TSTP Solution File: NUM477+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM477+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n020.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 11:48:02 EDT 2023
% Result : Theorem 12.81s 2.72s
% Output : Proof 17.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM477+2 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n020.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 09:48:45 EDT 2023
% 0.19/0.35 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.42/1.28 Prover 4: Preprocessing ...
% 3.42/1.28 Prover 1: Preprocessing ...
% 3.42/1.34 Prover 6: Preprocessing ...
% 3.42/1.34 Prover 2: Preprocessing ...
% 3.42/1.34 Prover 5: Preprocessing ...
% 3.42/1.35 Prover 0: Preprocessing ...
% 3.42/1.35 Prover 3: Preprocessing ...
% 9.34/2.20 Prover 1: Constructing countermodel ...
% 10.65/2.37 Prover 3: Constructing countermodel ...
% 11.28/2.48 Prover 6: Proving ...
% 11.60/2.50 Prover 5: Constructing countermodel ...
% 12.81/2.69 Prover 2: Proving ...
% 12.81/2.72 Prover 3: proved (2076ms)
% 12.81/2.72
% 12.81/2.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.81/2.72
% 12.81/2.74 Prover 5: stopped
% 12.81/2.74 Prover 6: stopped
% 12.81/2.74 Prover 2: stopped
% 12.81/2.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.81/2.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.81/2.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.81/2.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.51/2.89 Prover 4: Constructing countermodel ...
% 13.51/2.90 Prover 11: Preprocessing ...
% 13.51/2.92 Prover 8: Preprocessing ...
% 13.51/2.95 Prover 7: Preprocessing ...
% 13.51/2.98 Prover 10: Preprocessing ...
% 15.62/3.08 Prover 1: Found proof (size 72)
% 15.62/3.08 Prover 1: proved (2439ms)
% 15.62/3.09 Prover 11: stopped
% 15.62/3.09 Prover 4: stopped
% 16.09/3.13 Prover 8: Warning: ignoring some quantifiers
% 16.09/3.14 Prover 8: Constructing countermodel ...
% 16.09/3.15 Prover 10: Constructing countermodel ...
% 16.09/3.16 Prover 8: stopped
% 16.52/3.16 Prover 0: Proving ...
% 16.52/3.17 Prover 0: stopped
% 16.52/3.17 Prover 7: Constructing countermodel ...
% 16.52/3.17 Prover 10: stopped
% 16.52/3.19 Prover 7: stopped
% 16.52/3.19
% 16.52/3.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.52/3.19
% 16.52/3.21 % SZS output start Proof for theBenchmark
% 16.52/3.21 Assumptions after simplification:
% 16.52/3.21 ---------------------------------
% 16.52/3.21
% 16.52/3.21 (mLETotal)
% 16.97/3.26 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) =
% 16.97/3.26 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 16.97/3.26 (sdtlseqdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 16.97/3.26 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v5 = 0 & ~ (v1 = v0)))))
% 16.97/3.26
% 16.97/3.26 (mMonMul2)
% 16.97/3.26 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 |
% 16.97/3.26 v0 = sz00 | ~ (sdtlseqdt0(v1, v2) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ~
% 16.97/3.26 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (aNaturalNumber0(v1) = v5
% 16.97/3.26 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))
% 16.97/3.26
% 16.97/3.26 (mMulComm)
% 16.97/3.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 16.97/3.26 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 16.97/3.26 (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3
% 16.97/3.26 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 16.97/3.26
% 16.97/3.26 (m_MulZero)
% 16.97/3.27 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~
% 16.97/3.27 $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtasdt0(v0, sz00) = v3 &
% 16.97/3.27 aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = sz00 & v1 =
% 16.97/3.27 sz00))))
% 16.97/3.27
% 16.97/3.27 (m__)
% 16.97/3.27 $i(xn) & $i(xm) & ? [v0: int] : ( ~ (v0 = 0) & sdtlseqdt0(xm, xn) = v0 & !
