TSTP Solution File: COM017+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM017+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 : n008.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 13.54s 2.61s
% Output : Proof 16.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : COM017+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.37 % Computer : n008.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Tue Aug 29 13:06:32 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.23/0.63 ________ _____
% 0.23/0.63 ___ __ \_________(_)________________________________
% 0.23/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.23/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.23/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.23/0.63
% 0.23/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.23/0.63 (2023-06-19)
% 0.23/0.63
% 0.23/0.63 (c) Philipp Rümmer, 2009-2023
% 0.23/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.23/0.63 Amanda Stjerna.
% 0.23/0.63 Free software under BSD-3-Clause.
% 0.23/0.63
% 0.23/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.23/0.63
% 0.23/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.23/0.65 Running up to 7 provers in parallel.
% 0.23/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.23/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.23/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.23/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.23/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.23/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.23/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.82/1.15 Prover 4: Preprocessing ...
% 2.82/1.16 Prover 1: Preprocessing ...
% 3.12/1.19 Prover 6: Preprocessing ...
% 3.12/1.19 Prover 3: Preprocessing ...
% 3.12/1.19 Prover 5: Preprocessing ...
% 3.12/1.19 Prover 2: Preprocessing ...
% 3.12/1.19 Prover 0: Preprocessing ...
% 5.71/1.55 Prover 2: Constructing countermodel ...
% 5.71/1.56 Prover 5: Constructing countermodel ...
% 6.62/1.67 Prover 6: Proving ...
% 6.62/1.68 Prover 3: Constructing countermodel ...
% 6.62/1.71 Prover 1: Constructing countermodel ...
% 8.88/2.15 Prover 4: Constructing countermodel ...
% 10.46/2.23 Prover 0: Proving ...
% 13.54/2.61 Prover 5: proved (1933ms)
% 13.54/2.61
% 13.54/2.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.54/2.61
% 13.54/2.62 Prover 0: stopped
% 13.54/2.62 Prover 2: stopped
% 13.54/2.65 Prover 6: stopped
% 13.54/2.66 Prover 3: stopped
% 13.54/2.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.54/2.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.54/2.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.54/2.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.54/2.68 Prover 7: Preprocessing ...
% 13.54/2.68 Prover 8: Preprocessing ...
% 13.54/2.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.54/2.71 Prover 7: Constructing countermodel ...
% 13.90/2.78 Prover 10: Preprocessing ...
% 13.90/2.79 Prover 11: Preprocessing ...
% 13.90/2.81 Prover 13: Preprocessing ...
% 13.90/2.81 Prover 10: Constructing countermodel ...
% 15.12/2.84 Prover 8: Warning: ignoring some quantifiers
% 15.12/2.87 Prover 8: Constructing countermodel ...
% 15.12/2.88 Prover 13: Constructing countermodel ...
% 15.71/2.95 Prover 10: Found proof (size 12)
% 15.71/2.95 Prover 10: proved (284ms)
% 15.71/2.96 Prover 4: stopped
% 15.71/2.96 Prover 7: stopped
% 15.71/2.96 Prover 8: stopped
% 15.71/2.96 Prover 13: stopped
% 15.71/2.96 Prover 1: stopped
% 16.12/3.03 Prover 11: Constructing countermodel ...
% 16.12/3.04 Prover 11: stopped
% 16.12/3.04
% 16.12/3.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.12/3.04
% 16.12/3.04 % SZS output start Proof for theBenchmark
% 16.12/3.04 Assumptions after simplification:
% 16.12/3.04 ---------------------------------
% 16.12/3.05
% 16.12/3.05 (mWCRDef)
% 16.12/3.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 16.12/3.05 | ~ $i(v1) | ~ $i(v0) | ~ isLocallyConfluent0(v0) | ~ aReductOfIn0(v3,
% 16.12/3.05 v1, v0) | ~ aReductOfIn0(v2, v1, v0) | ~ aRewritingSystem0(v0) | ~
% 16.12/3.05 aElement0(v3) | ~ aElement0(v2) | ~ aElement0(v1) | ? [v4: $i] : ($i(v4)
% 16.12/3.05 & sdtmndtasgtdt0(v3, v0, v4) & sdtmndtasgtdt0(v2, v0, v4) &
