%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : NUM390+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : Mon Jul 18 08:44:06 EDT 2022

% Result   : Theorem 3.06s 1.41s
% Output   : Proof 4.43s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM390+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Wed Jul  6 07:13:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.58/0.59          ____       _                          
% 0.58/0.59    ___  / __ \_____(_)___  ________  __________
% 0.58/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.58/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.58/0.59  
% 0.58/0.59  A Theorem Prover for First-Order Logic
% 0.58/0.60  (ePrincess v.1.0)
% 0.58/0.60  
% 0.58/0.60  (c) Philipp Rümmer, 2009-2015
% 0.58/0.60  (c) Peter Backeman, 2014-2015
% 0.58/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.60  Bug reports to peter@backeman.se
% 0.58/0.60  
% 0.58/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.60  
% 0.58/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.65  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.59/0.93  Prover 0: Preprocessing ...
% 2.08/1.10  Prover 0: Warning: ignoring some quantifiers
% 2.08/1.12  Prover 0: Constructing countermodel ...
% 3.06/1.41  Prover 0: proved (763ms)
% 3.06/1.41  
% 3.06/1.41  No countermodel exists, formula is valid
% 3.06/1.41  % SZS status Theorem for theBenchmark
% 3.06/1.41  
% 3.06/1.41  Generating proof ... Warning: ignoring some quantifiers
% 4.12/1.63  found it (size 18)
% 4.12/1.63  
% 4.12/1.63  % SZS output start Proof for theBenchmark
% 4.12/1.63  Assumed formulas after preprocessing and simplification: 
% 4.12/1.63  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] : (relation_non_empty(v3) & relation_empty_yielding(v5) & relation_empty_yielding(v4) & relation_empty_yielding(empty_set) & subset(v0, v1) & one_to_one(v6) & relation(v13) & relation(v11) & relation(v9) & relation(v8) & relation(v6) & relation(v5) & relation(v4) & relation(v3) & relation(empty_set) & epsilon_connected(v12) & epsilon_transitive(v12) & epsilon_transitive(v0) & ordinal(v12) & ordinal(v2) & ordinal(v1) & function(v13) & function(v9) & function(v6) & function(v4) & function(v3) & empty(v11) & empty(v10) & empty(v9) & empty(empty_set) & in(v1, v2) &  ~ empty(v8) &  ~ empty(v7) &  ~ in(v0, v2) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (powerset(v16) = v17) |  ~ element(v15, v17) |  ~ empty(v16) |  ~ in(v14, v15)) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (powerset(v16) = v17) |  ~ element(v15, v17) |  ~ in(v14, v15) | element(v14, v16)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (powerset(v16) = v15) |  ~ (powerset(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (powerset(v15) = v16) |  ~ element(v14, v16) | subset(v14, v15)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (powerset(v15) = v16) |  ~ subset(v14, v15) | element(v14, v16)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ subset(v15, v16) |  ~ subset(v14, v15) | subset(v14, v16)) &  ! [v14] :  ! [v15] : (v15 = v14 |  ~ subset(v14, v15) | proper_subset(v14, v15)) &  ! [v14] :  ! [v15] : (v15 = v14 |  ~ empty(v15) |  ~ empty(v14)) &  ! [v14] :  ! [v15] : ( ~ element(v14, v15) | empty(v15) | in(v14, v15)) &  ! [v14] :  ! [v15] : ( ~ subset(v15, v14) |  ~ in(v14, v15)) &  ! [v14] :  ! [v15] : ( ~ epsilon_transitive(v14) |  ~ ordinal(v15) |  ~ proper_subset(v14, v15) | in(v14, v15)) &  ! [v14] :  ! [v15] : ( ~ epsilon_transitive(v14) |  ~ in(v15, v14) | subset(v15, v14)) &  ! [v14] :  ! [v15] : ( ~ empty(v15) |  ~ in(v14, v15)) &  ! [v14] :  ! [v15] : ( ~ proper_subset(v15, v14) |  ~ proper_subset(v14, v15)) &  ! [v14] :  ! [v15] : ( ~ proper_subset(v14, v15) | subset(v14, v15)) &  ! [v14] :  ! [v15] : ( ~ in(v15, v14) |  ~ in(v14, v15)) &  ! [v14] :  ! [v15] : ( ~ in(v14, v15) | element(v14, v15)) &  ! [v14] : (v14 = empty_set |  ~ empty(v14)) &  ! [v14] : ( ~ relation(v14) |  ~ function(v14) |  ~ empty(v14) | one_to_one(v14)) &  ! [v14] : ( ~ epsilon_connected(v14) |  ~ epsilon_transitive(v14) | ordinal(v14)) &  ! [v14] : ( ~ ordinal(v14) | epsilon_connected(v14)) &  ! [v14] : ( ~ ordinal(v14) | epsilon_transitive(v14)) &  ! [v14] : ( ~ empty(v14) | relation(v14)) &  ! [v14] : ( ~ empty(v14) | function(v14)) &  ! [v14] :  ~ proper_subset(v14, v14) &  ? [v14] :  ? [v15] : element(v15, v14) &  ? [v14] : subset(v14, v14) &  ? [v14] : (epsilon_transitive(v14) |  ? [v15] : (in(v15, v14) &  ~ subset(v15, v14))))
% 4.12/1.68  | 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, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13 yields:
% 4.12/1.68  | (1) relation_non_empty(all_0_10_10) & relation_empty_yielding(all_0_8_8) & relation_empty_yielding(all_0_9_9) & relation_empty_yielding(empty_set) & subset(all_0_13_13, all_0_12_12) & one_to_one(all_0_7_7) & relation(all_0_0_0) & relation(all_0_2_2) & relation(all_0_4_4) & relation(all_0_5_5) & relation(all_0_7_7) & relation(all_0_8_8) & relation(all_0_9_9) & relation(all_0_10_10) & relation(empty_set) & epsilon_connected(all_0_1_1) & epsilon_transitive(all_0_1_1) & epsilon_transitive(all_0_13_13) & ordinal(all_0_1_1) & ordinal(all_0_11_11) & ordinal(all_0_12_12) & function(all_0_0_0) & function(all_0_4_4) & function(all_0_7_7) & function(all_0_9_9) & function(all_0_10_10) & empty(all_0_2_2) & empty(all_0_3_3) & empty(all_0_4_4) & empty(empty_set) & in(all_0_12_12, all_0_11_11) &  ~ empty(all_0_5_5) &  ~ empty(all_0_6_6) &  ~ in(all_0_13_13, all_0_11_11) &  ! [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 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0)) &  ! [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] : ( ~ subset(v1, v2) |  ~ subset(v0, v1) | subset(v0, v2)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v0, v1) | proper_subset(v0, v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ subset(v1, v0) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ epsilon_transitive(v0) |  ~ ordinal(v1) |  ~ proper_subset(v0, v1) | in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ epsilon_transitive(v0) |  ~ in(v1, v0) | subset(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ proper_subset(v1, v0) |  ~ proper_subset(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ proper_subset(v0, v1) | subset(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] : ( ~ relation(v0) |  ~ function(v0) |  ~ empty(v0) | one_to_one(v0)) &  ! [v0] : ( ~ epsilon_connected(v0) |  ~ epsilon_transitive(v0) | ordinal(v0)) &  ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0)) &  ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) &  ! [v0] : ( ~ empty(v0) | relation(v0)) &  ! [v0] : ( ~ empty(v0) | function(v0)) &  ! [v0] :  ~ proper_subset(v0, v0) &  ? [v0] :  ? [v1] : element(v1, v0) &  ? [v0] : subset(v0, v0) &  ? [v0] : (epsilon_transitive(v0) |  ? [v1] : (in(v1, v0) &  ~ subset(v1, v0)))
% 4.43/1.69  |
