TSTP Solution File: RNG089+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG089+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 : n015.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 13:57:47 EDT 2023
% Result : Theorem 11.77s 2.38s
% Output : Proof 15.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG089+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 02:17:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.02/1.15 Prover 1: Preprocessing ...
% 3.02/1.15 Prover 4: Preprocessing ...
% 3.44/1.19 Prover 5: Preprocessing ...
% 3.44/1.19 Prover 2: Preprocessing ...
% 3.44/1.19 Prover 0: Preprocessing ...
% 3.44/1.19 Prover 3: Preprocessing ...
% 3.44/1.19 Prover 6: Preprocessing ...
% 8.13/1.88 Prover 3: Constructing countermodel ...
% 8.25/1.88 Prover 1: Constructing countermodel ...
% 8.25/1.90 Prover 6: Proving ...
% 8.25/1.91 Prover 5: Proving ...
% 8.46/2.01 Prover 4: Constructing countermodel ...
% 8.46/2.05 Prover 2: Proving ...
% 8.94/2.09 Prover 0: Proving ...
% 11.77/2.38 Prover 3: proved (1736ms)
% 11.77/2.38
% 11.77/2.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.77/2.38
% 11.77/2.38 Prover 2: stopped
% 11.77/2.38 Prover 5: stopped
% 11.77/2.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.77/2.39 Prover 0: stopped
% 11.77/2.40 Prover 6: stopped
% 11.77/2.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.77/2.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.77/2.41 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.77/2.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.19/2.44 Prover 8: Preprocessing ...
% 12.44/2.46 Prover 7: Preprocessing ...
% 12.44/2.48 Prover 10: Preprocessing ...
% 12.44/2.49 Prover 13: Preprocessing ...
% 12.44/2.52 Prover 11: Preprocessing ...
% 13.29/2.63 Prover 7: Constructing countermodel ...
% 13.79/2.64 Prover 10: Constructing countermodel ...
% 13.79/2.65 Prover 8: Warning: ignoring some quantifiers
% 13.79/2.66 Prover 8: Constructing countermodel ...
% 13.79/2.74 Prover 13: Warning: ignoring some quantifiers
% 13.79/2.75 Prover 13: Constructing countermodel ...
% 13.79/2.79 Prover 11: Constructing countermodel ...
% 15.40/2.88 Prover 10: Found proof (size 14)
% 15.40/2.88 Prover 1: Found proof (size 55)
% 15.40/2.88 Prover 10: proved (488ms)
% 15.40/2.88 Prover 1: proved (2254ms)
% 15.40/2.89 Prover 11: stopped
% 15.40/2.89 Prover 13: stopped
% 15.40/2.89 Prover 7: stopped
% 15.40/2.89 Prover 4: stopped
% 15.40/2.89 Prover 8: stopped
% 15.40/2.89
% 15.40/2.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.40/2.89
% 15.62/2.90 % SZS output start Proof for theBenchmark
% 15.62/2.91 Assumptions after simplification:
% 15.62/2.91 ---------------------------------
% 15.62/2.91
% 15.62/2.91 (mMulComm)
% 15.80/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 15.80/2.93 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 15.80/2.93 (sdtasdt0(v1, v0) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & $i(v5) &
% 15.80/2.93 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 15.80/2.93
% 15.80/2.93 (m__)
% 15.80/2.93 $i(xl) & $i(xk) & $i(xz) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: any] : ?
