TSTP Solution File: RNG093+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG093+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:57:49 EDT 2023
% Result : Theorem 62.99s 9.11s
% Output : Proof 63.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : RNG093+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Aug 27 02:52:24 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.61 ________ _____
% 0.17/0.61 ___ __ \_________(_)________________________________
% 0.17/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.61
% 0.17/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.61 (2023-06-19)
% 0.17/0.61
% 0.17/0.61 (c) Philipp Rümmer, 2009-2023
% 0.17/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.61 Amanda Stjerna.
% 0.17/0.61 Free software under BSD-3-Clause.
% 0.17/0.61
% 0.17/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.61
% 0.17/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.17/0.63 Running up to 7 provers in parallel.
% 0.17/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.88/1.17 Prover 1: Preprocessing ...
% 2.88/1.17 Prover 4: Preprocessing ...
% 3.23/1.22 Prover 0: Preprocessing ...
% 3.23/1.22 Prover 6: Preprocessing ...
% 3.23/1.22 Prover 2: Preprocessing ...
% 3.23/1.22 Prover 3: Preprocessing ...
% 3.23/1.22 Prover 5: Preprocessing ...
% 9.00/2.04 Prover 3: Constructing countermodel ...
% 9.00/2.05 Prover 1: Constructing countermodel ...
% 9.00/2.05 Prover 6: Proving ...
% 9.00/2.06 Prover 5: Proving ...
% 9.82/2.11 Prover 2: Proving ...
% 9.96/2.16 Prover 4: Constructing countermodel ...
% 11.22/2.32 Prover 0: Proving ...
% 14.74/2.81 Prover 3: gave up
% 14.74/2.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.74/2.90 Prover 7: Preprocessing ...
% 15.85/2.95 Prover 1: gave up
% 15.85/2.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.85/3.02 Prover 8: Preprocessing ...
% 17.86/3.23 Prover 7: Constructing countermodel ...
% 17.86/3.24 Prover 8: Warning: ignoring some quantifiers
% 18.18/3.25 Prover 8: Constructing countermodel ...
% 22.66/3.88 Prover 8: gave up
% 22.66/3.90 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 23.52/4.00 Prover 9: Preprocessing ...
% 27.73/4.60 Prover 9: Constructing countermodel ...
% 59.84/8.71 Prover 2: stopped
% 59.84/8.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 60.65/8.81 Prover 10: Preprocessing ...
% 61.40/8.95 Prover 10: Constructing countermodel ...
% 62.93/9.10 Prover 10: Found proof (size 34)
% 62.93/9.10 Prover 10: proved (378ms)
% 62.93/9.10 Prover 0: stopped
% 62.93/9.10 Prover 5: stopped
% 62.93/9.10 Prover 6: stopped
% 62.99/9.10 Prover 9: stopped
% 62.99/9.10 Prover 4: stopped
% 62.99/9.11 Prover 7: stopped
% 62.99/9.11
% 62.99/9.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 62.99/9.11
% 62.99/9.11 % SZS output start Proof for theBenchmark
% 62.99/9.12 Assumptions after simplification:
% 62.99/9.12 ---------------------------------
% 62.99/9.12
% 62.99/9.12 (mAddComm)
% 62.99/9.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 62.99/9.16 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtpldt0(v1, v0)
% 62.99/9.16 = v2 & $i(v2)))
% 62.99/9.16
% 62.99/9.16 (mDefIdeal)
% 62.99/9.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v1)
% 62.99/9.16 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~
% 62.99/9.16 aElementOf0(v1, v0) | ~ aElement0(v2) | aElementOf0(v3, v0)) & ! [v0: $i]
% 62.99/9.16 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v1, v2) = v3) | ~
% 62.99/9.16 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ aElementOf0(v2, v0) |
% 62.99/9.16 ~ aElementOf0(v1, v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 62.99/9.16 aIdeal0(v0) | aSet0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aSet0(v0) |
% 62.99/9.16 aIdeal0(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ?
