%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU388+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n007.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 08:49:25 EDT 2022

% Result   : Theorem 7.49s 2.29s
% Output   : Proof 11.86s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU388+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 20 10:27:00 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.61/0.60          ____       _                          
% 0.61/0.60    ___  / __ \_____(_)___  ________  __________
% 0.61/0.60   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.61/0.60  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.61/0.60  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.61/0.60  
% 0.61/0.60  A Theorem Prover for First-Order Logic
% 0.61/0.61  (ePrincess v.1.0)
% 0.61/0.61  
% 0.61/0.61  (c) Philipp Rümmer, 2009-2015
% 0.61/0.61  (c) Peter Backeman, 2014-2015
% 0.61/0.61  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.61  Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.61  Bug reports to peter@backeman.se
% 0.61/0.61  
% 0.61/0.61  For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.61  
% 0.61/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.68  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.36/1.09  Prover 0: Preprocessing ...
% 4.42/1.55  Prover 0: Warning: ignoring some quantifiers
% 4.42/1.59  Prover 0: Constructing countermodel ...
% 7.49/2.28  Prover 0: proved (1607ms)
% 7.49/2.29  
% 7.49/2.29  No countermodel exists, formula is valid
% 7.49/2.29  % SZS status Theorem for theBenchmark
% 7.49/2.29  
% 7.49/2.29  Generating proof ... Warning: ignoring some quantifiers
% 11.00/3.10  found it (size 40)
% 11.00/3.10  
% 11.00/3.10  % SZS output start Proof for theBenchmark
% 11.00/3.10  Assumed formulas after preprocessing and simplification: 
% 11.40/3.10  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] : (neighborhood_system(v0, v2) = v3 & the_carrier(v0) = v1 & directed_relstr(v5) & boolean_relstr(v12) & complemented_relstr(v12) & heyting_relstr(v12) & distributive_relstr(v12) & relation_empty_yielding(v7) & relation_empty_yielding(empty_set) & one_sorted_str(v18) & one_sorted_str(v6) & connected_relstr(v17) & trivial_carrier(v11) & top_str(v19) & top_str(v0) & topological_space(v0) & element(v2, v1) & relation(v13) & relation(v9) & relation(v7) & relation(empty_set) & finite(v15) & empty(v13) & empty(empty_set) & bounded_relstr(v16) & bounded_relstr(v12) & bounded_relstr(v8) & upper_bounded_relstr(v16) & upper_bounded_relstr(v12) & upper_bounded_relstr(v8) & with_infima_relstr(v16) & with_infima_relstr(v12) & with_infima_relstr(v11) & with_infima_relstr(v10) & with_infima_relstr(v8) & with_suprema_relstr(v16) & with_suprema_relstr(v12) & with_suprema_relstr(v11) & with_suprema_relstr(v10) & with_suprema_relstr(v8) & antisymmetric_relstr(v17) & antisymmetric_relstr(v16) & antisymmetric_relstr(v14) & antisymmetric_relstr(v12) & antisymmetric_relstr(v11) & antisymmetric_relstr(v10) & antisymmetric_relstr(v8) & transitive_relstr(v17) & transitive_relstr(v16) & transitive_relstr(v14) & transitive_relstr(v12) & transitive_relstr(v11) & transitive_relstr(v10) & transitive_relstr(v8) & transitive_relstr(v5) & lower_bounded_relstr(v16) & lower_bounded_relstr(v12) & lower_bounded_relstr(v8) & join_complete_relstr(v16) & up_complete_relstr(v16) & complete_relstr(v16) & complete_relstr(v14) & complete_relstr(v11) & complete_relstr(v10) & complete_relstr(v8) & reflexive_relstr(v17) & reflexive_relstr(v16) & reflexive_relstr(v14) & reflexive_relstr(v12) & reflexive_relstr(v11) & reflexive_relstr(v10) & reflexive_relstr(v8) & strict_rel_str(v16) & strict_rel_str(v14) & strict_rel_str(v12) & strict_rel_str(v11) & strict_rel_str(v10) & strict_rel_str(v5) & rel_str(v20) & rel_str(v17) & rel_str(v16) & rel_str(v14) & rel_str(v12) & rel_str(v11) & rel_str(v10) & rel_str(v8) & rel_str(v5) &  ~ v1_yellow_3(v12) &  ~ trivial_carrier(v12) &  ~ empty(v15) &  ~ empty(v9) &  ~ empty_carrier(v17) &  ~ empty_carrier(v16) &  ~ empty_carrier(v14) &  ~ empty_carrier(v12) &  ~ empty_carrier(v11) &  ~ empty_carrier(v10) &  ~ empty_carrier(v8) &  ~ empty_carrier(v6) &  ~ empty_carrier(v5) &  ~ empty_carrier(v0) &  ! [v21] :  ! [v22] :  ! [v23] :  ! [v24] :  ! [v25] : (v25 = v22 |  ~ (rel_str_of(v24, v25) = v23) |  ~ (rel_str_of(v21, v22) = v23) |  ~ relation_of2(v22, v21, v21)) &  ! [v21] :  ! [v22] :  ! [v23] :  ! [v24] :  ! [v25] : (v24 = v21 |  ~ (rel_str_of(v24, v25) = v23) |  ~ (rel_str_of(v21, v22) = v23) |  ~ relation_of2(v22, v21, v21)) &  ! [v21] :  ! [v22] :  ! [v23] :  ! [v24] : (v24 = v21 |  ~ (the_carrier(v21) = v22) |  ~ (the_InternalRel(v21) = v23) |  ~ (rel_str_of(v22, v23) = v24) |  ~ strict_rel_str(v21) |  ~ rel_str(v21)) &  ! [v21] :  ! [v22] :  ! [v23] :  ! [v24] : (v22 = v21 |  ~ (neighborhood_system(v24, v23) = v22) |  ~ (neighborhood_system(v24, v23) = v21)) &  ! [v21] :  ! [v22] :  ! [v23] :  ! [v24] : (v22 = v21 |  ~ (a_2_0_yellow19(v24, v23) = v22) |  ~ (a_2_0_yellow19(v24, v23) = v21)) &  ! [v21] :  ! [v22] :  ! [v23] :  ! [v24] : (v22 = v21 |  ~ (cartesian_product2(v24, v23) = v22) |  ~ (cartesian_product2(v24, v23) = v21)) &  ! [v21] :  ! [v22] :  ! [v23] :  ! [v24] : (v22 = v21 |  ~ (rel_str_of(v24, v23) = v22) |  ~ (rel_str_of(v24, v23) = v21)) &  ! [v21] :  ! [v22] :  ! [v23] :  ! [v24] : ( ~ (neighborhood_system(v21, v23) = v24) |  ~ (the_carrier(v21) = v22) |  ~ top_str(v21) |  ~ topological_space(v21) |  ~ element(v23, v22) | a_2_0_yellow19(v21, v23) = v24 | empty_carrier(v21)) &  ! [v21] :  ! [v22] :  ! [v23] :  ! [v24] : ( ~ (a_2_0_yellow19(v22, v23) = v24) |  ~ point_neighbourhood(v21, v22, v23) |  ~ top_str(v22) |  ~ topological_space(v22) | empty_carrier(v22) | in(v21, v24) |  ? [v25] : (the_carrier(v22) = v25 &  ~ element(v23, v25))) &  ! [v21] :  ! [v22] :  ! [v23] :  ! [v24] : ( ~ (a_2_0_yellow19(v22, v23) = v24) |  ~ top_str(v22) |  ~ topological_space(v22) |  ~ in(v21, v24) | empty_carrier(v22) |  ? [v25] : ((v25 = v21 & point_neighbourhood(v21, v22, v23)) | (the_carrier(v22) = v25 &  ~ element(v23, v25)))) &  ! [v21] :  ! [v22] :  ! [v23] :  ! [v24] : ( ~ (a_2_0_yellow19(v21, v23) = v24) |  ~ (the_carrier(v21) = v22) |  ~ top_str(v21) |  ~ topological_space(v21) |  ~ element(v23, v22) | neighborhood_system(v21, v23) = v24 | empty_carrier(v21)) &  ! [v21] :  ! [v22] :  ! [v23] :  ! [v24] : ( ~ (cartesian_product2(v21, v22) = v24) |  ~ relation_of2_as_subset(v23, v21, v22) |  ? [v25] : (powerset(v24) = v25 & element(v23, v25))) &  ! [v21] :  ! [v22] :  ! [v23] :  ! [v24] : ( ~ (powerset(v23) = v24) |  ~ element(v22, v24) |  ~ empty(v23) |  ~ in(v21, v22)) &  ! [v21] :  ! [v22] :  ! [v23] :  ! [v24] : ( ~ (powerset(v23) = v24) |  ~ element(v22, v24) |  ~ in(v21, v22) | element(v21, v23)) &  ? [v21] :  ! [v22] :  ! [v23] :  ! [v24] : ( ~ (cartesian_product2(v22, v23) = v24) | relation(v21) |  ? [v25] : (powerset(v24) = v25 &  ~ element(v21, v25))) &  ! [v21] :  ! [v22] :  ! [v23] : (v22 = v21 |  ~ (cast_as_carrier_subset(v23) = v22) |  ~ (cast_as_carrier_subset(v23) = v21)) &  ! [v21] :  ! [v22] :  ! [v23] : (v22 = v21 |  ~ (boole_POSet(v23) = v22) |  ~ (boole_POSet(v23) = v21)) &  ! [v21] :  ! [v22] :  ! [v23] : (v22 = v21 |  ~ (powerset(v23) = v22) |  ~ (powerset(v23) = v21)) &  ! [v21] :  ! [v22] :  ! [v23] : (v22 = v21 |  ~ (the_carrier(v23) = v22) |  ~ (the_carrier(v23) = v21)) &  ! [v21] :  ! [v22] :  ! [v23] : (v22 = v21 |  ~ (the_InternalRel(v23) = v22) |  ~ (the_InternalRel(v23) = v21)) &  ! [v21] :  ! [v22] :  ! [v23] : ( ~ (neighborhood_system(v21, v22) = v23) |  ~ top_str(v21) |  ~ topological_space(v21) | empty_carrier(v21) |  ? [v24] :  ? [v25] :  ? [v26] :  ? [v27] :  ? [v28] : (cast_as_carrier_subset(v21) = v25 & boole_POSet(v25) = v26 & powerset(v27) = v28 & the_carrier(v26) = v27 & the_carrier(v21) = v24 & ( ~ element(v22, v24) | element(v23, v28)))) &  ! [v21] :  ! [v22] :  ! [v23] : ( ~ (cartesian_product2(v21, v22) = v23) |  ~ finite(v22) |  ~ finite(v21) | finite(v23)) &  ! [v21] :  ! [v22] :  ! [v23] : ( ~ (cartesian_product2(v21, v22) = v23) |  ~ empty(v23) | empty(v22) | empty(v21)) &  ! [v21] :  ! [v22] :  ! [v23] : ( ~ (powerset(v22) = v23) |  ~ subset(v21, v22) | element(v21, v23)) &  ! [v21] :  ! [v22] :  ! [v23] : ( ~ (powerset(v22) = v23) |  ~ element(v21, v23) | subset(v21, v22)) &  ! [v21] :  ! [v22] :  ! [v23] : ( ~ (powerset(v21) = v22) |  ~ element(v23, v22) |  ~ finite(v21) | finite(v23)) &  ! [v21] :  ! [v22] :  ! [v23] : ( ~ (the_carrier(v21) = v23) |  ~ top_str(v21) |  ~ topological_space(v21) |  ~ element(v22, v23) | empty_carrier(v21) |  ? [v24] : (powerset(v23) = v24 &  ! [v25] : ( ~ point_neighbourhood(v25, v21, v22) | element(v25, v24)))) &  ! [v21] :  ! [v22] :  ! [v23] : ( ~ (the_carrier(v21) = v23) |  ~ top_str(v21) |  ~ topological_space(v21) |  ~ element(v22, v23) | empty_carrier(v21) |  ? [v24] : point_neighbourhood(v24, v21, v22)) &  ! [v21] :  ! [v22] :  ! [v23] : ( ~ (rel_str_of(v21, v22) = v23) |  ~ relation_of2(v22, v21, v21) | strict_rel_str(v23)) &  ! [v21] :  ! [v22] :  ! [v23] : ( ~ (rel_str_of(v21, v22) = v23) |  ~ relation_of2(v22, v21, v21) | rel_str(v23)) &  ! [v21] :  ! [v22] :  ! [v23] : ( ~ relation_of2_as_subset(v23, v21, v22) | relation_of2(v23, v21, v22)) &  ! [v21] :  ! [v22] :  ! [v23] : ( ~ relation_of2(v23, v21, v22) | relation_of2_as_subset(v23, v21, v22)) &  ! [v21] :  ! [v22] : (v22 = v21 |  ~ empty(v22) |  ~ empty(v21)) &  ! [v21] :  ! [v22] : ( ~ (cast_as_carrier_subset(v21) = v22) |  ~ one_sorted_str(v21) |  ~ empty(v22) | empty_carrier(v21)) &  ! [v21] :  ! [v22] : ( ~ (cast_as_carrier_subset(v21) = v22) |  ~ one_sorted_str(v21) |  ? [v23] :  ? [v24] : (powerset(v23) = v24 & the_carrier(v21) = v23 & element(v22, v24))) &  ! [v21] :  ! [v22] : ( ~ (cast_as_carrier_subset(v21) = v22) |  ~ top_str(v21) |  ~ topological_space(v21) | closed_subset(v22, v21)) &  ! [v21] :  ! [v22] : ( ~ (cast_as_carrier_subset(v21) = v22) |  ~ top_str(v21) |  ~ topological_space(v21) | open_subset(v22, v21)) &  ! [v21] :  ! [v22] : ( ~ (cast_as_carrier_subset(v21) = v22) |  ~ top_str(v21) | dense(v22, v21)) &  ! [v21] :  ! [v22] : ( ~ (cast_as_carrier_subset(v21) = v22) |  ~ empty(v22) |  ~ upper_bounded_relstr(v21) |  ~ rel_str(v21) | empty_carrier(v21)) &  ! [v21] :  ! [v22] : ( ~ (cast_as_carrier_subset(v21) = v22) |  ~ empty(v22) |  ~ with_infima_relstr(v21) |  ~ rel_str(v21)) &  ! [v21] :  ! [v22] : ( ~ (cast_as_carrier_subset(v21) = v22) |  ~ empty(v22) |  ~ with_suprema_relstr(v21) |  ~ rel_str(v21)) &  ! [v21] :  ! [v22] : ( ~ (cast_as_carrier_subset(v21) = v22) |  ~ empty(v22) |  ~ lower_bounded_relstr(v21) |  ~ rel_str(v21) | empty_carrier(v21)) &  ! [v21] :  ! [v22] : ( ~ (cast_as_carrier_subset(v21) = v22) |  ~ empty(v22) |  ~ rel_str(v21) | empty_carrier(v21)) &  ! [v21] :  ! [v22] : ( ~ (cast_as_carrier_subset(v21) = v22) |  ~ upper_bounded_relstr(v21) |  ~ rel_str(v21) | directed_subset(v22, v21) | empty_carrier(v21)) &  ! [v21] :  ! [v22] : ( ~ (cast_as_carrier_subset(v21) = v22) |  ~ with_infima_relstr(v21) |  ~ rel_str(v21) | filtered_subset(v22, v21)) &  ! [v21] :  ! [v22] : ( ~ (cast_as_carrier_subset(v21) = v22) |  ~ with_suprema_relstr(v21) |  ~ rel_str(v21) | directed_subset(v22, v21)) &  ! [v21] :  ! [v22] : ( ~ (cast_as_carrier_subset(v21) = v22) |  ~ lower_bounded_relstr(v21) |  ~ rel_str(v21) | filtered_subset(v22, v21) | empty_carrier(v21)) &  ! [v21] :  ! [v22] : ( ~ (cast_as_carrier_subset(v21) = v22) |  ~ rel_str(v21) | upper_relstr_subset(v22, v21) | empty_carrier(v21)) &  ! [v21] :  ! [v22] : ( ~ (cast_as_carrier_subset(v21) = v22) |  ~ rel_str(v21) | lower_relstr_subset(v22, v21) | empty_carrier(v21)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) |  ~ v1_yellow_3(v22) | empty(v21)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) |  ~ v1_yellow_3(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) |  ~ trivial_carrier(v22) | empty(v21)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) |  ~ empty_carrier(v22) | empty(v21)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) |  ~ empty_carrier(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | directed_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | boolean_relstr(v22) | empty(v21)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | boolean_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | complemented_relstr(v22) | empty(v21)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | complemented_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | heyting_relstr(v22) | empty(v21)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | heyting_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | distributive_relstr(v22) | empty(v21)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | distributive_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | empty(v21) | bounded_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | empty(v21) | upper_bounded_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | empty(v21) | with_infima_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | empty(v21) | with_suprema_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | empty(v21) | antisymmetric_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | empty(v21) | transitive_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | empty(v21) | lower_bounded_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | empty(v21) | join_complete_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | empty(v21) | up_complete_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | empty(v21) | complete_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | empty(v21) | reflexive_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | empty(v21) | strict_rel_str(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | bounded_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | upper_bounded_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | with_infima_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | with_suprema_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | antisymmetric_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | transitive_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | lower_bounded_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | join_complete_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | up_complete_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | complete_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | reflexive_relstr(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | strict_rel_str(v22)) &  ! [v21] :  ! [v22] : ( ~ (boole_POSet(v21) = v22) | rel_str(v22)) &  ! [v21] :  ! [v22] : ( ~ (powerset(v21) = v22) |  ~ empty(v22)) &  ! [v21] :  ! [v22] : ( ~ (powerset(v21) = v22) | empty(v21) |  ? [v23] : (element(v23, v22) & finite(v23) &  ~ empty(v23))) &  ! [v21] :  ! [v22] : ( ~ (powerset(v21) = v22) | empty(v21) |  ? [v23] : (element(v23, v22) &  ~ empty(v23))) &  ! [v21] :  ! [v22] : ( ~ (powerset(v21) = v22) |  ? [v23] :  ? [v24] : (powerset(v22) = v23 & element(v24, v23) & finite(v24) &  ~ empty(v24))) &  ! [v21] :  ! [v22] : ( ~ (powerset(v21) = v22) |  ? [v23] : (element(v23, v22) & empty(v23))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ one_sorted_str(v21) |  ~ empty(v22) | empty_carrier(v21)) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ one_sorted_str(v21) | empty_carrier(v21) |  ? [v23] :  ? [v24] : (powerset(v22) = v23 & element(v24, v23) &  ~ empty(v24))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ one_sorted_str(v21) |  ? [v23] :  ? [v24] :  ? [v25] : (powerset(v23) = v24 & powerset(v22) = v23 & element(v25, v24) & finite(v25) &  ~ empty(v25))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ one_sorted_str(v21) |  ? [v23] :  ? [v24] : (cast_as_carrier_subset(v21) = v23 & powerset(v22) = v24 & element(v23, v24))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ top_str(v21) |  ~ topological_space(v21) | empty_carrier(v21) |  ? [v23] :  ? [v24] : (powerset(v22) = v23 & closed_subset(v24, v21) & open_subset(v24, v21) & element(v24, v23) &  ~ empty(v24))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ top_str(v21) |  ~ topological_space(v21) | empty_carrier(v21) |  ? [v23] :  ? [v24] : (powerset(v22) = v23 & closed_subset(v24, v21) & element(v24, v23) &  ~ empty(v24))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ top_str(v21) |  ~ topological_space(v21) |  ? [v23] :  ? [v24] : (powerset(v22) = v23 & v5_membered(v24) & v4_membered(v24) & v3_membered(v24) & v2_membered(v24) & v1_membered(v24) & nowhere_dense(v24, v21) & boundary_set(v24, v21) & closed_subset(v24, v21) & open_subset(v24, v21) & element(v24, v23) & empty(v24))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ top_str(v21) |  ~ topological_space(v21) |  ? [v23] :  ? [v24] : (powerset(v22) = v23 & closed_subset(v24, v21) & open_subset(v24, v21) & element(v24, v23))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ top_str(v21) |  ~ topological_space(v21) |  ? [v23] :  ? [v24] : (powerset(v22) = v23 & closed_subset(v24, v21) & element(v24, v23))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ top_str(v21) |  ~ topological_space(v21) |  ? [v23] :  ? [v24] : (powerset(v22) = v23 & open_subset(v24, v21) & element(v24, v23))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ top_str(v21) |  ~ topological_space(v21) |  ? [v23] : (powerset(v22) = v23 &  ! [v24] : ( ~ nowhere_dense(v24, v21) |  ~ open_subset(v24, v21) |  ~ element(v24, v23) | v5_membered(v24)) &  ! [v24] : ( ~ nowhere_dense(v24, v21) |  ~ open_subset(v24, v21) |  ~ element(v24, v23) | v4_membered(v24)) &  ! [v24] : ( ~ nowhere_dense(v24, v21) |  ~ open_subset(v24, v21) |  ~ element(v24, v23) | v3_membered(v24)) &  ! [v24] : ( ~ nowhere_dense(v24, v21) |  ~ open_subset(v24, v21) |  ~ element(v24, v23) | v2_membered(v24)) &  ! [v24] : ( ~ nowhere_dense(v24, v21) |  ~ open_subset(v24, v21) |  ~ element(v24, v23) | v1_membered(v24)) &  ! [v24] : ( ~ nowhere_dense(v24, v21) |  ~ open_subset(v24, v21) |  ~ element(v24, v23) | boundary_set(v24, v21)) &  ! [v24] : ( ~ nowhere_dense(v24, v21) |  ~ open_subset(v24, v21) |  ~ element(v24, v23) | closed_subset(v24, v21)) &  ! [v24] : ( ~ nowhere_dense(v24, v21) |  ~ open_subset(v24, v21) |  ~ element(v24, v23) | empty(v24)))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ top_str(v21) |  ~ topological_space(v21) |  ? [v23] : (powerset(v22) = v23 &  ! [v24] : ( ~ nowhere_dense(v24, v21) |  ~ element(v24, v23) | boundary_set(v24, v21)))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ top_str(v21) |  ~ topological_space(v21) |  ? [v23] : (powerset(v22) = v23 &  ! [v24] : ( ~ boundary_set(v24, v21) |  ~ closed_subset(v24, v21) |  ~ element(v24, v23) | nowhere_dense(v24, v21)))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ top_str(v21) |  ~ topological_space(v21) |  ? [v23] : (powerset(v22) = v23 &  ! [v24] : ( ~ element(v24, v23) |  ~ empty(v24) | nowhere_dense(v24, v21)))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ top_str(v21) |  ~ topological_space(v21) |  ? [v23] : (powerset(v22) = v23 &  ! [v24] : ( ~ element(v24, v23) |  ~ empty(v24) | closed_subset(v24, v21)) &  ! [v24] : ( ~ element(v24, v23) |  ~ empty(v24) | open_subset(v24, v21)))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ top_str(v21) |  ? [v23] :  ? [v24] : (powerset(v22) = v23 & v5_membered(v24) & v4_membered(v24) & v3_membered(v24) & v2_membered(v24) & v1_membered(v24) & boundary_set(v24, v21) & element(v24, v23) & empty(v24))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ top_str(v21) |  ? [v23] : (powerset(v22) = v23 &  ! [v24] : ( ~ element(v24, v23) |  ~ empty(v24) | boundary_set(v24, v21)))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ with_infima_relstr(v21) |  ~ with_suprema_relstr(v21) |  ~ antisymmetric_relstr(v21) |  ~ transitive_relstr(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) |  ? [v23] :  ? [v24] : (powerset(v22) = v23 & filtered_subset(v24, v21) & directed_subset(v24, v21) & upper_relstr_subset(v24, v21) & lower_relstr_subset(v24, v21) & element(v24, v23) &  ~ empty(v24))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ transitive_relstr(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | empty_carrier(v21) |  ? [v23] :  ? [v24] : (powerset(v22) = v23 & filtered_subset(v24, v21) & upper_relstr_subset(v24, v21) & element(v24, v23) &  ~ empty(v24))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ transitive_relstr(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | empty_carrier(v21) |  ? [v23] :  ? [v24] : (powerset(v22) = v23 & directed_subset(v24, v21) & lower_relstr_subset(v24, v21) & element(v24, v23) &  ~ empty(v24))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | empty_carrier(v21) |  ? [v23] :  ? [v24] : (powerset(v22) = v23 & filtered_subset(v24, v21) & directed_subset(v24, v21) & element(v24, v23) & finite(v24) &  ~ empty(v24))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ rel_str(v21) | empty_carrier(v21) |  ? [v23] :  ? [v24] : (powerset(v22) = v23 & upper_relstr_subset(v24, v21) & lower_relstr_subset(v24, v21) & element(v24, v23) &  ~ empty(v24))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ rel_str(v21) |  ? [v23] :  ? [v24] : (powerset(v22) = v23 & filtered_subset(v24, v21) & directed_subset(v24, v21) & element(v24, v23))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ rel_str(v21) |  ? [v23] :  ? [v24] : (powerset(v22) = v23 & upper_relstr_subset(v24, v21) & lower_relstr_subset(v24, v21) & element(v24, v23))) &  ! [v21] :  ! [v22] : ( ~ (the_carrier(v21) = v22) |  ~ rel_str(v21) |  ? [v23] : (the_InternalRel(v21) = v23 & relation_of2_as_subset(v23, v22, v22))) &  ! [v21] :  ! [v22] : ( ~ (the_InternalRel(v21) = v22) |  ~ rel_str(v21) |  ? [v23] : (the_carrier(v21) = v23 & relation_of2_as_subset(v22, v23, v23))) &  ! [v21] :  ! [v22] : ( ~ element(v21, v22) | empty(v22) | in(v21, v22)) &  ! [v21] :  ! [v22] : ( ~ empty(v22) |  ~ in(v21, v22)) &  ! [v21] :  ! [v22] : ( ~ in(v22, v21) |  ~ in(v21, v22)) &  ! [v21] :  ! [v22] : ( ~ in(v21, v22) | element(v21, v22)) &  ! [v21] : (v21 = empty_set |  ~ empty(v21)) &  ! [v21] : ( ~ trivial_carrier(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | connected_relstr(v21) | empty_carrier(v21)) &  ! [v21] : ( ~ trivial_carrier(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | antisymmetric_relstr(v21) | empty_carrier(v21)) &  ! [v21] : ( ~ trivial_carrier(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | transitive_relstr(v21) | empty_carrier(v21)) &  ! [v21] : ( ~ trivial_carrier(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | complete_relstr(v21) | empty_carrier(v21)) &  ! [v21] : ( ~ top_str(v21) | one_sorted_str(v21)) &  ! [v21] : ( ~ empty(v21) | relation(v21)) &  ! [v21] : ( ~ empty(v21) | finite(v21)) &  ! [v21] : ( ~ bounded_relstr(v21) |  ~ rel_str(v21) | upper_bounded_relstr(v21)) &  ! [v21] : ( ~ bounded_relstr(v21) |  ~ rel_str(v21) | lower_bounded_relstr(v21)) &  ! [v21] : ( ~ upper_bounded_relstr(v21) |  ~ antisymmetric_relstr(v21) |  ~ join_complete_relstr(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | with_suprema_relstr(v21) | empty_carrier(v21)) &  ! [v21] : ( ~ upper_bounded_relstr(v21) |  ~ lower_bounded_relstr(v21) |  ~ rel_str(v21) | bounded_relstr(v21)) &  ! [v21] : ( ~ with_infima_relstr(v21) |  ~ empty_carrier(v21) |  ~ rel_str(v21)) &  ! [v21] : ( ~ with_suprema_relstr(v21) |  ~ antisymmetric_relstr(v21) |  ~ transitive_relstr(v21) |  ~ lower_bounded_relstr(v21) |  ~ up_complete_relstr(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | bounded_relstr(v21) | empty_carrier(v21)) &  ! [v21] : ( ~ with_suprema_relstr(v21) |  ~ antisymmetric_relstr(v21) |  ~ transitive_relstr(v21) |  ~ lower_bounded_relstr(v21) |  ~ up_complete_relstr(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | upper_bounded_relstr(v21) | empty_carrier(v21)) &  ! [v21] : ( ~ with_suprema_relstr(v21) |  ~ antisymmetric_relstr(v21) |  ~ transitive_relstr(v21) |  ~ lower_bounded_relstr(v21) |  ~ up_complete_relstr(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | with_infima_relstr(v21) | empty_carrier(v21)) &  ! [v21] : ( ~ with_suprema_relstr(v21) |  ~ antisymmetric_relstr(v21) |  ~ transitive_relstr(v21) |  ~ lower_bounded_relstr(v21) |  ~ up_complete_relstr(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | complete_relstr(v21) | empty_carrier(v21)) &  ! [v21] : ( ~ with_suprema_relstr(v21) |  ~ up_complete_relstr(v21) |  ~ reflexive_relstr(v21) |  ~ empty_carrier(v21) |  ~ rel_str(v21)) &  ! [v21] : ( ~ with_suprema_relstr(v21) |  ~ up_complete_relstr(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | upper_bounded_relstr(v21)) &  ! [v21] : ( ~ with_suprema_relstr(v21) |  ~ empty_carrier(v21) |  ~ rel_str(v21)) &  ! [v21] : ( ~ antisymmetric_relstr(v21) |  ~ join_complete_relstr(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | with_infima_relstr(v21) | empty_carrier(v21)) &  ! [v21] : ( ~ join_complete_relstr(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | lower_bounded_relstr(v21) | empty_carrier(v21)) &  ! [v21] : ( ~ complete_relstr(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | join_complete_relstr(v21) | empty_carrier(v21)) &  ! [v21] : ( ~ complete_relstr(v21) |  ~ reflexive_relstr(v21) |  ~ rel_str(v21) | up_complete_relstr(v21) | empty_carrier(v21)) &  ! [v21] : ( ~ complete_relstr(v21) |  ~ rel_str(v21) | bounded_relstr(v21) | empty_carrier(v21)) &  ! [v21] : ( ~ complete_relstr(v21) |  ~ rel_str(v21) | with_infima_relstr(v21) | empty_carrier(v21)) &  ! [v21] : ( ~ complete_relstr(v21) |  ~ rel_str(v21) | with_suprema_relstr(v21) | empty_carrier(v21)) &  ! [v21] : ( ~ rel_str(v21) | one_sorted_str(v21)) &  ? [v21] :  ? [v22] :  ? [v23] : relation_of2_as_subset(v23, v21, v22) &  ? [v21] :  ? [v22] :  ? [v23] : relation_of2(v23, v21, v22) &  ? [v21] :  ? [v22] : (v22 = v21 |  ? [v23] : (( ~ in(v23, v22) |  ~ in(v23, v21)) & (in(v23, v22) | in(v23, v21)))) &  ? [v21] :  ? [v22] : element(v22, v21) &  ? [v21] : subset(v21, v21) & ((point_neighbourhood(v4, v0, v2) &  ~ in(v4, v3)) | (in(v4, v3) &  ~ point_neighbourhood(v4, v0, v2))))
% 11.40/3.17  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20 yields:
% 11.40/3.17  | (1) neighborhood_system(all_0_20_20, all_0_18_18) = all_0_17_17 & the_carrier(all_0_20_20) = all_0_19_19 & directed_relstr(all_0_15_15) & boolean_relstr(all_0_8_8) & complemented_relstr(all_0_8_8) & heyting_relstr(all_0_8_8) & distributive_relstr(all_0_8_8) & relation_empty_yielding(all_0_13_13) & relation_empty_yielding(empty_set) & one_sorted_str(all_0_2_2) & one_sorted_str(all_0_14_14) & connected_relstr(all_0_3_3) & trivial_carrier(all_0_9_9) & top_str(all_0_1_1) & top_str(all_0_20_20) & topological_space(all_0_20_20) & element(all_0_18_18, all_0_19_19) & relation(all_0_7_7) & relation(all_0_11_11) & relation(all_0_13_13) & relation(empty_set) & finite(all_0_5_5) & empty(all_0_7_7) & empty(empty_set) & bounded_relstr(all_0_4_4) & bounded_relstr(all_0_8_8) & bounded_relstr(all_0_12_12) & upper_bounded_relstr(all_0_4_4) & upper_bounded_relstr(all_0_8_8) & upper_bounded_relstr(all_0_12_12) & with_infima_relstr(all_0_4_4) & with_infima_relstr(all_0_8_8) & with_infima_relstr(all_0_9_9) & with_infima_relstr(all_0_10_10) & with_infima_relstr(all_0_12_12) & with_suprema_relstr(all_0_4_4) & with_suprema_relstr(all_0_8_8) & with_suprema_relstr(all_0_9_9) & with_suprema_relstr(all_0_10_10) & with_suprema_relstr(all_0_12_12) & antisymmetric_relstr(all_0_3_3) & antisymmetric_relstr(all_0_4_4) & antisymmetric_relstr(all_0_6_6) & antisymmetric_relstr(all_0_8_8) & antisymmetric_relstr(all_0_9_9) & antisymmetric_relstr(all_0_10_10) & antisymmetric_relstr(all_0_12_12) & transitive_relstr(all_0_3_3) & transitive_relstr(all_0_4_4) & transitive_relstr(all_0_6_6) & transitive_relstr(all_0_8_8) & transitive_relstr(all_0_9_9) & transitive_relstr(all_0_10_10) & transitive_relstr(all_0_12_12) & transitive_relstr(all_0_15_15) & lower_bounded_relstr(all_0_4_4) & lower_bounded_relstr(all_0_8_8) & lower_bounded_relstr(all_0_12_12) & join_complete_relstr(all_0_4_4) & up_complete_relstr(all_0_4_4) & complete_relstr(all_0_4_4) & complete_relstr(all_0_6_6) & complete_relstr(all_0_9_9) & complete_relstr(all_0_10_10) & complete_relstr(all_0_12_12) & reflexive_relstr(all_0_3_3) & reflexive_relstr(all_0_4_4) & reflexive_relstr(all_0_6_6) & reflexive_relstr(all_0_8_8) & reflexive_relstr(all_0_9_9) & reflexive_relstr(all_0_10_10) & reflexive_relstr(all_0_12_12) & strict_rel_str(all_0_4_4) & strict_rel_str(all_0_6_6) & strict_rel_str(all_0_8_8) & strict_rel_str(all_0_9_9) & strict_rel_str(all_0_10_10) & strict_rel_str(all_0_15_15) & rel_str(all_0_0_0) & rel_str(all_0_3_3) & rel_str(all_0_4_4) & rel_str(all_0_6_6) & rel_str(all_0_8_8) & rel_str(all_0_9_9) & rel_str(all_0_10_10) & rel_str(all_0_12_12) & rel_str(all_0_15_15) &  ~ v1_yellow_3(all_0_8_8) &  ~ trivial_carrier(all_0_8_8) &  ~ empty(all_0_5_5) &  ~ empty(all_0_11_11) &  ~ empty_carrier(all_0_3_3) &  ~ empty_carrier(all_0_4_4) &  ~ empty_carrier(all_0_6_6) &  ~ empty_carrier(all_0_8_8) &  ~ empty_carrier(all_0_9_9) &  ~ empty_carrier(all_0_10_10) &  ~ empty_carrier(all_0_12_12) &  ~ empty_carrier(all_0_14_14) &  ~ empty_carrier(all_0_15_15) &  ~ empty_carrier(all_0_20_20) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v1 |  ~ (rel_str_of(v3, v4) = v2) |  ~ (rel_str_of(v0, v1) = v2) |  ~ relation_of2(v1, v0, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v0 |  ~ (rel_str_of(v3, v4) = v2) |  ~ (rel_str_of(v0, v1) = v2) |  ~ relation_of2(v1, v0, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (the_carrier(v0) = v1) |  ~ (the_InternalRel(v0) = v2) |  ~ (rel_str_of(v1, v2) = v3) |  ~ strict_rel_str(v0) |  ~ rel_str(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (neighborhood_system(v3, v2) = v1) |  ~ (neighborhood_system(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (a_2_0_yellow19(v3, v2) = v1) |  ~ (a_2_0_yellow19(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cartesian_product2(v3, v2) = v1) |  ~ (cartesian_product2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (rel_str_of(v3, v2) = v1) |  ~ (rel_str_of(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (neighborhood_system(v0, v2) = v3) |  ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ~ element(v2, v1) | a_2_0_yellow19(v0, v2) = v3 | empty_carrier(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (a_2_0_yellow19(v1, v2) = v3) |  ~ point_neighbourhood(v0, v1, v2) |  ~ top_str(v1) |  ~ topological_space(v1) | empty_carrier(v1) | in(v0, v3) |  ? [v4] : (the_carrier(v1) = v4 &  ~ element(v2, v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (a_2_0_yellow19(v1, v2) = v3) |  ~ top_str(v1) |  ~ topological_space(v1) |  ~ in(v0, v3) | empty_carrier(v1) |  ? [v4] : ((v4 = v0 & point_neighbourhood(v0, v1, v2)) | (the_carrier(v1) = v4 &  ~ element(v2, v4)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (a_2_0_yellow19(v0, v2) = v3) |  ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ~ element(v2, v1) | neighborhood_system(v0, v2) = v3 | empty_carrier(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) |  ~ relation_of2_as_subset(v2, v0, v1) |  ? [v4] : (powerset(v3) = v4 & element(v2, v4))) &  ! [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] :  ! [v3] : ( ~ (cartesian_product2(v1, v2) = v3) | relation(v0) |  ? [v4] : (powerset(v3) = v4 &  ~ element(v0, v4))) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (cast_as_carrier_subset(v2) = v1) |  ~ (cast_as_carrier_subset(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (boole_POSet(v2) = v1) |  ~ (boole_POSet(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (the_carrier(v2) = v1) |  ~ (the_carrier(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (the_InternalRel(v2) = v1) |  ~ (the_InternalRel(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (neighborhood_system(v0, v1) = v2) |  ~ top_str(v0) |  ~ topological_space(v0) | empty_carrier(v0) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (cast_as_carrier_subset(v0) = v4 & boole_POSet(v4) = v5 & powerset(v6) = v7 & the_carrier(v5) = v6 & the_carrier(v0) = v3 & ( ~ element(v1, v3) | element(v2, v7)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ finite(v1) |  ~ finite(v0) | finite(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ empty(v2) | empty(v1) | empty(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] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ element(v2, v1) |  ~ finite(v0) | finite(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (the_carrier(v0) = v2) |  ~ top_str(v0) |  ~ topological_space(v0) |  ~ element(v1, v2) | empty_carrier(v0) |  ? [v3] : (powerset(v2) = v3 &  ! [v4] : ( ~ point_neighbourhood(v4, v0, v1) | element(v4, v3)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (the_carrier(v0) = v2) |  ~ top_str(v0) |  ~ topological_space(v0) |  ~ element(v1, v2) | empty_carrier(v0) |  ? [v3] : point_neighbourhood(v3, v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (rel_str_of(v0, v1) = v2) |  ~ relation_of2(v1, v0, v0) | strict_rel_str(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (rel_str_of(v0, v1) = v2) |  ~ relation_of2(v1, v0, v0) | rel_str(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ relation_of2(v2, v0, v1) | relation_of2_as_subset(v2, v0, v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ one_sorted_str(v0) |  ~ empty(v1) | empty_carrier(v0)) &  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ one_sorted_str(v0) |  ? [v2] :  ? [v3] : (powerset(v2) = v3 & the_carrier(v0) = v2 & element(v1, v3))) &  