% 15.80/2.93 [v2: $i] : ? [v3: any] : (aElementOf0(v2, xJ) = v3 & aElementOf0(v0, xI) = v1
% 15.80/2.93 & sdtasdt0(xz, xl) = v2 & sdtasdt0(xz, xk) = v0 & $i(v2) & $i(v0) & ( ~ (v3
% 15.80/2.93 = 0) | ~ (v1 = 0)))
% 15.80/2.93
% 15.80/2.93 (m__870)
% 15.80/2.94 aIdeal0(xJ) = 0 & aIdeal0(xI) = 0 & aSet0(xJ) = 0 & aSet0(xI) = 0 & $i(xJ) &
% 15.80/2.94 $i(xI) & ! [v0: $i] : ( ~ (aElementOf0(v0, xJ) = 0) | ~ $i(v0) | ( ! [v1:
% 15.80/2.94 $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3:
% 15.80/2.94 any] : ? [v4: any] : (aElementOf0(v2, xJ) = v4 & aElement0(v1) = v3 &
% 15.80/2.94 ( ~ (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~ (aElementOf0(v1, xJ) = 0)
% 15.80/2.94 | ~ $i(v1) | ? [v2: $i] : (aElementOf0(v2, xJ) = 0 & sdtpldt0(v0, v1)
% 15.80/2.94 = v2 & $i(v2))))) & ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~
% 15.80/2.94 $i(v0) | ( ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~
% 15.80/2.94 $i(v1) | ? [v3: any] : ? [v4: any] : (aElementOf0(v2, xI) = v4 &
% 15.80/2.94 aElement0(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~
% 15.80/2.94 (aElementOf0(v1, xI) = 0) | ~ $i(v1) | ? [v2: $i] : (aElementOf0(v2,
% 15.80/2.94 xI) = 0 & sdtpldt0(v0, v1) = v2 & $i(v2)))))
% 15.80/2.94
% 15.80/2.94 (m__901)
% 15.80/2.94 $i(xz) & $i(xy) & $i(xx) & $i(xJ) & $i(xI) & ? [v0: $i] : (sdtpldt1(xI, xJ) =
% 15.80/2.94 v0 & aElementOf0(xy, v0) = 0 & aElementOf0(xx, v0) = 0 & aElement0(xz) = 0 &
% 15.80/2.94 $i(v0) & ? [v1: $i] : ? [v2: $i] : (aElementOf0(v2, xJ) = 0 &
% 15.80/2.94 aElementOf0(v1, xI) = 0 & sdtpldt0(v1, v2) = xy & $i(v2) & $i(v1)) & ?
% 15.80/2.94 [v1: $i] : ? [v2: $i] : (aElementOf0(v2, xJ) = 0 & aElementOf0(v1, xI) = 0
% 15.80/2.94 & sdtpldt0(v1, v2) = xx & $i(v2) & $i(v1)))
% 15.80/2.94
% 15.80/2.94 (m__934)
% 15.80/2.94 aElementOf0(xl, xJ) = 0 & aElementOf0(xk, xI) = 0 & sdtpldt0(xk, xl) = xx &
% 15.80/2.94 $i(xl) & $i(xk) & $i(xx) & $i(xJ) & $i(xI)
% 15.80/2.94
% 15.80/2.94 (function-axioms)
% 15.80/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.80/2.95 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 15.80/2.95 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) |
% 15.80/2.95 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.80/2.95 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.80/2.95 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: $i] :
% 15.80/2.95 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1)
% 15.80/2.95 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 15.80/2.95 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 15.80/2.95 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 15.80/2.95 = v0 | ~ (aIdeal0(v2) = v1) | ~ (aIdeal0(v2) = v0)) & ! [v0:
% 15.80/2.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 15.80/2.95 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 15.80/2.95 [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0:
% 15.80/2.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 15.80/2.95 ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0))
% 15.80/2.95
% 15.80/2.95 Further assumptions not needed in the proof:
% 15.80/2.95 --------------------------------------------
% 15.80/2.95 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mDefIdeal, mDefSInt,
% 15.80/2.95 mDefSSum, mEOfElem, mElmSort, mMulAsso, mMulMnOne, mMulUnit, mMulZero, mSetEq,
% 15.80/2.95 mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__967,
% 15.80/2.95 m__994
% 15.80/2.95
% 15.80/2.95 Those formulas are unsatisfiable:
% 15.80/2.95 ---------------------------------
% 15.80/2.95
% 15.80/2.95 Begin of proof
% 15.80/2.95 |
% 15.80/2.95 | ALPHA: (m__870) implies:
% 15.80/2.95 | (1) ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ( ! [v1: $i]
% 15.80/2.95 | : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3:
% 15.80/2.95 | any] : ? [v4: any] : (aElementOf0(v2, xI) = v4 & aElement0(v1)
% 15.80/2.95 | = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~
% 15.80/2.95 | (aElementOf0(v1, xI) = 0) | ~ $i(v1) | ? [v2: $i] :
% 15.80/2.95 | (aElementOf0(v2, xI) = 0 & sdtpldt0(v0, v1) = v2 & $i(v2)))))
% 15.80/2.95 | (2) ! [v0: $i] : ( ~ (aElementOf0(v0, xJ) = 0) | ~ $i(v0) | ( ! [v1: $i]
% 15.80/2.95 | : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3:
% 15.80/2.95 | any] : ? [v4: any] : (aElementOf0(v2, xJ) = v4 & aElement0(v1)
% 15.80/2.95 | = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~
% 15.80/2.95 | (aElementOf0(v1, xJ) = 0) | ~ $i(v1) | ? [v2: $i] :
% 15.80/2.95 | (aElementOf0(v2, xJ) = 0 & sdtpldt0(v0, v1) = v2 & $i(v2)))))
% 15.80/2.95 |
% 15.80/2.95 | ALPHA: (m__901) implies:
% 15.80/2.95 | (3) ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & aElementOf0(xy, v0) = 0 &
% 15.80/2.95 | aElementOf0(xx, v0) = 0 & aElement0(xz) = 0 & $i(v0) & ? [v1: $i] :
% 15.80/2.95 | ? [v2: $i] : (aElementOf0(v2, xJ) = 0 & aElementOf0(v1, xI) = 0 &
% 15.80/2.96 | sdtpldt0(v1, v2) = xy & $i(v2) & $i(v1)) & ? [v1: $i] : ? [v2:
% 15.80/2.96 | $i] : (aElementOf0(v2, xJ) = 0 & aElementOf0(v1, xI) = 0 &
% 15.80/2.96 | sdtpldt0(v1, v2) = xx & $i(v2) & $i(v1)))
% 15.80/2.96 |
% 15.80/2.96 | ALPHA: (m__934) implies:
% 15.80/2.96 | (4) aElementOf0(xk, xI) = 0
% 15.80/2.96 | (5) aElementOf0(xl, xJ) = 0
% 15.80/2.96 |
% 15.80/2.96 | ALPHA: (m__) implies:
% 15.80/2.96 | (6) $i(xz)
% 15.80/2.96 | (7) $i(xk)
% 15.80/2.96 | (8) $i(xl)
% 15.80/2.96 | (9) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 15.80/2.96 | (aElementOf0(v2, xJ) = v3 & aElementOf0(v0, xI) = v1 & sdtasdt0(xz, xl)
% 15.80/2.96 | = v2 & sdtasdt0(xz, xk) = v0 & $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~
% 15.80/2.96 | (v1 = 0)))
% 15.80/2.96 |
% 15.80/2.96 | ALPHA: (function-axioms) implies:
% 15.80/2.96 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.80/2.96 | : (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0))
% 15.80/2.96 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.80/2.96 | : ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~
% 15.80/2.96 | (aElementOf0(v3, v2) = v0))
% 15.80/2.96 |
% 15.80/2.96 | DELTA: instantiating (9) with fresh symbols all_25_0, all_25_1, all_25_2,
% 15.80/2.96 | all_25_3 gives:
% 15.80/2.96 | (12) aElementOf0(all_25_1, xJ) = all_25_0 & aElementOf0(all_25_3, xI) =
% 15.80/2.96 | all_25_2 & sdtasdt0(xz, xl) = all_25_1 & sdtasdt0(xz, xk) = all_25_3 &
% 15.80/2.96 | $i(all_25_1) & $i(all_25_3) & ( ~ (all_25_0 = 0) | ~ (all_25_2 = 0))
% 15.80/2.96 |
% 15.80/2.96 | ALPHA: (12) implies:
% 15.80/2.96 | (13) sdtasdt0(xz, xk) = all_25_3
% 15.80/2.96 | (14) sdtasdt0(xz, xl) = all_25_1
% 15.80/2.96 | (15) aElementOf0(all_25_3, xI) = all_25_2
% 15.80/2.96 | (16) aElementOf0(all_25_1, xJ) = all_25_0
% 15.80/2.96 | (17) ~ (all_25_0 = 0) | ~ (all_25_2 = 0)
% 15.80/2.96 |
% 15.80/2.96 | DELTA: instantiating (3) with fresh symbol all_30_0 gives:
% 15.80/2.96 | (18) sdtpldt1(xI, xJ) = all_30_0 & aElementOf0(xy, all_30_0) = 0 &
% 15.80/2.96 | aElementOf0(xx, all_30_0) = 0 & aElement0(xz) = 0 & $i(all_30_0) & ?
