TSTP Solution File: SYN415+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN415+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%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 : 600s
% DateTime : Thu Jul 21 05:02:14 EDT 2022
% Result : Theorem 1.56s 1.09s
% Output : Proof 2.24s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN415+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%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 : 600
% 0.12/0.33 % DateTime : Tue Jul 12 04:40:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.58/0.60 ____ _
% 0.58/0.60 ___ / __ \_____(_)___ ________ __________
% 0.58/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.60
% 0.58/0.60 A Theorem Prover for First-Order Logic
% 0.64/0.60 (ePrincess v.1.0)
% 0.64/0.60
% 0.64/0.60 (c) Philipp Rümmer, 2009-2015
% 0.64/0.60 (c) Peter Backeman, 2014-2015
% 0.64/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.64/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.64/0.60 Bug reports to peter@backeman.se
% 0.64/0.60
% 0.64/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.64/0.60
% 0.64/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.32/0.92 Prover 0: Preprocessing ...
% 1.37/0.99 Prover 0: Constructing countermodel ...
% 1.56/1.09 Prover 0: proved (410ms)
% 1.56/1.09
% 1.56/1.09 No countermodel exists, formula is valid
% 1.56/1.09 % SZS status Theorem for theBenchmark
% 1.56/1.09
% 1.56/1.09 Generating proof ... found it (size 20)
% 2.24/1.23
% 2.24/1.23 % SZS output start Proof for theBenchmark
% 2.24/1.23 Assumed formulas after preprocessing and simplification:
% 2.24/1.23 | (0) ? [v0] : ? [v1] : ? [v2] : ((f(v2) & ! [v3] : (v3 = v2 | ~ f(v3)) & ( ! [v3] : ~ f(v3) | ( ~ (v1 = v0) & f(v1) & f(v0)))) | (f(v0) & ! [v3] : ! [v4] : (v4 = v3 | ~ f(v4) | ~ f(v3)) & ! [v3] : ( ~ f(v3) | ? [v4] : ( ~ (v4 = v3) & f(v4)))))
% 2.24/1.23 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 2.24/1.23 | (1) (f(all_0_0_0) & ! [v0] : (v0 = all_0_0_0 | ~ f(v0)) & ( ! [v0] : ~ f(v0) | ( ~ (all_0_1_1 = all_0_2_2) & f(all_0_1_1) & f(all_0_2_2)))) | (f(all_0_2_2) & ! [v0] : ! [v1] : (v1 = v0 | ~ f(v1) | ~ f(v0)) & ! [v0] : ( ~ f(v0) | ? [v1] : ( ~ (v1 = v0) & f(v1))))
% 2.24/1.24 |
% 2.24/1.24 +-Applying beta-rule and splitting (1), into two cases.
% 2.24/1.24 |-Branch one:
% 2.24/1.24 | (2) f(all_0_0_0) & ! [v0] : (v0 = all_0_0_0 | ~ f(v0)) & ( ! [v0] : ~ f(v0) | ( ~ (all_0_1_1 = all_0_2_2) & f(all_0_1_1) & f(all_0_2_2)))
% 2.24/1.24 |
% 2.24/1.24 | Applying alpha-rule on (2) yields:
% 2.24/1.24 | (3) f(all_0_0_0)
% 2.24/1.24 | (4) ! [v0] : (v0 = all_0_0_0 | ~ f(v0))
% 2.24/1.24 | (5) ! [v0] : ~ f(v0) | ( ~ (all_0_1_1 = all_0_2_2) & f(all_0_1_1) & f(all_0_2_2))
% 2.24/1.24 |
% 2.24/1.24 +-Applying beta-rule and splitting (5), into two cases.