% 16.97/3.27 [v1: $i] : ( ~ (sdtpldt0(xm, v1) = xn) | ~ $i(v1) | ? [v2: int] : ( ~ (v2
% 16.97/3.27 = 0) & aNaturalNumber0(v1) = v2)))
% 16.97/3.27
% 16.97/3.27 (m__1494)
% 16.97/3.27 aNaturalNumber0(xn) = 0 & aNaturalNumber0(xm) = 0 & $i(xn) & $i(xm)
% 16.97/3.27
% 16.97/3.27 (m__1494_04)
% 16.97/3.27 ~ (xn = sz00) & doDivides0(xm, xn) = 0 & $i(xn) & $i(xm) & $i(sz00) & ? [v0:
% 16.97/3.27 $i] : (sdtasdt0(xm, v0) = xn & aNaturalNumber0(v0) = 0 & $i(v0))
% 16.97/3.27
% 16.97/3.27 (function-axioms)
% 16.97/3.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.97/3.28 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0:
% 16.97/3.28 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 16.97/3.28 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & !
% 16.97/3.28 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 16.97/3.28 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & !
% 16.97/3.28 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.97/3.28 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0:
% 16.97/3.28 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 16.97/3.28 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 16.97/3.28 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.97/3.28 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 16.97/3.28 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 16.97/3.28 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.97/3.28 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1)
% 16.97/3.28 | ~ (aNaturalNumber0(v2) = v0))
% 16.97/3.28
% 16.97/3.28 Further assumptions not needed in the proof:
% 16.97/3.28 --------------------------------------------
% 16.97/3.28 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDefQuot,
% 16.97/3.28 mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, mLERefl, mLETran,
% 16.97/3.28 mMonAdd, mMonMul, mMulAsso, mMulCanc, mNatSort, mSortsB, mSortsB_02, mSortsC,
% 16.97/3.28 mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit
% 16.97/3.28
% 16.97/3.28 Those formulas are unsatisfiable:
% 16.97/3.28 ---------------------------------
% 16.97/3.28
% 16.97/3.28 Begin of proof
% 16.97/3.28 |
% 16.97/3.29 | ALPHA: (m_MulZero) implies:
% 16.97/3.29 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) |
% 16.97/3.29 | ? [v2: any] : ? [v3: $i] : (sdtasdt0(v0, sz00) = v3 &
% 16.97/3.29 | aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = sz00 & v1
% 16.97/3.29 | = sz00))))
% 16.97/3.29 |
% 17.16/3.29 | ALPHA: (mMonMul2) implies:
% 17.16/3.29 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v0 =
% 17.16/3.29 | sz00 | ~ (sdtlseqdt0(v1, v2) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ~
% 17.16/3.29 | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 17.16/3.29 | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) |
% 17.16/3.29 | ~ (v4 = 0))))
% 17.16/3.29 |
% 17.16/3.29 | ALPHA: (m__1494) implies:
% 17.16/3.29 | (3) aNaturalNumber0(xm) = 0
% 17.16/3.29 |
% 17.16/3.29 | ALPHA: (m__1494_04) implies:
% 17.16/3.29 | (4) ~ (xn = sz00)
% 17.16/3.29 | (5) ? [v0: $i] : (sdtasdt0(xm, v0) = xn & aNaturalNumber0(v0) = 0 &
% 17.16/3.29 | $i(v0))
% 17.16/3.29 |
% 17.16/3.29 | ALPHA: (m__) implies:
% 17.16/3.30 | (6) $i(xm)
% 17.16/3.30 | (7) $i(xn)
% 17.16/3.30 | (8) ? [v0: int] : ( ~ (v0 = 0) & sdtlseqdt0(xm, xn) = v0 & ! [v1: $i] : (
