%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU209+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n013.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 08:47:38 EDT 2022

% Result   : Theorem 4.37s 1.73s
% Output   : Proof 6.65s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SEU209+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n013.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jun 19 18:54:14 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.49/0.57          ____       _                          
% 0.49/0.57    ___  / __ \_____(_)___  ________  __________
% 0.49/0.57   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.57  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.49/0.57  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.49/0.57  
% 0.49/0.57  A Theorem Prover for First-Order Logic
% 0.49/0.57  (ePrincess v.1.0)
% 0.49/0.57  
% 0.49/0.57  (c) Philipp Rümmer, 2009-2015
% 0.49/0.57  (c) Peter Backeman, 2014-2015
% 0.49/0.57  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.57  Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.57  Bug reports to peter@backeman.se
% 0.49/0.57  
% 0.49/0.57  For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.57  
% 0.49/0.57  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.49/0.62  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.35/0.92  Prover 0: Preprocessing ...
% 2.19/1.16  Prover 0: Warning: ignoring some quantifiers
% 2.19/1.18  Prover 0: Constructing countermodel ...
% 3.32/1.47  Prover 0: gave up
% 3.32/1.47  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.32/1.50  Prover 1: Preprocessing ...
% 3.85/1.61  Prover 1: Warning: ignoring some quantifiers
% 3.85/1.62  Prover 1: Constructing countermodel ...
% 4.37/1.73  Prover 1: proved (259ms)
% 4.37/1.73  
% 4.37/1.73  No countermodel exists, formula is valid
% 4.37/1.73  % SZS status Theorem for theBenchmark
% 4.37/1.73  
% 4.37/1.73  Generating proof ... Warning: ignoring some quantifiers
% 6.35/2.14  found it (size 25)
% 6.35/2.14  
% 6.35/2.14  % SZS output start Proof for theBenchmark
% 6.35/2.14  Assumed formulas after preprocessing and simplification: 
% 6.35/2.14  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : ( ~ (v8 = 0) &  ~ (v6 = 0) &  ~ (v4 = 0) & relation_dom(v1) = v3 & subset(v2, v3) = v4 & relation_inverse_image(v1, v0) = v2 & relation(v10) = 0 & relation(v7) = 0 & relation(v1) = 0 & relation(empty_set) = 0 & empty(v10) = 0 & empty(v9) = 0 & empty(v7) = v8 & empty(v5) = v6 & empty(empty_set) = 0 &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v15 = 0 |  ~ (relation_inverse_image(v11, v12) = v13) |  ~ (ordered_pair(v14, v16) = v17) |  ~ (relation(v11) = 0) |  ~ (in(v17, v11) = 0) |  ~ (in(v14, v13) = v15) |  ? [v18] : ( ~ (v18 = 0) & in(v16, v12) = v18)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : (v14 = 0 |  ~ (relation_dom(v11) = v12) |  ~ (ordered_pair(v13, v15) = v16) |  ~ (in(v16, v11) = 0) |  ~ (in(v13, v12) = v14) |  ? [v17] : ( ~ (v17 = 0) & relation(v11) = v17)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = 0 |  ~ (powerset(v13) = v14) |  ~ (element(v12, v14) = 0) |  ~ (element(v11, v13) = v15) |  ? [v16] : ( ~ (v16 = 0) & in(v11, v12) = v16)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (singleton(v11) = v14) |  ~ (unordered_pair(v13, v14) = v15) |  ~ (unordered_pair(v11, v12) = v13) | ordered_pair(v11, v12) = v15) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (powerset(v12) = v13) |  ~ (element(v11, v13) = v14) |  ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (element(v14, v13) = v12) |  ~ (element(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (subset(v14, v13) = v12) |  ~ (subset(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (relation_inverse_image(v14, v13) = v12) |  ~ (relation_inverse_image(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (ordered_pair(v14, v13) = v12) |  ~ (ordered_pair(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (unordered_pair(v14, v13) = v12) |  ~ (unordered_pair(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (in(v14, v13) = v12) |  ~ (in(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (powerset(v13) = v14) |  ~ (element(v12, v14) = 0) |  ~ (in(v11, v12) = 0) |  ? [v15] : ( ~ (v15 = 0) & empty(v13) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (relation_inverse_image(v11, v12) = v13) |  ~ (relation(v11) = 0) |  ~ (in(v14, v13) = 0) |  ? [v15] :  ? [v16] : (ordered_pair(v14, v15) = v16 & in(v16, v11) = 0 & in(v15, v12) = 0)) &  ? [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = v11 |  ~ (relation_inverse_image(v12, v13) = v14) |  ~ (relation(v12) = 0) |  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] : (in(v15, v11) = v16 & ( ~ (v16 = 0) |  ! [v21] :  ! [v22] : ( ~ (ordered_pair(v15, v21) = v22) |  ~ (in(v22, v12) = 0) |  ? [v23] : ( ~ (v23 = 0) & in(v21, v13) = v23))) & (v16 = 0 | (v20 = 0 & v19 = 0 & ordered_pair(v15, v17) = v18 & in(v18, v12) = 0 & in(v17, v13) = 0)))) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (element(v11, v12) = v13) |  ? [v14] : ( ~ (v14 = 0) & in(v11, v12) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (subset(v11, v12) = v13) |  ? [v14] :  ? [v15] : ( ~ (v15 = 0) & in(v14, v12) = v15 & in(v14, v11) = 0)) &  ! [v11] :  ! [v12] :  ! [v13] : (v12 = v11 |  ~ (powerset(v13) = v12) |  ~ (powerset(v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] : (v12 = v11 |  ~ (singleton(v13) = v12) |  ~ (singleton(v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] : (v12 = v11 |  ~ (relation_dom(v13) = v12) |  ~ (relation_dom(v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] : (v12 = v11 |  ~ (relation(v13) = v12) |  ~ (relation(v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] : (v12 = v11 |  ~ (empty(v13) = v12) |  ~ (empty(v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (powerset(v12) = v13) |  ~ (element(v11, v13) = 0) | subset(v11, v12) = 0) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (relation_dom(v11) = v12) |  ~ (in(v13, v12) = 0) |  ? [v14] :  ? [v15] :  ? [v16] : ((v16 = 0 & ordered_pair(v13, v14) = v15 & in(v15, v11) = 0) | ( ~ (v14 = 0) & relation(v11) = v14))) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (subset(v11, v12) = 0) |  ~ (in(v13, v11) = 0) | in(v13, v12) = 0) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) |  ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | unordered_pair(v12, v11) = v13) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) |  ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) &  ? [v11] :  ! [v12] :  ! [v13] : (v13 = v11 |  ~ (relation_dom(v12) = v13) |  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] : (( ~ (v14 = 0) & relation(v12) = v14) | (in(v14, v11) = v15 & ( ~ (v15 = 0) |  ! [v19] :  ! [v20] : ( ~ (ordered_pair(v14, v19) = v20) |  ~ (in(v20, v12) = 0))) & (v15 = 0 | (v18 = 0 & ordered_pair(v14, v16) = v17 & in(v17, v12) = 0))))) &  ! [v11] :  ! [v12] : (v12 = v11 |  ~ (empty(v12) = 0) |  ~ (empty(v11) = 0)) &  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (subset(v11, v11) = v12)) &  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (relation(v11) = v12) |  ? [v13] : ( ~ (v13 = 0) & empty(v11) = v13)) &  ! [v11] :  ! [v12] : ( ~ (powerset(v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : ((v14 = 0 &  ~ (v15 = 0) & element(v13, v12) = 0 & empty(v13) = v15) | (v13 = 0 & empty(v11) = 0))) &  ! [v11] :  ! [v12] : ( ~ (powerset(v11) = v12) |  ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) &  ! [v11] :  ! [v12] : ( ~ (powerset(v11) = v12) |  ? [v13] : (element(v13, v12) = 0 & empty(v13) = 0)) &  ! [v11] :  ! [v12] : ( ~ (element(v11, v12) = 0) |  ? [v13] :  ? [v14] : (empty(v12) = v13 & in(v11, v12) = v14 & (v14 = 0 | v13 = 0))) &  ! [v11] :  ! [v12] : ( ~ (singleton(v11) = v12) |  ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) &  ! [v11] :  ! [v12] : ( ~ (relation_dom(v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : (relation(v12) = v15 & empty(v12) = v14 & empty(v11) = v13 & ( ~ (v13 = 0) | (v15 = 0 & v14 = 0)))) &  ! [v11] :  ! [v12] : ( ~ (relation_dom(v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : (relation(v11) = v14 & empty(v12) = v15 & empty(v11) = v13 & ( ~ (v15 = 0) |  ~ (v14 = 0) | v13 = 0))) &  ! [v11] :  ! [v12] : ( ~ (in(v11, v12) = 0) |  ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) &  ! [v11] :  ! [v12] : ( ~ (in(v11, v12) = 0) |  ? [v13] : ( ~ (v13 = 0) & in(v12, v11) = v13)) &  ! [v11] : (v11 = empty_set |  ~ (empty(v11) = 0)) &  ? [v11] :  ? [v12] : element(v12, v11) = 0)
% 6.65/2.18  | 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 yields:
% 6.65/2.18  | (1)  ~ (all_0_2_2 = 0) &  ~ (all_0_4_4 = 0) &  ~ (all_0_6_6 = 0) & relation_dom(all_0_9_9) = all_0_7_7 & subset(all_0_8_8, all_0_7_7) = all_0_6_6 & relation_inverse_image(all_0_9_9, all_0_10_10) = all_0_8_8 & relation(all_0_0_0) = 0 & relation(all_0_3_3) = 0 & relation(all_0_9_9) = 0 & relation(empty_set) = 0 & empty(all_0_0_0) = 0 & empty(all_0_1_1) = 0 & empty(all_0_3_3) = all_0_2_2 & empty(all_0_5_5) = all_0_4_4 & empty(empty_set) = 0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = 0 |  ~ (relation_inverse_image(v0, v1) = v2) |  ~ (ordered_pair(v3, v5) = v6) |  ~ (relation(v0) = 0) |  ~ (in(v6, v0) = 0) |  ~ (in(v3, v2) = v4) |  ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = 0 |  ~ (relation_dom(v0) = v1) |  ~ (ordered_pair(v2, v4) = v5) |  ~ (in(v5, v0) = 0) |  ~ (in(v2, v1) = v3) |  ? [v6] : ( ~ (v6 = 0) & relation(v0) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (powerset(v2) = v3) |  ~ (element(v1, v3) = 0) |  ~ (element(v0, v2) = v4) |  ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (powerset(v1) = v2) |  ~ (element(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (element(v3, v2) = v1) |  ~ (element(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_inverse_image(v3, v2) = v1) |  ~ (relation_inverse_image(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ (element(v1, v3) = 0) |  ~ (in(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) |  ~ (relation(v0) = 0) |  ~ (in(v3, v2) = 0) |  ? [v4] :  ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0)) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (relation_inverse_image(v1, v2) = v3) |  ~ (relation(v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) |  ! [v10] :  ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) |  ~ (in(v11, v1) = 0) |  ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v4, v6) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (element(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation(v2) = v1) |  ~ (relation(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom(v0) = v1) |  ~ (in(v2, v1) = 0) |  ? [v3] :  ? [v4] :  ? [v5] : ((v5 = 0 & ordered_pair(v2, v3) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) | in(v2, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) &  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (relation_dom(v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (in(v3, v0) = v4 & ( ~ (v4 = 0) |  ! [v8] :  ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) |  ~ (in(v9, v1) = 0))) & (v4 = 0 | (v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v1) = 0))))) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (relation(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v3 = 0 &  ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) &  ! [v0] :  ! [v1] : ( ~ (element(v0, v1) = 0) |  ? [v2] :  ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v2 = 0))) &  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) &  ! [v0] : (v0 = empty_set |  ~ (empty(v0) = 0)) &  ? [v0] :  ? [v1] : element(v1, v0) = 0
