%------------------------------------------------------------------------------
% File     : ITP077+4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : topology.ax [Gau19]
%          : HL4077+4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  119 (  54 unt;   0 def)
%            Number of atoms       :  283 (  85 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  170 (   6   ~;   3   |;  50   &)
%                                         (  31 <=>;  80  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :   15 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :   76 (  76 usr;  39 con; 0-3 aty)
%            Number of variables   :  422 ( 413   !;   9   ?)
% SPC      : FOF_SAT_RFO_SEQ

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eboolext,axiom,
    ! [V0_2E0,V1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
      <=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
     => s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ) ).

fof(reserved_2Eho_2Etruth,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).

fof(reserved_2Eho_2Enotfalse,axiom,
    ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ).

fof(reserved_2Eho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0] :
      ( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
      | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).

fof(reserved_2Eho_2Ei__thm,axiom,
    ! [A_27a,V0x_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ).

fof(reserved_2Eho_2Ek__thm,axiom,
    ! [A_27a,A_27b,V0x_2E0,V1y_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ).

fof(reserved_2Eho_2Es__thm,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ).

fof(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
        & p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
        | p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_7E,axiom,
    ! [V0_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
    <=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ).

fof(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
       => p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a,V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0))))
    <=> s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ) ).

fof(reserved_2Equant_2E_21,axiom,
    ! [A_27a,V0f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
    <=> ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).

fof(reserved_2Equant_2E_3F,axiom,
    ! [A_27a,V0f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
    <=> ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).

fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
        & p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
        | p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0] :
      ( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ) ).

fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
       => p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] :
      ( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) ) ).

fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Epred__set_2EBIGINTER_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGINTER_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Etopology_2Eclosed_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed_2E1(s(tyop_2Etopology_2Etopology(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Ebool),c_2Etopology_2Eclosed_2E0),s(tyop_2Etopology_2Etopology(A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Etopology_2Eistopology_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Etopology_2Eistopology_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Etopology_2Eistopology_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Etopology_2Eopen__in_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Etopology_2Eopen__in_2E1(s(tyop_2Etopology_2Etopology(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Etopology_2Eopen__in_2E0),s(tyop_2Etopology_2Etopology(A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Etopology_2Eopen_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen_2E1(s(tyop_2Etopology_2Etopology(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Ebool),c_2Etopology_2Eopen_2E0),s(tyop_2Etopology_2Etopology(A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Etopology_2Etopology_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Etopology_2Etopology(A_27a),c_2Etopology_2Etopology_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Etopology_2Etopology(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Etopology_2Etopology(A_27a)),c_2Etopology_2Etopology_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Etopology_2Etopspace_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Etopspace_2E1(s(tyop_2Etopology_2Etopology(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Etopology_2Etopspace_2E0),s(tyop_2Etopology_2Etopology(A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Etopology_2Ehull_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Etopology_2Ehull_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).

fof(arityeq2_2Ec_2Etopology_2Eopen__in_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Etopology_2Eopen__in_2E0),s(tyop_2Etopology_2Etopology(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Etopology_2Etopology_28A_27a_29,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0))) ).

fof(arityeq2_2Ec_2Etopology_2Eclosed__in_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Etopology_2Eclosed__in_2E0),s(tyop_2Etopology_2Etopology(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EDIFF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) ).

fof(arityeq2_2Ec_2Etopology_2Eneigh_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Etopology_2Eneigh_2E2(s(tyop_2Etopology_2Etopology(A_27a),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Emin_2Ebool)),c_2Etopology_2Eneigh_2E0),s(tyop_2Etopology_2Etopology(A_27a),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),X1_2E0))) ).

fof(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2ECOMPL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq3_2Ec_2Etopology_2Elimpt_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Etopology_2Elimpt_2E3(s(tyop_2Etopology_2Etopology(A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Etopology_2Elimpt_2E0),s(tyop_2Etopology_2Etopology(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) ).

fof(thm_2Etopology_2Eistopology,axiom,
    ! [A_27a,V0L_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eistopology_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0L_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0L_2E0))))
        & ! [V1s_2E0,V2t_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0L_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0L_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0L_2E0)))) )
        & ! [V3k_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3k_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0L_2E0))))
           => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3k_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0L_2E0)))) ) ) ) ).

fof(thm_2Etopology_2Etopology__TY__DEF,axiom,
    ! [A_27a] :
    ? [V0rep_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Etopology_2Eistopology_2E0),s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V0rep_2E0)))) ).

