%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU219+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n029.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 08:47:47 EDT 2022

% Result   : Theorem 3.44s 1.67s
% Output   : Proof 5.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU219+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n029.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jun 19 19:42:15 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.66/0.67          ____       _                          
% 0.66/0.67    ___  / __ \_____(_)___  ________  __________
% 0.66/0.67   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.66/0.67  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.66/0.67  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.66/0.67  
% 0.66/0.67  A Theorem Prover for First-Order Logic
% 0.66/0.67  (ePrincess v.1.0)
% 0.66/0.67  
% 0.66/0.67  (c) Philipp Rümmer, 2009-2015
% 0.66/0.67  (c) Peter Backeman, 2014-2015
% 0.66/0.67  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.66/0.67  Free software under GNU Lesser General Public License (LGPL).
% 0.66/0.67  Bug reports to peter@backeman.se
% 0.66/0.67  
% 0.66/0.67  For more information, visit http://user.uu.se/~petba168/breu/
% 0.66/0.67  
% 0.66/0.67  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.88/0.73  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.80/1.12  Prover 0: Preprocessing ...
% 2.45/1.42  Prover 0: Warning: ignoring some quantifiers
% 2.63/1.46  Prover 0: Constructing countermodel ...
% 3.31/1.67  Prover 0: proved (936ms)
% 3.44/1.67  
% 3.44/1.67  No countermodel exists, formula is valid
% 3.44/1.67  % SZS status Theorem for theBenchmark
% 3.44/1.67  
% 3.44/1.67  Generating proof ... Warning: ignoring some quantifiers
% 4.85/2.00  found it (size 23)
% 4.85/2.00  
% 4.85/2.00  % SZS output start Proof for theBenchmark
% 4.85/2.00  Assumed formulas after preprocessing and simplification: 
% 4.85/2.00  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] : (relation_rng(v2) = v5 & relation_rng(v0) = v1 & relation_dom(v2) = v3 & relation_dom(v0) = v4 & function_inverse(v0) = v2 & relation_empty_yielding(v6) & relation_empty_yielding(empty_set) & one_to_one(v7) & one_to_one(v0) & relation(v13) & relation(v12) & relation(v10) & relation(v9) & relation(v7) & relation(v6) & relation(v0) & relation(empty_set) & function(v13) & function(v10) & function(v7) & function(v0) & empty(v12) & empty(v11) & empty(v10) & empty(empty_set) &  ~ empty(v9) &  ~ empty(v8) &  ! [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 |  ~ (relation_rng(v16) = v15) |  ~ (relation_rng(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (relation_dom(v16) = v15) |  ~ (relation_dom(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (powerset(v16) = v15) |  ~ (powerset(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (relation_inverse(v16) = v15) |  ~ (relation_inverse(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (function_inverse(v16) = v15) |  ~ (function_inverse(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (powerset(v15) = v16) |  ~ subset(v14, v15) | element(v14, v16)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (powerset(v15) = v16) |  ~ element(v14, v16) | subset(v14, v15)) &  ! [v14] :  ! [v15] : (v15 = v14 |  ~ empty(v15) |  ~ empty(v14)) &  ! [v14] :  ! [v15] : ( ~ (relation_rng(v14) = v15) |  ~ relation(v14) |  ~ empty(v15) | empty(v14)) &  ! [v14] :  ! [v15] : ( ~ (relation_rng(v14) = v15) |  ~ relation(v14) |  ? [v16] :  ? [v17] : (relation_rng(v16) = v17 & relation_dom(v16) = v15 & relation_dom(v14) = v17 & relation_inverse(v14) = v16)) &  ! [v14] :  ! [v15] : ( ~ (relation_rng(v14) = v15) |  ~ empty(v14) | relation(v15)) &  ! [v14] :  ! [v15] : ( ~ (relation_rng(v14) = v15) |  ~ empty(v14) | empty(v15)) &  ! [v14] :  ! [v15] : ( ~ (relation_dom(v14) = v15) |  ~ relation(v14) |  ~ empty(v15) | empty(v14)) &  ! [v14] :  ! [v15] : ( ~ (relation_dom(v14) = v15) |  ~ relation(v14) |  ? [v16] :  ? [v17] : (relation_rng(v17) = v15 & relation_rng(v14) = v16 & relation_dom(v17) = v16 & relation_inverse(v14) = v17)) &  ! [v14] :  ! [v15] : ( ~ (relation_dom(v14) = v15) |  ~ empty(v14) | relation(v15)) &  ! [v14] :  ! [v15] : ( ~ (relation_dom(v14) = v15) |  ~ empty(v14) | empty(v15)) &  ! [v14] :  ! [v15] : ( ~ (powerset(v14) = v15) |  ~ empty(v15)) &  ! [v14] :  ! [v15] : ( ~ (powerset(v14) = v15) | empty(v14) |  ? [v16] : (element(v16, v15) &  ~ empty(v16))) &  ! [v14] :  ! [v15] : ( ~ (powerset(v14) = v15) |  ? [v16] : (element(v16, v15) & empty(v16))) &  ! [v14] :  ! [v15] : ( ~ (relation_inverse(v14) = v15) |  ~ one_to_one(v14) |  ~ relation(v14) |  ~ function(v14) | function_inverse(v14) = v15) &  ! [v14] :  ! [v15] : ( ~ (relation_inverse(v14) = v15) |  ~ one_to_one(v14) |  ~ relation(v14) |  ~ function(v14) | relation(v15)) &  ! [v14] :  ! [v15] : ( ~ (relation_inverse(v14) = v15) |  ~ one_to_one(v14) |  ~ relation(v14) |  ~ function(v14) | function(v15)) &  ! [v14] :  ! [v15] : ( ~ (relation_inverse(v14) = v15) |  ~ relation(v14) | relation_inverse(v15) = v14) &  ! [v14] :  ! [v15] : ( ~ (relation_inverse(v14) = v15) |  ~ relation(v14) | relation(v15)) &  ! [v14] :  ! [v15] : ( ~ (relation_inverse(v14) = v15) |  ~ relation(v14) |  ? [v16] :  ? [v17] : (relation_rng(v15) = v17 & relation_rng(v14) = v16 & relation_dom(v15) = v16 & relation_dom(v14) = v17)) &  ! [v14] :  ! [v15] : ( ~ (relation_inverse(v14) = v15) |  ~ empty(v14) | relation(v15)) &  ! [v14] :  ! [v15] : ( ~ (relation_inverse(v14) = v15) |  ~ empty(v14) | empty(v15)) &  ! [v14] :  ! [v15] : ( ~ (function_inverse(v14) = v15) |  ~ one_to_one(v14) |  ~ relation(v14) |  ~ function(v14) | relation_inverse(v14) = v15) &  ! [v14] :  ! [v15] : ( ~ (function_inverse(v14) = v15) |  ~ relation(v14) |  ~ function(v14) | relation(v15)) &  ! [v14] :  ! [v15] : ( ~ (function_inverse(v14) = v15) |  ~ relation(v14) |  ~ function(v14) | function(v15)) &  ! [v14] :  ! [v15] : ( ~ element(v14, v15) | empty(v15) | in(v14, v15)) &  ! [v14] :  ! [v15] : ( ~ empty(v15) |  ~ in(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] : ( ~ empty(v14) | relation(v14)) &  ! [v14] : ( ~ empty(v14) | function(v14)) &  ? [v14] :  ? [v15] : element(v15, v14) &  ? [v14] : subset(v14, v14) & ( ~ (v5 = v4) |  ~ (v3 = v1)))
% 5.20/2.06  | 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:
