TSTP Solution File: SET602+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET602+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 00:20:39 EDT 2022
% Result : Theorem 2.46s 1.31s
% Output : Proof 3.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET602+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % 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 23:28:53 EDT 2022
% 0.13/0.33 % 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
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.35/0.90 Prover 0: Preprocessing ...
% 1.65/1.03 Prover 0: Warning: ignoring some quantifiers
% 1.65/1.05 Prover 0: Constructing countermodel ...
% 2.21/1.19 Prover 0: gave up
% 2.21/1.19 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.29/1.21 Prover 1: Preprocessing ...
% 2.46/1.29 Prover 1: Constructing countermodel ...
% 2.46/1.31 Prover 1: proved (118ms)
% 2.46/1.31
% 2.46/1.31 No countermodel exists, formula is valid
% 2.46/1.31 % SZS status Theorem for theBenchmark
% 2.46/1.31
% 2.46/1.31 Generating proof ... found it (size 11)
% 3.08/1.46
% 3.08/1.46 % SZS output start Proof for theBenchmark
% 3.08/1.46 Assumed formulas after preprocessing and simplification:
% 3.08/1.46 | (0) ? [v0] : ? [v1] : ( ~ (v1 = empty_set) & difference(v0, v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (member(v4, v5) = v6) | ~ (difference(v2, v3) = v5) | ? [v7] : ? [v8] : (member(v4, v3) = v8 & member(v4, v2) = v7 & ( ~ (v7 = 0) | v8 = 0))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (member(v5, v4) = v3) | ~ (member(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (difference(v5, v4) = v3) | ~ (difference(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (subset(v5, v4) = v3) | ~ (subset(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (member(v4, v5) = 0) | ~ (difference(v2, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & member(v4, v3) = v6 & member(v4, v2) = 0)) & ! [v2] : ! [v3] : ! [v4] : (v4 = empty_set | ~ (difference(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & subset(v2, v3) = v5)) & ! [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] : ( ~ (member(v4, v2) = 0) | ~ (subset(v2, v3) = 0) | member(v4, v3) = 0) & ! [v2] : ! [v3] : (v3 = v2 | ~ (subset(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v3, v2) = v4)) & ! [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] : ! [v3] : ( ~ (difference(v2, v3) = empty_set) | subset(v2, v3) = 0) & ! [v2] : ~ (member(v2, empty_set) = 0))
% 3.08/1.50 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 3.08/1.50 | (1) ~ (all_0_0_0 = empty_set) & difference(all_0_1_1, all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (member(v2, v3) = v4) | ~ (difference(v0, v1) = v3) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (member(v2, v3) = 0) | ~ (difference(v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4 & member(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [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] : ( ~ (member(v2, v0) = 0) | ~ (subset(v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [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] : ! [v1] : ( ~ (difference(v0, v1) = empty_set) | subset(v0, v1) = 0) & ! [v0] : ~ (member(v0, empty_set) = 0)
% 3.22/1.51 |
% 3.22/1.51 | Applying alpha-rule on (1) yields:
% 3.22/1.51 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : member(v2, v0) = 0)
% 3.22/1.51 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 3.22/1.51 | (4) ! [v0] : ! [v1] : ( ~ (difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 3.22/1.51 | (5) ! [v0] : ~ (member(v0, empty_set) = 0)
% 3.22/1.51 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (member(v2, v3) = 0) | ~ (difference(v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4 & member(v2, v0) = 0))
% 3.22/1.51 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (member(v2, v0) = 0) | ~ (subset(v0, v1) = 0) | member(v2, v1) = 0)
% 3.22/1.51 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 3.22/1.52 | (9) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 3.22/1.52 | (10) difference(all_0_1_1, all_0_1_1) = all_0_0_0
% 3.22/1.52 | (11) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 3.22/1.52 | (12) ~ (all_0_0_0 = empty_set)
% 3.22/1.52 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 3.22/1.52 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 3.22/1.52 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (member(v2, v3) = v4) | ~ (difference(v0, v1) = v3) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 3.22/1.52 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 3.22/1.52 | (17) ! [v0] : ! [v1] : ( ~ (empty(v0) = 0) | ~ (member(v1, v0) = 0))
% 3.22/1.52 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 3.22/1.52 |
% 3.22/1.52 | Instantiating formula (18) with all_0_0_0, all_0_1_1, all_0_1_1 and discharging atoms difference(all_0_1_1, all_0_1_1) = all_0_0_0, yields:
% 3.22/1.52 | (19) all_0_0_0 = empty_set | ? [v0] : ( ~ (v0 = 0) & subset(all_0_1_1, all_0_1_1) = v0)
% 3.22/1.52 |
% 3.22/1.52 +-Applying beta-rule and splitting (19), into two cases.
% 3.22/1.52 |-Branch one:
% 3.22/1.52 | (20) all_0_0_0 = empty_set
% 3.22/1.52 |
% 3.22/1.52 | Equations (20) can reduce 12 to:
% 3.22/1.52 | (21) $false
% 3.22/1.52 |
% 3.22/1.52 |-The branch is then unsatisfiable
% 3.22/1.52 |-Branch two:
% 3.22/1.52 | (12) ~ (all_0_0_0 = empty_set)
% 3.22/1.52 | (23) ? [v0] : ( ~ (v0 = 0) & subset(all_0_1_1, all_0_1_1) = v0)
% 3.22/1.52 |
% 3.22/1.52 | Instantiating (23) with all_10_0_2 yields:
% 3.22/1.52 | (24) ~ (all_10_0_2 = 0) & subset(all_0_1_1, all_0_1_1) = all_10_0_2
% 3.22/1.52 |
% 3.22/1.52 | Applying alpha-rule on (24) yields:
% 3.22/1.52 | (25) ~ (all_10_0_2 = 0)
% 3.22/1.52 | (26) subset(all_0_1_1, all_0_1_1) = all_10_0_2
% 3.22/1.52 |
% 3.22/1.52 | Instantiating formula (9) with all_10_0_2, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_1_1) = all_10_0_2, yields:
% 3.22/1.52 | (27) all_10_0_2 = 0
% 3.22/1.52 |
% 3.22/1.52 | Equations (27) can reduce 25 to:
% 3.22/1.52 | (21) $false
% 3.22/1.52 |
% 3.22/1.52 |-The branch is then unsatisfiable
% 3.22/1.52 % SZS output end Proof for theBenchmark
% 3.22/1.52
% 3.22/1.52 934ms
%------------------------------------------------------------------------------