fof(thm_2Etopology_2Etopology__tybij,axiom,
    ! [A_27a] :
      ( ! [V0a_2E0] : s(tyop_2Etopology_2Etopology(A_27a),c_2Etopology_2Etopology_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Etopology_2Eopen__in_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0a_2E0))))) = s(tyop_2Etopology_2Etopology(A_27a),V0a_2E0)
      & ! [V1r_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eistopology_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1r_2E0))))
        <=> s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Etopology_2Eopen__in_2E1(s(tyop_2Etopology_2Etopology(A_27a),c_2Etopology_2Etopology_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1r_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1r_2E0) ) ) ).

fof(thm_2Etopology_2Eopen__DEF,axiom,
    ! [A_27a,V0s_2E0] : s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0s_2E0))) = s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) ).

fof(thm_2Etopology_2Etopspace,axiom,
    ! [A_27a,F0_2E0] :
      ( ! [V0top_2E0,V1s_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))
     => ! [V0top_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Etopspace_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0))))))) ) ).

fof(thm_2Etopology_2Eneigh,axiom,
    ! [A_27a,V0top_2E0,V1N_2E0,V2x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eneigh_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1N_2E0),s(A_27a,V2x_2E0))))))
    <=> ? [V3P_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1N_2E0))))
          & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V2x_2E0)))) ) ) ).

fof(thm_2Etopology_2Eclosed__in,axiom,
    ! [A_27a,V0top_2E0,V1s_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Etopspace_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Etopspace_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) ) ) ).

fof(thm_2Etopology_2Eclosed__DEF,axiom,
    ! [A_27a,V0s_2E0] : s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0s_2E0))) = s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) ).

fof(thm_2Etopology_2Elimpt,axiom,
    ! [A_27a,V0top_2E0,V1x_2E0,V2S_27_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Elimpt_2E3(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2S_27_2E0))))
    <=> ! [V3N_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eneigh_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3N_2E0),s(A_27a,V1x_2E0))))))
         => ? [V4y_2E0] :
              ( s(A_27a,V1x_2E0) != s(A_27a,V4y_2E0)
              & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2S_27_2E0),s(A_27a,V4y_2E0))))
              & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3N_2E0),s(A_27a,V4y_2E0)))) ) ) ) ).

fof(thm_2Etopology_2Ehull,axiom,
    ! [A_27a,F1_2E0,F0_2E0] :
      ( ! [V0P_2E0,V2t_2E0,V1s_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
        <=> ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) ) )
     => ( ! [V0P_2E0,V1s_2E0,V2t_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))
       => ! [V0P_2E0,V1s_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) ) ) ).

fof(thm_2Etopology_2EISTOPOLOGY__OPEN__IN,axiom,
    ! [A_27a,V0top_2E0] : p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eistopology_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Etopology_2Eopen__in_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0)))))) ).

fof(thm_2Etopology_2ETOPOLOGY__EQ,axiom,
    ! [A_27a,V0top1_2E0,V1top2_2E0] :
      ( s(tyop_2Etopology_2Etopology(A_27a),V0top1_2E0) = s(tyop_2Etopology_2Etopology(A_27a),V1top2_2E0)
    <=> ! [V2s_2E0] : s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))) = s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V1top2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))) ) ).

fof(thm_2Etopology_2Eopen__topspace,axiom,
    ! [A_27a,V0top_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0))))
     => s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Etopspace_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) ) ).

fof(thm_2Etopology_2EOPEN__IN__CLAUSES,axiom,
    ! [A_27a,V0top_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))
      & ! [V1s_2E0,V2t_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) )
      & ! [V3k_2E0] :
          ( ! [V4s_2E0] :
              ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3k_2E0))))
             => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3k_2E0)))))) ) ) ).

fof(thm_2Etopology_2EOPEN__IN__SUBSET,axiom,
    ! [A_27a,V0top_2E0,V1s_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Etopspace_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0)))))) ) ).

fof(thm_2Etopology_2EOPEN__IN__EMPTY,axiom,
    ! [A_27a,V0top_2E0] : p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) ).

fof(thm_2Etopology_2EOPEN__IN__INTER,axiom,
    ! [A_27a,V0top_2E0,V1s_2E0,V2t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) ) ).

fof(thm_2Etopology_2EOPEN__IN__BIGUNION,axiom,
    ! [A_27a,V0top_2E0,V1k_2E0] :
      ( ! [V2s_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1k_2E0))))
         => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1k_2E0)))))) ) ).

