TSTP Solution File: RNG088+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG088+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 : n016.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 9.34s 2.05s
% Output : Proof 12.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG088+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 03:39:27 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.74/1.09 Prover 1: Preprocessing ...
% 2.74/1.10 Prover 4: Preprocessing ...
% 2.74/1.13 Prover 5: Preprocessing ...
% 2.74/1.13 Prover 6: Preprocessing ...
% 2.74/1.13 Prover 2: Preprocessing ...
% 2.74/1.13 Prover 3: Preprocessing ...
% 2.74/1.13 Prover 0: Preprocessing ...
% 6.61/1.70 Prover 1: Constructing countermodel ...
% 7.16/1.73 Prover 3: Constructing countermodel ...
% 7.16/1.73 Prover 6: Proving ...
% 7.68/1.79 Prover 5: Proving ...
% 7.68/1.84 Prover 4: Constructing countermodel ...
% 8.73/1.95 Prover 2: Proving ...
% 8.73/2.00 Prover 0: Proving ...
% 9.34/2.05 Prover 3: proved (1412ms)
% 9.34/2.05
% 9.34/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.34/2.05
% 9.34/2.05 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.34/2.05 Prover 5: stopped
% 9.34/2.07 Prover 0: stopped
% 9.34/2.07 Prover 6: stopped
% 9.34/2.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.34/2.07 Prover 2: stopped
% 9.34/2.08 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.34/2.08 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.34/2.09 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.34/2.14 Prover 13: Preprocessing ...
% 9.34/2.15 Prover 10: Preprocessing ...
% 9.34/2.15 Prover 8: Preprocessing ...
% 9.34/2.16 Prover 7: Preprocessing ...
% 9.34/2.17 Prover 11: Preprocessing ...
% 10.07/2.27 Prover 10: Constructing countermodel ...
% 11.76/2.36 Prover 13: Warning: ignoring some quantifiers
% 11.76/2.37 Prover 1: Found proof (size 37)
% 11.76/2.37 Prover 1: proved (1742ms)
% 11.76/2.37 Prover 8: Warning: ignoring some quantifiers
% 11.76/2.37 Prover 4: stopped
% 11.76/2.37 Prover 10: stopped
% 11.76/2.37 Prover 8: Constructing countermodel ...
% 11.76/2.38 Prover 13: Constructing countermodel ...
% 11.76/2.38 Prover 8: stopped
% 11.76/2.39 Prover 7: Constructing countermodel ...
% 11.76/2.39 Prover 13: stopped
% 11.76/2.41 Prover 7: stopped
% 12.24/2.46 Prover 11: Constructing countermodel ...
% 12.47/2.47 Prover 11: stopped
% 12.47/2.47
% 12.47/2.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.47/2.47
% 12.47/2.48 % SZS output start Proof for theBenchmark
% 12.47/2.48 Assumptions after simplification:
% 12.47/2.48 ---------------------------------
% 12.47/2.48
% 12.47/2.48 (mDefIdeal)
% 12.47/2.51 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aIdeal0(v0) = v1) | ~ $i(v0) | ?
% 12.47/2.51 [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2) | ? [v2: $i] : (aElementOf0(v2,
% 12.47/2.51 v0) = 0 & $i(v2) & ( ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 =
% 12.47/2.51 0) & aElementOf0(v4, v0) = v5 & aElementOf0(v3, v0) = 0 &
% 12.47/2.51 sdtpldt0(v2, v3) = v4 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] :
% 12.47/2.51 ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v4, v0) = v5 & sdtasdt0(v3,
% 12.47/2.51 v2) = v4 & aElement0(v3) = 0 & $i(v4) & $i(v3))))) & ! [v0: $i] : (
% 12.47/2.51 ~ (aIdeal0(v0) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i] : ( ~
% 12.47/2.51 (aElementOf0(v1, v0) = 0) | ~ $i(v1) | ( ! [v2: $i] : ! [v3: $i] : !
