TSTP Solution File: NUM468+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM468+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 : n023.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 11:47:57 EDT 2023
% Result : Theorem 9.82s 2.07s
% Output : Proof 15.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM468+2 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 12:12:42 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.20/0.58 ________ _____
% 0.20/0.58 ___ __ \_________(_)________________________________
% 0.20/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.58
% 0.20/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.58 (2023-06-19)
% 0.20/0.58
% 0.20/0.58 (c) Philipp Rümmer, 2009-2023
% 0.20/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.58 Amanda Stjerna.
% 0.20/0.58 Free software under BSD-3-Clause.
% 0.20/0.58
% 0.20/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.58
% 0.20/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.64/0.60 Running up to 7 provers in parallel.
% 0.67/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.67/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.67/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.67/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.67/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.67/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.67/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.17/1.11 Prover 1: Preprocessing ...
% 3.17/1.11 Prover 4: Preprocessing ...
% 3.17/1.14 Prover 3: Preprocessing ...
% 3.17/1.14 Prover 2: Preprocessing ...
% 3.17/1.14 Prover 0: Preprocessing ...
% 3.17/1.14 Prover 6: Preprocessing ...
% 3.17/1.14 Prover 5: Preprocessing ...
% 7.54/1.77 Prover 1: Constructing countermodel ...
% 7.54/1.77 Prover 3: Constructing countermodel ...
% 8.24/1.78 Prover 6: Proving ...
% 8.51/1.83 Prover 5: Constructing countermodel ...
% 9.82/2.02 Prover 2: Proving ...
% 9.82/2.07 Prover 3: proved (1455ms)
% 9.82/2.07
% 9.82/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.82/2.07
% 9.82/2.07 Prover 6: stopped
% 9.82/2.07 Prover 5: stopped
% 10.45/2.08 Prover 2: stopped
% 10.45/2.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.45/2.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.45/2.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.49/2.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.49/2.10 Prover 4: Constructing countermodel ...
% 10.76/2.16 Prover 10: Preprocessing ...
% 10.76/2.17 Prover 7: Preprocessing ...
% 10.76/2.20 Prover 8: Preprocessing ...
% 10.76/2.21 Prover 0: Proving ...
% 11.50/2.21 Prover 0: stopped
% 11.50/2.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.50/2.23 Prover 11: Preprocessing ...
% 11.50/2.28 Prover 13: Preprocessing ...
% 12.16/2.32 Prover 10: Constructing countermodel ...
% 12.88/2.40 Prover 7: Constructing countermodel ...
% 12.98/2.44 Prover 8: Warning: ignoring some quantifiers
% 12.98/2.44 Prover 8: Constructing countermodel ...
% 13.69/2.53 Prover 13: Constructing countermodel ...
% 14.35/2.65 Prover 11: Constructing countermodel ...
% 15.25/2.77 Prover 10: Found proof (size 53)
% 15.25/2.77 Prover 10: proved (689ms)
% 15.25/2.77 Prover 11: stopped
% 15.25/2.77 Prover 13: stopped
% 15.25/2.77 Prover 4: stopped
% 15.25/2.77 Prover 8: stopped
% 15.25/2.77 Prover 7: stopped
% 15.25/2.79 Prover 1: Found proof (size 243)
% 15.25/2.79 Prover 1: proved (2181ms)
% 15.25/2.79
% 15.25/2.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.25/2.79
% 15.25/2.80 % SZS output start Proof for theBenchmark
% 15.25/2.80 Assumptions after simplification:
% 15.25/2.80 ---------------------------------
% 15.25/2.80
% 15.25/2.80 (mAMDistr)
% 15.90/2.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 15.90/2.83 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~
% 15.90/2.83 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 15.90/2.83 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ?
% 15.90/2.83 [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v7
% 15.90/2.83 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 &
% 15.90/2.83 sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) &
% 15.90/2.83 $i(v6) & $i(v5)))
% 15.90/2.83
% 15.90/2.83 (mDefQuot)
% 15.90/2.84 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 |
% 15.90/2.84 v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~
% 15.90/2.84 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 15.90/2.84 aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & !
% 15.90/2.84 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v0 = sz00 | ~
% 15.90/2.84 (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 15.90/2.84 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~
% 15.90/2.84 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 15.90/2.84 : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~
% 15.90/2.84 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 15.90/2.84 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 15.90/2.84
% 15.90/2.84 (mMulComm)
% 15.90/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 15.90/2.84 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 15.90/2.84 (sdtasdt0(v1, v0) = v2 & $i(v2)))
% 15.90/2.84
% 15.90/2.84 (m__)
% 15.90/2.84 $i(xn) & $i(xm) & $i(xl) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 15.90/2.84 : ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v2) & ~ (xl = sz00) & sdtsldt0(xn,
% 15.90/2.84 xl) = v1 & sdtsldt0(xm, xl) = v0 & sdtasdt0(xl, v3) = v4 & sdtasdt0(xl,
% 15.90/2.84 v1) = xn & sdtasdt0(xl, v0) = xm & sdtpldt0(v0, v1) = v3 & sdtpldt0(xm,
% 15.90/2.84 xn) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 15.90/2.84 aNaturalNumber0(v1) & aNaturalNumber0(v0))
% 15.90/2.84
% 15.90/2.84 (m__1240)
% 15.90/2.84 $i(xn) & $i(xm) & $i(xl) & aNaturalNumber0(xn) & aNaturalNumber0(xm) &
% 15.90/2.84 aNaturalNumber0(xl)
% 15.90/2.84
% 15.90/2.84 (m__1240_04)
% 15.90/2.84 $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xl, v1) = xm
% 15.90/2.84 & sdtasdt0(xl, v0) = xn & $i(v1) & $i(v0) & doDivides0(xl, xn) &
% 15.90/2.84 doDivides0(xl, xm) & aNaturalNumber0(v1) & aNaturalNumber0(v0))
% 15.90/2.84
% 15.90/2.84 (function-axioms)
% 15.90/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.90/2.84 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 15.90/2.84 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) |
% 15.90/2.84 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 15.90/2.84 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 15.90/2.84 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.90/2.84 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 15.90/2.84
% 15.90/2.84 Further assumptions not needed in the proof:
% 15.90/2.84 --------------------------------------------
% 15.90/2.84 mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDivTrans, mIH, mIH_03,
% 15.90/2.84 mLEAsym, mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2,
% 15.90/2.84 mMulAsso, mMulCanc, mNatSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01,
% 15.90/2.84 mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero
% 15.90/2.84
% 15.90/2.84 Those formulas are unsatisfiable:
% 15.90/2.84 ---------------------------------
% 15.90/2.84
% 15.90/2.84 Begin of proof
% 15.90/2.84 |
% 15.90/2.84 | ALPHA: (mDefQuot) implies:
% 15.90/2.85 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v0 =
% 15.90/2.85 | sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~
% 15.90/2.85 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 15.90/2.85 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~
% 15.90/2.85 | aNaturalNumber0(v0))
% 15.90/2.85 |
% 15.90/2.85 | ALPHA: (m__1240) implies:
% 15.90/2.85 | (2) aNaturalNumber0(xl)
% 15.90/2.85 | (3) aNaturalNumber0(xm)
% 15.90/2.85 | (4) aNaturalNumber0(xn)
% 15.90/2.85 |
% 15.90/2.85 | ALPHA: (m__1240_04) implies:
% 15.90/2.85 | (5) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xl, v1) = xm & sdtasdt0(xl, v0) =
% 15.90/2.85 | xn & $i(v1) & $i(v0) & doDivides0(xl, xn) & doDivides0(xl, xm) &
% 15.90/2.85 | aNaturalNumber0(v1) & aNaturalNumber0(v0))
% 15.90/2.85 |
% 15.90/2.85 | ALPHA: (m__) implies:
% 15.90/2.85 | (6) $i(xl)
% 15.90/2.85 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (
% 15.90/2.85 | ~ (v4 = v2) & ~ (xl = sz00) & sdtsldt0(xn, xl) = v1 & sdtsldt0(xm,
% 15.90/2.85 | xl) = v0 & sdtasdt0(xl, v3) = v4 & sdtasdt0(xl, v1) = xn &
% 15.90/2.85 | sdtasdt0(xl, v0) = xm & sdtpldt0(v0, v1) = v3 & sdtpldt0(xm, xn) = v2
% 15.90/2.85 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aNaturalNumber0(v1) &
% 15.90/2.85 | aNaturalNumber0(v0))
% 15.90/2.85 |
% 15.90/2.85 | ALPHA: (function-axioms) implies:
% 15.90/2.85 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.90/2.85 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 15.90/2.85 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.90/2.85 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 15.90/2.85 |
% 15.90/2.85 | DELTA: instantiating (5) with fresh symbols all_32_0, all_32_1 gives:
% 15.90/2.85 | (10) sdtasdt0(xl, all_32_0) = xm & sdtasdt0(xl, all_32_1) = xn &
% 15.90/2.85 | $i(all_32_0) & $i(all_32_1) & doDivides0(xl, xn) & doDivides0(xl, xm)
% 15.90/2.85 | & aNaturalNumber0(all_32_0) & aNaturalNumber0(all_32_1)
% 15.90/2.85 |
% 15.90/2.85 | ALPHA: (10) implies:
% 15.90/2.85 | (11) aNaturalNumber0(all_32_1)
% 15.90/2.85 | (12) aNaturalNumber0(all_32_0)
% 15.90/2.85 | (13) doDivides0(xl, xm)
% 15.90/2.85 | (14) doDivides0(xl, xn)
% 15.90/2.85 | (15) $i(all_32_1)
% 15.90/2.85 | (16) $i(all_32_0)
% 15.90/2.85 | (17) sdtasdt0(xl, all_32_1) = xn
% 15.90/2.85 | (18) sdtasdt0(xl, all_32_0) = xm
% 15.90/2.85 |
% 15.90/2.85 | DELTA: instantiating (7) with fresh symbols all_34_0, all_34_1, all_34_2,
% 15.90/2.85 | all_34_3, all_34_4 gives:
% 15.90/2.85 | (19) ~ (all_34_0 = all_34_2) & ~ (xl = sz00) & sdtsldt0(xn, xl) =
