TSTP Solution File: RNG112+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG112+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 : n010.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 13:57:57 EDT 2023
% Result : Theorem 37.09s 5.88s
% Output : Proof 44.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG112+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Aug 27 01:44:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.51/1.18 Prover 1: Preprocessing ...
% 3.51/1.19 Prover 4: Preprocessing ...
% 3.85/1.23 Prover 2: Preprocessing ...
% 3.85/1.23 Prover 6: Preprocessing ...
% 3.85/1.23 Prover 3: Preprocessing ...
% 3.85/1.23 Prover 5: Preprocessing ...
% 3.85/1.23 Prover 0: Preprocessing ...
% 9.78/2.13 Prover 1: Constructing countermodel ...
% 9.78/2.18 Prover 3: Constructing countermodel ...
% 9.78/2.20 Prover 6: Proving ...
% 9.78/2.21 Prover 5: Proving ...
% 10.87/2.30 Prover 2: Proving ...
% 12.54/2.49 Prover 4: Constructing countermodel ...
% 12.54/2.55 Prover 0: Proving ...
% 37.09/5.88 Prover 3: proved (5250ms)
% 37.09/5.88
% 37.09/5.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.09/5.88
% 37.09/5.89 Prover 5: stopped
% 37.09/5.89 Prover 2: stopped
% 38.22/5.91 Prover 0: stopped
% 38.22/5.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 38.22/5.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 38.22/5.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 38.22/5.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 38.22/5.92 Prover 6: stopped
% 38.22/5.93 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 38.22/5.95 Prover 7: Preprocessing ...
% 38.94/5.99 Prover 8: Preprocessing ...
% 39.09/6.05 Prover 10: Preprocessing ...
% 39.09/6.06 Prover 11: Preprocessing ...
% 39.09/6.06 Prover 13: Preprocessing ...
% 39.79/6.10 Prover 7: Constructing countermodel ...
% 40.48/6.20 Prover 10: Constructing countermodel ...
% 40.48/6.21 Prover 8: Warning: ignoring some quantifiers
% 40.48/6.22 Prover 8: Constructing countermodel ...
% 40.48/6.26 Prover 13: Warning: ignoring some quantifiers
% 40.48/6.28 Prover 13: Constructing countermodel ...
% 41.41/6.36 Prover 11: Constructing countermodel ...
% 43.75/6.69 Prover 10: Found proof (size 30)
% 43.75/6.69 Prover 10: proved (775ms)
% 43.75/6.69 Prover 13: stopped
% 43.75/6.69 Prover 1: stopped
% 43.75/6.70 Prover 4: stopped
% 43.75/6.70 Prover 8: stopped
% 43.75/6.70 Prover 11: stopped
% 43.75/6.70 Prover 7: stopped
% 43.75/6.70
% 43.75/6.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 43.75/6.70
% 43.75/6.71 % SZS output start Proof for theBenchmark
% 44.43/6.71 Assumptions after simplification:
% 44.43/6.71 ---------------------------------
% 44.43/6.71
% 44.43/6.71 (m__)
% 44.43/6.73 $i(xI) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ (sbrdtbr0(v0)
% 44.43/6.73 = v1) | ~ $i(v0) | ~ aElementOf0(v0, xI) | ? [v2: $i] : ? [v3: $i] : (
% 44.43/6.73 ~ (v2 = sz00) & sbrdtbr0(v2) = v3 & $i(v3) & $i(v2) & iLess0(v3, v1) &
% 44.43/6.73 aElementOf0(v2, xI)))
% 44.43/6.73
% 44.43/6.73 (m__2174)
% 44.43/6.74 $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 &
% 44.43/6.74 slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = xI & $i(v1) & $i(v0) & aIdeal0(xI))
% 44.43/6.74
% 44.43/6.74 (m__2228)
