TSTP Solution File: NUM504+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM504+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 : n009.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 11:48:13 EDT 2023
% Result : Theorem 11.76s 2.40s
% Output : Proof 32.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM504+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 13:33:51 EDT 2023
% 0.14/0.34 % 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 ...
% 0.50/0.62 Running up to 7 provers in parallel.
% 0.50/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.50/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.50/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.50/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.50/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.50/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.50/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.47/1.23 Prover 4: Preprocessing ...
% 3.47/1.23 Prover 1: Preprocessing ...
% 3.71/1.28 Prover 2: Preprocessing ...
% 3.71/1.28 Prover 6: Preprocessing ...
% 3.71/1.28 Prover 0: Preprocessing ...
% 3.71/1.28 Prover 5: Preprocessing ...
% 3.71/1.28 Prover 3: Preprocessing ...
% 9.49/2.03 Prover 1: Constructing countermodel ...
% 9.49/2.03 Prover 3: Constructing countermodel ...
% 9.49/2.06 Prover 6: Proving ...
% 9.49/2.09 Prover 5: Constructing countermodel ...
% 11.58/2.32 Prover 2: Proving ...
% 11.76/2.35 Prover 4: Constructing countermodel ...
% 11.76/2.40 Prover 3: proved (1768ms)
% 11.76/2.40
% 11.76/2.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.76/2.40
% 11.76/2.40 Prover 2: stopped
% 11.76/2.40 Prover 5: stopped
% 11.76/2.41 Prover 6: stopped
% 11.76/2.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.76/2.43 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.76/2.43 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.76/2.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.60/2.55 Prover 7: Preprocessing ...
% 13.70/2.61 Prover 8: Preprocessing ...
% 13.70/2.62 Prover 0: Proving ...
% 13.70/2.62 Prover 11: Preprocessing ...
% 13.70/2.62 Prover 0: stopped
% 13.70/2.64 Prover 10: Preprocessing ...
% 13.70/2.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.48/2.70 Prover 13: Preprocessing ...
% 15.48/2.88 Prover 10: Constructing countermodel ...
% 16.03/2.93 Prover 8: Warning: ignoring some quantifiers
% 16.03/2.94 Prover 8: Constructing countermodel ...
% 16.80/3.04 Prover 13: Constructing countermodel ...
% 16.80/3.05 Prover 7: Constructing countermodel ...
% 18.30/3.26 Prover 11: Constructing countermodel ...
% 31.31/4.94 Prover 8: Found proof (size 266)
% 31.31/4.94 Prover 8: proved (2508ms)
% 31.31/4.94 Prover 4: stopped
% 31.31/4.94 Prover 11: stopped
% 31.31/4.94 Prover 10: stopped
% 31.31/4.94 Prover 7: stopped
% 31.31/4.94 Prover 13: stopped
% 31.31/4.94 Prover 1: stopped
% 31.31/4.94
% 31.31/4.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.31/4.95
% 31.86/4.98 % SZS output start Proof for theBenchmark
% 31.86/4.99 Assumptions after simplification:
% 31.86/4.99 ---------------------------------
% 31.86/4.99
% 31.86/4.99 (mAddAsso)
% 31.94/5.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 31.94/5.02 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 31.94/5.02 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ?
% 31.94/5.02 [v9: $i] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 &
% 31.94/5.02 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0)
% 31.94/5.02 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 =
% 31.94/5.02 v4)))
% 31.94/5.02
% 31.94/5.02 (mAddComm)
% 31.94/5.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 31.94/5.02 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 31.94/5.02 (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3
% 31.94/5.02 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 31.94/5.02
% 31.94/5.02 (mDefPrime)
% 31.94/5.02 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: any] : ( ~ (isPrime0(v0) = v1) |
% 31.94/5.02 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (( ~
% 31.94/5.02 (v1 = 0) | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v2: $i] : (v2 = v0 |
% 31.94/5.02 v2 = sz10 | ~ (doDivides0(v2, v0) = 0) | ~ $i(v2) | ? [v3: int] :
% 31.94/5.02 ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)))) & (v1 = 0 | v0 = sz10 |
% 31.94/5.02 v0 = sz00 | ? [v2: $i] : ( ~ (v2 = v0) & ~ (v2 = sz10) &
% 31.94/5.02 doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0 & $i(v2)))))
% 31.94/5.02
% 31.94/5.02 (mDefQuot)
% 31.94/5.02 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~
% 31.94/5.02 (sdtsldt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 31.94/5.02 any] : ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4
% 31.94/5.02 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))) |
% 31.94/5.02 ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | ~ $i(v3) | ? [v4:
% 31.94/5.02 int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) & ! [v3: $i] : ( ~
% 31.94/5.02 (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | (v3 = v1 & aNaturalNumber0(v2) =
% 31.94/5.02 0))))
% 31.94/5.02
% 31.94/5.02 (mLEAsym)
% 31.94/5.03 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ $i(v1)
% 31.94/5.03 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (sdtlseqdt0(v1,
% 31.94/5.03 v0) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v4
% 31.94/5.03 = 0) | ~ (v3 = 0) | ~ (v2 = 0))))
% 31.94/5.03
% 31.94/5.03 (mLETran)
% 31.94/5.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 31.94/5.03 (sdtlseqdt0(v0, v2) = v3) | ~ (sdtlseqdt0(v0, v1) = 0) | ~ $i(v2) | ~
% 31.94/5.03 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7:
% 31.94/5.03 any] : (sdtlseqdt0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 &
% 31.94/5.03 aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~
% 31.94/5.03 (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 31.94/5.03
% 31.94/5.03 (mMulComm)
% 31.94/5.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 31.94/5.03 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 31.94/5.03 (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3
% 31.94/5.03 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 31.94/5.03
% 31.94/5.03 (mSortsB)
% 31.94/5.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 31.94/5.03 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 31.94/5.03 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 31.94/5.03 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 31.94/5.03
% 31.94/5.03 (mSortsB_02)
% 31.94/5.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 31.94/5.03 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 31.94/5.03 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 31.94/5.03 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 31.94/5.03
% 31.94/5.03 (m__1799)
% 31.94/5.03 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, xp) = v1
% 31.94/5.03 & sdtpldt0(xn, xm) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : !
% 31.94/5.03 [v4: $i] : ! [v5: $i] : ( ~ (doDivides0(v4, v5) = 0) | ~ (sdtasdt0(v2, v3)
% 31.94/5.03 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any]
% 31.94/5.03 : ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: $i] : ? [v12:
% 31.94/5.03 any] : ? [v13: any] : ? [v14: any] : (isPrime0(v4) = v9 &
% 31.94/5.03 doDivides0(v4, v3) = v14 & doDivides0(v4, v2) = v13 & iLess0(v11, v1) =
% 31.94/5.03 v12 & sdtpldt0(v10, v4) = v11 & sdtpldt0(v2, v3) = v10 &
% 31.94/5.03 aNaturalNumber0(v4) = v8 & aNaturalNumber0(v3) = v7 &
% 31.94/5.03 aNaturalNumber0(v2) = v6 & $i(v11) & $i(v10) & ( ~ (v12 = 0) | ~ (v9 =
% 31.94/5.03 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | v14 = 0 | v13 = 0))))
% 31.94/5.03
% 31.94/5.03 (m__1837)
% 31.94/5.03 aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 &
% 31.94/5.03 $i(xp) & $i(xm) & $i(xn)
% 31.94/5.03
% 31.94/5.03 (m__1860)
% 31.94/5.04 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (isPrime0(xp) = 0 & doDivides0(xp,
% 31.94/5.04 v0) = 0 & sdtasdt0(xn, xm) = v0 & $i(v0))
% 31.94/5.04
% 31.94/5.04 (m__1870)
% 31.94/5.04 $i(xp) & $i(xn) & ? [v0: int] : ( ~ (v0 = 0) & sdtlseqdt0(xp, xn) = v0)
% 31.94/5.04
% 31.94/5.04 (m__2075)
% 31.94/5.04 $i(xp) & $i(xm) & ? [v0: int] : ( ~ (v0 = 0) & sdtlseqdt0(xp, xm) = v0)
% 31.94/5.04
% 31.94/5.04 (m__2306)
% 31.94/5.04 $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (sdtsldt0(v0, xp) = xk &
% 31.94/5.04 sdtasdt0(xn, xm) = v0 & $i(v0))
% 31.94/5.04
% 31.94/5.04 (m__2362)
% 31.94/5.04 $i(xr) & $i(xk) & $i(xm) & $i(xn) & ? [v0: $i] : (doDivides0(xr, v0) = 0 &
% 31.94/5.04 sdtlseqdt0(xr, xk) = 0 & sdtasdt0(xn, xm) = v0 & $i(v0))
% 31.94/5.04
% 31.94/5.04 (m__2389)
% 31.94/5.04 sdtlseqdt0(xp, xk) = 0 & $i(xk) & $i(xp)
% 31.94/5.04
% 31.94/5.04 (m__2414)
% 31.94/5.04 $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 31.94/5.04 ( ~ (v2 = v1) & ~ (v1 = v0) & sdtlseqdt0(v1, v2) = 0 & sdtlseqdt0(v0, v1) = 0
% 31.94/5.04 & sdtasdt0(xp, xk) = v2 & sdtasdt0(xp, xm) = v1 & sdtasdt0(xn, xm) = v0 &
% 31.94/5.04 $i(v2) & $i(v1) & $i(v0))
% 31.94/5.04
% 31.94/5.04 (function-axioms)
% 31.94/5.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 31.94/5.04 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0:
% 31.94/5.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 31.94/5.04 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & !
% 31.94/5.04 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 31.94/5.04 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & !
% 31.94/5.04 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 31.94/5.04 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0:
% 31.94/5.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 31.94/5.04 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 31.94/5.04 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 31.94/5.04 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 31.94/5.04 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 31.94/5.04 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 31.94/5.05 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~
% 31.94/5.05 (isPrime0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 31.94/5.05 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1)
% 31.94/5.05 | ~ (aNaturalNumber0(v2) = v0)) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 31.94/5.05 MultipleValueBool] : (doDivides0(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] :
% 31.94/5.05 ? [v2: MultipleValueBool] : (iLess0(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i]
% 31.94/5.05 : ? [v2: MultipleValueBool] : (sdtlseqdt0(v1, v0) = v2) & ? [v0: $i] : ?
% 31.94/5.05 [v1: $i] : ? [v2: $i] : (sdtsldt0(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ?
% 31.94/5.05 [v1: $i] : ? [v2: $i] : (sdtmndt0(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ?
% 31.94/5.05 [v1: $i] : ? [v2: $i] : (sdtasdt0(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ?
% 31.94/5.05 [v1: $i] : ? [v2: $i] : (sdtpldt0(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ?