% 5.20/2.06  | (1) relation_rng(all_0_11_11) = all_0_8_8 & relation_rng(all_0_13_13) = all_0_12_12 & relation_dom(all_0_11_11) = all_0_10_10 & relation_dom(all_0_13_13) = all_0_9_9 & function_inverse(all_0_13_13) = all_0_11_11 & relation_empty_yielding(all_0_7_7) & relation_empty_yielding(empty_set) & one_to_one(all_0_6_6) & one_to_one(all_0_13_13) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_4_4) & relation(all_0_6_6) & relation(all_0_7_7) & relation(all_0_13_13) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & function(all_0_13_13) & empty(all_0_1_1) & empty(all_0_2_2) & empty(all_0_3_3) & empty(empty_set) &  ~ empty(all_0_4_4) &  ~ empty(all_0_5_5) &  ! [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 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0)) &  ! [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] : (v1 = v0 |  ~ (relation_inverse(v2) = v1) |  ~ (relation_inverse(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (function_inverse(v2) = v1) |  ~ (function_inverse(v2) = v0)) &  ! [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] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3 & relation_inverse(v0) = v2)) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | relation(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | empty(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2 & relation_inverse(v0) = v3)) &  ! [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] : ( ~ (relation_inverse(v0) = v1) |  ~ one_to_one(v0) |  ~ relation(v0) |  ~ function(v0) | function_inverse(v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (relation_inverse(v0) = v1) |  ~ one_to_one(v0) |  ~ relation(v0) |  ~ function(v0) | relation(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_inverse(v0) = v1) |  ~ one_to_one(v0) |  ~ relation(v0) |  ~ function(v0) | function(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_inverse(v0) = v1) |  ~ relation(v0) | relation_inverse(v1) = v0) &  ! [v0] :  ! [v1] : ( ~ (relation_inverse(v0) = v1) |  ~ relation(v0) | relation(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_inverse(v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) &  ! [v0] :  ! [v1] : ( ~ (relation_inverse(v0) = v1) |  ~ empty(v0) | relation(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_inverse(v0) = v1) |  ~ empty(v0) | empty(v1)) &  ! [v0] :  ! [v1] : ( ~ (function_inverse(v0) = v1) |  ~ one_to_one(v0) |  ~ relation(v0) |  ~ function(v0) | relation_inverse(v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (function_inverse(v0) = v1) |  ~ relation(v0) |  ~ function(v0) | relation(v1)) &  ! [v0] :  ! [v1] : ( ~ (function_inverse(v0) = v1) |  ~ relation(v0) |  ~ function(v0) | function(v1)) &  ! [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] : ( ~ relation(v0) |  ~ function(v0) |  ~ empty(v0) | one_to_one(v0)) &  ! [v0] : ( ~ empty(v0) | relation(v0)) &  ! [v0] : ( ~ empty(v0) | function(v0)) &  ? [v0] :  ? [v1] : element(v1, v0) &  ? [v0] : subset(v0, v0) & ( ~ (all_0_8_8 = all_0_9_9) |  ~ (all_0_10_10 = all_0_12_12))
% 5.20/2.08  |
% 5.20/2.08  | Applying alpha-rule on (1) yields:
% 5.20/2.08  | (2)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 5.20/2.08  | (3)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2 & relation_inverse(v0) = v3))
