TSTP Solution File: COM018+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM018+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 : n032.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 18:44:17 EDT 2023
% Result : Theorem 51.80s 7.51s
% Output : Proof 58.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : COM018+4 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.31 % Computer : n032.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Aug 29 13:00:31 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.53 ________ _____
% 0.16/0.53 ___ __ \_________(_)________________________________
% 0.16/0.53 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.53 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.53 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.53
% 0.16/0.53 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.53 (2023-06-19)
% 0.16/0.53
% 0.16/0.53 (c) Philipp Rümmer, 2009-2023
% 0.16/0.53 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.53 Amanda Stjerna.
% 0.16/0.53 Free software under BSD-3-Clause.
% 0.16/0.53
% 0.16/0.53 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.53
% 0.16/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.55 Running up to 7 provers in parallel.
% 0.16/0.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.56 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.56 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.09/1.08 Prover 4: Preprocessing ...
% 3.09/1.08 Prover 1: Preprocessing ...
% 3.46/1.12 Prover 3: Preprocessing ...
% 3.46/1.12 Prover 0: Preprocessing ...
% 3.46/1.12 Prover 6: Preprocessing ...
% 3.46/1.12 Prover 5: Preprocessing ...
% 3.46/1.12 Prover 2: Preprocessing ...
% 5.97/1.51 Prover 5: Constructing countermodel ...
% 8.16/1.78 Prover 1: Constructing countermodel ...
% 8.69/1.82 Prover 3: Constructing countermodel ...
% 8.69/1.87 Prover 6: Proving ...
% 8.69/1.92 Prover 2: Constructing countermodel ...
% 14.75/2.66 Prover 4: Constructing countermodel ...
% 15.36/2.73 Prover 0: Proving ...
% 51.80/7.51 Prover 3: proved (6954ms)
% 51.80/7.51
% 51.80/7.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 51.80/7.51
% 51.80/7.51 Prover 5: stopped
% 51.80/7.51 Prover 2: stopped
% 51.80/7.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 51.80/7.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 51.80/7.51 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 52.40/7.52 Prover 6: stopped
% 52.40/7.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 52.88/7.63 Prover 0: stopped
% 52.88/7.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 52.88/7.64 Prover 8: Preprocessing ...
% 53.50/7.70 Prover 10: Preprocessing ...
% 53.50/7.70 Prover 7: Preprocessing ...
% 53.50/7.70 Prover 11: Preprocessing ...
% 53.50/7.73 Prover 8: Warning: ignoring some quantifiers
% 53.50/7.75 Prover 8: Constructing countermodel ...
% 53.50/7.75 Prover 13: Preprocessing ...
% 54.58/7.82 Prover 10: Constructing countermodel ...
% 54.73/7.85 Prover 7: Constructing countermodel ...
% 54.73/7.90 Prover 13: Constructing countermodel ...
% 58.37/8.29 Prover 11: Constructing countermodel ...
% 58.37/8.35 Prover 13: Found proof (size 12)
% 58.37/8.35 Prover 13: proved (713ms)
% 58.37/8.35 Prover 10: stopped
% 58.37/8.35 Prover 11: stopped
% 58.37/8.35 Prover 1: stopped
% 58.37/8.35 Prover 7: stopped
% 58.37/8.35 Prover 4: stopped
% 58.37/8.37 Prover 8: stopped
% 58.37/8.37
% 58.37/8.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 58.37/8.37
% 58.37/8.37 % SZS output start Proof for theBenchmark
% 58.37/8.38 Assumptions after simplification:
% 58.37/8.38 ---------------------------------
% 58.37/8.38
% 58.37/8.38 (mTermNF)
% 58.37/8.38 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ isTerminating0(v0) |
% 58.37/8.38 ~ aRewritingSystem0(v0) | ~ aElement0(v1) | ? [v2: $i] : ($i(v2) &
% 58.37/8.38 aNormalFormOfIn0(v2, v1, v0)))
% 58.37/8.38
% 58.37/8.38 (m__)
% 58.37/8.39 $i(xw) & $i(xR) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 58.37/8.39 sdtmndtplgtdt0(v1, xR, v0) | ~ aReductOfIn0(v1, xw, xR) | ~ aElement0(v1)
% 58.37/8.39 | ~ aElement0(v0) | ? [v2: $i] : ($i(v2) & aReductOfIn0(v2, v0, xR))) & !