% 62.99/9.16 [v5: $i] : ($i(v4) & $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2,
% 62.99/9.16 v1) = v3 & $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) |
% 62.99/9.16 (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~
% 62.99/9.16 aElementOf0(v5, v0)))))
% 62.99/9.16
% 62.99/9.17 (mDefSInt)
% 62.99/9.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 62.99/9.17 (sdtasasdt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ aSet0(v3)
% 62.99/9.17 | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & ( ~ aElementOf0(v4,
% 62.99/9.17 v3) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v4, v0)) &
% 62.99/9.17 (aElementOf0(v4, v3) | (aElementOf0(v4, v1) & aElementOf0(v4, v0))))) & !
% 62.99/9.17 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasasdt0(v0, v1) =
% 62.99/9.17 v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3,
% 62.99/9.17 v2) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v1)) & ! [v0: $i] :
% 62.99/9.17 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~
% 62.99/9.17 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~
% 62.99/9.17 aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i]
% 62.99/9.17 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ $i(v3) | ~
% 62.99/9.17 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v1) | ~ aElementOf0(v3,
% 62.99/9.17 v0) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] :
% 62.99/9.17 ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ $i(v2) | ~
% 62.99/9.17 $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2))
% 62.99/9.17
% 62.99/9.17 (mEOfElem)
% 62.99/9.18 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) |
% 62.99/9.18 ~ aSet0(v0) | aElement0(v1))
% 62.99/9.18
% 62.99/9.18 (mMulComm)
% 62.99/9.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 62.99/9.18 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtasdt0(v1, v0)
% 62.99/9.18 = v2 & $i(v2)))
% 62.99/9.18
% 62.99/9.18 (m__)
% 62.99/9.18 $i(xJ) & $i(xI) & ? [v0: $i] : (sdtasasdt0(xI, xJ) = v0 & $i(v0) & ~
% 62.99/9.18 aIdeal0(v0))
% 62.99/9.18
% 62.99/9.18 (m__1150)
% 62.99/9.18 $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI)
% 62.99/9.18
% 62.99/9.18 Further assumptions not needed in the proof:
% 62.99/9.18 --------------------------------------------
% 62.99/9.18 mAMDistr, mAddAsso, mAddInvr, mAddZero, mCancel, mDefSSum, mElmSort, mIdeSum,
% 62.99/9.18 mMulAsso, mMulMnOne, mMulUnit, mMulZero, mSetEq, mSetSort, mSortsB, mSortsB_02,
% 62.99/9.18 mSortsC, mSortsC_01, mSortsU, mUnNeZr
% 62.99/9.18
% 62.99/9.18 Those formulas are unsatisfiable:
% 62.99/9.18 ---------------------------------
% 62.99/9.18
% 62.99/9.18 Begin of proof
% 62.99/9.18 |
% 62.99/9.18 | ALPHA: (mDefSInt) implies:
% 62.99/9.18 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasasdt0(v0, v1) = v2)
% 62.99/9.18 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) |
% 62.99/9.18 | aSet0(v2))
% 62.99/9.18 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 62.99/9.18 | (sdtasasdt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 62.99/9.18 | $i(v0) | ~ aElementOf0(v3, v1) | ~ aElementOf0(v3, v0) | ~
% 62.99/9.18 | aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2))