% 31.94/5.05 [v1: MultipleValueBool] : (isPrime0(v0) = v1) & ? [v0: $i] : ? [v1:
% 31.94/5.05 MultipleValueBool] : (aNaturalNumber0(v0) = v1)
% 31.94/5.05
% 31.94/5.05 Further assumptions not needed in the proof:
% 31.94/5.05 --------------------------------------------
% 31.94/5.05 mAMDistr, mAddCanc, mDefDiff, mDefDiv, mDefLE, mDivAsso, mDivLE, mDivMin,
% 31.94/5.05 mDivSum, mDivTrans, mIH, mIH_03, mLENTr, mLERefl, mLETotal, mMonAdd, mMonMul,
% 31.94/5.05 mMonMul2, mMulAsso, mMulCanc, mNatSort, mPrimDiv, mSortsC, mSortsC_01, mZeroAdd,
% 31.94/5.05 mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__, m__2287, m__2315, m__2327,
% 31.94/5.05 m__2342
% 31.94/5.05
% 31.94/5.05 Those formulas are unsatisfiable:
% 31.94/5.05 ---------------------------------
% 31.94/5.05
% 31.94/5.05 Begin of proof
% 31.94/5.05 |
% 31.94/5.05 | ALPHA: (mDefQuot) implies:
% 31.94/5.05 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ (sdtsldt0(v1,
% 31.94/5.05 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 31.94/5.05 | ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 &
% 31.94/5.05 | aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 =
% 31.94/5.05 | 0))) | ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) |
% 31.94/5.05 | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) =
% 31.94/5.05 | v4)) & ! [v3: $i] : ( ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) |
% 31.94/5.05 | (v3 = v1 & aNaturalNumber0(v2) = 0))))
% 31.94/5.05 |
% 31.94/5.05 | ALPHA: (mDefPrime) implies:
% 31.94/5.05 | (2) ! [v0: $i] : ! [v1: any] : ( ~ (isPrime0(v0) = v1) | ~ $i(v0) | ?
% 31.94/5.05 | [v2: int] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (( ~ (v1 = 0)
% 31.94/5.05 | | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v2: $i] : (v2 = v0 | v2
% 31.94/5.05 | = sz10 | ~ (doDivides0(v2, v0) = 0) | ~ $i(v2) | ? [v3:
% 31.94/5.05 | int] : ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)))) & (v1 =
% 31.94/5.05 | 0 | v0 = sz10 | v0 = sz00 | ? [v2: $i] : ( ~ (v2 = v0) & ~ (v2
% 31.94/5.05 | = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0 &
% 31.94/5.05 | $i(v2)))))
% 31.94/5.05 |
% 31.94/5.05 | ALPHA: (m__1837) implies:
% 31.94/5.05 | (3) aNaturalNumber0(xn) = 0
% 31.94/5.05 | (4) aNaturalNumber0(xm) = 0
% 31.94/5.05 | (5) aNaturalNumber0(xp) = 0
% 31.94/5.05 |
% 31.94/5.05 | ALPHA: (m__1799) implies:
% 31.94/5.06 | (6) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) =
% 31.94/5.06 | v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 31.94/5.06 | [v5: $i] : ( ~ (doDivides0(v4, v5) = 0) | ~ (sdtasdt0(v2, v3) = v5)
% 31.94/5.06 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] :
% 31.94/5.06 | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: $i] : ?
% 31.94/5.06 | [v12: any] : ? [v13: any] : ? [v14: any] : (isPrime0(v4) = v9 &
% 31.94/5.06 | doDivides0(v4, v3) = v14 & doDivides0(v4, v2) = v13 & iLess0(v11,
% 31.94/5.06 | v1) = v12 & sdtpldt0(v10, v4) = v11 & sdtpldt0(v2, v3) = v10 &
% 31.94/5.06 | aNaturalNumber0(v4) = v8 & aNaturalNumber0(v3) = v7 &
% 31.94/5.06 | aNaturalNumber0(v2) = v6 & $i(v11) & $i(v10) & ( ~ (v12 = 0) | ~
% 31.94/5.06 | (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | v14 = 0 |
% 31.94/5.06 | v13 = 0))))
% 31.94/5.06 |
% 31.94/5.06 | ALPHA: (m__1860) implies:
% 31.94/5.06 | (7) ? [v0: $i] : (isPrime0(xp) = 0 & doDivides0(xp, v0) = 0 & sdtasdt0(xn,
% 31.94/5.06 | xm) = v0 & $i(v0))
% 31.94/5.06 |
% 31.94/5.06 | ALPHA: (m__1870) implies:
% 31.94/5.06 | (8) ? [v0: int] : ( ~ (v0 = 0) & sdtlseqdt0(xp, xn) = v0)
% 31.94/5.06 |
% 31.94/5.06 | ALPHA: (m__2075) implies:
% 31.94/5.06 | (9) ? [v0: int] : ( ~ (v0 = 0) & sdtlseqdt0(xp, xm) = v0)
% 31.94/5.06 |
% 31.94/5.06 | ALPHA: (m__2306) implies:
% 31.94/5.06 | (10) ? [v0: $i] : (sdtsldt0(v0, xp) = xk & sdtasdt0(xn, xm) = v0 & $i(v0))
% 31.94/5.06 |
% 31.94/5.06 | ALPHA: (m__2362) implies:
% 31.94/5.06 | (11) $i(xr)
% 31.94/5.06 | (12) ? [v0: $i] : (doDivides0(xr, v0) = 0 & sdtlseqdt0(xr, xk) = 0 &
% 31.94/5.06 | sdtasdt0(xn, xm) = v0 & $i(v0))
% 31.94/5.06 |
% 31.94/5.06 | ALPHA: (m__2389) implies:
% 31.94/5.06 | (13) sdtlseqdt0(xp, xk) = 0
% 31.94/5.06 |
% 31.94/5.06 | ALPHA: (m__2414) implies:
% 31.94/5.06 | (14) $i(xn)
% 31.94/5.06 | (15) $i(xm)
% 31.94/5.06 | (16) $i(xp)
% 31.94/5.06 | (17) $i(xk)
% 31.94/5.06 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & ~ (v1 = v0)
% 31.94/5.06 | & sdtlseqdt0(v1, v2) = 0 & sdtlseqdt0(v0, v1) = 0 & sdtasdt0(xp, xk)
% 31.94/5.06 | = v2 & sdtasdt0(xp, xm) = v1 & sdtasdt0(xn, xm) = v0 & $i(v2) &
% 31.94/5.06 | $i(v1) & $i(v0))
% 31.94/5.06 |
% 31.94/5.06 | ALPHA: (function-axioms) implies:
% 31.94/5.06 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 31.94/5.06 | : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) =
% 31.94/5.06 | v0))
% 31.94/5.06 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 31.94/5.06 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 31.94/5.06 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 31.94/5.06 | : ! [v3: $i] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~
% 31.94/5.06 | (sdtlseqdt0(v3, v2) = v0))
% 31.94/5.06 | (22) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 31.94/5.06 | : ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~
% 31.94/5.06 | (doDivides0(v3, v2) = v0))
% 31.94/5.06 |
% 31.94/5.06 | DELTA: instantiating (8) with fresh symbol all_54_0 gives:
% 31.94/5.06 | (23) ~ (all_54_0 = 0) & sdtlseqdt0(xp, xn) = all_54_0
% 31.94/5.06 |
% 31.94/5.06 | ALPHA: (23) implies:
% 31.94/5.07 | (24) ~ (all_54_0 = 0)
% 31.94/5.07 | (25) sdtlseqdt0(xp, xn) = all_54_0
% 31.94/5.07 |
% 31.94/5.07 | DELTA: instantiating (9) with fresh symbol all_58_0 gives:
% 31.94/5.07 | (26) ~ (all_58_0 = 0) & sdtlseqdt0(xp, xm) = all_58_0
% 31.94/5.07 |
% 31.94/5.07 | ALPHA: (26) implies:
% 31.94/5.07 | (27) ~ (all_58_0 = 0)
% 31.94/5.07 | (28) sdtlseqdt0(xp, xm) = all_58_0
% 31.94/5.07 |
% 31.94/5.07 | DELTA: instantiating (10) with fresh symbol all_60_0 gives:
% 31.94/5.07 | (29) sdtsldt0(all_60_0, xp) = xk & sdtasdt0(xn, xm) = all_60_0 &
% 31.94/5.07 | $i(all_60_0)
% 31.94/5.07 |
% 31.94/5.07 | ALPHA: (29) implies:
% 31.94/5.07 | (30) sdtasdt0(xn, xm) = all_60_0
% 31.94/5.07 | (31) sdtsldt0(all_60_0, xp) = xk
% 31.94/5.07 |
% 31.94/5.07 | DELTA: instantiating (12) with fresh symbol all_62_0 gives:
% 31.94/5.07 | (32) doDivides0(xr, all_62_0) = 0 & sdtlseqdt0(xr, xk) = 0 & sdtasdt0(xn,
% 31.94/5.07 | xm) = all_62_0 & $i(all_62_0)
% 31.94/5.07 |
% 31.94/5.07 | ALPHA: (32) implies:
% 31.94/5.07 | (33) $i(all_62_0)
% 31.94/5.07 | (34) sdtasdt0(xn, xm) = all_62_0
% 31.94/5.07 | (35) doDivides0(xr, all_62_0) = 0
% 31.94/5.07 |
% 31.94/5.07 | DELTA: instantiating (7) with fresh symbol all_64_0 gives:
% 31.94/5.07 | (36) isPrime0(xp) = 0 & doDivides0(xp, all_64_0) = 0 & sdtasdt0(xn, xm) =
% 31.94/5.07 | all_64_0 & $i(all_64_0)
% 31.94/5.07 |
% 31.94/5.07 | ALPHA: (36) implies:
% 31.94/5.07 | (37) sdtasdt0(xn, xm) = all_64_0
% 31.94/5.07 | (38) doDivides0(xp, all_64_0) = 0
% 31.94/5.07 | (39) isPrime0(xp) = 0
% 31.94/5.07 |
% 31.94/5.07 | DELTA: instantiating (18) with fresh symbols all_66_0, all_66_1, all_66_2
% 31.94/5.07 | gives:
% 31.94/5.07 | (40) ~ (all_66_0 = all_66_1) & ~ (all_66_1 = all_66_2) &
% 31.94/5.07 | sdtlseqdt0(all_66_1, all_66_0) = 0 & sdtlseqdt0(all_66_2, all_66_1) =
% 31.94/5.07 | 0 & sdtasdt0(xp, xk) = all_66_0 & sdtasdt0(xp, xm) = all_66_1 &
% 31.94/5.07 | sdtasdt0(xn, xm) = all_66_2 & $i(all_66_0) & $i(all_66_1) &
% 31.94/5.07 | $i(all_66_2)
% 31.94/5.07 |
% 31.94/5.07 | ALPHA: (40) implies:
% 31.94/5.07 | (41) ~ (all_66_1 = all_66_2)