% 58.37/8.39 [v0: $i] : ( ~ $i(v0) | ~ aNormalFormOfIn0(v0, xw, xR)) & ! [v0: $i] : ( ~
% 58.37/8.39 $i(v0) | ~ sdtmndtasgtdt0(xw, xR, v0) | ~ aElement0(v0) | ? [v1: $i] :
% 58.37/8.39 ($i(v1) & aReductOfIn0(v1, v0, xR))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 58.37/8.39 sdtmndtplgtdt0(xw, xR, v0) | ~ aElement0(v0) | ? [v1: $i] : ($i(v1) &
% 58.37/8.39 aReductOfIn0(v1, v0, xR))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 58.37/8.39 aReductOfIn0(v0, xw, xR) | ~ aElement0(v0) | ? [v1: $i] : ($i(v1) &
% 58.37/8.39 aReductOfIn0(v1, v0, xR))) & ( ~ aElement0(xw) | ? [v0: $i] : ($i(v0) &
% 58.37/8.39 aReductOfIn0(v0, xw, xR)))
% 58.37/8.39
% 58.37/8.39 (m__656)
% 58.37/8.39 $i(xR) & aRewritingSystem0(xR)
% 58.37/8.39
% 58.37/8.39 (m__656_01)
% 58.37/8.39 $i(xR) & isTerminating0(xR) & isLocallyConfluent0(xR) & ! [v0: $i] : ! [v1:
% 58.37/8.39 $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 58.37/8.39 sdtmndtplgtdt0(v2, xR, v1) | ~ aReductOfIn0(v2, v0, xR) | ~ aElement0(v2)
% 58.37/8.39 | ~ aElement0(v1) | ~ aElement0(v0) | iLess0(v1, v0)) & ! [v0: $i] : !
% 58.37/8.39 [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 58.37/8.39 aReductOfIn0(v2, v0, xR) | ~ aReductOfIn0(v1, v0, xR) | ~ aElement0(v2) |
% 58.37/8.39 ~ aElement0(v1) | ~ aElement0(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i]
% 58.37/8.39 : ($i(v5) & $i(v4) & $i(v3) & sdtmndtasgtdt0(v2, xR, v3) &
% 58.37/8.39 sdtmndtasgtdt0(v1, xR, v3) & aElement0(v3) & (v3 = v2 |
% 58.37/8.39 (sdtmndtplgtdt0(v2, xR, v3) & (aReductOfIn0(v3, v2, xR) |
% 58.37/8.39 (sdtmndtplgtdt0(v4, xR, v3) & aReductOfIn0(v4, v2, xR) &
% 58.37/8.39 aElement0(v4))))) & (v3 = v1 | (sdtmndtplgtdt0(v1, xR, v3) &
% 58.37/8.39 (aReductOfIn0(v3, v1, xR) | (sdtmndtplgtdt0(v5, xR, v3) &
% 58.37/8.39 aReductOfIn0(v5, v1, xR) & aElement0(v5))))))) & ! [v0: $i] : !
% 58.37/8.39 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtmndtplgtdt0(v0, xR, v1) | ~
% 58.37/8.39 aElement0(v1) | ~ aElement0(v0) | iLess0(v1, v0)) & ! [v0: $i] : ! [v1:
% 58.37/8.39 $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aReductOfIn0(v1, v0, xR) | ~
% 58.37/8.39 aElement0(v1) | ~ aElement0(v0) | iLess0(v1, v0))
% 58.37/8.39
% 58.37/8.39 (m__799)
% 58.37/8.39 $i(xw) & $i(xv) & $i(xu) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ($i(v1) &
% 58.37/8.39 $i(v0) & sdtmndtasgtdt0(xv, xR, xw) & sdtmndtasgtdt0(xu, xR, xw) &
% 58.37/8.39 aElement0(xw) & (xw = xv | (sdtmndtplgtdt0(xv, xR, xw) & (aReductOfIn0(xw,
% 58.37/8.39 xv, xR) | (sdtmndtplgtdt0(v0, xR, xw) & aReductOfIn0(v0, xv, xR) &
% 58.37/8.39 aElement0(v0))))) & (xw = xu | (sdtmndtplgtdt0(xu, xR, xw) &
% 58.37/8.39 (aReductOfIn0(xw, xu, xR) | (sdtmndtplgtdt0(v1, xR, xw) &
% 58.37/8.39 aReductOfIn0(v1, xu, xR) & aElement0(v1))))))
% 58.37/8.39
% 58.37/8.39 Further assumptions not needed in the proof:
% 58.37/8.39 --------------------------------------------
