%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU045+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n027.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 08:46:21 EDT 2022

% Result   : Theorem 3.06s 1.38s
% Output   : Proof 4.88s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SEU045+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.32  % Computer : n027.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % 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 20:47:54 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.57          ____       _                          
% 0.19/0.57    ___  / __ \_____(_)___  ________  __________
% 0.19/0.57   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.57  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.57  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.57  
% 0.19/0.57  A Theorem Prover for First-Order Logic
% 0.19/0.57  (ePrincess v.1.0)
% 0.19/0.57  
% 0.19/0.57  (c) Philipp Rümmer, 2009-2015
% 0.19/0.57  (c) Peter Backeman, 2014-2015
% 0.19/0.57  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.57  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.57  Bug reports to peter@backeman.se
% 0.19/0.57  
% 0.19/0.57  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.57  
% 0.19/0.57  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.62  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.52/0.93  Prover 0: Preprocessing ...
% 1.96/1.17  Prover 0: Warning: ignoring some quantifiers
% 2.24/1.20  Prover 0: Constructing countermodel ...
% 2.80/1.38  Prover 0: proved (760ms)
% 3.06/1.38  
% 3.06/1.38  No countermodel exists, formula is valid
% 3.06/1.38  % SZS status Theorem for theBenchmark
% 3.06/1.38  
% 3.06/1.38  Generating proof ... Warning: ignoring some quantifiers
% 4.51/1.70  found it (size 11)
% 4.51/1.70  
% 4.51/1.70  % SZS output start Proof for theBenchmark
% 4.51/1.70  Assumed formulas after preprocessing and simplification: 
% 4.51/1.70  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : ( ~ (v6 = v5) & apply(v3, v1) = v5 & apply(v2, v1) = v6 & relation_rng_restriction(v0, v2) = v3 & relation_dom(v3) = v4 & in(v1, v4) & 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] : ( ~ (relation_rng_restriction(v15, v18) = v19) |  ~ (relation_dom(v16) = v17) |  ~ function(v18) |  ~ function(v16) |  ~ relation(v18) |  ~ relation(v16) |  ? [v20] :  ? [v21] :  ? [v22] :  ? [v23] : (relation_dom(v18) = v20 & ( ~ (v19 = v16) | ( ! [v24] :  ! [v25] : ( ~ (apply(v18, v24) = v25) |  ~ in(v25, v15) |  ~ in(v24, v20) | in(v24, v17)) &  ! [v24] :  ! [v25] : ( ~ (apply(v18, v24) = v25) |  ~ in(v24, v17) | apply(v16, v24) = v25) &  ! [v24] :  ! [v25] : ( ~ (apply(v18, v24) = v25) |  ~ in(v24, v17) | in(v25, v15)) &  ! [v24] :  ! [v25] : ( ~ (apply(v18, v24) = v25) |  ~ in(v24, v17) | in(v24, v20)) &  ! [v24] :  ! [v25] : ( ~ (apply(v16, v24) = v25) |  ~ in(v24, v17) | apply(v18, v24) = v25))) & (v19 = v16 | ( ~ (v23 = v22) & apply(v18, v21) = v23 & apply(v16, v21) = v22 & in(v21, v17)) | (apply(v18, v21) = v22 & ( ~ in(v22, v15) |  ~ in(v21, v20) |  ~ in(v21, v17)) & (in(v21, v17) | (in(v22, v15) & in(v21, v20))))))) &  ? [v15] :  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] : ( ~ (relation_dom(v18) = v19) |  ~ (relation_dom(v16) = v17) |  ~ function(v18) |  ~ function(v16) |  ~ relation(v18) |  ~ relation(v16) |  ? [v20] :  ? [v21] :  ? [v22] :  ? [v23] : (relation_rng_restriction(v15, v18) = v20 & ( ~ (v20 = v16) | ( ! [v24] :  ! [v25] : ( ~ (apply(v18, v24) = v25) |  ~ in(v25, v15) |  ~ in(v24, v19) | in(v24, v17)) &  ! [v24] :  ! [v25] : ( ~ (apply(v18, v24) = v25) |  ~ in(v24, v17) | apply(v16, v24) = v25) &  ! [v24] :  ! [v25] : ( ~ (apply(v18, v24) = v25) |  ~ in(v24, v17) | in(v25, v15)) &  ! [v24] :  ! [v25] : ( ~ (apply(v18, v24) = v25) |  ~ in(v24, v17) | in(v24, v19)) &  ! [v24] :  ! [v25] : ( ~ (apply(v16, v24) = v25) |  ~ in(v24, v17) | apply(v18, v24) = v25))) & (v20 = v16 | ( ~ (v23 = v22) & apply(v18, v21) = v23 & apply(v16, v21) = v22 & in(v21, v17)) | (apply(v18, v21) = v22 & ( ~ in(v22, v15) |  ~ in(v21, v19) |  ~ in(v21, v17)) & (in(v21, v17) | (in(v22, v15) & in(v21, v19))))))) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : (v16 = v15 |  ~ (apply(v18, v17) = v16) |  ~ (apply(v18, v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : (v16 = v15 |  ~ (relation_rng_restriction(v18, v17) = v16) |  ~ (relation_rng_restriction(v18, v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (powerset(v17) = v18) |  ~ in(v15, v16) |  ~ element(v16, v18) |  ~ empty(v17)) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (powerset(v17) = v18) |  ~ in(v15, v16) |  ~ element(v16, v18) | element(v15, v17)) &  ! [v15] :  ! [v16] :  ! [v17] : (v16 = v15 |  ~ (relation_dom(v17) = v16) |  ~ (relation_dom(v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] : (v16 = v15 |  ~ (powerset(v17) = v16) |  ~ (powerset(v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) |  ~ function(v16) |  ~ relation(v16) | function(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) |  ~ function(v16) |  ~ relation(v16) | relation(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) |  ~ relation(v16) | relation(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (powerset(v16) = v17) |  ~ element(v15, v17) | subset(v15, v16)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (powerset(v16) = v17) |  ~ subset(v15, v16) | element(v15, v17)) &  ! [v15] :  ! [v16] : (v16 = v15 |  ~ empty(v16) |  ~ empty(v15)) &  ! [v15] :  ! [v16] : ( ~ (relation_dom(v15) = v16) |  ~ relation(v15) |  ~ empty(v16) | empty(v15)) &  ! [v15] :  ! [v16] : ( ~ (relation_dom(v15) = v16) |  ~ empty(v15) | relation(v16)) &  ! [v15] :  ! [v16] : ( ~ (relation_dom(v15) = v16) |  ~ empty(v15) | empty(v16)) &  ! [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] : ( ~ in(v16, v15) |  ~ in(v15, v16)) &  ! [v15] :  ! [v16] : ( ~ in(v15, v16) |  ~ empty(v16)) &  ! [v15] :  ! [v16] : ( ~ in(v15, v16) | element(v15, v16)) &  ! [v15] :  ! [v16] : ( ~ element(v15, v16) | in(v15, v16) | empty(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))
% 4.51/1.74  | 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:
% 4.51/1.74  | (1)  ~ (all_0_8_8 = all_0_9_9) & apply(all_0_11_11, all_0_13_13) = all_0_9_9 & apply(all_0_12_12, all_0_13_13) = all_0_8_8 & relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11 & relation_dom(all_0_11_11) = all_0_10_10 & in(all_0_13_13, all_0_10_10) & 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] : ( ~ (relation_rng_restriction(v0, v3) = v4) |  ~ (relation_dom(v1) = v2) |  ~ function(v3) |  ~ function(v1) |  ~ relation(v3) |  ~ relation(v1) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (relation_dom(v3) = v5 & ( ~ (v4 = v1) | ( ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v10, v0) |  ~ in(v9, v5) | in(v9, v2)) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | apply(v1, v9) = v10) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | in(v10, v0)) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | in(v9, v5)) &  ! [v9] :  ! [v10] : ( ~ (apply(v1, v9) = v10) |  ~ in(v9, v2) | apply(v3, v9) = v10))) & (v4 = v1 | ( ~ (v8 = v7) & apply(v3, v6) = v8 & apply(v1, v6) = v7 & in(v6, v2)) | (apply(v3, v6) = v7 & ( ~ in(v7, v0) |  ~ in(v6, v5) |  ~ in(v6, v2)) & (in(v6, v2) | (in(v7, v0) & in(v6, v5))))))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ (relation_dom(v1) = v2) |  ~ function(v3) |  ~ function(v1) |  ~ relation(v3) |  ~ relation(v1) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (relation_rng_restriction(v0, v3) = v5 & ( ~ (v5 = v1) | ( ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v10, v0) |  ~ in(v9, v4) | in(v9, v2)) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | apply(v1, v9) = v10) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | in(v10, v0)) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | in(v9, v4)) &  ! [v9] :  ! [v10] : ( ~ (apply(v1, v9) = v10) |  ~ in(v9, v2) | apply(v3, v9) = v10))) & (v5 = v1 | ( ~ (v8 = v7) & apply(v3, v6) = v8 & apply(v1, v6) = v7 & in(v6, v2)) | (apply(v3, v6) = v7 & ( ~ in(v7, v0) |  ~ in(v6, v4) |  ~ in(v6, v2)) & (in(v6, v2) | (in(v7, v0) & in(v6, v4))))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_rng_restriction(v3, v2) = v1) |  ~ (relation_rng_restriction(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ in(v0, v1) |  ~ element(v1, v3) |  ~ empty(v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ in(v0, v1) |  ~ element(v1, v3) | element(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ function(v1) |  ~ relation(v1) | function(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ function(v1) |  ~ relation(v1) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ relation(v1) | relation(v2)) &  ! [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] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1)) &  ! [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] : ( ~ in(v1, v0) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ in(v0, v1) |  ~ empty(v1)) &  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(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)
% 4.51/1.76  |
% 4.51/1.76  | Applying alpha-rule on (1) yields:
% 4.51/1.76  | (2) relation_empty_yielding(all_0_5_5)
% 4.51/1.76  | (3) relation(all_0_0_0)
% 4.51/1.76  | (4)  ? [v0] : subset(v0, v0)
% 4.51/1.76  | (5) function(all_0_12_12)
% 4.51/1.76  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_rng_restriction(v3, v2) = v1) |  ~ (relation_rng_restriction(v3, v2) = v0))
% 4.51/1.76  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ in(v0, v1) |  ~ element(v1, v3) |  ~ empty(v2))
% 4.51/1.76  | (8)  ! [v0] : ( ~ function(v0) |  ~ relation(v0) |  ~ empty(v0) | one_to_one(v0))
% 4.51/1.76  | (9)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 4.51/1.76  | (10) relation_dom(all_0_11_11) = all_0_10_10
% 4.51/1.76  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0))
% 4.51/1.76  | (12) function(all_0_2_2)
% 4.51/1.76  | (13)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 4.51/1.76  | (14)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1))
% 4.51/1.76  | (15) empty(all_0_3_3)
% 4.51/1.76  | (16)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1))
% 4.51/1.76  | (17)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 4.51/1.76  | (18)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 4.51/1.76  | (19)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 4.51/1.76  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ relation(v1) | relation(v2))
% 4.51/1.76  | (21) empty(all_0_1_1)
% 4.51/1.76  | (22) in(all_0_13_13, all_0_10_10)
% 4.51/1.76  | (23)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1))
% 4.51/1.76  | (24) relation(all_0_5_5)
% 4.51/1.76  | (25)  ? [v0] :  ? [v1] : element(v1, v0)