% 31.94/5.07 | (42) ~ (all_66_0 = all_66_1)
% 31.94/5.07 | (43) $i(all_66_1)
% 31.94/5.07 | (44) $i(all_66_0)
% 31.94/5.07 | (45) sdtasdt0(xn, xm) = all_66_2
% 31.94/5.07 | (46) sdtasdt0(xp, xm) = all_66_1
% 31.94/5.07 | (47) sdtasdt0(xp, xk) = all_66_0
% 31.94/5.07 | (48) sdtlseqdt0(all_66_2, all_66_1) = 0
% 31.94/5.07 | (49) sdtlseqdt0(all_66_1, all_66_0) = 0
% 31.94/5.07 |
% 31.94/5.07 | DELTA: instantiating (6) with fresh symbols all_68_0, all_68_1 gives:
% 31.94/5.07 | (50) sdtpldt0(all_68_1, xp) = all_68_0 & sdtpldt0(xn, xm) = all_68_1 &
% 31.94/5.07 | $i(all_68_0) & $i(all_68_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 31.94/5.07 | : ! [v3: $i] : ( ~ (doDivides0(v2, v3) = 0) | ~ (sdtasdt0(v0, v1) =
% 31.94/5.07 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 32.08/5.07 | any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] :
% 32.08/5.07 | ? [v10: any] : ? [v11: any] : ? [v12: any] : (isPrime0(v2) = v7 &
% 32.08/5.07 | doDivides0(v2, v1) = v12 & doDivides0(v2, v0) = v11 & iLess0(v9,
% 32.08/5.07 | all_68_0) = v10 & sdtpldt0(v8, v2) = v9 & sdtpldt0(v0, v1) = v8
% 32.08/5.07 | & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 &
% 32.08/5.07 | aNaturalNumber0(v0) = v4 & $i(v9) & $i(v8) & ( ~ (v10 = 0) | ~
% 32.08/5.07 | (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v12 = 0 |
% 32.08/5.07 | v11 = 0)))
% 32.08/5.07 |
% 32.08/5.07 | ALPHA: (50) implies:
% 32.08/5.07 | (51) $i(all_68_1)
% 32.08/5.07 | (52) sdtpldt0(xn, xm) = all_68_1
% 32.08/5.07 | (53) sdtpldt0(all_68_1, xp) = all_68_0
% 32.08/5.08 | (54) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 32.08/5.08 | (doDivides0(v2, v3) = 0) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) |
% 32.08/5.08 | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 32.08/5.08 | ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: any] : ? [v11:
% 32.08/5.08 | any] : ? [v12: any] : (isPrime0(v2) = v7 & doDivides0(v2, v1) =
% 32.08/5.08 | v12 & doDivides0(v2, v0) = v11 & iLess0(v9, all_68_0) = v10 &
% 32.08/5.08 | sdtpldt0(v8, v2) = v9 & sdtpldt0(v0, v1) = v8 &
% 32.08/5.08 | aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 &
% 32.08/5.08 | aNaturalNumber0(v0) = v4 & $i(v9) & $i(v8) & ( ~ (v10 = 0) | ~
% 32.08/5.08 | (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v12 = 0 |
% 32.08/5.08 | v11 = 0)))
% 32.08/5.08 |
% 32.08/5.08 | GROUND_INST: instantiating (20) with all_62_0, all_64_0, xm, xn, simplifying
% 32.08/5.08 | with (34), (37) gives:
% 32.08/5.08 | (55) all_64_0 = all_62_0
% 32.08/5.08 |
% 32.08/5.08 | GROUND_INST: instantiating (20) with all_64_0, all_66_2, xm, xn, simplifying
% 32.08/5.08 | with (37), (45) gives:
% 32.08/5.08 | (56) all_66_2 = all_64_0
% 32.08/5.08 |
% 32.08/5.08 | GROUND_INST: instantiating (20) with all_60_0, all_66_2, xm, xn, simplifying
% 32.08/5.08 | with (30), (45) gives:
% 32.08/5.08 | (57) all_66_2 = all_60_0
% 32.08/5.08 |
% 32.08/5.08 | COMBINE_EQS: (56), (57) imply:
% 32.08/5.08 | (58) all_64_0 = all_60_0
% 32.08/5.08 |
% 32.08/5.08 | SIMP: (58) implies:
% 32.08/5.08 | (59) all_64_0 = all_60_0
% 32.08/5.08 |
% 32.08/5.08 | COMBINE_EQS: (55), (59) imply:
% 32.08/5.08 | (60) all_62_0 = all_60_0
% 32.08/5.08 |
% 32.08/5.08 | REDUCE: (41), (57) imply:
% 32.08/5.08 | (61) ~ (all_66_1 = all_60_0)
% 32.08/5.08 |
% 32.08/5.08 | REDUCE: (35), (60) imply:
% 32.08/5.08 | (62) doDivides0(xr, all_60_0) = 0
% 32.08/5.08 |
% 32.08/5.08 | REDUCE: (38), (59) imply:
% 32.08/5.08 | (63) doDivides0(xp, all_60_0) = 0
% 32.08/5.08 |
% 32.08/5.08 | REDUCE: (48), (57) imply:
% 32.08/5.08 | (64) sdtlseqdt0(all_60_0, all_66_1) = 0
% 32.08/5.08 |
% 32.08/5.08 | REDUCE: (33), (60) imply:
% 32.08/5.08 | (65) $i(all_60_0)
% 32.08/5.08 |
% 32.08/5.08 | GROUND_INST: instantiating (mAddComm) with xn, xm, all_68_1, simplifying with
% 32.08/5.08 | (14), (15), (52) gives:
% 32.08/5.08 | (66) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xm, xn) = v2 &
% 32.08/5.08 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v2) & ( ~
% 32.08/5.08 | (v1 = 0) | ~ (v0 = 0) | v2 = all_68_1))
% 32.08/5.08 |
% 32.08/5.08 | GROUND_INST: instantiating (mSortsB) with xn, xm, all_68_1, simplifying with
% 32.08/5.08 | (14), (15), (52) gives:
% 32.08/5.08 | (67) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 32.08/5.08 | (aNaturalNumber0(all_68_1) = v2 & aNaturalNumber0(xm) = v1 &
% 32.08/5.08 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 32.08/5.08 |
% 32.08/5.08 | GROUND_INST: instantiating (mAddAsso) with xn, xm, xp, all_68_1, all_68_0,
% 32.08/5.08 | simplifying with (14), (15), (16), (52), (53) gives:
% 32.08/5.08 | (68) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i]
% 32.08/5.08 | : (sdtpldt0(xm, xp) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(xp)
% 32.08/5.08 | = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v4)
% 32.08/5.08 | & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 =
% 32.08/5.08 | all_68_0))
% 32.08/5.08 |
% 32.08/5.08 | GROUND_INST: instantiating (mAddComm) with all_68_1, xp, all_68_0, simplifying
% 32.08/5.08 | with (16), (51), (53) gives:
% 32.08/5.09 | (69) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xp, all_68_1) =
% 32.08/5.09 | v2 & aNaturalNumber0(all_68_1) = v0 & aNaturalNumber0(xp) = v1 &
% 32.08/5.09 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_68_0))
% 32.08/5.09 |
% 32.08/5.09 | GROUND_INST: instantiating (mSortsB) with all_68_1, xp, all_68_0, simplifying
% 32.08/5.09 | with (16), (51), (53) gives:
% 32.08/5.09 | (70) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 32.08/5.09 | (aNaturalNumber0(all_68_0) = v2 & aNaturalNumber0(all_68_1) = v0 &
% 32.08/5.09 | aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 32.08/5.09 |
% 32.08/5.09 | GROUND_INST: instantiating (mMulComm) with xn, xm, all_60_0, simplifying with
% 32.08/5.09 | (14), (15), (30) gives:
% 32.08/5.09 | (71) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xm, xn) = v2 &
% 32.08/5.09 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v2) & ( ~
% 32.08/5.09 | (v1 = 0) | ~ (v0 = 0) | v2 = all_60_0))
% 32.08/5.09 |
% 32.08/5.09 | GROUND_INST: instantiating (mSortsB_02) with xn, xm, all_60_0, simplifying
% 32.08/5.09 | with (14), (15), (30) gives:
% 32.08/5.09 | (72) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 32.08/5.09 | (aNaturalNumber0(all_60_0) = v2 & aNaturalNumber0(xm) = v1 &
% 32.08/5.09 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 32.08/5.09 |
% 32.08/5.09 | GROUND_INST: instantiating (mMulComm) with xp, xm, all_66_1, simplifying with
% 32.08/5.09 | (15), (16), (46) gives:
% 32.08/5.09 | (73) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xm, xp) = v2 &
% 32.08/5.09 | aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v1 & $i(v2) & ( ~
% 32.08/5.09 | (v1 = 0) | ~ (v0 = 0) | v2 = all_66_1))
% 32.08/5.09 |
% 32.08/5.09 | GROUND_INST: instantiating (mSortsB_02) with xp, xm, all_66_1, simplifying
% 32.08/5.09 | with (15), (16), (46) gives:
% 32.08/5.09 | (74) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 32.08/5.09 | (aNaturalNumber0(all_66_1) = v2 & aNaturalNumber0(xp) = v0 &
% 32.08/5.09 | aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 32.08/5.09 |
% 32.08/5.09 | GROUND_INST: instantiating (mMulComm) with xp, xk, all_66_0, simplifying with
% 32.08/5.09 | (16), (17), (47) gives:
% 32.08/5.09 | (75) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xk, xp) = v2 &
% 32.08/5.09 | aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & $i(v2) & ( ~
% 32.08/5.09 | (v1 = 0) | ~ (v0 = 0) | v2 = all_66_0))
% 32.08/5.09 |
% 32.08/5.09 | GROUND_INST: instantiating (mSortsB_02) with xp, xk, all_66_0, simplifying
