%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET642+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n023.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 3.29s 1.58s
% Output   : Proof 5.79s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08  % Problem  : SET642+3 : TPTP v8.1.0. Released v2.2.0.
% 0.02/0.09  % Command  : ePrincess-casc -timeout=%d %s
% 0.08/0.28  % Computer : n023.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit : 300
% 0.08/0.28  % WCLimit  : 600
% 0.08/0.28  % DateTime : Sun Jul 10 09:29:55 EDT 2022
% 0.08/0.28  % CPUTime  : 
% 0.13/0.52          ____       _                          
% 0.13/0.52    ___  / __ \_____(_)___  ________  __________
% 0.13/0.52   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.13/0.52  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.13/0.52  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.13/0.52  
% 0.13/0.52  A Theorem Prover for First-Order Logic
% 0.13/0.52  (ePrincess v.1.0)
% 0.13/0.52  
% 0.13/0.52  (c) Philipp Rümmer, 2009-2015
% 0.13/0.52  (c) Peter Backeman, 2014-2015
% 0.13/0.52  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.13/0.52  Free software under GNU Lesser General Public License (LGPL).
% 0.13/0.52  Bug reports to peter@backeman.se
% 0.13/0.52  
% 0.13/0.52  For more information, visit http://user.uu.se/~petba168/breu/
% 0.13/0.52  
% 0.13/0.52  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.61/0.58  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.61/0.95  Prover 0: Preprocessing ...
% 2.29/1.27  Prover 0: Warning: ignoring some quantifiers
% 2.47/1.31  Prover 0: Constructing countermodel ...
% 3.29/1.58  Prover 0: proved (1000ms)
% 3.29/1.58  
% 3.29/1.58  No countermodel exists, formula is valid
% 3.29/1.58  % SZS status Theorem for theBenchmark
% 3.29/1.58  
% 3.29/1.58  Generating proof ... Warning: ignoring some quantifiers
% 4.97/1.96  found it (size 38)
% 4.97/1.96  
% 4.97/1.96  % SZS output start Proof for theBenchmark
% 4.97/1.96  Assumed formulas after preprocessing and simplification: 
% 4.97/1.96  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (relation_type(v1, v2) = v3 & subset(v0, v4) & ilf_type(v4, v3) & ilf_type(v2, set_type) & ilf_type(v1, set_type) & ilf_type(v0, set_type) &  ~ ilf_type(v0, v3) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (ordered_pair(v8, v7) = v6) |  ~ (ordered_pair(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (cross_product(v8, v7) = v6) |  ~ (cross_product(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (relation_type(v8, v7) = v6) |  ~ (relation_type(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (power_set(v6) = v7) |  ~ member(v8, v5) |  ~ member(v5, v7) |  ~ ilf_type(v8, set_type) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) | member(v8, v6)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (cross_product(v6, v7) = v8) |  ~ subset(v5, v8) |  ~ ilf_type(v7, set_type) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) |  ? [v9] : (relation_type(v6, v7) = v9 & ilf_type(v5, v9))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (cross_product(v6, v7) = v8) |  ~ ilf_type(v7, set_type) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) |  ? [v9] : (relation_type(v6, v7) = v9 &  ! [v10] : ( ~ subset(v5, v10) |  ~ ilf_type(v10, v9) | subset(v5, v8)))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (relation_type(v6, v7) = v8) |  ~ ilf_type(v7, set_type) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) | ilf_type(v5, v8) |  ? [v9] : (cross_product(v6, v7) = v9 &  ~ subset(v5, v9))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (relation_type(v6, v7) = v8) |  ~ ilf_type(v7, set_type) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) |  ? [v9] : (cross_product(v6, v7) = v9 &  ! [v10] : ( ~ subset(v5, v10) |  ~ ilf_type(v10, v8) | subset(v5, v9)))) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (power_set(v7) = v6) |  ~ (power_set(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (member_type(v7) = v6) |  ~ (member_type(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (subset_type(v7) = v6) |  ~ (subset_type(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (ordered_pair(v5, v6) = v7) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) | ilf_type(v7, set_type)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (power_set(v6) = v7) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) | member(v5, v7) |  ? [v8] : (member(v8, v5) & ilf_type(v8, set_type) &  ~ member(v8, v6))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (member_type(v6) = v7) |  ~ member(v5, v6) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) | empty(v6) | ilf_type(v5, v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (member_type(v6) = v7) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, v7) |  ~ ilf_type(v5, set_type) | empty(v6) | member(v5, v6)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (cross_product(v5, v6) = v7) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) | ilf_type(v7, set_type)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (cross_product(v5, v6) = v7) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) |  ? [v8] :  ? [v9] : (subset_type(v7) = v8 & relation_type(v5, v6) = v9 &  ! [v10] : ( ~ ilf_type(v10, v9) | ilf_type(v10, v8)) &  ! [v10] : ( ~ ilf_type(v10, v8) | ilf_type(v10, v9)))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (cross_product(v5, v6) = v7) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) |  ? [v8] : (subset_type(v7) = v8 &  ! [v9] : ( ~ ilf_type(v9, v8) | relation_like(v9)))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (relation_type(v6, v5) = v7) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) |  ? [v8] : ilf_type(v8, v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (relation_type(v5, v6) = v7) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) |  ? [v8] :  ? [v9] : (subset_type(v8) = v9 & cross_product(v5, v6) = v8 &  ! [v10] : ( ~ ilf_type(v10, v9) | ilf_type(v10, v7)) &  ! [v10] : ( ~ ilf_type(v10, v7) | ilf_type(v10, v9)))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ member(v7, v5) |  ~ subset(v5, v6) |  ~ ilf_type(v7, set_type) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) | member(v7, v6)) &  ! [v5] :  ! [v6] : ( ~ (power_set(v5) = v6) |  ~ empty(v6) |  ~ ilf_type(v5, set_type)) &  ! [v5] :  ! [v6] : ( ~ (power_set(v5) = v6) |  ~ ilf_type(v5, set_type) | ilf_type(v6, set_type)) &  ! [v5] :  ! [v6] : ( ~ (power_set(v5) = v6) |  ~ ilf_type(v5, set_type) |  ? [v7] :  ? [v8] : (member_type(v6) = v8 & subset_type(v5) = v7 &  ! [v9] : ( ~ ilf_type(v9, v8) |  ~ ilf_type(v9, set_type) | ilf_type(v9, v7)) &  ! [v9] : ( ~ ilf_type(v9, v7) |  ~ ilf_type(v9, set_type) | ilf_type(v9, v8)))) &  ! [v5] :  ! [v6] : ( ~ (member_type(v5) = v6) |  ~ ilf_type(v5, set_type) | empty(v5) |  ? [v7] : ilf_type(v7, v6)) &  ! [v5] :  ! [v6] : ( ~ (subset_type(v5) = v6) |  ~ ilf_type(v5, set_type) |  ? [v7] :  ? [v8] : (power_set(v5) = v7 & member_type(v7) = v8 &  ! [v9] : ( ~ ilf_type(v9, v8) |  ~ ilf_type(v9, set_type) | ilf_type(v9, v6)) &  ! [v9] : ( ~ ilf_type(v9, v6) |  ~ ilf_type(v9, set_type) | ilf_type(v9, v8)))) &  ! [v5] :  ! [v6] : ( ~ (subset_type(v5) = v6) |  ~ ilf_type(v5, set_type) |  ? [v7] : ilf_type(v7, v6)) &  ! [v5] :  ! [v6] : ( ~ relation_like(v5) |  ~ member(v6, v5) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) |  ? [v7] :  ? [v8] : (ordered_pair(v7, v8) = v6 & ilf_type(v8, set_type) & ilf_type(v7, set_type))) &  ! [v5] :  ! [v6] : ( ~ empty(v5) |  ~ member(v6, v5) |  ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type)) &  ! [v5] :  ! [v6] : ( ~ ilf_type(v6, set_type) |  ~ ilf_type(v5, set_type) | subset(v5, v6) |  ? [v7] : (member(v7, v5) & ilf_type(v7, set_type) &  ~ member(v7, v6))) &  ! [v5] : ( ~ empty(v5) |  ~ ilf_type(v5, set_type) | relation_like(v5)) &  ! [v5] : ( ~ ilf_type(v5, set_type) | relation_like(v5) |  ? [v6] : (member(v6, v5) & ilf_type(v6, set_type) &  ! [v7] :  ! [v8] : ( ~ (ordered_pair(v7, v8) = v6) |  ~ ilf_type(v8, set_type) |  ~ ilf_type(v7, set_type)))) &  ! [v5] : ( ~ ilf_type(v5, set_type) | empty(v5) |  ? [v6] : (member(v6, v5) & ilf_type(v6, set_type))) &  ! [v5] : ( ~ ilf_type(v5, set_type) | subset(v5, v5)) &  ? [v5] : ilf_type(v5, set_type))
% 5.35/2.03  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 5.35/2.03  | (1) relation_type(all_0_3_3, all_0_2_2) = all_0_1_1 & subset(all_0_4_4, all_0_0_0) & ilf_type(all_0_0_0, all_0_1_1) & ilf_type(all_0_2_2, set_type) & ilf_type(all_0_3_3, set_type) & ilf_type(all_0_4_4, set_type) &  ~ ilf_type(all_0_4_4, all_0_1_1) &  ! [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(v1, v2) = v3) |  ~ ilf_type(v2, set_type) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v4] : (relation_type(v1, v2) = v4 &  ! [v5] : ( ~ subset(v0, v5) |  ~ ilf_type(v5, v4) | subset(v0, v3)))) &  ! [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] :  ! [v3] : ( ~ (relation_type(v1, v2) = v3) |  ~ ilf_type(v2, set_type) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v4] : (cross_product(v1, v2) = v4 &  ! [v5] : ( ~ subset(v0, v5) |  ~ ilf_type(v5, v3) | 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] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | ilf_type(v2, set_type)) &  ! [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] : ( ~ (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)
% 5.35/2.04  |
% 5.35/2.04  | Applying alpha-rule on (1) yields:
% 5.35/2.05  | (2)  ! [v0] :  ! [v1] : ( ~ (power_set(v0) = v1) |  ~ ilf_type(v0, set_type) | ilf_type(v1, set_type))
% 5.35/2.05  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cross_product(v1, v2) = v3) |  ~ ilf_type(v2, set_type) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v4] : (relation_type(v1, v2) = v4 &  ! [v5] : ( ~ subset(v0, v5) |  ~ ilf_type(v5, v4) | subset(v0, v3))))
% 5.35/2.05  | (4)  ! [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)))
% 5.35/2.05  | (5)  ! [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))
% 5.35/2.05  | (6)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (subset_type(v2) = v1) |  ~ (subset_type(v2) = v0))
% 5.35/2.05  | (7) ilf_type(all_0_4_4, set_type)
% 5.35/2.05  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | ilf_type(v2, set_type))
% 5.35/2.05  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_type(v3, v2) = v1) |  ~ (relation_type(v3, v2) = v0))
% 5.35/2.05  | (10) ilf_type(all_0_0_0, all_0_1_1)
% 5.35/2.05  | (11) relation_type(all_0_3_3, all_0_2_2) = all_0_1_1
% 5.35/2.05  | (12) ilf_type(all_0_3_3, set_type)
% 5.35/2.05  | (13)  ! [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)))
% 5.35/2.05  | (14)  ! [v0] : ( ~ empty(v0) |  ~ ilf_type(v0, set_type) | relation_like(v0))
% 5.35/2.05  | (15)  ! [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)))
% 5.35/2.05  | (16)  ! [v0] : ( ~ ilf_type(v0, set_type) | empty(v0) |  ? [v1] : (member(v1, v0) & ilf_type(v1, set_type)))
% 5.35/2.05  | (17)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (member_type(v2) = v1) |  ~ (member_type(v2) = v0))
% 5.35/2.05  | (18)  ! [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))))
% 5.35/2.05  | (19)  ! [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))
% 5.35/2.05  | (20)  ! [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)))
% 5.35/2.06  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0))
% 5.35/2.06  | (22)  ! [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))))
% 5.35/2.06  | (23)  ! [v0] :  ! [v1] : ( ~ (subset_type(v0) = v1) |  ~ ilf_type(v0, set_type) |  ? [v2] : ilf_type(v2, v1))
% 5.35/2.06  | (24)  ! [v0] :  ! [v1] : ( ~ (member_type(v0) = v1) |  ~ ilf_type(v0, set_type) | empty(v0) |  ? [v2] : ilf_type(v2, v1))
% 5.35/2.06  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_type(v1, v0) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v3] : ilf_type(v3, v2))
% 5.35/2.06  | (26)  ! [v0] : ( ~ ilf_type(v0, set_type) | subset(v0, v0))
% 5.35/2.06  | (27)  ! [v0] :  ! [v1] : ( ~ empty(v0) |  ~ member(v1, v0) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type))
% 5.35/2.06  | (28)  ! [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))
% 5.35/2.06  | (29)  ! [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))))
% 5.35/2.06  | (30)  ~ ilf_type(all_0_4_4, all_0_1_1)
% 5.35/2.06  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cross_product(v3, v2) = v1) |  ~ (cross_product(v3, v2) = v0))
% 5.35/2.06  | (32)  ! [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)))
% 5.35/2.06  | (33)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cross_product(v0, v1) = v2) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) | ilf_type(v2, set_type))