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) | closed_subset(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) | open_subset(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ top_str(v0) | dense(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ empty(v1) |  ~ upper_bounded_relstr(v0) |  ~ rel_str(v0) | empty_carrier(v0)) &  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ empty(v1) |  ~ with_infima_relstr(v0) |  ~ rel_str(v0)) &  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ empty(v1) |  ~ with_suprema_relstr(v0) |  ~ rel_str(v0)) &  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ empty(v1) |  ~ lower_bounded_relstr(v0) |  ~ rel_str(v0) | empty_carrier(v0)) &  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ empty(v1) |  ~ rel_str(v0) | empty_carrier(v0)) &  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ upper_bounded_relstr(v0) |  ~ rel_str(v0) | directed_subset(v1, v0) | empty_carrier(v0)) &  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ with_infima_relstr(v0) |  ~ rel_str(v0) | filtered_subset(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ with_suprema_relstr(v0) |  ~ rel_str(v0) | directed_subset(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ lower_bounded_relstr(v0) |  ~ rel_str(v0) | filtered_subset(v1, v0) | empty_carrier(v0)) &  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ rel_str(v0) | upper_relstr_subset(v1, v0) | empty_carrier(v0)) &  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ rel_str(v0) | lower_relstr_subset(v1, v0) | empty_carrier(v0)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) |  ~ v1_yellow_3(v1) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) |  ~ v1_yellow_3(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) |  ~ trivial_carrier(v1) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) |  ~ empty_carrier(v1) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) |  ~ empty_carrier(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | directed_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | boolean_relstr(v1) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | boolean_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | complemented_relstr(v1) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | complemented_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | heyting_relstr(v1) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | heyting_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | distributive_relstr(v1) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | distributive_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | bounded_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | upper_bounded_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | with_infima_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | with_suprema_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | antisymmetric_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | transitive_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | lower_bounded_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | join_complete_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | up_complete_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | complete_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | reflexive_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | strict_rel_str(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | bounded_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | upper_bounded_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | with_infima_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | with_suprema_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | antisymmetric_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | transitive_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | lower_bounded_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | join_complete_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | up_complete_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | complete_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | reflexive_relstr(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | strict_rel_str(v1)) &  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | rel_str(v1)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) & finite(v2) &  ~ empty(v2))) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2))) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & element(v3, v2) & finite(v3) &  ~ empty(v3))) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) & empty(v2))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ one_sorted_str(v0) |  ~ empty(v1) | empty_carrier(v0)) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ one_sorted_str(v0) | empty_carrier(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & element(v3, v2) &  ~ empty(v3))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ one_sorted_str(v0) |  ? [v2] :  ? [v3] :  ? [v4] : (powerset(v2) = v3 & powerset(v1) = v2 & element(v4, v3) & finite(v4) &  ~ empty(v4))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ one_sorted_str(v0) |  ? [v2] :  ? [v3] : (cast_as_carrier_subset(v0) = v2 & powerset(v1) = v3 & element(v2, v3))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) | empty_carrier(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & closed_subset(v3, v0) & open_subset(v3, v0) & element(v3, v2) &  ~ empty(v3))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) | empty_carrier(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & closed_subset(v3, v0) & element(v3, v2) &  ~ empty(v3))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & v5_membered(v3) & v4_membered(v3) & v3_membered(v3) & v2_membered(v3) & v1_membered(v3) & nowhere_dense(v3, v0) & boundary_set(v3, v0) & closed_subset(v3, v0) & open_subset(v3, v0) & element(v3, v2) & empty(v3))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & closed_subset(v3, v0) & open_subset(v3, v0) & element(v3, v2))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & closed_subset(v3, v0) & element(v3, v2))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & open_subset(v3, v0) & element(v3, v2))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] : (powerset(v1) = v2 &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ open_subset(v3, v0) |  ~ element(v3, v2) | v5_membered(v3)) &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ open_subset(v3, v0) |  ~ element(v3, v2) | v4_membered(v3)) &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ open_subset(v3, v0) |  ~ element(v3, v2) | v3_membered(v3)) &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ open_subset(v3, v0) |  ~ element(v3, v2) | v2_membered(v3)) &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ open_subset(v3, v0) |  ~ element(v3, v2) | v1_membered(v3)) &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ open_subset(v3, v0) |  ~ element(v3, v2) | boundary_set(v3, v0)) &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ open_subset(v3, v0) |  ~ element(v3, v2) | closed_subset(v3, v0)) &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ open_subset(v3, v0) |  ~ element(v3, v2) | empty(v3)))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] : (powerset(v1) = v2 &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ element(v3, v2) | boundary_set(v3, v0)))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] : (powerset(v1) = v2 &  ! [v3] : ( ~ boundary_set(v3, v0) |  ~ closed_subset(v3, v0) |  ~ element(v3, v2) | nowhere_dense(v3, v0)))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] : (powerset(v1) = v2 &  ! [v3] : ( ~ element(v3, v2) |  ~ empty(v3) | nowhere_dense(v3, v0)))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] : (powerset(v1) = v2 &  ! [v3] : ( ~ element(v3, v2) |  ~ empty(v3) | closed_subset(v3, v0)) &  ! [v3] : ( ~ element(v3, v2) |  ~ empty(v3) | open_subset(v3, v0)))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & v5_membered(v3) & v4_membered(v3) & v3_membered(v3) & v2_membered(v3) & v1_membered(v3) & boundary_set(v3, v0) & element(v3, v2) & empty(v3))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ? [v2] : (powerset(v1) = v2 &  ! [v3] : ( ~ element(v3, v2) |  ~ empty(v3) | boundary_set(v3, v0)))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ with_infima_relstr(v0) |  ~ with_suprema_relstr(v0) |  ~ antisymmetric_relstr(v0) |  ~ transitive_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & filtered_subset(v3, v0) & directed_subset(v3, v0) & upper_relstr_subset(v3, v0) & lower_relstr_subset(v3, v0) & element(v3, v2) &  ~ empty(v3))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ transitive_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | empty_carrier(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & filtered_subset(v3, v0) & upper_relstr_subset(v3, v0) & element(v3, v2) &  ~ empty(v3))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ transitive_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | empty_carrier(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & directed_subset(v3, v0) & lower_relstr_subset(v3, v0) & element(v3, v2) &  ~ empty(v3))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | empty_carrier(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & filtered_subset(v3, v0) & directed_subset(v3, v0) & element(v3, v2) & finite(v3) &  ~ empty(v3))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ rel_str(v0) | empty_carrier(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & upper_relstr_subset(v3, v0) & lower_relstr_subset(v3, v0) & element(v3, v2) &  ~ empty(v3))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ rel_str(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & filtered_subset(v3, v0) & directed_subset(v3, v0) & element(v3, v2))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ rel_str(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & upper_relstr_subset(v3, v0) & lower_relstr_subset(v3, v0) & element(v3, v2))) &  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ rel_str(v0) |  ? [v2] : (the_InternalRel(v0) = v2 & relation_of2_as_subset(v2, v1, v1))) &  ! [v0] :  ! [v1] : ( ~ (the_InternalRel(v0) = v1) |  ~ rel_str(v0) |  ? [v2] : (the_carrier(v0) = v2 & relation_of2_as_subset(v1, v2, v2))) &  ! [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] : ( ~ trivial_carrier(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | connected_relstr(v0) | empty_carrier(v0)) &  ! [v0] : ( ~ trivial_carrier(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | antisymmetric_relstr(v0) | empty_carrier(v0)) &  ! [v0] : ( ~ trivial_carrier(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | transitive_relstr(v0) | empty_carrier(v0)) &  ! [v0] : ( ~ trivial_carrier(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | complete_relstr(v0) | empty_carrier(v0)) &  ! [v0] : ( ~ top_str(v0) | one_sorted_str(v0)) &  ! [v0] : ( ~ empty(v0) | relation(v0)) &  ! [v0] : ( ~ empty(v0) | finite(v0)) &  ! [v0] : ( ~ bounded_relstr(v0) |  ~ rel_str(v0) | upper_bounded_relstr(v0)) &  ! [v0] : ( ~ bounded_relstr(v0) |  ~ rel_str(v0) | lower_bounded_relstr(v0)) &  ! [v0] : ( ~ upper_bounded_relstr(v0) |  ~ antisymmetric_relstr(v0) |  ~ join_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | with_suprema_relstr(v0) | empty_carrier(v0)) &  ! [v0] : ( ~ upper_bounded_relstr(v0) |  ~ lower_bounded_relstr(v0) |  ~ rel_str(v0) | bounded_relstr(v0)) &  ! [v0] : ( ~ with_infima_relstr(v0) |  ~ empty_carrier(v0) |  ~ rel_str(v0)) &  ! [v0] : ( ~ with_suprema_relstr(v0) |  ~ antisymmetric_relstr(v0) |  ~ transitive_relstr(v0) |  ~ lower_bounded_relstr(v0) |  ~ up_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | bounded_relstr(v0) | empty_carrier(v0)) &  ! [v0] : ( ~ with_suprema_relstr(v0) |  ~ antisymmetric_relstr(v0) |  ~ transitive_relstr(v0) |  ~ lower_bounded_relstr(v0) |  ~ up_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | upper_bounded_relstr(v0) | empty_carrier(v0)) &  ! [v0] : ( ~ with_suprema_relstr(v0) |  ~ antisymmetric_relstr(v0) |  ~ transitive_relstr(v0) |  ~ lower_bounded_relstr(v0) |  ~ up_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | with_infima_relstr(v0) | empty_carrier(v0)) &  ! [v0] : ( ~ with_suprema_relstr(v0) |  ~ antisymmetric_relstr(v0) |  ~ transitive_relstr(v0) |  ~ lower_bounded_relstr(v0) |  ~ up_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | complete_relstr(v0) | empty_carrier(v0)) &  ! [v0] : ( ~ with_suprema_relstr(v0) |  ~ up_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ empty_carrier(v0) |  ~ rel_str(v0)) &  ! [v0] : ( ~ with_suprema_relstr(v0) |  ~ up_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | upper_bounded_relstr(v0)) &  ! [v0] : ( ~ with_suprema_relstr(v0) |  ~ empty_carrier(v0) |  ~ rel_str(v0)) &  ! [v0] : ( ~ antisymmetric_relstr(v0) |  ~ join_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | with_infima_relstr(v0) | empty_carrier(v0)) &  ! [v0] : ( ~ join_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | lower_bounded_relstr(v0) | empty_carrier(v0)) &  ! [v0] : ( ~ complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | join_complete_relstr(v0) | empty_carrier(v0)) &  ! [v0] : ( ~ complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | up_complete_relstr(v0) | empty_carrier(v0)) &  ! [v0] : ( ~ complete_relstr(v0) |  ~ rel_str(v0) | bounded_relstr(v0) | empty_carrier(v0)) &  ! [v0] : ( ~ complete_relstr(v0) |  ~ rel_str(v0) | with_infima_relstr(v0) | empty_carrier(v0)) &  ! [v0] : ( ~ complete_relstr(v0) |  ~ rel_str(v0) | with_suprema_relstr(v0) | empty_carrier(v0)) &  ! [v0] : ( ~ rel_str(v0) | one_sorted_str(v0)) &  ? [v0] :  ? [v1] :  ? [v2] : relation_of2_as_subset(v2, v0, v1) &  ? [v0] :  ? [v1] :  ? [v2] : relation_of2(v2, v0, v1) &  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] : (( ~ in(v2, v1) |  ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) &  ? [v0] :  ? [v1] : element(v1, v0) &  ? [v0] : subset(v0, v0) & ((point_neighbourhood(all_0_16_16, all_0_20_20, all_0_18_18) &  ~ in(all_0_16_16, all_0_17_17)) | (in(all_0_16_16, all_0_17_17) &  ~ point_neighbourhood(all_0_16_16, all_0_20_20, all_0_18_18)))
% 11.86/3.20  |
% 11.86/3.20  | Applying alpha-rule on (1) yields:
% 11.86/3.20  | (2)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (cast_as_carrier_subset(v2) = v1) |  ~ (cast_as_carrier_subset(v2) = v0))
% 11.86/3.20  | (3)  ! [v0] : ( ~ with_suprema_relstr(v0) |  ~ antisymmetric_relstr(v0) |  ~ transitive_relstr(v0) |  ~ lower_bounded_relstr(v0) |  ~ up_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | upper_bounded_relstr(v0) | empty_carrier(v0))
% 11.86/3.20  | (4)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ rel_str(v0) | empty_carrier(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & upper_relstr_subset(v3, v0) & lower_relstr_subset(v3, v0) & element(v3, v2) &  ~ empty(v3)))
% 11.86/3.20  | (5)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | boolean_relstr(v1))
% 11.86/3.20  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v1 |  ~ (rel_str_of(v3, v4) = v2) |  ~ (rel_str_of(v0, v1) = v2) |  ~ relation_of2(v1, v0, v0))
% 11.86/3.20  | (7)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & open_subset(v3, v0) & element(v3, v2)))
% 11.86/3.20  | (8) reflexive_relstr(all_0_3_3)
% 11.86/3.20  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (the_carrier(v0) = v1) |  ~ (the_InternalRel(v0) = v2) |  ~ (rel_str_of(v1, v2) = v3) |  ~ strict_rel_str(v0) |  ~ rel_str(v0))
% 11.86/3.20  | (10)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & v5_membered(v3) & v4_membered(v3) & v3_membered(v3) & v2_membered(v3) & v1_membered(v3) & boundary_set(v3, v0) & element(v3, v2) & empty(v3)))
% 11.86/3.20  | (11)  ! [v0] : ( ~ complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | up_complete_relstr(v0) | empty_carrier(v0))
% 11.86/3.20  | (12)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | reflexive_relstr(v1))
% 11.86/3.20  | (13)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & closed_subset(v3, v0) & element(v3, v2)))
% 11.86/3.20  | (14)  ! [v0] : ( ~ with_suprema_relstr(v0) |  ~ empty_carrier(v0) |  ~ rel_str(v0))
% 11.86/3.20  | (15)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (boole_POSet(v2) = v1) |  ~ (boole_POSet(v2) = v0))
% 11.86/3.20  | (16)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ rel_str(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & filtered_subset(v3, v0) & directed_subset(v3, v0) & element(v3, v2)))
% 11.86/3.20  | (17)  ~ v1_yellow_3(all_0_8_8)
% 11.86/3.20  | (18)  ? [v0] : subset(v0, v0)
% 11.86/3.20  | (19)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | with_suprema_relstr(v1))
% 11.86/3.20  | (20) lower_bounded_relstr(all_0_12_12)
% 11.86/3.20  | (21) bounded_relstr(all_0_12_12)
% 11.86/3.20  | (22)  ! [v0] : ( ~ empty(v0) | finite(v0))
% 11.86/3.20  | (23)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | strict_rel_str(v1))
% 11.86/3.20  | (24)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) |  ~ empty_carrier(v1) | empty(v0))
% 11.86/3.20  | (25) reflexive_relstr(all_0_9_9)
% 11.86/3.20  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (a_2_0_yellow19(v0, v2) = v3) |  ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ~ element(v2, v1) | neighborhood_system(v0, v2) = v3 | empty_carrier(v0))
% 11.86/3.20  | (27)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ rel_str(v0) |  ? [v2] : (the_InternalRel(v0) = v2 & relation_of2_as_subset(v2, v1, v1)))
% 11.86/3.20  | (28)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | lower_bounded_relstr(v1))
% 11.86/3.20  | (29) the_carrier(all_0_20_20) = all_0_19_19
% 11.86/3.20  | (30)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | strict_rel_str(v1))
% 11.86/3.20  | (31) strict_rel_str(all_0_9_9)
% 11.86/3.20  | (32)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | distributive_relstr(v1) | empty(v0))
% 11.86/3.20  | (33)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | rel_str(v1))
% 11.86/3.20  | (34)  ! [v0] : ( ~ complete_relstr(v0) |  ~ rel_str(v0) | with_suprema_relstr(v0) | empty_carrier(v0))
% 11.86/3.20  | (35) trivial_carrier(all_0_9_9)
% 11.86/3.20  | (36) lower_bounded_relstr(all_0_4_4)
% 11.86/3.20  | (37)  ~ empty(all_0_5_5)
% 11.86/3.20  | (38) rel_str(all_0_9_9)
% 11.86/3.20  | (39) complete_relstr(all_0_6_6)
% 11.86/3.20  | (40) with_suprema_relstr(all_0_12_12)
% 11.86/3.20  | (41)  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ empty(v1) |  ~ lower_bounded_relstr(v0) |  ~ rel_str(v0) | empty_carrier(v0))
% 11.86/3.20  | (42) reflexive_relstr(all_0_12_12)
% 11.86/3.20  | (43) with_infima_relstr(all_0_12_12)
% 11.86/3.20  | (44)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | join_complete_relstr(v1))
% 11.86/3.20  | (45) strict_rel_str(all_0_8_8)
% 11.86/3.20  | (46)  ? [v0] :  ? [v1] :  ? [v2] : relation_of2(v2, v0, v1)
% 11.86/3.20  | (47) rel_str(all_0_0_0)
% 11.86/3.20  | (48)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) |  ~ trivial_carrier(v1) | empty(v0))
% 11.86/3.20  | (49) one_sorted_str(all_0_14_14)
% 11.86/3.20  | (50)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | empty_carrier(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & filtered_subset(v3, v0) & directed_subset(v3, v0) & element(v3, v2) & finite(v3) &  ~ empty(v3)))
% 11.86/3.20  | (51)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) |  ~ empty_carrier(v1))
% 11.86/3.20  | (52) relation_empty_yielding(all_0_13_13)
% 11.86/3.21  | (53)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | antisymmetric_relstr(v1))
% 11.86/3.21  | (54)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] : (powerset(v1) = v2 &  ! [v3] : ( ~ element(v3, v2) |  ~ empty(v3) | nowhere_dense(v3, v0))))
% 11.86/3.21  | (55)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | boolean_relstr(v1) | empty(v0))
% 11.86/3.21  | (56)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | heyting_relstr(v1))
% 11.86/3.21  | (57)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) |  ~ v1_yellow_3(v1) | empty(v0))
% 11.86/3.21  | (58) transitive_relstr(all_0_8_8)
% 11.86/3.21  | (59)  ! [v0] : ( ~ join_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | lower_bounded_relstr(v0) | empty_carrier(v0))
% 11.86/3.21  | (60) relation(empty_set)
% 11.86/3.21  | (61) directed_relstr(all_0_15_15)
% 11.86/3.21  | (62) antisymmetric_relstr(all_0_12_12)
% 11.86/3.21  | (63)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | bounded_relstr(v1))
% 11.86/3.21  | (64)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ empty(v2) |  ~ in(v0, v1))
% 11.86/3.21  | (65)  ~ empty_carrier(all_0_6_6)
% 11.86/3.21  | (66) up_complete_relstr(all_0_4_4)
% 11.86/3.21  | (67) complete_relstr(all_0_9_9)
% 11.86/3.21  | (68)  ! [v0] : ( ~ trivial_carrier(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | connected_relstr(v0) | empty_carrier(v0))
% 11.86/3.21  | (69)  ! [v0] : ( ~ antisymmetric_relstr(v0) |  ~ join_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | with_infima_relstr(v0) | empty_carrier(v0))
% 11.86/3.21  | (70)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | up_complete_relstr(v1))
% 11.86/3.21  | (71) rel_str(all_0_15_15)
% 11.86/3.21  | (72)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (the_carrier(v2) = v1) |  ~ (the_carrier(v2) = v0))
% 11.86/3.21  | (73) antisymmetric_relstr(all_0_9_9)
% 11.86/3.21  | (74) transitive_relstr(all_0_4_4)
% 11.86/3.21  | (75)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | distributive_relstr(v1))
% 11.86/3.21  | (76)  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ lower_bounded_relstr(v0) |  ~ rel_str(v0) | filtered_subset(v1, v0) | empty_carrier(v0))
% 11.86/3.21  | (77)  ! [v0] : ( ~ trivial_carrier(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | transitive_relstr(v0) | empty_carrier(v0))
% 11.86/3.21  | (78) with_suprema_relstr(all_0_4_4)
% 11.86/3.21  | (79)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ empty(v2) | empty(v1) | empty(v0))
% 11.86/3.21  | (80) complete_relstr(all_0_10_10)
% 11.86/3.21  | (81) bounded_relstr(all_0_8_8)
% 11.86/3.21  | (82)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | complemented_relstr(v1) | empty(v0))
% 11.86/3.21  | (83)  ! [v0] : ( ~ trivial_carrier(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | antisymmetric_relstr(v0) | empty_carrier(v0))
% 11.86/3.21  | (84) relation_empty_yielding(empty_set)