% 6.65/2.19  |
% 6.65/2.19  | Applying alpha-rule on (1) yields:
% 6.65/2.20  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) |  ~ (relation(v0) = 0) |  ~ (in(v3, v2) = 0) |  ? [v4] :  ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0))
% 6.65/2.20  | (3)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 6.65/2.20  | (4)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation(v2) = v1) |  ~ (relation(v2) = v0))
% 6.65/2.20  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 6.65/2.20  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 6.65/2.20  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 6.65/2.20  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_inverse_image(v3, v2) = v1) |  ~ (relation_inverse_image(v3, v2) = v0))
% 6.65/2.20  | (9)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 6.65/2.20  | (10) relation(all_0_0_0) = 0
% 6.65/2.20  | (11)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 6.65/2.20  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 6.65/2.20  | (13)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (element(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 6.65/2.20  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 6.65/2.20  | (15)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 6.65/2.20  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = 0 |  ~ (relation_inverse_image(v0, v1) = v2) |  ~ (ordered_pair(v3, v5) = v6) |  ~ (relation(v0) = 0) |  ~ (in(v6, v0) = 0) |  ~ (in(v3, v2) = v4) |  ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7))
% 6.65/2.20  | (17) empty(all_0_5_5) = all_0_4_4
% 6.65/2.20  | (18)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 6.65/2.20  | (19)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v3 = 0 &  ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0)))
% 6.65/2.20  | (20)  ! [v0] : (v0 = empty_set |  ~ (empty(v0) = 0))
% 6.65/2.20  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0))
% 6.65/2.20  | (22)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 6.65/2.20  | (23) relation_inverse_image(all_0_9_9, all_0_10_10) = all_0_8_8
% 6.65/2.20  | (24)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 6.65/2.20  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom(v0) = v1) |  ~ (in(v2, v1) = 0) |  ? [v3] :  ? [v4] :  ? [v5] : ((v5 = 0 & ordered_pair(v2, v3) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 6.65/2.20  | (26) empty(all_0_0_0) = 0
% 6.65/2.20  | (27)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1))
% 6.65/2.20  | (28)  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (relation_dom(v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (in(v3, v0) = v4 & ( ~ (v4 = 0) |  ! [v8] :  ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) |  ~ (in(v9, v1) = 0))) & (v4 = 0 | (v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v1) = 0)))))
% 6.65/2.20  | (29) empty(all_0_1_1) = 0
% 6.65/2.20  | (30)  ~ (all_0_4_4 = 0)
% 6.65/2.20  | (31) relation(empty_set) = 0
% 6.65/2.20  | (32) subset(all_0_8_8, all_0_7_7) = all_0_6_6
% 6.65/2.20  | (33)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 6.65/2.21  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0))