% 44.43/6.74 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 44.43/6.74 $i] : ( ~ (v3 = sz00) & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sdtpldt1(v0,
% 44.43/6.74 v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v2))
% 44.43/6.74
% 44.43/6.74 (m__2351)
% 44.43/6.74 $i(xI) & $i(sz00) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0,
% 44.43/6.74 xI) | ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = sz00) & sbrdtbr0(v1) = v2 &
% 44.43/6.74 $i(v2) & $i(v1) & aElementOf0(v1, xI) & ! [v3: $i] : ! [v4: $i] : (v3 =
% 44.43/6.74 sz00 | ~ (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ iLess0(v4, v2) | ~
% 44.43/6.74 aElementOf0(v3, xI))))
% 44.43/6.74
% 44.43/6.74 (function-axioms)
% 44.43/6.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 44.43/6.74 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 44.43/6.74 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) |
% 44.43/6.74 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 44.43/6.74 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 44.43/6.74 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 44.43/6.74 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 44.43/6.74 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) | ~ (slsdtgt0(v2)
% 44.43/6.74 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 44.43/6.74 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 44.43/6.74 ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0))
% 44.43/6.74
% 44.43/6.74 Further assumptions not needed in the proof:
% 44.43/6.74 --------------------------------------------
% 44.43/6.74 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder,
% 44.43/6.74 mDefDiv, mDefDvs, mDefGCD, mDefIdeal, mDefMod, mDefPrIdeal, mDefRel, mDefSInt,
% 44.43/6.74 mDefSSum, mDivision, mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso,
% 44.43/6.74 mMulComm, mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mPrIdeal, mSetEq,
% 44.43/6.74 mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__2091,
% 44.43/6.74 m__2110, m__2129, m__2203
% 44.43/6.74
% 44.43/6.74 Those formulas are unsatisfiable:
% 44.43/6.74 ---------------------------------
% 44.43/6.74
% 44.43/6.74 Begin of proof
% 44.43/6.74 |
% 44.43/6.74 | ALPHA: (m__2174) implies:
% 44.43/6.74 | (1) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 44.43/6.74 | sdtpldt1(v0, v1) = xI & $i(v1) & $i(v0) & aIdeal0(xI))
% 44.43/6.74 |
% 44.43/6.74 | ALPHA: (m__2228) implies:
% 44.43/6.74 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = sz00)
% 44.43/6.74 | & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = v2 &
% 44.43/6.74 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v2))
% 44.43/6.74 |
% 44.43/6.74 | ALPHA: (m__2351) implies:
% 44.43/6.75 | (3) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, xI) | ? [v1:
% 44.43/6.75 | $i] : ? [v2: $i] : ( ~ (v1 = sz00) & sbrdtbr0(v1) = v2 & $i(v2) &
% 44.43/6.75 | $i(v1) & aElementOf0(v1, xI) & ! [v3: $i] : ! [v4: $i] : (v3 =
% 44.43/6.75 | sz00 | ~ (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ iLess0(v4, v2) |
% 44.43/6.75 | ~ aElementOf0(v3, xI))))
% 44.43/6.75 |
% 44.43/6.75 | ALPHA: (m__) implies:
% 44.43/6.75 | (4) ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ (sbrdtbr0(v0) = v1) | ~