% 17.16/3.30 | ~ (sdtpldt0(xm, v1) = xn) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0)
% 17.16/3.30 | & aNaturalNumber0(v1) = v2)))
% 17.16/3.30 |
% 17.16/3.30 | ALPHA: (function-axioms) implies:
% 17.16/3.30 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.16/3.30 | (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) =
% 17.16/3.30 | v0))
% 17.16/3.30 |
% 17.16/3.30 | DELTA: instantiating (5) with fresh symbol all_34_0 gives:
% 17.16/3.30 | (10) sdtasdt0(xm, all_34_0) = xn & aNaturalNumber0(all_34_0) = 0 &
% 17.16/3.30 | $i(all_34_0)
% 17.16/3.30 |
% 17.16/3.30 | ALPHA: (10) implies:
% 17.16/3.30 | (11) $i(all_34_0)
% 17.16/3.30 | (12) aNaturalNumber0(all_34_0) = 0
% 17.16/3.30 | (13) sdtasdt0(xm, all_34_0) = xn
% 17.16/3.30 |
% 17.16/3.30 | DELTA: instantiating (8) with fresh symbol all_36_0 gives:
% 17.16/3.30 | (14) ~ (all_36_0 = 0) & sdtlseqdt0(xm, xn) = all_36_0 & ! [v0: $i] : ( ~
% 17.16/3.30 | (sdtpldt0(xm, v0) = xn) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 17.16/3.30 | aNaturalNumber0(v0) = v1))
% 17.16/3.30 |
% 17.16/3.30 | ALPHA: (14) implies:
% 17.16/3.30 | (15) ~ (all_36_0 = 0)
% 17.16/3.30 | (16) sdtlseqdt0(xm, xn) = all_36_0
% 17.16/3.30 |
% 17.16/3.30 | GROUND_INST: instantiating (mMulComm) with xm, all_34_0, xn, simplifying with
% 17.16/3.30 | (6), (11), (13) gives:
% 17.16/3.31 | (17) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_34_0, xm) =
% 17.16/3.31 | v2 & aNaturalNumber0(all_34_0) = v1 & aNaturalNumber0(xm) = v0 &
% 17.16/3.31 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xn))
% 17.16/3.31 |
% 17.16/3.31 | GROUND_INST: instantiating (2) with all_34_0, xm, xn, all_36_0, simplifying
% 17.16/3.31 | with (6), (11), (13), (16) gives:
% 17.16/3.31 | (18) all_36_0 = 0 | all_34_0 = sz00 | ? [v0: any] : ? [v1: any] :
% 17.16/3.31 | (aNaturalNumber0(all_34_0) = v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 =
% 17.16/3.31 | 0) | ~ (v0 = 0)))
% 17.16/3.31 |
% 17.16/3.31 | GROUND_INST: instantiating (mLETotal) with xm, xn, all_36_0, simplifying with
% 17.16/3.31 | (6), (7), (16) gives:
% 17.16/3.31 | (19) all_36_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.16/3.31 | (sdtlseqdt0(xn, xm) = v2 & aNaturalNumber0(xn) = v1 &
% 17.16/3.31 | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~
% 17.16/3.31 | (xn = xm))))
% 17.16/3.31 |
% 17.16/3.31 | DELTA: instantiating (17) with fresh symbols all_44_0, all_44_1, all_44_2
% 17.16/3.31 | gives:
% 17.16/3.31 | (20) sdtasdt0(all_34_0, xm) = all_44_0 & aNaturalNumber0(all_34_0) =
% 17.16/3.31 | all_44_1 & aNaturalNumber0(xm) = all_44_2 & $i(all_44_0) & ( ~
% 17.16/3.31 | (all_44_1 = 0) | ~ (all_44_2 = 0) | all_44_0 = xn)
% 17.16/3.31 |
% 17.16/3.31 | ALPHA: (20) implies:
% 17.16/3.31 | (21) aNaturalNumber0(xm) = all_44_2
% 17.16/3.31 | (22) aNaturalNumber0(all_34_0) = all_44_1
% 17.16/3.31 | (23) sdtasdt0(all_34_0, xm) = all_44_0
% 17.16/3.31 | (24) ~ (all_44_1 = 0) | ~ (all_44_2 = 0) | all_44_0 = xn
% 17.16/3.31 |
% 17.16/3.31 | BETA: splitting (19) gives:
% 17.16/3.31 |
% 17.16/3.31 | Case 1:
% 17.16/3.31 | |
% 17.16/3.31 | | (25) all_36_0 = 0
% 17.16/3.31 | |
% 17.16/3.31 | | REDUCE: (15), (25) imply:
% 17.16/3.31 | | (26) $false
% 17.16/3.32 | |
% 17.16/3.32 | | CLOSE: (26) is inconsistent.