% 11.86/3.21  | (85) antisymmetric_relstr(all_0_10_10)
% 11.86/3.21  | (86)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | transitive_relstr(v1))
% 11.86/3.21  | (87)  ? [v0] :  ? [v1] :  ? [v2] : relation_of2_as_subset(v2, v0, v1)
% 11.86/3.21  | (88)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v0 |  ~ (rel_str_of(v3, v4) = v2) |  ~ (rel_str_of(v0, v1) = v2) |  ~ relation_of2(v1, v0, v0))
% 11.86/3.21  | (89) complete_relstr(all_0_4_4)
% 11.86/3.21  | (90)  ! [v0] : ( ~ rel_str(v0) | one_sorted_str(v0))
% 11.86/3.21  | (91)  ! [v0] : ( ~ complete_relstr(v0) |  ~ rel_str(v0) | bounded_relstr(v0) | empty_carrier(v0))
% 11.86/3.21  | (92)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] : (powerset(v1) = v2 &  ! [v3] : ( ~ element(v3, v2) |  ~ empty(v3) | closed_subset(v3, v0)) &  ! [v3] : ( ~ element(v3, v2) |  ~ empty(v3) | open_subset(v3, v0))))
% 11.86/3.21  | (93)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) |  ~ relation_of2_as_subset(v2, v0, v1) |  ? [v4] : (powerset(v3) = v4 & element(v2, v4)))
% 11.86/3.21  | (94)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | directed_relstr(v1))
% 11.86/3.21  | (95)  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) | open_subset(v1, v0))
% 11.86/3.21  | (96)  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ empty(v1) |  ~ rel_str(v0) | empty_carrier(v0))
% 11.86/3.21  | (97) distributive_relstr(all_0_8_8)
% 11.86/3.21  | (98)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | with_infima_relstr(v1))
% 11.86/3.21  | (99) with_infima_relstr(all_0_10_10)
% 11.86/3.21  | (100)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) | empty_carrier(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & closed_subset(v3, v0) & open_subset(v3, v0) & element(v3, v2) &  ~ empty(v3)))
% 11.86/3.21  | (101) lower_bounded_relstr(all_0_8_8)
% 11.86/3.21  | (102)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | with_suprema_relstr(v1))
% 11.86/3.21  | (103)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cartesian_product2(v3, v2) = v1) |  ~ (cartesian_product2(v3, v2) = v0))
% 11.86/3.21  | (104) strict_rel_str(all_0_6_6)
% 11.86/3.21  | (105) strict_rel_str(all_0_10_10)
% 11.86/3.21  | (106)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 11.86/3.21  | (107) join_complete_relstr(all_0_4_4)
% 11.86/3.21  | (108)  ~ empty(all_0_11_11)
% 11.86/3.21  | (109) reflexive_relstr(all_0_10_10)
% 11.86/3.21  | (110)  ! [v0] : ( ~ upper_bounded_relstr(v0) |  ~ lower_bounded_relstr(v0) |  ~ rel_str(v0) | bounded_relstr(v0))
% 11.86/3.21  | (111) transitive_relstr(all_0_6_6)
% 11.86/3.21  | (112)  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ empty(v1) |  ~ with_infima_relstr(v0) |  ~ rel_str(v0))
% 11.86/3.21  | (113)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (neighborhood_system(v0, v2) = v3) |  ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ~ element(v2, v1) | a_2_0_yellow19(v0, v2) = v3 | empty_carrier(v0))
% 11.86/3.21  | (114)  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ one_sorted_str(v0) |  ? [v2] :  ? [v3] : (powerset(v2) = v3 & the_carrier(v0) = v2 & element(v1, v3)))
% 11.86/3.21  | (115)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | reflexive_relstr(v1))
% 11.86/3.21  | (116)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ transitive_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | empty_carrier(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & filtered_subset(v3, v0) & upper_relstr_subset(v3, v0) & element(v3, v2) &  ~ empty(v3)))
% 11.86/3.21  | (117) complete_relstr(all_0_12_12)
% 11.86/3.21  | (118) topological_space(all_0_20_20)
% 11.86/3.21  | (119)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] : (( ~ in(v2, v1) |  ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 11.86/3.21  | (120) bounded_relstr(all_0_4_4)
% 11.86/3.21  | (121)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ rel_str(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & upper_relstr_subset(v3, v0) & lower_relstr_subset(v3, v0) & element(v3, v2)))
% 11.86/3.22  | (122)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & element(v3, v2) & finite(v3) &  ~ empty(v3)))
% 11.86/3.22  | (123)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & closed_subset(v3, v0) & open_subset(v3, v0) & element(v3, v2)))
% 11.86/3.22  | (124)  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ with_suprema_relstr(v0) |  ~ rel_str(v0) | directed_subset(v1, v0))
% 11.86/3.22  | (125) connected_relstr(all_0_3_3)
% 11.86/3.22  | (126)  ~ empty_carrier(all_0_8_8)
% 11.86/3.22  | (127)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (neighborhood_system(v3, v2) = v1) |  ~ (neighborhood_system(v3, v2) = v0))
% 11.86/3.22  | (128)  ! [v0] : ( ~ top_str(v0) | one_sorted_str(v0))
% 11.86/3.22  | (129) with_suprema_relstr(all_0_10_10)
% 11.86/3.22  | (130)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & v5_membered(v3) & v4_membered(v3) & v3_membered(v3) & v2_membered(v3) & v1_membered(v3) & nowhere_dense(v3, v0) & boundary_set(v3, v0) & closed_subset(v3, v0) & open_subset(v3, v0) & element(v3, v2) & empty(v3)))
% 11.86/3.22  | (131)  ? [v0] :  ? [v1] : element(v1, v0)
% 11.86/3.22  | (132)  ! [v0] :  ! [v1] : ( ~ (the_InternalRel(v0) = v1) |  ~ rel_str(v0) |  ? [v2] : (the_carrier(v0) = v2 & relation_of2_as_subset(v1, v2, v2)))
% 11.86/3.22  | (133)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ? [v2] : (powerset(v1) = v2 &  ! [v3] : ( ~ element(v3, v2) |  ~ empty(v3) | boundary_set(v3, v0))))
% 11.86/3.22  | (134) rel_str(all_0_3_3)
% 11.86/3.22  | (135)  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ upper_bounded_relstr(v0) |  ~ rel_str(v0) | directed_subset(v1, v0) | empty_carrier(v0))
% 11.86/3.22  | (136)  ! [v0] : ( ~ trivial_carrier(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | complete_relstr(v0) | empty_carrier(v0))
% 11.86/3.22  | (137) reflexive_relstr(all_0_6_6)
% 11.86/3.22  | (138) (point_neighbourhood(all_0_16_16, all_0_20_20, all_0_18_18) &  ~ in(all_0_16_16, all_0_17_17)) | (in(all_0_16_16, all_0_17_17) &  ~ point_neighbourhood(all_0_16_16, all_0_20_20, all_0_18_18))
% 11.86/3.22  | (139) rel_str(all_0_4_4)
% 11.86/3.22  | (140)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) & finite(v2) &  ~ empty(v2)))
% 11.86/3.22  | (141) transitive_relstr(all_0_12_12)
% 11.86/3.22  | (142) with_suprema_relstr(all_0_8_8)
% 11.86/3.22  | (143)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 11.86/3.22  | (144)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 11.86/3.22  | (145)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (a_2_0_yellow19(v1, v2) = v3) |  ~ top_str(v1) |  ~ topological_space(v1) |  ~ in(v0, v3) | empty_carrier(v1) |  ? [v4] : ((v4 = v0 & point_neighbourhood(v0, v1, v2)) | (the_carrier(v1) = v4 &  ~ element(v2, v4))))
% 11.86/3.22  | (146)  ! [v0] : ( ~ complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | join_complete_relstr(v0) | empty_carrier(v0))
% 11.86/3.22  | (147) antisymmetric_relstr(all_0_6_6)
% 11.86/3.22  | (148)  ! [v0] : ( ~ bounded_relstr(v0) |  ~ rel_str(v0) | lower_bounded_relstr(v0))
% 11.86/3.22  | (149) reflexive_relstr(all_0_4_4)
% 11.86/3.22  | (150)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) & empty(v2)))
% 11.86/3.22  | (151)  ! [v0] : ( ~ with_suprema_relstr(v0) |  ~ antisymmetric_relstr(v0) |  ~ transitive_relstr(v0) |  ~ lower_bounded_relstr(v0) |  ~ up_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | bounded_relstr(v0) | empty_carrier(v0))
% 11.86/3.22  | (152) heyting_relstr(all_0_8_8)
% 11.86/3.22  | (153) top_str(all_0_1_1)
% 11.86/3.22  | (154) rel_str(all_0_6_6)
% 11.86/3.22  | (155)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ one_sorted_str(v0) |  ~ empty(v1) | empty_carrier(v0))
% 11.86/3.22  | (156) element(all_0_18_18, all_0_19_19)
% 11.86/3.22  | (157) empty(empty_set)
% 11.86/3.22  | (158)  ! [v0] : ( ~ with_suprema_relstr(v0) |  ~ up_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | upper_bounded_relstr(v0))
% 11.86/3.22  | (159) antisymmetric_relstr(all_0_3_3)
% 11.86/3.22  | (160)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ one_sorted_str(v0) |  ? [v2] :  ? [v3] :  ? [v4] : (powerset(v2) = v3 & powerset(v1) = v2 & element(v4, v3) & finite(v4) &  ~ empty(v4)))
% 11.86/3.22  | (161)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 11.86/3.22  | (162) antisymmetric_relstr(all_0_8_8)
% 11.86/3.22  | (163)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (rel_str_of(v3, v2) = v1) |  ~ (rel_str_of(v3, v2) = v0))
% 11.86/3.22  | (164)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (the_InternalRel(v2) = v1) |  ~ (the_InternalRel(v2) = v0))
% 11.86/3.22  | (165)  ~ empty_carrier(all_0_12_12)
% 11.86/3.22  | (166)  ~ empty_carrier(all_0_3_3)
% 11.86/3.22  | (167)  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ empty(v1) |  ~ with_suprema_relstr(v0) |  ~ rel_str(v0))
% 11.86/3.22  | (168) with_infima_relstr(all_0_9_9)
% 11.86/3.22  | (169)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] : (powerset(v1) = v2 &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ open_subset(v3, v0) |  ~ element(v3, v2) | v5_membered(v3)) &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ open_subset(v3, v0) |  ~ element(v3, v2) | v4_membered(v3)) &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ open_subset(v3, v0) |  ~ element(v3, v2) | v3_membered(v3)) &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ open_subset(v3, v0) |  ~ element(v3, v2) | v2_membered(v3)) &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ open_subset(v3, v0) |  ~ element(v3, v2) | v1_membered(v3)) &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ open_subset(v3, v0) |  ~ element(v3, v2) | boundary_set(v3, v0)) &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ open_subset(v3, v0) |  ~ element(v3, v2) | closed_subset(v3, v0)) &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ open_subset(v3, v0) |  ~ element(v3, v2) | empty(v3))))
% 11.86/3.22  | (170) relation(all_0_11_11)
% 11.86/3.22  | (171)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 11.86/3.22  | (172)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 11.86/3.22  | (173) finite(all_0_5_5)
% 11.86/3.22  | (174) upper_bounded_relstr(all_0_12_12)
% 11.86/3.22  | (175)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | complete_relstr(v1))
% 11.86/3.22  | (176)  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ rel_str(v0) | upper_relstr_subset(v1, v0) | empty_carrier(v0))
% 11.86/3.22  | (177)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ element(v2, v1) |  ~ finite(v0) | finite(v2))
% 11.86/3.22  | (178) strict_rel_str(all_0_4_4)
% 11.86/3.22  | (179) rel_str(all_0_8_8)
% 11.86/3.22  | (180)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ one_sorted_str(v0) |  ? [v2] :  ? [v3] : (cast_as_carrier_subset(v0) = v2 & powerset(v1) = v3 & element(v2, v3)))
% 11.86/3.22  | (181) transitive_relstr(all_0_9_9)
% 11.86/3.22  | (182)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | antisymmetric_relstr(v1))
