TSTP Solution File: SEU115+1 by ePrincess---1.0

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%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU115+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 2.78s 1.40s
% Output   : Proof 4.38s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU115+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.33  % Computer : n028.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 : Sun Jun 19 09:06:00 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.54/0.62          ____       _                          
% 0.54/0.62    ___  / __ \_____(_)___  ________  __________
% 0.54/0.62   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.62  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.54/0.62  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.54/0.62  
% 0.54/0.62  A Theorem Prover for First-Order Logic
% 0.54/0.62  (ePrincess v.1.0)
% 0.54/0.62  
% 0.54/0.62  (c) Philipp Rümmer, 2009-2015
% 0.54/0.62  (c) Peter Backeman, 2014-2015
% 0.54/0.62  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.62  Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.62  Bug reports to peter@backeman.se
% 0.54/0.62  
% 0.54/0.62  For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.62  
% 0.54/0.62  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.69  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.69/1.03  Prover 0: Preprocessing ...
% 2.26/1.25  Prover 0: Warning: ignoring some quantifiers
% 2.26/1.27  Prover 0: Constructing countermodel ...
% 2.78/1.40  Prover 0: proved (709ms)
% 2.78/1.40  
% 2.78/1.40  No countermodel exists, formula is valid
% 2.78/1.40  % SZS status Theorem for theBenchmark
% 2.78/1.40  
% 2.78/1.40  Generating proof ... Warning: ignoring some quantifiers
% 4.00/1.71  found it (size 17)
% 4.00/1.71  
% 4.00/1.71  % SZS output start Proof for theBenchmark
% 4.00/1.71  Assumed formulas after preprocessing and simplification: 
% 4.00/1.71  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v1 = v0) & singleton(empty_set) = v0 & finite_subsets(empty_set) = v1 & powerset(empty_set) = v0 & cap_closed(v5) & finite(v4) & diff_closed(v5) & cup_closed(v5) & preboolean(v5) & empty(v3) & empty(empty_set) &  ~ empty(v5) &  ~ empty(v4) &  ~ empty(v2) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (powerset(v8) = v9) |  ~ empty(v8) |  ~ element(v7, v9) |  ~ in(v6, v7)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (powerset(v8) = v9) |  ~ element(v7, v9) |  ~ in(v6, v7) | element(v6, v8)) &  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v6 |  ~ (singleton(v8) = v7) |  ~ (singleton(v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v6 |  ~ (finite_subsets(v8) = v7) |  ~ (finite_subsets(v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v6 |  ~ (powerset(v8) = v7) |  ~ (powerset(v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (finite_subsets(v6) = v8) |  ~ element(v7, v8) | finite(v7)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (powerset(v7) = v8) |  ~ element(v6, v8) | subset(v6, v7)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (powerset(v7) = v8) |  ~ subset(v6, v7) | element(v6, v8)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (powerset(v6) = v7) |  ~ finite(v6) |  ~ element(v8, v7) | finite(v8)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ empty(v7) |  ~ empty(v6)) &  ! [v6] :  ! [v7] : ( ~ (singleton(v6) = v7) |  ~ empty(v7)) &  ! [v6] :  ! [v7] : ( ~ (singleton(v6) = v7) | finite(v7)) &  ! [v6] :  ! [v7] : ( ~ (finite_subsets(v6) = v7) |  ~ finite(v6) | powerset(v6) = v7) &  ! [v6] :  ! [v7] : ( ~ (finite_subsets(v6) = v7) |  ~ empty(v7)) &  ! [v6] :  ! [v7] : ( ~ (finite_subsets(v6) = v7) | diff_closed(v7)) &  ! [v6] :  ! [v7] : ( ~ (finite_subsets(v6) = v7) | cup_closed(v7)) &  ! [v6] :  ! [v7] : ( ~ (finite_subsets(v6) = v7) | preboolean(v7)) &  ! [v6] :  ! [v7] : ( ~ (powerset(v6) = v7) |  ~ finite(v6) | finite_subsets(v6) = v7) &  ! [v6] :  ! [v7] : ( ~ (powerset(v6) = v7) |  ~ empty(v7)) &  ! [v6] :  ! [v7] : ( ~ (powerset(v6) = v7) | diff_closed(v7)) &  ! [v6] :  ! [v7] : ( ~ (powerset(v6) = v7) | cup_closed(v7)) &  ! [v6] :  ! [v7] : ( ~ (powerset(v6) = v7) | preboolean(v7)) &  ! [v6] :  ! [v7] : ( ~ (powerset(v6) = v7) | empty(v6) |  ? [v8] : (finite(v8) & element(v8, v7) &  ~ empty(v8))) &  ! [v6] :  ! [v7] : ( ~ (powerset(v6) = v7) | empty(v6) |  ? [v8] : (element(v8, v7) &  ~ empty(v8))) &  ! [v6] :  ! [v7] : ( ~ (powerset(v6) = v7) |  ? [v8] : (natural(v8) & ordinal(v8) & epsilon_connected(v8) & epsilon_transitive(v8) & one_to_one(v8) & function(v8) & relation(v8) & finite(v8) & empty(v8) & element(v8, v7))) &  ! [v6] :  ! [v7] : ( ~ (powerset(v6) = v7) |  ? [v8] : (empty(v8) & element(v8, v7))) &  ! [v6] :  ! [v7] : ( ~ empty(v7) |  ~ in(v6, v7)) &  ! [v6] :  ! [v7] : ( ~ element(v6, v7) | empty(v7) | in(v6, v7)) &  ! [v6] :  ! [v7] : ( ~ in(v7, v6) |  ~ in(v6, v7)) &  ! [v6] :  ! [v7] : ( ~ in(v6, v7) | element(v6, v7)) &  ! [v6] : (v6 = empty_set |  ~ empty(v6)) &  ! [v6] : ( ~ diff_closed(v6) |  ~ cup_closed(v6) | preboolean(v6)) &  ! [v6] : ( ~ preboolean(v6) | diff_closed(v6)) &  ! [v6] : ( ~ preboolean(v6) | cup_closed(v6)) &  ! [v6] : ( ~ empty(v6) | finite(v6)) &  ? [v6] :  ? [v7] : element(v7, v6) &  ? [v6] : subset(v6, v6))
% 4.00/1.75  | 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:
% 4.00/1.75  | (1)  ~ (all_0_4_4 = all_0_5_5) & singleton(empty_set) = all_0_5_5 & finite_subsets(empty_set) = all_0_4_4 & powerset(empty_set) = all_0_5_5 & cap_closed(all_0_0_0) & finite(all_0_1_1) & diff_closed(all_0_0_0) & cup_closed(all_0_0_0) & preboolean(all_0_0_0) & empty(all_0_2_2) & empty(empty_set) &  ~ empty(all_0_0_0) &  ~ empty(all_0_1_1) &  ~ empty(all_0_3_3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ empty(v2) |  ~ element(v1, v3) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [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] : ( ~ (singleton(v0) = v1) |  ~ empty(v1)) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | finite(v1)) &  ! [v0] :  ! [v1] : ( ~ (finite_subsets(v0) = v1) |  ~ finite(v0) | powerset(v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (finite_subsets(v0) = v1) |  ~ empty(v1)) &  ! [v0] :  ! [v1] : ( ~ (finite_subsets(v0) = v1) | diff_closed(v1)) &  ! [v0] :  ! [v1] : ( ~ (finite_subsets(v0) = v1) | cup_closed(v1)) &  ! [v0] :  ! [v1] : ( ~ (finite_subsets(v0) = v1) | preboolean(v1)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ finite(v0) | finite_subsets(v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(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) & empty(v2) & element(v2, v1))) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (empty(v2) & element(v2, v1))) &  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ element(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] : ( ~ diff_closed(v0) |  ~ cup_closed(v0) | preboolean(v0)) &  ! [v0] : ( ~ preboolean(v0) | diff_closed(v0)) &  ! [v0] : ( ~ preboolean(v0) | cup_closed(v0)) &  ! [v0] : ( ~ empty(v0) | finite(v0)) &  ? [v0] :  ? [v1] : element(v1, v0) &  ? [v0] : subset(v0, v0)
