TSTP Solution File: RNG099+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG099+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 : n029.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 13:57:51 EDT 2023
% Result : Theorem 12.43s 2.48s
% Output : Proof 18.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG099+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.34 % Computer : n029.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sun Aug 27 02:05:10 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.63/1.10 Prover 4: Preprocessing ...
% 2.63/1.11 Prover 1: Preprocessing ...
% 3.12/1.14 Prover 2: Preprocessing ...
% 3.12/1.14 Prover 5: Preprocessing ...
% 3.12/1.14 Prover 3: Preprocessing ...
% 3.12/1.15 Prover 6: Preprocessing ...
% 3.12/1.15 Prover 0: Preprocessing ...
% 7.83/1.80 Prover 1: Constructing countermodel ...
% 8.35/1.84 Prover 3: Constructing countermodel ...
% 8.35/1.86 Prover 6: Proving ...
% 9.00/1.93 Prover 5: Proving ...
% 9.20/2.00 Prover 2: Proving ...
% 9.20/2.00 Prover 4: Constructing countermodel ...
% 9.87/2.13 Prover 0: Proving ...
% 12.43/2.48 Prover 3: proved (1851ms)
% 12.43/2.48
% 12.43/2.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.43/2.48
% 12.94/2.49 Prover 5: stopped
% 12.94/2.49 Prover 6: stopped
% 12.94/2.51 Prover 2: stopped
% 12.94/2.51 Prover 0: stopped
% 12.94/2.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.94/2.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.94/2.51 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.94/2.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.94/2.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.94/2.55 Prover 7: Preprocessing ...
% 13.55/2.57 Prover 8: Preprocessing ...
% 13.86/2.61 Prover 10: Preprocessing ...
% 13.86/2.61 Prover 13: Preprocessing ...
% 13.86/2.63 Prover 11: Preprocessing ...
% 13.99/2.70 Prover 7: Constructing countermodel ...
% 13.99/2.71 Prover 8: Warning: ignoring some quantifiers
% 14.65/2.73 Prover 8: Constructing countermodel ...
% 15.13/2.81 Prover 13: Warning: ignoring some quantifiers
% 15.13/2.82 Prover 10: Constructing countermodel ...
% 15.13/2.83 Prover 13: Constructing countermodel ...
% 15.87/2.98 Prover 11: Constructing countermodel ...
% 17.58/3.18 Prover 10: Found proof (size 48)
% 17.58/3.18 Prover 10: proved (675ms)
% 17.58/3.18 Prover 13: stopped
% 17.58/3.18 Prover 8: stopped
% 17.58/3.18 Prover 1: stopped
% 17.58/3.19 Prover 4: stopped
% 17.58/3.19 Prover 7: stopped
% 17.58/3.19 Prover 11: stopped
% 17.58/3.19
% 17.58/3.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.58/3.19
% 17.58/3.20 % SZS output start Proof for theBenchmark
% 17.58/3.20 Assumptions after simplification:
% 17.58/3.20 ---------------------------------
% 17.58/3.20
% 17.58/3.20 (mAddComm)
% 18.22/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 18.22/3.23 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtpldt0(v1, v0)
% 18.22/3.23 = v2 & $i(v2)))
% 18.22/3.23
% 18.22/3.23 (mDefIdeal)
% 18.22/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v1)
% 18.22/3.23 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~
% 18.22/3.23 aElementOf0(v1, v0) | ~ aElement0(v2) | aElementOf0(v3, v0)) & ! [v0: $i]
% 18.22/3.23 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v1, v2) = v3) | ~
% 18.22/3.23 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ aElementOf0(v2, v0) |
% 18.22/3.23 ~ aElementOf0(v1, v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 18.22/3.23 aIdeal0(v0) | aSet0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aSet0(v0) |
% 18.22/3.23 aIdeal0(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ?
% 18.22/3.23 [v5: $i] : ($i(v4) & $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2,
% 18.22/3.23 v1) = v3 & $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) |
% 18.22/3.23 (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~
% 18.22/3.23 aElementOf0(v5, v0)))))
% 18.22/3.23
% 18.22/3.23 (mDefMod)
% 18.22/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 18.22/3.24 (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 18.22/3.24 $i(v0) | ~ sdteqdtlpzmzozddtrp0(v0, v1, v2) | ~ aIdeal0(v2) | ~
% 18.22/3.24 aElement0(v1) | ~ aElement0(v0) | aElementOf0(v4, v2)) & ! [v0: $i] : !