% 11.86/3.22  | (183)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (neighborhood_system(v0, v1) = v2) |  ~ top_str(v0) |  ~ topological_space(v0) | empty_carrier(v0) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (cast_as_carrier_subset(v0) = v4 & boole_POSet(v4) = v5 & powerset(v6) = v7 & the_carrier(v5) = v6 & the_carrier(v0) = v3 & ( ~ element(v1, v3) | element(v2, v7))))
% 11.86/3.22  | (184)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 11.86/3.22  | (185)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | lower_bounded_relstr(v1))
% 11.86/3.22  | (186)  ~ empty_carrier(all_0_14_14)
% 11.86/3.22  | (187)  ! [v0] : ( ~ complete_relstr(v0) |  ~ rel_str(v0) | with_infima_relstr(v0) | empty_carrier(v0))
% 11.86/3.22  | (188)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | with_infima_relstr(v1))
% 11.86/3.23  | (189) strict_rel_str(all_0_15_15)
% 11.86/3.23  | (190) one_sorted_str(all_0_2_2)
% 11.86/3.23  | (191)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 11.86/3.23  | (192)  ~ empty_carrier(all_0_20_20)
% 11.86/3.23  | (193)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | heyting_relstr(v1) | empty(v0))
% 11.86/3.23  | (194) with_infima_relstr(all_0_4_4)
% 11.86/3.23  | (195)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 11.86/3.23  | (196) neighborhood_system(all_0_20_20, all_0_18_18) = all_0_17_17
% 11.86/3.23  | (197)  ! [v0] : ( ~ with_suprema_relstr(v0) |  ~ antisymmetric_relstr(v0) |  ~ transitive_relstr(v0) |  ~ lower_bounded_relstr(v0) |  ~ up_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | with_infima_relstr(v0) | empty_carrier(v0))
% 11.86/3.23  | (198) transitive_relstr(all_0_3_3)
% 11.86/3.23  | (199)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (a_2_0_yellow19(v1, v2) = v3) |  ~ point_neighbourhood(v0, v1, v2) |  ~ top_str(v1) |  ~ topological_space(v1) | empty_carrier(v1) | in(v0, v3) |  ? [v4] : (the_carrier(v1) = v4 &  ~ element(v2, v4)))
% 11.86/3.23  | (200)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | upper_bounded_relstr(v1))
% 11.86/3.23  | (201)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | bounded_relstr(v1))
% 11.86/3.23  | (202) relation(all_0_13_13)
% 11.86/3.23  | (203)  ~ empty_carrier(all_0_4_4)
% 11.86/3.23  | (204) empty(all_0_7_7)
% 11.86/3.23  | (205) rel_str(all_0_12_12)
% 11.86/3.23  | (206) with_suprema_relstr(all_0_9_9)
% 11.86/3.23  | (207) rel_str(all_0_10_10)
% 11.86/3.23  | (208)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ relation_of2(v2, v0, v1) | relation_of2_as_subset(v2, v0, v1))
% 11.86/3.23  | (209)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0, v1))
% 11.86/3.23  | (210)  ~ empty_carrier(all_0_15_15)
% 11.86/3.23  | (211)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | complemented_relstr(v1))
% 11.86/3.23  | (212)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] : (powerset(v1) = v2 &  ! [v3] : ( ~ boundary_set(v3, v0) |  ~ closed_subset(v3, v0) |  ~ element(v3, v2) | nowhere_dense(v3, v0))))
% 11.86/3.23  | (213)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (rel_str_of(v0, v1) = v2) |  ~ relation_of2(v1, v0, v0) | strict_rel_str(v2))
% 11.86/3.23  | (214)  ! [v0] : ( ~ upper_bounded_relstr(v0) |  ~ antisymmetric_relstr(v0) |  ~ join_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | with_suprema_relstr(v0) | empty_carrier(v0))
% 11.86/3.23  | (215)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 11.86/3.23  | (216)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 11.86/3.23  | (217) transitive_relstr(all_0_10_10)
% 11.86/3.23  | (218)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ finite(v1) |  ~ finite(v0) | finite(v2))
% 11.86/3.23  | (219) transitive_relstr(all_0_15_15)
% 11.86/3.23  | (220)  ! [v0] : ( ~ with_suprema_relstr(v0) |  ~ up_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ empty_carrier(v0) |  ~ rel_str(v0))
% 11.86/3.23  | (221)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) |  ~ v1_yellow_3(v1))
% 11.86/3.23  | (222)  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ top_str(v0) | dense(v1, v0))
% 11.86/3.23  | (223)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) |  ? [v2] : (powerset(v1) = v2 &  ! [v3] : ( ~ nowhere_dense(v3, v0) |  ~ element(v3, v2) | boundary_set(v3, v0))))
% 11.86/3.23  | (224) upper_bounded_relstr(all_0_4_4)
% 11.86/3.23  | (225)  ! [v0] : ( ~ bounded_relstr(v0) |  ~ rel_str(v0) | upper_bounded_relstr(v0))
% 11.86/3.23  | (226) upper_bounded_relstr(all_0_8_8)
% 11.86/3.23  | (227)  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) | closed_subset(v1, v0))
% 11.86/3.23  | (228)  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ one_sorted_str(v0) |  ~ empty(v1) | empty_carrier(v0))
% 11.86/3.23  | (229)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (the_carrier(v0) = v2) |  ~ top_str(v0) |  ~ topological_space(v0) |  ~ element(v1, v2) | empty_carrier(v0) |  ? [v3] : (powerset(v2) = v3 &  ! [v4] : ( ~ point_neighbourhood(v4, v0, v1) | element(v4, v3))))
% 11.86/3.23  | (230) relation(all_0_7_7)
% 11.86/3.23  | (231)  ~ empty_carrier(all_0_9_9)
% 11.86/3.23  | (232) complemented_relstr(all_0_8_8)
% 11.86/3.23  | (233)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ top_str(v0) |  ~ topological_space(v0) | empty_carrier(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & closed_subset(v3, v0) & element(v3, v2) &  ~ empty(v3)))
% 11.86/3.23  | (234) reflexive_relstr(all_0_8_8)
% 11.86/3.23  | (235)  ~ trivial_carrier(all_0_8_8)
% 11.86/3.23  | (236)  ! [v0] : ( ~ with_suprema_relstr(v0) |  ~ antisymmetric_relstr(v0) |  ~ transitive_relstr(v0) |  ~ lower_bounded_relstr(v0) |  ~ up_complete_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | complete_relstr(v0) | empty_carrier(v0))
% 11.86/3.23  | (237)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ one_sorted_str(v0) | empty_carrier(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & element(v3, v2) &  ~ empty(v3)))
% 11.86/3.23  | (238) antisymmetric_relstr(all_0_4_4)
% 11.86/3.23  | (239)  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ empty(v1) |  ~ upper_bounded_relstr(v0) |  ~ rel_str(v0) | empty_carrier(v0))
% 11.86/3.23  | (240)  ~ empty_carrier(all_0_10_10)
% 11.86/3.23  | (241)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | complete_relstr(v1))
% 11.86/3.23  | (242) with_infima_relstr(all_0_8_8)
% 11.86/3.23  | (243)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ transitive_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) | empty_carrier(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & directed_subset(v3, v0) & lower_relstr_subset(v3, v0) & element(v3, v2) &  ~ empty(v3)))
% 11.86/3.23  | (244)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product2(v1, v2) = v3) | relation(v0) |  ? [v4] : (powerset(v3) = v4 &  ~ element(v0, v4)))
% 11.86/3.23  | (245) boolean_relstr(all_0_8_8)
% 11.86/3.23  | (246)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | transitive_relstr(v1))
% 11.86/3.23  | (247)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (the_carrier(v0) = v2) |  ~ top_str(v0) |  ~ topological_space(v0) |  ~ element(v1, v2) | empty_carrier(v0) |  ? [v3] : point_neighbourhood(v3, v0, v1))
% 11.86/3.23  | (248)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | up_complete_relstr(v1))
% 11.86/3.23  | (249)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (a_2_0_yellow19(v3, v2) = v1) |  ~ (a_2_0_yellow19(v3, v2) = v0))
% 11.86/3.23  | (250)  ! [v0] : ( ~ with_infima_relstr(v0) |  ~ empty_carrier(v0) |  ~ rel_str(v0))
% 11.86/3.23  | (251)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 11.86/3.23  | (252)  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ with_infima_relstr(v0) |  ~ rel_str(v0) | filtered_subset(v1, v0))
% 11.86/3.23  | (253)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 11.86/3.23  | (254)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | upper_bounded_relstr(v1))
% 11.86/3.23  | (255)  ! [v0] :  ! [v1] : ( ~ (boole_POSet(v0) = v1) | empty(v0) | join_complete_relstr(v1))
% 11.86/3.23  | (256)  ! [v0] :  ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) |  ~ rel_str(v0) | lower_relstr_subset(v1, v0) | empty_carrier(v0))
% 11.86/3.23  | (257)  ! [v0] :  ! [v1] : ( ~ (the_carrier(v0) = v1) |  ~ with_infima_relstr(v0) |  ~ with_suprema_relstr(v0) |  ~ antisymmetric_relstr(v0) |  ~ transitive_relstr(v0) |  ~ reflexive_relstr(v0) |  ~ rel_str(v0) |  ? [v2] :  ? [v3] : (powerset(v1) = v2 & filtered_subset(v3, v0) & directed_subset(v3, v0) & upper_relstr_subset(v3, v0) & lower_relstr_subset(v3, v0) & element(v3, v2) &  ~ empty(v3)))
% 11.86/3.24  | (258)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (rel_str_of(v0, v1) = v2) |  ~ relation_of2(v1, v0, v0) | rel_str(v2))
% 11.86/3.24  | (259) top_str(all_0_20_20)
% 11.86/3.24  |
% 11.86/3.24  | Instantiating formula (128) with all_0_20_20 and discharging atoms top_str(all_0_20_20), yields:
% 11.86/3.24  | (260) one_sorted_str(all_0_20_20)
% 11.86/3.24  |
% 11.86/3.24  | Instantiating formula (183) with all_0_17_17, all_0_18_18, all_0_20_20 and discharging atoms neighborhood_system(all_0_20_20, all_0_18_18) = all_0_17_17, top_str(all_0_20_20), topological_space(all_0_20_20),  ~ empty_carrier(all_0_20_20), yields:
% 11.86/3.24  | (261)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (cast_as_carrier_subset(all_0_20_20) = v1 & boole_POSet(v1) = v2 & powerset(v3) = v4 & the_carrier(v2) = v3 & the_carrier(all_0_20_20) = v0 & ( ~ element(all_0_18_18, v0) | element(all_0_17_17, v4)))
% 11.86/3.24  |
% 11.86/3.24  | Instantiating formula (113) with all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20 and discharging atoms neighborhood_system(all_0_20_20, all_0_18_18) = all_0_17_17, the_carrier(all_0_20_20) = all_0_19_19, top_str(all_0_20_20), topological_space(all_0_20_20), element(all_0_18_18, all_0_19_19),  ~ empty_carrier(all_0_20_20), yields:
% 11.86/3.24  | (262) a_2_0_yellow19(all_0_20_20, all_0_18_18) = all_0_17_17
% 11.86/3.24  |
% 11.86/3.24  | Instantiating (261) with all_42_0_43, all_42_1_44, all_42_2_45, all_42_3_46, all_42_4_47 yields:
% 11.86/3.24  | (263) cast_as_carrier_subset(all_0_20_20) = all_42_3_46 & boole_POSet(all_42_3_46) = all_42_2_45 & powerset(all_42_1_44) = all_42_0_43 & the_carrier(all_42_2_45) = all_42_1_44 & the_carrier(all_0_20_20) = all_42_4_47 & ( ~ element(all_0_18_18, all_42_4_47) | element(all_0_17_17, all_42_0_43))
% 11.86/3.24  |
% 11.86/3.24  | Applying alpha-rule on (263) yields:
% 11.86/3.24  | (264) boole_POSet(all_42_3_46) = all_42_2_45
% 11.86/3.24  | (265) powerset(all_42_1_44) = all_42_0_43
% 11.86/3.24  | (266) the_carrier(all_0_20_20) = all_42_4_47
% 11.86/3.24  | (267) cast_as_carrier_subset(all_0_20_20) = all_42_3_46
% 11.86/3.24  | (268) the_carrier(all_42_2_45) = all_42_1_44
% 11.86/3.24  | (269)  ~ element(all_0_18_18, all_42_4_47) | element(all_0_17_17, all_42_0_43)
% 11.86/3.24  |
% 11.86/3.24  | Instantiating formula (72) with all_0_20_20, all_42_4_47, all_0_19_19 and discharging atoms the_carrier(all_0_20_20) = all_42_4_47, the_carrier(all_0_20_20) = all_0_19_19, yields:
% 11.86/3.24  | (270) all_42_4_47 = all_0_19_19
% 11.86/3.24  |
% 11.86/3.24  | From (270) and (266) follows:
% 11.86/3.24  | (29) the_carrier(all_0_20_20) = all_0_19_19
% 11.86/3.24  |
% 11.86/3.24  +-Applying beta-rule and splitting (269), into two cases.