fof(thm_2Etopology_2EBIGUNION__2,axiom,
    ! [A_27a,V0s_2E0,V1t_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) ).

fof(thm_2Etopology_2EOPEN__IN__UNION,axiom,
    ! [A_27a,V0top_2E0,V1s_2E0,V2t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) ) ).

fof(thm_2Etopology_2EOPEN__IN__TOPSPACE,axiom,
    ! [A_27a,V0top_2E0] : p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Etopspace_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0)))))) ).

fof(thm_2Etopology_2EOPEN__IN__BIGINTER,axiom,
    ! [A_27a,V0top_2E0,V1s_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))))
        & s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0) != s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)
        & ! [V2t_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))))
           => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) ) )
     => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))))) ) ).

fof(thm_2Etopology_2EOPEN__IN__SUBOPEN,axiom,
    ! [A_27a,V0top_2E0,V1s_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
    <=> ! [V2x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
         => ? [V3t_2E0] :
              ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) ) ) ) ).

fof(thm_2Etopology_2EOPEN__OWN__NEIGH,axiom,
    ! [A_27a,V0S_27_2E0,V1top_2E0,V2x_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V1top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0))))
        & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0),s(A_27a,V2x_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eneigh_2E2(s(tyop_2Etopology_2Etopology(A_27a),V1top_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0),s(A_27a,V2x_2E0)))))) ) ).

fof(thm_2Etopology_2EOPEN__UNOPEN,axiom,
    ! [A_27a,F1_2E0,F0_2E0] :
      ( ! [V1top_2E0,V2P_2E0,V0S_27_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Etopology_2Etopology(A_27a),V1top_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0))))
        <=> ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V1top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0)))) ) )
     => ( ! [V1top_2E0,V0S_27_2E0,V2P_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Etopology_2Etopology(A_27a),V1top_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Etopology_2Etopology(A_27a),V1top_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0)))))
       => ! [V0S_27_2E0,V1top_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V1top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0))))
          <=> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etopology_2Etopology(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Etopology_2Etopology(A_27a),V1top_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0) ) ) ) ).

fof(thm_2Etopology_2EOPEN__SUBOPEN,axiom,
    ! [A_27a,V0S_27_2E0,V1top_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V1top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0))))
    <=> ! [V2x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0),s(A_27a,V2x_2E0))))
         => ? [V3P_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V2x_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V1top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0)))) ) ) ) ).

fof(thm_2Etopology_2EOPEN__NEIGH,axiom,
    ! [A_27a,V0S_27_2E0,V1top_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V1top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0))))
    <=> ! [V2x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0),s(A_27a,V2x_2E0))))
         => ? [V3N_2E0] :
              ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eneigh_2E2(s(tyop_2Etopology_2Etopology(A_27a),V1top_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3N_2E0),s(A_27a,V2x_2E0))))))
              & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3N_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_27_2E0)))) ) ) ) ).

fof(thm_2Etopology_2Eclosed__topspace,axiom,
    ! [A_27a,V0top_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0))))
     => s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Etopspace_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) ) ).

fof(thm_2Etopology_2ECLOSED__IN__OPEN__IN__COMPL,axiom,
    ! [A_27a,V0top_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0))))
     => ! [V1s_2E0] : s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) ) ).

fof(thm_2Etopology_2ECLOSED__IN__SUBSET,axiom,
    ! [A_27a,V0top_2E0,V1s_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Etopspace_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0)))))) ) ).

fof(thm_2Etopology_2ECLOSED__IN__EMPTY,axiom,
    ! [A_27a,V0top_2E0] : p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) ).

fof(thm_2Etopology_2ECLOSED__IN__TOPSPACE,axiom,
    ! [A_27a,V0top_2E0] : p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Etopspace_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0)))))) ).

fof(thm_2Etopology_2ECLOSED__IN__UNION,axiom,
    ! [A_27a,V0top_2E0,V1s_2E0,V2t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) ) ).

fof(thm_2Etopology_2ECLOSED__IN__BIGINTER,axiom,
    ! [A_27a,V0top_2E0,V1k_2E0] :
      ( ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1k_2E0) != s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)
        & ! [V2s_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1k_2E0))))
           => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) ) )
     => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1k_2E0)))))) ) ).

fof(thm_2Etopology_2EBIGINTER__2,axiom,
    ! [A_27a,V0P_2E0,V1Q_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))) ).

