TSTP Solution File: RNG050+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG050+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 : n005.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 13:57:33 EDT 2023
% Result : Theorem 9.31s 2.61s
% Output : Proof 12.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : RNG050+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36 % Computer : n005.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 02:29:08 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.68 ________ _____
% 0.21/0.68 ___ __ \_________(_)________________________________
% 0.21/0.68 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.68 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.68 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.68
% 0.21/0.68 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.68 (2023-06-19)
% 0.21/0.68
% 0.21/0.68 (c) Philipp Rümmer, 2009-2023
% 0.21/0.68 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.68 Amanda Stjerna.
% 0.21/0.68 Free software under BSD-3-Clause.
% 0.21/0.68
% 0.21/0.68 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.68
% 0.21/0.68 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.69 Running up to 7 provers in parallel.
% 0.57/0.74 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.57/0.74 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.57/0.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.57/0.74 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.57/0.74 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.57/0.74 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.57/0.75 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.92/1.28 Prover 1: Preprocessing ...
% 2.92/1.28 Prover 4: Preprocessing ...
% 3.22/1.37 Prover 6: Preprocessing ...
% 3.22/1.37 Prover 3: Preprocessing ...
% 3.22/1.37 Prover 2: Preprocessing ...
% 3.22/1.37 Prover 0: Preprocessing ...
% 3.22/1.37 Prover 5: Preprocessing ...
% 7.88/2.30 Prover 1: Constructing countermodel ...
% 7.88/2.32 Prover 3: Constructing countermodel ...
% 8.20/2.34 Prover 6: Proving ...
% 9.31/2.60 Prover 3: proved (1877ms)
% 9.31/2.61
% 9.31/2.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.31/2.61
% 9.31/2.63 Prover 6: proved (1854ms)
% 9.31/2.63
% 9.31/2.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.31/2.63
% 9.66/2.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.66/2.66 Prover 5: Constructing countermodel ...
% 9.66/2.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.78/2.67 Prover 5: stopped
% 9.78/2.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.78/2.76 Prover 7: Preprocessing ...
% 9.78/2.78 Prover 8: Preprocessing ...
% 9.78/2.79 Prover 10: Preprocessing ...
% 10.72/2.92 Prover 2: Proving ...
% 10.72/2.93 Prover 2: stopped
% 10.72/2.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.11/2.94 Prover 4: Constructing countermodel ...
% 11.32/2.97 Prover 0: Proving ...
% 11.32/2.99 Prover 0: stopped
% 11.32/3.01 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.32/3.01 Prover 1: Found proof (size 92)
% 11.32/3.01 Prover 1: proved (2295ms)
% 11.32/3.01 Prover 4: stopped
% 11.32/3.01 Prover 8: Warning: ignoring some quantifiers
% 11.32/3.02 Prover 11: Preprocessing ...
% 11.32/3.02 Prover 8: Constructing countermodel ...
% 11.67/3.03 Prover 8: stopped
% 11.78/3.06 Prover 10: Constructing countermodel ...
% 11.78/3.06 Prover 10: stopped
% 11.78/3.08 Prover 7: Constructing countermodel ...
% 11.78/3.09 Prover 7: stopped
% 11.78/3.10 Prover 13: Preprocessing ...
% 12.10/3.13 Prover 11: stopped
% 12.10/3.16 Prover 13: stopped
% 12.10/3.16
% 12.10/3.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.10/3.16
% 12.30/3.17 % SZS output start Proof for theBenchmark
% 12.30/3.18 Assumptions after simplification:
% 12.30/3.18 ---------------------------------
% 12.30/3.18
% 12.30/3.18 (mDefSPZ)
% 12.30/3.21 $i(sz0z00) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz0z00
% 12.30/3.21 | ~ (sdtasasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ?
