TSTP Solution File: COM017+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM017+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n001.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 : Wed Aug 30 18:44:16 EDT 2023
% Result : Theorem 49.89s 7.46s
% Output : Proof 55.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : COM017+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 13:50:52 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.47/1.20 Prover 1: Preprocessing ...
% 3.47/1.20 Prover 4: Preprocessing ...
% 3.75/1.23 Prover 3: Preprocessing ...
% 3.75/1.23 Prover 2: Preprocessing ...
% 3.75/1.23 Prover 0: Preprocessing ...
% 3.75/1.23 Prover 5: Preprocessing ...
% 3.75/1.24 Prover 6: Preprocessing ...
% 6.59/1.72 Prover 5: Constructing countermodel ...
% 8.14/1.92 Prover 3: Constructing countermodel ...
% 8.14/1.94 Prover 1: Constructing countermodel ...
% 8.90/1.97 Prover 6: Proving ...
% 9.48/2.06 Prover 2: Constructing countermodel ...
% 14.52/2.74 Prover 4: Constructing countermodel ...
% 16.40/2.98 Prover 0: Proving ...
% 49.89/7.46 Prover 3: proved (6816ms)
% 49.89/7.46
% 49.89/7.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.89/7.46
% 49.89/7.46 Prover 0: stopped
% 49.89/7.46 Prover 2: stopped
% 49.89/7.46 Prover 5: stopped
% 49.89/7.46 Prover 6: stopped
% 49.89/7.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 49.89/7.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 49.89/7.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 49.89/7.48 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 49.89/7.48 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 51.14/7.60 Prover 7: Preprocessing ...
% 51.14/7.62 Prover 11: Preprocessing ...
% 51.14/7.64 Prover 10: Preprocessing ...
% 51.14/7.64 Prover 8: Preprocessing ...
% 51.14/7.65 Prover 13: Preprocessing ...
% 52.06/7.73 Prover 10: Constructing countermodel ...
% 52.06/7.74 Prover 8: Warning: ignoring some quantifiers
% 52.06/7.74 Prover 8: Constructing countermodel ...
% 52.06/7.75 Prover 7: Constructing countermodel ...
% 52.06/7.78 Prover 13: Constructing countermodel ...
% 55.06/8.16 Prover 10: Found proof (size 15)
% 55.06/8.16 Prover 10: proved (683ms)
% 55.06/8.16 Prover 7: stopped
% 55.06/8.16 Prover 13: stopped
% 55.06/8.16 Prover 1: stopped
% 55.06/8.16 Prover 8: stopped
% 55.06/8.16 Prover 4: stopped
% 55.48/8.22 Prover 11: Constructing countermodel ...
% 55.48/8.23 Prover 11: stopped
% 55.48/8.23
% 55.48/8.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 55.48/8.23
% 55.48/8.23 % SZS output start Proof for theBenchmark
% 55.48/8.23 Assumptions after simplification:
% 55.48/8.23 ---------------------------------
% 55.48/8.23
% 55.48/8.23 (m__)
% 55.48/8.25 $i(xv) & $i(xu) & $i(xR) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 55.48/8.25 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtmndtplgtdt0(v2, xR, v0) | ~
% 55.48/8.25 sdtmndtplgtdt0(v1, xR, v0) | ~ aReductOfIn0(v2, xu, xR) | ~
% 55.48/8.25 aReductOfIn0(v1, xv, xR) | ~ aElement0(v2) | ~ aElement0(v1) | ~
% 55.48/8.25 aElement0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 55.48/8.25 sdtmndtasgtdt0(xv, xR, v0) | ~ sdtmndtplgtdt0(v1, xR, v0) | ~
% 55.48/8.25 aReductOfIn0(v1, xu, xR) | ~ aElement0(v1) | ~ aElement0(v0)) & ! [v0:
% 55.48/8.25 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtmndtasgtdt0(xu, xR, v0) |