% 11.86/3.24  |-Branch one:
% 11.86/3.24  | (272)  ~ element(all_0_18_18, all_42_4_47)
% 11.86/3.24  |
% 11.86/3.24  	| From (270) and (272) follows:
% 11.86/3.24  	| (273)  ~ element(all_0_18_18, all_0_19_19)
% 11.86/3.24  	|
% 11.86/3.24  	| Using (156) and (273) yields:
% 11.86/3.24  	| (274) $false
% 11.86/3.24  	|
% 11.86/3.24  	|-The branch is then unsatisfiable
% 11.86/3.24  |-Branch two:
% 11.86/3.24  | (275) element(all_0_18_18, all_42_4_47)
% 11.86/3.24  | (276) element(all_0_17_17, all_42_0_43)
% 11.86/3.24  |
% 11.86/3.24  	| From (270) and (275) follows:
% 11.86/3.24  	| (156) element(all_0_18_18, all_0_19_19)
% 11.86/3.24  	|
% 11.86/3.24  	| Instantiating formula (114) with all_42_3_46, all_0_20_20 and discharging atoms cast_as_carrier_subset(all_0_20_20) = all_42_3_46, one_sorted_str(all_0_20_20), yields:
% 11.86/3.24  	| (278)  ? [v0] :  ? [v1] : (powerset(v0) = v1 & the_carrier(all_0_20_20) = v0 & element(all_42_3_46, v1))
% 11.86/3.24  	|
% 11.86/3.24  	| Instantiating (278) with all_81_0_64, all_81_1_65 yields:
% 11.86/3.24  	| (279) powerset(all_81_1_65) = all_81_0_64 & the_carrier(all_0_20_20) = all_81_1_65 & element(all_42_3_46, all_81_0_64)
% 11.86/3.24  	|
% 11.86/3.24  	| Applying alpha-rule on (279) yields:
% 11.86/3.24  	| (280) powerset(all_81_1_65) = all_81_0_64
% 11.86/3.24  	| (281) the_carrier(all_0_20_20) = all_81_1_65
% 11.86/3.24  	| (282) element(all_42_3_46, all_81_0_64)
% 11.86/3.24  	|
% 11.86/3.24  	| Instantiating formula (72) with all_0_20_20, all_81_1_65, all_0_19_19 and discharging atoms the_carrier(all_0_20_20) = all_81_1_65, the_carrier(all_0_20_20) = all_0_19_19, yields:
% 11.86/3.24  	| (283) all_81_1_65 = all_0_19_19
% 11.86/3.24  	|
% 11.86/3.24  	| From (283) and (281) follows:
% 11.86/3.24  	| (29) the_carrier(all_0_20_20) = all_0_19_19
% 11.86/3.24  	|
% 11.86/3.24  	+-Applying beta-rule and splitting (138), into two cases.
% 11.86/3.24  	|-Branch one:
% 11.86/3.24  	| (285) point_neighbourhood(all_0_16_16, all_0_20_20, all_0_18_18) &  ~ in(all_0_16_16, all_0_17_17)
% 11.86/3.24  	|
% 11.86/3.24  		| Applying alpha-rule on (285) yields:
% 11.86/3.24  		| (286) point_neighbourhood(all_0_16_16, all_0_20_20, all_0_18_18)
% 11.86/3.24  		| (287)  ~ in(all_0_16_16, all_0_17_17)
% 11.86/3.24  		|
% 11.86/3.24  		| Instantiating formula (199) with all_0_17_17, all_0_18_18, all_0_20_20, all_0_16_16 and discharging atoms a_2_0_yellow19(all_0_20_20, all_0_18_18) = all_0_17_17, point_neighbourhood(all_0_16_16, all_0_20_20, all_0_18_18), top_str(all_0_20_20), topological_space(all_0_20_20),  ~ empty_carrier(all_0_20_20),  ~ in(all_0_16_16, all_0_17_17), yields:
% 11.86/3.24  		| (288)  ? [v0] : (the_carrier(all_0_20_20) = v0 &  ~ element(all_0_18_18, v0))
% 11.86/3.24  		|
% 11.86/3.24  		| Instantiating (288) with all_143_0_88 yields:
% 11.86/3.24  		| (289) the_carrier(all_0_20_20) = all_143_0_88 &  ~ element(all_0_18_18, all_143_0_88)
% 11.86/3.24  		|
% 11.86/3.24  		| Applying alpha-rule on (289) yields:
% 11.86/3.24  		| (290) the_carrier(all_0_20_20) = all_143_0_88
% 11.86/3.24  		| (291)  ~ element(all_0_18_18, all_143_0_88)
% 11.86/3.24  		|
% 11.86/3.24  		| Instantiating formula (72) with all_0_20_20, all_143_0_88, all_0_19_19 and discharging atoms the_carrier(all_0_20_20) = all_143_0_88, the_carrier(all_0_20_20) = all_0_19_19, yields:
% 11.86/3.24  		| (292) all_143_0_88 = all_0_19_19
% 11.86/3.24  		|
% 11.86/3.24  		| From (292) and (291) follows:
% 11.86/3.24  		| (273)  ~ element(all_0_18_18, all_0_19_19)
% 11.86/3.24  		|
% 11.86/3.24  		| Using (156) and (273) yields:
% 11.86/3.24  		| (274) $false
% 11.86/3.24  		|
% 11.86/3.24  		|-The branch is then unsatisfiable
% 11.86/3.24  	|-Branch two:
% 11.86/3.24  	| (295) in(all_0_16_16, all_0_17_17) &  ~ point_neighbourhood(all_0_16_16, all_0_20_20, all_0_18_18)
% 11.86/3.24  	|
% 11.86/3.24  		| Applying alpha-rule on (295) yields:
% 11.86/3.24  		| (296) in(all_0_16_16, all_0_17_17)
% 11.86/3.24  		| (297)  ~ point_neighbourhood(all_0_16_16, all_0_20_20, all_0_18_18)
% 11.86/3.24  		|
% 11.86/3.24  		| Instantiating formula (145) with all_0_17_17, all_0_18_18, all_0_20_20, all_0_16_16 and discharging atoms a_2_0_yellow19(all_0_20_20, all_0_18_18) = all_0_17_17, top_str(all_0_20_20), topological_space(all_0_20_20), in(all_0_16_16, all_0_17_17),  ~ empty_carrier(all_0_20_20), yields:
% 11.86/3.24  		| (298)  ? [v0] : ((v0 = all_0_16_16 & point_neighbourhood(all_0_16_16, all_0_20_20, all_0_18_18)) | (the_carrier(all_0_20_20) = v0 &  ~ element(all_0_18_18, v0)))
% 11.86/3.24  		|
% 11.86/3.24  		| Instantiating (298) with all_147_0_103 yields:
% 11.86/3.24  		| (299) (all_147_0_103 = all_0_16_16 & point_neighbourhood(all_0_16_16, all_0_20_20, all_0_18_18)) | (the_carrier(all_0_20_20) = all_147_0_103 &  ~ element(all_0_18_18, all_147_0_103))
% 11.86/3.24  		|
% 11.86/3.24  		+-Applying beta-rule and splitting (299), into two cases.
% 11.86/3.24  		|-Branch one:
% 11.86/3.24  		| (300) all_147_0_103 = all_0_16_16 & point_neighbourhood(all_0_16_16, all_0_20_20, all_0_18_18)
% 11.86/3.24  		|
% 11.86/3.24  			| Applying alpha-rule on (300) yields:
% 11.86/3.24  			| (301) all_147_0_103 = all_0_16_16
% 11.86/3.24  			| (286) point_neighbourhood(all_0_16_16, all_0_20_20, all_0_18_18)
% 11.86/3.24  			|
% 11.86/3.24  			| Using (286) and (297) yields:
% 11.86/3.24  			| (274) $false
% 11.86/3.24  			|
% 11.86/3.24  			|-The branch is then unsatisfiable
% 11.86/3.24  		|-Branch two:
% 11.86/3.24  		| (304) the_carrier(all_0_20_20) = all_147_0_103 &  ~ element(all_0_18_18, all_147_0_103)
% 11.86/3.25  		|
% 11.86/3.25  			| Applying alpha-rule on (304) yields:
% 11.86/3.25  			| (305) the_carrier(all_0_20_20) = all_147_0_103
% 11.86/3.25  			| (306)  ~ element(all_0_18_18, all_147_0_103)
% 11.86/3.25  			|
% 11.86/3.25  			| Instantiating formula (72) with all_0_20_20, all_147_0_103, all_0_19_19 and discharging atoms the_carrier(all_0_20_20) = all_147_0_103, the_carrier(all_0_20_20) = all_0_19_19, yields:
% 11.86/3.25  			| (307) all_147_0_103 = all_0_19_19
% 11.86/3.25  			|
% 11.86/3.25  			| From (307) and (306) follows:
% 11.86/3.25  			| (273)  ~ element(all_0_18_18, all_0_19_19)
% 11.86/3.25  			|
% 11.86/3.25  			| Using (156) and (273) yields:
% 11.86/3.25  			| (274) $false
% 11.86/3.25  			|
% 11.86/3.25  			|-The branch is then unsatisfiable
% 11.86/3.25  % SZS output end Proof for theBenchmark
% 11.86/3.25  
% 11.86/3.25  2624ms
%------------------------------------------------------------------------------