TSTP Solution File: SET062+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET062+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 00:16:51 EDT 2022
% Result : Theorem 2.08s 1.17s
% Output : Proof 2.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET062+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.11 % Command : ePrincess-casc -timeout=%d %s
% 0.10/0.31 % Computer : n028.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 600
% 0.10/0.31 % DateTime : Sun Jul 10 12:24:42 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.47/0.57 ____ _
% 0.47/0.57 ___ / __ \_____(_)___ ________ __________
% 0.47/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.47/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.47/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.47/0.57
% 0.47/0.57 A Theorem Prover for First-Order Logic
% 0.47/0.57 (ePrincess v.1.0)
% 0.47/0.57
% 0.47/0.57 (c) Philipp Rümmer, 2009-2015
% 0.47/0.57 (c) Peter Backeman, 2014-2015
% 0.47/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.47/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.47/0.57 Bug reports to peter@backeman.se
% 0.47/0.57
% 0.47/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.47/0.57
% 0.47/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.47/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.17/0.87 Prover 0: Preprocessing ...
% 1.37/0.94 Prover 0: Warning: ignoring some quantifiers
% 1.37/0.95 Prover 0: Constructing countermodel ...
% 1.49/1.06 Prover 0: gave up
% 1.49/1.06 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.82/1.08 Prover 1: Preprocessing ...
% 1.98/1.14 Prover 1: Constructing countermodel ...
% 2.08/1.17 Prover 1: proved (110ms)
% 2.08/1.17
% 2.08/1.17 No countermodel exists, formula is valid
% 2.08/1.17 % SZS status Theorem for theBenchmark
% 2.08/1.17
% 2.08/1.17 Generating proof ... found it (size 10)
% 2.45/1.32
% 2.45/1.32 % SZS output start Proof for theBenchmark
% 2.45/1.32 Assumed formulas after preprocessing and simplification:
% 2.45/1.32 | (0) ? [v0] : ? [v1] : ( ~ (v1 = 0) & subset(empty_set, v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (subset(v5, v4) = v3) | ~ (subset(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (member(v5, v4) = v3) | ~ (member(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & member(v5, v3) = v6 & member(v5, v2) = 0)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (empty(v4) = v3) | ~ (empty(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (subset(v2, v3) = 0) | ~ (member(v4, v2) = 0) | member(v4, v3) = 0) & ! [v2] : ! [v3] : (v3 = 0 | ~ (empty(v2) = v3) | ? [v4] : member(v4, v2) = 0) & ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v2) = v3)) & ! [v2] : ! [v3] : ( ~ (empty(v2) = 0) | ~ (member(v3, v2) = 0)) & ! [v2] : ~ (member(v2, empty_set) = 0))
% 2.62/1.35 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 2.62/1.35 | (1) ~ (all_0_0_0 = 0) & subset(empty_set, all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : member(v2, v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (empty(v0) = 0) | ~ (member(v1, v0) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0)
% 2.62/1.36 |
% 2.62/1.36 | Applying alpha-rule on (1) yields:
% 2.62/1.36 | (2) subset(empty_set, all_0_1_1) = all_0_0_0
% 2.62/1.36 | (3) ! [v0] : ~ (member(v0, empty_set) = 0)
% 2.62/1.36 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 2.62/1.36 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 2.62/1.36 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 2.62/1.36 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 2.62/1.36 | (8) ! [v0] : ! [v1] : ( ~ (empty(v0) = 0) | ~ (member(v1, v0) = 0))
% 2.62/1.36 | (9) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : member(v2, v0) = 0)
% 2.62/1.36 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 2.62/1.36 | (11) ~ (all_0_0_0 = 0)
% 2.62/1.36 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 2.67/1.36 |
% 2.67/1.37 | Instantiating formula (10) with all_0_0_0, all_0_1_1, empty_set and discharging atoms subset(empty_set, all_0_1_1) = all_0_0_0, yields:
% 2.67/1.37 | (13) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, empty_set) = 0)
% 2.67/1.37 |
% 2.67/1.37 +-Applying beta-rule and splitting (13), into two cases.
% 2.67/1.37 |-Branch one:
% 2.67/1.37 | (14) all_0_0_0 = 0
% 2.67/1.37 |
% 2.67/1.37 | Equations (14) can reduce 11 to:
% 2.67/1.37 | (15) $false
% 2.67/1.37 |
% 2.67/1.37 |-The branch is then unsatisfiable
% 2.67/1.37 |-Branch two:
% 2.67/1.37 | (11) ~ (all_0_0_0 = 0)
% 2.67/1.37 | (17) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, empty_set) = 0)
% 2.67/1.37 |
% 2.67/1.37 | Instantiating (17) with all_14_0_2, all_14_1_3 yields:
% 2.67/1.37 | (18) ~ (all_14_0_2 = 0) & member(all_14_1_3, all_0_1_1) = all_14_0_2 & member(all_14_1_3, empty_set) = 0
% 2.67/1.37 |
% 2.67/1.37 | Applying alpha-rule on (18) yields:
% 2.67/1.37 | (19) ~ (all_14_0_2 = 0)
% 2.67/1.37 | (20) member(all_14_1_3, all_0_1_1) = all_14_0_2
% 2.67/1.37 | (21) member(all_14_1_3, empty_set) = 0
% 2.67/1.37 |
% 2.67/1.37 | Instantiating formula (3) with all_14_1_3 and discharging atoms member(all_14_1_3, empty_set) = 0, yields:
% 2.67/1.37 | (22) $false
% 2.67/1.37 |
% 2.67/1.37 |-The branch is then unsatisfiable
% 2.67/1.37 % SZS output end Proof for theBenchmark
% 2.67/1.37
% 2.67/1.37 789ms
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