% 17.16/3.32 | |
% 17.16/3.32 | Case 2:
% 17.16/3.32 | |
% 17.16/3.32 | | (27) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(xn, xm) =
% 17.16/3.32 | | v2 & aNaturalNumber0(xn) = v1 & aNaturalNumber0(xm) = v0 & ( ~ (v1
% 17.16/3.32 | | = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xn = xm))))
% 17.16/3.32 | |
% 17.16/3.32 | | DELTA: instantiating (27) with fresh symbols all_58_0, all_58_1, all_58_2
% 17.16/3.32 | | gives:
% 17.16/3.32 | | (28) sdtlseqdt0(xn, xm) = all_58_0 & aNaturalNumber0(xn) = all_58_1 &
% 17.16/3.32 | | aNaturalNumber0(xm) = all_58_2 & ( ~ (all_58_1 = 0) | ~ (all_58_2 =
% 17.16/3.32 | | 0) | (all_58_0 = 0 & ~ (xn = xm)))
% 17.16/3.32 | |
% 17.16/3.32 | | ALPHA: (28) implies:
% 17.16/3.32 | | (29) aNaturalNumber0(xm) = all_58_2
% 17.16/3.32 | |
% 17.16/3.32 | | GROUND_INST: instantiating (9) with 0, all_58_2, xm, simplifying with (3),
% 17.16/3.32 | | (29) gives:
% 17.16/3.32 | | (30) all_58_2 = 0
% 17.16/3.32 | |
% 17.16/3.32 | | GROUND_INST: instantiating (9) with all_44_2, all_58_2, xm, simplifying with
% 17.16/3.32 | | (21), (29) gives:
% 17.16/3.32 | | (31) all_58_2 = all_44_2
% 17.16/3.32 | |
% 17.16/3.32 | | GROUND_INST: instantiating (9) with 0, all_44_1, all_34_0, simplifying with
% 17.16/3.32 | | (12), (22) gives:
% 17.16/3.32 | | (32) all_44_1 = 0
% 17.16/3.32 | |
% 17.16/3.32 | | COMBINE_EQS: (30), (31) imply:
% 17.16/3.32 | | (33) all_44_2 = 0
% 17.16/3.32 | |
% 17.16/3.32 | | SIMP: (33) implies:
% 17.16/3.32 | | (34) all_44_2 = 0
% 17.16/3.32 | |
% 17.16/3.32 | | BETA: splitting (18) gives:
% 17.16/3.32 | |
% 17.16/3.32 | | Case 1:
% 17.16/3.32 | | |
% 17.16/3.32 | | | (35) all_34_0 = sz00
% 17.16/3.32 | | |
% 17.16/3.32 | | | REDUCE: (23), (35) imply:
% 17.16/3.32 | | | (36) sdtasdt0(sz00, xm) = all_44_0
% 17.16/3.32 | | |
% 17.16/3.32 | | | DELTA: instantiating (5) with fresh symbol all_79_0 gives:
% 17.16/3.32 | | | (37) sdtasdt0(xm, all_79_0) = xn & aNaturalNumber0(all_79_0) = 0 &
% 17.16/3.32 | | | $i(all_79_0)
% 17.16/3.32 | | |
% 17.16/3.32 | | | ALPHA: (37) implies:
% 17.16/3.32 | | | (38) $i(all_79_0)
% 17.16/3.32 | | | (39) sdtasdt0(xm, all_79_0) = xn
% 17.16/3.32 | | |
% 17.16/3.32 | | | BETA: splitting (24) gives:
% 17.16/3.32 | | |
% 17.16/3.32 | | | Case 1:
% 17.16/3.32 | | | |
% 17.16/3.32 | | | | (40) ~ (all_44_1 = 0)
% 17.16/3.32 | | | |
% 17.16/3.32 | | | | REDUCE: (32), (40) imply:
% 17.16/3.32 | | | | (41) $false
% 17.16/3.32 | | | |
% 17.16/3.32 | | | | CLOSE: (41) is inconsistent.