% 58.37/8.39 mCRDef, mElmSort, mNFRDef, mReduct, mRelSort, mTCDef, mTCRDef, mTCRTrans,
% 58.37/8.39 mTCTrans, mTCbr, mTermin, mWCRDef, mWFOrd, m__715, m__731, m__731_02, m__755,
% 58.37/8.39 m__779
% 58.37/8.39
% 58.37/8.39 Those formulas are unsatisfiable:
% 58.37/8.39 ---------------------------------
% 58.37/8.39
% 58.37/8.39 Begin of proof
% 58.37/8.40 |
% 58.37/8.40 | ALPHA: (m__) implies:
% 58.37/8.40 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ aNormalFormOfIn0(v0, xw, xR))
% 58.37/8.40 |
% 58.37/8.40 | ALPHA: (m__799) implies:
% 58.37/8.40 | (2) $i(xw)
% 58.37/8.40 | (3) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & sdtmndtasgtdt0(xv, xR,
% 58.37/8.40 | xw) & sdtmndtasgtdt0(xu, xR, xw) & aElement0(xw) & (xw = xv |
% 58.37/8.40 | (sdtmndtplgtdt0(xv, xR, xw) & (aReductOfIn0(xw, xv, xR) |
% 58.37/8.40 | (sdtmndtplgtdt0(v0, xR, xw) & aReductOfIn0(v0, xv, xR) &
% 58.37/8.40 | aElement0(v0))))) & (xw = xu | (sdtmndtplgtdt0(xu, xR, xw) &
% 58.37/8.40 | (aReductOfIn0(xw, xu, xR) | (sdtmndtplgtdt0(v1, xR, xw) &
% 58.37/8.40 | aReductOfIn0(v1, xu, xR) & aElement0(v1))))))
% 58.37/8.40 |
% 58.37/8.40 | ALPHA: (m__656_01) implies:
% 58.37/8.40 | (4) isTerminating0(xR)
% 58.37/8.40 |
% 58.37/8.40 | ALPHA: (m__656) implies:
% 58.37/8.40 | (5) aRewritingSystem0(xR)
% 58.37/8.40 | (6) $i(xR)
% 58.37/8.40 |
% 58.37/8.40 | DELTA: instantiating (3) with fresh symbols all_22_0, all_22_1 gives:
% 58.37/8.40 | (7) $i(all_22_0) & $i(all_22_1) & sdtmndtasgtdt0(xv, xR, xw) &
% 58.37/8.40 | sdtmndtasgtdt0(xu, xR, xw) & aElement0(xw) & (xw = xv |
% 58.37/8.40 | (sdtmndtplgtdt0(xv, xR, xw) & (aReductOfIn0(xw, xv, xR) |
% 58.37/8.40 | (sdtmndtplgtdt0(all_22_1, xR, xw) & aReductOfIn0(all_22_1, xv,
% 58.37/8.40 | xR) & aElement0(all_22_1))))) & (xw = xu |
% 58.37/8.40 | (sdtmndtplgtdt0(xu, xR, xw) & (aReductOfIn0(xw, xu, xR) |
% 58.37/8.40 | (sdtmndtplgtdt0(all_22_0, xR, xw) & aReductOfIn0(all_22_0, xu,
% 58.37/8.40 | xR) & aElement0(all_22_0)))))
% 58.37/8.40 |
% 58.37/8.40 | ALPHA: (7) implies:
% 58.37/8.40 | (8) aElement0(xw)
% 58.37/8.40 |
% 58.37/8.40 | GROUND_INST: instantiating (mTermNF) with xR, xw, simplifying with (2), (4),
% 58.37/8.40 | (5), (6), (8) gives:
% 58.37/8.40 | (9) ? [v0: $i] : ($i(v0) & aNormalFormOfIn0(v0, xw, xR))
% 58.37/8.40 |
% 58.37/8.40 | DELTA: instantiating (9) with fresh symbol all_42_0 gives:
% 58.37/8.40 | (10) $i(all_42_0) & aNormalFormOfIn0(all_42_0, xw, xR)
% 58.37/8.40 |
% 58.37/8.40 | ALPHA: (10) implies:
% 58.37/8.40 | (11) aNormalFormOfIn0(all_42_0, xw, xR)
% 58.37/8.40 | (12) $i(all_42_0)
% 58.37/8.40 |
% 58.37/8.40 | GROUND_INST: instantiating (1) with all_42_0, simplifying with (11), (12)
% 58.37/8.40 | gives:
% 58.37/8.40 | (13) $false
% 58.37/8.41 |
% 58.37/8.41 | CLOSE: (13) is inconsistent.
% 58.37/8.41 |
% 58.37/8.41 End of proof
% 58.37/8.41 % SZS output end Proof for theBenchmark
% 58.37/8.41
% 58.37/8.41 7871ms
%------------------------------------------------------------------------------