% 12.47/2.51 [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, v0) = v4) | ~ (sdtasdt0(v2,
% 12.47/2.51 v1) = v3) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) &
% 12.47/2.51 aElement0(v2) = v5)) & ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 12.47/2.51 (v4 = 0 | ~ (aElementOf0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) |
% 12.47/2.51 ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v2, v0) =
% 12.47/2.51 v5))))))
% 12.47/2.51
% 12.47/2.51 (m__)
% 12.47/2.51 $i(xn) & $i(xm) & $i(xl) & $i(xk) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1:
% 12.47/2.51 any] : ? [v2: $i] : ? [v3: any] : (aElementOf0(v2, xJ) = v3 &
% 12.47/2.51 aElementOf0(v0, xI) = v1 & sdtpldt0(xl, xn) = v2 & sdtpldt0(xk, xm) = v0 &
% 12.47/2.51 $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0)))
% 12.47/2.51
% 12.47/2.51 (m__870)
% 12.47/2.51 aIdeal0(xJ) = 0 & aIdeal0(xI) = 0 & $i(xJ) & $i(xI)
% 12.47/2.51
% 12.47/2.51 (m__934)
% 12.47/2.52 aElementOf0(xl, xJ) = 0 & aElementOf0(xk, xI) = 0 & sdtpldt0(xk, xl) = xx &
% 12.47/2.52 $i(xl) & $i(xk) & $i(xx) & $i(xJ) & $i(xI)
% 12.47/2.52
% 12.47/2.52 (m__967)
% 12.47/2.52 aElementOf0(xn, xJ) = 0 & aElementOf0(xm, xI) = 0 & sdtpldt0(xm, xn) = xy &
% 12.47/2.52 $i(xn) & $i(xm) & $i(xy) & $i(xJ) & $i(xI)
% 12.47/2.52
% 12.47/2.52 (function-axioms)
% 12.47/2.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.47/2.52 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 12.47/2.52 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) |
% 12.47/2.52 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.47/2.52 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.47/2.52 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: $i] :
% 12.47/2.52 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1)
% 12.47/2.52 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 12.47/2.52 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 12.47/2.52 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 12.47/2.52 = v0 | ~ (aIdeal0(v2) = v1) | ~ (aIdeal0(v2) = v0)) & ! [v0:
% 12.47/2.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 12.47/2.52 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 12.47/2.52 [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0:
% 12.47/2.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 12.47/2.52 ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0))
% 12.47/2.52
% 12.47/2.52 Further assumptions not needed in the proof:
% 12.47/2.52 --------------------------------------------
% 12.47/2.52 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mDefSInt, mDefSSum,
% 12.47/2.52 mEOfElem, mElmSort, mMulAsso, mMulComm, mMulMnOne, mMulUnit, mMulZero, mSetEq,
% 12.47/2.52 mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__901
% 12.47/2.52
% 12.47/2.52 Those formulas are unsatisfiable:
% 12.47/2.52 ---------------------------------
% 12.47/2.52
% 12.47/2.52 Begin of proof
% 12.47/2.53 |
% 12.47/2.53 | ALPHA: (mDefIdeal) implies:
% 12.47/2.53 | (1) ! [v0: $i] : ( ~ (aIdeal0(v0) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & !
% 12.47/2.53 | [v1: $i] : ( ~ (aElementOf0(v1, v0) = 0) | ~ $i(v1) | ( ! [v2: $i]
% 12.47/2.53 | : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3,
% 12.47/2.53 | v0) = v4) | ~ (sdtasdt0(v2, v1) = v3) | ~ $i(v2) | ?
% 12.47/2.53 | [v5: int] : ( ~ (v5 = 0) & aElement0(v2) = v5)) & ! [v2: $i]
% 12.47/2.53 | : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3,
% 12.47/2.53 | v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ?