% 5.33/2.08  | (4)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 5.33/2.08  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 5.33/2.08  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 5.33/2.08  | (7)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1))
% 5.33/2.08  | (8)  ! [v0] :  ! [v1] : ( ~ (relation_inverse(v0) = v1) |  ~ empty(v0) | relation(v1))
% 5.33/2.08  | (9)  ! [v0] :  ! [v1] : ( ~ (relation_inverse(v0) = v1) |  ~ empty(v0) | empty(v1))
% 5.33/2.08  | (10) one_to_one(all_0_6_6)
% 5.33/2.08  | (11)  ! [v0] :  ! [v1] : ( ~ (relation_inverse(v0) = v1) |  ~ one_to_one(v0) |  ~ relation(v0) |  ~ function(v0) | function(v1))
% 5.33/2.08  | (12)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | relation(v1))
% 5.33/2.08  | (13)  ! [v0] :  ! [v1] : ( ~ (relation_inverse(v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3))
% 5.33/2.08  | (14) relation_dom(all_0_13_13) = all_0_9_9
% 5.33/2.08  | (15)  ! [v0] :  ! [v1] : ( ~ (function_inverse(v0) = v1) |  ~ relation(v0) |  ~ function(v0) | relation(v1))
% 5.33/2.08  | (16) empty(all_0_1_1)
% 5.33/2.09  | (17)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 5.33/2.09  | (18)  ! [v0] :  ! [v1] : ( ~ (relation_inverse(v0) = v1) |  ~ one_to_one(v0) |  ~ relation(v0) |  ~ function(v0) | relation(v1))
% 5.33/2.09  | (19)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 5.33/2.09  | (20) function(all_0_0_0)
% 5.33/2.09  | (21)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 5.33/2.09  | (22)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 5.33/2.09  | (23)  ! [v0] : ( ~ empty(v0) | function(v0))
% 5.33/2.09  | (24)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 5.33/2.09  | (25)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0))
% 5.33/2.09  | (26)  ~ empty(all_0_5_5)
% 5.33/2.09  | (27) function_inverse(all_0_13_13) = all_0_11_11
% 5.33/2.09  | (28)  ? [v0] :  ? [v1] : element(v1, v0)
% 5.33/2.09  | (29) relation_empty_yielding(all_0_7_7)
% 5.33/2.09  | (30)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 5.33/2.09  | (31) function(all_0_13_13)
% 5.33/2.09  | (32)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 5.33/2.09  | (33) empty(all_0_2_2)
% 5.33/2.09  | (34)  ! [v0] :  ! [v1] : ( ~ (function_inverse(v0) = v1) |  ~ one_to_one(v0) |  ~ relation(v0) |  ~ function(v0) | relation_inverse(v0) = v1)
% 5.33/2.09  | (35) relation_dom(all_0_11_11) = all_0_10_10
% 5.33/2.09  | (36) empty(empty_set)
% 5.33/2.09  | (37) relation_rng(all_0_13_13) = all_0_12_12
% 5.33/2.09  | (38)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3 & relation_inverse(v0) = v2))
% 5.33/2.09  | (39)  ~ empty(all_0_4_4)
% 5.33/2.09  | (40) relation_rng(all_0_11_11) = all_0_8_8
% 5.33/2.09  | (41)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_inverse(v2) = v1) |  ~ (relation_inverse(v2) = v0))
% 5.33/2.10  | (42)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 5.33/2.10  | (43)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (function_inverse(v2) = v1) |  ~ (function_inverse(v2) = v0))
% 5.33/2.10  | (44)  ! [v0] :  ! [v1] : ( ~ (function_inverse(v0) = v1) |  ~ relation(v0) |  ~ function(v0) | function(v1))
