | all_56_4 & $i(all_56_0) & $i(all_56_1) & ( ~ (all_56_2 = 0) |
% 11.83/3.67 | | | | | ~ (all_56_3 = 0) | ~ (all_56_4 = 0) | all_56_0 = xl)
% 11.83/3.67 | | | | |
% 11.83/3.67 | | | | | ALPHA: (75) implies:
% 11.83/3.67 | | | | | (76) $i(all_56_1)
% 11.83/3.67 | | | | | (77) aNaturalNumber0(xm) = all_56_4
% 11.83/3.67 | | | | | (78) aNaturalNumber0(all_30_0) = all_56_2
% 11.83/3.67 | | | | | (79) aNaturalNumber0(all_40_0) = all_56_3
% 11.83/3.67 | | | | | (80) sdtpldt0(xm, all_56_1) = all_56_0
% 11.83/3.67 | | | | | (81) sdtpldt0(all_40_0, all_30_0) = all_56_1
% 11.83/3.67 | | | | | (82) ~ (all_56_2 = 0) | ~ (all_56_3 = 0) | ~ (all_56_4 = 0) |
% 11.83/3.67 | | | | | all_56_0 = xl
% 11.83/3.67 | | | | |
% 11.83/3.67 | | | | | GROUND_INST: instantiating (8) with 0, all_56_4, xm, simplifying with
% 11.83/3.67 | | | | | (1), (77) gives:
% 11.83/3.67 | | | | | (83) all_56_4 = 0
% 11.83/3.67 | | | | |
% 11.83/3.67 | | | | | GROUND_INST: instantiating (8) with all_54_2, all_56_4, xm,
% 11.83/3.67 | | | | | simplifying with (71), (77) gives:
% 11.83/3.67 | | | | | (84) all_56_4 = all_54_2
% 11.83/3.67 | | | | |
% 11.83/3.67 | | | | | GROUND_INST: instantiating (8) with 0, all_56_2, all_30_0, simplifying
% 11.83/3.67 | | | | | with (31), (78) gives:
% 11.83/3.67 | | | | | (85) all_56_2 = 0
% 11.83/3.67 | | | | |
% 11.83/3.67 | | | | | GROUND_INST: instantiating (8) with all_52_1, all_56_2, all_30_0,
% 11.83/3.67 | | | | | simplifying with (69), (78) gives:
% 11.83/3.67 | | | | | (86) all_56_2 = all_52_1
% 11.83/3.67 | | | | |
% 11.83/3.67 | | | | | GROUND_INST: instantiating (8) with 0, all_56_3, all_40_0, simplifying
% 11.83/3.67 | | | | | with (60), (79) gives:
% 11.83/3.67 | | | | | (87) all_56_3 = 0
% 11.83/3.67 | | | | |
% 11.83/3.67 | | | | | GROUND_INST: instantiating (8) with all_54_1, all_56_3, all_40_0,
% 11.83/3.67 | | | | | simplifying with (72), (79) gives:
% 11.83/3.67 | | | | | (88) all_56_3 = all_54_1
% 11.83/3.67 | | | | |
% 11.83/3.67 | | | | | COMBINE_EQS: (85), (86) imply:
% 11.83/3.67 | | | | | (89) all_52_1 = 0
% 11.83/3.67 | | | | |
% 11.83/3.67 | | | | | SIMP: (89) implies:
% 11.83/3.67 | | | | | (90) all_52_1 = 0
% 11.83/3.67 | | | | |
% 11.83/3.67 | | | | | COMBINE_EQS: (87), (88) imply:
% 11.83/3.67 | | | | | (91) all_54_1 = 0
% 11.83/3.67 | | | | |
% 11.83/3.67 | | | | | SIMP: (91) implies:
% 11.83/3.67 | | | | | (92) all_54_1 = 0
% 11.83/3.67 | | | | |
% 11.83/3.67 | | | | | COMBINE_EQS: (83), (84) imply:
% 11.83/3.67 | | | | | (93) all_54_2 = 0
% 11.83/3.67 | | | | |
% 11.83/3.67 | | | | | SIMP: (93) implies:
% 11.83/3.67 | | | | | (94) all_54_2 = 0
% 11.83/3.67 | | | | |
% 11.83/3.67 | | | | | BETA: splitting (82) gives:
% 11.83/3.67 | | | | |
% 11.83/3.67 | | | | | Case 1:
% 11.83/3.67 | | | | | |
% 11.83/3.67 | | | | | | (95) ~ (all_56_2 = 0)
% 11.83/3.67 | | | | | |
% 11.83/3.67 | | | | | | REDUCE: (85), (95) imply:
% 11.83/3.67 | | | | | | (96) $false
% 11.83/3.67 | | | | | |
% 11.83/3.67 | | | | | | CLOSE: (96) is inconsistent.