% 15.80/2.96 | [v0: $i] : ? [v1: $i] : (aElementOf0(v1, xJ) = 0 & aElementOf0(v0,
% 15.80/2.96 | xI) = 0 & sdtpldt0(v0, v1) = xy & $i(v1) & $i(v0)) & ? [v0: $i] :
% 15.80/2.96 | ? [v1: $i] : (aElementOf0(v1, xJ) = 0 & aElementOf0(v0, xI) = 0 &
% 15.80/2.96 | sdtpldt0(v0, v1) = xx & $i(v1) & $i(v0))
% 15.80/2.96 |
% 15.80/2.96 | ALPHA: (18) implies:
% 15.80/2.96 | (19) aElement0(xz) = 0
% 15.80/2.96 |
% 15.80/2.96 | GROUND_INST: instantiating (mMulComm) with xz, xk, all_25_3, simplifying with
% 15.80/2.96 | (6), (7), (13) gives:
% 15.80/2.96 | (20) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xk, xz) = v2 &
% 15.80/2.96 | aElement0(xk) = v1 & aElement0(xz) = v0 & $i(v2) & ( ~ (v1 = 0) | ~
% 15.80/2.96 | (v0 = 0) | v2 = all_25_3))
% 15.80/2.96 |
% 15.80/2.96 | GROUND_INST: instantiating (mMulComm) with xz, xl, all_25_1, simplifying with
% 15.80/2.96 | (6), (8), (14) gives:
% 15.80/2.97 | (21) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xl, xz) = v2 &
% 15.80/2.97 | aElement0(xl) = v1 & aElement0(xz) = v0 & $i(v2) & ( ~ (v1 = 0) | ~
% 15.80/2.97 | (v0 = 0) | v2 = all_25_1))
% 15.80/2.97 |
% 15.80/2.97 | GROUND_INST: instantiating (1) with xk, simplifying with (4), (7) gives:
% 15.80/2.97 | (22) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, xk) = v1) | ~ $i(v0) |
% 15.80/2.97 | ? [v2: any] : ? [v3: any] : (aElementOf0(v1, xI) = v3 &
% 15.80/2.97 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 15.80/2.97 | (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ? [v1: $i] :
% 15.80/2.97 | (aElementOf0(v1, xI) = 0 & sdtpldt0(xk, v0) = v1 & $i(v1)))
% 15.80/2.97 |
% 15.80/2.97 | ALPHA: (22) implies:
% 15.80/2.97 | (23) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, xk) = v1) | ~ $i(v0) |
% 15.80/2.97 | ? [v2: any] : ? [v3: any] : (aElementOf0(v1, xI) = v3 &
% 15.80/2.97 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 15.80/2.97 |
% 15.80/2.97 | GROUND_INST: instantiating (2) with xl, simplifying with (5), (8) gives:
% 15.80/2.97 | (24) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, xl) = v1) | ~ $i(v0) |
% 15.80/2.97 | ? [v2: any] : ? [v3: any] : (aElementOf0(v1, xJ) = v3 &
% 15.80/2.97 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 15.80/2.97 | (aElementOf0(v0, xJ) = 0) | ~ $i(v0) | ? [v1: $i] :
% 15.80/2.97 | (aElementOf0(v1, xJ) = 0 & sdtpldt0(xl, v0) = v1 & $i(v1)))
% 15.80/2.97 |
% 15.80/2.97 | ALPHA: (24) implies:
% 15.80/2.97 | (25) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, xl) = v1) | ~ $i(v0) |
% 15.80/2.97 | ? [v2: any] : ? [v3: any] : (aElementOf0(v1, xJ) = v3 &
% 15.80/2.97 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 15.80/2.97 |
% 15.80/2.97 | GROUND_INST: instantiating (25) with xz, all_25_1, simplifying with (6), (14)
% 15.80/2.97 | gives:
% 15.80/2.97 | (26) ? [v0: any] : ? [v1: any] : (aElementOf0(all_25_1, xJ) = v1 &
% 15.80/2.97 | aElement0(xz) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 15.80/2.97 |
