TSTP Solution File: SYN082+1 by ePrincess---1.0
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- Process Solution
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% File : ePrincess---1.0
% Problem : SYN082+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n009.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 04:59:49 EDT 2022
% Result : Theorem 1.62s 1.09s
% Output : Proof 2.28s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : SYN082+1 : TPTP v8.1.0. Released v2.0.0.
% 0.05/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.36 % Computer : n009.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jul 11 19:52:37 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.52/0.62 ____ _
% 0.52/0.62 ___ / __ \_____(_)___ ________ __________
% 0.52/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.52/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.52/0.62
% 0.52/0.62 A Theorem Prover for First-Order Logic
% 0.52/0.62 (ePrincess v.1.0)
% 0.52/0.62
% 0.52/0.62 (c) Philipp Rümmer, 2009-2015
% 0.52/0.62 (c) Peter Backeman, 2014-2015
% 0.52/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.62 Bug reports to peter@backeman.se
% 0.52/0.62
% 0.52/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.62
% 0.52/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.20/0.92 Prover 0: Preprocessing ...
% 1.43/1.00 Prover 0: Constructing countermodel ...
% 1.62/1.09 Prover 0: proved (418ms)
% 1.62/1.09
% 1.62/1.09 No countermodel exists, formula is valid
% 1.62/1.09 % SZS status Theorem for theBenchmark
% 1.62/1.09
% 1.62/1.09 Generating proof ... found it (size 9)
% 2.15/1.21
% 2.15/1.21 % SZS output start Proof for theBenchmark
% 2.15/1.21 Assumed formulas after preprocessing and simplification:
% 2.15/1.21 | (0) ? [v0] : ? [v1] : ? [v2] : (f(v0) = v1 & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (f(v5) = v4) | ~ (f(v5) = v3)) & ((big_f(v0, v2) & ~ big_f(v0, v1) & ! [v3] : ( ~ big_f(v3, v2) | big_f(v3, v1))) | (big_f(v0, v1) & ! [v3] : ( ~ big_f(v0, v3) | ? [v4] : (big_f(v4, v3) & ~ big_f(v4, v1))))))
% 2.28/1.26 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 2.28/1.26 | (1) f(all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) & ((big_f(all_0_2_2, all_0_0_0) & ~ big_f(all_0_2_2, all_0_1_1) & ! [v0] : ( ~ big_f(v0, all_0_0_0) | big_f(v0, all_0_1_1))) | (big_f(all_0_2_2, all_0_1_1) & ! [v0] : ( ~ big_f(all_0_2_2, v0) | ? [v1] : (big_f(v1, v0) & ~ big_f(v1, all_0_1_1)))))
% 2.28/1.26 |
% 2.28/1.26 | Applying alpha-rule on (1) yields:
% 2.28/1.26 | (2) f(all_0_2_2) = all_0_1_1
% 2.28/1.26 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0))
% 2.28/1.26 | (4) (big_f(all_0_2_2, all_0_0_0) & ~ big_f(all_0_2_2, all_0_1_1) & ! [v0] : ( ~ big_f(v0, all_0_0_0) | big_f(v0, all_0_1_1))) | (big_f(all_0_2_2, all_0_1_1) & ! [v0] : ( ~ big_f(all_0_2_2, v0) | ? [v1] : (big_f(v1, v0) & ~ big_f(v1, all_0_1_1))))
% 2.28/1.26 |
% 2.28/1.26 +-Applying beta-rule and splitting (4), into two cases.
% 2.28/1.26 |-Branch one:
% 2.28/1.26 | (5) big_f(all_0_2_2, all_0_0_0) & ~ big_f(all_0_2_2, all_0_1_1) & ! [v0] : ( ~ big_f(v0, all_0_0_0) | big_f(v0, all_0_1_1))
% 2.28/1.26 |
% 2.28/1.26 | Applying alpha-rule on (5) yields:
% 2.28/1.26 | (6) big_f(all_0_2_2, all_0_0_0)
% 2.28/1.27 | (7) ~ big_f(all_0_2_2, all_0_1_1)
% 2.28/1.27 | (8) ! [v0] : ( ~ big_f(v0, all_0_0_0) | big_f(v0, all_0_1_1))
% 2.28/1.27 |
% 2.28/1.27 | Instantiating formula (8) with all_0_2_2 and discharging atoms big_f(all_0_2_2, all_0_0_0), ~ big_f(all_0_2_2, all_0_1_1), yields:
% 2.28/1.27 | (9) $false
% 2.28/1.27 |
% 2.28/1.27 |-The branch is then unsatisfiable
% 2.28/1.27 |-Branch two:
% 2.28/1.27 | (10) big_f(all_0_2_2, all_0_1_1) & ! [v0] : ( ~ big_f(all_0_2_2, v0) | ? [v1] : (big_f(v1, v0) & ~ big_f(v1, all_0_1_1)))
% 2.28/1.27 |
% 2.28/1.27 | Applying alpha-rule on (10) yields:
% 2.28/1.27 | (11) big_f(all_0_2_2, all_0_1_1)
% 2.28/1.27 | (12) ! [v0] : ( ~ big_f(all_0_2_2, v0) | ? [v1] : (big_f(v1, v0) & ~ big_f(v1, all_0_1_1)))
% 2.28/1.27 |
% 2.28/1.27 | Instantiating formula (12) with all_0_1_1 and discharging atoms big_f(all_0_2_2, all_0_1_1), yields:
% 2.28/1.27 | (9) $false
% 2.28/1.27 |
% 2.28/1.27 |-The branch is then unsatisfiable
% 2.28/1.27 % SZS output end Proof for theBenchmark
% 2.28/1.27
% 2.28/1.27 641ms
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