TSTP Solution File: NUM435+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM435+3 : 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 11:47:44 EDT 2023
% Result : Theorem 9.94s 2.12s
% Output : Proof 15.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM435+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 11:45:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.78/1.08 Prover 4: Preprocessing ...
% 2.78/1.08 Prover 1: Preprocessing ...
% 3.09/1.12 Prover 5: Preprocessing ...
% 3.09/1.12 Prover 0: Preprocessing ...
% 3.09/1.12 Prover 2: Preprocessing ...
% 3.09/1.12 Prover 3: Preprocessing ...
% 3.09/1.14 Prover 6: Preprocessing ...
% 6.23/1.64 Prover 1: Constructing countermodel ...
% 6.92/1.66 Prover 3: Constructing countermodel ...
% 6.92/1.66 Prover 6: Proving ...
% 7.32/1.74 Prover 5: Constructing countermodel ...
% 7.66/1.78 Prover 4: Constructing countermodel ...
% 7.66/1.79 Prover 2: Proving ...
% 8.79/1.92 Prover 0: Proving ...
% 9.94/2.07 Prover 3: proved (1436ms)
% 9.94/2.12
% 9.94/2.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.94/2.12
% 9.94/2.13 Prover 5: stopped
% 9.94/2.13 Prover 0: stopped
% 9.94/2.13 Prover 6: stopped
% 9.94/2.13 Prover 2: stopped
% 9.94/2.13 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.94/2.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.94/2.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.94/2.13 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.94/2.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.45/2.20 Prover 7: Preprocessing ...
% 10.45/2.21 Prover 10: Preprocessing ...
% 10.45/2.21 Prover 11: Preprocessing ...
% 10.45/2.21 Prover 13: Preprocessing ...
% 11.13/2.22 Prover 8: Preprocessing ...
% 11.13/2.30 Prover 10: Constructing countermodel ...
% 11.89/2.32 Prover 7: Constructing countermodel ...
% 11.89/2.32 Prover 8: Warning: ignoring some quantifiers
% 11.89/2.32 Prover 8: Constructing countermodel ...
% 11.89/2.34 Prover 13: Constructing countermodel ...
% 12.49/2.43 Prover 11: Constructing countermodel ...
% 14.76/2.74 Prover 10: Found proof (size 40)
% 14.76/2.74 Prover 10: proved (614ms)
% 14.76/2.75 Prover 11: stopped
% 14.76/2.75 Prover 4: stopped
% 14.76/2.75 Prover 13: stopped
% 14.76/2.75 Prover 7: stopped
% 14.76/2.75 Prover 1: stopped
% 14.76/2.75 Prover 8: stopped
% 14.76/2.75
% 14.76/2.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.76/2.75
% 14.76/2.75 % SZS output start Proof for theBenchmark
% 14.76/2.76 Assumptions after simplification:
% 14.76/2.76 ---------------------------------
% 14.76/2.76
% 14.76/2.76 (mEquModRef)
% 14.76/2.76 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~
% 14.76/2.76 aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1))
% 14.76/2.76
% 14.76/2.76 (mMulAsso)
% 15.34/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 15.34/2.78 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 15.34/2.79 | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | ?
% 15.34/2.79 [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4 & $i(v5) &
% 15.34/2.79 $i(v4)))
% 15.34/2.79
% 15.34/2.79 (mMulComm)
% 15.34/2.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 15.34/2.79 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | (sdtasdt0(v1, v0)
% 15.34/2.79 = v2 & $i(v2)))
% 15.34/2.79
% 15.34/2.79 (m__)
% 15.34/2.79 $i(xm) & $i(xq) & $i(xp) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ?
% 15.34/2.79 [v2: $i] : ? [v3: $i] : ( ~ (v3 = v1) & sdtasdt0(xq, v2) = v3 & sdtasdt0(xp,
% 15.34/2.79 xm) = v2 & sdtpldt0(xa, v0) = v1 & smndt0(xb) = v0 & $i(v3) & $i(v2) &
% 15.34/2.79 $i(v1) & $i(v0))
% 15.34/2.79
% 15.34/2.79 (m__1003)
% 15.34/2.79 $i(xq) & $i(xp) & $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ?
% 15.34/2.79 [v2: $i] : ? [v3: $i] : ( ~ (v0 = sz00) & sdtasdt0(v0, v3) = v2 &
% 15.34/2.79 sdtasdt0(xp, xq) = v0 & sdtpldt0(xa, v1) = v2 & smndt0(xb) = v1 & $i(v3) &
% 15.34/2.79 $i(v2) & $i(v1) & $i(v0) & sdteqdtlpzmzozddtrp0(xa, xb, v0) &
% 15.34/2.79 aDivisorOf0(v0, v2) & aInteger0(v3))
% 15.34/2.79
% 15.34/2.79 (m__1032)
% 15.34/2.79 $i(xm) & $i(xq) & $i(xp) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ?