% 4.00/1.76  |
% 4.00/1.76  | Applying alpha-rule on (1) yields:
% 4.00/1.76  | (2)  ~ empty(all_0_1_1)
% 4.00/1.76  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 4.00/1.76  | (4)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 4.00/1.76  | (5)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 4.00/1.76  | (6)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 4.00/1.76  | (7)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 4.00/1.76  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 4.00/1.76  | (9)  ~ (all_0_4_4 = all_0_5_5)
% 4.00/1.76  | (10)  ! [v0] :  ! [v1] : ( ~ (finite_subsets(v0) = v1) |  ~ empty(v1))
% 4.00/1.76  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (finite_subsets(v0) = v2) |  ~ element(v1, v2) | finite(v1))
% 4.00/1.76  | (12)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 4.00/1.76  | (13)  ! [v0] :  ! [v1] : ( ~ (finite_subsets(v0) = v1) | diff_closed(v1))
% 4.00/1.76  | (14)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ finite(v0) | finite_subsets(v0) = v1)
% 4.00/1.76  | (15)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 4.00/1.76  | (16) powerset(empty_set) = all_0_5_5
% 4.00/1.76  | (17)  ~ empty(all_0_0_0)
% 4.00/1.76  | (18) empty(all_0_2_2)
% 4.00/1.76  | (19)  ! [v0] : ( ~ diff_closed(v0) |  ~ cup_closed(v0) | preboolean(v0))
% 4.00/1.76  | (20) empty(empty_set)
% 4.00/1.76  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ empty(v2) |  ~ element(v1, v3) |  ~ in(v0, v1))
% 4.00/1.76  | (22)  ! [v0] :  ! [v1] : ( ~ (finite_subsets(v0) = v1) |  ~ finite(v0) | powerset(v0) = v1)
% 4.00/1.77  | (23) finite_subsets(empty_set) = all_0_4_4
% 4.00/1.77  | (24)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (finite(v2) & element(v2, v1) &  ~ empty(v2)))
% 4.00/1.77  | (25) diff_closed(all_0_0_0)
% 4.00/1.77  | (26)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 4.00/1.77  | (27)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 4.00/1.77  | (28)  ~ empty(all_0_3_3)
% 4.00/1.77  | (29)  ! [v0] : ( ~ preboolean(v0) | cup_closed(v0))
% 4.00/1.77  | (30)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (empty(v2) & element(v2, v1)))
% 4.00/1.77  | (31)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (finite_subsets(v2) = v1) |  ~ (finite_subsets(v2) = v0))
% 4.00/1.77  | (32) singleton(empty_set) = all_0_5_5
% 4.00/1.77  | (33) preboolean(all_0_0_0)
% 4.00/1.77  | (34)  ! [v0] :  ! [v1] : ( ~ (finite_subsets(v0) = v1) | preboolean(v1))
% 4.00/1.77  | (35)  ? [v0] :  ? [v1] : element(v1, v0)
% 4.00/1.77  | (36)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ~ empty(v1))
% 4.00/1.77  | (37) cup_closed(all_0_0_0)
% 4.00/1.77  | (38)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1))
% 4.00/1.77  | (39)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ finite(v0) |  ~ element(v2, v1) | finite(v2))
% 4.00/1.77  | (40)  ? [v0] : subset(v0, v0)
% 4.00/1.77  | (41)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 4.00/1.77  | (42)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1))
% 4.00/1.77  | (43)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | finite(v1))
% 4.00/1.77  | (44)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 4.00/1.77  | (45)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1))
% 4.00/1.77  | (46)  ! [v0] : ( ~ empty(v0) | finite(v0))
% 4.00/1.77  | (47) finite(all_0_1_1)
% 4.00/1.77  | (48)  ! [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) & empty(v2) & element(v2, v1)))