% 15.90/2.85 | all_34_3 & sdtsldt0(xm, xl) = all_34_4 & sdtasdt0(xl, all_34_1) =
% 15.90/2.85 | all_34_0 & sdtasdt0(xl, all_34_3) = xn & sdtasdt0(xl, all_34_4) = xm &
% 15.90/2.85 | sdtpldt0(all_34_4, all_34_3) = all_34_1 & sdtpldt0(xm, xn) = all_34_2
% 15.90/2.85 | & $i(all_34_0) & $i(all_34_1) & $i(all_34_2) & $i(all_34_3) &
% 15.90/2.85 | $i(all_34_4) & aNaturalNumber0(all_34_3) & aNaturalNumber0(all_34_4)
% 15.90/2.85 |
% 15.90/2.85 | ALPHA: (19) implies:
% 15.90/2.86 | (20) ~ (xl = sz00)
% 15.90/2.86 | (21) ~ (all_34_0 = all_34_2)
% 15.90/2.86 | (22) aNaturalNumber0(all_34_4)
% 15.90/2.86 | (23) aNaturalNumber0(all_34_3)
% 15.90/2.86 | (24) $i(all_34_4)
% 15.90/2.86 | (25) $i(all_34_3)
% 15.90/2.86 | (26) sdtpldt0(xm, xn) = all_34_2
% 15.90/2.86 | (27) sdtpldt0(all_34_4, all_34_3) = all_34_1
% 15.90/2.86 | (28) sdtasdt0(xl, all_34_4) = xm
% 15.90/2.86 | (29) sdtasdt0(xl, all_34_3) = xn
% 15.90/2.86 | (30) sdtasdt0(xl, all_34_1) = all_34_0
% 15.90/2.86 | (31) sdtsldt0(xm, xl) = all_34_4
% 15.90/2.86 | (32) sdtsldt0(xn, xl) = all_34_3
% 15.90/2.86 |
% 15.90/2.86 | GROUND_INST: instantiating (mAMDistr) with xl, all_32_0, all_32_1, xm, xn,
% 15.90/2.86 | all_34_2, simplifying with (2), (6), (11), (12), (15), (16),
% 15.90/2.86 | (17), (18), (26) gives:
% 15.90/2.86 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0,
% 15.90/2.86 | xl) = v1 & sdtasdt0(all_32_0, xl) = v2 & sdtasdt0(all_32_1, xl) =
% 15.90/2.86 | v3 & sdtasdt0(xl, v0) = all_34_2 & sdtpldt0(v2, v3) = v1 &
% 15.90/2.86 | sdtpldt0(all_32_0, all_32_1) = v0 & $i(v3) & $i(v2) & $i(v1) &
% 15.90/2.86 | $i(v0) & $i(all_34_2))
% 15.90/2.86 |
% 15.90/2.86 | GROUND_INST: instantiating (mAMDistr) with xl, all_34_4, all_32_1, xm, xn,
% 15.90/2.86 | all_34_2, simplifying with (2), (6), (11), (15), (17), (22),
% 15.90/2.86 | (24), (26), (28) gives:
% 15.90/2.86 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0,
% 15.90/2.86 | xl) = v1 & sdtasdt0(all_34_4, xl) = v2 & sdtasdt0(all_32_1, xl) =
% 15.90/2.86 | v3 & sdtasdt0(xl, v0) = all_34_2 & sdtpldt0(v2, v3) = v1 &
% 15.90/2.86 | sdtpldt0(all_34_4, all_32_1) = v0 & $i(v3) & $i(v2) & $i(v1) &
% 15.90/2.86 | $i(v0) & $i(all_34_2))
% 15.90/2.86 |
% 15.90/2.86 | GROUND_INST: instantiating (mMulComm) with xl, all_34_4, xm, simplifying with
% 15.90/2.86 | (2), (6), (22), (24), (28) gives:
% 15.90/2.86 | (35) sdtasdt0(all_34_4, xl) = xm & $i(xm)
% 15.90/2.86 |
% 15.90/2.86 | ALPHA: (35) implies:
% 15.90/2.86 | (36) $i(xm)
% 15.90/2.86 |
% 15.90/2.86 | GROUND_INST: instantiating (mAMDistr) with xl, all_34_4, all_34_3, xm, xn,
% 15.90/2.86 | all_34_2, simplifying with (2), (6), (22), (23), (24), (25),