% 4.43/1.69  | Applying alpha-rule on (1) yields:
% 4.43/1.69  | (2) ordinal(all_0_12_12)
% 4.43/1.69  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 4.43/1.69  | (4)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 4.43/1.69  | (5) function(all_0_10_10)
% 4.43/1.69  | (6)  ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0))
% 4.43/1.69  | (7) empty(all_0_2_2)
% 4.43/1.69  | (8) epsilon_transitive(all_0_1_1)
% 4.43/1.69  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ empty(v2) |  ~ in(v0, v1))
% 4.43/1.69  | (10)  ~ in(all_0_13_13, all_0_11_11)
% 4.43/1.69  | (11)  ? [v0] : (epsilon_transitive(v0) |  ? [v1] : (in(v1, v0) &  ~ subset(v1, v0)))
% 4.43/1.69  | (12)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 4.43/1.69  | (13) function(all_0_0_0)
% 4.43/1.69  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ subset(v1, v2) |  ~ subset(v0, v1) | subset(v0, v2))
% 4.43/1.69  | (15) relation(all_0_2_2)
% 4.43/1.69  | (16) function(all_0_7_7)
% 4.43/1.69  | (17) relation(all_0_8_8)
% 4.43/1.69  | (18) relation(all_0_10_10)
% 4.43/1.69  | (19)  ! [v0] : ( ~ empty(v0) | function(v0))
% 4.43/1.69  | (20) relation_empty_yielding(all_0_8_8)
% 4.43/1.69  | (21) relation(all_0_5_5)
% 4.43/1.69  | (22)  ! [v0] :  ~ proper_subset(v0, v0)
% 4.43/1.69  | (23) relation(all_0_4_4)
% 4.43/1.69  | (24)  ? [v0] : subset(v0, v0)
% 4.43/1.69  | (25) relation(all_0_9_9)
% 4.43/1.69  | (26) ordinal(all_0_1_1)
% 4.43/1.69  | (27)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 4.43/1.69  | (28) relation(all_0_7_7)
% 4.43/1.70  | (29)  ~ empty(all_0_5_5)
% 4.43/1.70  | (30) function(all_0_4_4)
% 4.43/1.70  | (31)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 4.43/1.70  | (32)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 4.43/1.70  | (33) empty(all_0_4_4)
% 4.43/1.70  | (34)  ! [v0] :  ! [v1] : ( ~ epsilon_transitive(v0) |  ~ ordinal(v1) |  ~ proper_subset(v0, v1) | in(v0, v1))
% 4.43/1.70  | (35)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v0, v1) | proper_subset(v0, v1))
% 4.43/1.70  | (36) relation_empty_yielding(all_0_9_9)
% 4.43/1.70  | (37) epsilon_connected(all_0_1_1)
% 4.43/1.70  | (38)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 4.43/1.70  | (39)  ! [v0] :  ! [v1] : ( ~ epsilon_transitive(v0) |  ~ in(v1, v0) | subset(v1, v0))
% 4.43/1.70  | (40) ordinal(all_0_11_11)
% 4.43/1.70  | (41)  ~ empty(all_0_6_6)
% 4.43/1.70  | (42)  ! [v0] : ( ~ epsilon_connected(v0) |  ~ epsilon_transitive(v0) | ordinal(v0))
% 4.43/1.70  | (43) relation(empty_set)
% 4.43/1.70  | (44) function(all_0_9_9)
% 4.43/1.70  | (45) relation_non_empty(all_0_10_10)
% 4.43/1.70  | (46)  ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0))
% 4.43/1.70  | (47) epsilon_transitive(all_0_13_13)
% 4.43/1.70  | (48)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 4.43/1.70  | (49)  ! [v0] :  ! [v1] : ( ~ proper_subset(v1, v0) |  ~ proper_subset(v0, v1))
% 4.43/1.70  | (50)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 4.43/1.70  | (51) in(all_0_12_12, all_0_11_11)
% 4.43/1.70  | (52)  ! [v0] : ( ~ relation(v0) |  ~ function(v0) |  ~ empty(v0) | one_to_one(v0))
% 4.43/1.70  | (53) relation_empty_yielding(empty_set)
% 4.43/1.70  | (54)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 4.43/1.70  | (55) one_to_one(all_0_7_7)
% 4.43/1.70  | (56)  ! [v0] :  ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1))
% 4.43/1.70  | (57) relation(all_0_0_0)
% 4.43/1.70  | (58)  ! [v0] :  ! [v1] : ( ~ subset(v1, v0) |  ~ in(v0, v1))
