%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU041+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n020.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 08:46:20 EDT 2022

% Result   : Theorem 2.65s 1.30s
% Output   : Proof 3.84s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU041+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.33  % Computer : n020.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 : Mon Jun 20 11:08:03 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.51/0.58          ____       _                          
% 0.51/0.58    ___  / __ \_____(_)___  ________  __________
% 0.51/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.51/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.51/0.58  
% 0.51/0.58  A Theorem Prover for First-Order Logic
% 0.51/0.58  (ePrincess v.1.0)
% 0.51/0.58  
% 0.51/0.58  (c) Philipp Rümmer, 2009-2015
% 0.51/0.58  (c) Peter Backeman, 2014-2015
% 0.51/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.58  Bug reports to peter@backeman.se
% 0.51/0.58  
% 0.51/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.58  
% 0.51/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.76/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.64/0.96  Prover 0: Preprocessing ...
% 2.17/1.14  Prover 0: Warning: ignoring some quantifiers
% 2.26/1.16  Prover 0: Constructing countermodel ...
% 2.65/1.30  Prover 0: proved (670ms)
% 2.65/1.30  
% 2.65/1.30  No countermodel exists, formula is valid
% 2.65/1.30  % SZS status Theorem for theBenchmark
% 2.65/1.30  
% 2.65/1.30  Generating proof ... Warning: ignoring some quantifiers
% 3.73/1.56  found it (size 10)
% 3.73/1.56  
% 3.73/1.56  % SZS output start Proof for theBenchmark
% 3.73/1.56  Assumed formulas after preprocessing and simplification: 
% 3.73/1.56  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (relation_dom_restriction(v5, v0) = v6 & relation_dom_restriction(v3, v1) = v4 & relation_dom_restriction(v2, v1) = v5 & relation_dom_restriction(v2, v0) = v3 & subset(v0, v1) & one_to_one(v12) & function(v14) & function(v13) & function(v12) & function(v2) & relation_empty_yielding(v9) & relation_empty_yielding(empty_set) & relation(v14) & relation(v13) & relation(v12) & relation(v11) & relation(v10) & relation(v9) & relation(v2) & relation(empty_set) & empty(v13) & empty(v11) & empty(v8) & empty(empty_set) &  ~ empty(v10) &  ~ empty(v7) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] : (v19 = v18 |  ~ (relation_dom_restriction(v18, v16) = v19) |  ~ (relation_dom_restriction(v17, v15) = v18) |  ~ subset(v15, v16) |  ~ relation(v17)) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] : ( ~ (relation_dom_restriction(v18, v15) = v19) |  ~ (relation_dom_restriction(v17, v16) = v18) |  ~ subset(v15, v16) |  ~ relation(v17) | relation_dom_restriction(v17, v15) = v19) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : (v16 = v15 |  ~ (relation_dom_restriction(v18, v17) = v16) |  ~ (relation_dom_restriction(v18, v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (powerset(v17) = v18) |  ~ element(v16, v18) |  ~ empty(v17) |  ~ in(v15, v16)) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (powerset(v17) = v18) |  ~ element(v16, v18) |  ~ in(v15, v16) | element(v15, v17)) &  ! [v15] :  ! [v16] :  ! [v17] : (v16 = v15 |  ~ (powerset(v17) = v16) |  ~ (powerset(v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) |  ~ function(v15) |  ~ relation(v15) | function(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) |  ~ function(v15) |  ~ relation(v15) | relation(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) |  ~ relation_empty_yielding(v15) |  ~ relation(v15) | relation_empty_yielding(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) |  ~ relation_empty_yielding(v15) |  ~ relation(v15) | relation(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) |  ~ relation(v15) | relation(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (powerset(v16) = v17) |  ~ subset(v15, v16) | element(v15, v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (powerset(v16) = v17) |  ~ element(v15, v17) | subset(v15, v16)) &  ! [v15] :  ! [v16] : (v16 = v15 |  ~ empty(v16) |  ~ empty(v15)) &  ! [v15] :  ! [v16] : ( ~ (powerset(v15) = v16) |  ~ empty(v16)) &  ! [v15] :  ! [v16] : ( ~ (powerset(v15) = v16) | empty(v15) |  ? [v17] : (element(v17, v16) &  ~ empty(v17))) &  ! [v15] :  ! [v16] : ( ~ (powerset(v15) = v16) |  ? [v17] : (element(v17, v16) & empty(v17))) &  ! [v15] :  ! [v16] : ( ~ element(v15, v16) | empty(v16) | in(v15, v16)) &  ! [v15] :  ! [v16] : ( ~ empty(v16) |  ~ in(v15, v16)) &  ! [v15] :  ! [v16] : ( ~ in(v16, v15) |  ~ in(v15, v16)) &  ! [v15] :  ! [v16] : ( ~ in(v15, v16) | element(v15, v16)) &  ! [v15] : (v15 = empty_set |  ~ empty(v15)) &  ! [v15] : ( ~ function(v15) |  ~ relation(v15) |  ~ empty(v15) | one_to_one(v15)) &  ! [v15] : ( ~ empty(v15) | function(v15)) &  ! [v15] : ( ~ empty(v15) | relation(v15)) &  ? [v15] :  ? [v16] : element(v16, v15) &  ? [v15] : subset(v15, v15) & ( ~ (v6 = v3) |  ~ (v4 = v3)))
% 3.84/1.60  | 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, all_0_14_14 yields:
% 3.84/1.60  | (1) relation_dom_restriction(all_0_9_9, all_0_14_14) = all_0_8_8 & relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10 & relation_dom_restriction(all_0_12_12, all_0_13_13) = all_0_9_9 & relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_11_11 & subset(all_0_14_14, all_0_13_13) & one_to_one(all_0_2_2) & function(all_0_0_0) & function(all_0_1_1) & function(all_0_2_2) & function(all_0_12_12) & relation_empty_yielding(all_0_5_5) & relation_empty_yielding(empty_set) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_2_2) & relation(all_0_3_3) & relation(all_0_4_4) & relation(all_0_5_5) & relation(all_0_12_12) & relation(empty_set) & empty(all_0_1_1) & empty(all_0_3_3) & empty(all_0_6_6) & empty(empty_set) &  ~ empty(all_0_4_4) &  ~ empty(all_0_7_7) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (relation_dom_restriction(v3, v1) = v4) |  ~ (relation_dom_restriction(v2, v0) = v3) |  ~ subset(v0, v1) |  ~ relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom_restriction(v3, v0) = v4) |  ~ (relation_dom_restriction(v2, v1) = v3) |  ~ subset(v0, v1) |  ~ relation(v2) | relation_dom_restriction(v2, v0) = v4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_dom_restriction(v3, v2) = v1) |  ~ (relation_dom_restriction(v3, v2) = v0)) &  ! [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] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ function(v0) |  ~ relation(v0) | function(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ function(v0) |  ~ relation(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation_empty_yielding(v0) |  ~ relation(v0) | relation_empty_yielding(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation_empty_yielding(v0) |  ~ relation(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [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] : ( ~ function(v0) |  ~ relation(v0) |  ~ empty(v0) | one_to_one(v0)) &  ! [v0] : ( ~ empty(v0) | function(v0)) &  ! [v0] : ( ~ empty(v0) | relation(v0)) &  ? [v0] :  ? [v1] : element(v1, v0) &  ? [v0] : subset(v0, v0) & ( ~ (all_0_8_8 = all_0_11_11) |  ~ (all_0_10_10 = all_0_11_11))
% 3.84/1.61  |
% 3.84/1.61  | Applying alpha-rule on (1) yields:
% 3.84/1.61  | (2) relation(all_0_5_5)
% 3.84/1.61  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ empty(v2) |  ~ in(v0, v1))
% 3.84/1.61  | (4)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 3.84/1.61  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 3.84/1.61  | (6) relation_dom_restriction(all_0_12_12, all_0_13_13) = all_0_9_9
% 3.84/1.61  | (7) relation(all_0_12_12)
% 3.84/1.61  | (8)  ? [v0] :  ? [v1] : element(v1, v0)
% 3.84/1.61  | (9) empty(all_0_3_3)
% 3.84/1.61  | (10) relation(all_0_3_3)
% 3.84/1.61  | (11)  ~ empty(all_0_4_4)
% 3.84/1.61  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ function(v0) |  ~ relation(v0) | function(v2))
% 3.84/1.61  | (13)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 3.84/1.61  | (14) function(all_0_1_1)
% 3.84/1.61  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom_restriction(v3, v0) = v4) |  ~ (relation_dom_restriction(v2, v1) = v3) |  ~ subset(v0, v1) |  ~ relation(v2) | relation_dom_restriction(v2, v0) = v4)
% 3.84/1.61  | (16)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 3.84/1.61  | (17)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 3.84/1.61  | (18)  ! [v0] : ( ~ empty(v0) | function(v0))
% 3.84/1.61  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation_empty_yielding(v0) |  ~ relation(v0) | relation(v2))
% 3.84/1.61  | (20) function(all_0_2_2)
