TSTP Solution File: COM016+4 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM016+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 : n022.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 14.51s 2.90s
% Output : Proof 22.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : COM016+4 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n022.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 12:52:39 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.65 Running up to 7 provers in parallel.
% 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.24/1.31 Prover 1: Preprocessing ...
% 3.24/1.31 Prover 4: Preprocessing ...
% 3.86/1.37 Prover 5: Preprocessing ...
% 3.86/1.37 Prover 0: Preprocessing ...
% 3.86/1.37 Prover 6: Preprocessing ...
% 3.86/1.37 Prover 2: Preprocessing ...
% 3.86/1.37 Prover 3: Preprocessing ...
% 7.24/1.85 Prover 5: Constructing countermodel ...
% 9.49/2.17 Prover 3: Constructing countermodel ...
% 10.11/2.25 Prover 1: Constructing countermodel ...
% 10.59/2.31 Prover 6: Proving ...
% 11.31/2.39 Prover 2: Constructing countermodel ...
% 14.51/2.89 Prover 2: proved (2226ms)
% 14.51/2.89
% 14.51/2.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.51/2.90
% 14.51/2.90 Prover 5: stopped
% 14.51/2.90 Prover 3: stopped
% 14.51/2.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.51/2.90 Prover 6: stopped
% 15.20/2.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.20/2.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.20/2.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.84/3.01 Prover 8: Preprocessing ...
% 15.84/3.01 Prover 10: Preprocessing ...
% 15.84/3.03 Prover 11: Preprocessing ...
% 16.53/3.09 Prover 7: Preprocessing ...
% 17.42/3.28 Prover 10: Constructing countermodel ...
% 17.42/3.29 Prover 8: Warning: ignoring some quantifiers
% 18.15/3.33 Prover 8: Constructing countermodel ...
% 18.15/3.35 Prover 7: Constructing countermodel ...
% 18.15/3.41 Prover 4: Constructing countermodel ...
% 18.15/3.50 Prover 0: Proving ...
% 19.41/3.52 Prover 0: stopped
% 19.41/3.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 19.41/3.58 Prover 13: Preprocessing ...
% 19.41/3.59 Prover 10: Found proof (size 14)
% 19.41/3.59 Prover 10: proved (684ms)
% 19.41/3.59 Prover 7: stopped
% 19.41/3.59 Prover 8: stopped
% 19.41/3.59 Prover 1: stopped
% 19.41/3.59 Prover 4: stopped
% 19.41/3.60 Prover 13: stopped
% 21.68/3.94 Prover 11: Constructing countermodel ...
% 21.68/3.95 Prover 11: stopped
% 21.68/3.96
% 21.68/3.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.68/3.96
% 21.68/3.96 % SZS output start Proof for theBenchmark
% 21.68/3.97 Assumptions after simplification:
% 21.68/3.97 ---------------------------------
% 21.68/3.97
% 21.68/3.97 (m__)
% 21.68/3.98 $i(xb) & $i(xa) & $i(xR) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0)
% 21.68/3.98 | ~ sdtmndtplgtdt0(v1, xR, xb) | ~ aReductOfIn0(v1, v0, xR) | ~
% 21.68/3.98 aReductOfIn0(v0, xa, xR) | ~ aElement0(v1) | ~ aElement0(v0)) & ! [v0:
% 21.68/3.98 $i] : ( ~ $i(v0) | ~ sdtmndtasgtdt0(v0, xR, xb) | ~ aReductOfIn0(v0, xa,
% 21.68/3.98 xR) | ~ aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ sdtmndtplgtdt0(v0,
% 21.68/3.98 xR, xb) | ~ aReductOfIn0(v0, xa, xR) | ~ aElement0(v0)) & ! [v0: $i] :
% 21.68/3.98 ( ~ $i(v0) | ~ aReductOfIn0(v0, xa, xR) | ~ aReductOfIn0(xb, v0, xR) | ~
% 21.68/3.98 aElement0(v0)) & ( ~ aReductOfIn0(xb, xa, xR) | ~ aElement0(xb))
% 21.68/3.98
% 21.68/3.98 (m__731)
% 21.68/3.98 $i(xc) & $i(xb) & $i(xa) & aElement0(xc) & aElement0(xb) & aElement0(xa)
% 21.68/3.98
% 21.68/3.98 (m__731_02)
% 21.68/3.99 $i(xc) & $i(xb) & $i(xa) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ($i(v1) &
% 21.68/3.99 $i(v0) & sdtmndtplgtdt0(xa, xR, xc) & sdtmndtplgtdt0(xa, xR, xb) &
% 21.68/3.99 (aReductOfIn0(xc, xa, xR) | (sdtmndtplgtdt0(v0, xR, xc) & aReductOfIn0(v0,