% 4.43/1.70  | (59) empty(empty_set)
% 4.43/1.70  | (60)  ? [v0] :  ? [v1] : element(v1, v0)
% 4.43/1.70  | (61)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 4.43/1.70  | (62) subset(all_0_13_13, all_0_12_12)
% 4.43/1.70  | (63) empty(all_0_3_3)
% 4.43/1.70  |
% 4.43/1.71  | Instantiating formula (35) with all_0_12_12, all_0_13_13 and discharging atoms subset(all_0_13_13, all_0_12_12), yields:
% 4.43/1.71  | (64) all_0_12_12 = all_0_13_13 | proper_subset(all_0_13_13, all_0_12_12)
% 4.43/1.71  |
% 4.43/1.71  | Instantiating formula (46) with all_0_11_11 and discharging atoms ordinal(all_0_11_11), yields:
% 4.43/1.71  | (65) epsilon_transitive(all_0_11_11)
% 4.43/1.71  |
% 4.43/1.71  | Instantiating formula (39) with all_0_12_12, all_0_11_11 and discharging atoms epsilon_transitive(all_0_11_11), in(all_0_12_12, all_0_11_11), yields:
% 4.43/1.71  | (66) subset(all_0_12_12, all_0_11_11)
% 4.43/1.71  |
% 4.43/1.71  | Instantiating formula (14) with all_0_11_11, all_0_12_12, all_0_13_13 and discharging atoms subset(all_0_12_12, all_0_11_11), subset(all_0_13_13, all_0_12_12), yields:
% 4.43/1.71  | (67) subset(all_0_13_13, all_0_11_11)
% 4.43/1.71  |
% 4.43/1.71  | Instantiating formula (35) with all_0_11_11, all_0_13_13 and discharging atoms subset(all_0_13_13, all_0_11_11), yields:
% 4.43/1.71  | (68) all_0_11_11 = all_0_13_13 | proper_subset(all_0_13_13, all_0_11_11)
% 4.43/1.71  |
% 4.43/1.71  +-Applying beta-rule and splitting (64), into two cases.
% 4.43/1.71  |-Branch one:
% 4.43/1.71  | (69) proper_subset(all_0_13_13, all_0_12_12)
% 4.43/1.71  |
% 4.43/1.71  	| Instantiating formula (34) with all_0_12_12, all_0_13_13 and discharging atoms epsilon_transitive(all_0_13_13), ordinal(all_0_12_12), proper_subset(all_0_13_13, all_0_12_12), yields:
% 4.43/1.71  	| (70) in(all_0_13_13, all_0_12_12)
% 4.43/1.71  	|
% 4.43/1.71  	+-Applying beta-rule and splitting (68), into two cases.
% 4.43/1.71  	|-Branch one:
% 4.43/1.71  	| (71) proper_subset(all_0_13_13, all_0_11_11)
% 4.43/1.71  	|
% 4.43/1.71  		| Instantiating formula (34) with all_0_11_11, all_0_13_13 and discharging atoms epsilon_transitive(all_0_13_13), ordinal(all_0_11_11), proper_subset(all_0_13_13, all_0_11_11),  ~ in(all_0_13_13, all_0_11_11), yields:
% 4.43/1.71  		| (72) $false
% 4.43/1.71  		|
% 4.43/1.71  		|-The branch is then unsatisfiable
% 4.43/1.71  	|-Branch two:
% 4.43/1.71  	| (73)  ~ proper_subset(all_0_13_13, all_0_11_11)
% 4.43/1.71  	| (74) all_0_11_11 = all_0_13_13
% 4.43/1.71  	|
% 4.43/1.71  		| From (74) and (51) follows:
% 4.43/1.71  		| (75) in(all_0_12_12, all_0_13_13)
% 4.43/1.71  		|
% 4.43/1.71  		| Instantiating formula (27) with all_0_12_12, all_0_13_13 and discharging atoms in(all_0_12_12, all_0_13_13), in(all_0_13_13, all_0_12_12), yields:
% 4.43/1.71  		| (72) $false
% 4.43/1.71  		|
% 4.43/1.71  		|-The branch is then unsatisfiable
% 4.43/1.71  |-Branch two:
% 4.43/1.71  | (77)  ~ proper_subset(all_0_13_13, all_0_12_12)
% 4.43/1.71  | (78) all_0_12_12 = all_0_13_13
% 4.43/1.71  |
% 4.43/1.71  	| From (78) and (51) follows:
% 4.43/1.71  	| (79) in(all_0_13_13, all_0_11_11)
% 4.43/1.71  	|
% 4.43/1.71  	| Using (79) and (10) yields:
% 4.43/1.71  	| (72) $false
% 4.43/1.71  	|
% 4.43/1.71  	|-The branch is then unsatisfiable
% 4.43/1.71  % SZS output end Proof for theBenchmark
% 4.43/1.71  
% 4.43/1.71  1107ms
%------------------------------------------------------------------------------