TSTP Solution File: SEU116+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU116+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 08:46:40 EDT 2022
% Result : Theorem 2.40s 1.24s
% Output : Proof 3.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU116+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n028.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 Jun 19 11:53:45 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.46/0.61 ____ _
% 0.46/0.61 ___ / __ \_____(_)___ ________ __________
% 0.46/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.46/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.46/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.46/0.61
% 0.46/0.61 A Theorem Prover for First-Order Logic
% 0.46/0.61 (ePrincess v.1.0)
% 0.46/0.61
% 0.46/0.61 (c) Philipp Rümmer, 2009-2015
% 0.46/0.61 (c) Peter Backeman, 2014-2015
% 0.46/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.46/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.46/0.61 Bug reports to peter@backeman.se
% 0.46/0.61
% 0.46/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.46/0.61
% 0.46/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.57/0.95 Prover 0: Preprocessing ...
% 2.06/1.13 Prover 0: Warning: ignoring some quantifiers
% 2.06/1.15 Prover 0: Constructing countermodel ...
% 2.40/1.24 Prover 0: proved (583ms)
% 2.40/1.24
% 2.40/1.24 No countermodel exists, formula is valid
% 2.40/1.24 % SZS status Theorem for theBenchmark
% 2.40/1.24
% 2.40/1.24 Generating proof ... Warning: ignoring some quantifiers
% 3.33/1.45 found it (size 4)
% 3.33/1.45
% 3.33/1.45 % SZS output start Proof for theBenchmark
% 3.33/1.45 Assumed formulas after preprocessing and simplification:
% 3.33/1.45 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (finite_subsets(v0) = v2 & cap_closed(v6) & finite(v5) & preboolean(v6) & diff_closed(v6) & cup_closed(v6) & element(v1, v2) & empty(v4) & empty(empty_set) & ~ finite(v1) & ~ empty(v6) & ~ empty(v5) & ~ empty(v3) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ element(v8, v10) | ~ empty(v9) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ element(v8, v10) | ~ in(v7, v8) | element(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (finite_subsets(v9) = v8) | ~ (finite_subsets(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (powerset(v9) = v8) | ~ (powerset(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (finite_subsets(v7) = v9) | ~ element(v8, v9) | finite(v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ~ element(v7, v9) | subset(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ~ subset(v7, v8) | element(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v7) = v8) | ~ finite(v7) | ~ element(v9, v8) | finite(v9)) & ! [v7] : ! [v8] : (v8 = v7 | ~ empty(v8) | ~ empty(v7)) & ! [v7] : ! [v8] : ( ~ (finite_subsets(v7) = v8) | ~ empty(v8)) & ! [v7] : ! [v8] : ( ~ (finite_subsets(v7) = v8) | preboolean(v8)) & ! [v7] : ! [v8] : ( ~ (finite_subsets(v7) = v8) | diff_closed(v8)) & ! [v7] : ! [v8] : ( ~ (finite_subsets(v7) = v8) | cup_closed(v8)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ~ empty(v8)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | preboolean(v8)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | diff_closed(v8)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | cup_closed(v8)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | empty(v7) | ? [v9] : (finite(v9) & element(v9, v8) & ~ empty(v9))) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | empty(v7) | ? [v9] : (element(v9, v8) & ~ empty(v9))) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ? [v9] : (natural(v9) & ordinal(v9) & epsilon_connected(v9) & epsilon_transitive(v9) & one_to_one(v9) & function(v9) & relation(v9) & finite(v9) & element(v9, v8) & empty(v9))) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ? [v9] : (element(v9, v8) & empty(v9))) & ! [v7] : ! [v8] : ( ~ element(v7, v8) | empty(v8) | in(v7, v8)) & ! [v7] : ! [v8] : ( ~ empty(v8) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ( ~ in(v7, v8) | element(v7, v8)) & ! [v7] : (v7 = empty_set | ~ empty(v7)) & ! [v7] : ( ~ preboolean(v7) | diff_closed(v7)) & ! [v7] : ( ~ preboolean(v7) | cup_closed(v7)) & ! [v7] : ( ~ diff_closed(v7) | ~ cup_closed(v7) | preboolean(v7)) & ! [v7] : ( ~ empty(v7) | finite(v7)) & ? [v7] : ? [v8] : element(v8, v7) & ? [v7] : subset(v7, v7))
% 3.33/1.50 | 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, all_0_6_6 yields:
% 3.33/1.50 | (1) finite_subsets(all_0_6_6) = all_0_4_4 & cap_closed(all_0_0_0) & finite(all_0_1_1) & preboolean(all_0_0_0) & diff_closed(all_0_0_0) & cup_closed(all_0_0_0) & element(all_0_5_5, all_0_4_4) & empty(all_0_2_2) & empty(empty_set) & ~ finite(all_0_5_5) & ~ empty(all_0_0_0) & ~ empty(all_0_1_1) & ~ empty(all_0_3_3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite_subsets(v2) = v1) | ~ (finite_subsets(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v2) | ~ element(v1, v2) | finite(v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ finite(v0) | ~ element(v2, v1) | finite(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | preboolean(v1)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | diff_closed(v1)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | cup_closed(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (finite(v2) & element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (natural(v2) & ordinal(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & one_to_one(v2) & function(v2) & relation(v2) & finite(v2) & element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ preboolean(v0) | diff_closed(v0)) & ! [v0] : ( ~ preboolean(v0) | cup_closed(v0)) & ! [v0] : ( ~ diff_closed(v0) | ~ cup_closed(v0) | preboolean(v0)) & ! [v0] : ( ~ empty(v0) | finite(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0)
% 3.33/1.50 |
% 3.33/1.50 | Applying alpha-rule on (1) yields:
% 3.33/1.50 | (2) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | diff_closed(v1))
% 3.33/1.50 | (3) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 3.33/1.50 | (4) ! [v0] : ( ~ preboolean(v0) | diff_closed(v0))
% 3.33/1.50 | (5) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 3.33/1.50 | (6) ~ empty(all_0_1_1)
% 3.33/1.50 | (7) ! [v0] : ( ~ empty(v0) | finite(v0))
% 3.33/1.50 | (8) preboolean(all_0_0_0)
% 3.33/1.50 | (9) ? [v0] : subset(v0, v0)
% 3.33/1.50 | (10) ! [v0] : ( ~ preboolean(v0) | cup_closed(v0))
% 3.33/1.51 | (11) ! [v0] : ( ~ diff_closed(v0) | ~ cup_closed(v0) | preboolean(v0))
% 3.33/1.51 | (12) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | cup_closed(v1))
% 3.33/1.51 | (13) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | ~ empty(v1))
% 3.33/1.51 | (14) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1))
% 3.33/1.51 | (15) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1))
% 3.33/1.51 | (16) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 3.33/1.51 | (17) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (natural(v2) & ordinal(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & one_to_one(v2) & function(v2) & relation(v2) & finite(v2) & element(v2, v1) & empty(v2)))
% 3.33/1.51 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ finite(v0) | ~ element(v2, v1) | finite(v2))
% 3.33/1.51 | (19) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 3.33/1.51 | (20) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (finite(v2) & element(v2, v1) & ~ empty(v2)))
% 3.33/1.51 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite_subsets(v2) = v1) | ~ (finite_subsets(v2) = v0))
% 3.33/1.51 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 3.33/1.51 | (23) ~ empty(all_0_3_3)
% 3.33/1.51 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 3.33/1.51 | (25) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 3.33/1.51 | (26) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1))
% 3.33/1.51 | (27) diff_closed(all_0_0_0)
% 3.33/1.51 | (28) ~ empty(all_0_0_0)
% 3.33/1.51 | (29) element(all_0_5_5, all_0_4_4)
% 3.33/1.51 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v2) | ~ element(v1, v2) | finite(v1))
% 3.33/1.51 | (31) finite(all_0_1_1)
% 3.33/1.51 | (32) cup_closed(all_0_0_0)
% 3.33/1.51 | (33) empty(all_0_2_2)
% 3.33/1.51 | (34) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 3.33/1.51 | (35) finite_subsets(all_0_6_6) = all_0_4_4
% 3.33/1.51 | (36) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 3.33/1.51 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 3.33/1.51 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 3.33/1.51 | (39) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 3.33/1.51 | (40) ~ finite(all_0_5_5)
% 3.33/1.51 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 3.33/1.51 | (42) empty(empty_set)
% 3.33/1.51 | (43) cap_closed(all_0_0_0)
% 3.33/1.51 | (44) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | preboolean(v1))
% 3.33/1.51 | (45) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 3.33/1.51 | (46) ? [v0] : ? [v1] : element(v1, v0)
% 3.33/1.51 |
% 3.33/1.52 | Instantiating formula (30) with all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms finite_subsets(all_0_6_6) = all_0_4_4, element(all_0_5_5, all_0_4_4), ~ finite(all_0_5_5), yields:
% 3.33/1.52 | (47) $false
% 3.33/1.52 |
% 3.33/1.52 |-The branch is then unsatisfiable
% 3.33/1.52 % SZS output end Proof for theBenchmark
% 3.33/1.52
% 3.33/1.52 897ms
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