% 6.65/2.21  | (35)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 6.65/2.21  | (36)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (relation(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 6.65/2.21  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = 0 |  ~ (relation_dom(v0) = v1) |  ~ (ordered_pair(v2, v4) = v5) |  ~ (in(v5, v0) = 0) |  ~ (in(v2, v1) = v3) |  ? [v6] : ( ~ (v6 = 0) & relation(v0) = v6))
% 6.65/2.21  | (38) relation(all_0_3_3) = 0
% 6.65/2.21  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (powerset(v1) = v2) |  ~ (element(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 6.65/2.21  | (40) relation_dom(all_0_9_9) = all_0_7_7
% 6.65/2.21  | (41) empty(empty_set) = 0
% 6.65/2.21  | (42)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 6.65/2.21  | (43)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 6.65/2.21  | (44)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0))
% 6.65/2.21  | (45)  ~ (all_0_2_2 = 0)
% 6.65/2.21  | (46)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v2 = 0)))
% 6.65/2.21  | (47)  ? [v0] :  ? [v1] : element(v1, v0) = 0
% 6.65/2.21  | (48)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (relation_inverse_image(v1, v2) = v3) |  ~ (relation(v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) |  ! [v10] :  ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) |  ~ (in(v11, v1) = 0) |  ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v4, v6) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0))))
% 6.65/2.21  | (49)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 6.65/2.21  | (50)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 6.65/2.21  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (powerset(v2) = v3) |  ~ (element(v1, v3) = 0) |  ~ (element(v0, v2) = v4) |  ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 6.65/2.21  | (52)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (element(v3, v2) = v1) |  ~ (element(v3, v2) = v0))
% 6.65/2.21  | (53)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 6.65/2.21  | (54)  ~ (all_0_6_6 = 0)
% 6.65/2.21  | (55)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ (element(v1, v3) = 0) |  ~ (in(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 6.65/2.21  | (56)  ! [v0] :  ! [v1] : ( ~ (element(v0, v1) = 0) |  ? [v2] :  ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 6.65/2.21  | (57) relation(all_0_9_9) = 0
% 6.65/2.21  | (58) empty(all_0_3_3) = all_0_2_2
% 6.65/2.21  |
% 6.65/2.21  | Instantiating formula (46) with all_0_7_7, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_7_7, yields:
% 6.65/2.21  | (59)  ? [v0] :  ? [v1] :  ? [v2] : (relation(all_0_9_9) = v1 & empty(all_0_7_7) = v2 & empty(all_0_9_9) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) | v0 = 0))
% 6.65/2.21  |
% 6.65/2.21  | Instantiating formula (11) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms subset(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 6.65/2.22  | (60) all_0_6_6 = 0 |  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = v1 & in(v0, all_0_8_8) = 0)
% 6.65/2.22  |
% 6.65/2.22  | Instantiating (59) with all_26_0_15, all_26_1_16, all_26_2_17 yields:
% 6.65/2.22  | (61) relation(all_0_9_9) = all_26_1_16 & empty(all_0_7_7) = all_26_0_15 & empty(all_0_9_9) = all_26_2_17 & ( ~ (all_26_0_15 = 0) |  ~ (all_26_1_16 = 0) | all_26_2_17 = 0)
% 6.65/2.22  |
% 6.65/2.22  | Applying alpha-rule on (61) yields:
% 6.65/2.22  | (62) relation(all_0_9_9) = all_26_1_16
% 6.65/2.22  | (63) empty(all_0_7_7) = all_26_0_15
% 6.65/2.22  | (64) empty(all_0_9_9) = all_26_2_17
% 6.65/2.22  | (65)  ~ (all_26_0_15 = 0) |  ~ (all_26_1_16 = 0) | all_26_2_17 = 0
% 6.65/2.22  |
% 6.65/2.22  +-Applying beta-rule and splitting (60), into two cases.