% 5.35/2.06  | (34)  ! [v0] :  ! [v1] : ( ~ (power_set(v0) = v1) |  ~ empty(v1) |  ~ ilf_type(v0, set_type))
% 5.35/2.06  | (35)  ? [v0] : ilf_type(v0, set_type)
% 5.35/2.06  | (36)  ! [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))))
% 5.35/2.06  | (37) subset(all_0_4_4, all_0_0_0)
% 5.35/2.06  | (38)  ! [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))))
% 5.35/2.07  | (39) ilf_type(all_0_2_2, set_type)
% 5.35/2.07  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_type(v1, v2) = v3) |  ~ ilf_type(v2, set_type) |  ~ ilf_type(v1, set_type) |  ~ ilf_type(v0, set_type) |  ? [v4] : (cross_product(v1, v2) = v4 &  ! [v5] : ( ~ subset(v0, v5) |  ~ ilf_type(v5, v3) | subset(v0, v4))))
% 5.35/2.07  | (41)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (power_set(v2) = v1) |  ~ (power_set(v2) = v0))
% 5.35/2.07  | (42)  ! [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))
% 5.35/2.07  | (43)  ! [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))))
% 5.35/2.07  |
% 5.35/2.07  | Instantiating (35) with all_3_0_5 yields:
% 5.35/2.07  | (44) ilf_type(all_3_0_5, set_type)
% 5.35/2.07  |
% 5.35/2.07  | Instantiating formula (40) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms relation_type(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:
% 5.35/2.07  | (45)  ? [v0] : (cross_product(all_0_3_3, all_0_2_2) = v0 &  ! [v1] : ( ~ subset(all_0_3_3, v1) |  ~ ilf_type(v1, all_0_1_1) | subset(all_0_3_3, v0)))
% 5.35/2.07  |
% 5.35/2.07  | Instantiating formula (40) with all_0_1_1, all_0_2_2, all_0_3_3, all_3_0_5 and discharging atoms relation_type(all_0_3_3, all_0_2_2) = all_0_1_1, ilf_type(all_3_0_5, set_type), ilf_type(all_0_2_2, set_type), ilf_type(all_0_3_3, set_type), yields:
% 5.35/2.07  | (46)  ? [v0] : (cross_product(all_0_3_3, all_0_2_2) = v0 &  ! [v1] : ( ~ subset(all_3_0_5, v1) |  ~ ilf_type(v1, all_0_1_1) | subset(all_3_0_5, v0)))
% 5.35/2.07  |
% 5.35/2.07  | Instantiating formula (40) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_2_2 and discharging atoms relation_type(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:
% 5.35/2.07  | (47)  ? [v0] : (cross_product(all_0_3_3, all_0_2_2) = v0 &  ! [v1] : ( ~ subset(all_0_2_2, v1) |  ~ ilf_type(v1, all_0_1_1) | subset(all_0_2_2, v0)))
% 5.35/2.07  |
% 5.35/2.07  | Instantiating formula (38) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms relation_type(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:
% 5.35/2.07  | (48)  ? [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_1_1)) &  ! [v2] : ( ~ ilf_type(v2, all_0_1_1) | ilf_type(v2, v1)))
% 5.35/2.07  |
% 5.35/2.07  | Instantiating formula (15) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms relation_type(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), ilf_type(all_0_4_4, set_type),  ~ ilf_type(all_0_4_4, all_0_1_1), yields:
% 5.35/2.07  | (49)  ? [v0] : (cross_product(all_0_3_3, all_0_2_2) = v0 &  ~ subset(all_0_4_4, v0))
% 5.35/2.08  |
% 5.35/2.08  | Instantiating formula (40) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms relation_type(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), ilf_type(all_0_4_4, set_type), yields:
% 5.35/2.08  | (50)  ? [v0] : (cross_product(all_0_3_3, all_0_2_2) = v0 &  ! [v1] : ( ~ subset(all_0_4_4, v1) |  ~ ilf_type(v1, all_0_1_1) | subset(all_0_4_4, v0)))
% 5.35/2.08  |
% 5.35/2.08  | Instantiating (50) with all_11_0_6 yields:
% 5.35/2.08  | (51) cross_product(all_0_3_3, all_0_2_2) = all_11_0_6 &  ! [v0] : ( ~ subset(all_0_4_4, v0) |  ~ ilf_type(v0, all_0_1_1) | subset(all_0_4_4, all_11_0_6))
% 5.35/2.08  |
% 5.35/2.08  | Applying alpha-rule on (51) yields:
% 5.35/2.08  | (52) cross_product(all_0_3_3, all_0_2_2) = all_11_0_6
% 5.35/2.08  | (53)  ! [v0] : ( ~ subset(all_0_4_4, v0) |  ~ ilf_type(v0, all_0_1_1) | subset(all_0_4_4, all_11_0_6))
% 5.35/2.08  |
% 5.35/2.08  | Instantiating formula (53) with all_0_0_0 and discharging atoms subset(all_0_4_4, all_0_0_0), ilf_type(all_0_0_0, all_0_1_1), yields:
% 5.35/2.08  | (54) subset(all_0_4_4, all_11_0_6)
% 5.35/2.08  |
% 5.35/2.08  | Instantiating (49) with all_15_0_7 yields:
% 5.35/2.08  | (55) cross_product(all_0_3_3, all_0_2_2) = all_15_0_7 &  ~ subset(all_0_4_4, all_15_0_7)
% 5.35/2.08  |
% 5.35/2.08  | Applying alpha-rule on (55) yields:
% 5.35/2.08  | (56) cross_product(all_0_3_3, all_0_2_2) = all_15_0_7
% 5.35/2.08  | (57)  ~ subset(all_0_4_4, all_15_0_7)
% 5.35/2.08  |
% 5.35/2.08  | Instantiating (48) with all_17_0_8, all_17_1_9 yields:
% 5.35/2.08  | (58) subset_type(all_17_1_9) = all_17_0_8 & cross_product(all_0_3_3, all_0_2_2) = all_17_1_9 &  ! [v0] : ( ~ ilf_type(v0, all_17_0_8) | ilf_type(v0, all_0_1_1)) &  ! [v0] : ( ~ ilf_type(v0, all_0_1_1) | ilf_type(v0, all_17_0_8))
% 5.35/2.08  |
% 5.35/2.08  | Applying alpha-rule on (58) yields:
% 5.35/2.08  | (59) subset_type(all_17_1_9) = all_17_0_8
% 5.35/2.08  | (60) cross_product(all_0_3_3, all_0_2_2) = all_17_1_9
% 5.35/2.08  | (61)  ! [v0] : ( ~ ilf_type(v0, all_17_0_8) | ilf_type(v0, all_0_1_1))
% 5.35/2.08  | (62)  ! [v0] : ( ~ ilf_type(v0, all_0_1_1) | ilf_type(v0, all_17_0_8))
% 5.35/2.08  |
% 5.35/2.08  | Instantiating (47) with all_21_0_10 yields:
% 5.35/2.08  | (63) cross_product(all_0_3_3, all_0_2_2) = all_21_0_10 &  ! [v0] : ( ~ subset(all_0_2_2, v0) |  ~ ilf_type(v0, all_0_1_1) | subset(all_0_2_2, all_21_0_10))
% 5.79/2.08  |
% 5.79/2.08  | Applying alpha-rule on (63) yields:
% 5.79/2.08  | (64) cross_product(all_0_3_3, all_0_2_2) = all_21_0_10
% 5.79/2.08  | (65)  ! [v0] : ( ~ subset(all_0_2_2, v0) |  ~ ilf_type(v0, all_0_1_1) | subset(all_0_2_2, all_21_0_10))
% 5.79/2.08  |
% 5.79/2.08  | Instantiating (46) with all_26_0_12 yields:
% 5.79/2.08  | (66) cross_product(all_0_3_3, all_0_2_2) = all_26_0_12 &  ! [v0] : ( ~ subset(all_3_0_5, v0) |  ~ ilf_type(v0, all_0_1_1) | subset(all_3_0_5, all_26_0_12))
% 5.79/2.08  |
% 5.79/2.08  | Applying alpha-rule on (66) yields:
% 5.79/2.08  | (67) cross_product(all_0_3_3, all_0_2_2) = all_26_0_12
% 5.79/2.08  | (68)  ! [v0] : ( ~ subset(all_3_0_5, v0) |  ~ ilf_type(v0, all_0_1_1) | subset(all_3_0_5, all_26_0_12))
% 5.79/2.08  |
% 5.79/2.08  | Instantiating (45) with all_29_0_13 yields:
% 5.79/2.08  | (69) cross_product(all_0_3_3, all_0_2_2) = all_29_0_13 &  ! [v0] : ( ~ subset(all_0_3_3, v0) |  ~ ilf_type(v0, all_0_1_1) | subset(all_0_3_3, all_29_0_13))
