TSTP Solution File: SET592+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n012.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 00:20:32 EDT 2022
% Result : Theorem 2.06s 1.19s
% Output : Proof 2.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 09:49:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.59 (ePrincess v.1.0)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2015
% 0.19/0.59 (c) Peter Backeman, 2014-2015
% 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59 Bug reports to peter@backeman.se
% 0.19/0.59
% 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.45/0.92 Prover 0: Preprocessing ...
% 1.85/1.09 Prover 0: Warning: ignoring some quantifiers
% 1.96/1.11 Prover 0: Constructing countermodel ...
% 2.06/1.19 Prover 0: proved (557ms)
% 2.06/1.19
% 2.06/1.19 No countermodel exists, formula is valid
% 2.06/1.19 % SZS status Theorem for theBenchmark
% 2.06/1.19
% 2.06/1.19 Generating proof ... Warning: ignoring some quantifiers
% 2.82/1.36 found it (size 6)
% 2.82/1.36
% 2.82/1.36 % SZS output start Proof for theBenchmark
% 2.82/1.36 Assumed formulas after preprocessing and simplification:
% 2.82/1.36 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v0 = empty_set) & intersection(v1, v2) = empty_set & subset(v0, v2) & subset(v0, v1) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (intersection(v6, v5) = v4) | ~ (intersection(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection(v4, v5) = v6) | ~ subset(v3, v5) | ~ subset(v3, v4) | subset(v3, v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection(v3, v4) = v6) | ~ member(v5, v6) | member(v5, v4)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection(v3, v4) = v6) | ~ member(v5, v6) | member(v5, v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection(v3, v4) = v6) | ~ member(v5, v4) | ~ member(v5, v3) | member(v5, v6)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection(v4, v3) = v5) | intersection(v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection(v3, v4) = v5) | intersection(v4, v3) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ member(v5, v3) | ~ subset(v3, v4) | member(v5, v4)) & ! [v3] : ! [v4] : (v4 = v3 | ~ subset(v4, v3) | ~ subset(v3, v4)) & ! [v3] : ! [v4] : ( ~ empty(v3) | ~ member(v4, v3)) & ! [v3] : (v3 = empty_set | ~ subset(v3, empty_set)) & ! [v3] : ~ member(v3, empty_set) & ? [v3] : ? [v4] : (v4 = v3 | ? [v5] : (( ~ member(v5, v4) | ~ member(v5, v3)) & (member(v5, v4) | member(v5, v3)))) & ? [v3] : ? [v4] : (subset(v3, v4) | ? [v5] : (member(v5, v3) & ~ member(v5, v4))) & ? [v3] : (empty(v3) | ? [v4] : member(v4, v3)) & ? [v3] : subset(v3, v3))
% 2.82/1.40 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 2.82/1.40 | (1) ~ (all_0_2_2 = empty_set) & intersection(all_0_1_1, all_0_0_0) = empty_set & subset(all_0_2_2, all_0_0_0) & subset(all_0_2_2, all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0)) & ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) & ! [v0] : ~ member(v0, empty_set) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) & ? [v0] : (empty(v0) | ? [v1] : member(v1, v0)) & ? [v0] : subset(v0, v0)
% 2.82/1.41 |
% 2.82/1.41 | Applying alpha-rule on (1) yields:
% 2.82/1.41 | (2) ! [v0] : ~ member(v0, empty_set)
% 2.82/1.41 | (3) ? [v0] : (empty(v0) | ? [v1] : member(v1, v0))
% 2.82/1.41 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3))
% 2.82/1.41 | (5) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 2.82/1.41 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 2.82/1.41 | (7) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set))
% 2.82/1.41 | (8) ~ (all_0_2_2 = empty_set)
% 2.82/1.41 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3))
% 2.82/1.41 | (10) subset(all_0_2_2, all_0_0_0)
% 2.82/1.41 | (11) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 2.82/1.42 | (12) subset(all_0_2_2, all_0_1_1)
% 2.82/1.42 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0))
% 2.82/1.42 | (14) ? [v0] : subset(v0, v0)
% 2.82/1.42 | (15) intersection(all_0_1_1, all_0_0_0) = empty_set
% 2.82/1.42 | (16) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1)))
% 2.82/1.42 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1))
% 2.82/1.42 | (18) ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0))
% 2.82/1.42 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1))
% 2.82/1.42 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2)
% 2.82/1.42 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2)
% 2.82/1.42 |
% 2.82/1.42 | Instantiating formula (9) with empty_set, all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms intersection(all_0_1_1, all_0_0_0) = empty_set, subset(all_0_2_2, all_0_0_0), subset(all_0_2_2, all_0_1_1), yields:
% 2.82/1.42 | (22) subset(all_0_2_2, empty_set)
% 2.82/1.42 |
% 2.82/1.42 | Instantiating formula (7) with all_0_2_2 and discharging atoms subset(all_0_2_2, empty_set), yields:
% 2.82/1.42 | (23) all_0_2_2 = empty_set
% 2.82/1.42 |
% 2.82/1.42 | Equations (23) can reduce 8 to:
% 2.82/1.42 | (24) $false
% 2.82/1.42 |
% 2.82/1.42 |-The branch is then unsatisfiable
% 2.82/1.42 % SZS output end Proof for theBenchmark
% 2.82/1.42
% 2.82/1.42 825ms
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