TSTP Solution File: COM023+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM023+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 : 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 : Wed Aug 30 18:44:18 EDT 2023
% Result : Theorem 12.68s 2.47s
% Output : Proof 15.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : COM023+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.12 % 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 : Tue Aug 29 13:30:55 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.57/0.59 ________ _____
% 0.57/0.60 ___ __ \_________(_)________________________________
% 0.57/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.57/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.57/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.57/0.60
% 0.57/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.57/0.60 (2023-06-19)
% 0.57/0.60
% 0.57/0.60 (c) Philipp Rümmer, 2009-2023
% 0.57/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.57/0.60 Amanda Stjerna.
% 0.57/0.60 Free software under BSD-3-Clause.
% 0.57/0.60
% 0.57/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.57/0.60
% 0.57/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.62/0.61 Running up to 7 provers in parallel.
% 0.62/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.62/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.62/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.62/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.62/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.62/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.62/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.57/1.09 Prover 1: Preprocessing ...
% 2.98/1.10 Prover 4: Preprocessing ...
% 2.98/1.13 Prover 5: Preprocessing ...
% 2.98/1.13 Prover 6: Preprocessing ...
% 2.98/1.13 Prover 0: Preprocessing ...
% 2.98/1.13 Prover 3: Preprocessing ...
% 2.98/1.13 Prover 2: Preprocessing ...
% 5.65/1.47 Prover 5: Constructing countermodel ...
% 5.65/1.48 Prover 2: Constructing countermodel ...
% 6.09/1.55 Prover 1: Constructing countermodel ...
% 6.09/1.56 Prover 3: Constructing countermodel ...
% 6.09/1.58 Prover 6: Proving ...
% 8.86/1.95 Prover 4: Constructing countermodel ...
% 10.46/2.13 Prover 0: Proving ...
% 12.68/2.46 Prover 3: proved (1847ms)
% 12.68/2.47
% 12.68/2.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.68/2.47
% 12.68/2.47 Prover 2: stopped
% 12.68/2.47 Prover 5: stopped
% 12.68/2.48 Prover 0: stopped
% 12.68/2.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.68/2.48 Prover 6: stopped
% 12.68/2.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.68/2.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.68/2.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.68/2.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.68/2.50 Prover 7: Preprocessing ...
% 13.42/2.53 Prover 7: Constructing countermodel ...
% 13.42/2.54 Prover 13: Preprocessing ...
% 13.42/2.54 Prover 10: Preprocessing ...
% 13.42/2.54 Prover 11: Preprocessing ...
% 13.42/2.57 Prover 8: Preprocessing ...
% 13.42/2.58 Prover 10: Constructing countermodel ...
% 14.07/2.60 Prover 13: Constructing countermodel ...
% 14.88/2.70 Prover 8: Warning: ignoring some quantifiers
% 14.88/2.72 Prover 8: Constructing countermodel ...
% 15.03/2.75 Prover 13: Found proof (size 12)
% 15.03/2.75 Prover 13: proved (259ms)
% 15.03/2.75 Prover 7: stopped
% 15.03/2.75 Prover 4: stopped
% 15.03/2.75 Prover 8: stopped
% 15.03/2.75 Prover 1: stopped
% 15.03/2.76 Prover 10: stopped
% 15.59/2.84 Prover 11: Constructing countermodel ...