% 15.90/2.86 | (26), (28), (29) gives:
% 15.90/2.86 | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0,
% 15.90/2.86 | xl) = v1 & sdtasdt0(all_34_3, xl) = v3 & sdtasdt0(all_34_4, xl) =
% 15.90/2.86 | v2 & sdtasdt0(xl, v0) = all_34_2 & sdtpldt0(v2, v3) = v1 &
% 15.90/2.86 | sdtpldt0(all_34_4, all_34_3) = v0 & $i(v3) & $i(v2) & $i(v1) &
% 15.90/2.86 | $i(v0) & $i(all_34_2))
% 15.90/2.86 |
% 15.90/2.87 | GROUND_INST: instantiating (mAMDistr) with xl, all_32_0, all_34_3, xm, xn,
% 15.90/2.87 | all_34_2, simplifying with (2), (6), (12), (16), (18), (23),
% 15.90/2.87 | (25), (26), (29) gives:
% 15.90/2.87 | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0,
% 15.90/2.87 | xl) = v1 & sdtasdt0(all_34_3, xl) = v3 & sdtasdt0(all_32_0, xl) =
% 15.90/2.87 | v2 & sdtasdt0(xl, v0) = all_34_2 & sdtpldt0(v2, v3) = v1 &
% 15.90/2.87 | sdtpldt0(all_32_0, all_34_3) = v0 & $i(v3) & $i(v2) & $i(v1) &
% 15.90/2.87 | $i(v0) & $i(all_34_2))
% 15.90/2.87 |
% 15.90/2.87 | GROUND_INST: instantiating (mMulComm) with xl, all_34_3, xn, simplifying with
% 15.90/2.87 | (2), (6), (23), (25), (29) gives:
% 15.90/2.87 | (39) sdtasdt0(all_34_3, xl) = xn & $i(xn)
% 15.90/2.87 |
% 15.90/2.87 | ALPHA: (39) implies:
% 15.90/2.87 | (40) $i(xn)
% 15.90/2.87 |
% 15.90/2.87 | GROUND_INST: instantiating (1) with xl, xm, all_34_4, all_32_0, simplifying
% 15.90/2.87 | with (2), (3), (6), (12), (13), (16), (18), (31), (36) gives:
% 15.90/2.87 | (41) all_34_4 = all_32_0 | xl = sz00
% 15.90/2.87 |
% 15.90/2.87 | GROUND_INST: instantiating (1) with xl, xn, all_34_3, all_32_1, simplifying
% 15.90/2.87 | with (2), (4), (6), (11), (14), (15), (17), (32), (40) gives:
% 15.90/2.87 | (42) all_34_3 = all_32_1 | xl = sz00
% 15.90/2.87 |
% 15.90/2.87 | DELTA: instantiating (33) with fresh symbols all_46_0, all_46_1, all_46_2,
% 15.90/2.87 | all_46_3 gives:
% 15.90/2.87 | (43) sdtasdt0(all_46_3, xl) = all_46_2 & sdtasdt0(all_32_0, xl) = all_46_1
% 15.90/2.87 | & sdtasdt0(all_32_1, xl) = all_46_0 & sdtasdt0(xl, all_46_3) =
% 15.90/2.87 | all_34_2 & sdtpldt0(all_46_1, all_46_0) = all_46_2 &
% 15.90/2.87 | sdtpldt0(all_32_0, all_32_1) = all_46_3 & $i(all_46_0) & $i(all_46_1)
% 15.90/2.87 | & $i(all_46_2) & $i(all_46_3) & $i(all_34_2)
% 15.90/2.87 |
% 15.90/2.87 | ALPHA: (43) implies:
% 15.90/2.87 | (44) sdtpldt0(all_32_0, all_32_1) = all_46_3
% 15.90/2.87 | (45) sdtasdt0(xl, all_46_3) = all_34_2
% 15.90/2.87 |
% 15.90/2.87 | DELTA: instantiating (38) with fresh symbols all_48_0, all_48_1, all_48_2,
% 15.90/2.87 | all_48_3 gives:
% 15.90/2.87 | (46) sdtasdt0(all_48_3, xl) = all_48_2 & sdtasdt0(all_34_3, xl) = all_48_0
% 15.90/2.87 | & sdtasdt0(all_32_0, xl) = all_48_1 & sdtasdt0(xl, all_48_3) =