% 15.80/2.97 | GROUND_INST: instantiating (23) with xz, all_25_3, simplifying with (6), (13)
% 15.80/2.97 | gives:
% 15.80/2.97 | (27) ? [v0: any] : ? [v1: any] : (aElementOf0(all_25_3, xI) = v1 &
% 15.80/2.97 | aElement0(xz) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 15.80/2.97 |
% 15.80/2.97 | DELTA: instantiating (21) with fresh symbols all_86_0, all_86_1, all_86_2
% 15.80/2.97 | gives:
% 15.80/2.97 | (28) sdtasdt0(xl, xz) = all_86_0 & aElement0(xl) = all_86_1 & aElement0(xz)
% 15.80/2.97 | = all_86_2 & $i(all_86_0) & ( ~ (all_86_1 = 0) | ~ (all_86_2 = 0) |
% 15.80/2.97 | all_86_0 = all_25_1)
% 15.80/2.97 |
% 15.80/2.97 | ALPHA: (28) implies:
% 15.80/2.97 | (29) aElement0(xz) = all_86_2
% 15.80/2.97 |
% 15.80/2.97 | DELTA: instantiating (20) with fresh symbols all_96_0, all_96_1, all_96_2
% 15.80/2.97 | gives:
% 15.80/2.97 | (30) sdtasdt0(xk, xz) = all_96_0 & aElement0(xk) = all_96_1 & aElement0(xz)
% 15.80/2.97 | = all_96_2 & $i(all_96_0) & ( ~ (all_96_1 = 0) | ~ (all_96_2 = 0) |
% 15.80/2.97 | all_96_0 = all_25_3)
% 15.80/2.97 |
% 15.80/2.97 | ALPHA: (30) implies:
% 15.80/2.97 | (31) aElement0(xz) = all_96_2
% 15.80/2.97 |
% 15.80/2.97 | DELTA: instantiating (26) with fresh symbols all_174_0, all_174_1 gives:
% 15.80/2.97 | (32) aElementOf0(all_25_1, xJ) = all_174_0 & aElement0(xz) = all_174_1 & (
% 15.80/2.97 | ~ (all_174_1 = 0) | all_174_0 = 0)
% 15.80/2.97 |
% 15.80/2.97 | ALPHA: (32) implies:
% 15.80/2.97 | (33) aElement0(xz) = all_174_1
% 15.80/2.97 | (34) aElementOf0(all_25_1, xJ) = all_174_0
% 15.80/2.97 | (35) ~ (all_174_1 = 0) | all_174_0 = 0
% 15.80/2.97 |
% 15.80/2.97 | DELTA: instantiating (27) with fresh symbols all_198_0, all_198_1 gives:
% 15.80/2.97 | (36) aElementOf0(all_25_3, xI) = all_198_0 & aElement0(xz) = all_198_1 & (
% 15.80/2.97 | ~ (all_198_1 = 0) | all_198_0 = 0)
% 15.80/2.97 |
% 15.80/2.97 | ALPHA: (36) implies:
% 15.80/2.97 | (37) aElement0(xz) = all_198_1
% 15.80/2.97 | (38) aElementOf0(all_25_3, xI) = all_198_0
% 15.80/2.97 | (39) ~ (all_198_1 = 0) | all_198_0 = 0
% 15.80/2.97 |
% 15.80/2.98 | GROUND_INST: instantiating (10) with 0, all_96_2, xz, simplifying with (19),
% 15.80/2.98 | (31) gives:
% 15.80/2.98 | (40) all_96_2 = 0
% 15.80/2.98 |
% 15.80/2.98 | GROUND_INST: instantiating (10) with all_174_1, all_198_1, xz, simplifying
% 15.80/2.98 | with (33), (37) gives:
% 15.80/2.98 | (41) all_198_1 = all_174_1
% 15.80/2.98 |
% 15.80/2.98 | GROUND_INST: instantiating (10) with all_96_2, all_198_1, xz, simplifying with
% 15.80/2.98 | (31), (37) gives:
% 15.80/2.98 | (42) all_198_1 = all_96_2
% 15.80/2.98 |
% 15.80/2.98 | GROUND_INST: instantiating (10) with all_86_2, all_198_1, xz, simplifying with
% 15.80/2.98 | (29), (37) gives:
% 15.80/2.98 | (43) all_198_1 = all_86_2
% 15.80/2.98 |
% 15.80/2.98 | GROUND_INST: instantiating (11) with all_25_2, all_198_0, xI, all_25_3,
% 15.80/2.98 | simplifying with (15), (38) gives:
% 15.80/2.98 | (44) all_198_0 = all_25_2
% 15.80/2.98 |
