TSTP Solution File: SET627+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET627+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 00:20:58 EDT 2022
% Result : Theorem 2.58s 1.31s
% Output : Proof 3.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET627+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n029.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jul 10 14:53:46 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.55/0.60 ____ _
% 0.55/0.60 ___ / __ \_____(_)___ ________ __________
% 0.55/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.60
% 0.55/0.60 A Theorem Prover for First-Order Logic
% 0.55/0.60 (ePrincess v.1.0)
% 0.55/0.60
% 0.55/0.60 (c) Philipp Rümmer, 2009-2015
% 0.55/0.60 (c) Peter Backeman, 2014-2015
% 0.55/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.60 Bug reports to peter@backeman.se
% 0.55/0.60
% 0.55/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.60
% 0.55/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.41/0.92 Prover 0: Preprocessing ...
% 1.47/1.00 Prover 0: Warning: ignoring some quantifiers
% 1.47/1.01 Prover 0: Constructing countermodel ...
% 2.08/1.19 Prover 0: gave up
% 2.08/1.19 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.15/1.20 Prover 1: Preprocessing ...
% 2.33/1.28 Prover 1: Constructing countermodel ...
% 2.58/1.31 Prover 1: proved (119ms)
% 2.58/1.31
% 2.58/1.31 No countermodel exists, formula is valid
% 2.58/1.31 % SZS status Theorem for theBenchmark
% 2.58/1.31
% 2.58/1.31 Generating proof ... found it (size 11)
% 2.84/1.46
% 2.84/1.46 % SZS output start Proof for theBenchmark
% 2.84/1.46 Assumed formulas after preprocessing and simplification:
% 2.84/1.46 | (0) ? [v0] : ? [v1] : ( ~ (v1 = 0) & disjoint(v0, empty_set) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (intersect(v2, v3) = v4) | ~ (member(v5, v2) = 0) | ? [v6] : ( ~ (v6 = 0) & member(v5, v3) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (disjoint(v5, v4) = v3) | ~ (disjoint(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (intersect(v5, v4) = v3) | ~ (intersect(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (member(v5, v4) = v3) | ~ (member(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (disjoint(v2, v3) = v4) | intersect(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (empty(v4) = v3) | ~ (empty(v4) = v2)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (empty(v2) = v3) | ? [v4] : member(v4, v2) = 0) & ! [v2] : ! [v3] : ( ~ (empty(v2) = 0) | ~ (member(v3, v2) = 0)) & ! [v2] : ! [v3] : ( ~ (disjoint(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & intersect(v2, v3) = v4)) & ! [v2] : ! [v3] : ( ~ (intersect(v2, v3) = 0) | intersect(v3, v2) = 0) & ! [v2] : ! [v3] : ( ~ (intersect(v2, v3) = 0) | ? [v4] : (member(v4, v3) = 0 & member(v4, v2) = 0)) & ! [v2] : ~ (member(v2, empty_set) = 0))
% 3.15/1.49 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 3.15/1.49 | (1) ~ (all_0_0_0 = 0) & disjoint(all_0_1_1, empty_set) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (intersect(v0, v1) = v2) | ~ (member(v3, v0) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | intersect(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : member(v2, v0) = 0) & ! [v0] : ! [v1] : ( ~ (empty(v0) = 0) | ~ (member(v1, v0) = 0)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & intersect(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (intersect(v0, v1) = 0) | intersect(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (intersect(v0, v1) = 0) | ? [v2] : (member(v2, v1) = 0 & member(v2, v0) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0)
% 3.15/1.50 |
% 3.15/1.50 | Applying alpha-rule on (1) yields:
% 3.15/1.50 | (2) disjoint(all_0_1_1, empty_set) = all_0_0_0
% 3.15/1.50 | (3) ! [v0] : ! [v1] : ( ~ (intersect(v0, v1) = 0) | intersect(v1, v0) = 0)
% 3.15/1.50 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) = v0))
% 3.15/1.50 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | intersect(v0, v1) = 0)
% 3.15/1.50 | (6) ~ (all_0_0_0 = 0)
% 3.15/1.50 | (7) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & intersect(v0, v1) = v2))
% 3.15/1.50 | (8) ! [v0] : ! [v1] : ( ~ (empty(v0) = 0) | ~ (member(v1, v0) = 0))
% 3.15/1.50 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 3.15/1.50 | (10) ! [v0] : ! [v1] : ( ~ (intersect(v0, v1) = 0) | ? [v2] : (member(v2, v1) = 0 & member(v2, v0) = 0))
% 3.15/1.50 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 3.15/1.50 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (intersect(v0, v1) = v2) | ~ (member(v3, v0) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4))
% 3.15/1.50 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : member(v2, v0) = 0)
% 3.15/1.50 | (14) ! [v0] : ~ (member(v0, empty_set) = 0)
% 3.15/1.50 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 3.15/1.50 |
% 3.15/1.50 | Instantiating formula (5) with all_0_0_0, empty_set, all_0_1_1 and discharging atoms disjoint(all_0_1_1, empty_set) = all_0_0_0, yields:
% 3.15/1.50 | (16) all_0_0_0 = 0 | intersect(all_0_1_1, empty_set) = 0
% 3.15/1.50 |
% 3.15/1.50 +-Applying beta-rule and splitting (16), into two cases.
% 3.15/1.50 |-Branch one:
% 3.15/1.50 | (17) intersect(all_0_1_1, empty_set) = 0
% 3.15/1.50 |
% 3.15/1.50 | Instantiating formula (10) with empty_set, all_0_1_1 and discharging atoms intersect(all_0_1_1, empty_set) = 0, yields:
% 3.15/1.50 | (18) ? [v0] : (member(v0, all_0_1_1) = 0 & member(v0, empty_set) = 0)
% 3.15/1.50 |
% 3.15/1.50 | Instantiating (18) with all_16_0_2 yields:
% 3.15/1.50 | (19) member(all_16_0_2, all_0_1_1) = 0 & member(all_16_0_2, empty_set) = 0
% 3.15/1.51 |
% 3.15/1.51 | Applying alpha-rule on (19) yields:
% 3.15/1.51 | (20) member(all_16_0_2, all_0_1_1) = 0
% 3.15/1.51 | (21) member(all_16_0_2, empty_set) = 0
% 3.15/1.51 |
% 3.15/1.51 | Instantiating formula (14) with all_16_0_2 and discharging atoms member(all_16_0_2, empty_set) = 0, yields:
% 3.15/1.51 | (22) $false
% 3.15/1.51 |
% 3.15/1.51 |-The branch is then unsatisfiable
% 3.15/1.51 |-Branch two:
% 3.15/1.51 | (23) ~ (intersect(all_0_1_1, empty_set) = 0)
% 3.15/1.51 | (24) all_0_0_0 = 0
% 3.15/1.51 |
% 3.15/1.51 | Equations (24) can reduce 6 to:
% 3.15/1.51 | (25) $false
% 3.15/1.51 |
% 3.15/1.51 |-The branch is then unsatisfiable
% 3.15/1.51 % SZS output end Proof for theBenchmark
% 3.15/1.51
% 3.15/1.51 889ms
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