% 55.48/8.25 ~ sdtmndtplgtdt0(v1, xR, v0) | ~ aReductOfIn0(v1, xv, xR) | ~
% 55.48/8.25 aElement0(v1) | ~ aElement0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) |
% 55.48/8.25 ~ $i(v0) | ~ sdtmndtplgtdt0(v1, xR, v0) | ~ sdtmndtplgtdt0(xv, xR, v0) |
% 55.48/8.25 ~ aReductOfIn0(v1, xu, xR) | ~ aElement0(v1) | ~ aElement0(v0)) & ! [v0:
% 55.48/8.25 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtmndtplgtdt0(v1, xR, v0) |
% 55.48/8.25 ~ sdtmndtplgtdt0(xu, xR, v0) | ~ aReductOfIn0(v1, xv, xR) | ~
% 55.48/8.25 aElement0(v1) | ~ aElement0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) |
% 55.48/8.25 ~ $i(v0) | ~ sdtmndtplgtdt0(v1, xR, v0) | ~ aReductOfIn0(v1, xv, xR) | ~
% 55.48/8.25 aReductOfIn0(v0, xu, xR) | ~ aElement0(v1) | ~ aElement0(v0)) & ! [v0:
% 55.48/8.25 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtmndtplgtdt0(v1, xR, v0) |
% 55.48/8.25 ~ aReductOfIn0(v1, xu, xR) | ~ aReductOfIn0(v0, xv, xR) | ~ aElement0(v1)
% 55.48/8.25 | ~ aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ sdtmndtasgtdt0(xv, xR,
% 55.48/8.25 v0) | ~ sdtmndtasgtdt0(xu, xR, v0) | ~ aElement0(v0)) & ! [v0: $i] : (
% 55.48/8.25 ~ $i(v0) | ~ sdtmndtasgtdt0(xv, xR, v0) | ~ sdtmndtplgtdt0(xu, xR, v0) |
% 55.48/8.25 ~ aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ sdtmndtasgtdt0(xv, xR, v0)
% 55.48/8.25 | ~ aReductOfIn0(v0, xu, xR) | ~ aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0)
% 55.48/8.25 | ~ sdtmndtasgtdt0(xu, xR, v0) | ~ sdtmndtplgtdt0(xv, xR, v0) | ~
% 55.48/8.25 aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ sdtmndtasgtdt0(xu, xR, v0) |
% 55.48/8.25 ~ aReductOfIn0(v0, xv, xR) | ~ aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) |
% 55.48/8.25 ~ sdtmndtplgtdt0(v0, xR, xv) | ~ aReductOfIn0(v0, xu, xR) | ~
% 55.48/8.25 aElement0(v0) | ~ aElement0(xv)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 55.48/8.25 sdtmndtplgtdt0(v0, xR, xu) | ~ aReductOfIn0(v0, xv, xR) | ~ aElement0(v0)
% 55.48/8.25 | ~ aElement0(xu)) & ! [v0: $i] : ( ~ $i(v0) | ~ sdtmndtplgtdt0(xv, xR,
% 55.48/8.25 v0) | ~ sdtmndtplgtdt0(xu, xR, v0) | ~ aElement0(v0)) & ! [v0: $i] : (
% 55.48/8.25 ~ $i(v0) | ~ sdtmndtplgtdt0(xv, xR, v0) | ~ aReductOfIn0(v0, xu, xR) | ~
% 55.48/8.25 aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ sdtmndtplgtdt0(xu, xR, v0) |
% 55.48/8.25 ~ aReductOfIn0(v0, xv, xR) | ~ aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) |
% 55.48/8.25 ~ aReductOfIn0(v0, xv, xR) | ~ aReductOfIn0(v0, xu, xR) | ~ aElement0(v0))
% 55.48/8.25 & ( ~ (xv = xu) | ~ aElement0(xu)) & ( ~ sdtmndtasgtdt0(xv, xR, xu) | ~
% 55.48/8.25 aElement0(xu)) & ( ~ sdtmndtasgtdt0(xu, xR, xv) | ~ aElement0(xv)) & ( ~
% 55.48/8.25 sdtmndtplgtdt0(xv, xR, xu) | ~ aElement0(xu)) & ( ~ sdtmndtplgtdt0(xu, xR,
% 55.48/8.25 xv) | ~ aElement0(xv)) & ( ~ aReductOfIn0(xv, xu, xR) | ~ aElement0(xv))
% 55.48/8.25 & ( ~ aReductOfIn0(xu, xv, xR) | ~ aElement0(xu))
% 55.48/8.25
% 55.48/8.25 (m__656_01)
% 55.48/8.25 $i(xR) & isTerminating0(xR) & isLocallyConfluent0(xR) & ! [v0: $i] : ! [v1:
% 55.48/8.25 $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 55.48/8.25 sdtmndtplgtdt0(v2, xR, v1) | ~ aReductOfIn0(v2, v0, xR) | ~ aElement0(v2)
% 55.48/8.25 | ~ aElement0(v1) | ~ aElement0(v0) | iLess0(v1, v0)) & ! [v0: $i] : !