% 12.47/2.53 | [v5: int] : ( ~ (v5 = 0) & aElementOf0(v2, v0) = v5))))))
% 12.47/2.53 |
% 12.47/2.53 | ALPHA: (m__870) implies:
% 12.47/2.53 | (2) aIdeal0(xI) = 0
% 12.47/2.53 | (3) aIdeal0(xJ) = 0
% 12.47/2.53 |
% 12.47/2.53 | ALPHA: (m__934) implies:
% 12.47/2.53 | (4) aElementOf0(xk, xI) = 0
% 12.47/2.53 | (5) aElementOf0(xl, xJ) = 0
% 12.47/2.53 |
% 12.47/2.53 | ALPHA: (m__967) implies:
% 12.47/2.53 | (6) aElementOf0(xm, xI) = 0
% 12.47/2.53 | (7) aElementOf0(xn, xJ) = 0
% 12.47/2.53 |
% 12.47/2.53 | ALPHA: (m__) implies:
% 12.47/2.53 | (8) $i(xI)
% 12.47/2.53 | (9) $i(xJ)
% 12.47/2.53 | (10) $i(xk)
% 12.47/2.53 | (11) $i(xl)
% 12.47/2.53 | (12) $i(xm)
% 12.47/2.53 | (13) $i(xn)
% 12.47/2.53 | (14) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 12.47/2.53 | (aElementOf0(v2, xJ) = v3 & aElementOf0(v0, xI) = v1 & sdtpldt0(xl,
% 12.47/2.53 | xn) = v2 & sdtpldt0(xk, xm) = v0 & $i(v2) & $i(v0) & ( ~ (v3 = 0)
% 12.47/2.53 | | ~ (v1 = 0)))
% 12.47/2.53 |
% 12.47/2.53 | ALPHA: (function-axioms) implies:
% 12.47/2.54 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 12.47/2.54 | : ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~
% 12.47/2.54 | (aElementOf0(v3, v2) = v0))
% 12.47/2.54 |
% 12.47/2.54 | DELTA: instantiating (14) with fresh symbols all_24_0, all_24_1, all_24_2,
% 12.47/2.54 | all_24_3 gives:
% 12.47/2.54 | (16) aElementOf0(all_24_1, xJ) = all_24_0 & aElementOf0(all_24_3, xI) =
% 12.47/2.54 | all_24_2 & sdtpldt0(xl, xn) = all_24_1 & sdtpldt0(xk, xm) = all_24_3 &
% 12.47/2.54 | $i(all_24_1) & $i(all_24_3) & ( ~ (all_24_0 = 0) | ~ (all_24_2 = 0))
% 12.47/2.54 |
% 12.47/2.54 | ALPHA: (16) implies:
% 12.47/2.54 | (17) sdtpldt0(xk, xm) = all_24_3
% 12.47/2.54 | (18) sdtpldt0(xl, xn) = all_24_1
% 12.47/2.54 | (19) aElementOf0(all_24_3, xI) = all_24_2
% 12.47/2.54 | (20) aElementOf0(all_24_1, xJ) = all_24_0
% 12.47/2.54 | (21) ~ (all_24_0 = 0) | ~ (all_24_2 = 0)
% 12.47/2.54 |
% 12.47/2.54 | GROUND_INST: instantiating (1) with xI, simplifying with (2), (8) gives:
% 12.47/2.54 | (22) aSet0(xI) = 0 & ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~
% 12.47/2.54 | $i(v0) | ( ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.47/2.54 | (aElementOf0(v2, xI) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ~
% 12.47/2.54 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aElement0(v1) = v4)) & !
% 12.47/2.54 | [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.47/2.54 | (aElementOf0(v2, xI) = v3) | ~ (sdtpldt0(v0, v1) = v2) | ~
% 12.47/2.54 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v1, xI) =
% 12.47/2.54 | v4))))
% 12.47/2.54 |
% 12.47/2.54 | ALPHA: (22) implies:
% 12.47/2.54 | (23) ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ( ! [v1: $i]
% 12.47/2.54 | : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xI) =
% 12.47/2.54 | v3) | ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v4: int] :
% 12.47/2.54 | ( ~ (v4 = 0) & aElement0(v1) = v4)) & ! [v1: $i] : ! [v2: $i]
% 12.47/2.54 | : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xI) = v3) | ~
% 12.47/2.54 | (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 =
% 12.47/2.54 | 0) & aElementOf0(v1, xI) = v4))))
% 12.47/2.54 |
% 12.47/2.54 | GROUND_INST: instantiating (1) with xJ, simplifying with (3), (9) gives:
% 12.85/2.54 | (24) aSet0(xJ) = 0 & ! [v0: $i] : ( ~ (aElementOf0(v0, xJ) = 0) | ~
% 12.85/2.54 | $i(v0) | ( ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.85/2.54 | (aElementOf0(v2, xJ) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ~
% 12.85/2.54 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aElement0(v1) = v4)) & !