% 4.51/1.76  | (26)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) |  ~ empty(v1))
% 4.51/1.76  | (27)  ~ empty(all_0_7_7)
% 4.51/1.76  | (28) empty(all_0_6_6)
% 4.51/1.76  | (29) relation(empty_set)
% 4.51/1.76  | (30)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ (relation_dom(v1) = v2) |  ~ function(v3) |  ~ function(v1) |  ~ relation(v3) |  ~ relation(v1) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (relation_rng_restriction(v0, v3) = v5 & ( ~ (v5 = v1) | ( ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v10, v0) |  ~ in(v9, v4) | in(v9, v2)) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | apply(v1, v9) = v10) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | in(v10, v0)) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | in(v9, v4)) &  ! [v9] :  ! [v10] : ( ~ (apply(v1, v9) = v10) |  ~ in(v9, v2) | apply(v3, v9) = v10))) & (v5 = v1 | ( ~ (v8 = v7) & apply(v3, v6) = v8 & apply(v1, v6) = v7 & in(v6, v2)) | (apply(v3, v6) = v7 & ( ~ in(v7, v0) |  ~ in(v6, v4) |  ~ in(v6, v2)) & (in(v6, v2) | (in(v7, v0) & in(v6, v4)))))))
% 4.51/1.77  | (31) relation(all_0_3_3)
% 4.51/1.77  | (32) one_to_one(all_0_2_2)
% 4.51/1.77  | (33)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 4.51/1.77  | (34)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 4.51/1.77  | (35) apply(all_0_11_11, all_0_13_13) = all_0_9_9
% 4.51/1.77  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ in(v0, v1) |  ~ element(v1, v3) | element(v0, v2))
% 4.51/1.77  | (37) relation(all_0_1_1)
% 4.51/1.77  | (38) relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11
% 4.51/1.77  | (39) empty(empty_set)
% 4.51/1.77  | (40)  ! [v0] : ( ~ empty(v0) | function(v0))
% 4.51/1.77  | (41) relation(all_0_4_4)
% 4.51/1.77  | (42) relation_empty_yielding(empty_set)
% 4.51/1.77  | (43) apply(all_0_12_12, all_0_13_13) = all_0_8_8
% 4.51/1.77  | (44)  ~ (all_0_8_8 = all_0_9_9)
% 4.51/1.77  | (45) function(all_0_0_0)
% 4.51/1.77  | (46)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ function(v1) |  ~ relation(v1) | relation(v2))
% 4.51/1.77  | (47)  ~ empty(all_0_4_4)
% 4.51/1.77  | (48) relation(all_0_12_12)
% 4.51/1.77  | (49)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ function(v1) |  ~ relation(v1) | function(v2))
% 4.51/1.77  | (50) relation(all_0_2_2)
% 4.51/1.77  | (51)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 4.51/1.77  | (52)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 4.51/1.77  | (53)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 4.51/1.77  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) |  ~ (relation_dom(v1) = v2) |  ~ function(v3) |  ~ function(v1) |  ~ relation(v3) |  ~ relation(v1) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (relation_dom(v3) = v5 & ( ~ (v4 = v1) | ( ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v10, v0) |  ~ in(v9, v5) | in(v9, v2)) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | apply(v1, v9) = v10) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | in(v10, v0)) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | in(v9, v5)) &  ! [v9] :  ! [v10] : ( ~ (apply(v1, v9) = v10) |  ~ in(v9, v2) | apply(v3, v9) = v10))) & (v4 = v1 | ( ~ (v8 = v7) & apply(v3, v6) = v8 & apply(v1, v6) = v7 & in(v6, v2)) | (apply(v3, v6) = v7 & ( ~ in(v7, v0) |  ~ in(v6, v5) |  ~ in(v6, v2)) & (in(v6, v2) | (in(v7, v0) & in(v6, v5)))))))
% 4.51/1.77  | (55) function(all_0_1_1)
% 4.51/1.77  | (56)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 4.51/1.77  | (57)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) & empty(v2)))
% 4.51/1.77  | (58)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 4.51/1.77  |