% 11.83/3.67 | | | | | |
% 11.83/3.67 | | | | | Case 2:
% 11.83/3.67 | | | | | |
% 11.83/3.67 | | | | | | (97) ~ (all_56_3 = 0) | ~ (all_56_4 = 0) | all_56_0 = xl
% 11.83/3.67 | | | | | |
% 11.83/3.67 | | | | | | BETA: splitting (74) gives:
% 11.83/3.67 | | | | | |
% 11.83/3.67 | | | | | | Case 1:
% 11.83/3.67 | | | | | | |
% 11.83/3.67 | | | | | | | (98) ~ (all_54_1 = 0)
% 11.83/3.67 | | | | | | |
% 11.83/3.67 | | | | | | | REDUCE: (92), (98) imply:
% 11.83/3.67 | | | | | | | (99) $false
% 11.83/3.67 | | | | | | |
% 11.83/3.67 | | | | | | | CLOSE: (99) is inconsistent.
% 11.83/3.67 | | | | | | |
% 11.83/3.67 | | | | | | Case 2:
% 11.83/3.67 | | | | | | |
% 11.83/3.67 | | | | | | | (100) ~ (all_54_2 = 0) | all_54_0 = xn
% 11.83/3.67 | | | | | | |
% 11.83/3.67 | | | | | | | BETA: splitting (100) gives:
% 11.83/3.67 | | | | | | |
% 11.83/3.67 | | | | | | | Case 1:
% 11.83/3.67 | | | | | | | |
% 11.83/3.68 | | | | | | | | (101) ~ (all_54_2 = 0)
% 11.83/3.68 | | | | | | | |
% 11.83/3.68 | | | | | | | | REDUCE: (94), (101) imply:
% 11.83/3.68 | | | | | | | | (102) $false
% 11.83/3.68 | | | | | | | |
% 11.83/3.68 | | | | | | | | CLOSE: (102) is inconsistent.
% 11.83/3.68 | | | | | | | |
% 11.83/3.68 | | | | | | | Case 2:
% 11.83/3.68 | | | | | | | |
% 11.83/3.68 | | | | | | | | (103) all_54_0 = xn
% 11.83/3.68 | | | | | | | |
% 11.83/3.68 | | | | | | | | REDUCE: (73), (103) imply:
% 11.83/3.68 | | | | | | | | (104) sdtpldt0(all_40_0, xm) = xn
% 11.83/3.68 | | | | | | | |
% 11.83/3.68 | | | | | | | | BETA: splitting (97) gives:
% 11.83/3.68 | | | | | | | |
% 11.83/3.68 | | | | | | | | Case 1:
% 11.83/3.68 | | | | | | | | |
% 11.83/3.68 | | | | | | | | | (105) ~ (all_56_3 = 0)
% 11.83/3.68 | | | | | | | | |
% 11.83/3.68 | | | | | | | | | REDUCE: (87), (105) imply:
% 11.83/3.68 | | | | | | | | | (106) $false
% 11.83/3.68 | | | | | | | | |
% 11.83/3.68 | | | | | | | | | CLOSE: (106) is inconsistent.