% 12.85/2.54 | [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.85/2.54 | (aElementOf0(v2, xJ) = v3) | ~ (sdtpldt0(v0, v1) = v2) | ~
% 12.85/2.54 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v1, xJ) =
% 12.85/2.54 | v4))))
% 12.85/2.54 |
% 12.85/2.54 | ALPHA: (24) implies:
% 12.85/2.54 | (25) ! [v0: $i] : ( ~ (aElementOf0(v0, xJ) = 0) | ~ $i(v0) | ( ! [v1: $i]
% 12.85/2.55 | : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xJ) =
% 12.85/2.55 | v3) | ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v4: int] :
% 12.85/2.55 | ( ~ (v4 = 0) & aElement0(v1) = v4)) & ! [v1: $i] : ! [v2: $i]
% 12.85/2.55 | : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xJ) = v3) | ~
% 12.85/2.55 | (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 =
% 12.85/2.55 | 0) & aElementOf0(v1, xJ) = v4))))
% 12.85/2.55 |
% 12.85/2.55 | GROUND_INST: instantiating (25) with xl, simplifying with (5), (11) gives:
% 12.85/2.55 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 12.85/2.55 | (aElementOf0(v1, xJ) = v2) | ~ (sdtasdt0(v0, xl) = v1) | ~ $i(v0)
% 12.85/2.55 | | ? [v3: int] : ( ~ (v3 = 0) & aElement0(v0) = v3)) & ! [v0: $i] :
% 12.85/2.55 | ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xJ) = v2) |
% 12.85/2.55 | ~ (sdtpldt0(xl, v0) = v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0)
% 12.85/2.55 | & aElementOf0(v0, xJ) = v3))
% 12.85/2.55 |
% 12.85/2.55 | ALPHA: (26) implies:
% 12.85/2.55 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 12.85/2.55 | (aElementOf0(v1, xJ) = v2) | ~ (sdtpldt0(xl, v0) = v1) | ~ $i(v0)
% 12.85/2.55 | | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v0, xJ) = v3))
% 12.85/2.55 |
% 12.85/2.55 | GROUND_INST: instantiating (23) with xk, simplifying with (4), (10) gives:
% 12.85/2.55 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 12.85/2.55 | (aElementOf0(v1, xI) = v2) | ~ (sdtasdt0(v0, xk) = v1) | ~ $i(v0)
% 12.85/2.55 | | ? [v3: int] : ( ~ (v3 = 0) & aElement0(v0) = v3)) & ! [v0: $i] :
% 12.85/2.55 | ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xI) = v2) |
% 12.85/2.55 | ~ (sdtpldt0(xk, v0) = v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0)
% 12.85/2.55 | & aElementOf0(v0, xI) = v3))
% 12.85/2.55 |
% 12.85/2.55 | ALPHA: (28) implies:
% 12.85/2.55 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 12.85/2.55 | (aElementOf0(v1, xI) = v2) | ~ (sdtpldt0(xk, v0) = v1) | ~ $i(v0)
% 12.85/2.55 | | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v0, xI) = v3))
% 12.85/2.55 |
% 12.85/2.55 | GROUND_INST: instantiating (27) with xn, all_24_1, all_24_0, simplifying with
% 12.85/2.55 | (13), (18), (20) gives:
% 12.85/2.55 | (30) all_24_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xn, xJ) = v0)
% 12.85/2.55 |
% 12.85/2.55 | GROUND_INST: instantiating (29) with xm, all_24_3, all_24_2, simplifying with
% 12.85/2.55 | (12), (17), (19) gives:
% 12.85/2.55 | (31) all_24_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xm, xI) = v0)
% 12.85/2.55 |
% 12.85/2.55 | BETA: splitting (31) gives:
% 12.85/2.55 |
% 12.85/2.55 | Case 1:
% 12.85/2.55 | |
% 12.85/2.55 | | (32) all_24_2 = 0
% 12.85/2.55 | |
% 12.85/2.55 | | BETA: splitting (21) gives:
% 12.85/2.55 | |
% 12.85/2.55 | | Case 1:
% 12.85/2.55 | | |
% 12.85/2.55 | | | (33) ~ (all_24_0 = 0)
% 12.85/2.55 | | |
% 12.85/2.55 | | | BETA: splitting (30) gives:
% 12.85/2.55 | | |
% 12.85/2.55 | | | Case 1:
% 12.85/2.55 | | | |
% 12.85/2.55 | | | | (34) all_24_0 = 0
% 12.85/2.55 | | | |
% 12.85/2.55 | | | | REDUCE: (33), (34) imply:
% 12.85/2.55 | | | | (35) $false
% 12.85/2.55 | | | |
% 12.85/2.55 | | | | CLOSE: (35) is inconsistent.