% 44.43/6.75 | $i(v0) | ~ aElementOf0(v0, xI) | ? [v2: $i] : ? [v3: $i] : ( ~ (v2
% 44.43/6.75 | = sz00) & sbrdtbr0(v2) = v3 & $i(v3) & $i(v2) & iLess0(v3, v1) &
% 44.43/6.75 | aElementOf0(v2, xI)))
% 44.43/6.75 |
% 44.43/6.75 | ALPHA: (function-axioms) implies:
% 44.43/6.75 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) =
% 44.43/6.75 | v1) | ~ (slsdtgt0(v2) = v0))
% 44.43/6.75 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 44.43/6.75 | (sdtpldt1(v3, v2) = v1) | ~ (sdtpldt1(v3, v2) = v0))
% 44.43/6.75 |
% 44.43/6.75 | DELTA: instantiating (1) with fresh symbols all_36_0, all_36_1 gives:
% 44.43/6.75 | (7) slsdtgt0(xb) = all_36_0 & slsdtgt0(xa) = all_36_1 & sdtpldt1(all_36_1,
% 44.43/6.75 | all_36_0) = xI & $i(all_36_0) & $i(all_36_1) & aIdeal0(xI)
% 44.43/6.75 |
% 44.43/6.75 | ALPHA: (7) implies:
% 44.43/6.75 | (8) sdtpldt1(all_36_1, all_36_0) = xI
% 44.43/6.75 | (9) slsdtgt0(xa) = all_36_1
% 44.43/6.75 | (10) slsdtgt0(xb) = all_36_0
% 44.43/6.75 |
% 44.43/6.75 | DELTA: instantiating (2) with fresh symbols all_43_0, all_43_1, all_43_2,
% 44.43/6.75 | all_43_3 gives:
% 44.43/6.75 | (11) ~ (all_43_0 = sz00) & slsdtgt0(xb) = all_43_2 & slsdtgt0(xa) =
% 44.43/6.75 | all_43_3 & sdtpldt1(all_43_3, all_43_2) = all_43_1 & $i(all_43_0) &
% 44.43/6.75 | $i(all_43_1) & $i(all_43_2) & $i(all_43_3) & aElementOf0(all_43_0,
% 44.43/6.75 | all_43_1)
% 44.43/6.75 |
% 44.43/6.75 | ALPHA: (11) implies:
% 44.43/6.75 | (12) ~ (all_43_0 = sz00)
% 44.43/6.75 | (13) aElementOf0(all_43_0, all_43_1)
% 44.43/6.75 | (14) $i(all_43_0)
% 44.43/6.75 | (15) sdtpldt1(all_43_3, all_43_2) = all_43_1
% 44.43/6.75 | (16) slsdtgt0(xa) = all_43_3
% 44.43/6.75 | (17) slsdtgt0(xb) = all_43_2
% 44.43/6.75 |
% 44.43/6.75 | GROUND_INST: instantiating (5) with all_36_1, all_43_3, xa, simplifying with
% 44.43/6.75 | (9), (16) gives:
% 44.43/6.75 | (18) all_43_3 = all_36_1
% 44.43/6.75 |
% 44.43/6.75 | GROUND_INST: instantiating (5) with all_36_0, all_43_2, xb, simplifying with
% 44.43/6.75 | (10), (17) gives:
% 44.43/6.75 | (19) all_43_2 = all_36_0
% 44.43/6.75 |
% 44.43/6.75 | REDUCE: (15), (18), (19) imply:
% 44.43/6.75 | (20) sdtpldt1(all_36_1, all_36_0) = all_43_1
% 44.43/6.75 |
% 44.43/6.75 | GROUND_INST: instantiating (6) with xI, all_43_1, all_36_0, all_36_1,
% 44.43/6.75 | simplifying with (8), (20) gives:
% 44.43/6.75 | (21) all_43_1 = xI
% 44.43/6.75 |
% 44.43/6.75 | REDUCE: (13), (21) imply:
% 44.43/6.75 | (22) aElementOf0(all_43_0, xI)
% 44.43/6.75 |
% 44.43/6.75 | GROUND_INST: instantiating (3) with all_43_0, simplifying with (14), (22)
% 44.43/6.75 | gives:
% 44.43/6.75 | (23) all_43_0 = sz00 | ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = sz00) &
% 44.43/6.75 | sbrdtbr0(v0) = v1 & $i(v1) & $i(v0) & aElementOf0(v0, xI) & ! [v2:
% 44.43/6.75 | $i] : ! [v3: $i] : (v2 = sz00 | ~ (sbrdtbr0(v2) = v3) | ~
% 44.43/6.76 | $i(v2) | ~ iLess0(v3, v1) | ~ aElementOf0(v2, xI)))
% 44.43/6.76 |
% 44.43/6.76 | BETA: splitting (23) gives:
% 44.43/6.76 |
% 44.43/6.76 | Case 1:
% 44.43/6.76 | |
% 44.43/6.76 | | (24) all_43_0 = sz00
% 44.43/6.76 | |
% 44.43/6.76 | | REDUCE: (12), (24) imply:
% 44.43/6.76 | | (25) $false
% 44.43/6.76 | |
% 44.43/6.76 | | CLOSE: (25) is inconsistent.