% 4.00/1.77  | (49)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 4.00/1.77  | (50)  ! [v0] : ( ~ preboolean(v0) | diff_closed(v0))
% 4.00/1.77  | (51) cap_closed(all_0_0_0)
% 4.00/1.77  | (52)  ! [v0] :  ! [v1] : ( ~ (finite_subsets(v0) = v1) | cup_closed(v1))
% 4.00/1.77  |
% 4.00/1.77  | Instantiating formula (48) with all_0_5_5, empty_set and discharging atoms powerset(empty_set) = all_0_5_5, yields:
% 4.00/1.77  | (53)  ? [v0] : (natural(v0) & ordinal(v0) & epsilon_connected(v0) & epsilon_transitive(v0) & one_to_one(v0) & function(v0) & relation(v0) & finite(v0) & empty(v0) & element(v0, all_0_5_5))
% 4.00/1.77  |
% 4.00/1.77  | Instantiating formula (30) with all_0_5_5, empty_set and discharging atoms powerset(empty_set) = all_0_5_5, yields:
% 4.00/1.77  | (54)  ? [v0] : (empty(v0) & element(v0, all_0_5_5))
% 4.00/1.77  |
% 4.00/1.78  | Instantiating (54) with all_17_0_9 yields:
% 4.00/1.78  | (55) empty(all_17_0_9) & element(all_17_0_9, all_0_5_5)
% 4.00/1.78  |
% 4.00/1.78  | Applying alpha-rule on (55) yields:
% 4.00/1.78  | (56) empty(all_17_0_9)
% 4.00/1.78  | (57) element(all_17_0_9, all_0_5_5)
% 4.00/1.78  |
% 4.00/1.78  | Instantiating (53) with all_19_0_10 yields:
% 4.00/1.78  | (58) natural(all_19_0_10) & ordinal(all_19_0_10) & epsilon_connected(all_19_0_10) & epsilon_transitive(all_19_0_10) & one_to_one(all_19_0_10) & function(all_19_0_10) & relation(all_19_0_10) & finite(all_19_0_10) & empty(all_19_0_10) & element(all_19_0_10, all_0_5_5)
% 4.00/1.78  |
% 4.00/1.78  | Applying alpha-rule on (58) yields:
% 4.00/1.78  | (59) element(all_19_0_10, all_0_5_5)
% 4.00/1.78  | (60) epsilon_connected(all_19_0_10)
% 4.00/1.78  | (61) ordinal(all_19_0_10)
% 4.00/1.78  | (62) empty(all_19_0_10)
% 4.00/1.78  | (63) one_to_one(all_19_0_10)
% 4.00/1.78  | (64) epsilon_transitive(all_19_0_10)
% 4.00/1.78  | (65) natural(all_19_0_10)
% 4.00/1.78  | (66) relation(all_19_0_10)
% 4.00/1.78  | (67) finite(all_19_0_10)
% 4.00/1.78  | (68) function(all_19_0_10)
% 4.00/1.78  |
% 4.00/1.78  | Instantiating formula (27) with all_19_0_10 and discharging atoms empty(all_19_0_10), yields:
% 4.00/1.78  | (69) all_19_0_10 = empty_set
% 4.38/1.78  |
% 4.38/1.78  | Instantiating formula (12) with all_17_0_9, all_19_0_10 and discharging atoms empty(all_19_0_10), empty(all_17_0_9), yields:
% 4.38/1.78  | (70) all_19_0_10 = all_17_0_9
% 4.38/1.78  |
% 4.38/1.78  | Combining equations (69,70) yields a new equation:
% 4.38/1.78  | (71) all_17_0_9 = empty_set
% 4.38/1.78  |
% 4.38/1.78  | Combining equations (71,70) yields a new equation:
% 4.38/1.78  | (69) all_19_0_10 = empty_set
% 4.38/1.78  |
% 4.38/1.78  | From (69) and (67) follows:
% 4.38/1.78  | (73) finite(empty_set)
% 4.38/1.78  |
% 4.38/1.78  | Instantiating formula (22) with all_0_4_4, empty_set and discharging atoms finite_subsets(empty_set) = all_0_4_4, finite(empty_set), yields:
% 4.38/1.78  | (74) powerset(empty_set) = all_0_4_4
% 4.38/1.78  |
% 4.38/1.78  | Instantiating formula (44) with empty_set, all_0_4_4, all_0_5_5 and discharging atoms powerset(empty_set) = all_0_4_4, powerset(empty_set) = all_0_5_5, yields:
% 4.38/1.78  | (75) all_0_4_4 = all_0_5_5
% 4.38/1.78  |
% 4.38/1.78  | Equations (75) can reduce 9 to:
% 4.38/1.78  | (76) $false
% 4.38/1.78  |
% 4.38/1.78  |-The branch is then unsatisfiable
% 4.38/1.78  % SZS output end Proof for theBenchmark
% 4.38/1.78  
% 4.38/1.78  1148ms
%------------------------------------------------------------------------------