TSTP Solution File: SET639+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.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 00:21:06 EDT 2022
% Result : Theorem 2.19s 1.14s
% Output : Proof 2.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 21:09:38 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.55/0.58 ____ _
% 0.55/0.58 ___ / __ \_____(_)___ ________ __________
% 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.58
% 0.55/0.58 A Theorem Prover for First-Order Logic
% 0.55/0.58 (ePrincess v.1.0)
% 0.55/0.58
% 0.55/0.58 (c) Philipp Rümmer, 2009-2015
% 0.55/0.58 (c) Peter Backeman, 2014-2015
% 0.55/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.58 Bug reports to peter@backeman.se
% 0.55/0.58
% 0.55/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.58
% 0.55/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.55/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.43/0.89 Prover 0: Preprocessing ...
% 1.84/1.05 Prover 0: Warning: ignoring some quantifiers
% 1.84/1.06 Prover 0: Constructing countermodel ...
% 2.19/1.14 Prover 0: proved (515ms)
% 2.19/1.14
% 2.19/1.14 No countermodel exists, formula is valid
% 2.19/1.14 % SZS status Theorem for theBenchmark
% 2.19/1.15
% 2.19/1.15 Generating proof ... Warning: ignoring some quantifiers
% 2.49/1.32 found it (size 6)
% 2.49/1.32
% 2.49/1.32 % SZS output start Proof for theBenchmark
% 2.49/1.32 Assumed formulas after preprocessing and simplification:
% 2.49/1.32 | (0) ? [v0] : ? [v1] : ( ~ (v0 = empty_set) & intersection(v1, v0) = empty_set & subset(v0, v1) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (intersection(v5, v4) = v3) | ~ (intersection(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection(v2, v3) = v5) | ~ member(v4, v5) | member(v4, v3)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection(v2, v3) = v5) | ~ member(v4, v5) | member(v4, v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection(v2, v3) = v5) | ~ member(v4, v3) | ~ member(v4, v2) | member(v4, v5)) & ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (intersection(v2, v3) = v4) | ~ subset(v2, v3)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v3, v2) = v4) | intersection(v2, v3) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v2, v3) = v4) | intersection(v3, v2) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ member(v4, v2) | ~ subset(v2, v3) | member(v4, v3)) & ! [v2] : ! [v3] : (v3 = v2 | ~ subset(v3, v2) | ~ subset(v2, v3)) & ! [v2] : ! [v3] : ( ~ empty(v2) | ~ member(v3, v2)) & ! [v2] : ~ member(v2, empty_set) & ? [v2] : ? [v3] : (v3 = v2 | ? [v4] : (( ~ member(v4, v3) | ~ member(v4, v2)) & (member(v4, v3) | member(v4, v2)))) & ? [v2] : ? [v3] : (subset(v2, v3) | ? [v4] : (member(v4, v2) & ~ member(v4, v3))) & ? [v2] : (empty(v2) | ? [v3] : member(v3, v2)) & ? [v2] : subset(v2, v2))
% 2.67/1.36 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 2.67/1.36 | (1) ~ (all_0_1_1 = empty_set) & intersection(all_0_0_0, all_0_1_1) = empty_set & subset(all_0_1_1, all_0_0_0) & ! [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] : (v2 = v0 | ~ (intersection(v0, v1) = v2) | ~ subset(v0, v1)) & ! [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] : ~ 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)
% 2.67/1.36 |
% 2.67/1.36 | Applying alpha-rule on (1) yields:
% 2.67/1.36 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3))
% 2.67/1.36 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1))
% 2.67/1.36 | (4) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1)))
% 2.67/1.36 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 2.82/1.36 | (6) ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0))
% 2.82/1.36 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2)
% 2.82/1.37 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2)
% 2.82/1.37 | (9) ? [v0] : subset(v0, v0)
% 2.82/1.37 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0))
% 2.82/1.37 | (11) subset(all_0_1_1, all_0_0_0)
% 2.82/1.37 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 2.82/1.37 | (13) intersection(all_0_0_0, all_0_1_1) = empty_set
% 2.82/1.37 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1))
% 2.82/1.37 | (15) ? [v0] : (empty(v0) | ? [v1] : member(v1, v0))
% 2.82/1.37 | (16) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 2.82/1.37 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (intersection(v0, v1) = v2) | ~ subset(v0, v1))
% 2.82/1.37 | (18) ! [v0] : ~ member(v0, empty_set)
% 2.82/1.37 | (19) ~ (all_0_1_1 = empty_set)
% 2.82/1.37 |
% 2.82/1.37 | Instantiating formula (8) with empty_set, all_0_0_0, all_0_1_1 and discharging atoms intersection(all_0_0_0, all_0_1_1) = empty_set, yields:
% 2.82/1.37 | (20) intersection(all_0_1_1, all_0_0_0) = empty_set
% 2.82/1.37 |
% 2.82/1.37 | Instantiating formula (17) with empty_set, all_0_0_0, all_0_1_1 and discharging atoms intersection(all_0_1_1, all_0_0_0) = empty_set, subset(all_0_1_1, all_0_0_0), yields:
% 2.82/1.37 | (21) all_0_1_1 = empty_set
% 2.82/1.37 |
% 2.82/1.37 | Equations (21) can reduce 19 to:
% 2.82/1.37 | (22) $false
% 2.82/1.37 |
% 2.82/1.37 |-The branch is then unsatisfiable
% 2.82/1.37 % SZS output end Proof for theBenchmark
% 2.82/1.37
% 2.82/1.37 785ms
%------------------------------------------------------------------------------