% 32.08/5.09 | with (16), (17), (47) gives:
% 32.08/5.09 | (76) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 32.08/5.09 | (aNaturalNumber0(all_66_0) = v2 & aNaturalNumber0(xk) = v1 &
% 32.08/5.09 | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 32.08/5.09 |
% 32.08/5.09 | GROUND_INST: instantiating (mLETran) with xp, xk, xm, all_58_0, simplifying
% 32.08/5.09 | with (13), (15), (16), (17), (28) gives:
% 32.08/5.09 | (77) all_58_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 32.08/5.09 | any] : (sdtlseqdt0(xk, xm) = v3 & aNaturalNumber0(xk) = v1 &
% 32.08/5.09 | aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) |
% 32.08/5.09 | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 32.08/5.09 |
% 32.08/5.09 | GROUND_INST: instantiating (mLETran) with xp, xk, xn, all_54_0, simplifying
% 32.08/5.09 | with (13), (14), (16), (17), (25) gives:
% 32.08/5.09 | (78) all_54_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 32.08/5.09 | any] : (sdtlseqdt0(xk, xn) = v3 & aNaturalNumber0(xk) = v1 &
% 32.08/5.09 | aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) |
% 32.08/5.09 | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 32.08/5.09 |
% 32.08/5.09 | GROUND_INST: instantiating (mLEAsym) with all_60_0, all_66_1, simplifying with
% 32.08/5.09 | (43), (64), (65) gives:
% 32.08/5.10 | (79) all_66_1 = all_60_0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 32.08/5.10 | (sdtlseqdt0(all_66_1, all_60_0) = v2 & aNaturalNumber0(all_66_1) = v1
% 32.08/5.10 | & aNaturalNumber0(all_60_0) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 32.08/5.10 | (v0 = 0)))
% 32.08/5.10 |
% 32.08/5.10 | GROUND_INST: instantiating (mLEAsym) with all_66_1, all_66_0, simplifying with
% 32.08/5.10 | (43), (44), (49) gives:
% 32.08/5.10 | (80) all_66_0 = all_66_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 32.08/5.10 | (sdtlseqdt0(all_66_0, all_66_1) = v2 & aNaturalNumber0(all_66_0) = v1
% 32.08/5.10 | & aNaturalNumber0(all_66_1) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 32.08/5.10 | (v0 = 0)))
% 32.08/5.10 |
% 32.08/5.10 | GROUND_INST: instantiating (54) with xn, xm, xp, all_60_0, simplifying with
% 32.08/5.10 | (14), (15), (16), (30), (63) gives:
% 32.08/5.10 | (81) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 32.08/5.10 | $i] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 32.08/5.10 | (isPrime0(xp) = v3 & doDivides0(xp, xm) = v8 & doDivides0(xp, xn) = v7
% 32.08/5.10 | & iLess0(v5, all_68_0) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xn,
% 32.08/5.10 | xm) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 &
% 32.08/5.10 | aNaturalNumber0(xn) = v0 & $i(v5) & $i(v4) & ( ~ (v6 = 0) | ~ (v3 =
% 32.08/5.10 | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 32.08/5.10 |
% 32.08/5.10 | GROUND_INST: instantiating (54) with xn, xm, xr, all_60_0, simplifying with
% 32.08/5.10 | (11), (14), (15), (30), (62) gives:
% 32.08/5.10 | (82) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 32.08/5.10 | $i] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 32.08/5.10 | (isPrime0(xr) = v3 & doDivides0(xr, xm) = v8 & doDivides0(xr, xn) = v7
% 32.08/5.10 | & iLess0(v5, all_68_0) = v6 & sdtpldt0(v4, xr) = v5 & sdtpldt0(xn,
% 32.08/5.10 | xm) = v4 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xm) = v1 &
% 32.08/5.10 | aNaturalNumber0(xn) = v0 & $i(v5) & $i(v4) & ( ~ (v6 = 0) | ~ (v3 =
% 32.08/5.10 | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 32.08/5.10 |
% 32.08/5.10 | GROUND_INST: instantiating (1) with xp, all_60_0, xk, simplifying with (16),
% 32.08/5.10 | (31), (65) gives:
% 32.08/5.10 | (83) xp = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 32.08/5.10 | (doDivides0(xp, all_60_0) = v2 & aNaturalNumber0(all_60_0) = v1 &
% 32.08/5.10 | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 32.08/5.10 | 0))) | ( ! [v0: $i] : (v0 = xk | ~ (sdtasdt0(xp, v0) =
% 32.08/5.10 | all_60_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 32.08/5.10 | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xp, xk)
% 32.08/5.10 | = v0) | ~ $i(xk) | (v0 = all_60_0 & aNaturalNumber0(xk) = 0)))
% 32.08/5.10 |
% 32.08/5.10 | GROUND_INST: instantiating (2) with xp, 0, simplifying with (16), (39) gives:
% 32.08/5.10 | (84) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0) | ( ~ (xp =
% 32.08/5.10 | sz10) & ~ (xp = sz00) & ! [v0: $i] : (v0 = xp | v0 = sz10 | ~
% 32.08/5.10 | (doDivides0(v0, xp) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0)
% 32.08/5.10 | & aNaturalNumber0(v0) = v1)))
% 32.08/5.10 |
% 32.08/5.10 | DELTA: instantiating (76) with fresh symbols all_80_0, all_80_1, all_80_2
% 32.08/5.10 | gives:
% 32.08/5.10 | (85) aNaturalNumber0(all_66_0) = all_80_0 & aNaturalNumber0(xk) = all_80_1
% 32.08/5.10 | & aNaturalNumber0(xp) = all_80_2 & ( ~ (all_80_1 = 0) | ~ (all_80_2 =
% 32.08/5.10 | 0) | all_80_0 = 0)
% 32.08/5.10 |
% 32.08/5.10 | ALPHA: (85) implies:
% 32.08/5.10 | (86) aNaturalNumber0(xp) = all_80_2
% 32.08/5.10 |
% 32.08/5.10 | DELTA: instantiating (74) with fresh symbols all_82_0, all_82_1, all_82_2
% 32.08/5.10 | gives:
% 32.08/5.10 | (87) aNaturalNumber0(all_66_1) = all_82_0 & aNaturalNumber0(xp) = all_82_2
% 32.08/5.10 | & aNaturalNumber0(xm) = all_82_1 & ( ~ (all_82_1 = 0) | ~ (all_82_2 =
% 32.08/5.10 | 0) | all_82_0 = 0)
% 32.08/5.10 |
% 32.08/5.10 | ALPHA: (87) implies:
% 32.08/5.10 | (88) aNaturalNumber0(xm) = all_82_1
% 32.08/5.10 | (89) aNaturalNumber0(xp) = all_82_2
% 32.08/5.10 | (90) aNaturalNumber0(all_66_1) = all_82_0
% 32.08/5.10 | (91) ~ (all_82_1 = 0) | ~ (all_82_2 = 0) | all_82_0 = 0
% 32.08/5.10 |
% 32.08/5.10 | DELTA: instantiating (72) with fresh symbols all_84_0, all_84_1, all_84_2
% 32.08/5.10 | gives:
% 32.08/5.10 | (92) aNaturalNumber0(all_60_0) = all_84_0 & aNaturalNumber0(xm) = all_84_1
% 32.08/5.10 | & aNaturalNumber0(xn) = all_84_2 & ( ~ (all_84_1 = 0) | ~ (all_84_2 =
% 32.08/5.10 | 0) | all_84_0 = 0)
% 32.08/5.10 |
% 32.08/5.10 | ALPHA: (92) implies:
% 32.08/5.10 | (93) aNaturalNumber0(xn) = all_84_2
% 32.08/5.10 | (94) aNaturalNumber0(xm) = all_84_1
% 32.08/5.10 | (95) aNaturalNumber0(all_60_0) = all_84_0
% 32.08/5.10 | (96) ~ (all_84_1 = 0) | ~ (all_84_2 = 0) | all_84_0 = 0
% 32.08/5.10 |
% 32.08/5.10 | DELTA: instantiating (70) with fresh symbols all_86_0, all_86_1, all_86_2
% 32.08/5.10 | gives:
% 32.08/5.10 | (97) aNaturalNumber0(all_68_0) = all_86_0 & aNaturalNumber0(all_68_1) =
% 32.08/5.11 | all_86_2 & aNaturalNumber0(xp) = all_86_1 & ( ~ (all_86_1 = 0) | ~
% 32.08/5.11 | (all_86_2 = 0) | all_86_0 = 0)
% 32.08/5.11 |
% 32.08/5.11 | ALPHA: (97) implies:
% 32.08/5.11 | (98) aNaturalNumber0(xp) = all_86_1
% 32.08/5.11 |
% 32.08/5.11 | DELTA: instantiating (67) with fresh symbols all_88_0, all_88_1, all_88_2
% 32.08/5.11 | gives:
% 32.08/5.11 | (99) aNaturalNumber0(all_68_1) = all_88_0 & aNaturalNumber0(xm) = all_88_1
% 32.08/5.11 | & aNaturalNumber0(xn) = all_88_2 & ( ~ (all_88_1 = 0) | ~ (all_88_2 =
% 32.08/5.11 | 0) | all_88_0 = 0)
% 32.08/5.11 |
% 32.08/5.11 | ALPHA: (99) implies:
% 32.08/5.11 | (100) aNaturalNumber0(xn) = all_88_2
% 32.08/5.11 | (101) aNaturalNumber0(xm) = all_88_1
% 32.08/5.11 |
% 32.08/5.11 | DELTA: instantiating (69) with fresh symbols all_90_0, all_90_1, all_90_2
% 32.08/5.11 | gives:
% 32.08/5.11 | (102) sdtpldt0(xp, all_68_1) = all_90_0 & aNaturalNumber0(all_68_1) =
% 32.08/5.11 | all_90_2 & aNaturalNumber0(xp) = all_90_1 & $i(all_90_0) & ( ~
% 32.08/5.11 | (all_90_1 = 0) | ~ (all_90_2 = 0) | all_90_0 = all_68_0)
% 32.08/5.11 |
% 32.08/5.11 | ALPHA: (102) implies:
% 32.08/5.11 | (103) aNaturalNumber0(xp) = all_90_1