% 5.79/2.08  |
% 5.79/2.08  | Applying alpha-rule on (69) yields:
% 5.79/2.08  | (70) cross_product(all_0_3_3, all_0_2_2) = all_29_0_13
% 5.79/2.08  | (71)  ! [v0] : ( ~ subset(all_0_3_3, v0) |  ~ ilf_type(v0, all_0_1_1) | subset(all_0_3_3, all_29_0_13))
% 5.79/2.08  |
% 5.79/2.08  | Instantiating formula (31) with all_0_3_3, all_0_2_2, all_26_0_12, all_29_0_13 and discharging atoms cross_product(all_0_3_3, all_0_2_2) = all_29_0_13, cross_product(all_0_3_3, all_0_2_2) = all_26_0_12, yields:
% 5.79/2.08  | (72) all_29_0_13 = all_26_0_12
% 5.79/2.09  |
% 5.79/2.09  | Instantiating formula (31) with all_0_3_3, all_0_2_2, all_21_0_10, all_26_0_12 and discharging atoms cross_product(all_0_3_3, all_0_2_2) = all_26_0_12, cross_product(all_0_3_3, all_0_2_2) = all_21_0_10, yields:
% 5.79/2.09  | (73) all_26_0_12 = all_21_0_10
% 5.79/2.09  |
% 5.79/2.09  | Instantiating formula (31) with all_0_3_3, all_0_2_2, all_17_1_9, all_26_0_12 and discharging atoms cross_product(all_0_3_3, all_0_2_2) = all_26_0_12, cross_product(all_0_3_3, all_0_2_2) = all_17_1_9, yields:
% 5.79/2.09  | (74) all_26_0_12 = all_17_1_9
% 5.79/2.09  |
% 5.79/2.09  | Instantiating formula (31) with all_0_3_3, all_0_2_2, all_15_0_7, all_29_0_13 and discharging atoms cross_product(all_0_3_3, all_0_2_2) = all_29_0_13, cross_product(all_0_3_3, all_0_2_2) = all_15_0_7, yields:
% 5.79/2.09  | (75) all_29_0_13 = all_15_0_7
% 5.79/2.09  |
% 5.79/2.09  | Instantiating formula (31) with all_0_3_3, all_0_2_2, all_11_0_6, all_26_0_12 and discharging atoms cross_product(all_0_3_3, all_0_2_2) = all_26_0_12, cross_product(all_0_3_3, all_0_2_2) = all_11_0_6, yields:
% 5.79/2.09  | (76) all_26_0_12 = all_11_0_6
% 5.79/2.09  |
% 5.79/2.09  | Combining equations (72,75) yields a new equation:
% 5.79/2.09  | (77) all_26_0_12 = all_15_0_7
% 5.79/2.09  |
% 5.79/2.09  | Simplifying 77 yields:
% 5.79/2.09  | (78) all_26_0_12 = all_15_0_7
% 5.79/2.09  |
% 5.79/2.09  | Combining equations (76,73) yields a new equation:
% 5.79/2.09  | (79) all_21_0_10 = all_11_0_6
% 5.79/2.09  |
% 5.79/2.09  | Combining equations (74,73) yields a new equation:
% 5.79/2.09  | (80) all_21_0_10 = all_17_1_9
% 5.79/2.09  |
% 5.79/2.09  | Combining equations (78,73) yields a new equation:
% 5.79/2.09  | (81) all_21_0_10 = all_15_0_7
% 5.79/2.09  |
% 5.79/2.09  | Combining equations (79,80) yields a new equation:
% 5.79/2.09  | (82) all_17_1_9 = all_11_0_6
% 5.79/2.09  |
% 5.79/2.09  | Combining equations (81,80) yields a new equation:
% 5.79/2.09  | (83) all_17_1_9 = all_15_0_7
% 5.79/2.09  |
% 5.79/2.09  | Combining equations (82,83) yields a new equation:
% 5.79/2.09  | (84) all_15_0_7 = all_11_0_6
% 5.79/2.09  |
% 5.79/2.09  | From (84) and (57) follows:
% 5.79/2.09  | (85)  ~ subset(all_0_4_4, all_11_0_6)
% 5.79/2.09  |
% 5.79/2.09  | Using (54) and (85) yields:
% 5.79/2.09  | (86) $false
% 5.79/2.09  |
% 5.79/2.09  |-The branch is then unsatisfiable
% 5.79/2.09  % SZS output end Proof for theBenchmark
% 5.79/2.09  
% 5.79/2.09  1558ms
%------------------------------------------------------------------------------