% 12.30/3.21 [v4: any] : ? [v5: $i] : ? [v6: $i] : (aVector0(v1) = v4 & aVector0(v0) =
% 12.30/3.21 v3 & aDimensionOf0(v1) = v6 & aDimensionOf0(v0) = v5 & $i(v6) & $i(v5) & (
% 12.30/3.21 ~ (v6 = sz00) | ~ (v5 = sz00) | ~ (v4 = 0) | ~ (v3 = 0))))
% 12.30/3.21
% 12.30/3.21 (mLETot)
% 12.30/3.21 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) =
% 12.30/3.21 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 12.30/3.21 (sdtlseqdt0(v1, v0) = v5 & aScalar0(v1) = v4 & aScalar0(v0) = v3 & ( ~ (v4 =
% 12.30/3.21 0) | ~ (v3 = 0) | v5 = 0)))
% 12.30/3.21
% 12.30/3.21 (mSZeroSc)
% 12.30/3.21 aScalar0(sz0z00) = 0 & $i(sz0z00)
% 12.30/3.21
% 12.30/3.21 (mScPr)
% 12.30/3.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~
% 12.30/3.21 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : ? [v6: $i]
% 12.30/3.21 : ? [v7: any] : (aVector0(v1) = v4 & aVector0(v0) = v3 & aDimensionOf0(v1)
% 12.30/3.21 = v6 & aDimensionOf0(v0) = v5 & aScalar0(v2) = v7 & $i(v6) & $i(v5) & ( ~
% 12.30/3.21 (v6 = v5) | ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0)))
% 12.30/3.21
% 12.30/3.21 (m__)
% 12.30/3.22 $i(xs) & $i(sz0z00) & $i(sz00) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 12.30/3.22 sdtasasdt0(xs, xs) = v0 & aDimensionOf0(xs) = sz00 & sdtlseqdt0(sz0z00, v0)
% 12.30/3.22 = v1 & $i(v0))
% 12.30/3.22
% 12.30/3.22 (m__1516)
% 12.30/3.22 $i(xs) & $i(sz0z00) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1:
% 12.30/3.22 $i] : ! [v2: $i] : ( ~ (sdtasasdt0(v1, v1) = v2) | ~ $i(v1) | ? [v3:
% 12.30/3.22 any] : ? [v4: $i] : ? [v5: any] : ? [v6: any] : (aVector0(v1) = v3 &
% 12.30/3.22 aDimensionOf0(v1) = v4 & sdtlseqdt0(sz0z00, v2) = v6 & iLess0(v4, v0) =
% 12.30/3.22 v5 & $i(v4) & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0))))
% 12.30/3.22
% 12.30/3.22 (m__1542)
% 12.30/3.22 aVector0(xs) = 0 & $i(xs)
% 12.30/3.22
% 12.30/3.22 (function-axioms)
% 12.30/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.30/3.23 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 12.30/3.23 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1)
% 12.30/3.23 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.30/3.23 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.30/3.23 (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 12.30/3.23 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) |
% 12.30/3.23 ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 12.30/3.23 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 12.30/3.23 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.30/3.23 [v3: $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) &
% 12.30/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1)
% 12.30/3.23 | ~ (sziznziztdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.30/3.23 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aVector0(v2) = v1) | ~
% 12.30/3.23 (aVector0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 12.30/3.23 ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0: $i] : !
% 12.30/3.23 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) =
% 12.30/3.23 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 12.30/3.23 $i] : (v1 = v0 | ~ (aScalar0(v2) = v1) | ~ (aScalar0(v2) = v0)) & ! [v0:
% 12.30/3.23 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~
% 12.30/3.23 (szszuzczcdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.30/3.23 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1)
% 12.30/3.23 | ~ (aNaturalNumber0(v2) = v0))
% 12.30/3.23
% 12.30/3.23 Further assumptions not needed in the proof:
% 12.30/3.23 --------------------------------------------
% 12.30/3.23 mArith, mDefInit, mDefSPN, mDimNat, mDistr, mDistr2, mElmSc, mEqInit, mIH,
% 12.30/3.23 mIHOrd, mLEASm, mLEMon, mLEMonM, mLERef, mLETrn, mLess, mMDNeg, mMNeg, mMulSc,
% 12.30/3.23 mNatExtr, mNatSort, mNegSc, mPosMon, mScSort, mScZero, mSqPos, mSqrt, mSuccEqu,
% 12.30/3.23 mSuccNat, mSumSc, mVcSort, mZeroNat
% 12.30/3.23
% 12.30/3.23 Those formulas are unsatisfiable:
% 12.30/3.23 ---------------------------------
% 12.30/3.23
% 12.30/3.23 Begin of proof
% 12.30/3.23 |
% 12.30/3.23 | ALPHA: (mSZeroSc) implies:
% 12.30/3.23 | (1) aScalar0(sz0z00) = 0
% 12.30/3.23 |
% 12.30/3.23 | ALPHA: (mDefSPZ) implies:
% 12.30/3.23 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz0z00 | ~
% 12.30/3.23 | (sdtasasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ?
% 12.30/3.23 | [v4: any] : ? [v5: $i] : ? [v6: $i] : (aVector0(v1) = v4 &
% 12.30/3.23 | aVector0(v0) = v3 & aDimensionOf0(v1) = v6 & aDimensionOf0(v0) = v5
% 12.30/3.24 | & $i(v6) & $i(v5) & ( ~ (v6 = sz00) | ~ (v5 = sz00) | ~ (v4 = 0)
% 12.30/3.24 | | ~ (v3 = 0))))
% 12.30/3.24 |
% 12.30/3.24 | ALPHA: (m__1542) implies:
% 12.30/3.24 | (3) aVector0(xs) = 0
% 12.30/3.24 |
% 12.30/3.24 | ALPHA: (m__1516) implies:
% 12.67/3.24 | (4) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 12.67/3.24 | $i] : ( ~ (sdtasasdt0(v1, v1) = v2) | ~ $i(v1) | ? [v3: any] : ?