% 32.08/5.11 |
% 32.08/5.11 | DELTA: instantiating (66) with fresh symbols all_92_0, all_92_1, all_92_2
% 32.08/5.11 | gives:
% 32.08/5.11 | (104) sdtpldt0(xm, xn) = all_92_0 & aNaturalNumber0(xm) = all_92_1 &
% 32.08/5.11 | aNaturalNumber0(xn) = all_92_2 & $i(all_92_0) & ( ~ (all_92_1 = 0) |
% 32.08/5.11 | ~ (all_92_2 = 0) | all_92_0 = all_68_1)
% 32.08/5.11 |
% 32.08/5.11 | ALPHA: (104) implies:
% 32.08/5.11 | (105) aNaturalNumber0(xn) = all_92_2
% 32.08/5.11 | (106) aNaturalNumber0(xm) = all_92_1
% 32.08/5.11 |
% 32.08/5.11 | DELTA: instantiating (75) with fresh symbols all_94_0, all_94_1, all_94_2
% 32.08/5.11 | gives:
% 32.08/5.11 | (107) sdtasdt0(xk, xp) = all_94_0 & aNaturalNumber0(xk) = all_94_1 &
% 32.08/5.11 | aNaturalNumber0(xp) = all_94_2 & $i(all_94_0) & ( ~ (all_94_1 = 0) |
% 32.08/5.11 | ~ (all_94_2 = 0) | all_94_0 = all_66_0)
% 32.08/5.11 |
% 32.08/5.11 | ALPHA: (107) implies:
% 32.08/5.11 | (108) aNaturalNumber0(xp) = all_94_2
% 32.08/5.11 |
% 32.08/5.11 | DELTA: instantiating (73) with fresh symbols all_96_0, all_96_1, all_96_2
% 32.08/5.11 | gives:
% 32.08/5.11 | (109) sdtasdt0(xm, xp) = all_96_0 & aNaturalNumber0(xp) = all_96_2 &
% 32.08/5.11 | aNaturalNumber0(xm) = all_96_1 & $i(all_96_0) & ( ~ (all_96_1 = 0) |
% 32.08/5.11 | ~ (all_96_2 = 0) | all_96_0 = all_66_1)
% 32.08/5.11 |
% 32.08/5.11 | ALPHA: (109) implies:
% 32.08/5.11 | (110) aNaturalNumber0(xm) = all_96_1
% 32.08/5.11 | (111) aNaturalNumber0(xp) = all_96_2
% 32.08/5.11 |
% 32.08/5.11 | DELTA: instantiating (71) with fresh symbols all_98_0, all_98_1, all_98_2
% 32.08/5.11 | gives:
% 32.08/5.11 | (112) sdtasdt0(xm, xn) = all_98_0 & aNaturalNumber0(xm) = all_98_1 &
% 32.08/5.11 | aNaturalNumber0(xn) = all_98_2 & $i(all_98_0) & ( ~ (all_98_1 = 0) |
% 32.08/5.11 | ~ (all_98_2 = 0) | all_98_0 = all_60_0)
% 32.08/5.11 |
% 32.08/5.11 | ALPHA: (112) implies:
% 32.08/5.11 | (113) aNaturalNumber0(xn) = all_98_2
% 32.08/5.11 | (114) aNaturalNumber0(xm) = all_98_1
% 32.08/5.11 |
% 32.08/5.11 | DELTA: instantiating (68) with fresh symbols all_100_0, all_100_1, all_100_2,
% 32.08/5.11 | all_100_3, all_100_4 gives:
% 32.08/5.11 | (115) sdtpldt0(xm, xp) = all_100_1 & sdtpldt0(xn, all_100_1) = all_100_0 &
% 32.08/5.11 | aNaturalNumber0(xp) = all_100_2 & aNaturalNumber0(xm) = all_100_3 &
% 32.08/5.11 | aNaturalNumber0(xn) = all_100_4 & $i(all_100_0) & $i(all_100_1) & ( ~
% 32.08/5.11 | (all_100_2 = 0) | ~ (all_100_3 = 0) | ~ (all_100_4 = 0) |
% 32.08/5.11 | all_100_0 = all_68_0)
% 32.08/5.11 |
% 32.08/5.11 | ALPHA: (115) implies:
% 32.08/5.11 | (116) aNaturalNumber0(xn) = all_100_4
% 32.08/5.11 | (117) aNaturalNumber0(xm) = all_100_3
% 32.08/5.11 | (118) aNaturalNumber0(xp) = all_100_2
% 32.08/5.11 |
% 32.08/5.11 | DELTA: instantiating (82) with fresh symbols all_102_0, all_102_1, all_102_2,
% 32.08/5.11 | all_102_3, all_102_4, all_102_5, all_102_6, all_102_7, all_102_8 gives:
% 32.08/5.11 | (119) isPrime0(xr) = all_102_5 & doDivides0(xr, xm) = all_102_0 &
% 32.08/5.11 | doDivides0(xr, xn) = all_102_1 & iLess0(all_102_3, all_68_0) =
% 32.08/5.11 | all_102_2 & sdtpldt0(all_102_4, xr) = all_102_3 & sdtpldt0(xn, xm) =
% 32.08/5.11 | all_102_4 & aNaturalNumber0(xr) = all_102_6 & aNaturalNumber0(xm) =
% 32.08/5.11 | all_102_7 & aNaturalNumber0(xn) = all_102_8 & $i(all_102_3) &
% 32.08/5.11 | $i(all_102_4) & ( ~ (all_102_2 = 0) | ~ (all_102_5 = 0) | ~
% 32.08/5.11 | (all_102_6 = 0) | ~ (all_102_7 = 0) | ~ (all_102_8 = 0) |
% 32.08/5.11 | all_102_0 = 0 | all_102_1 = 0)
% 32.08/5.11 |
% 32.08/5.11 | ALPHA: (119) implies:
% 32.08/5.11 | (120) aNaturalNumber0(xn) = all_102_8
% 32.08/5.11 | (121) aNaturalNumber0(xm) = all_102_7
% 32.08/5.11 |
% 32.08/5.11 | DELTA: instantiating (81) with fresh symbols all_104_0, all_104_1, all_104_2,
% 32.08/5.11 | all_104_3, all_104_4, all_104_5, all_104_6, all_104_7, all_104_8 gives:
% 32.08/5.11 | (122) isPrime0(xp) = all_104_5 & doDivides0(xp, xm) = all_104_0 &
% 32.08/5.11 | doDivides0(xp, xn) = all_104_1 & iLess0(all_104_3, all_68_0) =
% 32.08/5.11 | all_104_2 & sdtpldt0(all_104_4, xp) = all_104_3 & sdtpldt0(xn, xm) =
% 32.08/5.11 | all_104_4 & aNaturalNumber0(xp) = all_104_6 & aNaturalNumber0(xm) =
% 32.08/5.11 | all_104_7 & aNaturalNumber0(xn) = all_104_8 & $i(all_104_3) &
% 32.08/5.11 | $i(all_104_4) & ( ~ (all_104_2 = 0) | ~ (all_104_5 = 0) | ~
% 32.08/5.11 | (all_104_6 = 0) | ~ (all_104_7 = 0) | ~ (all_104_8 = 0) |
% 32.08/5.11 | all_104_0 = 0 | all_104_1 = 0)
% 32.08/5.11 |
% 32.08/5.11 | ALPHA: (122) implies:
% 32.08/5.11 | (123) aNaturalNumber0(xn) = all_104_8
% 32.08/5.11 | (124) aNaturalNumber0(xm) = all_104_7
% 32.08/5.11 | (125) aNaturalNumber0(xp) = all_104_6
% 32.08/5.11 |
% 32.08/5.11 | BETA: splitting (80) gives:
% 32.08/5.11 |
% 32.08/5.11 | Case 1:
% 32.08/5.11 | |
% 32.08/5.11 | | (126) all_66_0 = all_66_1
% 32.08/5.11 | |
% 32.08/5.11 | | REDUCE: (42), (126) imply:
% 32.08/5.11 | | (127) $false
% 32.08/5.11 | |
% 32.08/5.11 | | CLOSE: (127) is inconsistent.
% 32.08/5.11 | |
% 32.08/5.11 | Case 2:
% 32.08/5.11 | |
% 32.08/5.11 | | (128) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(all_66_0,
% 32.08/5.11 | | all_66_1) = v2 & aNaturalNumber0(all_66_0) = v1 &
% 32.08/5.11 | | aNaturalNumber0(all_66_1) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 32.08/5.11 | | (v0 = 0)))
% 32.08/5.11 | |
% 32.08/5.11 | | DELTA: instantiating (128) with fresh symbols all_114_0, all_114_1,
% 32.08/5.11 | | all_114_2 gives:
% 32.08/5.11 | | (129) sdtlseqdt0(all_66_0, all_66_1) = all_114_0 &
% 32.08/5.11 | | aNaturalNumber0(all_66_0) = all_114_1 & aNaturalNumber0(all_66_1) =
% 32.08/5.11 | | all_114_2 & ( ~ (all_114_0 = 0) | ~ (all_114_1 = 0) | ~
% 32.08/5.11 | | (all_114_2 = 0))
% 32.08/5.11 | |
% 32.08/5.11 | | ALPHA: (129) implies:
% 32.08/5.12 | | (130) aNaturalNumber0(all_66_1) = all_114_2
% 32.08/5.12 | |
% 32.08/5.12 | | BETA: splitting (79) gives:
% 32.08/5.12 | |
% 32.08/5.12 | | Case 1:
% 32.08/5.12 | | |
% 32.08/5.12 | | | (131) all_66_1 = all_60_0
% 32.08/5.12 | | |
% 32.08/5.12 | | | REDUCE: (61), (131) imply:
% 32.08/5.12 | | | (132) $false
% 32.08/5.12 | | |
% 32.08/5.12 | | | CLOSE: (132) is inconsistent.
% 32.08/5.12 | | |
% 32.08/5.12 | | Case 2:
% 32.08/5.12 | | |
% 32.08/5.12 | | | (133) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 32.08/5.12 | | | (sdtlseqdt0(all_66_1, all_60_0) = v2 & aNaturalNumber0(all_66_1)
% 32.08/5.12 | | | = v1 & aNaturalNumber0(all_60_0) = v0 & ( ~ (v2 = 0) | ~ (v1 =
% 32.08/5.12 | | | 0) | ~ (v0 = 0)))
% 32.08/5.12 | | |
% 32.08/5.12 | | | DELTA: instantiating (133) with fresh symbols all_119_0, all_119_1,
% 32.08/5.12 | | | all_119_2 gives:
% 32.08/5.12 | | | (134) sdtlseqdt0(all_66_1, all_60_0) = all_119_0 &
% 32.08/5.12 | | | aNaturalNumber0(all_66_1) = all_119_1 & aNaturalNumber0(all_60_0)
% 32.08/5.12 | | | = all_119_2 & ( ~ (all_119_0 = 0) | ~ (all_119_1 = 0) | ~
% 32.08/5.12 | | | (all_119_2 = 0))
% 32.08/5.12 | | |
% 32.08/5.12 | | | ALPHA: (134) implies:
% 32.08/5.12 | | | (135) aNaturalNumber0(all_60_0) = all_119_2
% 32.08/5.12 | | | (136) aNaturalNumber0(all_66_1) = all_119_1
% 32.08/5.12 | | | (137) sdtlseqdt0(all_66_1, all_60_0) = all_119_0
% 32.08/5.12 | | | (138) ~ (all_119_0 = 0) | ~ (all_119_1 = 0) | ~ (all_119_2 = 0)
% 32.08/5.12 | | |
% 32.08/5.12 | | | BETA: splitting (78) gives:
% 32.08/5.12 | | |
% 32.08/5.12 | | | Case 1:
% 32.08/5.12 | | | |
% 32.08/5.12 | | | | (139) all_54_0 = 0
% 32.08/5.12 | | | |
% 32.08/5.12 | | | | REDUCE: (24), (139) imply:
% 32.08/5.12 | | | | (140) $false
% 32.08/5.12 | | | |
% 32.08/5.12 | | | | CLOSE: (140) is inconsistent.