% 15.90/2.87 | all_34_2 & sdtpldt0(all_48_1, all_48_0) = all_48_2 &
% 15.90/2.87 | sdtpldt0(all_32_0, all_34_3) = all_48_3 & $i(all_48_0) & $i(all_48_1)
% 15.90/2.87 | & $i(all_48_2) & $i(all_48_3) & $i(all_34_2)
% 15.90/2.87 |
% 15.90/2.87 | ALPHA: (46) implies:
% 15.90/2.87 | (47) sdtpldt0(all_32_0, all_34_3) = all_48_3
% 15.90/2.87 |
% 15.90/2.87 | DELTA: instantiating (37) with fresh symbols all_50_0, all_50_1, all_50_2,
% 15.90/2.87 | all_50_3 gives:
% 15.90/2.87 | (48) sdtasdt0(all_50_3, xl) = all_50_2 & sdtasdt0(all_34_3, xl) = all_50_0
% 15.90/2.87 | & sdtasdt0(all_34_4, xl) = all_50_1 & sdtasdt0(xl, all_50_3) =
% 15.90/2.87 | all_34_2 & sdtpldt0(all_50_1, all_50_0) = all_50_2 &
% 15.90/2.87 | sdtpldt0(all_34_4, all_34_3) = all_50_3 & $i(all_50_0) & $i(all_50_1)
% 15.90/2.87 | & $i(all_50_2) & $i(all_50_3) & $i(all_34_2)
% 15.90/2.87 |
% 15.90/2.87 | ALPHA: (48) implies:
% 15.90/2.87 | (49) sdtpldt0(all_34_4, all_34_3) = all_50_3
% 15.90/2.87 |
% 15.90/2.87 | DELTA: instantiating (34) with fresh symbols all_52_0, all_52_1, all_52_2,
% 15.90/2.87 | all_52_3 gives:
% 15.90/2.87 | (50) sdtasdt0(all_52_3, xl) = all_52_2 & sdtasdt0(all_34_4, xl) = all_52_1
% 15.90/2.87 | & sdtasdt0(all_32_1, xl) = all_52_0 & sdtasdt0(xl, all_52_3) =
% 15.90/2.87 | all_34_2 & sdtpldt0(all_52_1, all_52_0) = all_52_2 &
% 15.90/2.87 | sdtpldt0(all_34_4, all_32_1) = all_52_3 & $i(all_52_0) & $i(all_52_1)
% 15.90/2.87 | & $i(all_52_2) & $i(all_52_3) & $i(all_34_2)
% 15.90/2.87 |
% 15.90/2.87 | ALPHA: (50) implies:
% 15.90/2.87 | (51) sdtpldt0(all_34_4, all_32_1) = all_52_3
% 15.90/2.87 |
% 15.90/2.87 | BETA: splitting (42) gives:
% 15.90/2.87 |
% 15.90/2.87 | Case 1:
% 15.90/2.87 | |
% 15.90/2.87 | | (52) xl = sz00
% 15.90/2.87 | |
% 15.90/2.88 | | REDUCE: (20), (52) imply:
% 15.90/2.88 | | (53) $false
% 15.90/2.88 | |
% 15.90/2.88 | | CLOSE: (53) is inconsistent.
% 15.90/2.88 | |
% 15.90/2.88 | Case 2:
% 15.90/2.88 | |
% 15.90/2.88 | | (54) all_34_3 = all_32_1
% 15.90/2.88 | |
% 15.90/2.88 | | REDUCE: (49), (54) imply:
% 15.90/2.88 | | (55) sdtpldt0(all_34_4, all_32_1) = all_50_3
% 15.90/2.88 | |
% 15.90/2.88 | | REDUCE: (27), (54) imply:
% 15.90/2.88 | | (56) sdtpldt0(all_34_4, all_32_1) = all_34_1
% 15.90/2.88 | |
% 15.90/2.88 | | REDUCE: (47), (54) imply:
% 15.90/2.88 | | (57) sdtpldt0(all_32_0, all_32_1) = all_48_3
% 15.90/2.88 | |
% 15.90/2.88 | | BETA: splitting (41) gives:
% 15.90/2.88 | |
% 15.90/2.88 | | Case 1:
% 15.90/2.88 | | |
% 15.90/2.88 | | | (58) xl = sz00
% 15.90/2.88 | | |
% 15.90/2.88 | | | REDUCE: (20), (58) imply:
% 15.90/2.88 | | | (59) $false
% 15.90/2.88 | | |
% 15.90/2.88 | | | CLOSE: (59) is inconsistent.