% 55.48/8.25 [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 55.48/8.25 aReductOfIn0(v2, v0, xR) | ~ aReductOfIn0(v1, v0, xR) | ~ aElement0(v2) |
% 55.48/8.25 ~ aElement0(v1) | ~ aElement0(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i]
% 55.48/8.25 : ($i(v5) & $i(v4) & $i(v3) & sdtmndtasgtdt0(v2, xR, v3) &
% 55.48/8.25 sdtmndtasgtdt0(v1, xR, v3) & aElement0(v3) & (v3 = v2 |
% 55.48/8.25 (sdtmndtplgtdt0(v2, xR, v3) & (aReductOfIn0(v3, v2, xR) |
% 55.48/8.25 (sdtmndtplgtdt0(v4, xR, v3) & aReductOfIn0(v4, v2, xR) &
% 55.48/8.25 aElement0(v4))))) & (v3 = v1 | (sdtmndtplgtdt0(v1, xR, v3) &
% 55.48/8.25 (aReductOfIn0(v3, v1, xR) | (sdtmndtplgtdt0(v5, xR, v3) &
% 55.48/8.25 aReductOfIn0(v5, v1, xR) & aElement0(v5))))))) & ! [v0: $i] : !
% 55.48/8.25 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtmndtplgtdt0(v0, xR, v1) | ~
% 55.48/8.25 aElement0(v1) | ~ aElement0(v0) | iLess0(v1, v0)) & ! [v0: $i] : ! [v1:
% 55.48/8.25 $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aReductOfIn0(v1, v0, xR) | ~
% 55.48/8.25 aElement0(v1) | ~ aElement0(v0) | iLess0(v1, v0))
% 55.48/8.25
% 55.48/8.25 (m__731)
% 55.48/8.25 $i(xc) & $i(xb) & $i(xa) & aElement0(xc) & aElement0(xb) & aElement0(xa)
% 55.48/8.25
% 55.48/8.25 (m__755)
% 55.48/8.25 $i(xu) & $i(xb) & $i(xa) & $i(xR) & ? [v0: $i] : ($i(v0) & sdtmndtasgtdt0(xu,
% 55.48/8.25 xR, xb) & aReductOfIn0(xu, xa, xR) & aElement0(xu) & (xu = xb |
% 55.48/8.25 (sdtmndtplgtdt0(xu, xR, xb) & (aReductOfIn0(xb, xu, xR) |
% 55.48/8.25 (sdtmndtplgtdt0(v0, xR, xb) & aReductOfIn0(v0, xu, xR) &
% 55.48/8.25 aElement0(v0))))))
% 55.48/8.25
% 55.48/8.25 (m__779)
% 55.48/8.25 $i(xv) & $i(xc) & $i(xa) & $i(xR) & ? [v0: $i] : ($i(v0) & sdtmndtasgtdt0(xv,
% 55.48/8.26 xR, xc) & aReductOfIn0(xv, xa, xR) & aElement0(xv) & (xv = xc |
% 55.48/8.26 (sdtmndtplgtdt0(xv, xR, xc) & (aReductOfIn0(xc, xv, xR) |
% 55.48/8.26 (sdtmndtplgtdt0(v0, xR, xc) & aReductOfIn0(v0, xv, xR) &
% 55.48/8.26 aElement0(v0))))))
% 55.48/8.26
% 55.48/8.26 Further assumptions not needed in the proof:
% 55.48/8.26 --------------------------------------------
% 55.48/8.26 mCRDef, mElmSort, mNFRDef, mReduct, mRelSort, mTCDef, mTCRDef, mTCRTrans,
% 55.48/8.26 mTCTrans, mTCbr, mTermNF, mTermin, mWCRDef, mWFOrd, m__656, m__715, m__731_02
% 55.48/8.26
% 55.48/8.26 Those formulas are unsatisfiable:
% 55.48/8.26 ---------------------------------
% 55.48/8.26
% 55.48/8.26 Begin of proof
% 55.48/8.26 |
% 55.48/8.26 | ALPHA: (m__) implies:
% 55.48/8.26 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ sdtmndtasgtdt0(xv, xR, v0) | ~
% 55.48/8.26 | sdtmndtasgtdt0(xu, xR, v0) | ~ aElement0(v0))
% 55.48/8.26 |
% 55.48/8.26 | ALPHA: (m__779) implies:
% 55.48/8.26 | (2) $i(xv)
% 55.48/8.26 | (3) ? [v0: $i] : ($i(v0) & sdtmndtasgtdt0(xv, xR, xc) & aReductOfIn0(xv,
% 55.48/8.26 | xa, xR) & aElement0(xv) & (xv = xc | (sdtmndtplgtdt0(xv, xR, xc) &
% 55.48/8.26 | (aReductOfIn0(xc, xv, xR) | (sdtmndtplgtdt0(v0, xR, xc) &
% 55.48/8.26 | aReductOfIn0(v0, xv, xR) & aElement0(v0))))))
% 55.48/8.26 |
% 55.48/8.26 | ALPHA: (m__755) implies:
% 55.48/8.26 | (4) $i(xu)
% 55.48/8.26 | (5) ? [v0: $i] : ($i(v0) & sdtmndtasgtdt0(xu, xR, xb) & aReductOfIn0(xu,
% 55.48/8.26 | xa, xR) & aElement0(xu) & (xu = xb | (sdtmndtplgtdt0(xu, xR, xb) &
% 55.48/8.26 | (aReductOfIn0(xb, xu, xR) | (sdtmndtplgtdt0(v0, xR, xb) &
% 55.48/8.26 | aReductOfIn0(v0, xu, xR) & aElement0(v0))))))
% 55.48/8.26 |
% 55.85/8.26 | ALPHA: (m__731) implies:
% 55.85/8.26 | (6) aElement0(xa)
% 55.85/8.26 | (7) $i(xa)
% 55.85/8.26 |
% 55.85/8.26 | ALPHA: (m__656_01) implies:
% 55.85/8.26 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 55.85/8.26 | $i(v0) | ~ aReductOfIn0(v2, v0, xR) | ~ aReductOfIn0(v1, v0, xR) |
% 55.85/8.26 | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v3: $i] :
% 55.85/8.26 | ? [v4: $i] : ? [v5: $i] : ($i(v5) & $i(v4) & $i(v3) &
% 55.85/8.26 | sdtmndtasgtdt0(v2, xR, v3) & sdtmndtasgtdt0(v1, xR, v3) &
% 55.85/8.26 | aElement0(v3) & (v3 = v2 | (sdtmndtplgtdt0(v2, xR, v3) &
% 55.85/8.26 | (aReductOfIn0(v3, v2, xR) | (sdtmndtplgtdt0(v4, xR, v3) &
% 55.85/8.26 | aReductOfIn0(v4, v2, xR) & aElement0(v4))))) & (v3 = v1 |
% 55.85/8.26 | (sdtmndtplgtdt0(v1, xR, v3) & (aReductOfIn0(v3, v1, xR) |
% 55.85/8.26 | (sdtmndtplgtdt0(v5, xR, v3) & aReductOfIn0(v5, v1, xR) &
% 55.85/8.26 | aElement0(v5)))))))
% 55.85/8.26 |
% 55.85/8.26 | DELTA: instantiating (5) with fresh symbol all_16_0 gives:
% 55.85/8.26 | (9) $i(all_16_0) & sdtmndtasgtdt0(xu, xR, xb) & aReductOfIn0(xu, xa, xR) &
% 55.85/8.27 | aElement0(xu) & (xu = xb | (sdtmndtplgtdt0(xu, xR, xb) &
% 55.85/8.27 | (aReductOfIn0(xb, xu, xR) | (sdtmndtplgtdt0(all_16_0, xR, xb) &
% 55.85/8.27 | aReductOfIn0(all_16_0, xu, xR) & aElement0(all_16_0)))))
% 55.85/8.27 |
% 55.85/8.27 | ALPHA: (9) implies:
% 55.85/8.27 | (10) aElement0(xu)
% 55.85/8.27 | (11) aReductOfIn0(xu, xa, xR)
% 55.85/8.27 |
% 55.85/8.27 | DELTA: instantiating (3) with fresh symbol all_18_0 gives:
% 55.85/8.27 | (12) $i(all_18_0) & sdtmndtasgtdt0(xv, xR, xc) & aReductOfIn0(xv, xa, xR) &
