TSTP Solution File: SYN373+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN373+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 : 600s
% DateTime : Thu Jul 21 05:01:54 EDT 2022
% Result : Theorem 1.96s 1.12s
% Output : Proof 2.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SYN373+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 12 05:55:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.59 ____ _
% 0.19/0.59 ___ / __ \_____(_)___ ________ __________
% 0.19/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic
% 0.19/0.59 (ePrincess v.1.0)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2015
% 0.19/0.59 (c) Peter Backeman, 2014-2015
% 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59 Bug reports to peter@backeman.se
% 0.19/0.59
% 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.17/0.88 Prover 0: Preprocessing ...
% 1.30/0.93 Prover 0: Warning: ignoring some quantifiers
% 1.30/0.94 Prover 0: Constructing countermodel ...
% 1.43/1.02 Prover 0: gave up
% 1.43/1.02 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.43/1.04 Prover 1: Preprocessing ...
% 1.79/1.08 Prover 1: Constructing countermodel ...
% 1.96/1.12 Prover 1: proved (97ms)
% 1.96/1.12
% 1.96/1.12 No countermodel exists, formula is valid
% 1.96/1.12 % SZS status Theorem for theBenchmark
% 1.96/1.12
% 1.96/1.12 Generating proof ... found it (size 20)
% 2.35/1.26
% 2.35/1.26 % SZS output start Proof for theBenchmark
% 2.35/1.26 Assumed formulas after preprocessing and simplification:
% 2.35/1.26 | (0) ? [v0] : ? [v1] : ? [v2] : ( ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (big_p(v5) = v4) | ~ (big_p(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (big_q(v5) = v4) | ~ (big_q(v5) = v3)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (big_p(v3) = v4)) & ! [v3] : ~ (big_q(v3) = 0) & ((v1 = 0 & big_q(v0) = 0) | ( ~ (v1 = 0) & big_p(v0) = v1) | (big_p(v0) = v1 & big_q(v0) = v2 & ( ~ (v1 = 0) | v2 = 0))))
% 2.46/1.30 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 2.46/1.30 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_q(v2) = v1) | ~ (big_q(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : ~ (big_q(v0) = 0) & ((all_0_1_1 = 0 & big_q(all_0_2_2) = 0) | ( ~ (all_0_1_1 = 0) & big_p(all_0_2_2) = all_0_1_1) | (big_p(all_0_2_2) = all_0_1_1 & big_q(all_0_2_2) = all_0_0_0 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)))
% 2.46/1.30 |
% 2.46/1.30 | Applying alpha-rule on (1) yields:
% 2.46/1.30 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0))
% 2.46/1.30 | (3) (all_0_1_1 = 0 & big_q(all_0_2_2) = 0) | ( ~ (all_0_1_1 = 0) & big_p(all_0_2_2) = all_0_1_1) | (big_p(all_0_2_2) = all_0_1_1 & big_q(all_0_2_2) = all_0_0_0 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0))
% 2.46/1.30 | (4) ! [v0] : ~ (big_q(v0) = 0)
% 2.46/1.30 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_q(v2) = v1) | ~ (big_q(v2) = v0))
% 2.46/1.30 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))
% 2.46/1.30 |
% 2.46/1.30 +-Applying beta-rule and splitting (3), into two cases.
% 2.46/1.30 |-Branch one:
% 2.46/1.30 | (7) (all_0_1_1 = 0 & big_q(all_0_2_2) = 0) | ( ~ (all_0_1_1 = 0) & big_p(all_0_2_2) = all_0_1_1)
% 2.46/1.31 |
% 2.46/1.31 +-Applying beta-rule and splitting (7), into two cases.
% 2.46/1.31 |-Branch one:
% 2.46/1.31 | (8) all_0_1_1 = 0 & big_q(all_0_2_2) = 0
% 2.46/1.31 |
% 2.46/1.31 | Applying alpha-rule on (8) yields:
% 2.46/1.31 | (9) all_0_1_1 = 0
% 2.46/1.31 | (10) big_q(all_0_2_2) = 0
% 2.46/1.31 |
% 2.46/1.31 | Instantiating formula (4) with all_0_2_2 and discharging atoms big_q(all_0_2_2) = 0, yields:
% 2.46/1.31 | (11) $false
% 2.46/1.31 |
% 2.46/1.31 |-The branch is then unsatisfiable
% 2.46/1.31 |-Branch two:
% 2.46/1.31 | (12) ~ (all_0_1_1 = 0) & big_p(all_0_2_2) = all_0_1_1
% 2.46/1.31 |
% 2.46/1.31 | Applying alpha-rule on (12) yields:
% 2.46/1.31 | (13) ~ (all_0_1_1 = 0)
% 2.46/1.31 | (14) big_p(all_0_2_2) = all_0_1_1
% 2.46/1.31 |
% 2.46/1.31 | Instantiating formula (6) with all_0_1_1, all_0_2_2 and discharging atoms big_p(all_0_2_2) = all_0_1_1, yields:
% 2.46/1.31 | (9) all_0_1_1 = 0
% 2.46/1.31 |
% 2.46/1.31 | Equations (9) can reduce 13 to:
% 2.46/1.31 | (16) $false
% 2.46/1.31 |
% 2.46/1.31 |-The branch is then unsatisfiable
% 2.46/1.31 |-Branch two:
% 2.46/1.31 | (17) big_p(all_0_2_2) = all_0_1_1 & big_q(all_0_2_2) = all_0_0_0 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)
% 2.46/1.31 |
% 2.46/1.31 | Applying alpha-rule on (17) yields:
% 2.46/1.31 | (14) big_p(all_0_2_2) = all_0_1_1
% 2.46/1.31 | (19) big_q(all_0_2_2) = all_0_0_0
% 2.46/1.31 | (20) ~ (all_0_1_1 = 0) | all_0_0_0 = 0
% 2.46/1.31 |
% 2.46/1.31 | Instantiating formula (6) with all_0_1_1, all_0_2_2 and discharging atoms big_p(all_0_2_2) = all_0_1_1, yields:
% 2.46/1.31 | (9) all_0_1_1 = 0
% 2.46/1.31 |
% 2.46/1.31 | Instantiating formula (4) with all_0_2_2 yields:
% 2.46/1.31 | (22) ~ (big_q(all_0_2_2) = 0)
% 2.46/1.31 |
% 2.46/1.31 +-Applying beta-rule and splitting (20), into two cases.
% 2.46/1.31 |-Branch one:
% 2.46/1.31 | (13) ~ (all_0_1_1 = 0)
% 2.46/1.31 |
% 2.46/1.31 | Equations (9) can reduce 13 to:
% 2.46/1.31 | (16) $false
% 2.46/1.31 |
% 2.46/1.31 |-The branch is then unsatisfiable
% 2.46/1.31 |-Branch two:
% 2.46/1.31 | (9) all_0_1_1 = 0
% 2.46/1.31 | (26) all_0_0_0 = 0
% 2.46/1.31 |
% 2.46/1.31 | From (26) and (19) follows:
% 2.46/1.31 | (10) big_q(all_0_2_2) = 0
% 2.46/1.31 |
% 2.46/1.31 | Using (10) and (22) yields:
% 2.46/1.31 | (11) $false
% 2.46/1.31 |
% 2.46/1.31 |-The branch is then unsatisfiable
% 2.46/1.31 % SZS output end Proof for theBenchmark
% 2.46/1.31
% 2.46/1.31 712ms
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