fof(thm_2Etopology_2ECLOSED__IN__INTER,axiom,
    ! [A_27a,V0top_2E0,V1s_2E0,V2t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) ) ).

fof(thm_2Etopology_2EOPEN__IN__CLOSED__IN__EQ,axiom,
    ! [A_27a,V0top_2E0,V1s_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Etopspace_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Etopspace_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) ) ) ).

fof(thm_2Etopology_2EOPEN__IN__CLOSED__IN,axiom,
    ! [A_27a,V0top_2E0,V1s_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Etopspace_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0))))))
     => s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Etopspace_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) ) ).

fof(thm_2Etopology_2EOPEN__IN__DIFF,axiom,
    ! [A_27a,V0top_2E0,V1s_2E0,V2t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) ) ).

fof(thm_2Etopology_2ECLOSED__IN__DIFF,axiom,
    ! [A_27a,V0top_2E0,V1s_2E0,V2t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eopen__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) ) ).

fof(thm_2Etopology_2ECLOSED__IN__BIGUNION,axiom,
    ! [A_27a,V0top_2E0,V1s_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))))
        & ! [V2t_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))))
           => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) ) )
     => p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))))) ) ).

fof(thm_2Etopology_2ECLOSED__LIMPT,axiom,
    ! [A_27a,V0top_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed_2E1(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0))))
     => ! [V1S_27_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Eclosed__in_2E2(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1S_27_2E0))))
        <=> ! [V2x_2E0] :
              ( p(s(tyop_2Emin_2Ebool,c_2Etopology_2Elimpt_2E3(s(tyop_2Etopology_2Etopology(A_27a),V0top_2E0),s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1S_27_2E0))))
             => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1S_27_2E0),s(A_27a,V2x_2E0)))) ) ) ) ).

fof(thm_2Etopology_2EHULL__P,axiom,
    ! [A_27a,V0P_2E0,V1s_2E0] :
      ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
     => s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) ) ).

fof(thm_2Etopology_2EP__HULL,axiom,
    ! [A_27a,V0P_2E0,V1s_2E0] :
      ( ! [V2f_2E0] :
          ( ! [V3s_2E0] :
              ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2f_2E0))))
             => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2f_2E0)))))) )
     => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) ) ).

fof(thm_2Etopology_2EHULL__EQ,axiom,
    ! [A_27a,V0P_2E0,V1s_2E0] :
      ( ! [V2f_2E0] :
          ( ! [V3s_2E0] :
              ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2f_2E0))))
             => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2f_2E0)))))) )
     => ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)
      <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) ) ) ).

fof(thm_2Etopology_2EHULL__HULL,axiom,
    ! [A_27a,V0P_2E0,V1s_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) ).

fof(thm_2Etopology_2EHULL__SUBSET,axiom,
    ! [A_27a,V0P_2E0,V1s_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) ).

fof(thm_2Etopology_2EHULL__MONO,axiom,
    ! [A_27a,V0P_2E0,V1s_2E0,V2t_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) ) ).

fof(thm_2Etopology_2EHULL__ANTIMONO,axiom,
    ! [A_27a,V0P_2E0,V1Q_2E0,V2s_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1Q_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) ) ).

fof(thm_2Etopology_2EHULL__MINIMAL,axiom,
    ! [A_27a,V0P_2E0,V1s_2E0,V2t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))
        & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) ) ).

fof(thm_2Etopology_2ESUBSET__HULL,axiom,
    ! [A_27a,V0P_2E0,V1s_2E0,V2t_2E0] :
      ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))
     => s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))) ) ).

fof(thm_2Etopology_2EHULL__UNIQUE,axiom,
    ! [A_27a,V0P_2E0,V1s_2E0,V2t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))
        & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))
        & ! [V3t_27_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_27_2E0))))
              & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_27_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_27_2E0)))) ) )
     => s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0) ) ).

fof(thm_2Etopology_2EHULL__UNION__SUBSET,axiom,
    ! [A_27a,V0P_2E0,V1s_2E0,V2t_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))))) ).

fof(thm_2Etopology_2EHULL__UNION,axiom,
    ! [A_27a,V0P_2E0,V1s_2E0,V2t_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))))) ).

fof(thm_2Etopology_2EHULL__UNION__LEFT,axiom,
    ! [A_27a,V0P_2E0,V1s_2E0,V2t_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))) ).

fof(thm_2Etopology_2EHULL__UNION__RIGHT,axiom,
    ! [A_27a,V0P_2E0,V1s_2E0,V2t_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))))) ).