% 15.34/2.79 [v2: $i] : (sdtasdt0(v0, xm) = v1 & sdtasdt0(xp, xq) = v0 & sdtpldt0(xa, v2) =
% 15.34/2.79 v1 & smndt0(xb) = v2 & $i(v2) & $i(v1) & $i(v0) & aInteger0(xm))
% 15.34/2.79
% 15.34/2.79 (m__979)
% 15.34/2.79 ~ (xq = sz00) & ~ (xp = sz00) & $i(xq) & $i(xp) & $i(xb) & $i(xa) & $i(sz00)
% 15.34/2.79 & aInteger0(xq) & aInteger0(xp) & aInteger0(xb) & aInteger0(xa)
% 15.34/2.79
% 15.34/2.79 (function-axioms)
% 15.34/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.34/2.80 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 15.34/2.80 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 15.34/2.80 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 15.34/2.80 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0))
% 15.34/2.80
% 15.34/2.80 Further assumptions not needed in the proof:
% 15.34/2.80 --------------------------------------------
% 15.34/2.80 mAddAsso, mAddComm, mAddNeg, mAddZero, mDistrib, mDivisor, mEquMod, mEquModSym,
% 15.34/2.80 mEquModTrn, mIntMult, mIntNeg, mIntOne, mIntPlus, mIntZero, mIntegers,
% 15.34/2.80 mMulMinOne, mMulOne, mMulZero, mZeroDiv
% 15.34/2.80
% 15.34/2.80 Those formulas are unsatisfiable:
% 15.34/2.80 ---------------------------------
% 15.34/2.80
% 15.34/2.80 Begin of proof
% 15.34/2.80 |
% 15.34/2.80 | ALPHA: (mEquModRef) implies:
% 15.34/2.80 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~
% 15.34/2.80 | aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1))
% 15.34/2.80 |
% 15.34/2.80 | ALPHA: (m__979) implies:
% 15.34/2.80 | (2) ~ (xp = sz00)
% 15.34/2.80 | (3) aInteger0(xp)
% 15.34/2.80 | (4) aInteger0(xq)
% 15.34/2.80 |
% 15.34/2.80 | ALPHA: (m__1003) implies:
% 15.34/2.80 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v0 = sz00)
% 15.34/2.80 | & sdtasdt0(v0, v3) = v2 & sdtasdt0(xp, xq) = v0 & sdtpldt0(xa, v1) =
% 15.34/2.80 | v2 & smndt0(xb) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 15.34/2.80 | sdteqdtlpzmzozddtrp0(xa, xb, v0) & aDivisorOf0(v0, v2) &
% 15.34/2.80 | aInteger0(v3))
% 15.34/2.80 |
% 15.34/2.80 | ALPHA: (m__1032) implies:
% 15.34/2.80 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(v0, xm) = v1 &
% 15.34/2.80 | sdtasdt0(xp, xq) = v0 & sdtpldt0(xa, v2) = v1 & smndt0(xb) = v2 &
% 15.34/2.80 | $i(v2) & $i(v1) & $i(v0) & aInteger0(xm))
% 15.34/2.80 |
% 15.34/2.80 | ALPHA: (m__) implies:
% 15.34/2.80 | (7) $i(xp)
% 15.34/2.80 | (8) $i(xq)
% 15.34/2.80 | (9) $i(xm)
% 15.34/2.81 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v1)
% 15.34/2.81 | & sdtasdt0(xq, v2) = v3 & sdtasdt0(xp, xm) = v2 & sdtpldt0(xa, v0) =
% 15.34/2.81 | v1 & smndt0(xb) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 15.34/2.81 |
% 15.34/2.81 | ALPHA: (function-axioms) implies:
% 15.34/2.81 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) =
% 15.34/2.81 | v1) | ~ (smndt0(v2) = v0))
% 15.34/2.81 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.34/2.81 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 15.34/2.81 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.34/2.81 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 15.34/2.81 |
