%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET643+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n028.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 00:21:07 EDT 2022

% Result   : Theorem 3.26s 1.53s
% Output   : Proof 4.87s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : SET643+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.14  % Command  : ePrincess-casc -timeout=%d %s
% 0.14/0.36  % Computer : n028.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Sun Jul 10 04:17:42 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.51/0.61          ____       _                          
% 0.51/0.61    ___  / __ \_____(_)___  ________  __________
% 0.51/0.62   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.62  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.51/0.62  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.51/0.62  
% 0.51/0.62  A Theorem Prover for First-Order Logic
% 0.51/0.62  (ePrincess v.1.0)
% 0.51/0.62  
% 0.51/0.62  (c) Philipp Rümmer, 2009-2015
% 0.51/0.62  (c) Peter Backeman, 2014-2015
% 0.51/0.62  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.62  Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.62  Bug reports to peter@backeman.se
% 0.51/0.62  
% 0.51/0.62  For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.62  
% 0.51/0.62  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.81/0.67  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.69/1.02  Prover 0: Preprocessing ...
% 2.43/1.28  Prover 0: Warning: ignoring some quantifiers
% 2.60/1.31  Prover 0: Constructing countermodel ...
% 3.26/1.53  Prover 0: proved (866ms)
% 3.26/1.53  
% 3.26/1.53  No countermodel exists, formula is valid
% 3.26/1.53  % SZS status Theorem for theBenchmark
% 3.26/1.53  
% 3.26/1.53  Generating proof ... Warning: ignoring some quantifiers
% 4.82/1.82  found it (size 21)
% 4.82/1.82  
% 4.82/1.82  % SZS output start Proof for theBenchmark
% 4.82/1.82  Assumed formulas after preprocessing and simplification: 
% 4.82/1.82  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (cross_product(v0, v1) = v2 & relation_type(v0, v1) = v3 & ilf_type(v1, set_type) & ilf_type(v0, set_type) &  ~ ilf_type(v2, v3) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (ordered_pair(v8, v9) = v7) |  ~ (cross_product(v4, v5) = v6) |  ~ member(v9, v5) |  ~ member(v8, v4) |  ~ ilf_type(v9, set_type) |  ~ ilf_type(v8, set_type) |  ~ ilf_type(v7, set_type) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) | member(v7, v6)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (ordered_pair(v7, v6) = v5) |  ~ (ordered_pair(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (cross_product(v7, v6) = v5) |  ~ (cross_product(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (relation_type(v7, v6) = v5) |  ~ (relation_type(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (power_set(v5) = v6) |  ~ member(v7, v4) |  ~ member(v4, v6) |  ~ ilf_type(v7, set_type) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) | member(v7, v5)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (cross_product(v5, v6) = v7) |  ~ subset(v4, v7) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) |  ? [v8] : (relation_type(v5, v6) = v8 & ilf_type(v4, v8))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (cross_product(v4, v5) = v6) |  ~ member(v7, v6) |  ~ ilf_type(v7, set_type) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) |  ? [v8] :  ? [v9] : (ordered_pair(v8, v9) = v7 & member(v9, v5) & member(v8, v4) & ilf_type(v9, set_type) & ilf_type(v8, set_type))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (relation_type(v5, v6) = v7) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) | ilf_type(v4, v7) |  ? [v8] : (cross_product(v5, v6) = v8 &  ~ subset(v4, v8))) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (power_set(v6) = v5) |  ~ (power_set(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (member_type(v6) = v5) |  ~ (member_type(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (subset_type(v6) = v5) |  ~ (subset_type(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (power_set(v5) = v6) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) | member(v4, v6) |  ? [v7] : (member(v7, v4) & ilf_type(v7, set_type) &  ~ member(v7, v5))) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (member_type(v5) = v6) |  ~ member(v4, v5) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) | empty(v5) | ilf_type(v4, v6)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (member_type(v5) = v6) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, v6) |  ~ ilf_type(v4, set_type) | empty(v5) | member(v4, v5)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (ordered_pair(v4, v5) = v6) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) | ilf_type(v6, set_type)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (cross_product(v4, v5) = v6) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) | ilf_type(v6, set_type)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (cross_product(v4, v5) = v6) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) |  ? [v7] :  ? [v8] : (subset_type(v6) = v7 & relation_type(v4, v5) = v8 &  ! [v9] : ( ~ ilf_type(v9, v8) | ilf_type(v9, v7)) &  ! [v9] : ( ~ ilf_type(v9, v7) | ilf_type(v9, v8)))) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (cross_product(v4, v5) = v6) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) |  ? [v7] : (subset_type(v6) = v7 &  ! [v8] : ( ~ ilf_type(v8, v7) | relation_like(v8)))) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (relation_type(v5, v4) = v6) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) |  ? [v7] : ilf_type(v7, v6)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (relation_type(v4, v5) = v6) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) |  ? [v7] :  ? [v8] : (subset_type(v7) = v8 & cross_product(v4, v5) = v7 &  ! [v9] : ( ~ ilf_type(v9, v8) | ilf_type(v9, v6)) &  ! [v9] : ( ~ ilf_type(v9, v6) | ilf_type(v9, v8)))) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ member(v6, v4) |  ~ subset(v4, v5) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) | member(v6, v5)) &  ! [v4] :  ! [v5] : ( ~ (power_set(v4) = v5) |  ~ empty(v5) |  ~ ilf_type(v4, set_type)) &  ! [v4] :  ! [v5] : ( ~ (power_set(v4) = v5) |  ~ ilf_type(v4, set_type) | ilf_type(v5, set_type)) &  ! [v4] :  ! [v5] : ( ~ (power_set(v4) = v5) |  ~ ilf_type(v4, set_type) |  ? [v6] :  ? [v7] : (member_type(v5) = v7 & subset_type(v4) = v6 &  ! [v8] : ( ~ ilf_type(v8, v7) |  ~ ilf_type(v8, set_type) | ilf_type(v8, v6)) &  ! [v8] : ( ~ ilf_type(v8, v6) |  ~ ilf_type(v8, set_type) | ilf_type(v8, v7)))) &  ! [v4] :  ! [v5] : ( ~ (member_type(v4) = v5) |  ~ ilf_type(v4, set_type) | empty(v4) |  ? [v6] : ilf_type(v6, v5)) &  ! [v4] :  ! [v5] : ( ~ (subset_type(v4) = v5) |  ~ ilf_type(v4, set_type) |  ? [v6] :  ? [v7] : (power_set(v4) = v6 & member_type(v6) = v7 &  ! [v8] : ( ~ ilf_type(v8, v7) |  ~ ilf_type(v8, set_type) | ilf_type(v8, v5)) &  ! [v8] : ( ~ ilf_type(v8, v5) |  ~ ilf_type(v8, set_type) | ilf_type(v8, v7)))) &  ! [v4] :  ! [v5] : ( ~ (subset_type(v4) = v5) |  ~ ilf_type(v4, set_type) |  ? [v6] : ilf_type(v6, v5)) &  ! [v4] :  ! [v5] : ( ~ relation_like(v4) |  ~ member(v5, v4) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) |  ? [v6] :  ? [v7] : (ordered_pair(v6, v7) = v5 & ilf_type(v7, set_type) & ilf_type(v6, set_type))) &  ! [v4] :  ! [v5] : ( ~ empty(v4) |  ~ member(v5, v4) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type)) &  ! [v4] :  ! [v5] : ( ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) | subset(v4, v5) |  ? [v6] : (member(v6, v4) & ilf_type(v6, set_type) &  ~ member(v6, v5))) &  ! [v4] : ( ~ empty(v4) |  ~ ilf_type(v4, set_type) | relation_like(v4)) &  ! [v4] : ( ~ ilf_type(v4, set_type) | relation_like(v4) |  ? [v5] : (member(v5, v4) & ilf_type(v5, set_type) &  ! [v6] :  ! [v7] : ( ~ (ordered_pair(v6, v7) = v5) |  ~ ilf_type(v7, set_type) |  ~ ilf_type(v6, set_type)))) &  ! [v4] : ( ~ ilf_type(v4, set_type) | empty(v4) |  ? [v5] : (member(v5, v4) & ilf_type(v5, set_type))) &  ! [v4] : ( ~ ilf_type(v4, set_type) | subset(v4, v4)) &  ? [v4] : ilf_type(v4, set_type))
% 4.87/1.86  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 4.87/1.86  | (1) cross_product(all_0_3_3, all_0_2_2) = all_0_1_1 & relation_type(all_0_3_3, all_0_2_2) = all_0_0_0 & ilf_type(all_0_2_2, set_type) & ilf_type(all_0_3_3, set_type) &  ~ ilf_type(all_0_1_1, all_0_0_0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (ordered_pair(v4, v5) = v3) |  ~ (cross_product(v0, v1) = v2) |  ~ member(v5, v1) |  ~ member(v4, v0) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) |  ~ ilf_type(v3, set_type) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | member(v3, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cross_product(v3, v2) = v1) |  ~ (cross_product(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_type(v3, v2) = v1) |  ~ (relation_type(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (power_set(v1) = v2) |  ~ member(v3, v0) |  ~ member(v0, v2) |  ~ ilf_type(v3, set_type) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | member(v3, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cross_product(v1, v2) = v3) |  ~ subset(v0, v3) |  ~ ilf_type(v2, set_type) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v4] : (relation_type(v1, v2) = v4 & ilf_type(v0, v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cross_product(v0, v1) = v2) |  ~ member(v3, v2) |  ~ ilf_type(v3, set_type) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v4] :  ? [v5] : (ordered_pair(v4, v5) = v3 & member(v5, v1) & member(v4, v0) & ilf_type(v5, set_type) & ilf_type(v4, set_type))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_type(v1, v2) = v3) |  ~ ilf_type(v2, set_type) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | ilf_type(v0, v3) |  ? [v4] : (cross_product(v1, v2) = v4 &  ~ subset(v0, v4))) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (power_set(v2) = v1) |  ~ (power_set(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (member_type(v2) = v1) |  ~ (member_type(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (subset_type(v2) = v1) |  ~ (subset_type(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (power_set(v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | member(v0, v2) |  ? [v3] : (member(v3, v0) & ilf_type(v3, set_type) &  ~ member(v3, v1))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (member_type(v1) = v2) |  ~ member(v0, v1) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | empty(v1) | ilf_type(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (member_type(v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, v2) |  ~ ilf_type(v0, set_type) | empty(v1) | member(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | ilf_type(v2, set_type)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cross_product(v0, v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | ilf_type(v2, set_type)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cross_product(v0, v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v3] :  ? [v4] : (subset_type(v2) = v3 & relation_type(v0, v1) = v4 &  ! [v5] : ( ~ ilf_type(v5, v4) | ilf_type(v5, v3)) &  ! [v5] : ( ~ ilf_type(v5, v3) | ilf_type(v5, v4)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cross_product(v0, v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v3] : (subset_type(v2) = v3 &  ! [v4] : ( ~ ilf_type(v4, v3) | relation_like(v4)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_type(v1, v0) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v3] : ilf_type(v3, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_type(v0, v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v3] :  ? [v4] : (subset_type(v3) = v4 & cross_product(v0, v1) = v3 &  ! [v5] : ( ~ ilf_type(v5, v4) | ilf_type(v5, v2)) &  ! [v5] : ( ~ ilf_type(v5, v2) | ilf_type(v5, v4)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ member(v2, v0) |  ~ subset(v0, v1) |  ~ ilf_type(v2, set_type) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | member(v2, v1)) &  ! [v0] :  ! [v1] : ( ~ (power_set(v0) = v1) |  ~ empty(v1) |  ~ ilf_type(v0, set_type)) &  ! [v0] :  ! [v1] : ( ~ (power_set(v0) = v1) |  ~ ilf_type(v0, set_type) | ilf_type(v1, set_type)) &  ! [v0] :  ! [v1] : ( ~ (power_set(v0) = v1) |  ~ ilf_type(v0, set_type) |  ? [v2] :  ? [v3] : (member_type(v1) = v3 & subset_type(v0) = v2 &  ! [v4] : ( ~ ilf_type(v4, v3) |  ~ ilf_type(v4, set_type) | ilf_type(v4, v2)) &  ! [v4] : ( ~ ilf_type(v4, v2) |  ~ ilf_type(v4, set_type) | ilf_type(v4, v3)))) &  ! [v0] :  ! [v1] : ( ~ (member_type(v0) = v1) |  ~ ilf_type(v0, set_type) | empty(v0) |  ? [v2] : ilf_type(v2, v1)) &  ! [v0] :  ! [v1] : ( ~ (subset_type(v0) = v1) |  ~ ilf_type(v0, set_type) |  ? [v2] :  ? [v3] : (power_set(v0) = v2 & member_type(v2) = v3 &  ! [v4] : ( ~ ilf_type(v4, v3) |  ~ ilf_type(v4, set_type) | ilf_type(v4, v1)) &  ! [v4] : ( ~ ilf_type(v4, v1) |  ~ ilf_type(v4, set_type) | ilf_type(v4, v3)))) &  ! [v0] :  ! [v1] : ( ~ (subset_type(v0) = v1) |  ~ ilf_type(v0, set_type) |  ? [v2] : ilf_type(v2, v1)) &  ! [v0] :  ! [v1] : ( ~ relation_like(v0) |  ~ member(v1, v0) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v2] :  ? [v3] : (ordered_pair(v2, v3) = v1 & ilf_type(v3, set_type) & ilf_type(v2, set_type))) &  ! [v0] :  ! [v1] : ( ~ empty(v0) |  ~ member(v1, v0) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type)) &  ! [v0] :  ! [v1] : ( ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | subset(v0, v1) |  ? [v2] : (member(v2, v0) & ilf_type(v2, set_type) &  ~ member(v2, v1))) &  ! [v0] : ( ~ empty(v0) |  ~ ilf_type(v0, set_type) | relation_like(v0)) &  ! [v0] : ( ~ ilf_type(v0, set_type) | relation_like(v0) |  ? [v1] : (member(v1, v0) & ilf_type(v1, set_type) &  ! [v2] :  ! [v3] : ( ~ (ordered_pair(v2, v3) = v1) |  ~ ilf_type(v3, set_type) |  ~ ilf_type(v2, set_type)))) &  ! [v0] : ( ~ ilf_type(v0, set_type) | empty(v0) |  ? [v1] : (member(v1, v0) & ilf_type(v1, set_type))) &  ! [v0] : ( ~ ilf_type(v0, set_type) | subset(v0, v0)) &  ? [v0] : ilf_type(v0, set_type)
% 4.87/1.88  |
% 4.87/1.88  | Applying alpha-rule on (1) yields:
% 4.87/1.88  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (power_set(v1) = v2) |  ~ member(v3, v0) |  ~ member(v0, v2) |  ~ ilf_type(v3, set_type) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | member(v3, v1))
% 4.87/1.88  | (3)  ! [v0] :  ! [v1] : ( ~ (member_type(v0) = v1) |  ~ ilf_type(v0, set_type) | empty(v0) |  ? [v2] : ilf_type(v2, v1))
% 4.87/1.88  | (4)  ! [v0] :  ! [v1] : ( ~ empty(v0) |  ~ member(v1, v0) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type))
% 4.87/1.88  | (5)  ! [v0] : ( ~ ilf_type(v0, set_type) | subset(v0, v0))