% 15.59/2.85 Prover 11: stopped
% 15.59/2.85
% 15.59/2.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.59/2.85
% 15.59/2.85 % SZS output start Proof for theBenchmark
% 15.59/2.85 Assumptions after simplification:
% 15.59/2.85 ---------------------------------
% 15.59/2.85
% 15.59/2.85 (mCRDef)
% 15.59/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 15.59/2.86 | ~ $i(v1) | ~ $i(v0) | ~ isConfluent0(v0) | ~ sdtmndtasgtdt0(v1, v0,
% 15.59/2.86 v3) | ~ sdtmndtasgtdt0(v1, v0, v2) | ~ aRewritingSystem0(v0) | ~
% 15.59/2.86 aElement0(v3) | ~ aElement0(v2) | ~ aElement0(v1) | ? [v4: $i] : ($i(v4)
% 15.59/2.86 & sdtmndtasgtdt0(v3, v0, v4) & sdtmndtasgtdt0(v2, v0, v4) &
% 15.59/2.86 aElement0(v4))) & ! [v0: $i] : ( ~ $i(v0) | ~ aRewritingSystem0(v0) |
% 15.59/2.86 isConfluent0(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v3) &
% 15.59/2.86 $i(v2) & $i(v1) & sdtmndtasgtdt0(v1, v0, v3) & sdtmndtasgtdt0(v1, v0, v2)
% 15.59/2.86 & aElement0(v3) & aElement0(v2) & aElement0(v1) & ! [v4: $i] : ( ~ $i(v4)
% 15.59/2.86 | ~ sdtmndtasgtdt0(v3, v0, v4) | ~ sdtmndtasgtdt0(v2, v0, v4) | ~
% 15.59/2.86 aElement0(v4))))
% 15.59/2.86
% 15.59/2.86 (m__)
% 15.59/2.86 $i(xR) & ~ isConfluent0(xR)
% 15.59/2.86
% 15.59/2.86 (m__656)
% 15.59/2.86 $i(xR) & aRewritingSystem0(xR)
% 15.59/2.86
% 15.59/2.86 (m__715)
% 15.59/2.86 $i(xR) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 15.59/2.86 $i(v0) | ~ sdtmndtasgtdt0(v0, xR, v2) | ~ sdtmndtasgtdt0(v0, xR, v1) | ~
% 15.59/2.86 aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v3: $i] : ($i(v3)
% 15.59/2.86 & sdtmndtasgtdt0(v2, xR, v3) & sdtmndtasgtdt0(v1, xR, v3) &
% 15.59/2.86 aElement0(v3)))
% 15.59/2.86
% 15.59/2.86 Further assumptions not needed in the proof:
% 15.59/2.86 --------------------------------------------
% 15.59/2.86 mElmSort, mNFRDef, mReduct, mRelSort, mTCDef, mTCRDef, mTCRTrans, mTCTrans,
% 15.59/2.86 mTCbr, mTermNF, mTermin, mWCRDef, mWFOrd, m__656_01
% 15.59/2.86
% 15.59/2.86 Those formulas are unsatisfiable:
% 15.59/2.86 ---------------------------------
% 15.59/2.86
% 15.59/2.86 Begin of proof
% 15.59/2.86 |
% 15.59/2.86 | ALPHA: (m__) implies:
% 15.59/2.87 | (1) ~ isConfluent0(xR)
% 15.59/2.87 |
% 15.59/2.87 | ALPHA: (m__715) implies:
% 15.59/2.87 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 15.59/2.87 | $i(v0) | ~ sdtmndtasgtdt0(v0, xR, v2) | ~ sdtmndtasgtdt0(v0, xR,
% 15.59/2.87 | v1) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ?
% 15.59/2.87 | [v3: $i] : ($i(v3) & sdtmndtasgtdt0(v2, xR, v3) & sdtmndtasgtdt0(v1,
% 15.59/2.87 | xR, v3) & aElement0(v3)))
% 15.59/2.87 |
% 15.59/2.87 | ALPHA: (m__656) implies:
% 15.59/2.87 | (3) aRewritingSystem0(xR)
% 15.59/2.87 | (4) $i(xR)
% 15.59/2.87 |
% 15.59/2.87 | ALPHA: (mCRDef) implies:
% 15.59/2.87 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ aRewritingSystem0(v0) | isConfluent0(v0)
% 15.59/2.87 | | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v3) & $i(v2) & $i(v1)
% 15.59/2.87 | & sdtmndtasgtdt0(v1, v0, v3) & sdtmndtasgtdt0(v1, v0, v2) &
% 15.59/2.87 | aElement0(v3) & aElement0(v2) & aElement0(v1) & ! [v4: $i] : ( ~
% 15.59/2.87 | $i(v4) | ~ sdtmndtasgtdt0(v3, v0, v4) | ~ sdtmndtasgtdt0(v2,
% 15.59/2.87 | v0, v4) | ~ aElement0(v4))))
% 15.59/2.87 |
% 15.59/2.87 | GROUND_INST: instantiating (5) with xR, simplifying with (1), (3), (4) gives:
% 15.59/2.87 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & $i(v0) &
% 15.59/2.87 | sdtmndtasgtdt0(v0, xR, v2) & sdtmndtasgtdt0(v0, xR, v1) &
% 15.59/2.87 | aElement0(v2) & aElement0(v1) & aElement0(v0) & ! [v3: $i] : ( ~
% 15.59/2.87 | $i(v3) | ~ sdtmndtasgtdt0(v2, xR, v3) | ~ sdtmndtasgtdt0(v1, xR,
% 15.59/2.87 | v3) | ~ aElement0(v3)))
% 15.59/2.87 |
% 15.59/2.87 | DELTA: instantiating (6) with fresh symbols all_19_0, all_19_1, all_19_2
% 15.59/2.87 | gives:
% 15.59/2.87 | (7) $i(all_19_0) & $i(all_19_1) & $i(all_19_2) & sdtmndtasgtdt0(all_19_2,
% 15.59/2.87 | xR, all_19_0) & sdtmndtasgtdt0(all_19_2, xR, all_19_1) &
% 15.59/2.87 | aElement0(all_19_0) & aElement0(all_19_1) & aElement0(all_19_2) & !