% 15.34/2.81 | DELTA: instantiating (6) with fresh symbols all_22_0, all_22_1, all_22_2
% 15.34/2.81 | gives:
% 15.34/2.81 | (14) sdtasdt0(all_22_2, xm) = all_22_1 & sdtasdt0(xp, xq) = all_22_2 &
% 15.34/2.81 | sdtpldt0(xa, all_22_0) = all_22_1 & smndt0(xb) = all_22_0 &
% 15.34/2.81 | $i(all_22_0) & $i(all_22_1) & $i(all_22_2) & aInteger0(xm)
% 15.34/2.81 |
% 15.34/2.81 | ALPHA: (14) implies:
% 15.34/2.81 | (15) aInteger0(xm)
% 15.34/2.81 | (16) smndt0(xb) = all_22_0
% 15.34/2.81 | (17) sdtpldt0(xa, all_22_0) = all_22_1
% 15.34/2.81 | (18) sdtasdt0(xp, xq) = all_22_2
% 15.34/2.81 | (19) sdtasdt0(all_22_2, xm) = all_22_1
% 15.34/2.81 |
% 15.34/2.81 | DELTA: instantiating (10) with fresh symbols all_27_0, all_27_1, all_27_2,
% 15.34/2.81 | all_27_3 gives:
% 15.34/2.81 | (20) ~ (all_27_0 = all_27_2) & sdtasdt0(xq, all_27_1) = all_27_0 &
% 15.34/2.81 | sdtasdt0(xp, xm) = all_27_1 & sdtpldt0(xa, all_27_3) = all_27_2 &
% 15.34/2.81 | smndt0(xb) = all_27_3 & $i(all_27_0) & $i(all_27_1) & $i(all_27_2) &
% 15.34/2.81 | $i(all_27_3)
% 15.34/2.81 |
% 15.34/2.81 | ALPHA: (20) implies:
% 15.34/2.81 | (21) ~ (all_27_0 = all_27_2)
% 15.34/2.81 | (22) smndt0(xb) = all_27_3
% 15.34/2.81 | (23) sdtpldt0(xa, all_27_3) = all_27_2
% 15.34/2.81 | (24) sdtasdt0(xp, xm) = all_27_1
% 15.34/2.81 | (25) sdtasdt0(xq, all_27_1) = all_27_0
% 15.34/2.81 |
% 15.34/2.81 | DELTA: instantiating (5) with fresh symbols all_29_0, all_29_1, all_29_2,
% 15.34/2.81 | all_29_3 gives:
% 15.34/2.81 | (26) ~ (all_29_3 = sz00) & sdtasdt0(all_29_3, all_29_0) = all_29_1 &
% 15.34/2.81 | sdtasdt0(xp, xq) = all_29_3 & sdtpldt0(xa, all_29_2) = all_29_1 &
% 15.34/2.81 | smndt0(xb) = all_29_2 & $i(all_29_0) & $i(all_29_1) & $i(all_29_2) &
% 15.34/2.81 | $i(all_29_3) & sdteqdtlpzmzozddtrp0(xa, xb, all_29_3) &
% 15.34/2.81 | aDivisorOf0(all_29_3, all_29_1) & aInteger0(all_29_0)
% 15.34/2.81 |
% 15.34/2.81 | ALPHA: (26) implies:
% 15.34/2.81 | (27) aInteger0(all_29_0)
% 15.34/2.81 | (28) $i(all_29_0)
% 15.34/2.81 | (29) smndt0(xb) = all_29_2
% 15.34/2.81 | (30) sdtpldt0(xa, all_29_2) = all_29_1
% 15.34/2.81 | (31) sdtasdt0(xp, xq) = all_29_3
% 15.34/2.81 |
% 15.34/2.82 | GROUND_INST: instantiating (11) with all_27_3, all_29_2, xb, simplifying with
% 15.34/2.82 | (22), (29) gives:
% 15.34/2.82 | (32) all_29_2 = all_27_3
% 15.34/2.82 |
% 15.34/2.82 | GROUND_INST: instantiating (11) with all_22_0, all_29_2, xb, simplifying with
% 15.34/2.82 | (16), (29) gives:
% 15.34/2.82 | (33) all_29_2 = all_22_0
% 15.34/2.82 |
% 15.34/2.82 | GROUND_INST: instantiating (13) with all_22_2, all_29_3, xq, xp, simplifying
% 15.34/2.82 | with (18), (31) gives:
% 15.34/2.82 | (34) all_29_3 = all_22_2
% 15.34/2.82 |
% 15.34/2.82 | COMBINE_EQS: (32), (33) imply:
% 15.34/2.82 | (35) all_27_3 = all_22_0
% 15.34/2.82 |
% 15.34/2.82 | SIMP: (35) implies:
% 15.34/2.82 | (36) all_27_3 = all_22_0
% 15.34/2.82 |
% 15.34/2.82 | REDUCE: (30), (33) imply:
% 15.34/2.82 | (37) sdtpldt0(xa, all_22_0) = all_29_1
% 15.34/2.82 |
% 15.34/2.82 | REDUCE: (23), (36) imply:
% 15.34/2.82 | (38) sdtpldt0(xa, all_22_0) = all_27_2
% 15.34/2.82 |