% 62.99/9.19 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 62.99/9.19 | (sdtasasdt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 62.99/9.19 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) |
% 62.99/9.19 | aElementOf0(v3, v0))
% 62.99/9.19 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 62.99/9.19 | (sdtasasdt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 62.99/9.19 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) |
% 62.99/9.19 | aElementOf0(v3, v1))
% 62.99/9.19 |
% 62.99/9.19 | ALPHA: (mDefIdeal) implies:
% 62.99/9.19 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ aSet0(v0) | aIdeal0(v0) | ? [v1: $i] :
% 62.99/9.19 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) &
% 62.99/9.19 | $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2, v1) = v3 &
% 62.99/9.19 | $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) |
% 62.99/9.19 | (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~
% 62.99/9.19 | aElementOf0(v5, v0)))))
% 62.99/9.19 | (6) ! [v0: $i] : ( ~ $i(v0) | ~ aIdeal0(v0) | aSet0(v0))
% 62.99/9.19 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 62.99/9.19 | (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 62.99/9.19 | aIdeal0(v0) | ~ aElementOf0(v2, v0) | ~ aElementOf0(v1, v0) |
% 62.99/9.19 | aElementOf0(v3, v0))
% 62.99/9.19 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 62.99/9.19 | (sdtasdt0(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 62.99/9.19 | aIdeal0(v0) | ~ aElementOf0(v1, v0) | ~ aElement0(v2) |
% 62.99/9.19 | aElementOf0(v3, v0))
% 62.99/9.19 |
% 62.99/9.19 | ALPHA: (m__1150) implies:
% 62.99/9.19 | (9) aIdeal0(xI)
% 62.99/9.19 | (10) aIdeal0(xJ)
% 62.99/9.19 |
% 62.99/9.19 | ALPHA: (m__) implies:
% 62.99/9.19 | (11) $i(xI)
% 62.99/9.19 | (12) $i(xJ)
% 62.99/9.19 | (13) ? [v0: $i] : (sdtasasdt0(xI, xJ) = v0 & $i(v0) & ~ aIdeal0(v0))
% 62.99/9.19 |
% 62.99/9.20 | DELTA: instantiating (13) with fresh symbol all_23_0 gives:
% 62.99/9.20 | (14) sdtasasdt0(xI, xJ) = all_23_0 & $i(all_23_0) & ~ aIdeal0(all_23_0)
% 62.99/9.20 |
% 62.99/9.20 | ALPHA: (14) implies:
% 62.99/9.20 | (15) ~ aIdeal0(all_23_0)
% 62.99/9.20 | (16) $i(all_23_0)
% 62.99/9.20 | (17) sdtasasdt0(xI, xJ) = all_23_0
% 62.99/9.20 |
% 62.99/9.20 | GROUND_INST: instantiating (6) with xI, simplifying with (9), (11) gives:
% 62.99/9.20 | (18) aSet0(xI)
% 62.99/9.20 |
% 62.99/9.20 | GROUND_INST: instantiating (6) with xJ, simplifying with (10), (12) gives:
% 62.99/9.20 | (19) aSet0(xJ)
% 62.99/9.20 |
% 62.99/9.20 | GROUND_INST: instantiating (1) with xI, xJ, all_23_0, simplifying with (11),
% 62.99/9.20 | (12), (16), (17), (18), (19) gives:
% 62.99/9.20 | (20) aSet0(all_23_0)
% 62.99/9.20 |
% 62.99/9.20 | GROUND_INST: instantiating (5) with all_23_0, simplifying with (15), (16),
% 62.99/9.20 | (20) gives:
% 62.99/9.20 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 62.99/9.20 | ($i(v3) & $i(v1) & $i(v0) & aElementOf0(v0, all_23_0) & ((sdtasdt0(v1,
% 62.99/9.20 | v0) = v2 & $i(v2) & aElement0(v1) & ~ aElementOf0(v2,
% 62.99/9.20 | all_23_0)) | (sdtpldt0(v0, v3) = v4 & $i(v4) & aElementOf0(v3,
% 62.99/9.20 | all_23_0) & ~ aElementOf0(v4, all_23_0))))
% 62.99/9.20 |
% 62.99/9.20 | DELTA: instantiating (21) with fresh symbols all_45_0, all_45_1, all_45_2,