% 4.87/1.88  | (6)  ! [v0] :  ! [v1] : ( ~ (power_set(v0) = v1) |  ~ ilf_type(v0, set_type) |  ? [v2] :  ? [v3] : (member_type(v1) = v3 & subset_type(v0) = v2 &  ! [v4] : ( ~ ilf_type(v4, v3) |  ~ ilf_type(v4, set_type) | ilf_type(v4, v2)) &  ! [v4] : ( ~ ilf_type(v4, v2) |  ~ ilf_type(v4, set_type) | ilf_type(v4, v3))))
% 4.87/1.88  | (7)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (subset_type(v2) = v1) |  ~ (subset_type(v2) = v0))
% 4.87/1.88  | (8)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (power_set(v2) = v1) |  ~ (power_set(v2) = v0))
% 4.87/1.88  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_type(v1, v0) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v3] : ilf_type(v3, v2))
% 4.87/1.88  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cross_product(v0, v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | ilf_type(v2, set_type))
% 4.87/1.88  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cross_product(v0, v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v3] : (subset_type(v2) = v3 &  ! [v4] : ( ~ ilf_type(v4, v3) | relation_like(v4))))
% 4.87/1.88  | (12) relation_type(all_0_3_3, all_0_2_2) = all_0_0_0
% 4.87/1.88  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cross_product(v0, v1) = v2) |  ~ member(v3, v2) |  ~ ilf_type(v3, set_type) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v4] :  ? [v5] : (ordered_pair(v4, v5) = v3 & member(v5, v1) & member(v4, v0) & ilf_type(v5, set_type) & ilf_type(v4, set_type)))
% 4.87/1.88  | (14)  ! [v0] : ( ~ ilf_type(v0, set_type) | empty(v0) |  ? [v1] : (member(v1, v0) & ilf_type(v1, set_type)))
% 4.87/1.88  | (15)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (power_set(v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | member(v0, v2) |  ? [v3] : (member(v3, v0) & ilf_type(v3, set_type) &  ~ member(v3, v1)))
% 4.87/1.88  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_type(v1, v2) = v3) |  ~ ilf_type(v2, set_type) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | ilf_type(v0, v3) |  ? [v4] : (cross_product(v1, v2) = v4 &  ~ subset(v0, v4)))
% 4.87/1.88  | (17)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | ilf_type(v2, set_type))
% 4.87/1.88  | (18)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_type(v0, v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v3] :  ? [v4] : (subset_type(v3) = v4 & cross_product(v0, v1) = v3 &  ! [v5] : ( ~ ilf_type(v5, v4) | ilf_type(v5, v2)) &  ! [v5] : ( ~ ilf_type(v5, v2) | ilf_type(v5, v4))))
% 4.87/1.88  | (19) ilf_type(all_0_3_3, set_type)
% 4.87/1.88  | (20)  ! [v0] :  ! [v1] : ( ~ (subset_type(v0) = v1) |  ~ ilf_type(v0, set_type) |  ? [v2] : ilf_type(v2, v1))
% 4.87/1.88  | (21)  ? [v0] : ilf_type(v0, set_type)
% 4.87/1.89  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (ordered_pair(v4, v5) = v3) |  ~ (cross_product(v0, v1) = v2) |  ~ member(v5, v1) |  ~ member(v4, v0) |  ~ ilf_type(v5, set_type) |  ~ ilf_type(v4, set_type) |  ~ ilf_type(v3, set_type) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | member(v3, v2))
% 4.87/1.89  | (23)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cross_product(v0, v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v3] :  ? [v4] : (subset_type(v2) = v3 & relation_type(v0, v1) = v4 &  ! [v5] : ( ~ ilf_type(v5, v4) | ilf_type(v5, v3)) &  ! [v5] : ( ~ ilf_type(v5, v3) | ilf_type(v5, v4))))
% 4.87/1.89  | (24)  ! [v0] : ( ~ ilf_type(v0, set_type) | relation_like(v0) |  ? [v1] : (member(v1, v0) & ilf_type(v1, set_type) &  ! [v2] :  ! [v3] : ( ~ (ordered_pair(v2, v3) = v1) |  ~ ilf_type(v3, set_type) |  ~ ilf_type(v2, set_type))))
% 4.87/1.89  | (25) cross_product(all_0_3_3, all_0_2_2) = all_0_1_1
% 4.87/1.89  | (26)  ! [v0] : ( ~ empty(v0) |  ~ ilf_type(v0, set_type) | relation_like(v0))
