TSTP Solution File: SET633+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET633+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n023.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 00:21:02 EDT 2022
% Result : Theorem 2.24s 1.20s
% Output : Proof 3.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET633+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.33 % Computer : n023.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Sat Jul 9 22:22:10 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.59 ____ _
% 0.20/0.59 ___ / __ \_____(_)___ ________ __________
% 0.20/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic
% 0.20/0.59 (ePrincess v.1.0)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2015
% 0.20/0.59 (c) Peter Backeman, 2014-2015
% 0.20/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.59 Bug reports to peter@backeman.se
% 0.20/0.59
% 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.59
% 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.41/0.91 Prover 0: Preprocessing ...
% 1.87/1.08 Prover 0: Warning: ignoring some quantifiers
% 1.87/1.10 Prover 0: Constructing countermodel ...
% 2.24/1.20 Prover 0: proved (556ms)
% 2.24/1.20
% 2.24/1.20 No countermodel exists, formula is valid
% 2.24/1.20 % SZS status Theorem for theBenchmark
% 2.24/1.20
% 2.24/1.20 Generating proof ... Warning: ignoring some quantifiers
% 2.90/1.39 found it (size 10)
% 2.90/1.39
% 2.90/1.39 % SZS output start Proof for theBenchmark
% 2.90/1.40 Assumed formulas after preprocessing and simplification:
% 2.90/1.40 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & symmetric_difference(v0, v1) = v5 & subset(v4, v2) & subset(v3, v2) & ~ subset(v5, v2) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (difference(v7, v6) = v9) | ~ (difference(v6, v7) = v8) | ~ (union(v8, v9) = v10) | symmetric_difference(v6, v7) = v10) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (difference(v9, v8) = v7) | ~ (difference(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (union(v9, v8) = v7) | ~ (union(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (symmetric_difference(v9, v8) = v7) | ~ (symmetric_difference(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (difference(v6, v7) = v9) | ~ member(v8, v9) | ~ member(v8, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (difference(v6, v7) = v9) | ~ member(v8, v9) | member(v8, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (difference(v6, v7) = v9) | ~ member(v8, v6) | member(v8, v9) | member(v8, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (union(v6, v8) = v9) | ~ subset(v8, v7) | ~ subset(v6, v7) | subset(v9, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v7, v6) = v8) | union(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v6, v7) = v8) | union(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (symmetric_difference(v7, v6) = v8) | symmetric_difference(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (symmetric_difference(v6, v7) = v8) | symmetric_difference(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (symmetric_difference(v6, v7) = v8) | ? [v9] : ? [v10] : (difference(v7, v6) = v10 & difference(v6, v7) = v9 & union(v9, v10) = v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ member(v8, v6) | ~ subset(v6, v7) | member(v8, v7)) & ? [v6] : ? [v7] : (v7 = v6 | ? [v8] : (( ~ member(v8, v7) | ~ member(v8, v6)) & (member(v8, v7) | member(v8, v6)))) & ? [v6] : ? [v7] : (subset(v6, v7) | ? [v8] : (member(v8, v6) & ~ member(v8, v7))) & ? [v6] : subset(v6, v6))
% 2.90/1.43 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 2.90/1.43 | (1) difference(all_0_4_4, all_0_5_5) = all_0_1_1 & difference(all_0_5_5, all_0_4_4) = all_0_2_2 & symmetric_difference(all_0_5_5, all_0_4_4) = all_0_0_0 & subset(all_0_1_1, all_0_3_3) & subset(all_0_2_2, all_0_3_3) & ~ subset(all_0_0_0, all_0_3_3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v0) = v3) | ~ (difference(v0, v1) = v2) | ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | ~ member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) & ? [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] : subset(v0, v0)