% 11.83/3.68 | | | | | | | | |
% 11.83/3.68 | | | | | | | | Case 2:
% 11.83/3.68 | | | | | | | | |
% 11.83/3.68 | | | | | | | | | (107) ~ (all_56_4 = 0) | all_56_0 = xl
% 11.83/3.68 | | | | | | | | |
% 11.83/3.68 | | | | | | | | | BETA: splitting (107) gives:
% 11.83/3.68 | | | | | | | | |
% 11.83/3.68 | | | | | | | | | Case 1:
% 11.83/3.68 | | | | | | | | | |
% 11.83/3.68 | | | | | | | | | | (108) ~ (all_56_4 = 0)
% 11.83/3.68 | | | | | | | | | |
% 11.83/3.68 | | | | | | | | | | REDUCE: (83), (108) imply:
% 11.83/3.68 | | | | | | | | | | (109) $false
% 11.83/3.68 | | | | | | | | | |
% 11.83/3.68 | | | | | | | | | | CLOSE: (109) is inconsistent.
% 11.83/3.68 | | | | | | | | | |
% 11.83/3.68 | | | | | | | | | Case 2:
% 11.83/3.68 | | | | | | | | | |
% 11.83/3.68 | | | | | | | | | | (110) all_56_0 = xl
% 11.83/3.68 | | | | | | | | | |
% 11.83/3.68 | | | | | | | | | | REDUCE: (80), (110) imply:
% 11.83/3.68 | | | | | | | | | | (111) sdtpldt0(xm, all_56_1) = xl
% 11.83/3.68 | | | | | | | | | |
% 11.83/3.68 | | | | | | | | | | GROUND_INST: instantiating (64) with all_56_1, simplifying with
% 11.83/3.68 | | | | | | | | | | (76), (111) gives:
% 11.83/3.68 | | | | | | | | | | (112) ? [v0: int] : ( ~ (v0 = 0) &
% 11.83/3.68 | | | | | | | | | | aNaturalNumber0(all_56_1) = v0)
% 11.83/3.68 | | | | | | | | | |
% 11.83/3.68 | | | | | | | | | | GROUND_INST: instantiating (mAddComm) with xm, all_56_1, xl,
% 11.83/3.68 | | | | | | | | | | simplifying with (4), (76), (111) gives:
% 11.83/3.68 | | | | | | | | | | (113) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 11.83/3.68 | | | | | | | | | | (sdtpldt0(all_56_1, xm) = v2 &
% 11.83/3.68 | | | | | | | | | | aNaturalNumber0(all_56_1) = v1 &
% 11.83/3.68 | | | | | | | | | | aNaturalNumber0(xm) = v0 & $i(v2) & ( ~ (v1 = 0)
% 11.83/3.68 | | | | | | | | | | | ~ (v0 = 0) | v2 = xl))
% 11.83/3.68 | | | | | | | | | |
% 11.83/3.68 | | | | | | | | | | GROUND_INST: instantiating (mSortsB) with xm, all_56_1, xl,
% 11.83/3.68 | | | | | | | | | | simplifying with (4), (76), (111) gives:
% 11.83/3.68 | | | | | | | | | | (114) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 11.83/3.68 | | | | | | | | | | (aNaturalNumber0(all_56_1) = v1 &
% 11.83/3.68 | | | | | | | | | | aNaturalNumber0(xl) = v2 & aNaturalNumber0(xm) =
% 11.83/3.68 | | | | | | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 11.83/3.68 | | | | | | | | | |
% 11.83/3.68 | | | | | | | | | | GROUND_INST: instantiating (mAddAsso) with all_40_0, xm,
% 11.83/3.68 | | | | | | | | | | all_30_0, xn, xl, simplifying with (4), (30),
% 11.83/3.68 | | | | | | | | | | (32), (59), (104) gives:
% 11.83/3.68 | | | | | | | | | | (115) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 11.83/3.69 | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtpldt0(all_40_0, v3) =
% 11.83/3.69 | | | | | | | | | | v4 & sdtpldt0(xm, all_30_0) = v3 &
% 11.83/3.69 | | | | | | | | | | aNaturalNumber0(all_40_0) = v0 &
% 11.83/3.69 | | | | | | | | | | aNaturalNumber0(all_30_0) = v2 &
% 11.83/3.69 | | | | | | | | | | aNaturalNumber0(xm) = v1 & $i(v4) & $i(v3) & ( ~
% 11.83/3.69 | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 =