% 4.87/1.89  | (27)  ! [v0] :  ! [v1] : ( ~ (power_set(v0) = v1) |  ~ ilf_type(v0, set_type) | ilf_type(v1, set_type))
% 4.87/1.89  | (28)  ! [v0] :  ! [v1] : ( ~ (subset_type(v0) = v1) |  ~ ilf_type(v0, set_type) |  ? [v2] :  ? [v3] : (power_set(v0) = v2 & member_type(v2) = v3 &  ! [v4] : ( ~ ilf_type(v4, v3) |  ~ ilf_type(v4, set_type) | ilf_type(v4, v1)) &  ! [v4] : ( ~ ilf_type(v4, v1) |  ~ ilf_type(v4, set_type) | ilf_type(v4, v3))))
% 4.87/1.89  | (29) ilf_type(all_0_2_2, set_type)
% 4.87/1.89  | (30)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (member_type(v2) = v1) |  ~ (member_type(v2) = v0))
% 4.87/1.89  | (31)  ! [v0] :  ! [v1] : ( ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | subset(v0, v1) |  ? [v2] : (member(v2, v0) & ilf_type(v2, set_type) &  ~ member(v2, v1)))
% 4.87/1.89  | (32)  ~ ilf_type(all_0_1_1, all_0_0_0)
% 4.87/1.89  | (33)  ! [v0] :  ! [v1] : ( ~ (power_set(v0) = v1) |  ~ empty(v1) |  ~ ilf_type(v0, set_type))
% 4.87/1.89  | (34)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ member(v2, v0) |  ~ subset(v0, v1) |  ~ ilf_type(v2, set_type) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | member(v2, v1))
% 4.87/1.89  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_type(v3, v2) = v1) |  ~ (relation_type(v3, v2) = v0))
% 4.87/1.89  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cross_product(v1, v2) = v3) |  ~ subset(v0, v3) |  ~ ilf_type(v2, set_type) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v4] : (relation_type(v1, v2) = v4 & ilf_type(v0, v4)))
% 4.87/1.89  | (37)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (member_type(v1) = v2) |  ~ member(v0, v1) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | empty(v1) | ilf_type(v0, v2))
% 4.87/1.89  | (38)  ! [v0] :  ! [v1] : ( ~ relation_like(v0) |  ~ member(v1, v0) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v2] :  ? [v3] : (ordered_pair(v2, v3) = v1 & ilf_type(v3, set_type) & ilf_type(v2, set_type)))
% 4.87/1.89  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cross_product(v3, v2) = v1) |  ~ (cross_product(v3, v2) = v0))
% 4.87/1.89  | (40)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (member_type(v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, v2) |  ~ ilf_type(v0, set_type) | empty(v1) | member(v0, v1))
% 4.87/1.89  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0))
% 4.87/1.89  |
% 4.87/1.89  | Instantiating formula (10) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms cross_product(all_0_3_3, all_0_2_2) = all_0_1_1, ilf_type(all_0_2_2, set_type), ilf_type(all_0_3_3, set_type), yields:
% 4.87/1.89  | (42) ilf_type(all_0_1_1, set_type)
% 4.87/1.89  |
% 4.87/1.89  | Instantiating formula (23) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms cross_product(all_0_3_3, all_0_2_2) = all_0_1_1, ilf_type(all_0_2_2, set_type), ilf_type(all_0_3_3, set_type), yields:
% 4.87/1.89  | (43)  ? [v0] :  ? [v1] : (subset_type(all_0_1_1) = v0 & relation_type(all_0_3_3, all_0_2_2) = v1 &  ! [v2] : ( ~ ilf_type(v2, v1) | ilf_type(v2, v0)) &  ! [v2] : ( ~ ilf_type(v2, v0) | ilf_type(v2, v1)))
% 4.87/1.89  |
% 4.87/1.89  | Instantiating formula (18) with all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms relation_type(all_0_3_3, all_0_2_2) = all_0_0_0, ilf_type(all_0_2_2, set_type), ilf_type(all_0_3_3, set_type), yields:
% 4.87/1.90  | (44)  ? [v0] :  ? [v1] : (subset_type(v0) = v1 & cross_product(all_0_3_3, all_0_2_2) = v0 &  ! [v2] : ( ~ ilf_type(v2, v1) | ilf_type(v2, all_0_0_0)) &  ! [v2] : ( ~ ilf_type(v2, all_0_0_0) | ilf_type(v2, v1)))
% 4.87/1.90  |
% 4.87/1.90  | Instantiating (44) with all_11_0_5, all_11_1_6 yields:
% 4.87/1.90  | (45) subset_type(all_11_1_6) = all_11_0_5 & cross_product(all_0_3_3, all_0_2_2) = all_11_1_6 &  ! [v0] : ( ~ ilf_type(v0, all_11_0_5) | ilf_type(v0, all_0_0_0)) &  ! [v0] : ( ~ ilf_type(v0, all_0_0_0) | ilf_type(v0, all_11_0_5))
% 4.87/1.90  |
% 4.87/1.90  | Applying alpha-rule on (45) yields:
% 4.87/1.90  | (46) subset_type(all_11_1_6) = all_11_0_5
% 4.87/1.90  | (47) cross_product(all_0_3_3, all_0_2_2) = all_11_1_6
% 4.87/1.90  | (48)  ! [v0] : ( ~ ilf_type(v0, all_11_0_5) | ilf_type(v0, all_0_0_0))
% 4.87/1.90  | (49)  ! [v0] : ( ~ ilf_type(v0, all_0_0_0) | ilf_type(v0, all_11_0_5))
% 4.87/1.90  |
% 4.87/1.90  | Instantiating (43) with all_16_0_8, all_16_1_9 yields:
% 4.87/1.90  | (50) subset_type(all_0_1_1) = all_16_1_9 & relation_type(all_0_3_3, all_0_2_2) = all_16_0_8 &  ! [v0] : ( ~ ilf_type(v0, all_16_0_8) | ilf_type(v0, all_16_1_9)) &  ! [v0] : ( ~ ilf_type(v0, all_16_1_9) | ilf_type(v0, all_16_0_8))
% 4.87/1.90  |
% 4.87/1.90  | Applying alpha-rule on (50) yields:
% 4.87/1.90  | (51) subset_type(all_0_1_1) = all_16_1_9
% 4.87/1.90  | (52) relation_type(all_0_3_3, all_0_2_2) = all_16_0_8
% 4.87/1.90  | (53)  ! [v0] : ( ~ ilf_type(v0, all_16_0_8) | ilf_type(v0, all_16_1_9))
% 4.87/1.90  | (54)  ! [v0] : ( ~ ilf_type(v0, all_16_1_9) | ilf_type(v0, all_16_0_8))
% 4.87/1.90  |
% 4.87/1.90  | Instantiating formula (39) with all_0_3_3, all_0_2_2, all_11_1_6, all_0_1_1 and discharging atoms cross_product(all_0_3_3, all_0_2_2) = all_11_1_6, cross_product(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 4.87/1.90  | (55) all_11_1_6 = all_0_1_1
% 4.87/1.90  |
% 4.87/1.90  | Instantiating formula (35) with all_0_3_3, all_0_2_2, all_16_0_8, all_0_0_0 and discharging atoms relation_type(all_0_3_3, all_0_2_2) = all_16_0_8, relation_type(all_0_3_3, all_0_2_2) = all_0_0_0, yields:
% 4.87/1.90  | (56) all_16_0_8 = all_0_0_0
% 4.87/1.90  |
% 4.87/1.90  | From (55) and (47) follows:
% 4.87/1.90  | (25) cross_product(all_0_3_3, all_0_2_2) = all_0_1_1
% 4.87/1.90  |
% 4.87/1.90  | From (56) and (52) follows:
% 4.87/1.90  | (12) relation_type(all_0_3_3, all_0_2_2) = all_0_0_0
% 4.87/1.90  |
% 4.87/1.90  | Instantiating formula (16) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_1_1 and discharging atoms relation_type(all_0_3_3, all_0_2_2) = all_0_0_0, ilf_type(all_0_1_1, set_type), ilf_type(all_0_2_2, set_type), ilf_type(all_0_3_3, set_type),  ~ ilf_type(all_0_1_1, all_0_0_0), yields:
% 4.87/1.90  | (59)  ? [v0] : (cross_product(all_0_3_3, all_0_2_2) = v0 &  ~ subset(all_0_1_1, v0))
% 4.87/1.90  |
% 4.87/1.90  | Instantiating formula (31) with all_0_1_1, all_0_1_1 and discharging atoms ilf_type(all_0_1_1, set_type), yields:
% 4.87/1.90  | (60) subset(all_0_1_1, all_0_1_1)
% 4.87/1.90  |
% 4.87/1.90  | Instantiating (59) with all_41_0_14 yields:
% 4.87/1.90  | (61) cross_product(all_0_3_3, all_0_2_2) = all_41_0_14 &  ~ subset(all_0_1_1, all_41_0_14)
% 4.87/1.90  |
% 4.87/1.90  | Applying alpha-rule on (61) yields:
% 4.87/1.90  | (62) cross_product(all_0_3_3, all_0_2_2) = all_41_0_14
% 4.87/1.90  | (63)  ~ subset(all_0_1_1, all_41_0_14)
% 4.87/1.90  |
% 4.87/1.90  | Instantiating formula (39) with all_0_3_3, all_0_2_2, all_41_0_14, all_0_1_1 and discharging atoms cross_product(all_0_3_3, all_0_2_2) = all_41_0_14, cross_product(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 4.87/1.90  | (64) all_41_0_14 = all_0_1_1
% 4.87/1.90  |
% 4.87/1.90  | From (64) and (63) follows:
% 4.87/1.90  | (65)  ~ subset(all_0_1_1, all_0_1_1)
% 4.87/1.90  |
% 4.87/1.90  | Using (60) and (65) yields:
% 4.87/1.90  | (66) $false
% 4.87/1.90  |
% 4.87/1.90  |-The branch is then unsatisfiable
% 4.87/1.90  % SZS output end Proof for theBenchmark
% 4.87/1.90  
% 4.87/1.90  1276ms
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