% 16.12/3.06 aElement0(v4))) & ! [v0: $i] : ( ~ $i(v0) | ~ aRewritingSystem0(v0) |
% 16.12/3.06 isLocallyConfluent0(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v3)
% 16.12/3.06 & $i(v2) & $i(v1) & aReductOfIn0(v3, v1, v0) & aReductOfIn0(v2, v1, v0) &
% 16.12/3.06 aElement0(v3) & aElement0(v2) & aElement0(v1) & ! [v4: $i] : ( ~ $i(v4) |
% 16.12/3.06 ~ sdtmndtasgtdt0(v3, v0, v4) | ~ sdtmndtasgtdt0(v2, v0, v4) | ~
% 16.12/3.06 aElement0(v4))))
% 16.12/3.06
% 16.12/3.06 (m__)
% 16.12/3.06 $i(xv) & $i(xu) & $i(xR) & ! [v0: $i] : ( ~ $i(v0) | ~ sdtmndtasgtdt0(xv,
% 16.12/3.06 xR, v0) | ~ sdtmndtasgtdt0(xu, xR, v0) | ~ aElement0(v0))
% 16.12/3.06
% 16.12/3.06 (m__656)
% 16.12/3.06 $i(xR) & aRewritingSystem0(xR)
% 16.12/3.06
% 16.12/3.06 (m__656_01)
% 16.12/3.06 $i(xR) & isTerminating0(xR) & isLocallyConfluent0(xR)
% 16.12/3.06
% 16.12/3.06 (m__731)
% 16.12/3.06 $i(xc) & $i(xb) & $i(xa) & aElement0(xc) & aElement0(xb) & aElement0(xa)
% 16.12/3.06
% 16.12/3.06 (m__755)
% 16.50/3.06 $i(xu) & $i(xb) & $i(xa) & $i(xR) & sdtmndtasgtdt0(xu, xR, xb) &
% 16.50/3.06 aReductOfIn0(xu, xa, xR) & aElement0(xu)
% 16.50/3.06
% 16.50/3.06 (m__779)
% 16.50/3.06 $i(xv) & $i(xc) & $i(xa) & $i(xR) & sdtmndtasgtdt0(xv, xR, xc) &
% 16.50/3.06 aReductOfIn0(xv, xa, xR) & aElement0(xv)
% 16.50/3.06
% 16.50/3.06 Further assumptions not needed in the proof:
% 16.50/3.06 --------------------------------------------
% 16.50/3.06 mCRDef, mElmSort, mNFRDef, mReduct, mRelSort, mTCDef, mTCRDef, mTCRTrans,
% 16.50/3.06 mTCTrans, mTCbr, mTermNF, mTermin, mWFOrd, m__715, m__731_02
% 16.50/3.06
% 16.50/3.06 Those formulas are unsatisfiable:
% 16.50/3.06 ---------------------------------
% 16.50/3.06
% 16.50/3.06 Begin of proof
% 16.50/3.06 |
% 16.50/3.06 | ALPHA: (m__) implies:
% 16.50/3.06 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ sdtmndtasgtdt0(xv, xR, v0) | ~
% 16.50/3.06 | sdtmndtasgtdt0(xu, xR, v0) | ~ aElement0(v0))
% 16.50/3.06 |
% 16.50/3.06 | ALPHA: (m__779) implies:
% 16.50/3.06 | (2) aElement0(xv)
% 16.50/3.06 | (3) aReductOfIn0(xv, xa, xR)
% 16.50/3.06 | (4) $i(xv)
% 16.50/3.06 |
% 16.50/3.06 | ALPHA: (m__755) implies:
% 16.50/3.06 | (5) aElement0(xu)
% 16.50/3.06 | (6) aReductOfIn0(xu, xa, xR)
% 16.50/3.06 | (7) $i(xu)
% 16.50/3.06 |
% 16.50/3.06 | ALPHA: (m__731) implies:
% 16.50/3.07 | (8) aElement0(xa)
% 16.50/3.07 | (9) $i(xa)
% 16.50/3.07 |
% 16.50/3.07 | ALPHA: (m__656_01) implies:
% 16.50/3.07 | (10) isLocallyConfluent0(xR)
% 16.50/3.07 |
% 16.50/3.07 | ALPHA: (m__656) implies:
% 16.50/3.07 | (11) aRewritingSystem0(xR)
% 16.50/3.07 | (12) $i(xR)
% 16.50/3.07 |
% 16.50/3.07 | ALPHA: (mWCRDef) implies:
% 16.50/3.07 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) |
% 16.50/3.07 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ isLocallyConfluent0(v0) | ~
% 16.50/3.07 | aReductOfIn0(v3, v1, v0) | ~ aReductOfIn0(v2, v1, v0) | ~
% 16.50/3.07 | aRewritingSystem0(v0) | ~ aElement0(v3) | ~ aElement0(v2) | ~
% 16.50/3.07 | aElement0(v1) | ? [v4: $i] : ($i(v4) & sdtmndtasgtdt0(v3, v0, v4) &
% 16.50/3.07 | sdtmndtasgtdt0(v2, v0, v4) & aElement0(v4)))
% 16.50/3.07 |
% 16.50/3.07 | GROUND_INST: instantiating (13) with xR, xa, xu, xv, simplifying with (2),
% 16.50/3.07 | (3), (4), (5), (6), (7), (8), (9), (10), (11), (12) gives:
% 16.50/3.07 | (14) ? [v0: $i] : ($i(v0) & sdtmndtasgtdt0(xv, xR, v0) &
% 16.50/3.07 | sdtmndtasgtdt0(xu, xR, v0) & aElement0(v0))
% 16.50/3.07 |
% 16.50/3.07 | DELTA: instantiating (14) with fresh symbol all_35_0 gives:
% 16.50/3.07 | (15) $i(all_35_0) & sdtmndtasgtdt0(xv, xR, all_35_0) & sdtmndtasgtdt0(xu,
% 16.50/3.07 | xR, all_35_0) & aElement0(all_35_0)
% 16.50/3.07 |
% 16.50/3.07 | ALPHA: (15) implies:
% 16.50/3.07 | (16) aElement0(all_35_0)
% 16.50/3.07 | (17) sdtmndtasgtdt0(xu, xR, all_35_0)
% 16.50/3.07 | (18) sdtmndtasgtdt0(xv, xR, all_35_0)
% 16.50/3.07 | (19) $i(all_35_0)
% 16.50/3.07 |
% 16.50/3.07 | GROUND_INST: instantiating (1) with all_35_0, simplifying with (16), (17),
% 16.50/3.07 | (18), (19) gives:
% 16.50/3.07 | (20) $false
% 16.50/3.07 |
% 16.50/3.07 | CLOSE: (20) is inconsistent.
% 16.50/3.07 |
% 16.50/3.07 End of proof
% 16.50/3.07 % SZS output end Proof for theBenchmark
% 16.50/3.07
% 16.50/3.07 2441ms
%------------------------------------------------------------------------------