% 11.83/3.69 | | | | | | | | | | xl))
% 11.83/3.69 | | | | | | | | | |
% 11.83/3.69 | | | | | | | | | | GROUND_INST: instantiating (mAddComm) with all_40_0, all_30_0,
% 11.83/3.69 | | | | | | | | | | all_56_1, simplifying with (30), (59), (81) gives:
% 11.83/3.69 | | | | | | | | | | (116) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 11.83/3.69 | | | | | | | | | | (sdtpldt0(all_30_0, all_40_0) = v2 &
% 11.83/3.69 | | | | | | | | | | aNaturalNumber0(all_40_0) = v0 &
% 11.83/3.69 | | | | | | | | | | aNaturalNumber0(all_30_0) = v1 & $i(v2) & ( ~ (v1
% 11.83/3.69 | | | | | | | | | | = 0) | ~ (v0 = 0) | v2 = all_56_1))
% 11.83/3.69 | | | | | | | | | |
% 11.83/3.69 | | | | | | | | | | GROUND_INST: instantiating (mSortsB) with all_40_0, all_30_0,
% 11.83/3.69 | | | | | | | | | | all_56_1, simplifying with (30), (59), (81) gives:
% 11.83/3.69 | | | | | | | | | | (117) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 11.83/3.69 | | | | | | | | | | (aNaturalNumber0(all_56_1) = v2 &
% 11.83/3.69 | | | | | | | | | | aNaturalNumber0(all_40_0) = v0 &
% 11.83/3.69 | | | | | | | | | | aNaturalNumber0(all_30_0) = v1 & ( ~ (v1 = 0) |
% 11.83/3.69 | | | | | | | | | | ~ (v0 = 0) | v2 = 0))
% 11.83/3.69 | | | | | | | | | |
% 11.83/3.69 | | | | | | | | | | DELTA: instantiating (112) with fresh symbol all_95_0 gives:
% 11.83/3.69 | | | | | | | | | | (118) ~ (all_95_0 = 0) & aNaturalNumber0(all_56_1) =
% 11.83/3.69 | | | | | | | | | | all_95_0
% 11.83/3.69 | | | | | | | | | |
% 11.83/3.69 | | | | | | | | | | ALPHA: (118) implies:
% 11.83/3.69 | | | | | | | | | | (119) ~ (all_95_0 = 0)
% 11.83/3.69 | | | | | | | | | | (120) aNaturalNumber0(all_56_1) = all_95_0
% 11.83/3.69 | | | | | | | | | |
% 11.83/3.69 | | | | | | | | | | DELTA: instantiating (117) with fresh symbols all_97_0,
% 11.83/3.69 | | | | | | | | | | all_97_1, all_97_2 gives:
% 11.83/3.69 | | | | | | | | | | (121) aNaturalNumber0(all_56_1) = all_97_0 &
% 11.83/3.69 | | | | | | | | | | aNaturalNumber0(all_40_0) = all_97_2 &
% 11.83/3.69 | | | | | | | | | | aNaturalNumber0(all_30_0) = all_97_1 & ( ~
% 11.83/3.69 | | | | | | | | | | (all_97_1 = 0) | ~ (all_97_2 = 0) | all_97_0 =
% 11.83/3.69 | | | | | | | | | | 0)
% 11.83/3.69 | | | | | | | | | |
% 11.83/3.69 | | | | | | | | | | ALPHA: (121) implies:
% 11.83/3.69 | | | | | | | | | | (122) aNaturalNumber0(all_30_0) = all_97_1
% 11.83/3.69 | | | | | | | | | | (123) aNaturalNumber0(all_40_0) = all_97_2
% 11.83/3.69 | | | | | | | | | | (124) aNaturalNumber0(all_56_1) = all_97_0
% 11.83/3.69 | | | | | | | | | | (125) ~ (all_97_1 = 0) | ~ (all_97_2 = 0) | all_97_0 =
% 11.83/3.69 | | | | | | | | | | 0
% 11.83/3.69 | | | | | | | | | |
% 11.83/3.69 | | | | | | | | | | DELTA: instantiating (114) with fresh symbols all_99_0,
% 11.83/3.69 | | | | | | | | | | all_99_1, all_99_2 gives:
% 11.83/3.69 | | | | | | | | | | (126) aNaturalNumber0(all_56_1) = all_99_1 &
% 11.83/3.69 | | | | | | | | | | aNaturalNumber0(xl) = all_99_0 &
% 11.83/3.69 | | | | | | | | | | aNaturalNumber0(xm) = all_99_2 & ( ~ (all_99_1 = 0)
% 11.83/3.69 | | | | | | | | | | | ~ (all_99_2 = 0) | all_99_0 = 0)