% 3.84/1.61  | (21)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 3.84/1.61  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_dom_restriction(v3, v2) = v1) |  ~ (relation_dom_restriction(v3, v2) = v0))
% 3.84/1.61  | (23) empty(empty_set)
% 3.84/1.61  | (24)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 3.84/1.62  | (25)  ~ empty(all_0_7_7)
% 3.84/1.62  | (26)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 3.84/1.62  | (27) relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_11_11
% 3.84/1.62  | (28) relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10
% 3.84/1.62  | (29) function(all_0_0_0)
% 3.84/1.62  | (30)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 3.84/1.62  | (31)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 3.84/1.62  | (32)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) & empty(v2)))
% 3.84/1.62  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 3.84/1.62  | (34) subset(all_0_14_14, all_0_13_13)
% 3.84/1.62  | (35) empty(all_0_6_6)
% 3.84/1.62  | (36)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ function(v0) |  ~ relation(v0) | relation(v2))
% 3.84/1.62  | (37) relation(empty_set)
% 3.84/1.62  | (38) relation(all_0_4_4)
% 3.84/1.62  | (39) empty(all_0_1_1)
% 3.84/1.62  | (40)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 3.84/1.62  | (41) relation(all_0_0_0)
% 3.84/1.62  | (42)  ? [v0] : subset(v0, v0)
% 3.84/1.62  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (relation_dom_restriction(v3, v1) = v4) |  ~ (relation_dom_restriction(v2, v0) = v3) |  ~ subset(v0, v1) |  ~ relation(v2))
% 3.84/1.62  | (44) one_to_one(all_0_2_2)
% 3.84/1.62  | (45)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 3.84/1.62  | (46) relation(all_0_2_2)
% 3.84/1.62  | (47)  ~ (all_0_8_8 = all_0_11_11) |  ~ (all_0_10_10 = all_0_11_11)
% 3.84/1.62  | (48)  ! [v0] : ( ~ function(v0) |  ~ relation(v0) |  ~ empty(v0) | one_to_one(v0))
% 3.84/1.62  | (49) relation(all_0_1_1)
% 3.84/1.62  | (50)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation(v0) | relation(v2))
% 3.84/1.62  | (51) relation_empty_yielding(empty_set)
% 3.84/1.62  | (52)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation_empty_yielding(v0) |  ~ relation(v0) | relation_empty_yielding(v2))
% 3.84/1.62  | (53) relation_empty_yielding(all_0_5_5)
% 3.84/1.62  | (54) function(all_0_12_12)
% 3.84/1.62  | (55) relation_dom_restriction(all_0_9_9, all_0_14_14) = all_0_8_8
% 3.84/1.62  |
% 3.84/1.62  | Instantiating formula (43) with all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14 and discharging atoms relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10, relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_11_11, subset(all_0_14_14, all_0_13_13), relation(all_0_12_12), yields:
% 3.84/1.62  | (56) all_0_10_10 = all_0_11_11
% 3.84/1.62  |
% 3.84/1.62  +-Applying beta-rule and splitting (47), into two cases.
% 3.84/1.62  |-Branch one:
% 3.84/1.62  | (57)  ~ (all_0_8_8 = all_0_11_11)
% 3.84/1.62  |
% 3.84/1.62  	| Instantiating formula (15) with all_0_8_8, all_0_9_9, all_0_12_12, all_0_13_13, all_0_14_14 and discharging atoms relation_dom_restriction(all_0_9_9, all_0_14_14) = all_0_8_8, relation_dom_restriction(all_0_12_12, all_0_13_13) = all_0_9_9, subset(all_0_14_14, all_0_13_13), relation(all_0_12_12), yields:
% 3.84/1.63  	| (58) relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_8_8
% 3.84/1.63  	|
% 3.84/1.63  	| Instantiating formula (22) with all_0_12_12, all_0_14_14, all_0_8_8, all_0_11_11 and discharging atoms relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_8_8, relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_11_11, yields:
% 3.84/1.63  	| (59) all_0_8_8 = all_0_11_11
% 3.84/1.63  	|
% 3.84/1.63  	| Equations (59) can reduce 57 to:
% 3.84/1.63  	| (60) $false
% 3.84/1.63  	|
% 3.84/1.63  	|-The branch is then unsatisfiable
% 3.84/1.63  |-Branch two:
% 3.84/1.63  | (59) all_0_8_8 = all_0_11_11
% 3.84/1.63  | (62)  ~ (all_0_10_10 = all_0_11_11)
% 3.84/1.63  |
% 3.84/1.63  	| Equations (56) can reduce 62 to:
% 3.84/1.63  	| (60) $false
% 3.84/1.63  	|
% 3.84/1.63  	|-The branch is then unsatisfiable
% 3.84/1.63  % SZS output end Proof for theBenchmark
% 3.84/1.63  
% 3.84/1.63  1039ms
%------------------------------------------------------------------------------