% 12.67/3.24 | [v4: $i] : ? [v5: any] : ? [v6: any] : (aVector0(v1) = v3 &
% 12.67/3.24 | aDimensionOf0(v1) = v4 & sdtlseqdt0(sz0z00, v2) = v6 & iLess0(v4,
% 12.67/3.24 | v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0))))
% 12.67/3.24 |
% 12.67/3.24 | ALPHA: (m__) implies:
% 12.67/3.24 | (5) $i(sz0z00)
% 12.67/3.24 | (6) $i(xs)
% 12.67/3.24 | (7) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & sdtasasdt0(xs, xs) = v0 &
% 12.67/3.24 | aDimensionOf0(xs) = sz00 & sdtlseqdt0(sz0z00, v0) = v1 & $i(v0))
% 12.67/3.24 |
% 12.67/3.24 | ALPHA: (function-axioms) implies:
% 12.67/3.24 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.67/3.24 | (v1 = v0 | ~ (aScalar0(v2) = v1) | ~ (aScalar0(v2) = v0))
% 12.67/3.24 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 12.67/3.24 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0))
% 12.67/3.24 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 12.67/3.24 | : (v1 = v0 | ~ (aVector0(v2) = v1) | ~ (aVector0(v2) = v0))
% 12.67/3.24 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 12.67/3.24 | : ! [v3: $i] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~
% 12.67/3.24 | (sdtlseqdt0(v3, v2) = v0))
% 12.67/3.24 |
% 12.67/3.24 | DELTA: instantiating (7) with fresh symbols all_32_0, all_32_1 gives:
% 12.67/3.24 | (12) ~ (all_32_0 = 0) & sdtasasdt0(xs, xs) = all_32_1 & aDimensionOf0(xs)
% 12.67/3.24 | = sz00 & sdtlseqdt0(sz0z00, all_32_1) = all_32_0 & $i(all_32_1)
% 12.67/3.24 |
% 12.67/3.24 | ALPHA: (12) implies:
% 12.67/3.25 | (13) ~ (all_32_0 = 0)
% 12.67/3.25 | (14) $i(all_32_1)
% 12.67/3.25 | (15) sdtlseqdt0(sz0z00, all_32_1) = all_32_0
% 12.67/3.25 | (16) aDimensionOf0(xs) = sz00
% 12.67/3.25 | (17) sdtasasdt0(xs, xs) = all_32_1
% 12.67/3.25 |
% 12.67/3.25 | DELTA: instantiating (4) with fresh symbol all_34_0 gives:
% 12.67/3.25 | (18) aDimensionOf0(xs) = all_34_0 & $i(all_34_0) & ! [v0: $i] : ! [v1:
% 12.67/3.25 | $i] : ( ~ (sdtasasdt0(v0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 12.67/3.25 | [v3: $i] : ? [v4: any] : ? [v5: any] : (aVector0(v0) = v2 &
% 12.67/3.25 | aDimensionOf0(v0) = v3 & sdtlseqdt0(sz0z00, v1) = v5 & iLess0(v3,
% 12.67/3.25 | all_34_0) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = 0)))
% 12.67/3.25 |
% 12.67/3.25 | ALPHA: (18) implies:
% 12.67/3.25 | (19) aDimensionOf0(xs) = all_34_0
% 12.67/3.25 | (20) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasasdt0(v0, v0) = v1) | ~ $i(v0)
% 12.67/3.25 | | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: any] :
% 12.67/3.25 | (aVector0(v0) = v2 & aDimensionOf0(v0) = v3 & sdtlseqdt0(sz0z00, v1)
% 12.67/3.25 | = v5 & iLess0(v3, all_34_0) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2
% 12.67/3.25 | = 0) | v5 = 0)))
% 12.67/3.25 |
% 12.67/3.25 | GROUND_INST: instantiating (9) with sz00, all_34_0, xs, simplifying with (16),
% 12.67/3.25 | (19) gives:
% 12.67/3.25 | (21) all_34_0 = sz00
% 12.67/3.25 |
% 12.67/3.25 | GROUND_INST: instantiating (mLETot) with sz0z00, all_32_1, all_32_0,
% 12.67/3.25 | simplifying with (5), (14), (15) gives:
% 12.67/3.25 | (22) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 12.67/3.25 | (sdtlseqdt0(all_32_1, sz0z00) = v2 & aScalar0(all_32_1) = v1 &
% 12.67/3.25 | aScalar0(sz0z00) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 12.67/3.25 |
% 12.67/3.25 | GROUND_INST: instantiating (20) with xs, all_32_1, simplifying with (6), (17)
% 12.67/3.25 | gives:
% 12.67/3.25 | (23) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] :
% 12.67/3.25 | (aVector0(xs) = v0 & aDimensionOf0(xs) = v1 & sdtlseqdt0(sz0z00,
% 12.67/3.25 | all_32_1) = v3 & iLess0(v1, all_34_0) = v2 & $i(v1) & ( ~ (v2 = 0)
% 12.67/3.25 | | ~ (v0 = 0) | v3 = 0))
% 12.67/3.25 |
% 12.67/3.25 | GROUND_INST: instantiating (2) with xs, xs, all_32_1, simplifying with (6),
% 12.67/3.25 | (17) gives:
% 12.67/3.26 | (24) all_32_1 = sz0z00 | ? [v0: any] : ? [v1: any] : ? [v2: $i] : ?