% 44.43/6.76 | |
% 44.43/6.76 | Case 2:
% 44.43/6.76 | |
% 44.43/6.76 | | (26) ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = sz00) & sbrdtbr0(v0) = v1 &
% 44.43/6.76 | | $i(v1) & $i(v0) & aElementOf0(v0, xI) & ! [v2: $i] : ! [v3: $i]
% 44.43/6.76 | | : (v2 = sz00 | ~ (sbrdtbr0(v2) = v3) | ~ $i(v2) | ~ iLess0(v3,
% 44.43/6.76 | | v1) | ~ aElementOf0(v2, xI)))
% 44.43/6.76 | |
% 44.43/6.76 | | DELTA: instantiating (26) with fresh symbols all_71_0, all_71_1 gives:
% 44.43/6.76 | | (27) ~ (all_71_1 = sz00) & sbrdtbr0(all_71_1) = all_71_0 & $i(all_71_0)
% 44.43/6.76 | | & $i(all_71_1) & aElementOf0(all_71_1, xI) & ! [v0: $i] : ! [v1:
% 44.43/6.76 | | $i] : (v0 = sz00 | ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~
% 44.43/6.76 | | iLess0(v1, all_71_0) | ~ aElementOf0(v0, xI))
% 44.43/6.76 | |
% 44.43/6.76 | | ALPHA: (27) implies:
% 44.43/6.76 | | (28) ~ (all_71_1 = sz00)
% 44.43/6.76 | | (29) aElementOf0(all_71_1, xI)
% 44.43/6.76 | | (30) $i(all_71_1)
% 44.43/6.76 | | (31) sbrdtbr0(all_71_1) = all_71_0
% 44.43/6.76 | | (32) ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ (sbrdtbr0(v0) = v1) | ~
% 44.43/6.76 | | $i(v0) | ~ iLess0(v1, all_71_0) | ~ aElementOf0(v0, xI))
% 44.43/6.76 | |
% 44.43/6.76 | | GROUND_INST: instantiating (4) with all_71_1, all_71_0, simplifying with
% 44.43/6.76 | | (29), (30), (31) gives:
% 44.43/6.76 | | (33) all_71_1 = sz00 | ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = sz00) &
% 44.43/6.76 | | sbrdtbr0(v0) = v1 & $i(v1) & $i(v0) & iLess0(v1, all_71_0) &
% 44.43/6.76 | | aElementOf0(v0, xI))
% 44.43/6.76 | |
% 44.43/6.76 | | BETA: splitting (33) gives:
% 44.43/6.76 | |
% 44.43/6.76 | | Case 1:
% 44.43/6.76 | | |
% 44.43/6.76 | | | (34) all_71_1 = sz00
% 44.43/6.76 | | |
% 44.43/6.76 | | | REDUCE: (28), (34) imply:
% 44.43/6.76 | | | (35) $false
% 44.43/6.76 | | |
% 44.43/6.76 | | | CLOSE: (35) is inconsistent.
% 44.43/6.76 | | |
% 44.43/6.76 | | Case 2:
% 44.43/6.76 | | |
% 44.43/6.76 | | | (36) ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = sz00) & sbrdtbr0(v0) = v1 &
% 44.43/6.76 | | | $i(v1) & $i(v0) & iLess0(v1, all_71_0) & aElementOf0(v0, xI))
% 44.43/6.76 | | |
% 44.43/6.76 | | | DELTA: instantiating (36) with fresh symbols all_258_0, all_258_1 gives:
% 44.43/6.76 | | | (37) ~ (all_258_1 = sz00) & sbrdtbr0(all_258_1) = all_258_0 &
% 44.43/6.76 | | | $i(all_258_0) & $i(all_258_1) & iLess0(all_258_0, all_71_0) &
% 44.43/6.76 | | | aElementOf0(all_258_1, xI)
% 44.43/6.76 | | |
% 44.43/6.76 | | | ALPHA: (37) implies:
% 44.43/6.76 | | | (38) ~ (all_258_1 = sz00)
% 44.43/6.76 | | | (39) aElementOf0(all_258_1, xI)
% 44.43/6.76 | | | (40) iLess0(all_258_0, all_71_0)
% 44.43/6.76 | | | (41) $i(all_258_1)
% 44.43/6.76 | | | (42) sbrdtbr0(all_258_1) = all_258_0
% 44.43/6.76 | | |
% 44.43/6.76 | | | GROUND_INST: instantiating (32) with all_258_1, all_258_0, simplifying
% 44.43/6.76 | | | with (39), (40), (41), (42) gives:
% 44.43/6.76 | | | (43) all_258_1 = sz00
% 44.43/6.76 | | |
% 44.43/6.76 | | | REDUCE: (38), (43) imply:
% 44.43/6.76 | | | (44) $false
% 44.43/6.76 | | |
% 44.43/6.76 | | | CLOSE: (44) is inconsistent.
% 44.43/6.76 | | |
% 44.43/6.76 | | End of split
% 44.43/6.76 | |
% 44.43/6.76 | End of split
% 44.43/6.76 |
% 44.43/6.76 End of proof
% 44.43/6.76 % SZS output end Proof for theBenchmark
% 44.43/6.76
% 44.43/6.76 6160ms
%------------------------------------------------------------------------------