TSTP Solution File: SET618+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n008.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 00:20:52 EDT 2022
% Result : Theorem 2.10s 1.22s
% Output : Proof 3.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 06:47:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.67/0.63 ____ _
% 0.67/0.63 ___ / __ \_____(_)___ ________ __________
% 0.67/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.67/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.67/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.67/0.63
% 0.67/0.63 A Theorem Prover for First-Order Logic
% 0.67/0.63 (ePrincess v.1.0)
% 0.67/0.63
% 0.67/0.63 (c) Philipp Rümmer, 2009-2015
% 0.67/0.63 (c) Peter Backeman, 2014-2015
% 0.67/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.67/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.67/0.63 Bug reports to peter@backeman.se
% 0.67/0.63
% 0.67/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.67/0.63
% 0.67/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.52/0.93 Prover 0: Preprocessing ...
% 1.92/1.11 Prover 0: Warning: ignoring some quantifiers
% 2.01/1.12 Prover 0: Constructing countermodel ...
% 2.10/1.22 Prover 0: proved (533ms)
% 2.10/1.22
% 2.10/1.22 No countermodel exists, formula is valid
% 2.10/1.22 % SZS status Theorem for theBenchmark
% 2.10/1.22
% 2.10/1.22 Generating proof ... Warning: ignoring some quantifiers
% 2.83/1.42 found it (size 13)
% 2.83/1.42
% 2.83/1.42 % SZS output start Proof for theBenchmark
% 2.83/1.42 Assumed formulas after preprocessing and simplification:
% 2.83/1.42 | (0) ? [v0] : ? [v1] : ( ~ (v1 = empty_set) & symmetric_difference(v0, v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (difference(v3, v2) = v5) | ~ (difference(v2, v3) = v4) | ~ (union(v4, v5) = v6) | symmetric_difference(v2, v3) = v6) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (difference(v5, v4) = v3) | ~ (difference(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (union(v5, v4) = v3) | ~ (union(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (symmetric_difference(v5, v4) = v3) | ~ (symmetric_difference(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (union(v3, v2) = v4) | union(v2, v3) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (union(v2, v3) = v4) | union(v3, v2) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (symmetric_difference(v3, v2) = v4) | symmetric_difference(v2, v3) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (symmetric_difference(v2, v3) = v4) | symmetric_difference(v3, v2) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (symmetric_difference(v2, v3) = v4) | ? [v5] : ? [v6] : (difference(v3, v2) = v6 & difference(v2, v3) = v5 & union(v5, v6) = v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ subset(v2, v3) | ~ member(v4, v2) | member(v4, v3)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (union(v2, v2) = v3)) & ! [v2] : ! [v3] : (v3 = v2 | ~ subset(v3, v2) | ~ subset(v2, v3)) & ! [v2] : ! [v3] : (v3 = empty_set | ~ (difference(v2, 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))
% 3.03/1.46 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 3.03/1.46 | (1) ~ (all_0_0_0 = empty_set) & symmetric_difference(all_0_1_1, all_0_1_1) = all_0_0_0 & ! [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] : ( ~ (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] : ( ~ subset(v0, v1) | ~ member(v2, v0) | member(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (union(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (difference(v0, 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)
% 3.03/1.46 |
% 3.03/1.46 | Applying alpha-rule on (1) yields:
% 3.03/1.46 | (2) ! [v0] : ~ member(v0, empty_set)
% 3.03/1.46 | (3) ? [v0] : (empty(v0) | ? [v1] : member(v1, v0))
% 3.03/1.46 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 3.03/1.46 | (5) ! [v0] : ! [v1] : (v1 = empty_set | ~ (difference(v0, v0) = v1))
% 3.03/1.46 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0))
% 3.03/1.46 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2)
% 3.03/1.47 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2)
% 3.03/1.47 | (9) ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0))
% 3.03/1.47 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v0) = v3) | ~ (difference(v0, v1) = v2) | ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4)
% 3.03/1.47 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2)
% 3.03/1.47 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2)
% 3.03/1.47 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2))
% 3.03/1.47 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 3.03/1.47 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ (union(v0, v0) = v1))
% 3.03/1.47 | (16) symmetric_difference(all_0_1_1, all_0_1_1) = all_0_0_0
% 3.03/1.47 | (17) ? [v0] : subset(v0, v0)
% 3.03/1.47 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ member(v2, v0) | member(v2, v1))
% 3.03/1.47 | (19) ~ (all_0_0_0 = empty_set)
% 3.03/1.47 | (20) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1)))
% 3.03/1.47 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 3.03/1.47 | (22) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 3.03/1.47 |
% 3.03/1.47 | Instantiating formula (13) with all_0_0_0, all_0_1_1, all_0_1_1 and discharging atoms symmetric_difference(all_0_1_1, all_0_1_1) = all_0_0_0, yields:
% 3.03/1.47 | (23) ? [v0] : ? [v1] : (difference(all_0_1_1, all_0_1_1) = v1 & difference(all_0_1_1, all_0_1_1) = v0 & union(v0, v1) = all_0_0_0)
% 3.03/1.47 |
% 3.03/1.47 | Instantiating (23) with all_13_0_8, all_13_1_9 yields:
% 3.03/1.47 | (24) difference(all_0_1_1, all_0_1_1) = all_13_0_8 & difference(all_0_1_1, all_0_1_1) = all_13_1_9 & union(all_13_1_9, all_13_0_8) = all_0_0_0
% 3.03/1.47 |
% 3.03/1.47 | Applying alpha-rule on (24) yields:
% 3.03/1.47 | (25) difference(all_0_1_1, all_0_1_1) = all_13_0_8
% 3.03/1.47 | (26) difference(all_0_1_1, all_0_1_1) = all_13_1_9
% 3.03/1.47 | (27) union(all_13_1_9, all_13_0_8) = all_0_0_0
% 3.03/1.47 |
% 3.03/1.47 | Instantiating formula (5) with all_13_0_8, all_0_1_1 and discharging atoms difference(all_0_1_1, all_0_1_1) = all_13_0_8, yields:
% 3.03/1.47 | (28) all_13_0_8 = empty_set
% 3.03/1.47 |
% 3.03/1.47 | Instantiating formula (21) with all_0_1_1, all_0_1_1, all_13_1_9, all_13_0_8 and discharging atoms difference(all_0_1_1, all_0_1_1) = all_13_0_8, difference(all_0_1_1, all_0_1_1) = all_13_1_9, yields:
% 3.03/1.47 | (29) all_13_0_8 = all_13_1_9
% 3.03/1.47 |
% 3.03/1.47 | Combining equations (28,29) yields a new equation:
% 3.03/1.47 | (30) all_13_1_9 = empty_set
% 3.03/1.47 |
% 3.03/1.47 | Combining equations (30,29) yields a new equation:
% 3.03/1.47 | (28) all_13_0_8 = empty_set
% 3.03/1.47 |
% 3.03/1.47 | From (30)(28) and (27) follows:
% 3.03/1.48 | (32) union(empty_set, empty_set) = all_0_0_0
% 3.03/1.48 |
% 3.03/1.48 | Instantiating formula (15) with all_0_0_0, empty_set and discharging atoms union(empty_set, empty_set) = all_0_0_0, yields:
% 3.03/1.48 | (33) all_0_0_0 = empty_set
% 3.03/1.48 |
% 3.03/1.48 | Equations (33) can reduce 19 to:
% 3.03/1.48 | (34) $false
% 3.03/1.48 |
% 3.03/1.48 |-The branch is then unsatisfiable
% 3.03/1.48 % SZS output end Proof for theBenchmark
% 3.03/1.48
% 3.03/1.48 833ms
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