% 17.16/3.32 | | | |
% 17.16/3.32 | | | Case 2:
% 17.16/3.32 | | | |
% 17.16/3.33 | | | | (42) ~ (all_44_2 = 0) | all_44_0 = xn
% 17.16/3.33 | | | |
% 17.16/3.33 | | | | BETA: splitting (42) gives:
% 17.16/3.33 | | | |
% 17.16/3.33 | | | | Case 1:
% 17.16/3.33 | | | | |
% 17.16/3.33 | | | | | (43) ~ (all_44_2 = 0)
% 17.16/3.33 | | | | |
% 17.16/3.33 | | | | | REDUCE: (34), (43) imply:
% 17.16/3.33 | | | | | (44) $false
% 17.16/3.33 | | | | |
% 17.16/3.33 | | | | | CLOSE: (44) is inconsistent.
% 17.16/3.33 | | | | |
% 17.16/3.33 | | | | Case 2:
% 17.16/3.33 | | | | |
% 17.16/3.33 | | | | | (45) all_44_0 = xn
% 17.16/3.33 | | | | |
% 17.16/3.33 | | | | | REDUCE: (36), (45) imply:
% 17.16/3.33 | | | | | (46) sdtasdt0(sz00, xm) = xn
% 17.16/3.33 | | | | |
% 17.16/3.33 | | | | | GROUND_INST: instantiating (1) with xm, xn, simplifying with (6), (46)
% 17.16/3.33 | | | | | gives:
% 17.16/3.33 | | | | | (47) ? [v0: any] : ? [v1: $i] : (sdtasdt0(xm, sz00) = v1 &
% 17.16/3.33 | | | | | aNaturalNumber0(xm) = v0 & $i(v1) & ( ~ (v0 = 0) | (v1 =
% 17.16/3.33 | | | | | sz00 & xn = sz00)))
% 17.16/3.33 | | | | |
% 17.16/3.33 | | | | | GROUND_INST: instantiating (mMulComm) with xm, all_79_0, xn,
% 17.16/3.33 | | | | | simplifying with (6), (38), (39) gives:
% 17.16/3.33 | | | | | (48) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 17.16/3.33 | | | | | (sdtasdt0(all_79_0, xm) = v2 & aNaturalNumber0(all_79_0) = v1
% 17.16/3.33 | | | | | & aNaturalNumber0(xm) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0
% 17.16/3.33 | | | | | = 0) | v2 = xn))
% 17.16/3.33 | | | | |
% 17.16/3.33 | | | | | DELTA: instantiating (47) with fresh symbols all_99_0, all_99_1 gives:
% 17.16/3.33 | | | | | (49) sdtasdt0(xm, sz00) = all_99_0 & aNaturalNumber0(xm) = all_99_1
% 17.16/3.33 | | | | | & $i(all_99_0) & ( ~ (all_99_1 = 0) | (all_99_0 = sz00 & xn =
% 17.16/3.33 | | | | | sz00))
% 17.16/3.33 | | | | |
% 17.16/3.33 | | | | | ALPHA: (49) implies:
% 17.16/3.33 | | | | | (50) aNaturalNumber0(xm) = all_99_1
% 17.16/3.33 | | | | | (51) ~ (all_99_1 = 0) | (all_99_0 = sz00 & xn = sz00)
% 17.16/3.33 | | | | |
% 17.16/3.33 | | | | | DELTA: instantiating (48) with fresh symbols all_101_0, all_101_1,
% 17.16/3.33 | | | | | all_101_2 gives:
% 17.39/3.34 | | | | | (52) sdtasdt0(all_79_0, xm) = all_101_0 & aNaturalNumber0(all_79_0)
% 17.39/3.34 | | | | | = all_101_1 & aNaturalNumber0(xm) = all_101_2 & $i(all_101_0)