% 12.85/2.55 | | | |
% 12.85/2.55 | | | Case 2:
% 12.85/2.55 | | | |
% 12.85/2.55 | | | | (36) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xn, xJ) = v0)
% 12.85/2.55 | | | |
% 12.85/2.55 | | | | DELTA: instantiating (36) with fresh symbol all_73_0 gives:
% 12.85/2.55 | | | | (37) ~ (all_73_0 = 0) & aElementOf0(xn, xJ) = all_73_0
% 12.85/2.55 | | | |
% 12.85/2.55 | | | | ALPHA: (37) implies:
% 12.85/2.55 | | | | (38) ~ (all_73_0 = 0)
% 12.85/2.55 | | | | (39) aElementOf0(xn, xJ) = all_73_0
% 12.85/2.55 | | | |
% 12.85/2.55 | | | | GROUND_INST: instantiating (15) with 0, all_73_0, xJ, xn, simplifying
% 12.85/2.55 | | | | with (7), (39) gives:
% 12.85/2.55 | | | | (40) all_73_0 = 0
% 12.85/2.55 | | | |
% 12.85/2.55 | | | | REDUCE: (38), (40) imply:
% 12.85/2.55 | | | | (41) $false
% 12.85/2.55 | | | |
% 12.85/2.55 | | | | CLOSE: (41) is inconsistent.
% 12.85/2.55 | | | |
% 12.85/2.56 | | | End of split
% 12.85/2.56 | | |
% 12.85/2.56 | | Case 2:
% 12.85/2.56 | | |
% 12.85/2.56 | | | (42) ~ (all_24_2 = 0)
% 12.85/2.56 | | |
% 12.85/2.56 | | | REDUCE: (32), (42) imply:
% 12.85/2.56 | | | (43) $false
% 12.85/2.56 | | |
% 12.85/2.56 | | | CLOSE: (43) is inconsistent.
% 12.85/2.56 | | |
% 12.85/2.56 | | End of split
% 12.85/2.56 | |
% 12.85/2.56 | Case 2:
% 12.85/2.56 | |
% 12.85/2.56 | | (44) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xm, xI) = v0)
% 12.85/2.56 | |
% 12.85/2.56 | | DELTA: instantiating (44) with fresh symbol all_65_0 gives:
% 12.85/2.56 | | (45) ~ (all_65_0 = 0) & aElementOf0(xm, xI) = all_65_0
% 12.85/2.56 | |
% 12.85/2.56 | | ALPHA: (45) implies:
% 12.85/2.56 | | (46) ~ (all_65_0 = 0)
% 12.85/2.56 | | (47) aElementOf0(xm, xI) = all_65_0
% 12.85/2.56 | |
% 12.85/2.56 | | GROUND_INST: instantiating (15) with 0, all_65_0, xI, xm, simplifying with
% 12.85/2.56 | | (6), (47) gives:
% 12.85/2.56 | | (48) all_65_0 = 0
% 12.85/2.56 | |
% 12.85/2.56 | | REDUCE: (46), (48) imply:
% 12.85/2.56 | | (49) $false
% 12.85/2.56 | |
% 12.85/2.56 | | CLOSE: (49) is inconsistent.
% 12.85/2.56 | |
% 12.85/2.56 | End of split
% 12.85/2.56 |
% 12.85/2.56 End of proof
% 12.85/2.56 % SZS output end Proof for theBenchmark
% 12.85/2.56
% 12.85/2.56 1950ms
%------------------------------------------------------------------------------