% 12.67/3.26 | [v3: $i] : (aVector0(xs) = v1 & aVector0(xs) = v0 & aDimensionOf0(xs)
% 12.67/3.26 | = v3 & aDimensionOf0(xs) = v2 & $i(v3) & $i(v2) & ( ~ (v3 = sz00) |
% 12.67/3.26 | ~ (v2 = sz00) | ~ (v1 = 0) | ~ (v0 = 0)))
% 12.67/3.26 |
% 12.67/3.26 | GROUND_INST: instantiating (mScPr) with xs, xs, all_32_1, simplifying with
% 12.67/3.26 | (6), (17) gives:
% 12.67/3.26 | (25) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: any]
% 12.67/3.26 | : (aVector0(xs) = v1 & aVector0(xs) = v0 & aDimensionOf0(xs) = v3 &
% 12.67/3.26 | aDimensionOf0(xs) = v2 & aScalar0(all_32_1) = v4 & $i(v3) & $i(v2) &
% 12.67/3.26 | ( ~ (v3 = v2) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 12.67/3.26 |
% 12.67/3.26 | DELTA: instantiating (23) with fresh symbols all_51_0, all_51_1, all_51_2,
% 12.67/3.26 | all_51_3 gives:
% 12.67/3.26 | (26) aVector0(xs) = all_51_3 & aDimensionOf0(xs) = all_51_2 &
% 12.67/3.26 | sdtlseqdt0(sz0z00, all_32_1) = all_51_0 & iLess0(all_51_2, all_34_0) =
% 12.67/3.26 | all_51_1 & $i(all_51_2) & ( ~ (all_51_1 = 0) | ~ (all_51_3 = 0) |
% 12.67/3.26 | all_51_0 = 0)
% 12.67/3.26 |
% 12.67/3.26 | ALPHA: (26) implies:
% 12.67/3.26 | (27) sdtlseqdt0(sz0z00, all_32_1) = all_51_0
% 12.67/3.26 | (28) aDimensionOf0(xs) = all_51_2
% 12.67/3.26 | (29) aVector0(xs) = all_51_3
% 12.67/3.26 |
% 12.67/3.26 | DELTA: instantiating (25) with fresh symbols all_53_0, all_53_1, all_53_2,
% 12.67/3.26 | all_53_3, all_53_4 gives:
% 12.67/3.26 | (30) aVector0(xs) = all_53_3 & aVector0(xs) = all_53_4 & aDimensionOf0(xs)
% 12.67/3.26 | = all_53_1 & aDimensionOf0(xs) = all_53_2 & aScalar0(all_32_1) =
% 12.67/3.26 | all_53_0 & $i(all_53_1) & $i(all_53_2) & ( ~ (all_53_1 = all_53_2) |
% 12.67/3.26 | ~ (all_53_3 = 0) | ~ (all_53_4 = 0) | all_53_0 = 0)
% 12.67/3.26 |
% 12.67/3.26 | ALPHA: (30) implies:
% 12.67/3.26 | (31) aScalar0(all_32_1) = all_53_0
% 12.67/3.26 | (32) aDimensionOf0(xs) = all_53_2
% 12.67/3.26 | (33) aDimensionOf0(xs) = all_53_1
% 12.67/3.26 | (34) aVector0(xs) = all_53_4
% 12.67/3.26 | (35) aVector0(xs) = all_53_3
% 12.67/3.26 | (36) ~ (all_53_1 = all_53_2) | ~ (all_53_3 = 0) | ~ (all_53_4 = 0) |
% 12.67/3.26 | all_53_0 = 0
% 12.67/3.26 |
% 12.67/3.26 | BETA: splitting (22) gives:
% 12.67/3.26 |
% 12.67/3.26 | Case 1:
% 12.67/3.26 | |
% 12.67/3.26 | | (37) all_32_0 = 0
% 12.67/3.26 | |
% 12.67/3.26 | | REDUCE: (13), (37) imply:
% 12.67/3.26 | | (38) $false
% 12.67/3.26 | |
% 12.67/3.26 | | CLOSE: (38) is inconsistent.