% 2.24/1.24 |-Branch one:
% 2.24/1.24 | (6) ! [v0] : ~ f(v0)
% 2.24/1.24 |
% 2.24/1.24 | Instantiating formula (6) with all_0_0_0 and discharging atoms f(all_0_0_0), yields:
% 2.24/1.24 | (7) $false
% 2.24/1.24 |
% 2.24/1.24 |-The branch is then unsatisfiable
% 2.24/1.24 |-Branch two:
% 2.24/1.24 | (8) ~ (all_0_1_1 = all_0_2_2) & f(all_0_1_1) & f(all_0_2_2)
% 2.24/1.24 |
% 2.24/1.24 | Applying alpha-rule on (8) yields:
% 2.24/1.24 | (9) ~ (all_0_1_1 = all_0_2_2)
% 2.24/1.24 | (10) f(all_0_1_1)
% 2.24/1.24 | (11) f(all_0_2_2)
% 2.24/1.24 |
% 2.24/1.24 | Instantiating formula (4) with all_0_1_1 and discharging atoms f(all_0_1_1), yields:
% 2.24/1.24 | (12) all_0_0_0 = all_0_1_1
% 2.24/1.24 |
% 2.24/1.24 | Instantiating formula (4) with all_0_2_2 and discharging atoms f(all_0_2_2), yields:
% 2.24/1.24 | (13) all_0_0_0 = all_0_2_2
% 2.24/1.24 |
% 2.24/1.24 | Combining equations (12,13) yields a new equation:
% 2.24/1.24 | (14) all_0_1_1 = all_0_2_2
% 2.24/1.24 |
% 2.24/1.24 | Simplifying 14 yields:
% 2.24/1.24 | (15) all_0_1_1 = all_0_2_2
% 2.24/1.24 |
% 2.24/1.24 | Equations (15) can reduce 9 to:
% 2.24/1.24 | (16) $false
% 2.24/1.24 |
% 2.24/1.24 |-The branch is then unsatisfiable
% 2.24/1.24 |-Branch two:
% 2.24/1.24 | (17) f(all_0_2_2) & ! [v0] : ! [v1] : (v1 = v0 | ~ f(v1) | ~ f(v0)) & ! [v0] : ( ~ f(v0) | ? [v1] : ( ~ (v1 = v0) & f(v1)))
% 2.24/1.25 |
% 2.24/1.25 | Applying alpha-rule on (17) yields:
% 2.24/1.25 | (11) f(all_0_2_2)
% 2.24/1.25 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ f(v1) | ~ f(v0))
% 2.24/1.25 | (20) ! [v0] : ( ~ f(v0) | ? [v1] : ( ~ (v1 = v0) & f(v1)))
% 2.24/1.25 |
% 2.24/1.25 | Instantiating formula (20) with all_0_2_2 and discharging atoms f(all_0_2_2), yields:
% 2.24/1.25 | (21) ? [v0] : ( ~ (v0 = all_0_2_2) & f(v0))
% 2.24/1.25 |
% 2.24/1.25 | Instantiating (21) with all_9_0_3 yields:
% 2.24/1.25 | (22) ~ (all_9_0_3 = all_0_2_2) & f(all_9_0_3)
% 2.24/1.25 |
% 2.24/1.25 | Applying alpha-rule on (22) yields:
% 2.24/1.25 | (23) ~ (all_9_0_3 = all_0_2_2)
% 2.24/1.25 | (24) f(all_9_0_3)
% 2.24/1.25 |
% 2.24/1.25 | Instantiating formula (19) with all_9_0_3, all_0_2_2 and discharging atoms f(all_9_0_3), f(all_0_2_2), yields:
% 2.24/1.25 | (25) all_9_0_3 = all_0_2_2
% 2.24/1.25 |
% 2.24/1.25 | Equations (25) can reduce 23 to:
% 2.24/1.25 | (16) $false
% 2.24/1.25 |
% 2.24/1.25 |-The branch is then unsatisfiable
% 2.24/1.25 % SZS output end Proof for theBenchmark
% 2.24/1.25
% 2.24/1.25 629ms
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