% 4.51/1.77  | Instantiating formula (49) with all_0_11_11, all_0_12_12, all_0_14_14 and discharging atoms relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11, function(all_0_12_12), relation(all_0_12_12), yields:
% 4.51/1.78  | (59) function(all_0_11_11)
% 4.51/1.78  |
% 4.51/1.78  | Instantiating formula (20) with all_0_11_11, all_0_12_12, all_0_14_14 and discharging atoms relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11, relation(all_0_12_12), yields:
% 4.51/1.78  | (60) relation(all_0_11_11)
% 4.51/1.78  |
% 4.51/1.78  | Instantiating formula (54) with all_0_11_11, all_0_12_12, all_0_10_10, all_0_11_11, all_0_14_14 and discharging atoms relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11, relation_dom(all_0_11_11) = all_0_10_10, function(all_0_11_11), function(all_0_12_12), relation(all_0_11_11), relation(all_0_12_12), yields:
% 4.51/1.78  | (61)  ? [v0] : (relation_dom(all_0_12_12) = v0 &  ! [v1] :  ! [v2] : ( ~ (apply(all_0_11_11, v1) = v2) |  ~ in(v1, all_0_10_10) | apply(all_0_12_12, v1) = v2) &  ! [v1] :  ! [v2] : ( ~ (apply(all_0_12_12, v1) = v2) |  ~ in(v2, all_0_14_14) |  ~ in(v1, v0) | in(v1, all_0_10_10)) &  ! [v1] :  ! [v2] : ( ~ (apply(all_0_12_12, v1) = v2) |  ~ in(v1, all_0_10_10) | apply(all_0_11_11, v1) = v2) &  ! [v1] :  ! [v2] : ( ~ (apply(all_0_12_12, v1) = v2) |  ~ in(v1, all_0_10_10) | in(v2, all_0_14_14)) &  ! [v1] :  ! [v2] : ( ~ (apply(all_0_12_12, v1) = v2) |  ~ in(v1, all_0_10_10) | in(v1, v0)))
% 4.51/1.78  |
% 4.51/1.78  | Instantiating (61) with all_26_0_23 yields:
% 4.51/1.78  | (62) relation_dom(all_0_12_12) = all_26_0_23 &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) |  ~ in(v0, all_0_10_10) | apply(all_0_12_12, v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v1, all_0_14_14) |  ~ in(v0, all_26_0_23) | in(v0, all_0_10_10)) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | apply(all_0_11_11, v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | in(v1, all_0_14_14)) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | in(v0, all_26_0_23))
% 4.88/1.78  |
% 4.88/1.78  | Applying alpha-rule on (62) yields:
% 4.88/1.78  | (63)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v1, all_0_14_14) |  ~ in(v0, all_26_0_23) | in(v0, all_0_10_10))
% 4.88/1.78  | (64)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | apply(all_0_11_11, v0) = v1)
% 4.88/1.78  | (65)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | in(v0, all_26_0_23))
% 4.88/1.78  | (66)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) |  ~ in(v0, all_0_10_10) | apply(all_0_12_12, v0) = v1)
% 4.88/1.78  | (67)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | in(v1, all_0_14_14))
% 4.88/1.78  | (68) relation_dom(all_0_12_12) = all_26_0_23
% 4.88/1.78  |
% 4.88/1.78  | Instantiating formula (66) with all_0_9_9, all_0_13_13 and discharging atoms apply(all_0_11_11, all_0_13_13) = all_0_9_9, in(all_0_13_13, all_0_10_10), yields:
% 4.88/1.78  | (69) apply(all_0_12_12, all_0_13_13) = all_0_9_9
% 4.88/1.78  |
% 4.88/1.78  | Instantiating formula (11) with all_0_12_12, all_0_13_13, all_0_9_9, all_0_8_8 and discharging atoms apply(all_0_12_12, all_0_13_13) = all_0_8_8, apply(all_0_12_12, all_0_13_13) = all_0_9_9, yields:
% 4.88/1.78  | (70) all_0_8_8 = all_0_9_9
% 4.88/1.78  |
% 4.88/1.78  | Equations (70) can reduce 44 to:
% 4.88/1.78  | (71) $false
% 4.88/1.78  |
% 4.88/1.78  |-The branch is then unsatisfiable
% 4.88/1.78  % SZS output end Proof for theBenchmark
% 4.88/1.78  
% 4.88/1.78  1202ms
%------------------------------------------------------------------------------