% 12.67/3.26 | |
% 12.67/3.26 | Case 2:
% 12.67/3.26 | |
% 12.67/3.27 | | (39) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(all_32_1,
% 12.67/3.27 | | sz0z00) = v2 & aScalar0(all_32_1) = v1 & aScalar0(sz0z00) = v0 &
% 12.67/3.27 | | ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 12.67/3.27 | |
% 12.67/3.27 | | DELTA: instantiating (39) with fresh symbols all_59_0, all_59_1, all_59_2
% 12.67/3.27 | | gives:
% 12.67/3.27 | | (40) sdtlseqdt0(all_32_1, sz0z00) = all_59_0 & aScalar0(all_32_1) =
% 12.67/3.27 | | all_59_1 & aScalar0(sz0z00) = all_59_2 & ( ~ (all_59_1 = 0) | ~
% 12.67/3.27 | | (all_59_2 = 0) | all_59_0 = 0)
% 12.67/3.27 | |
% 12.67/3.27 | | ALPHA: (40) implies:
% 12.67/3.27 | | (41) aScalar0(sz0z00) = all_59_2
% 12.67/3.27 | | (42) aScalar0(all_32_1) = all_59_1
% 12.67/3.27 | | (43) sdtlseqdt0(all_32_1, sz0z00) = all_59_0
% 12.67/3.27 | | (44) ~ (all_59_1 = 0) | ~ (all_59_2 = 0) | all_59_0 = 0
% 12.67/3.27 | |
% 12.67/3.27 | | GROUND_INST: instantiating (8) with 0, all_59_2, sz0z00, simplifying with
% 12.67/3.27 | | (1), (41) gives:
% 12.67/3.27 | | (45) all_59_2 = 0
% 12.67/3.27 | |
% 12.67/3.27 | | GROUND_INST: instantiating (8) with all_53_0, all_59_1, all_32_1,
% 12.67/3.27 | | simplifying with (31), (42) gives:
% 12.67/3.27 | | (46) all_59_1 = all_53_0
% 12.67/3.27 | |
% 12.67/3.27 | | GROUND_INST: instantiating (11) with all_32_0, all_51_0, all_32_1, sz0z00,
% 12.67/3.27 | | simplifying with (15), (27) gives:
% 12.67/3.27 | | (47) all_51_0 = all_32_0
% 12.67/3.27 | |
% 12.67/3.27 | | GROUND_INST: instantiating (9) with all_51_2, all_53_2, xs, simplifying with
% 12.67/3.27 | | (28), (32) gives:
% 12.67/3.27 | | (48) all_53_2 = all_51_2
% 12.67/3.27 | |
% 12.67/3.27 | | GROUND_INST: instantiating (9) with sz00, all_53_1, xs, simplifying with
% 12.67/3.27 | | (16), (33) gives:
% 12.67/3.27 | | (49) all_53_1 = sz00
% 12.67/3.27 | |
% 12.83/3.27 | | GROUND_INST: instantiating (9) with all_53_2, all_53_1, xs, simplifying with
% 12.83/3.27 | | (32), (33) gives:
% 12.83/3.27 | | (50) all_53_1 = all_53_2
% 12.83/3.27 | |
% 12.83/3.27 | | GROUND_INST: instantiating (10) with 0, all_53_3, xs, simplifying with (3),
% 12.83/3.27 | | (35) gives:
% 12.83/3.27 | | (51) all_53_3 = 0
% 12.83/3.27 | |
% 12.83/3.27 | | GROUND_INST: instantiating (10) with all_53_4, all_53_3, xs, simplifying
% 12.83/3.27 | | with (34), (35) gives:
% 12.83/3.27 | | (52) all_53_3 = all_53_4
% 12.83/3.27 | |
% 12.83/3.27 | | GROUND_INST: instantiating (10) with all_51_3, all_53_3, xs, simplifying
% 12.83/3.27 | | with (29), (35) gives:
% 12.83/3.27 | | (53) all_53_3 = all_51_3
% 12.83/3.27 | |
% 12.83/3.27 | | COMBINE_EQS: (49), (50) imply:
% 12.83/3.27 | | (54) all_53_2 = sz00
% 12.83/3.27 | |
% 12.83/3.27 | | SIMP: (54) implies:
% 12.83/3.27 | | (55) all_53_2 = sz00
% 12.83/3.27 | |
% 12.83/3.27 | | COMBINE_EQS: (48), (55) imply:
% 12.83/3.27 | | (56) all_51_2 = sz00
% 12.83/3.27 | |
% 12.83/3.27 | | COMBINE_EQS: (51), (52) imply:
% 12.83/3.27 | | (57) all_53_4 = 0
% 12.83/3.27 | |
% 12.83/3.27 | | COMBINE_EQS: (52), (53) imply:
% 12.83/3.27 | | (58) all_53_4 = all_51_3
% 12.83/3.27 | |
% 12.83/3.28 | | COMBINE_EQS: (57), (58) imply:
% 12.83/3.28 | | (59) all_51_3 = 0
% 12.83/3.28 | |
% 12.83/3.28 | | BETA: splitting (24) gives:
% 12.83/3.28 | |
% 12.83/3.28 | | Case 1:
% 12.83/3.28 | | |
% 12.83/3.28 | | | (60) all_32_1 = sz0z00
% 12.83/3.28 | | |
% 12.83/3.28 | | | REDUCE: (43), (60) imply:
% 12.83/3.28 | | | (61) sdtlseqdt0(sz0z00, sz0z00) = all_59_0
% 12.83/3.28 | | |
% 12.83/3.28 | | | REDUCE: (15), (60) imply:
% 12.83/3.28 | | | (62) sdtlseqdt0(sz0z00, sz0z00) = all_32_0
% 12.83/3.28 | | |
% 12.83/3.28 | | | BETA: splitting (36) gives:
% 12.83/3.28 | | |
% 12.83/3.28 | | | Case 1:
% 12.83/3.28 | | | |
% 12.83/3.28 | | | | (63) ~ (all_53_3 = 0)
% 12.83/3.28 | | | |
% 12.83/3.28 | | | | REDUCE: (51), (63) imply:
% 12.83/3.28 | | | | (64) $false
% 12.83/3.28 | | | |
% 12.83/3.28 | | | | CLOSE: (64) is inconsistent.
% 12.83/3.28 | | | |
% 12.83/3.28 | | | Case 2:
% 12.83/3.28 | | | |
% 12.83/3.28 | | | | (65) ~ (all_53_1 = all_53_2) | ~ (all_53_4 = 0) | all_53_0 = 0
% 12.83/3.28 | | | |
% 12.83/3.28 | | | | BETA: splitting (65) gives:
% 12.83/3.28 | | | |
% 12.83/3.28 | | | | Case 1:
% 12.83/3.28 | | | | |
% 12.83/3.28 | | | | | (66) ~ (all_53_4 = 0)
% 12.83/3.28 | | | | |
% 12.83/3.28 | | | | | REDUCE: (57), (66) imply:
% 12.83/3.28 | | | | | (67) $false
% 12.83/3.28 | | | | |
% 12.83/3.28 | | | | | CLOSE: (67) is inconsistent.
% 12.83/3.28 | | | | |
% 12.83/3.28 | | | | Case 2:
% 12.83/3.28 | | | | |
% 12.83/3.28 | | | | | (68) ~ (all_53_1 = all_53_2) | all_53_0 = 0
% 12.83/3.28 | | | | |
% 12.83/3.28 | | | | | BETA: splitting (68) gives:
% 12.83/3.28 | | | | |
% 12.83/3.28 | | | | | Case 1:
% 12.83/3.28 | | | | | |
% 12.83/3.28 | | | | | | (69) ~ (all_53_1 = all_53_2)
% 12.83/3.28 | | | | | |
% 12.83/3.28 | | | | | | REDUCE: (49), (55), (69) imply:
% 12.83/3.28 | | | | | | (70) $false
% 12.83/3.28 | | | | | |
% 12.83/3.28 | | | | | | CLOSE: (70) is inconsistent.
% 12.83/3.28 | | | | | |
% 12.83/3.28 | | | | | Case 2:
% 12.83/3.28 | | | | | |
% 12.83/3.28 | | | | | | (71) all_53_0 = 0
% 12.83/3.28 | | | | | |
% 12.83/3.28 | | | | | | COMBINE_EQS: (46), (71) imply:
% 12.83/3.28 | | | | | | (72) all_59_1 = 0
% 12.83/3.28 | | | | | |
% 12.83/3.28 | | | | | | BETA: splitting (44) gives:
% 12.83/3.28 | | | | | |
% 12.83/3.28 | | | | | | Case 1:
% 12.83/3.28 | | | | | | |
% 12.83/3.28 | | | | | | | (73) ~ (all_59_1 = 0)
% 12.83/3.28 | | | | | | |
% 12.83/3.28 | | | | | | | REDUCE: (72), (73) imply:
% 12.83/3.28 | | | | | | | (74) $false
% 12.83/3.28 | | | | | | |
% 12.83/3.28 | | | | | | | CLOSE: (74) is inconsistent.