% 21.68/3.99 xa, xR) & aElement0(v0))) & (aReductOfIn0(xb, xa, xR) |
% 21.68/3.99 (sdtmndtplgtdt0(v1, xR, xb) & aReductOfIn0(v1, xa, xR) & aElement0(v1))))
% 21.68/3.99
% 21.68/3.99 Further assumptions not needed in the proof:
% 21.68/3.99 --------------------------------------------
% 21.68/3.99 mCRDef, mElmSort, mNFRDef, mReduct, mRelSort, mTCDef, mTCRDef, mTCRTrans,
% 21.68/3.99 mTCTrans, mTCbr, mTermNF, mTermin, mWCRDef, mWFOrd, m__656, m__656_01, m__715
% 21.68/3.99
% 21.68/3.99 Those formulas are unsatisfiable:
% 21.68/3.99 ---------------------------------
% 21.68/3.99
% 21.68/3.99 Begin of proof
% 21.68/3.99 |
% 21.68/3.99 | ALPHA: (m__) implies:
% 21.68/3.99 | (1) ~ aReductOfIn0(xb, xa, xR) | ~ aElement0(xb)
% 21.68/3.99 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ sdtmndtplgtdt0(v0, xR, xb) | ~
% 21.68/3.99 | aReductOfIn0(v0, xa, xR) | ~ aElement0(v0))
% 21.68/3.99 |
% 21.68/3.99 | ALPHA: (m__731_02) implies:
% 21.68/4.00 | (3) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & sdtmndtplgtdt0(xa, xR,
% 21.68/4.00 | xc) & sdtmndtplgtdt0(xa, xR, xb) & (aReductOfIn0(xc, xa, xR) |
% 21.68/4.00 | (sdtmndtplgtdt0(v0, xR, xc) & aReductOfIn0(v0, xa, xR) &
% 21.68/4.00 | aElement0(v0))) & (aReductOfIn0(xb, xa, xR) | (sdtmndtplgtdt0(v1,
% 21.68/4.00 | xR, xb) & aReductOfIn0(v1, xa, xR) & aElement0(v1))))
% 21.68/4.00 |
% 21.68/4.00 | ALPHA: (m__731) implies:
% 21.68/4.00 | (4) aElement0(xb)
% 21.68/4.00 |
% 21.68/4.00 | DELTA: instantiating (3) with fresh symbols all_16_0, all_16_1 gives:
% 21.68/4.00 | (5) $i(all_16_0) & $i(all_16_1) & sdtmndtplgtdt0(xa, xR, xc) &
% 21.68/4.00 | sdtmndtplgtdt0(xa, xR, xb) & (aReductOfIn0(xc, xa, xR) |
% 21.68/4.00 | (sdtmndtplgtdt0(all_16_1, xR, xc) & aReductOfIn0(all_16_1, xa, xR) &
% 21.68/4.00 | aElement0(all_16_1))) & (aReductOfIn0(xb, xa, xR) |
% 21.68/4.00 | (sdtmndtplgtdt0(all_16_0, xR, xb) & aReductOfIn0(all_16_0, xa, xR) &
% 21.68/4.00 | aElement0(all_16_0)))
% 21.68/4.00 |
% 21.68/4.00 | ALPHA: (5) implies:
% 21.68/4.00 | (6) $i(all_16_0)
% 21.68/4.00 | (7) aReductOfIn0(xb, xa, xR) | (sdtmndtplgtdt0(all_16_0, xR, xb) &
% 21.68/4.00 | aReductOfIn0(all_16_0, xa, xR) & aElement0(all_16_0))
% 21.68/4.00 |
% 21.68/4.00 | BETA: splitting (1) gives:
% 21.68/4.00 |
% 21.68/4.00 | Case 1:
% 21.68/4.00 | |
% 21.68/4.00 | | (8) ~ aReductOfIn0(xb, xa, xR)
% 21.68/4.00 | |
% 21.68/4.00 | | BETA: splitting (7) gives:
% 21.68/4.00 | |
% 21.68/4.00 | | Case 1:
% 21.68/4.00 | | |
% 21.68/4.00 | | | (9) aReductOfIn0(xb, xa, xR)
% 21.68/4.00 | | |
% 21.68/4.00 | | | PRED_UNIFY: (8), (9) imply:
% 21.68/4.00 | | | (10) $false
% 22.07/4.00 | | |
% 22.07/4.00 | | | CLOSE: (10) is inconsistent.
% 22.07/4.00 | | |
% 22.07/4.00 | | Case 2:
% 22.07/4.00 | | |
% 22.07/4.01 | | | (11) sdtmndtplgtdt0(all_16_0, xR, xb) & aReductOfIn0(all_16_0, xa, xR)
% 22.07/4.01 | | | & aElement0(all_16_0)
% 22.07/4.01 | | |
% 22.07/4.01 | | | ALPHA: (11) implies:
% 22.07/4.01 | | | (12) aElement0(all_16_0)
% 22.07/4.01 | | | (13) aReductOfIn0(all_16_0, xa, xR)
% 22.07/4.01 | | | (14) sdtmndtplgtdt0(all_16_0, xR, xb)
% 22.07/4.01 | | |
% 22.07/4.01 | | | GROUND_INST: instantiating (2) with all_16_0, simplifying with (6), (12),
% 22.07/4.01 | | | (13), (14) gives:
% 22.07/4.01 | | | (15) $false
% 22.07/4.01 | | |
% 22.07/4.01 | | | CLOSE: (15) is inconsistent.
% 22.07/4.01 | | |
% 22.07/4.01 | | End of split
% 22.07/4.01 | |
% 22.07/4.01 | Case 2:
% 22.07/4.01 | |
% 22.07/4.01 | | (16) ~ aElement0(xb)
% 22.07/4.01 | |
% 22.07/4.01 | | PRED_UNIFY: (4), (16) imply:
% 22.07/4.01 | | (17) $false
% 22.07/4.01 | |
% 22.07/4.01 | | CLOSE: (17) is inconsistent.
% 22.07/4.01 | |
% 22.07/4.01 | End of split
% 22.07/4.01 |
% 22.07/4.01 End of proof
% 22.07/4.01 % SZS output end Proof for theBenchmark
% 22.07/4.01
% 22.07/4.01 3377ms
%------------------------------------------------------------------------------