% 62.99/9.20 | all_45_3, all_45_4 gives:
% 62.99/9.20 | (22) $i(all_45_1) & $i(all_45_3) & $i(all_45_4) & aElementOf0(all_45_4,
% 62.99/9.20 | all_23_0) & ((sdtasdt0(all_45_3, all_45_4) = all_45_2 & $i(all_45_2)
% 62.99/9.20 | & aElement0(all_45_3) & ~ aElementOf0(all_45_2, all_23_0)) |
% 62.99/9.20 | (sdtpldt0(all_45_4, all_45_1) = all_45_0 & $i(all_45_0) &
% 62.99/9.20 | aElementOf0(all_45_1, all_23_0) & ~ aElementOf0(all_45_0,
% 62.99/9.20 | all_23_0)))
% 62.99/9.20 |
% 62.99/9.20 | ALPHA: (22) implies:
% 63.46/9.20 | (23) aElementOf0(all_45_4, all_23_0)
% 63.46/9.20 | (24) $i(all_45_4)
% 63.46/9.20 | (25) $i(all_45_3)
% 63.46/9.20 | (26) $i(all_45_1)
% 63.46/9.20 | (27) (sdtasdt0(all_45_3, all_45_4) = all_45_2 & $i(all_45_2) &
% 63.46/9.20 | aElement0(all_45_3) & ~ aElementOf0(all_45_2, all_23_0)) |
% 63.46/9.20 | (sdtpldt0(all_45_4, all_45_1) = all_45_0 & $i(all_45_0) &
% 63.46/9.20 | aElementOf0(all_45_1, all_23_0) & ~ aElementOf0(all_45_0,
% 63.46/9.20 | all_23_0))
% 63.46/9.20 |
% 63.46/9.21 | GROUND_INST: instantiating (4) with xI, xJ, all_23_0, all_45_4, simplifying
% 63.46/9.21 | with (11), (12), (16), (17), (18), (19), (23), (24) gives:
% 63.46/9.21 | (28) aElementOf0(all_45_4, xJ)
% 63.46/9.21 |
% 63.46/9.21 | GROUND_INST: instantiating (3) with xI, xJ, all_23_0, all_45_4, simplifying
% 63.46/9.21 | with (11), (12), (16), (17), (18), (19), (23), (24) gives:
% 63.46/9.21 | (29) aElementOf0(all_45_4, xI)
% 63.46/9.21 |
% 63.46/9.21 | GROUND_INST: instantiating (mEOfElem) with all_23_0, all_45_4, simplifying
% 63.46/9.21 | with (16), (20), (23), (24) gives:
% 63.46/9.21 | (30) aElement0(all_45_4)
% 63.46/9.21 |
% 63.46/9.21 | BETA: splitting (27) gives:
% 63.46/9.21 |
% 63.46/9.21 | Case 1:
% 63.46/9.21 | |
% 63.46/9.21 | | (31) sdtasdt0(all_45_3, all_45_4) = all_45_2 & $i(all_45_2) &
% 63.46/9.21 | | aElement0(all_45_3) & ~ aElementOf0(all_45_2, all_23_0)
% 63.46/9.21 | |
% 63.46/9.21 | | ALPHA: (31) implies:
% 63.46/9.21 | | (32) ~ aElementOf0(all_45_2, all_23_0)
% 63.46/9.21 | | (33) aElement0(all_45_3)
% 63.46/9.21 | | (34) sdtasdt0(all_45_3, all_45_4) = all_45_2
% 63.46/9.21 | |
% 63.46/9.21 | | GROUND_INST: instantiating (8) with xJ, all_45_4, all_45_3, all_45_2,
% 63.46/9.21 | | simplifying with (10), (12), (24), (25), (28), (33), (34)
% 63.46/9.21 | | gives:
% 63.46/9.21 | | (35) aElementOf0(all_45_2, xJ)
% 63.46/9.21 | |
% 63.46/9.21 | | GROUND_INST: instantiating (8) with xI, all_45_4, all_45_3, all_45_2,
% 63.46/9.21 | | simplifying with (9), (11), (24), (25), (29), (33), (34) gives:
% 63.46/9.21 | | (36) aElementOf0(all_45_2, xI)
% 63.46/9.21 | |
% 63.46/9.21 | | GROUND_INST: instantiating (mMulComm) with all_45_3, all_45_4, all_45_2,
% 63.46/9.21 | | simplifying with (24), (25), (30), (33), (34) gives:
% 63.46/9.21 | | (37) sdtasdt0(all_45_4, all_45_3) = all_45_2 & $i(all_45_2)
% 63.46/9.21 | |
% 63.46/9.22 | | ALPHA: (37) implies:
% 63.46/9.22 | | (38) $i(all_45_2)
% 63.46/9.22 | |
% 63.46/9.22 | | GROUND_INST: instantiating (2) with xI, xJ, all_23_0, all_45_2, simplifying
% 63.46/9.22 | | with (11), (12), (16), (17), (18), (19), (32), (35), (36), (38)
% 63.46/9.22 | | gives:
% 63.46/9.22 | | (39) $false
% 63.46/9.22 | |
% 63.46/9.22 | | CLOSE: (39) is inconsistent.