% 5.33/2.10  | (45)  ! [v0] :  ! [v1] : ( ~ (relation_inverse(v0) = v1) |  ~ one_to_one(v0) |  ~ relation(v0) |  ~ function(v0) | function_inverse(v0) = v1)
% 5.33/2.10  | (46)  ? [v0] : subset(v0, v0)
% 5.33/2.10  | (47)  ! [v0] :  ! [v1] : ( ~ (relation_inverse(v0) = v1) |  ~ relation(v0) | relation_inverse(v1) = v0)
% 5.33/2.10  | (48) relation(all_0_13_13)
% 5.33/2.10  | (49)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) & empty(v2)))
% 5.33/2.10  | (50)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | empty(v1))
% 5.33/2.10  | (51)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 5.33/2.10  | (52) relation(empty_set)
% 5.33/2.10  | (53)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 5.33/2.10  | (54)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 5.33/2.10  | (55)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1))
% 5.33/2.10  | (56) relation(all_0_7_7)
% 5.33/2.10  | (57)  ! [v0] :  ! [v1] : ( ~ (relation_inverse(v0) = v1) |  ~ relation(v0) | relation(v1))
% 5.33/2.10  | (58) relation(all_0_4_4)
% 5.33/2.10  | (59) function(all_0_3_3)
% 5.33/2.10  | (60) relation(all_0_1_1)
% 5.33/2.10  | (61) relation(all_0_3_3)
% 5.33/2.10  | (62) one_to_one(all_0_13_13)
% 5.33/2.10  | (63) relation(all_0_0_0)
% 5.33/2.10  | (64) empty(all_0_3_3)
% 5.33/2.10  | (65) relation_empty_yielding(empty_set)
% 5.33/2.10  | (66)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 5.33/2.11  | (67) relation(all_0_6_6)
% 5.33/2.11  | (68)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ empty(v2) |  ~ in(v0, v1))
% 5.33/2.11  | (69)  ! [v0] : ( ~ relation(v0) |  ~ function(v0) |  ~ empty(v0) | one_to_one(v0))
% 5.33/2.11  | (70)  ~ (all_0_8_8 = all_0_9_9) |  ~ (all_0_10_10 = all_0_12_12)
% 5.33/2.11  | (71) function(all_0_6_6)
% 5.33/2.11  |
% 5.33/2.11  | Instantiating formula (38) with all_0_12_12, all_0_13_13 and discharging atoms relation_rng(all_0_13_13) = all_0_12_12, relation(all_0_13_13), yields:
% 5.33/2.11  | (72)  ? [v0] :  ? [v1] : (relation_rng(v0) = v1 & relation_dom(v0) = all_0_12_12 & relation_dom(all_0_13_13) = v1 & relation_inverse(all_0_13_13) = v0)
% 5.33/2.11  |
% 5.33/2.11  | Instantiating formula (3) with all_0_9_9, all_0_13_13 and discharging atoms relation_dom(all_0_13_13) = all_0_9_9, relation(all_0_13_13), yields:
% 5.33/2.11  | (73)  ? [v0] :  ? [v1] : (relation_rng(v1) = all_0_9_9 & relation_rng(all_0_13_13) = v0 & relation_dom(v1) = v0 & relation_inverse(all_0_13_13) = v1)
% 5.33/2.11  |
% 5.33/2.11  | Instantiating formula (34) with all_0_11_11, all_0_13_13 and discharging atoms function_inverse(all_0_13_13) = all_0_11_11, one_to_one(all_0_13_13), relation(all_0_13_13), function(all_0_13_13), yields:
% 5.33/2.11  | (74) relation_inverse(all_0_13_13) = all_0_11_11
% 5.33/2.11  |
% 5.33/2.11  | Instantiating (73) with all_17_0_17, all_17_1_18 yields:
% 5.33/2.11  | (75) relation_rng(all_17_0_17) = all_0_9_9 & relation_rng(all_0_13_13) = all_17_1_18 & relation_dom(all_17_0_17) = all_17_1_18 & relation_inverse(all_0_13_13) = all_17_0_17
% 5.33/2.11  |
% 5.33/2.11  | Applying alpha-rule on (75) yields:
% 5.33/2.11  | (76) relation_rng(all_17_0_17) = all_0_9_9
% 5.33/2.11  | (77) relation_rng(all_0_13_13) = all_17_1_18