% 12.83/3.28 | | | | | | |
% 12.83/3.28 | | | | | | Case 2:
% 12.83/3.28 | | | | | | |
% 12.83/3.28 | | | | | | | (75) ~ (all_59_2 = 0) | all_59_0 = 0
% 12.83/3.28 | | | | | | |
% 12.83/3.28 | | | | | | | BETA: splitting (75) gives:
% 12.83/3.28 | | | | | | |
% 12.83/3.28 | | | | | | | Case 1:
% 12.83/3.28 | | | | | | | |
% 12.83/3.28 | | | | | | | | (76) ~ (all_59_2 = 0)
% 12.83/3.28 | | | | | | | |
% 12.83/3.28 | | | | | | | | REDUCE: (45), (76) imply:
% 12.83/3.28 | | | | | | | | (77) $false
% 12.83/3.28 | | | | | | | |
% 12.83/3.28 | | | | | | | | CLOSE: (77) is inconsistent.
% 12.83/3.28 | | | | | | | |
% 12.83/3.28 | | | | | | | Case 2:
% 12.83/3.28 | | | | | | | |
% 12.83/3.28 | | | | | | | | (78) all_59_0 = 0
% 12.83/3.28 | | | | | | | |
% 12.83/3.28 | | | | | | | | REDUCE: (61), (78) imply:
% 12.83/3.28 | | | | | | | | (79) sdtlseqdt0(sz0z00, sz0z00) = 0
% 12.83/3.28 | | | | | | | |
% 12.83/3.28 | | | | | | | | GROUND_INST: instantiating (11) with 0, all_32_0, sz0z00,
% 12.83/3.28 | | | | | | | | sz0z00, simplifying with (62), (79) gives:
% 12.83/3.28 | | | | | | | | (80) all_32_0 = 0
% 12.83/3.28 | | | | | | | |
% 12.83/3.28 | | | | | | | | REDUCE: (13), (80) imply:
% 12.83/3.28 | | | | | | | | (81) $false
% 12.83/3.28 | | | | | | | |
% 12.83/3.28 | | | | | | | | CLOSE: (81) is inconsistent.
% 12.83/3.28 | | | | | | | |
% 12.83/3.29 | | | | | | | End of split
% 12.83/3.29 | | | | | | |
% 12.83/3.29 | | | | | | End of split
% 12.83/3.29 | | | | | |
% 12.83/3.29 | | | | | End of split
% 12.83/3.29 | | | | |
% 12.83/3.29 | | | | End of split
% 12.83/3.29 | | | |
% 12.83/3.29 | | | End of split
% 12.83/3.29 | | |
% 12.83/3.29 | | Case 2:
% 12.83/3.29 | | |
% 12.83/3.29 | | | (82) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 12.83/3.29 | | | (aVector0(xs) = v1 & aVector0(xs) = v0 & aDimensionOf0(xs) = v3 &
% 12.83/3.29 | | | aDimensionOf0(xs) = v2 & $i(v3) & $i(v2) & ( ~ (v3 = sz00) | ~
% 12.83/3.29 | | | (v2 = sz00) | ~ (v1 = 0) | ~ (v0 = 0)))
% 12.83/3.29 | | |
% 12.83/3.29 | | | DELTA: instantiating (82) with fresh symbols all_69_0, all_69_1, all_69_2,
% 12.83/3.29 | | | all_69_3 gives:
% 12.83/3.29 | | | (83) aVector0(xs) = all_69_2 & aVector0(xs) = all_69_3 &
% 12.83/3.29 | | | aDimensionOf0(xs) = all_69_0 & aDimensionOf0(xs) = all_69_1 &
% 12.83/3.29 | | | $i(all_69_0) & $i(all_69_1) & ( ~ (all_69_0 = sz00) | ~ (all_69_1
% 12.83/3.29 | | | = sz00) | ~ (all_69_2 = 0) | ~ (all_69_3 = 0))
% 12.83/3.29 | | |
% 12.83/3.29 | | | ALPHA: (83) implies:
% 12.83/3.29 | | | (84) aDimensionOf0(xs) = all_69_1
% 12.83/3.29 | | | (85) aDimensionOf0(xs) = all_69_0
% 12.83/3.29 | | | (86) aVector0(xs) = all_69_3
% 12.83/3.29 | | | (87) aVector0(xs) = all_69_2
% 12.83/3.29 | | | (88) ~ (all_69_0 = sz00) | ~ (all_69_1 = sz00) | ~ (all_69_2 = 0) |
% 12.83/3.29 | | | ~ (all_69_3 = 0)
% 12.83/3.29 | | |
% 12.83/3.29 | | | GROUND_INST: instantiating (9) with sz00, all_69_0, xs, simplifying with
% 12.83/3.29 | | | (16), (85) gives:
% 12.83/3.29 | | | (89) all_69_0 = sz00
% 12.83/3.29 | | |