% 11.83/3.69 | | | | | | | | | |
% 11.83/3.69 | | | | | | | | | | ALPHA: (126) implies:
% 11.83/3.69 | | | | | | | | | | (127) aNaturalNumber0(all_56_1) = all_99_1
% 11.83/3.69 | | | | | | | | | |
% 11.83/3.69 | | | | | | | | | | DELTA: instantiating (113) with fresh symbols all_101_0,
% 11.83/3.69 | | | | | | | | | | all_101_1, all_101_2 gives:
% 11.83/3.69 | | | | | | | | | | (128) sdtpldt0(all_56_1, xm) = all_101_0 &
% 11.83/3.69 | | | | | | | | | | aNaturalNumber0(all_56_1) = all_101_1 &
% 11.83/3.69 | | | | | | | | | | aNaturalNumber0(xm) = all_101_2 & $i(all_101_0) & (
% 11.83/3.69 | | | | | | | | | | ~ (all_101_1 = 0) | ~ (all_101_2 = 0) |
% 11.83/3.69 | | | | | | | | | | all_101_0 = xl)
% 11.83/3.69 | | | | | | | | | |
% 11.83/3.69 | | | | | | | | | | ALPHA: (128) implies:
% 11.83/3.69 | | | | | | | | | | (129) aNaturalNumber0(all_56_1) = all_101_1
% 11.83/3.69 | | | | | | | | | |
% 11.83/3.69 | | | | | | | | | | DELTA: instantiating (116) with fresh symbols all_103_0,
% 11.83/3.69 | | | | | | | | | | all_103_1, all_103_2 gives:
% 11.83/3.70 | | | | | | | | | | (130) sdtpldt0(all_30_0, all_40_0) = all_103_0 &
% 11.83/3.70 | | | | | | | | | | aNaturalNumber0(all_40_0) = all_103_2 &
% 11.83/3.70 | | | | | | | | | | aNaturalNumber0(all_30_0) = all_103_1 &
% 11.83/3.70 | | | | | | | | | | $i(all_103_0) & ( ~ (all_103_1 = 0) | ~ (all_103_2
% 11.83/3.70 | | | | | | | | | | = 0) | all_103_0 = all_56_1)
% 11.83/3.70 | | | | | | | | | |
% 11.83/3.70 | | | | | | | | | | ALPHA: (130) implies:
% 11.83/3.70 | | | | | | | | | | (131) aNaturalNumber0(all_30_0) = all_103_1
% 11.83/3.70 | | | | | | | | | | (132) aNaturalNumber0(all_40_0) = all_103_2
% 11.83/3.70 | | | | | | | | | |
% 11.83/3.70 | | | | | | | | | | DELTA: instantiating (115) with fresh symbols all_105_0,
% 11.83/3.70 | | | | | | | | | | all_105_1, all_105_2, all_105_3, all_105_4 gives:
% 11.83/3.70 | | | | | | | | | | (133) sdtpldt0(all_40_0, all_105_1) = all_105_0 &
% 11.83/3.70 | | | | | | | | | | sdtpldt0(xm, all_30_0) = all_105_1 &
% 11.83/3.70 | | | | | | | | | | aNaturalNumber0(all_40_0) = all_105_4 &
% 11.83/3.70 | | | | | | | | | | aNaturalNumber0(all_30_0) = all_105_2 &
% 11.83/3.70 | | | | | | | | | | aNaturalNumber0(xm) = all_105_3 & $i(all_105_0) &
% 11.83/3.70 | | | | | | | | | | $i(all_105_1) & ( ~ (all_105_2 = 0) | ~ (all_105_3
% 11.83/3.70 | | | | | | | | | | = 0) | ~ (all_105_4 = 0) | all_105_0 = xl)
% 11.83/3.70 | | | | | | | | | |
% 11.83/3.70 | | | | | | | | | | ALPHA: (133) implies:
% 11.83/3.70 | | | | | | | | | | (134) aNaturalNumber0(all_30_0) = all_105_2
% 11.83/3.70 | | | | | | | | | | (135) aNaturalNumber0(all_40_0) = all_105_4
% 11.83/3.70 | | | | | | | | | |
% 11.97/3.70 | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_105_2, all_30_0,
% 11.97/3.70 | | | | | | | | | | simplifying with (31), (134) gives:
% 11.97/3.70 | | | | | | | | | | (136) all_105_2 = 0
% 11.97/3.70 | | | | | | | | | |
% 11.97/3.70 | | | | | | | | | | GROUND_INST: instantiating (8) with all_103_1, all_105_2,
% 11.97/3.70 | | | | | | | | | | all_30_0, simplifying with (131), (134) gives:
% 11.97/3.70 | | | | | | | | | | (137) all_105_2 = all_103_1
% 11.97/3.70 | | | | | | | | | |
% 11.97/3.70 | | | | | | | | | | GROUND_INST: instantiating (8) with all_97_1, all_105_2,
% 11.97/3.70 | | | | | | | | | | all_30_0, simplifying with (122), (134) gives:
% 11.97/3.70 | | | | | | | | | | (138) all_105_2 = all_97_1
% 11.97/3.70 | | | | | | | | | |
% 11.97/3.70 | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_103_2, all_40_0,
% 11.97/3.70 | | | | | | | | | | simplifying with (60), (132) gives:
% 11.97/3.70 | | | | | | | | | | (139) all_103_2 = 0
% 11.97/3.70 | | | | | | | | | |
% 11.97/3.70 | | | | | | | | | | GROUND_INST: instantiating (8) with all_103_2, all_105_4,
% 11.97/3.70 | | | | | | | | | | all_40_0, simplifying with (132), (135) gives:
% 11.97/3.70 | | | | | | | | | | (140) all_105_4 = all_103_2
% 11.97/3.70 | | | | | | | | | |
% 11.97/3.70 | | | | | | | | | | GROUND_INST: instantiating (8) with all_97_2, all_105_4,
% 11.97/3.70 | | | | | | | | | | all_40_0, simplifying with (123), (135) gives:
% 11.97/3.70 | | | | | | | | | | (141) all_105_4 = all_97_2
% 11.97/3.70 | | | | | | | | | |
% 11.97/3.70 | | | | | | | | | | GROUND_INST: instantiating (8) with all_97_0, all_99_1,
% 11.97/3.70 | | | | | | | | | | all_56_1, simplifying with (124), (127) gives:
% 11.97/3.70 | | | | | | | | | | (142) all_99_1 = all_97_0
% 11.97/3.70 | | | | | | | | | |
% 11.97/3.70 | | | | | | | | | | GROUND_INST: instantiating (8) with all_99_1, all_101_1,
% 11.97/3.70 | | | | | | | | | | all_56_1, simplifying with (127), (129) gives:
% 11.97/3.70 | | | | | | | | | | (143) all_101_1 = all_99_1
% 11.97/3.70 | | | | | | | | | |
% 11.97/3.70 | | | | | | | | | | GROUND_INST: instantiating (8) with all_95_0, all_101_1,
% 11.97/3.70 | | | | | | | | | | all_56_1, simplifying with (120), (129) gives:
% 11.97/3.70 | | | | | | | | | | (144) all_101_1 = all_95_0
% 11.97/3.70 | | | | | | | | | |
% 11.97/3.70 | | | | | | | | | | COMBINE_EQS: (137), (138) imply:
% 11.97/3.70 | | | | | | | | | | (145) all_103_1 = all_97_1
% 11.97/3.70 | | | | | | | | | |
% 11.97/3.70 | | | | | | | | | | COMBINE_EQS: (136), (137) imply:
% 11.97/3.70 | | | | | | | | | | (146) all_103_1 = 0
% 11.97/3.70 | | | | | | | | | |
% 11.97/3.70 | | | | | | | | | | COMBINE_EQS: (140), (141) imply:
% 11.97/3.70 | | | | | | | | | | (147) all_103_2 = all_97_2
% 11.97/3.70 | | | | | | | | | |
% 11.97/3.70 | | | | | | | | | | SIMP: (147) implies:
% 11.97/3.70 | | | | | | | | | | (148) all_103_2 = all_97_2
% 11.97/3.70 | | | | | | | | | |
% 11.97/3.70 | | | | | | | | | | COMBINE_EQS: (145), (146) imply:
% 11.97/3.70 | | | | | | | | | | (149) all_97_1 = 0
% 11.97/3.70 | | | | | | | | | |
% 11.97/3.70 | | | | | | | | | | COMBINE_EQS: (139), (148) imply:
% 11.97/3.70 | | | | | | | | | | (150) all_97_2 = 0
% 11.97/3.71 | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | COMBINE_EQS: (143), (144) imply:
% 11.97/3.71 | | | | | | | | | | (151) all_99_1 = all_95_0
% 11.97/3.71 | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | SIMP: (151) implies:
% 11.97/3.71 | | | | | | | | | | (152) all_99_1 = all_95_0
% 11.97/3.71 | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | COMBINE_EQS: (142), (152) imply:
% 11.97/3.71 | | | | | | | | | | (153) all_97_0 = all_95_0
% 11.97/3.71 | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | SIMP: (153) implies:
% 11.97/3.71 | | | | | | | | | | (154) all_97_0 = all_95_0
% 11.97/3.71 | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | BETA: splitting (125) gives:
% 11.97/3.71 | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | Case 1:
% 11.97/3.71 | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | | (155) ~ (all_97_1 = 0)
% 11.97/3.71 | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | | REDUCE: (149), (155) imply:
% 11.97/3.71 | | | | | | | | | | | (156) $false
% 11.97/3.71 | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | | CLOSE: (156) is inconsistent.
% 11.97/3.71 | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | Case 2:
% 11.97/3.71 | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | | (157) ~ (all_97_2 = 0) | all_97_0 = 0
% 11.97/3.71 | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | | BETA: splitting (157) gives:
% 11.97/3.71 | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | | Case 1:
% 11.97/3.71 | | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | | | (158) ~ (all_97_2 = 0)
% 11.97/3.71 | | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | | | REDUCE: (150), (158) imply:
% 11.97/3.71 | | | | | | | | | | | | (159) $false
% 11.97/3.71 | | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 11.97/3.71 | | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | | Case 2:
% 11.97/3.71 | | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | | | (160) all_97_0 = 0
% 11.97/3.71 | | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | | | COMBINE_EQS: (154), (160) imply:
% 11.97/3.71 | | | | | | | | | | | | (161) all_95_0 = 0
% 11.97/3.71 | | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | | | SIMP: (161) implies:
% 11.97/3.71 | | | | | | | | | | | | (162) all_95_0 = 0
% 11.97/3.71 | | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | | | REDUCE: (119), (162) imply:
% 11.97/3.71 | | | | | | | | | | | | (163) $false
% 11.97/3.71 | | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | | | CLOSE: (163) is inconsistent.
% 11.97/3.71 | | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | | End of split
% 11.97/3.71 | | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | | End of split
% 11.97/3.71 | | | | | | | | | |
% 11.97/3.71 | | | | | | | | | End of split
% 11.97/3.71 | | | | | | | | |
% 11.97/3.71 | | | | | | | | End of split
% 11.97/3.71 | | | | | | | |
% 11.97/3.71 | | | | | | | End of split
% 11.97/3.71 | | | | | | |
% 11.97/3.71 | | | | | | End of split
% 11.97/3.71 | | | | | |
% 11.97/3.71 | | | | | End of split
% 11.97/3.71 | | | | |
% 11.97/3.71 | | | | End of split
% 11.97/3.71 | | | |
% 11.97/3.71 | | | End of split
% 11.97/3.71 | | |
% 11.97/3.71 | | End of split
% 11.97/3.71 | |
% 11.97/3.71 | End of split
% 11.97/3.71 |
% 11.97/3.71 End of proof
% 11.97/3.71 % SZS output end Proof for theBenchmark
% 11.97/3.71
% 11.97/3.71 3118ms
%------------------------------------------------------------------------------