% 63.46/9.22 | |
% 63.46/9.22 | Case 2:
% 63.46/9.22 | |
% 63.46/9.22 | | (40) sdtpldt0(all_45_4, all_45_1) = all_45_0 & $i(all_45_0) &
% 63.46/9.22 | | aElementOf0(all_45_1, all_23_0) & ~ aElementOf0(all_45_0, all_23_0)
% 63.46/9.22 | |
% 63.46/9.22 | | ALPHA: (40) implies:
% 63.46/9.22 | | (41) ~ aElementOf0(all_45_0, all_23_0)
% 63.46/9.22 | | (42) aElementOf0(all_45_1, all_23_0)
% 63.46/9.22 | | (43) sdtpldt0(all_45_4, all_45_1) = all_45_0
% 63.46/9.22 | |
% 63.46/9.22 | | GROUND_INST: instantiating (4) with xI, xJ, all_23_0, all_45_1, simplifying
% 63.46/9.22 | | with (11), (12), (16), (17), (18), (19), (26), (42) gives:
% 63.46/9.22 | | (44) aElementOf0(all_45_1, xJ)
% 63.46/9.22 | |
% 63.46/9.22 | | GROUND_INST: instantiating (3) with xI, xJ, all_23_0, all_45_1, simplifying
% 63.46/9.22 | | with (11), (12), (16), (17), (18), (19), (26), (42) gives:
% 63.46/9.22 | | (45) aElementOf0(all_45_1, xI)
% 63.46/9.22 | |
% 63.46/9.22 | | GROUND_INST: instantiating (mEOfElem) with all_23_0, all_45_1, simplifying
% 63.46/9.22 | | with (16), (20), (26), (42) gives:
% 63.46/9.22 | | (46) aElement0(all_45_1)
% 63.46/9.22 | |
% 63.46/9.22 | | GROUND_INST: instantiating (mAddComm) with all_45_4, all_45_1, all_45_0,
% 63.46/9.22 | | simplifying with (24), (26), (30), (43), (46) gives:
% 63.46/9.23 | | (47) sdtpldt0(all_45_1, all_45_4) = all_45_0 & $i(all_45_0)
% 63.46/9.23 | |
% 63.46/9.23 | | ALPHA: (47) implies:
% 63.46/9.23 | | (48) $i(all_45_0)
% 63.46/9.23 | |
% 63.46/9.23 | | GROUND_INST: instantiating (7) with xI, all_45_4, all_45_1, all_45_0,
% 63.46/9.23 | | simplifying with (9), (11), (24), (26), (29), (43), (45) gives:
% 63.46/9.23 | | (49) aElementOf0(all_45_0, xI)
% 63.46/9.23 | |
% 63.46/9.23 | | GROUND_INST: instantiating (7) with xJ, all_45_4, all_45_1, all_45_0,
% 63.46/9.23 | | simplifying with (10), (12), (24), (26), (28), (43), (44)
% 63.46/9.23 | | gives:
% 63.46/9.23 | | (50) aElementOf0(all_45_0, xJ)
% 63.46/9.23 | |
% 63.46/9.23 | | GROUND_INST: instantiating (2) with xI, xJ, all_23_0, all_45_0, simplifying
% 63.46/9.23 | | with (11), (12), (16), (17), (18), (19), (41), (48), (49), (50)
% 63.46/9.23 | | gives:
% 63.46/9.23 | | (51) $false
% 63.46/9.23 | |
% 63.46/9.23 | | CLOSE: (51) is inconsistent.
% 63.46/9.23 | |
% 63.46/9.23 | End of split
% 63.46/9.23 |
% 63.46/9.23 End of proof
% 63.46/9.23 % SZS output end Proof for theBenchmark
% 63.46/9.23
% 63.46/9.23 8617ms
%------------------------------------------------------------------------------