% 6.65/2.22  |-Branch one:
% 6.65/2.22  | (66) all_0_6_6 = 0
% 6.65/2.22  |
% 6.65/2.22  	| Equations (66) can reduce 54 to:
% 6.65/2.22  	| (67) $false
% 6.65/2.22  	|
% 6.65/2.22  	|-The branch is then unsatisfiable
% 6.65/2.22  |-Branch two:
% 6.65/2.22  | (54)  ~ (all_0_6_6 = 0)
% 6.65/2.22  | (69)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = v1 & in(v0, all_0_8_8) = 0)
% 6.65/2.22  |
% 6.65/2.22  	| Instantiating (69) with all_36_0_23, all_36_1_24 yields:
% 6.65/2.22  	| (70)  ~ (all_36_0_23 = 0) & in(all_36_1_24, all_0_7_7) = all_36_0_23 & in(all_36_1_24, all_0_8_8) = 0
% 6.65/2.22  	|
% 6.65/2.22  	| Applying alpha-rule on (70) yields:
% 6.65/2.22  	| (71)  ~ (all_36_0_23 = 0)
% 6.65/2.22  	| (72) in(all_36_1_24, all_0_7_7) = all_36_0_23
% 6.65/2.22  	| (73) in(all_36_1_24, all_0_8_8) = 0
% 6.65/2.22  	|
% 6.65/2.22  	| Instantiating formula (4) with all_0_9_9, all_26_1_16, 0 and discharging atoms relation(all_0_9_9) = all_26_1_16, relation(all_0_9_9) = 0, yields:
% 6.65/2.22  	| (74) all_26_1_16 = 0
% 6.65/2.22  	|
% 6.65/2.22  	| From (74) and (62) follows:
% 6.65/2.22  	| (57) relation(all_0_9_9) = 0
% 6.65/2.22  	|
% 6.65/2.22  	| Instantiating formula (2) with all_36_1_24, all_0_8_8, all_0_10_10, all_0_9_9 and discharging atoms relation_inverse_image(all_0_9_9, all_0_10_10) = all_0_8_8, relation(all_0_9_9) = 0, in(all_36_1_24, all_0_8_8) = 0, yields:
% 6.65/2.22  	| (76)  ? [v0] :  ? [v1] : (ordered_pair(all_36_1_24, v0) = v1 & in(v1, all_0_9_9) = 0 & in(v0, all_0_10_10) = 0)
% 6.65/2.22  	|
% 6.65/2.22  	| Instantiating (76) with all_51_0_27, all_51_1_28 yields:
% 6.65/2.22  	| (77) ordered_pair(all_36_1_24, all_51_1_28) = all_51_0_27 & in(all_51_0_27, all_0_9_9) = 0 & in(all_51_1_28, all_0_10_10) = 0
% 6.65/2.22  	|
% 6.65/2.22  	| Applying alpha-rule on (77) yields:
% 6.65/2.22  	| (78) ordered_pair(all_36_1_24, all_51_1_28) = all_51_0_27
% 6.65/2.22  	| (79) in(all_51_0_27, all_0_9_9) = 0
% 6.65/2.22  	| (80) in(all_51_1_28, all_0_10_10) = 0
% 6.65/2.22  	|
% 6.65/2.22  	| Instantiating formula (37) with all_51_0_27, all_51_1_28, all_36_0_23, all_36_1_24, all_0_7_7, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_7_7, ordered_pair(all_36_1_24, all_51_1_28) = all_51_0_27, in(all_51_0_27, all_0_9_9) = 0, in(all_36_1_24, all_0_7_7) = all_36_0_23, yields:
% 6.65/2.22  	| (81) all_36_0_23 = 0 |  ? [v0] : ( ~ (v0 = 0) & relation(all_0_9_9) = v0)
% 6.65/2.22  	|
% 6.65/2.22  	+-Applying beta-rule and splitting (81), into two cases.
% 6.65/2.22  	|-Branch one:
% 6.65/2.22  	| (82) all_36_0_23 = 0
% 6.65/2.22  	|
% 6.65/2.22  		| Equations (82) can reduce 71 to:
% 6.65/2.22  		| (67) $false
% 6.65/2.22  		|
% 6.65/2.22  		|-The branch is then unsatisfiable
% 6.65/2.22  	|-Branch two:
% 6.65/2.22  	| (71)  ~ (all_36_0_23 = 0)
% 6.65/2.22  	| (85)  ? [v0] : ( ~ (v0 = 0) & relation(all_0_9_9) = v0)
% 6.65/2.22  	|
% 6.65/2.22  		| Instantiating (85) with all_72_0_34 yields:
% 6.65/2.22  		| (86)  ~ (all_72_0_34 = 0) & relation(all_0_9_9) = all_72_0_34
% 6.65/2.22  		|
% 6.65/2.22  		| Applying alpha-rule on (86) yields:
% 6.65/2.22  		| (87)  ~ (all_72_0_34 = 0)
% 6.65/2.22  		| (88) relation(all_0_9_9) = all_72_0_34
% 6.65/2.22  		|
% 6.65/2.22  		| Instantiating formula (4) with all_0_9_9, all_72_0_34, 0 and discharging atoms relation(all_0_9_9) = all_72_0_34, relation(all_0_9_9) = 0, yields:
% 6.65/2.23  		| (89) all_72_0_34 = 0
% 6.65/2.23  		|
% 6.65/2.23  		| Equations (89) can reduce 87 to:
% 6.65/2.23  		| (67) $false
% 6.65/2.23  		|
% 6.65/2.23  		|-The branch is then unsatisfiable
% 6.65/2.23  % SZS output end Proof for theBenchmark
% 6.65/2.23  
% 6.65/2.23  1647ms
%------------------------------------------------------------------------------