% 18.22/3.24 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v0, v3) =
% 18.22/3.24 v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 18.22/3.24 aIdeal0(v2) | ~ aElementOf0(v4, v2) | ~ aElement0(v1) | ~ aElement0(v0) |
% 18.22/3.24 sdteqdtlpzmzozddtrp0(v0, v1, v2))
% 18.22/3.24
% 18.22/3.24 (mDefSSum)
% 18.22/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 18.22/3.24 $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | ~ $i(v5) |
% 18.22/3.24 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 18.22/3.24 aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ aSet0(v0) |
% 18.22/3.24 aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 18.22/3.24 : (v3 = v2 | ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 18.22/3.24 ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4: $i] : ? [v5: $i] : ?
% 18.22/3.24 [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v5) & $i(v4) & ( ~ aElementOf0(v4, v3)
% 18.22/3.24 | ! [v8: $i] : ! [v9: $i] : ( ~ (sdtpldt0(v8, v9) = v4) | ~ $i(v9) |
% 18.22/3.24 ~ $i(v8) | ~ aElementOf0(v9, v1) | ~ aElementOf0(v8, v0))) &
% 18.22/3.24 (aElementOf0(v4, v3) | (v7 = v4 & sdtpldt0(v5, v6) = v4 & aElementOf0(v6,
% 18.22/3.24 v1) & aElementOf0(v5, v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 18.22/3.24 $i] : ! [v3: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 18.22/3.24 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) |
% 18.22/3.24 ? [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) &
% 18.22/3.24 aElementOf0(v5, v1) & aElementOf0(v4, v0))) & ! [v0: $i] : ! [v1: $i] :
% 18.22/3.24 ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 18.22/3.24 ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2))
% 18.22/3.24
% 18.22/3.25 (mEOfElem)
% 18.22/3.25 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) |
% 18.22/3.25 ~ aSet0(v0) | aElement0(v1))
% 18.22/3.25
% 18.22/3.25 (mIdeSum)
% 18.22/3.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~
% 18.22/3.25 $i(v1) | ~ $i(v0) | ~ aIdeal0(v1) | ~ aIdeal0(v0) | aIdeal0(v2))
% 18.22/3.25
% 18.22/3.25 (mMulComm)
% 18.22/3.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 18.22/3.25 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtasdt0(v1, v0)
% 18.22/3.25 = v2 & $i(v2)))
% 18.22/3.25
% 18.22/3.25 (m__)
% 18.22/3.25 $i(xy) & $i(xx) & $i(xJ) & $i(xI) & ! [v0: $i] : ( ~ $i(v0) | ~
% 18.22/3.25 sdteqdtlpzmzozddtrp0(v0, xy, xJ) | ~ sdteqdtlpzmzozddtrp0(v0, xx, xI) | ~
% 18.22/3.25 aElement0(v0))
% 18.22/3.25
% 18.22/3.25 (m__1205)
% 18.22/3.25 $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI)
% 18.22/3.25
% 18.22/3.25 (m__1205_03)
% 18.22/3.25 $i(xJ) & $i(xI) & ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & $i(v0) & ! [v1: $i]
% 18.22/3.25 : ( ~ $i(v1) | ~ aElement0(v1) | aElementOf0(v1, v0)))
% 18.22/3.25
% 18.22/3.25 (m__1217)
% 18.22/3.25 $i(xy) & $i(xx) & aElement0(xy) & aElement0(xx)