% 17.39/3.34 | | | | | & ( ~ (all_101_1 = 0) | ~ (all_101_2 = 0) | all_101_0 = xn)
% 17.39/3.34 | | | | |
% 17.39/3.34 | | | | | ALPHA: (52) implies:
% 17.39/3.34 | | | | | (53) aNaturalNumber0(xm) = all_101_2
% 17.39/3.34 | | | | |
% 17.39/3.34 | | | | | BETA: splitting (51) gives:
% 17.39/3.34 | | | | |
% 17.39/3.34 | | | | | Case 1:
% 17.39/3.34 | | | | | |
% 17.39/3.34 | | | | | | (54) ~ (all_99_1 = 0)
% 17.39/3.34 | | | | | |
% 17.39/3.34 | | | | | | GROUND_INST: instantiating (9) with 0, all_101_2, xm, simplifying
% 17.39/3.34 | | | | | | with (3), (53) gives:
% 17.39/3.34 | | | | | | (55) all_101_2 = 0
% 17.39/3.34 | | | | | |
% 17.39/3.34 | | | | | | GROUND_INST: instantiating (9) with all_99_1, all_101_2, xm,
% 17.39/3.34 | | | | | | simplifying with (50), (53) gives:
% 17.39/3.34 | | | | | | (56) all_101_2 = all_99_1
% 17.39/3.34 | | | | | |
% 17.39/3.34 | | | | | | COMBINE_EQS: (55), (56) imply:
% 17.39/3.34 | | | | | | (57) all_99_1 = 0
% 17.39/3.34 | | | | | |
% 17.39/3.34 | | | | | | SIMP: (57) implies:
% 17.39/3.34 | | | | | | (58) all_99_1 = 0
% 17.39/3.34 | | | | | |
% 17.39/3.34 | | | | | | REDUCE: (54), (58) imply:
% 17.39/3.34 | | | | | | (59) $false
% 17.39/3.34 | | | | | |
% 17.39/3.34 | | | | | | CLOSE: (59) is inconsistent.
% 17.39/3.34 | | | | | |
% 17.39/3.34 | | | | | Case 2:
% 17.39/3.34 | | | | | |
% 17.39/3.34 | | | | | | (60) all_99_0 = sz00 & xn = sz00
% 17.39/3.34 | | | | | |
% 17.39/3.34 | | | | | | ALPHA: (60) implies:
% 17.39/3.34 | | | | | | (61) xn = sz00
% 17.39/3.34 | | | | | |
% 17.39/3.34 | | | | | | REDUCE: (4), (61) imply:
% 17.39/3.34 | | | | | | (62) $false
% 17.39/3.34 | | | | | |
% 17.39/3.34 | | | | | | CLOSE: (62) is inconsistent.
% 17.39/3.34 | | | | | |
% 17.39/3.34 | | | | | End of split
% 17.39/3.34 | | | | |
% 17.39/3.34 | | | | End of split
% 17.39/3.34 | | | |
% 17.39/3.34 | | | End of split
% 17.39/3.34 | | |
% 17.39/3.34 | | Case 2:
% 17.39/3.34 | | |
% 17.42/3.34 | | | (63) all_36_0 = 0 | ? [v0: any] : ? [v1: any] :
% 17.42/3.34 | | | (aNaturalNumber0(all_34_0) = v0 & aNaturalNumber0(xm) = v1 & ( ~
% 17.42/3.34 | | | (v1 = 0) | ~ (v0 = 0)))
% 17.42/3.34 | | |
% 17.42/3.34 | | | BETA: splitting (63) gives:
% 17.42/3.34 | | |
% 17.42/3.34 | | | Case 1:
% 17.42/3.34 | | | |
% 17.42/3.34 | | | | (64) all_36_0 = 0
% 17.42/3.34 | | | |
% 17.42/3.34 | | | | REDUCE: (15), (64) imply:
% 17.42/3.34 | | | | (65) $false
% 17.42/3.34 | | | |
% 17.42/3.34 | | | | CLOSE: (65) is inconsistent.