% 15.80/2.98 | GROUND_INST: instantiating (11) with all_25_0, all_174_0, xJ, all_25_1,
% 15.80/2.98 | simplifying with (16), (34) gives:
% 15.80/2.98 | (45) all_174_0 = all_25_0
% 15.80/2.98 |
% 15.80/2.98 | COMBINE_EQS: (41), (43) imply:
% 15.80/2.98 | (46) all_174_1 = all_86_2
% 15.80/2.98 |
% 15.80/2.98 | COMBINE_EQS: (41), (42) imply:
% 15.80/2.98 | (47) all_174_1 = all_96_2
% 15.80/2.98 |
% 15.80/2.98 | COMBINE_EQS: (46), (47) imply:
% 15.80/2.98 | (48) all_96_2 = all_86_2
% 15.80/2.98 |
% 15.80/2.98 | SIMP: (48) implies:
% 15.80/2.98 | (49) all_96_2 = all_86_2
% 15.80/2.98 |
% 15.80/2.98 | COMBINE_EQS: (40), (49) imply:
% 15.80/2.98 | (50) all_86_2 = 0
% 15.80/2.98 |
% 15.80/2.98 | COMBINE_EQS: (46), (50) imply:
% 15.80/2.98 | (51) all_174_1 = 0
% 15.80/2.98 |
% 15.80/2.98 | COMBINE_EQS: (41), (51) imply:
% 15.80/2.98 | (52) all_198_1 = 0
% 15.80/2.98 |
% 15.80/2.98 | BETA: splitting (35) gives:
% 15.80/2.98 |
% 15.80/2.98 | Case 1:
% 15.80/2.98 | |
% 15.80/2.98 | | (53) ~ (all_174_1 = 0)
% 15.80/2.98 | |
% 15.80/2.98 | | REDUCE: (51), (53) imply:
% 15.80/2.98 | | (54) $false
% 15.80/2.98 | |
% 15.80/2.98 | | CLOSE: (54) is inconsistent.
% 15.80/2.98 | |
% 15.80/2.98 | Case 2:
% 15.80/2.98 | |
% 15.80/2.98 | | (55) all_174_0 = 0
% 15.80/2.98 | |
% 15.80/2.98 | | COMBINE_EQS: (45), (55) imply:
% 15.80/2.98 | | (56) all_25_0 = 0
% 15.80/2.98 | |
% 15.80/2.98 | | SIMP: (56) implies:
% 15.80/2.98 | | (57) all_25_0 = 0
% 15.80/2.98 | |
% 15.80/2.98 | | BETA: splitting (17) gives:
% 15.80/2.98 | |
% 15.80/2.98 | | Case 1:
% 15.80/2.98 | | |
% 15.80/2.98 | | | (58) ~ (all_25_0 = 0)
% 15.80/2.98 | | |
% 15.80/2.98 | | | REDUCE: (57), (58) imply:
% 15.80/2.98 | | | (59) $false
% 15.80/2.98 | | |
% 15.80/2.98 | | | CLOSE: (59) is inconsistent.
% 15.80/2.98 | | |
% 15.80/2.98 | | Case 2:
% 15.80/2.98 | | |
% 15.80/2.98 | | | (60) ~ (all_25_2 = 0)
% 15.80/2.98 | | |
% 15.80/2.98 | | | BETA: splitting (39) gives:
% 15.80/2.98 | | |
% 15.80/2.98 | | | Case 1:
% 15.80/2.98 | | | |
% 15.80/2.98 | | | | (61) ~ (all_198_1 = 0)
% 15.80/2.98 | | | |
% 15.80/2.98 | | | | REDUCE: (52), (61) imply:
% 15.80/2.98 | | | | (62) $false
% 15.80/2.98 | | | |
% 15.80/2.98 | | | | CLOSE: (62) is inconsistent.
% 15.80/2.98 | | | |
% 15.80/2.98 | | | Case 2:
% 15.80/2.98 | | | |
% 15.80/2.98 | | | | (63) all_198_0 = 0
% 15.80/2.98 | | | |
% 15.80/2.98 | | | | COMBINE_EQS: (44), (63) imply:
% 15.80/2.98 | | | | (64) all_25_2 = 0
% 15.80/2.98 | | | |
% 15.80/2.98 | | | | REDUCE: (60), (64) imply:
% 15.80/2.98 | | | | (65) $false
% 15.80/2.98 | | | |
% 15.80/2.98 | | | | CLOSE: (65) is inconsistent.
% 15.80/2.98 | | | |
% 15.80/2.98 | | | End of split
% 15.80/2.98 | | |
% 15.80/2.98 | | End of split
% 15.80/2.98 | |
% 15.80/2.98 | End of split
% 15.80/2.98 |
% 15.80/2.98 End of proof
% 15.80/2.98 % SZS output end Proof for theBenchmark
% 15.80/2.98
% 15.80/2.98 2372ms
%------------------------------------------------------------------------------