% 32.08/5.12 | | | |
% 32.08/5.12 | | | Case 2:
% 32.08/5.12 | | | |
% 32.08/5.12 | | | | (141) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 32.08/5.12 | | | | (sdtlseqdt0(xk, xn) = v3 & aNaturalNumber0(xk) = v1 &
% 32.08/5.12 | | | | aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3
% 32.08/5.12 | | | | = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 32.08/5.12 | | | |
% 32.08/5.12 | | | | DELTA: instantiating (141) with fresh symbols all_124_0, all_124_1,
% 32.08/5.12 | | | | all_124_2, all_124_3 gives:
% 32.08/5.12 | | | | (142) sdtlseqdt0(xk, xn) = all_124_0 & aNaturalNumber0(xk) =
% 32.08/5.12 | | | | all_124_2 & aNaturalNumber0(xp) = all_124_3 &
% 32.08/5.12 | | | | aNaturalNumber0(xn) = all_124_1 & ( ~ (all_124_0 = 0) | ~
% 32.08/5.12 | | | | (all_124_1 = 0) | ~ (all_124_2 = 0) | ~ (all_124_3 = 0))
% 32.08/5.12 | | | |
% 32.08/5.12 | | | | ALPHA: (142) implies:
% 32.08/5.12 | | | | (143) aNaturalNumber0(xn) = all_124_1
% 32.08/5.12 | | | | (144) aNaturalNumber0(xp) = all_124_3
% 32.08/5.12 | | | |
% 32.08/5.12 | | | | BETA: splitting (77) gives:
% 32.08/5.12 | | | |
% 32.08/5.12 | | | | Case 1:
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | (145) all_58_0 = 0
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | REDUCE: (27), (145) imply:
% 32.08/5.12 | | | | | (146) $false
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | CLOSE: (146) is inconsistent.
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | Case 2:
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | (147) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 32.08/5.12 | | | | | (sdtlseqdt0(xk, xm) = v3 & aNaturalNumber0(xk) = v1 &
% 32.08/5.12 | | | | | aNaturalNumber0(xp) = v0 & aNaturalNumber0(xm) = v2 & ( ~
% 32.08/5.12 | | | | | (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | DELTA: instantiating (147) with fresh symbols all_129_0, all_129_1,
% 32.08/5.12 | | | | | all_129_2, all_129_3 gives:
% 32.08/5.12 | | | | | (148) sdtlseqdt0(xk, xm) = all_129_0 & aNaturalNumber0(xk) =
% 32.08/5.12 | | | | | all_129_2 & aNaturalNumber0(xp) = all_129_3 &
% 32.08/5.12 | | | | | aNaturalNumber0(xm) = all_129_1 & ( ~ (all_129_0 = 0) | ~
% 32.08/5.12 | | | | | (all_129_1 = 0) | ~ (all_129_2 = 0) | ~ (all_129_3 = 0))
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | ALPHA: (148) implies:
% 32.08/5.12 | | | | | (149) aNaturalNumber0(xm) = all_129_1
% 32.08/5.12 | | | | | (150) aNaturalNumber0(xp) = all_129_3
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with 0, all_98_2, xn, simplifying with
% 32.08/5.12 | | | | | (3), (113) gives:
% 32.08/5.12 | | | | | (151) all_98_2 = 0
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with all_88_2, all_98_2, xn,
% 32.08/5.12 | | | | | simplifying with (100), (113) gives:
% 32.08/5.12 | | | | | (152) all_98_2 = all_88_2
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with all_102_8, all_104_8, xn,
% 32.08/5.12 | | | | | simplifying with (120), (123) gives:
% 32.08/5.12 | | | | | (153) all_104_8 = all_102_8
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with all_92_2, all_104_8, xn,
% 32.08/5.12 | | | | | simplifying with (105), (123) gives:
% 32.08/5.12 | | | | | (154) all_104_8 = all_92_2
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with all_102_8, all_124_1, xn,
% 32.08/5.12 | | | | | simplifying with (120), (143) gives:
% 32.08/5.12 | | | | | (155) all_124_1 = all_102_8
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with all_100_4, all_124_1, xn,
% 32.08/5.12 | | | | | simplifying with (116), (143) gives:
% 32.08/5.12 | | | | | (156) all_124_1 = all_100_4
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with all_98_2, all_124_1, xn,
% 32.08/5.12 | | | | | simplifying with (113), (143) gives:
% 32.08/5.12 | | | | | (157) all_124_1 = all_98_2
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with all_84_2, all_124_1, xn,
% 32.08/5.12 | | | | | simplifying with (93), (143) gives:
% 32.08/5.12 | | | | | (158) all_124_1 = all_84_2
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with 0, all_88_1, xm, simplifying with
% 32.08/5.12 | | | | | (4), (101) gives:
% 32.08/5.12 | | | | | (159) all_88_1 = 0
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with all_82_1, all_88_1, xm,
% 32.08/5.12 | | | | | simplifying with (88), (101) gives:
% 32.08/5.12 | | | | | (160) all_88_1 = all_82_1
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with all_88_1, all_92_1, xm,
% 32.08/5.12 | | | | | simplifying with (101), (106) gives:
% 32.08/5.12 | | | | | (161) all_92_1 = all_88_1
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with all_92_1, all_96_1, xm,
% 32.08/5.12 | | | | | simplifying with (106), (110) gives:
% 32.08/5.12 | | | | | (162) all_96_1 = all_92_1
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with all_100_3, all_102_7, xm,
% 32.08/5.12 | | | | | simplifying with (117), (121) gives:
% 32.08/5.12 | | | | | (163) all_102_7 = all_100_3
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with all_96_1, all_102_7, xm,
% 32.08/5.12 | | | | | simplifying with (110), (121) gives:
% 32.08/5.12 | | | | | (164) all_102_7 = all_96_1
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with all_102_7, all_104_7, xm,
% 32.08/5.12 | | | | | simplifying with (121), (124) gives:
% 32.08/5.12 | | | | | (165) all_104_7 = all_102_7
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with all_98_1, all_104_7, xm,
% 32.08/5.12 | | | | | simplifying with (114), (124) gives:
% 32.08/5.12 | | | | | (166) all_104_7 = all_98_1
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with all_100_3, all_129_1, xm,
% 32.08/5.12 | | | | | simplifying with (117), (149) gives:
% 32.08/5.12 | | | | | (167) all_129_1 = all_100_3
% 32.08/5.12 | | | | |
% 32.08/5.12 | | | | | GROUND_INST: instantiating (19) with all_84_1, all_129_1, xm,
% 32.08/5.12 | | | | | simplifying with (94), (149) gives:
% 32.08/5.12 | | | | | (168) all_129_1 = all_84_1
% 32.08/5.12 | | | | |
% 32.08/5.13 | | | | | GROUND_INST: instantiating (19) with 0, all_100_2, xp, simplifying
% 32.08/5.13 | | | | | with (5), (118) gives:
% 32.08/5.13 | | | | | (169) all_100_2 = 0
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | GROUND_INST: instantiating (19) with all_100_2, all_104_6, xp,
% 32.08/5.13 | | | | | simplifying with (118), (125) gives:
% 32.08/5.13 | | | | | (170) all_104_6 = all_100_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | GROUND_INST: instantiating (19) with all_86_1, all_104_6, xp,
% 32.08/5.13 | | | | | simplifying with (98), (125) gives:
% 32.08/5.13 | | | | | (171) all_104_6 = all_86_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | GROUND_INST: instantiating (19) with all_94_2, all_124_3, xp,
% 32.08/5.13 | | | | | simplifying with (108), (144) gives:
% 32.08/5.13 | | | | | (172) all_124_3 = all_94_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | GROUND_INST: instantiating (19) with all_80_2, all_124_3, xp,
% 32.08/5.13 | | | | | simplifying with (86), (144) gives:
% 32.08/5.13 | | | | | (173) all_124_3 = all_80_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | GROUND_INST: instantiating (19) with all_104_6, all_129_3, xp,
% 32.08/5.13 | | | | | simplifying with (125), (150) gives:
% 32.08/5.13 | | | | | (174) all_129_3 = all_104_6
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | GROUND_INST: instantiating (19) with all_96_2, all_129_3, xp,
% 32.08/5.13 | | | | | simplifying with (111), (150) gives:
% 32.08/5.13 | | | | | (175) all_129_3 = all_96_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | GROUND_INST: instantiating (19) with all_94_2, all_129_3, xp,
% 32.08/5.13 | | | | | simplifying with (108), (150) gives:
% 32.08/5.13 | | | | | (176) all_129_3 = all_94_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | GROUND_INST: instantiating (19) with all_90_1, all_129_3, xp,
% 32.08/5.13 | | | | | simplifying with (103), (150) gives:
% 32.08/5.13 | | | | | (177) all_129_3 = all_90_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | GROUND_INST: instantiating (19) with all_82_2, all_129_3, xp,
% 32.08/5.13 | | | | | simplifying with (89), (150) gives:
% 32.08/5.13 | | | | | (178) all_129_3 = all_82_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | GROUND_INST: instantiating (19) with all_84_0, all_119_2, all_60_0,
% 32.08/5.13 | | | | | simplifying with (95), (135) gives:
% 32.08/5.13 | | | | | (179) all_119_2 = all_84_0
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | GROUND_INST: instantiating (19) with all_114_2, all_119_1, all_66_1,
% 32.08/5.13 | | | | | simplifying with (130), (136) gives:
% 32.08/5.13 | | | | | (180) all_119_1 = all_114_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | GROUND_INST: instantiating (19) with all_82_0, all_119_1, all_66_1,
% 32.08/5.13 | | | | | simplifying with (90), (136) gives:
% 32.08/5.13 | | | | | (181) all_119_1 = all_82_0
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (167), (168) imply:
% 32.08/5.13 | | | | | (182) all_100_3 = all_84_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (182) implies:
% 32.08/5.13 | | | | | (183) all_100_3 = all_84_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (175), (176) imply:
% 32.08/5.13 | | | | | (184) all_96_2 = all_94_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (174), (175) imply:
% 32.08/5.13 | | | | | (185) all_104_6 = all_96_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (185) implies:
% 32.08/5.13 | | | | | (186) all_104_6 = all_96_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (175), (178) imply:
% 32.08/5.13 | | | | | (187) all_96_2 = all_82_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (175), (177) imply:
% 32.08/5.13 | | | | | (188) all_96_2 = all_90_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (156), (158) imply:
% 32.08/5.13 | | | | | (189) all_100_4 = all_84_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (156), (157) imply:
% 32.08/5.13 | | | | | (190) all_100_4 = all_98_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (155), (156) imply:
% 32.08/5.13 | | | | | (191) all_102_8 = all_100_4
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (191) implies:
% 32.08/5.13 | | | | | (192) all_102_8 = all_100_4
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (172), (173) imply:
% 32.08/5.13 | | | | | (193) all_94_2 = all_80_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (193) implies:
% 32.08/5.13 | | | | | (194) all_94_2 = all_80_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (180), (181) imply:
% 32.08/5.13 | | | | | (195) all_114_2 = all_82_0
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (171), (186) imply:
% 32.08/5.13 | | | | | (196) all_96_2 = all_86_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (196) implies:
% 32.08/5.13 | | | | | (197) all_96_2 = all_86_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (170), (171) imply:
% 32.08/5.13 | | | | | (198) all_100_2 = all_86_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (198) implies:
% 32.08/5.13 | | | | | (199) all_100_2 = all_86_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (165), (166) imply:
% 32.08/5.13 | | | | | (200) all_102_7 = all_98_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (200) implies:
% 32.08/5.13 | | | | | (201) all_102_7 = all_98_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (153), (154) imply:
% 32.08/5.13 | | | | | (202) all_102_8 = all_92_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (202) implies:
% 32.08/5.13 | | | | | (203) all_102_8 = all_92_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (164), (201) imply:
% 32.08/5.13 | | | | | (204) all_98_1 = all_96_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (163), (201) imply:
% 32.08/5.13 | | | | | (205) all_100_3 = all_98_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (205) implies:
% 32.08/5.13 | | | | | (206) all_100_3 = all_98_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (192), (203) imply:
% 32.08/5.13 | | | | | (207) all_100_4 = all_92_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (207) implies:
% 32.08/5.13 | | | | | (208) all_100_4 = all_92_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (169), (199) imply:
% 32.08/5.13 | | | | | (209) all_86_1 = 0
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (209) implies:
% 32.08/5.13 | | | | | (210) all_86_1 = 0
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (183), (206) imply:
% 32.08/5.13 | | | | | (211) all_98_1 = all_84_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (211) implies:
% 32.08/5.13 | | | | | (212) all_98_1 = all_84_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (189), (208) imply:
% 32.08/5.13 | | | | | (213) all_92_2 = all_84_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (190), (208) imply:
% 32.08/5.13 | | | | | (214) all_98_2 = all_92_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (214) implies:
% 32.08/5.13 | | | | | (215) all_98_2 = all_92_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (204), (212) imply:
% 32.08/5.13 | | | | | (216) all_96_1 = all_84_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (216) implies:
% 32.08/5.13 | | | | | (217) all_96_1 = all_84_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (151), (152) imply:
% 32.08/5.13 | | | | | (218) all_88_2 = 0
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (152), (215) imply:
% 32.08/5.13 | | | | | (219) all_92_2 = all_88_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (219) implies:
% 32.08/5.13 | | | | | (220) all_92_2 = all_88_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (162), (217) imply:
% 32.08/5.13 | | | | | (221) all_92_1 = all_84_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (221) implies:
% 32.08/5.13 | | | | | (222) all_92_1 = all_84_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (187), (188) imply:
% 32.08/5.13 | | | | | (223) all_90_1 = all_82_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (184), (188) imply:
% 32.08/5.13 | | | | | (224) all_94_2 = all_90_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (224) implies:
% 32.08/5.13 | | | | | (225) all_94_2 = all_90_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (188), (197) imply:
% 32.08/5.13 | | | | | (226) all_90_1 = all_86_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (194), (225) imply:
% 32.08/5.13 | | | | | (227) all_90_1 = all_80_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (227) implies:
% 32.08/5.13 | | | | | (228) all_90_1 = all_80_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (161), (222) imply:
% 32.08/5.13 | | | | | (229) all_88_1 = all_84_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (229) implies:
% 32.08/5.13 | | | | | (230) all_88_1 = all_84_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (213), (220) imply:
% 32.08/5.13 | | | | | (231) all_88_2 = all_84_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (231) implies:
% 32.08/5.13 | | | | | (232) all_88_2 = all_84_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (223), (228) imply:
% 32.08/5.13 | | | | | (233) all_82_2 = all_80_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (223), (226) imply:
% 32.08/5.13 | | | | | (234) all_86_1 = all_82_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (234) implies:
% 32.08/5.13 | | | | | (235) all_86_1 = all_82_2
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (159), (230) imply:
% 32.08/5.13 | | | | | (236) all_84_1 = 0
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (160), (230) imply:
% 32.08/5.13 | | | | | (237) all_84_1 = all_82_1
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (218), (232) imply:
% 32.08/5.13 | | | | | (238) all_84_2 = 0
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (238) implies:
% 32.08/5.13 | | | | | (239) all_84_2 = 0
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (210), (235) imply:
% 32.08/5.13 | | | | | (240) all_82_2 = 0
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (240) implies:
% 32.08/5.13 | | | | | (241) all_82_2 = 0
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (236), (237) imply:
% 32.08/5.13 | | | | | (242) all_82_1 = 0
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | COMBINE_EQS: (233), (241) imply:
% 32.08/5.13 | | | | | (243) all_80_2 = 0
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | SIMP: (243) implies:
% 32.08/5.13 | | | | | (244) all_80_2 = 0
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | BETA: splitting (91) gives:
% 32.08/5.13 | | | | |
% 32.08/5.13 | | | | | Case 1:
% 32.08/5.13 | | | | | |
% 32.08/5.13 | | | | | | (245) ~ (all_82_1 = 0)
% 32.08/5.13 | | | | | |
% 32.08/5.13 | | | | | | REDUCE: (242), (245) imply:
% 32.08/5.13 | | | | | | (246) $false
% 32.08/5.13 | | | | | |
% 32.08/5.13 | | | | | | CLOSE: (246) is inconsistent.
% 32.08/5.13 | | | | | |
% 32.08/5.13 | | | | | Case 2:
% 32.08/5.13 | | | | | |
% 32.08/5.13 | | | | | | (247) ~ (all_82_2 = 0) | all_82_0 = 0
% 32.08/5.14 | | | | | |
% 32.08/5.14 | | | | | | BETA: splitting (247) gives:
% 32.08/5.14 | | | | | |
% 32.08/5.14 | | | | | | Case 1:
% 32.08/5.14 | | | | | | |
% 32.08/5.14 | | | | | | | (248) ~ (all_82_2 = 0)
% 32.08/5.14 | | | | | | |
% 32.08/5.14 | | | | | | | REDUCE: (241), (248) imply:
% 32.08/5.14 | | | | | | | (249) $false
% 32.08/5.14 | | | | | | |
% 32.08/5.14 | | | | | | | CLOSE: (249) is inconsistent.
% 32.08/5.14 | | | | | | |
% 32.08/5.14 | | | | | | Case 2:
% 32.08/5.14 | | | | | | |
% 32.08/5.14 | | | | | | | (250) all_82_0 = 0
% 32.08/5.14 | | | | | | |
% 32.08/5.14 | | | | | | | COMBINE_EQS: (181), (250) imply:
% 32.08/5.14 | | | | | | | (251) all_119_1 = 0
% 32.08/5.14 | | | | | | |
% 32.08/5.14 | | | | | | | BETA: splitting (84) gives:
% 32.08/5.14 | | | | | | |
% 32.08/5.14 | | | | | | | Case 1:
% 32.08/5.14 | | | | | | | |
% 32.08/5.14 | | | | | | | | (252) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0)
% 32.08/5.14 | | | | | | | |
% 32.08/5.14 | | | | | | | | DELTA: instantiating (252) with fresh symbol all_189_0 gives:
% 32.08/5.14 | | | | | | | | (253) ~ (all_189_0 = 0) & aNaturalNumber0(xp) = all_189_0
% 32.08/5.14 | | | | | | | |
% 32.08/5.14 | | | | | | | | ALPHA: (253) implies:
% 32.08/5.14 | | | | | | | | (254) ~ (all_189_0 = 0)
% 32.08/5.14 | | | | | | | | (255) aNaturalNumber0(xp) = all_189_0
% 32.08/5.14 | | | | | | | |
% 32.08/5.14 | | | | | | | | GROUND_INST: instantiating (19) with 0, all_189_0, xp,
% 32.08/5.14 | | | | | | | | simplifying with (5), (255) gives:
% 32.08/5.14 | | | | | | | | (256) all_189_0 = 0
% 32.08/5.14 | | | | | | | |
% 32.08/5.14 | | | | | | | | REDUCE: (254), (256) imply:
% 32.08/5.14 | | | | | | | | (257) $false
% 32.08/5.14 | | | | | | | |
% 32.08/5.14 | | | | | | | | CLOSE: (257) is inconsistent.
% 32.08/5.14 | | | | | | | |
% 32.08/5.14 | | | | | | | Case 2:
% 32.08/5.14 | | | | | | | |
% 32.08/5.14 | | | | | | | | (258) ~ (xp = sz10) & ~ (xp = sz00) & ! [v0: $i] : (v0 =
% 32.08/5.14 | | | | | | | | xp | v0 = sz10 | ~ (doDivides0(v0, xp) = 0) | ~
% 32.08/5.14 | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 32.08/5.14 | | | | | | | | aNaturalNumber0(v0) = v1))
% 32.08/5.14 | | | | | | | |
% 32.08/5.14 | | | | | | | | ALPHA: (258) implies:
% 32.08/5.14 | | | | | | | | (259) ~ (xp = sz00)
% 32.08/5.14 | | | | | | | |
% 32.08/5.14 | | | | | | | | BETA: splitting (96) gives:
% 32.08/5.14 | | | | | | | |
% 32.08/5.14 | | | | | | | | Case 1:
% 32.08/5.14 | | | | | | | | |
% 32.08/5.14 | | | | | | | | | (260) ~ (all_84_1 = 0)
% 32.08/5.14 | | | | | | | | |
% 32.08/5.14 | | | | | | | | | REDUCE: (236), (260) imply:
% 32.08/5.14 | | | | | | | | | (261) $false
% 32.08/5.14 | | | | | | | | |
% 32.08/5.14 | | | | | | | | | CLOSE: (261) is inconsistent.
% 32.08/5.14 | | | | | | | | |
% 32.08/5.14 | | | | | | | | Case 2:
% 32.08/5.14 | | | | | | | | |
% 32.08/5.14 | | | | | | | | | (262) ~ (all_84_2 = 0) | all_84_0 = 0
% 32.08/5.14 | | | | | | | | |
% 32.08/5.14 | | | | | | | | | BETA: splitting (262) gives:
% 32.08/5.14 | | | | | | | | |
% 32.08/5.14 | | | | | | | | | Case 1:
% 32.08/5.14 | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | (263) ~ (all_84_2 = 0)
% 32.08/5.14 | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | REDUCE: (239), (263) imply:
% 32.08/5.14 | | | | | | | | | | (264) $false
% 32.08/5.14 | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | CLOSE: (264) is inconsistent.