fof(thm_2Etopology_2EHULL__REDUNDANT__EQ,axiom,
    ! [A_27a,V0P_2E0,V1a_2E0,V2s_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))
    <=> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))) ) ).

fof(thm_2Etopology_2EHULL__REDUNDANT,axiom,
    ! [A_27a,V0P_2E0,V1a_2E0,V2s_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))
     => s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))) ) ).

fof(thm_2Etopology_2EHULL__INDUCT,axiom,
    ! [A_27a,F0_2E0] :
      ( ! [V1p_2E0,V4x_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0))),s(A_27a,V4x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0),s(A_27a,V4x_2E0)))))
     => ! [V0P_2E0,V1p_2E0,V2s_2E0] :
          ( ( ! [V3x_2E0] :
                ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))
               => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0),s(A_27a,V3x_2E0)))) )
            & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0)))))))) )
         => ! [V5x_2E0] :
              ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))
             => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0),s(A_27a,V5x_2E0)))) ) ) ) ).

fof(thm_2Etopology_2EHULL__INC,axiom,
    ! [A_27a,V0P_2E0,V1s_2E0,V2x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) ) ).

fof(thm_2Etopology_2EHULL__IMAGE__SUBSET,axiom,
    ! [A_27a,V0P_2E0,V1f_2E0,V2s_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))
        & ! [V3s_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))))
           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))))) ) )
     => p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))))) ) ).

fof(thm_2Etopology_2EHULL__IMAGE__GALOIS,axiom,
    ! [A_27a,V0P_2E0,V1f_2E0,V2g_2E0,V3s_2E0] :
      ( ( ! [V4s_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0))))))
        & ! [V5s_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5s_2E0))))
           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5s_2E0)))))) )
        & ! [V6s_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6s_2E0))))
           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6s_2E0)))))) )
        & ! [V7s_2E0,V8t_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V7s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V8t_2E0))))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V7s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V8t_2E0))) )
     => s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))))) ) ).

fof(thm_2Etopology_2EHULL__IMAGE,axiom,
    ! [A_27a,V0P_2E0,V1f_2E0,V2s_2E0] :
      ( ( ! [V3s_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))))))
        & ! [V4s_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0)))
        & ! [V5x_2E0,V6y_2E0] :
            ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V5x_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V6y_2E0)))
           => s(A_27a,V5x_2E0) = s(A_27a,V6y_2E0) )
        & ! [V7y_2E0] :
          ? [V8x_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V8x_2E0))) = s(A_27a,V7y_2E0) )
     => s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) ) ).

fof(thm_2Etopology_2EIS__HULL,axiom,
    ! [A_27a,V0P_2E0,V1s_2E0] :
      ( ! [V2f_2E0] :
          ( ! [V3s_2E0] :
              ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2f_2E0))))
             => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2f_2E0)))))) )
     => ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
      <=> ? [V4t_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4t_2E0))) ) ) ).

fof(thm_2Etopology_2EHULLS__EQ,axiom,
    ! [A_27a,V0P_2E0,V1s_2E0,V2t_2E0] :
      ( ( ! [V3f_2E0] :
            ( ! [V4s_2E0] :
                ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3f_2E0))))
               => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3f_2E0)))))) )
        & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) )
     => s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))) ) ).

fof(thm_2Etopology_2EHULL__P__AND__Q,axiom,
    ! [A_27a,F0_2E0] :
      ( ! [V1P_2E0,V2Q_2E0,V8x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2Q_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V8x_2E0))))
        <=> ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V8x_2E0))))
            & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V8x_2E0)))) ) )
     => ! [V0s_2E0,V1P_2E0,V2Q_2E0] :
          ( ( ! [V3f_2E0] :
                ( ! [V4s_2E0] :
                    ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3f_2E0))))
                   => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0)))) )
               => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3f_2E0)))))) )
            & ! [V5f_2E0] :
                ( ! [V6s_2E0] :
                    ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V5f_2E0))))
                   => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6s_2E0)))) )
               => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V5f_2E0)))))) )
            & ! [V7s_2E0] :
                ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V7s_2E0))))
               => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V7s_2E0)))))) ) )
         => s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2Q_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Etopology_2Ehull_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) ) ) ).

fof(reserved_2Eho_2Eeq__ext,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
      ( ! [V2x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))
     => s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) ) ).

%------------------------------------------------------------------------------