% 17.42/3.34 | | | |
% 17.42/3.34 | | | Case 2:
% 17.42/3.34 | | | |
% 17.42/3.35 | | | | (66) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_34_0) = v0 &
% 17.42/3.35 | | | | aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 17.42/3.35 | | | |
% 17.42/3.35 | | | | DELTA: instantiating (66) with fresh symbols all_93_0, all_93_1 gives:
% 17.42/3.35 | | | | (67) aNaturalNumber0(all_34_0) = all_93_1 & aNaturalNumber0(xm) =
% 17.42/3.35 | | | | all_93_0 & ( ~ (all_93_0 = 0) | ~ (all_93_1 = 0))
% 17.42/3.35 | | | |
% 17.42/3.35 | | | | ALPHA: (67) implies:
% 17.42/3.35 | | | | (68) aNaturalNumber0(xm) = all_93_0
% 17.42/3.35 | | | | (69) aNaturalNumber0(all_34_0) = all_93_1
% 17.42/3.35 | | | | (70) ~ (all_93_0 = 0) | ~ (all_93_1 = 0)
% 17.42/3.35 | | | |
% 17.42/3.35 | | | | GROUND_INST: instantiating (9) with 0, all_93_0, xm, simplifying with
% 17.42/3.35 | | | | (3), (68) gives:
% 17.42/3.35 | | | | (71) all_93_0 = 0
% 17.42/3.35 | | | |
% 17.42/3.35 | | | | GROUND_INST: instantiating (9) with 0, all_93_1, all_34_0, simplifying
% 17.42/3.35 | | | | with (12), (69) gives:
% 17.42/3.35 | | | | (72) all_93_1 = 0
% 17.42/3.35 | | | |
% 17.42/3.35 | | | | BETA: splitting (70) gives:
% 17.42/3.35 | | | |
% 17.42/3.35 | | | | Case 1:
% 17.42/3.35 | | | | |
% 17.42/3.35 | | | | | (73) ~ (all_93_0 = 0)
% 17.42/3.35 | | | | |
% 17.42/3.35 | | | | | REDUCE: (71), (73) imply:
% 17.42/3.35 | | | | | (74) $false
% 17.42/3.35 | | | | |
% 17.42/3.35 | | | | | CLOSE: (74) is inconsistent.
% 17.42/3.35 | | | | |
% 17.42/3.35 | | | | Case 2:
% 17.42/3.35 | | | | |
% 17.42/3.35 | | | | | (75) ~ (all_93_1 = 0)
% 17.42/3.35 | | | | |
% 17.42/3.35 | | | | | REDUCE: (72), (75) imply:
% 17.42/3.35 | | | | | (76) $false
% 17.42/3.35 | | | | |
% 17.42/3.35 | | | | | CLOSE: (76) is inconsistent.
% 17.42/3.35 | | | | |
% 17.42/3.35 | | | | End of split
% 17.42/3.35 | | | |
% 17.42/3.35 | | | End of split
% 17.42/3.35 | | |
% 17.42/3.35 | | End of split
% 17.42/3.35 | |
% 17.42/3.35 | End of split
% 17.42/3.35 |
% 17.42/3.35 End of proof
% 17.42/3.35 % SZS output end Proof for theBenchmark
% 17.42/3.35
% 17.42/3.35 2737ms
%------------------------------------------------------------------------------