% 55.85/8.27 | aElement0(xv) & (xv = xc | (sdtmndtplgtdt0(xv, xR, xc) &
% 55.85/8.27 | (aReductOfIn0(xc, xv, xR) | (sdtmndtplgtdt0(all_18_0, xR, xc) &
% 55.85/8.27 | aReductOfIn0(all_18_0, xv, xR) & aElement0(all_18_0)))))
% 55.85/8.27 |
% 55.85/8.27 | ALPHA: (12) implies:
% 55.85/8.27 | (13) aElement0(xv)
% 55.85/8.27 | (14) aReductOfIn0(xv, xa, xR)
% 55.85/8.27 |
% 55.85/8.27 | GROUND_INST: instantiating (8) with xa, xv, xu, simplifying with (2), (4),
% 55.85/8.27 | (6), (7), (10), (11), (13), (14) gives:
% 55.85/8.27 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & $i(v0) &
% 55.85/8.27 | sdtmndtasgtdt0(xv, xR, v0) & sdtmndtasgtdt0(xu, xR, v0) &
% 55.85/8.27 | aElement0(v0) & (v0 = xv | (sdtmndtplgtdt0(xv, xR, v0) &
% 55.85/8.27 | (aReductOfIn0(v0, xv, xR) | (sdtmndtplgtdt0(v2, xR, v0) &
% 55.85/8.27 | aReductOfIn0(v2, xv, xR) & aElement0(v2))))) & (v0 = xu |
% 55.85/8.27 | (sdtmndtplgtdt0(xu, xR, v0) & (aReductOfIn0(v0, xu, xR) |
% 55.85/8.27 | (sdtmndtplgtdt0(v1, xR, v0) & aReductOfIn0(v1, xu, xR) &
% 55.85/8.27 | aElement0(v1))))))
% 55.85/8.27 |
% 55.85/8.27 | DELTA: instantiating (15) with fresh symbols all_78_0, all_78_1, all_78_2
% 55.85/8.27 | gives:
% 55.85/8.27 | (16) $i(all_78_0) & $i(all_78_1) & $i(all_78_2) & sdtmndtasgtdt0(xv, xR,
% 55.85/8.27 | all_78_2) & sdtmndtasgtdt0(xu, xR, all_78_2) & aElement0(all_78_2) &
% 55.85/8.27 | (all_78_2 = xv | (sdtmndtplgtdt0(xv, xR, all_78_2) &
% 55.85/8.27 | (aReductOfIn0(all_78_2, xv, xR) | (sdtmndtplgtdt0(all_78_0, xR,
% 55.85/8.27 | all_78_2) & aReductOfIn0(all_78_0, xv, xR) &
% 55.85/8.27 | aElement0(all_78_0))))) & (all_78_2 = xu | (sdtmndtplgtdt0(xu,
% 55.85/8.27 | xR, all_78_2) & (aReductOfIn0(all_78_2, xu, xR) |
% 55.85/8.27 | (sdtmndtplgtdt0(all_78_1, xR, all_78_2) & aReductOfIn0(all_78_1,
% 55.85/8.27 | xu, xR) & aElement0(all_78_1)))))
% 55.85/8.27 |
% 55.85/8.27 | ALPHA: (16) implies:
% 55.85/8.27 | (17) aElement0(all_78_2)
% 55.85/8.27 | (18) sdtmndtasgtdt0(xu, xR, all_78_2)
% 55.85/8.27 | (19) sdtmndtasgtdt0(xv, xR, all_78_2)
% 55.85/8.27 | (20) $i(all_78_2)
% 55.85/8.27 |
% 55.85/8.27 | GROUND_INST: instantiating (1) with all_78_2, simplifying with (17), (18),
% 55.85/8.27 | (19), (20) gives:
% 55.85/8.27 | (21) $false
% 55.85/8.27 |
% 55.85/8.27 | CLOSE: (21) is inconsistent.
% 55.85/8.27 |
% 55.85/8.27 End of proof
% 55.85/8.27 % SZS output end Proof for theBenchmark
% 55.85/8.27
% 55.85/8.27 7656ms
%------------------------------------------------------------------------------