% 12.83/3.29 | | | GROUND_INST: instantiating (9) with all_69_1, all_69_0, xs, simplifying
% 12.83/3.29 | | | with (84), (85) gives:
% 12.83/3.29 | | | (90) all_69_0 = all_69_1
% 12.83/3.29 | | |
% 12.83/3.29 | | | GROUND_INST: instantiating (10) with 0, all_69_2, xs, simplifying with
% 12.83/3.29 | | | (3), (87) gives:
% 12.83/3.29 | | | (91) all_69_2 = 0
% 12.83/3.29 | | |
% 12.83/3.29 | | | GROUND_INST: instantiating (10) with all_69_3, all_69_2, xs, simplifying
% 12.83/3.29 | | | with (86), (87) gives:
% 12.83/3.29 | | | (92) all_69_2 = all_69_3
% 12.83/3.29 | | |
% 12.83/3.29 | | | COMBINE_EQS: (89), (90) imply:
% 12.83/3.29 | | | (93) all_69_1 = sz00
% 12.83/3.29 | | |
% 12.83/3.29 | | | SIMP: (93) implies:
% 12.83/3.29 | | | (94) all_69_1 = sz00
% 12.83/3.29 | | |
% 12.83/3.29 | | | COMBINE_EQS: (91), (92) imply:
% 12.83/3.29 | | | (95) all_69_3 = 0
% 12.83/3.29 | | |
% 12.83/3.29 | | | BETA: splitting (88) gives:
% 12.83/3.29 | | |
% 12.83/3.29 | | | Case 1:
% 12.83/3.29 | | | |
% 12.83/3.29 | | | | (96) ~ (all_69_2 = 0)
% 12.83/3.29 | | | |
% 12.83/3.29 | | | | REDUCE: (91), (96) imply:
% 12.83/3.29 | | | | (97) $false
% 12.83/3.29 | | | |
% 12.83/3.29 | | | | CLOSE: (97) is inconsistent.
% 12.83/3.29 | | | |
% 12.83/3.29 | | | Case 2:
% 12.83/3.29 | | | |
% 12.83/3.29 | | | | (98) ~ (all_69_0 = sz00) | ~ (all_69_1 = sz00) | ~ (all_69_3 = 0)
% 12.83/3.29 | | | |
% 12.83/3.29 | | | | BETA: splitting (98) gives:
% 12.83/3.29 | | | |
% 12.83/3.29 | | | | Case 1:
% 12.83/3.29 | | | | |
% 12.83/3.29 | | | | | (99) ~ (all_69_3 = 0)
% 12.83/3.29 | | | | |
% 12.83/3.29 | | | | | REDUCE: (95), (99) imply:
% 12.83/3.29 | | | | | (100) $false
% 12.83/3.29 | | | | |
% 12.83/3.29 | | | | | CLOSE: (100) is inconsistent.
% 12.83/3.30 | | | | |
% 12.83/3.30 | | | | Case 2:
% 12.83/3.30 | | | | |
% 12.83/3.30 | | | | | (101) ~ (all_69_0 = sz00) | ~ (all_69_1 = sz00)
% 12.83/3.30 | | | | |
% 12.83/3.30 | | | | | BETA: splitting (101) gives:
% 12.83/3.30 | | | | |
% 12.83/3.30 | | | | | Case 1:
% 12.83/3.30 | | | | | |
% 12.83/3.30 | | | | | | (102) ~ (all_69_0 = sz00)
% 12.83/3.30 | | | | | |
% 12.83/3.30 | | | | | | REDUCE: (89), (102) imply:
% 12.83/3.30 | | | | | | (103) $false
% 12.83/3.30 | | | | | |
% 12.83/3.30 | | | | | | CLOSE: (103) is inconsistent.
% 12.83/3.30 | | | | | |
% 12.83/3.30 | | | | | Case 2:
% 12.83/3.30 | | | | | |
% 12.83/3.30 | | | | | | (104) ~ (all_69_1 = sz00)
% 12.83/3.30 | | | | | |
% 12.83/3.30 | | | | | | REDUCE: (94), (104) imply:
% 12.83/3.30 | | | | | | (105) $false
% 12.83/3.30 | | | | | |
% 12.83/3.30 | | | | | | CLOSE: (105) is inconsistent.
% 12.83/3.30 | | | | | |
% 12.83/3.30 | | | | | End of split
% 12.83/3.30 | | | | |
% 12.83/3.30 | | | | End of split
% 12.83/3.30 | | | |
% 12.83/3.30 | | | End of split
% 12.83/3.30 | | |
% 12.83/3.30 | | End of split
% 12.83/3.30 | |
% 12.83/3.30 | End of split
% 12.83/3.30 |
% 12.83/3.30 End of proof
% 12.83/3.30 % SZS output end Proof for theBenchmark
% 12.83/3.30
% 12.83/3.30 2617ms
%------------------------------------------------------------------------------