% 5.33/2.11  | (78) relation_dom(all_17_0_17) = all_17_1_18
% 5.33/2.11  | (79) relation_inverse(all_0_13_13) = all_17_0_17
% 5.33/2.11  |
% 5.33/2.11  | Instantiating (72) with all_19_0_19, all_19_1_20 yields:
% 5.33/2.11  | (80) relation_rng(all_19_1_20) = all_19_0_19 & relation_dom(all_19_1_20) = all_0_12_12 & relation_dom(all_0_13_13) = all_19_0_19 & relation_inverse(all_0_13_13) = all_19_1_20
% 5.33/2.11  |
% 5.33/2.11  | Applying alpha-rule on (80) yields:
% 5.33/2.11  | (81) relation_rng(all_19_1_20) = all_19_0_19
% 5.33/2.11  | (82) relation_dom(all_19_1_20) = all_0_12_12
% 5.33/2.12  | (83) relation_dom(all_0_13_13) = all_19_0_19
% 5.33/2.12  | (84) relation_inverse(all_0_13_13) = all_19_1_20
% 5.33/2.12  |
% 5.33/2.12  | Instantiating formula (25) with all_0_13_13, all_17_1_18, all_0_12_12 and discharging atoms relation_rng(all_0_13_13) = all_17_1_18, relation_rng(all_0_13_13) = all_0_12_12, yields:
% 5.33/2.12  | (85) all_17_1_18 = all_0_12_12
% 5.33/2.12  |
% 5.33/2.12  | Instantiating formula (41) with all_0_13_13, all_17_0_17, all_19_1_20 and discharging atoms relation_inverse(all_0_13_13) = all_19_1_20, relation_inverse(all_0_13_13) = all_17_0_17, yields:
% 5.33/2.12  | (86) all_19_1_20 = all_17_0_17
% 5.33/2.12  |
% 5.33/2.12  | Instantiating formula (41) with all_0_13_13, all_0_11_11, all_19_1_20 and discharging atoms relation_inverse(all_0_13_13) = all_19_1_20, relation_inverse(all_0_13_13) = all_0_11_11, yields:
% 5.33/2.12  | (87) all_19_1_20 = all_0_11_11
% 5.33/2.12  |
% 5.33/2.12  | Combining equations (86,87) yields a new equation:
% 5.33/2.12  | (88) all_17_0_17 = all_0_11_11
% 5.33/2.12  |
% 5.33/2.12  | Simplifying 88 yields:
% 5.33/2.12  | (89) all_17_0_17 = all_0_11_11
% 5.33/2.12  |
% 5.33/2.12  | From (89) and (76) follows:
% 5.33/2.12  | (90) relation_rng(all_0_11_11) = all_0_9_9
% 5.33/2.12  |
% 5.33/2.12  | From (89)(85) and (78) follows:
% 5.33/2.12  | (91) relation_dom(all_0_11_11) = all_0_12_12
% 5.33/2.12  |
% 5.33/2.12  | Instantiating formula (25) with all_0_11_11, all_0_9_9, all_0_8_8 and discharging atoms relation_rng(all_0_11_11) = all_0_8_8, relation_rng(all_0_11_11) = all_0_9_9, yields:
% 5.33/2.12  | (92) all_0_8_8 = all_0_9_9
% 5.33/2.12  |
% 5.33/2.12  | Instantiating formula (24) with all_0_11_11, all_0_12_12, all_0_10_10 and discharging atoms relation_dom(all_0_11_11) = all_0_10_10, relation_dom(all_0_11_11) = all_0_12_12, yields:
% 5.33/2.12  | (93) all_0_10_10 = all_0_12_12
% 5.33/2.12  |
% 5.33/2.12  +-Applying beta-rule and splitting (70), into two cases.
% 5.33/2.12  |-Branch one:
% 5.33/2.12  | (94)  ~ (all_0_8_8 = all_0_9_9)
% 5.33/2.12  |
% 5.33/2.12  	| Equations (92) can reduce 94 to:
% 5.33/2.12  	| (95) $false
% 5.33/2.12  	|
% 5.33/2.12  	|-The branch is then unsatisfiable
% 5.33/2.12  |-Branch two:
% 5.33/2.12  | (92) all_0_8_8 = all_0_9_9
% 5.33/2.12  | (97)  ~ (all_0_10_10 = all_0_12_12)
% 5.33/2.12  |
% 5.33/2.12  	| Equations (93) can reduce 97 to:
% 5.33/2.12  	| (95) $false
% 5.55/2.13  	|
% 5.55/2.13  	|-The branch is then unsatisfiable
% 5.55/2.13  % SZS output end Proof for theBenchmark
% 5.55/2.13  
% 5.55/2.13  1447ms
%------------------------------------------------------------------------------