% 15.90/2.88 | | |
% 15.90/2.88 | | Case 2:
% 15.90/2.88 | | |
% 15.90/2.88 | | | (60) all_34_4 = all_32_0
% 15.90/2.88 | | |
% 15.90/2.88 | | | REDUCE: (51), (60) imply:
% 15.90/2.88 | | | (61) sdtpldt0(all_32_0, all_32_1) = all_52_3
% 15.90/2.88 | | |
% 15.90/2.88 | | | REDUCE: (55), (60) imply:
% 15.90/2.88 | | | (62) sdtpldt0(all_32_0, all_32_1) = all_50_3
% 15.90/2.88 | | |
% 15.90/2.88 | | | REDUCE: (56), (60) imply:
% 15.90/2.88 | | | (63) sdtpldt0(all_32_0, all_32_1) = all_34_1
% 15.90/2.88 | | |
% 15.90/2.88 | | | GROUND_INST: instantiating (8) with all_46_3, all_50_3, all_32_1,
% 15.90/2.88 | | | all_32_0, simplifying with (44), (62) gives:
% 15.90/2.88 | | | (64) all_50_3 = all_46_3
% 15.90/2.88 | | |
% 15.90/2.88 | | | GROUND_INST: instantiating (8) with all_50_3, all_52_3, all_32_1,
% 15.90/2.88 | | | all_32_0, simplifying with (61), (62) gives:
% 15.90/2.88 | | | (65) all_52_3 = all_50_3
% 15.90/2.88 | | |
% 15.90/2.88 | | | GROUND_INST: instantiating (8) with all_48_3, all_52_3, all_32_1,
% 15.90/2.88 | | | all_32_0, simplifying with (57), (61) gives:
% 15.90/2.88 | | | (66) all_52_3 = all_48_3
% 15.90/2.88 | | |
% 15.90/2.88 | | | GROUND_INST: instantiating (8) with all_34_1, all_52_3, all_32_1,
% 15.90/2.88 | | | all_32_0, simplifying with (61), (63) gives:
% 15.90/2.88 | | | (67) all_52_3 = all_34_1
% 15.90/2.88 | | |
% 15.90/2.88 | | | COMBINE_EQS: (65), (66) imply:
% 15.90/2.88 | | | (68) all_50_3 = all_48_3
% 15.90/2.88 | | |
% 15.90/2.88 | | | SIMP: (68) implies:
% 15.90/2.88 | | | (69) all_50_3 = all_48_3
% 15.90/2.88 | | |
% 15.90/2.88 | | | COMBINE_EQS: (66), (67) imply:
% 15.90/2.88 | | | (70) all_48_3 = all_34_1
% 15.90/2.88 | | |
% 15.90/2.88 | | | COMBINE_EQS: (64), (69) imply:
% 15.90/2.88 | | | (71) all_48_3 = all_46_3
% 15.90/2.88 | | |
% 15.90/2.88 | | | SIMP: (71) implies:
% 15.90/2.88 | | | (72) all_48_3 = all_46_3
% 15.90/2.88 | | |
% 15.90/2.88 | | | COMBINE_EQS: (70), (72) imply:
% 15.90/2.88 | | | (73) all_46_3 = all_34_1
% 15.90/2.88 | | |
% 15.90/2.88 | | | REDUCE: (45), (73) imply:
% 15.90/2.88 | | | (74) sdtasdt0(xl, all_34_1) = all_34_2
% 15.90/2.88 | | |
% 15.90/2.88 | | | GROUND_INST: instantiating (9) with all_34_0, all_34_2, all_34_1, xl,
% 15.90/2.88 | | | simplifying with (30), (74) gives:
% 15.90/2.88 | | | (75) all_34_0 = all_34_2
% 15.90/2.88 | | |
% 15.90/2.88 | | | REDUCE: (21), (75) imply:
% 15.90/2.88 | | | (76) $false
% 15.90/2.88 | | |
% 15.90/2.88 | | | CLOSE: (76) is inconsistent.
% 15.90/2.88 | | |
% 15.90/2.88 | | End of split
% 15.90/2.88 | |
% 15.90/2.88 | End of split
% 15.90/2.88 |
% 15.90/2.88 End of proof
% 15.90/2.88 % SZS output end Proof for theBenchmark
% 15.90/2.88
% 15.90/2.88 2301ms
%------------------------------------------------------------------------------