TSTP Solution File: SET596+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET596+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n017.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 00:20:35 EDT 2022
% Result : Theorem 2.33s 1.27s
% Output : Proof 3.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SET596+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.15 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.37 % Computer : n017.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 600
% 0.14/0.37 % DateTime : Sun Jul 10 18:40:33 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.46/0.63 ____ _
% 0.46/0.63 ___ / __ \_____(_)___ ________ __________
% 0.46/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.46/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.46/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.46/0.63
% 0.46/0.63 A Theorem Prover for First-Order Logic
% 0.46/0.63 (ePrincess v.1.0)
% 0.46/0.63
% 0.46/0.63 (c) Philipp Rümmer, 2009-2015
% 0.46/0.63 (c) Peter Backeman, 2014-2015
% 0.46/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.46/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.46/0.63 Bug reports to peter@backeman.se
% 0.46/0.63
% 0.46/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.46/0.63
% 0.46/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.78/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.56/0.98 Prover 0: Preprocessing ...
% 1.96/1.16 Prover 0: Warning: ignoring some quantifiers
% 2.06/1.18 Prover 0: Constructing countermodel ...
% 2.33/1.27 Prover 0: proved (588ms)
% 2.33/1.27
% 2.33/1.27 No countermodel exists, formula is valid
% 2.33/1.27 % SZS status Theorem for theBenchmark
% 2.33/1.27
% 2.33/1.27 Generating proof ... Warning: ignoring some quantifiers
% 2.67/1.43 found it (size 6)
% 2.67/1.43
% 2.67/1.43 % SZS output start Proof for theBenchmark
% 2.67/1.43 Assumed formulas after preprocessing and simplification:
% 2.67/1.43 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = empty_set) & intersection(v1, v2) = empty_set & intersection(v0, v2) = v3 & subset(v0, v1) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection(v5, v6) = v8) | ~ (intersection(v4, v6) = v7) | ~ subset(v4, v5) | subset(v7, v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (intersection(v7, v6) = v5) | ~ (intersection(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection(v4, v5) = v7) | ~ member(v6, v7) | member(v6, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection(v4, v5) = v7) | ~ member(v6, v7) | member(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection(v4, v5) = v7) | ~ member(v6, v5) | ~ member(v6, v4) | member(v6, v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection(v5, v4) = v6) | intersection(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection(v4, v5) = v6) | intersection(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ member(v6, v4) | ~ subset(v4, v5) | member(v6, v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ subset(v5, v4) | ~ subset(v4, v5)) & ! [v4] : ! [v5] : ( ~ empty(v4) | ~ member(v5, v4)) & ! [v4] : (v4 = empty_set | ~ subset(v4, empty_set)) & ! [v4] : ~ member(v4, empty_set) & ? [v4] : ? [v5] : (v5 = v4 | ? [v6] : (( ~ member(v6, v5) | ~ member(v6, v4)) & (member(v6, v5) | member(v6, v4)))) & ? [v4] : ? [v5] : (subset(v4, v5) | ? [v6] : (member(v6, v4) & ~ member(v6, v5))) & ? [v4] : (empty(v4) | ? [v5] : member(v5, v4)) & ? [v4] : subset(v4, v4))
% 2.89/1.47 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 2.89/1.47 | (1) ~ (all_0_0_0 = empty_set) & intersection(all_0_2_2, all_0_1_1) = empty_set & intersection(all_0_3_3, all_0_1_1) = all_0_0_0 & subset(all_0_3_3, all_0_2_2) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v1, v2) = v4) | ~ (intersection(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [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)
% 3.00/1.48 |
% 3.00/1.48 | Applying alpha-rule on (1) yields:
% 3.00/1.48 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1))
% 3.00/1.48 | (3) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1)))
% 3.00/1.48 | (4) ? [v0] : (empty(v0) | ? [v1] : member(v1, v0))
% 3.00/1.48 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 3.00/1.48 | (6) subset(all_0_3_3, all_0_2_2)
% 3.00/1.48 | (7) ! [v0] : ~ member(v0, empty_set)
% 3.00/1.48 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1))
% 3.00/1.48 | (9) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 3.00/1.48 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v1, v2) = v4) | ~ (intersection(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 3.00/1.48 | (11) ~ (all_0_0_0 = empty_set)
% 3.00/1.48 | (12) intersection(all_0_2_2, all_0_1_1) = empty_set
% 3.00/1.48 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2)
% 3.00/1.48 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2)
% 3.00/1.48 | (15) ? [v0] : subset(v0, v0)
% 3.00/1.48 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 3.00/1.48 | (17) intersection(all_0_3_3, all_0_1_1) = all_0_0_0
% 3.00/1.48 | (18) ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0))
% 3.00/1.48 | (19) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set))
% 3.00/1.48 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0))
% 3.00/1.48 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3))
% 3.00/1.49 |
% 3.00/1.49 | Instantiating formula (10) with empty_set, all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms intersection(all_0_2_2, all_0_1_1) = empty_set, intersection(all_0_3_3, all_0_1_1) = all_0_0_0, subset(all_0_3_3, all_0_2_2), yields:
% 3.00/1.49 | (22) subset(all_0_0_0, empty_set)
% 3.00/1.49 |
% 3.00/1.49 | Instantiating formula (19) with all_0_0_0 and discharging atoms subset(all_0_0_0, empty_set), yields:
% 3.00/1.49 | (23) all_0_0_0 = empty_set
% 3.00/1.49 |
% 3.00/1.49 | Equations (23) can reduce 11 to:
% 3.00/1.49 | (24) $false
% 3.00/1.49 |
% 3.00/1.49 |-The branch is then unsatisfiable
% 3.00/1.49 % SZS output end Proof for theBenchmark
% 3.00/1.49
% 3.00/1.49 848ms
%------------------------------------------------------------------------------