% 15.59/2.87 | [v0: $i] : ( ~ $i(v0) | ~ sdtmndtasgtdt0(all_19_0, xR, v0) | ~
% 15.59/2.87 | sdtmndtasgtdt0(all_19_1, xR, v0) | ~ aElement0(v0))
% 15.59/2.87 |
% 15.59/2.87 | ALPHA: (7) implies:
% 15.59/2.87 | (8) aElement0(all_19_2)
% 15.59/2.87 | (9) aElement0(all_19_1)
% 15.59/2.87 | (10) aElement0(all_19_0)
% 15.59/2.87 | (11) sdtmndtasgtdt0(all_19_2, xR, all_19_1)
% 15.59/2.87 | (12) sdtmndtasgtdt0(all_19_2, xR, all_19_0)
% 15.59/2.87 | (13) $i(all_19_2)
% 15.59/2.87 | (14) $i(all_19_1)
% 15.59/2.87 | (15) $i(all_19_0)
% 15.59/2.87 | (16) ! [v0: $i] : ( ~ $i(v0) | ~ sdtmndtasgtdt0(all_19_0, xR, v0) | ~
% 15.59/2.87 | sdtmndtasgtdt0(all_19_1, xR, v0) | ~ aElement0(v0))
% 15.59/2.87 |
% 15.59/2.88 | GROUND_INST: instantiating (2) with all_19_2, all_19_1, all_19_0, simplifying
% 15.59/2.88 | with (8), (9), (10), (11), (12), (13), (14), (15) gives:
% 15.59/2.88 | (17) ? [v0: $i] : ($i(v0) & sdtmndtasgtdt0(all_19_0, xR, v0) &
% 15.59/2.88 | sdtmndtasgtdt0(all_19_1, xR, v0) & aElement0(v0))
% 15.59/2.88 |
% 15.59/2.88 | DELTA: instantiating (17) with fresh symbol all_38_0 gives:
% 15.59/2.88 | (18) $i(all_38_0) & sdtmndtasgtdt0(all_19_0, xR, all_38_0) &
% 15.59/2.88 | sdtmndtasgtdt0(all_19_1, xR, all_38_0) & aElement0(all_38_0)
% 15.59/2.88 |
% 15.59/2.88 | ALPHA: (18) implies:
% 15.59/2.88 | (19) aElement0(all_38_0)
% 15.59/2.88 | (20) sdtmndtasgtdt0(all_19_1, xR, all_38_0)
% 15.59/2.88 | (21) sdtmndtasgtdt0(all_19_0, xR, all_38_0)
% 15.59/2.88 | (22) $i(all_38_0)
% 15.59/2.88 |
% 15.59/2.88 | GROUND_INST: instantiating (16) with all_38_0, simplifying with (19), (20),
% 15.59/2.88 | (21), (22) gives:
% 15.59/2.88 | (23) $false
% 15.59/2.88 |
% 15.59/2.88 | CLOSE: (23) is inconsistent.
% 15.59/2.88 |
% 15.59/2.88 End of proof
% 15.59/2.88 % SZS output end Proof for theBenchmark
% 15.59/2.88
% 15.59/2.88 2282ms
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