% 32.08/5.14 | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | Case 2:
% 32.08/5.14 | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | (265) all_84_0 = 0
% 32.08/5.14 | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | COMBINE_EQS: (179), (265) imply:
% 32.08/5.14 | | | | | | | | | | (266) all_119_2 = 0
% 32.08/5.14 | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | REDUCE: (95), (265) imply:
% 32.08/5.14 | | | | | | | | | | (267) aNaturalNumber0(all_60_0) = 0
% 32.08/5.14 | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | BETA: splitting (138) gives:
% 32.08/5.14 | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | Case 1:
% 32.08/5.14 | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | (268) ~ (all_119_0 = 0)
% 32.08/5.14 | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | BETA: splitting (83) gives:
% 32.08/5.14 | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | Case 1:
% 32.08/5.14 | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | (269) xp = sz00
% 32.08/5.14 | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | REDUCE: (259), (269) imply:
% 32.08/5.14 | | | | | | | | | | | | (270) $false
% 32.08/5.14 | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | CLOSE: (270) is inconsistent.
% 32.08/5.14 | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | Case 2:
% 32.08/5.14 | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | (271) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 32.08/5.14 | | | | | | | | | | | | (doDivides0(xp, all_60_0) = v2 &
% 32.08/5.14 | | | | | | | | | | | | aNaturalNumber0(all_60_0) = v1 &
% 32.08/5.14 | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1
% 32.08/5.14 | | | | | | | | | | | | = 0) | ~ (v0 = 0))) | ( ! [v0: $i] : (v0 =
% 32.08/5.14 | | | | | | | | | | | | xk | ~ (sdtasdt0(xp, v0) = all_60_0) | ~
% 32.08/5.14 | | | | | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 32.08/5.14 | | | | | | | | | | | | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : (
% 32.08/5.14 | | | | | | | | | | | | ~ (sdtasdt0(xp, xk) = v0) | ~ $i(xk) | (v0 =
% 32.08/5.14 | | | | | | | | | | | | all_60_0 & aNaturalNumber0(xk) = 0)))
% 32.08/5.14 | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | BETA: splitting (271) gives:
% 32.08/5.14 | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | Case 1:
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | (272) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 32.08/5.14 | | | | | | | | | | | | | (doDivides0(xp, all_60_0) = v2 &
% 32.08/5.14 | | | | | | | | | | | | | aNaturalNumber0(all_60_0) = v1 &
% 32.08/5.14 | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1
% 32.08/5.14 | | | | | | | | | | | | | = 0) | ~ (v0 = 0)))
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | DELTA: instantiating (272) with fresh symbols all_301_0,
% 32.08/5.14 | | | | | | | | | | | | | all_301_1, all_301_2 gives:
% 32.08/5.14 | | | | | | | | | | | | | (273) doDivides0(xp, all_60_0) = all_301_0 &
% 32.08/5.14 | | | | | | | | | | | | | aNaturalNumber0(all_60_0) = all_301_1 &
% 32.08/5.14 | | | | | | | | | | | | | aNaturalNumber0(xp) = all_301_2 & ( ~ (all_301_0 =
% 32.08/5.14 | | | | | | | | | | | | | 0) | ~ (all_301_1 = 0) | ~ (all_301_2 = 0))
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | ALPHA: (273) implies:
% 32.08/5.14 | | | | | | | | | | | | | (274) aNaturalNumber0(xp) = all_301_2
% 32.08/5.14 | | | | | | | | | | | | | (275) aNaturalNumber0(all_60_0) = all_301_1
% 32.08/5.14 | | | | | | | | | | | | | (276) doDivides0(xp, all_60_0) = all_301_0
% 32.08/5.14 | | | | | | | | | | | | | (277) ~ (all_301_0 = 0) | ~ (all_301_1 = 0) | ~
% 32.08/5.14 | | | | | | | | | | | | | (all_301_2 = 0)
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_301_2, xp,
% 32.08/5.14 | | | | | | | | | | | | | simplifying with (5), (274) gives:
% 32.08/5.14 | | | | | | | | | | | | | (278) all_301_2 = 0
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_301_1, all_60_0,
% 32.08/5.14 | | | | | | | | | | | | | simplifying with (267), (275) gives:
% 32.08/5.14 | | | | | | | | | | | | | (279) all_301_1 = 0
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | GROUND_INST: instantiating (22) with 0, all_301_0, all_60_0,
% 32.08/5.14 | | | | | | | | | | | | | xp, simplifying with (63), (276) gives:
% 32.08/5.14 | | | | | | | | | | | | | (280) all_301_0 = 0
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | BETA: splitting (277) gives:
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | Case 1:
% 32.08/5.14 | | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | | (281) ~ (all_301_0 = 0)
% 32.08/5.14 | | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | | REDUCE: (280), (281) imply:
% 32.08/5.14 | | | | | | | | | | | | | | (282) $false
% 32.08/5.14 | | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | | CLOSE: (282) is inconsistent.
% 32.08/5.14 | | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | Case 2:
% 32.08/5.14 | | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | | (283) ~ (all_301_1 = 0) | ~ (all_301_2 = 0)
% 32.08/5.14 | | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 32.08/5.14 | | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | | Case 1:
% 32.08/5.14 | | | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | | | (284) ~ (all_301_1 = 0)
% 32.08/5.14 | | | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | | | REDUCE: (279), (284) imply:
% 32.08/5.14 | | | | | | | | | | | | | | | (285) $false
% 32.08/5.14 | | | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | | | CLOSE: (285) is inconsistent.
% 32.08/5.14 | | | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | | Case 2:
% 32.08/5.14 | | | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | | | (286) ~ (all_301_2 = 0)
% 32.08/5.14 | | | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | | | REDUCE: (278), (286) imply:
% 32.08/5.14 | | | | | | | | | | | | | | | (287) $false
% 32.08/5.14 | | | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | | | CLOSE: (287) is inconsistent.
% 32.08/5.14 | | | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | | End of split
% 32.08/5.14 | | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | End of split
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | Case 2:
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | (288) ! [v0: $i] : (v0 = xk | ~ (sdtasdt0(xp, v0) =
% 32.08/5.14 | | | | | | | | | | | | | all_60_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 32.08/5.14 | | | | | | | | | | | | | = 0) & aNaturalNumber0(v0) = v1)) & ! [v0:
% 32.08/5.14 | | | | | | | | | | | | | $i] : ( ~ (sdtasdt0(xp, xk) = v0) | ~ $i(xk) |
% 32.08/5.14 | | | | | | | | | | | | | (v0 = all_60_0 & aNaturalNumber0(xk) = 0))
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | ALPHA: (288) implies:
% 32.08/5.14 | | | | | | | | | | | | | (289) ! [v0: $i] : ( ~ (sdtasdt0(xp, xk) = v0) | ~
% 32.08/5.14 | | | | | | | | | | | | | $i(xk) | (v0 = all_60_0 & aNaturalNumber0(xk) =
% 32.08/5.14 | | | | | | | | | | | | | 0))
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | GROUND_INST: instantiating (289) with all_66_0, simplifying
% 32.08/5.14 | | | | | | | | | | | | | with (17), (47) gives:
% 32.08/5.14 | | | | | | | | | | | | | (290) all_66_0 = all_60_0 & aNaturalNumber0(xk) = 0
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | ALPHA: (290) implies:
% 32.08/5.14 | | | | | | | | | | | | | (291) all_66_0 = all_60_0
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | REDUCE: (49), (291) imply:
% 32.08/5.14 | | | | | | | | | | | | | (292) sdtlseqdt0(all_66_1, all_60_0) = 0
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_119_0, 0, all_60_0,
% 32.08/5.14 | | | | | | | | | | | | | all_66_1, simplifying with (137), (292) gives:
% 32.08/5.14 | | | | | | | | | | | | | (293) all_119_0 = 0
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | REDUCE: (268), (293) imply:
% 32.08/5.14 | | | | | | | | | | | | | (294) $false
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.14 | | | | | | | | | | | | | CLOSE: (294) is inconsistent.
% 32.08/5.14 | | | | | | | | | | | | |
% 32.08/5.15 | | | | | | | | | | | | End of split
% 32.08/5.15 | | | | | | | | | | | |
% 32.08/5.15 | | | | | | | | | | | End of split
% 32.08/5.15 | | | | | | | | | | |
% 32.08/5.15 | | | | | | | | | | Case 2:
% 32.08/5.15 | | | | | | | | | | |
% 32.08/5.15 | | | | | | | | | | | (295) ~ (all_119_1 = 0) | ~ (all_119_2 = 0)
% 32.08/5.15 | | | | | | | | | | |
% 32.08/5.15 | | | | | | | | | | | BETA: splitting (295) gives:
% 32.08/5.15 | | | | | | | | | | |
% 32.08/5.15 | | | | | | | | | | | Case 1:
% 32.08/5.15 | | | | | | | | | | | |
% 32.08/5.15 | | | | | | | | | | | | (296) ~ (all_119_1 = 0)
% 32.08/5.15 | | | | | | | | | | | |
% 32.08/5.15 | | | | | | | | | | | | REDUCE: (251), (296) imply:
% 32.08/5.15 | | | | | | | | | | | | (297) $false
% 32.08/5.15 | | | | | | | | | | | |
% 32.08/5.15 | | | | | | | | | | | | CLOSE: (297) is inconsistent.
% 32.08/5.15 | | | | | | | | | | | |
% 32.08/5.15 | | | | | | | | | | | Case 2:
% 32.08/5.15 | | | | | | | | | | | |
% 32.08/5.15 | | | | | | | | | | | | (298) ~ (all_119_2 = 0)
% 32.08/5.15 | | | | | | | | | | | |
% 32.08/5.15 | | | | | | | | | | | | REDUCE: (266), (298) imply:
% 32.08/5.15 | | | | | | | | | | | | (299) $false
% 32.08/5.15 | | | | | | | | | | | |
% 32.08/5.15 | | | | | | | | | | | | CLOSE: (299) is inconsistent.
% 32.08/5.15 | | | | | | | | | | | |
% 32.08/5.15 | | | | | | | | | | | End of split
% 32.08/5.15 | | | | | | | | | | |
% 32.08/5.15 | | | | | | | | | | End of split
% 32.08/5.15 | | | | | | | | | |
% 32.08/5.15 | | | | | | | | | End of split
% 32.08/5.15 | | | | | | | | |
% 32.08/5.15 | | | | | | | | End of split
% 32.08/5.15 | | | | | | | |
% 32.08/5.15 | | | | | | | End of split
% 32.08/5.15 | | | | | | |
% 32.08/5.15 | | | | | | End of split
% 32.08/5.15 | | | | | |
% 32.08/5.15 | | | | | End of split
% 32.08/5.15 | | | | |
% 32.08/5.15 | | | | End of split
% 32.08/5.15 | | | |
% 32.08/5.15 | | | End of split
% 32.08/5.15 | | |
% 32.08/5.15 | | End of split
% 32.08/5.15 | |
% 32.08/5.15 | End of split
% 32.08/5.15 |
% 32.08/5.15 End of proof
% 32.08/5.15 % SZS output end Proof for theBenchmark
% 32.08/5.15
% 32.08/5.15 4536ms
%------------------------------------------------------------------------------