% 15.34/2.82 | GROUND_INST: instantiating (12) with all_22_1, all_29_1, all_22_0, xa,
% 15.34/2.82 | simplifying with (17), (37) gives:
% 15.34/2.82 | (39) all_29_1 = all_22_1
% 15.34/2.82 |
% 15.34/2.82 | GROUND_INST: instantiating (12) with all_27_2, all_29_1, all_22_0, xa,
% 15.34/2.82 | simplifying with (37), (38) gives:
% 15.34/2.82 | (40) all_29_1 = all_27_2
% 15.34/2.82 |
% 15.34/2.82 | COMBINE_EQS: (39), (40) imply:
% 15.34/2.82 | (41) all_27_2 = all_22_1
% 15.34/2.82 |
% 15.34/2.82 | REDUCE: (21), (41) imply:
% 15.34/2.82 | (42) ~ (all_27_0 = all_22_1)
% 15.34/2.82 |
% 15.34/2.82 | GROUND_INST: instantiating (1) with all_29_0, xp, simplifying with (3), (7),
% 15.34/2.82 | (27), (28) gives:
% 15.34/2.82 | (43) xp = sz00 | sdteqdtlpzmzozddtrp0(all_29_0, all_29_0, xp)
% 15.34/2.82 |
% 15.34/2.82 | GROUND_INST: instantiating (mMulComm) with xp, xq, all_22_2, simplifying with
% 15.34/2.82 | (3), (4), (7), (8), (18) gives:
% 15.34/2.82 | (44) sdtasdt0(xq, xp) = all_22_2 & $i(all_22_2)
% 15.34/2.82 |
% 15.34/2.82 | ALPHA: (44) implies:
% 15.34/2.82 | (45) sdtasdt0(xq, xp) = all_22_2
% 15.34/2.82 |
% 15.34/2.82 | BETA: splitting (43) gives:
% 15.34/2.82 |
% 15.34/2.82 | Case 1:
% 15.34/2.82 | |
% 15.34/2.82 | |
% 15.34/2.82 | | GROUND_INST: instantiating (mMulAsso) with xq, xp, xm, all_22_2, all_22_1,
% 15.34/2.82 | | simplifying with (3), (4), (7), (8), (9), (15), (19), (45)
% 15.34/2.82 | | gives:
% 15.34/2.82 | | (46) ? [v0: $i] : (sdtasdt0(xq, v0) = all_22_1 & sdtasdt0(xp, xm) = v0 &
% 15.34/2.82 | | $i(v0) & $i(all_22_1))
% 15.34/2.82 | |
% 15.34/2.82 | | DELTA: instantiating (46) with fresh symbol all_119_0 gives:
% 15.34/2.82 | | (47) sdtasdt0(xq, all_119_0) = all_22_1 & sdtasdt0(xp, xm) = all_119_0 &
% 15.34/2.82 | | $i(all_119_0) & $i(all_22_1)
% 15.34/2.82 | |
% 15.34/2.82 | | ALPHA: (47) implies:
% 15.34/2.82 | | (48) sdtasdt0(xp, xm) = all_119_0
% 15.34/2.82 | | (49) sdtasdt0(xq, all_119_0) = all_22_1
% 15.34/2.82 | |
% 15.34/2.82 | | GROUND_INST: instantiating (13) with all_27_1, all_119_0, xm, xp,
% 15.34/2.82 | | simplifying with (24), (48) gives:
% 15.34/2.82 | | (50) all_119_0 = all_27_1
% 15.34/2.82 | |
% 15.34/2.82 | | REDUCE: (49), (50) imply:
% 15.34/2.82 | | (51) sdtasdt0(xq, all_27_1) = all_22_1
% 15.34/2.82 | |
% 15.34/2.82 | | GROUND_INST: instantiating (13) with all_27_0, all_22_1, all_27_1, xq,
% 15.34/2.82 | | simplifying with (25), (51) gives:
% 15.34/2.82 | | (52) all_27_0 = all_22_1
% 15.34/2.82 | |
% 15.34/2.82 | | REDUCE: (42), (52) imply:
% 15.34/2.82 | | (53) $false
% 15.34/2.83 | |
% 15.34/2.83 | | CLOSE: (53) is inconsistent.
% 15.34/2.83 | |
% 15.34/2.83 | Case 2:
% 15.34/2.83 | |
% 15.34/2.83 | | (54) xp = sz00
% 15.34/2.83 | |
% 15.34/2.83 | | REDUCE: (2), (54) imply:
% 15.34/2.83 | | (55) $false
% 15.34/2.83 | |
% 15.34/2.83 | | CLOSE: (55) is inconsistent.
% 15.34/2.83 | |
% 15.34/2.83 | End of split
% 15.34/2.83 |
% 15.34/2.83 End of proof
% 15.34/2.83 % SZS output end Proof for theBenchmark
% 15.34/2.83
% 15.34/2.83 2215ms
%------------------------------------------------------------------------------