TSTP Solution File: SEU123+1 by ePrincess---1.0
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% File : ePrincess---1.0
% Problem : SEU123+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 : Tue Jul 19 08:46:44 EDT 2022
% Result : Theorem 2.44s 1.28s
% Output : Proof 3.03s
% 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 : SEU123+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 05:21:29 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.59 ____ _
% 0.20/0.59 ___ / __ \_____(_)___ ________ __________
% 0.20/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic
% 0.20/0.59 (ePrincess v.1.0)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2015
% 0.20/0.59 (c) Peter Backeman, 2014-2015
% 0.20/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.59 Bug reports to peter@backeman.se
% 0.20/0.59
% 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.59
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.37/0.92 Prover 0: Preprocessing ...
% 1.61/1.00 Prover 0: Warning: ignoring some quantifiers
% 1.61/1.02 Prover 0: Constructing countermodel ...
% 1.75/1.14 Prover 0: gave up
% 1.75/1.14 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.75/1.16 Prover 1: Preprocessing ...
% 2.35/1.24 Prover 1: Constructing countermodel ...
% 2.44/1.28 Prover 1: proved (136ms)
% 2.44/1.28
% 2.44/1.28 No countermodel exists, formula is valid
% 2.44/1.28 % SZS status Theorem for theBenchmark
% 2.44/1.28
% 2.44/1.28 Generating proof ... found it (size 11)
% 2.81/1.43
% 2.81/1.43 % SZS output start Proof for theBenchmark
% 2.81/1.43 Assumed formulas after preprocessing and simplification:
% 2.81/1.43 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v2 = 0) & ~ (v0 = empty_set) & empty(v3) = 0 & empty(v1) = v2 & empty(empty_set) = 0 & subset(v0, empty_set) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (subset(v7, v6) = v5) | ~ (subset(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (in(v7, v6) = v5) | ~ (in(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (empty(v6) = v5) | ~ (empty(v6) = v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (empty(v5) = 0) | ~ (empty(v4) = 0)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (subset(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & subset(v5, v4) = v6)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v4, v4) = v5)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(empty_set, v4) = v5)) & ! [v4] : ! [v5] : ( ~ (in(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & empty(v5) = v6)) & ! [v4] : ! [v5] : ( ~ (in(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & in(v5, v4) = v6)) & ! [v4] : (v4 = empty_set | ~ (empty(v4) = 0)))
% 2.98/1.46 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 2.98/1.46 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = empty_set) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & subset(all_0_3_3, empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 3.03/1.46 |
% 3.03/1.46 | Applying alpha-rule on (1) yields:
% 3.03/1.46 | (2) ~ (all_0_1_1 = 0)
% 3.03/1.46 | (3) empty(all_0_2_2) = all_0_1_1
% 3.03/1.46 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 3.03/1.46 | (5) ~ (all_0_3_3 = empty_set)
% 3.03/1.46 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1))
% 3.03/1.47 | (7) empty(empty_set) = 0
% 3.03/1.47 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 3.03/1.47 | (9) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 3.03/1.47 | (10) empty(all_0_0_0) = 0
% 3.03/1.47 | (11) subset(all_0_3_3, empty_set) = 0
% 3.03/1.47 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 3.03/1.47 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 3.03/1.47 | (14) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 3.03/1.47 | (15) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 3.03/1.47 | (16) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 3.03/1.47 | (17) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 3.03/1.47 |
% 3.03/1.47 | Instantiating formula (17) with empty_set, all_0_3_3 and discharging atoms subset(all_0_3_3, empty_set) = 0, yields:
% 3.03/1.47 | (18) all_0_3_3 = empty_set | ? [v0] : ( ~ (v0 = 0) & subset(empty_set, all_0_3_3) = v0)
% 3.03/1.47 |
% 3.03/1.47 +-Applying beta-rule and splitting (18), into two cases.
% 3.03/1.47 |-Branch one:
% 3.03/1.47 | (19) all_0_3_3 = empty_set
% 3.03/1.47 |
% 3.03/1.47 | Equations (19) can reduce 5 to:
% 3.03/1.47 | (20) $false
% 3.03/1.47 |
% 3.03/1.47 |-The branch is then unsatisfiable
% 3.03/1.47 |-Branch two:
% 3.03/1.47 | (5) ~ (all_0_3_3 = empty_set)
% 3.03/1.47 | (22) ? [v0] : ( ~ (v0 = 0) & subset(empty_set, all_0_3_3) = v0)
% 3.03/1.47 |
% 3.03/1.47 | Instantiating (22) with all_18_0_4 yields:
% 3.03/1.47 | (23) ~ (all_18_0_4 = 0) & subset(empty_set, all_0_3_3) = all_18_0_4
% 3.03/1.47 |
% 3.03/1.47 | Applying alpha-rule on (23) yields:
% 3.03/1.47 | (24) ~ (all_18_0_4 = 0)
% 3.03/1.47 | (25) subset(empty_set, all_0_3_3) = all_18_0_4
% 3.03/1.47 |
% 3.03/1.47 | Instantiating formula (6) with all_18_0_4, all_0_3_3 and discharging atoms subset(empty_set, all_0_3_3) = all_18_0_4, yields:
% 3.03/1.47 | (26) all_18_0_4 = 0
% 3.03/1.47 |
% 3.03/1.47 | Equations (26) can reduce 24 to:
% 3.03/1.47 | (20) $false
% 3.03/1.47 |
% 3.03/1.47 |-The branch is then unsatisfiable
% 3.03/1.47 % SZS output end Proof for theBenchmark
% 3.03/1.48
% 3.03/1.48 871ms
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