% 2.90/1.44 |
% 2.90/1.44 | Applying alpha-rule on (1) yields:
% 2.90/1.44 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2)
% 2.90/1.44 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2)
% 2.90/1.44 | (4) ~ subset(all_0_0_0, all_0_3_3)
% 2.90/1.44 | (5) ? [v0] : subset(v0, v0)
% 2.90/1.44 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1))
% 2.90/1.44 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 2.90/1.44 | (8) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 2.90/1.44 | (9) subset(all_0_1_1, all_0_3_3)
% 2.90/1.44 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1))
% 2.90/1.45 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0))
% 2.90/1.45 | (12) symmetric_difference(all_0_5_5, all_0_4_4) = all_0_0_0
% 2.90/1.45 | (13) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1)))
% 2.90/1.45 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 2.90/1.45 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2)
% 2.90/1.45 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2)
% 2.90/1.45 | (17) subset(all_0_2_2, all_0_3_3)
% 2.90/1.45 | (18) difference(all_0_5_5, all_0_4_4) = all_0_2_2
% 2.90/1.45 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | ~ member(v2, v1))
% 2.90/1.45 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2))
% 2.90/1.45 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0))
% 2.90/1.45 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1))
% 2.90/1.45 | (23) difference(all_0_4_4, all_0_5_5) = all_0_1_1
% 2.90/1.45 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v0) = v3) | ~ (difference(v0, v1) = v2) | ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4)
% 2.90/1.45 |
% 2.90/1.45 | Instantiating formula (20) with all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms symmetric_difference(all_0_5_5, all_0_4_4) = all_0_0_0, yields:
% 2.90/1.45 | (25) ? [v0] : ? [v1] : (difference(all_0_4_4, all_0_5_5) = v1 & difference(all_0_5_5, all_0_4_4) = v0 & union(v0, v1) = all_0_0_0)
% 2.90/1.45 |
% 2.90/1.45 | Instantiating (25) with all_13_0_11, all_13_1_12 yields:
% 2.90/1.45 | (26) difference(all_0_4_4, all_0_5_5) = all_13_0_11 & difference(all_0_5_5, all_0_4_4) = all_13_1_12 & union(all_13_1_12, all_13_0_11) = all_0_0_0
% 2.90/1.45 |
% 2.90/1.45 | Applying alpha-rule on (26) yields:
% 2.90/1.45 | (27) difference(all_0_4_4, all_0_5_5) = all_13_0_11
% 2.90/1.45 | (28) difference(all_0_5_5, all_0_4_4) = all_13_1_12
% 2.90/1.45 | (29) union(all_13_1_12, all_13_0_11) = all_0_0_0
% 2.90/1.45 |
% 2.90/1.45 | Instantiating formula (14) with all_0_4_4, all_0_5_5, all_13_0_11, all_0_1_1 and discharging atoms difference(all_0_4_4, all_0_5_5) = all_13_0_11, difference(all_0_4_4, all_0_5_5) = all_0_1_1, yields:
% 2.90/1.45 | (30) all_13_0_11 = all_0_1_1
% 2.90/1.45 |
% 2.90/1.45 | Instantiating formula (14) with all_0_5_5, all_0_4_4, all_13_1_12, all_0_2_2 and discharging atoms difference(all_0_5_5, all_0_4_4) = all_13_1_12, difference(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 2.90/1.45 | (31) all_13_1_12 = all_0_2_2
% 2.90/1.45 |
% 3.11/1.45 | From (31)(30) and (29) follows:
% 3.11/1.46 | (32) union(all_0_2_2, all_0_1_1) = all_0_0_0
% 3.11/1.46 |
% 3.11/1.46 | Instantiating formula (10) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms union(all_0_2_2, all_0_1_1) = all_0_0_0, subset(all_0_1_1, all_0_3_3), subset(all_0_2_2, all_0_3_3), ~ subset(all_0_0_0, all_0_3_3), yields:
% 3.11/1.46 | (33) $false
% 3.11/1.46 |
% 3.11/1.46 |-The branch is then unsatisfiable
% 3.11/1.46 % SZS output end Proof for theBenchmark
% 3.11/1.46
% 3.11/1.46 854ms
%------------------------------------------------------------------------------