% 18.22/3.25
% 18.22/3.25 (m__1294)
% 18.22/3.25 sdtpldt0(xa, xb) = sz10 & $i(xb) & $i(xa) & $i(xJ) & $i(xI) & $i(sz10) &
% 18.22/3.25 aElementOf0(xb, xJ) & aElementOf0(xa, xI)
% 18.22/3.25
% 18.22/3.25 (m__1319)
% 18.22/3.25 $i(xw) & $i(xb) & $i(xa) & $i(xy) & $i(xx) & ? [v0: $i] : ? [v1: $i] :
% 18.22/3.25 (sdtasdt0(xy, xa) = v0 & sdtasdt0(xx, xb) = v1 & sdtpldt0(v0, v1) = xw &
% 18.22/3.25 $i(v1) & $i(v0))
% 18.22/3.25
% 18.22/3.25 (m__1332)
% 18.22/3.25 $i(xw) & $i(xx) & $i(xI) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xw, v0) = v1
% 18.22/3.25 & smndt0(xx) = v0 & $i(v1) & $i(v0) & aElementOf0(v1, xI))
% 18.22/3.25
% 18.22/3.25 (m__1409)
% 18.22/3.25 $i(xw) & $i(xy) & $i(xJ) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xw, v0) = v1
% 18.22/3.25 & smndt0(xy) = v0 & $i(v1) & $i(v0) & aElementOf0(v1, xJ))
% 18.22/3.25
% 18.22/3.25 Further assumptions not needed in the proof:
% 18.22/3.25 --------------------------------------------
% 18.22/3.25 mAMDistr, mAddAsso, mAddInvr, mAddZero, mCancel, mDefSInt, mElmSort, mIdeInt,
% 18.22/3.25 mMulAsso, mMulMnOne, mMulUnit, mMulZero, mSetEq, mSetSort, mSortsB, mSortsB_02,
% 18.22/3.25 mSortsC, mSortsC_01, mSortsU, mUnNeZr
% 18.22/3.25
% 18.22/3.25 Those formulas are unsatisfiable:
% 18.22/3.25 ---------------------------------
% 18.22/3.25
% 18.22/3.25 Begin of proof
% 18.22/3.25 |
% 18.22/3.25 | ALPHA: (mDefSSum) implies:
% 18.22/3.26 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 18.22/3.26 | (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 18.22/3.26 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | ?
% 18.22/3.26 | [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) &
% 18.22/3.26 | aElementOf0(v5, v1) & aElementOf0(v4, v0)))
% 18.22/3.26 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 18.22/3.26 | ! [v5: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) |
% 18.22/3.26 | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 18.22/3.26 | | ~ aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~
% 18.22/3.26 | aSet0(v0) | aElementOf0(v3, v2))
% 18.22/3.26 |
% 18.22/3.26 | ALPHA: (mDefIdeal) implies:
% 18.22/3.26 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ aIdeal0(v0) | aSet0(v0))
% 18.22/3.26 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 18.22/3.26 | (sdtasdt0(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 18.22/3.26 | aIdeal0(v0) | ~ aElementOf0(v1, v0) | ~ aElement0(v2) |
% 18.22/3.26 | aElementOf0(v3, v0))
% 18.22/3.26 |
% 18.22/3.26 | ALPHA: (mDefMod) implies:
% 18.22/3.26 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 18.22/3.26 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) | ~
% 18.22/3.26 | $i(v1) | ~ $i(v0) | ~ aIdeal0(v2) | ~ aElementOf0(v4, v2) | ~
% 18.22/3.26 | aElement0(v1) | ~ aElement0(v0) | sdteqdtlpzmzozddtrp0(v0, v1, v2))
% 18.22/3.26 |
% 18.22/3.26 | ALPHA: (m__1205) implies:
% 18.22/3.26 | (6) aIdeal0(xI)
% 18.22/3.26 | (7) aIdeal0(xJ)
% 18.22/3.26 |
% 18.22/3.26 | ALPHA: (m__1205_03) implies:
% 18.22/3.26 | (8) ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 18.22/3.26 | $i(v1) | ~ aElement0(v1) | aElementOf0(v1, v0)))
% 18.22/3.26 |
% 18.22/3.26 | ALPHA: (m__1217) implies:
% 18.22/3.26 | (9) aElement0(xx)
% 18.22/3.26 | (10) aElement0(xy)
% 18.22/3.26 |
% 18.22/3.26 | ALPHA: (m__1294) implies:
% 18.22/3.26 | (11) aElementOf0(xa, xI)
% 18.22/3.26 | (12) aElementOf0(xb, xJ)
% 18.22/3.26 |
% 18.22/3.26 | ALPHA: (m__1319) implies:
% 18.22/3.26 | (13) $i(xa)
% 18.22/3.26 | (14) $i(xb)
% 18.22/3.26 | (15) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xy, xa) = v0 & sdtasdt0(xx, xb)
% 18.22/3.26 | = v1 & sdtpldt0(v0, v1) = xw & $i(v1) & $i(v0))
% 18.22/3.26 |
% 18.22/3.26 | ALPHA: (m__1332) implies:
% 18.22/3.26 | (16) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xw, v0) = v1 & smndt0(xx) = v0 &
% 18.22/3.26 | $i(v1) & $i(v0) & aElementOf0(v1, xI))
% 18.22/3.26 |
% 18.22/3.26 | ALPHA: (m__1409) implies:
% 18.22/3.26 | (17) $i(xw)
% 18.22/3.26 | (18) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xw, v0) = v1 & smndt0(xy) = v0 &
% 18.22/3.26 | $i(v1) & $i(v0) & aElementOf0(v1, xJ))
% 18.22/3.26 |
% 18.22/3.26 | ALPHA: (m__) implies:
% 18.22/3.26 | (19) $i(xI)
% 18.22/3.26 | (20) $i(xJ)
% 18.22/3.26 | (21) $i(xx)
% 18.22/3.26 | (22) $i(xy)
% 18.22/3.26 | (23) ! [v0: $i] : ( ~ $i(v0) | ~ sdteqdtlpzmzozddtrp0(v0, xy, xJ) | ~
% 18.22/3.26 | sdteqdtlpzmzozddtrp0(v0, xx, xI) | ~ aElement0(v0))
% 18.22/3.26 |
% 18.22/3.27 | DELTA: instantiating (16) with fresh symbols all_26_0, all_26_1 gives:
% 18.22/3.27 | (24) sdtpldt0(xw, all_26_1) = all_26_0 & smndt0(xx) = all_26_1 &
% 18.22/3.27 | $i(all_26_0) & $i(all_26_1) & aElementOf0(all_26_0, xI)
% 18.22/3.27 |
% 18.22/3.27 | ALPHA: (24) implies:
% 18.22/3.27 | (25) aElementOf0(all_26_0, xI)
% 18.22/3.27 | (26) smndt0(xx) = all_26_1
% 18.22/3.27 | (27) sdtpldt0(xw, all_26_1) = all_26_0
% 18.22/3.27 |
% 18.22/3.27 | DELTA: instantiating (18) with fresh symbols all_28_0, all_28_1 gives:
% 18.22/3.27 | (28) sdtpldt0(xw, all_28_1) = all_28_0 & smndt0(xy) = all_28_1 &
% 18.22/3.27 | $i(all_28_0) & $i(all_28_1) & aElementOf0(all_28_0, xJ)
% 18.22/3.27 |
% 18.22/3.27 | ALPHA: (28) implies:
% 18.22/3.27 | (29) aElementOf0(all_28_0, xJ)
% 18.22/3.27 | (30) smndt0(xy) = all_28_1
% 18.22/3.27 | (31) sdtpldt0(xw, all_28_1) = all_28_0
% 18.22/3.27 |
% 18.22/3.27 | DELTA: instantiating (8) with fresh symbol all_30_0 gives:
% 18.22/3.27 | (32) sdtpldt1(xI, xJ) = all_30_0 & $i(all_30_0) & ! [v0: $i] : ( ~ $i(v0)
% 18.22/3.27 | | ~ aElement0(v0) | aElementOf0(v0, all_30_0))
% 18.22/3.27 |
% 18.22/3.27 | ALPHA: (32) implies:
% 18.22/3.27 | (33) $i(all_30_0)
% 18.22/3.27 | (34) sdtpldt1(xI, xJ) = all_30_0
% 18.22/3.27 |
% 18.22/3.27 | DELTA: instantiating (15) with fresh symbols all_33_0, all_33_1 gives:
% 18.22/3.27 | (35) sdtasdt0(xy, xa) = all_33_1 & sdtasdt0(xx, xb) = all_33_0 &
% 18.22/3.27 | sdtpldt0(all_33_1, all_33_0) = xw & $i(all_33_0) & $i(all_33_1)
% 18.22/3.27 |
% 18.22/3.27 | ALPHA: (35) implies:
% 18.22/3.27 | (36) $i(all_33_1)
% 18.22/3.27 | (37) $i(all_33_0)
% 18.22/3.27 | (38) sdtpldt0(all_33_1, all_33_0) = xw
% 18.22/3.27 | (39) sdtasdt0(xx, xb) = all_33_0
% 18.22/3.27 | (40) sdtasdt0(xy, xa) = all_33_1
% 18.22/3.27 |
% 18.22/3.27 | GROUND_INST: instantiating (3) with xI, simplifying with (6), (19) gives:
% 18.22/3.27 | (41) aSet0(xI)
% 18.22/3.27 |
% 18.22/3.27 | GROUND_INST: instantiating (3) with xJ, simplifying with (7), (20) gives:
% 18.22/3.27 | (42) aSet0(xJ)
% 18.22/3.27 |
% 18.22/3.27 | GROUND_INST: instantiating (4) with xJ, xb, xx, all_33_0, simplifying with
% 18.22/3.27 | (7), (9), (12), (14), (20), (21), (39) gives:
% 18.22/3.27 | (43) aElementOf0(all_33_0, xJ)
% 18.22/3.27 |
% 18.22/3.27 | GROUND_INST: instantiating (4) with xI, xa, xy, all_33_1, simplifying with
% 18.22/3.27 | (6), (10), (11), (13), (19), (22), (40) gives:
% 18.22/3.27 | (44) aElementOf0(all_33_1, xI)
% 18.22/3.27 |
% 18.22/3.27 | GROUND_INST: instantiating (mIdeSum) with xI, xJ, all_30_0, simplifying with
% 18.22/3.27 | (6), (7), (19), (20), (34) gives:
% 18.22/3.27 | (45) aIdeal0(all_30_0)
% 18.22/3.27 |
% 18.22/3.27 | GROUND_INST: instantiating (mEOfElem) with xI, xa, simplifying with (11),
% 18.22/3.27 | (13), (19), (41) gives:
% 18.22/3.27 | (46) aElement0(xa)
% 18.22/3.27 |
% 18.22/3.27 | GROUND_INST: instantiating (mEOfElem) with xJ, xb, simplifying with (12),
% 18.22/3.27 | (14), (20), (42) gives:
% 18.22/3.27 | (47) aElement0(xb)
% 18.22/3.27 |
% 18.22/3.27 | GROUND_INST: instantiating (mEOfElem) with xI, all_33_1, simplifying with
% 18.22/3.27 | (19), (36), (41), (44) gives:
% 18.22/3.27 | (48) aElement0(all_33_1)
% 18.22/3.27 |
% 18.22/3.28 | GROUND_INST: instantiating (2) with xI, xJ, all_30_0, xw, all_33_1, all_33_0,
% 18.22/3.28 | simplifying with (17), (19), (20), (33), (34), (36), (37), (38),
% 18.22/3.28 | (41), (42), (43), (44) gives:
% 18.22/3.28 | (49) aElementOf0(xw, all_30_0)
% 18.22/3.28 |
% 18.22/3.28 | GROUND_INST: instantiating (mEOfElem) with xJ, all_33_0, simplifying with
% 18.22/3.28 | (20), (37), (42), (43) gives:
% 18.22/3.28 | (50) aElement0(all_33_0)
% 18.22/3.28 |
% 18.22/3.28 | GROUND_INST: instantiating (3) with all_30_0, simplifying with (33), (45)
% 18.22/3.28 | gives:
% 18.22/3.28 | (51) aSet0(all_30_0)
% 18.22/3.28 |
% 18.22/3.28 | GROUND_INST: instantiating (mMulComm) with xy, xa, all_33_1, simplifying with
% 18.22/3.28 | (10), (13), (22), (40), (46) gives:
% 18.22/3.28 | (52) sdtasdt0(xa, xy) = all_33_1 & $i(all_33_1)
% 18.22/3.28 |
% 18.22/3.28 | GROUND_INST: instantiating (mMulComm) with xx, xb, all_33_0, simplifying with
% 18.22/3.28 | (9), (14), (21), (39), (47) gives:
% 18.22/3.28 | (53) sdtasdt0(xb, xx) = all_33_0 & $i(all_33_0)
% 18.22/3.28 |
% 18.22/3.28 | GROUND_INST: instantiating (mAddComm) with all_33_1, all_33_0, xw, simplifying
% 18.22/3.28 | with (36), (37), (38), (48), (50) gives:
% 18.22/3.28 | (54) sdtpldt0(all_33_0, all_33_1) = xw & $i(xw)
% 18.22/3.28 |
% 18.22/3.28 | GROUND_INST: instantiating (1) with xI, xJ, all_30_0, xw, simplifying with
% 18.22/3.28 | (17), (19), (20), (33), (34), (41), (42), (49) gives:
% 18.22/3.28 | (55) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, v1) = xw & $i(v1) & $i(v0) &
% 18.22/3.28 | aElementOf0(v1, xJ) & aElementOf0(v0, xI))
% 18.22/3.28 |
% 18.22/3.28 | GROUND_INST: instantiating (mEOfElem) with all_30_0, xw, simplifying with
% 18.22/3.28 | (17), (33), (49), (51) gives:
% 18.22/3.28 | (56) aElement0(xw)
% 18.22/3.28 |
% 18.22/3.28 | DELTA: instantiating (55) with fresh symbols all_72_0, all_72_1 gives:
% 18.22/3.28 | (57) sdtpldt0(all_72_1, all_72_0) = xw & $i(all_72_0) & $i(all_72_1) &
% 18.22/3.28 | aElementOf0(all_72_0, xJ) & aElementOf0(all_72_1, xI)
% 18.22/3.28 |
% 18.22/3.28 | ALPHA: (57) implies:
% 18.22/3.28 | (58) aElementOf0(all_72_1, xI)
% 18.22/3.28 | (59) aElementOf0(all_72_0, xJ)
% 18.22/3.28 | (60) $i(all_72_1)
% 18.22/3.28 | (61) $i(all_72_0)
% 18.22/3.28 | (62) sdtpldt0(all_72_1, all_72_0) = xw
% 18.22/3.28 |
% 18.22/3.28 | GROUND_INST: instantiating (5) with xw, xy, xJ, all_28_1, all_28_0,
% 18.22/3.28 | simplifying with (7), (10), (17), (20), (22), (29), (30), (31),
% 18.22/3.28 | (56) gives:
% 18.22/3.28 | (63) sdteqdtlpzmzozddtrp0(xw, xy, xJ)
% 18.22/3.28 |
% 18.62/3.28 | GROUND_INST: instantiating (5) with xw, xx, xI, all_26_1, all_26_0,
% 18.62/3.28 | simplifying with (6), (9), (17), (19), (21), (25), (26), (27),
% 18.62/3.28 | (56) gives:
% 18.62/3.28 | (64) sdteqdtlpzmzozddtrp0(xw, xx, xI)
% 18.62/3.28 |
% 18.62/3.29 | GROUND_INST: instantiating (mEOfElem) with xI, all_72_1, simplifying with
% 18.62/3.29 | (19), (41), (58), (60) gives:
% 18.62/3.29 | (65) aElement0(all_72_1)
% 18.62/3.29 |
% 18.62/3.29 | GROUND_INST: instantiating (mEOfElem) with xJ, all_72_0, simplifying with
% 18.62/3.29 | (20), (42), (59), (61) gives:
% 18.62/3.29 | (66) aElement0(all_72_0)
% 18.62/3.29 |
% 18.62/3.29 | GROUND_INST: instantiating (mAddComm) with all_72_1, all_72_0, xw, simplifying
% 18.62/3.29 | with (60), (61), (62), (65), (66) gives:
% 18.62/3.29 | (67) sdtpldt0(all_72_0, all_72_1) = xw & $i(xw)
% 18.62/3.29 |
% 18.62/3.29 | GROUND_INST: instantiating (23) with xw, simplifying with (17), (56), (63),
% 18.62/3.29 | (64) gives:
% 18.62/3.29 | (68) $false
% 18.62/3.29 |
% 18.62/3.29 | CLOSE: (68) is inconsistent.
% 18.62/3.29 |
% 18.62/3.29 End of proof
% 18.62/3.29 % SZS output end Proof for theBenchmark
% 18.62/3.29
% 18.62/3.29 2688ms
%------------------------------------------------------------------------------