SET007 Axioms: SET007+440.ax


%------------------------------------------------------------------------------
% File     : SET007+440 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Continuous, Stable, and Linear Maps of Coherence Spaces
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : cohsp_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  194 (  25 unit)
%            Number of atoms       : 1416 ( 111 equality)
%            Maximal formula depth :   19 (   8 average)
%            Number of connectives : 1465 ( 243 ~  ;   6  |; 814  &)
%                                         (  57 <=>; 345 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   32 (   1 propositional; 0-3 arity)
%            Number of functors    :   51 (   5 constant; 0-4 arity)
%            Number of variables   :  557 (   0 singleton; 517 !;  40 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_cohsp_1,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v1_classes1(A)
      & v1_finset_1(A)
      & v1_coh_sp(A) ) )).

fof(fc1_cohsp_1,axiom,
    ( ~ v1_xboole_0(k1_tarski(k1_xboole_0))
    & v1_classes1(k1_tarski(k1_xboole_0))
    & v1_finset_1(k1_tarski(k1_xboole_0))
    & v1_coh_sp(k1_tarski(k1_xboole_0)) )).

fof(fc2_cohsp_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(k1_zfmisc_1(A))
      & v1_finsub_1(k1_zfmisc_1(A))
      & v3_finsub_1(k1_zfmisc_1(A))
      & v4_finsub_1(k1_zfmisc_1(A))
      & v1_classes1(k1_zfmisc_1(A))
      & v1_coh_sp(k1_zfmisc_1(A)) ) )).

fof(fc3_cohsp_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(k1_cohsp_1(A))
      & v1_classes1(k1_cohsp_1(A))
      & v1_coh_sp(k1_cohsp_1(A)) ) )).

fof(fc4_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A) )
     => ( ~ v1_xboole_0(k2_cohsp_1(A))
        & v1_classes1(k2_cohsp_1(A)) ) ) )).

fof(rc2_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ? [B] :
          ( m1_subset_1(B,A)
          & v1_finset_1(B) ) ) )).

fof(cc1_cohsp_1,axiom,(
    ! [A] :
      ( v1_cohsp_1(A)
     => ~ v1_xboole_0(A) ) )).

fof(cc2_cohsp_1,axiom,(
    ! [A] :
      ( v2_cohsp_1(A)
     => ~ v1_xboole_0(A) ) )).

fof(rc3_cohsp_1,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_cohsp_1(A)
      & v2_cohsp_1(A) ) )).

fof(rc4_cohsp_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B)
          & v1_cohsp_1(B)
          & v2_cohsp_1(B) ) ) )).

fof(fc5_cohsp_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(k5_finsub_1(A))
      & v1_finsub_1(k5_finsub_1(A))
      & v3_finsub_1(k5_finsub_1(A))
      & v4_finsub_1(k5_finsub_1(A))
      & v1_cohsp_1(k5_finsub_1(A))
      & v2_cohsp_1(k5_finsub_1(A)) ) )).

fof(rc5_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finsub_1(B)
          & v3_finsub_1(B)
          & v4_finsub_1(B) ) ) )).

fof(cc3_cohsp_1,axiom,(
    ! [A] :
      ( v1_classes1(A)
     => v2_finsub_1(A) ) )).

fof(cc4_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ( ~ v1_xboole_0(A)
        & v2_finsub_1(A)
        & v1_classes1(A)
        & v1_coh_sp(A)
        & v3_cohsp_1(A) ) ) )).

fof(rc6_cohsp_1,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v2_finsub_1(A)
      & v1_classes1(A)
      & v1_coh_sp(A)
      & v3_cohsp_1(A) ) )).

fof(cc5_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_cohsp_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v6_cohsp_1(A) ) ) )).

fof(cc6_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v4_cohsp_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_cohsp_1(A) ) ) )).

fof(rc7_cohsp_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A)
        & ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ? [C] :
          ( m1_relset_1(C,A,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v4_cohsp_1(C)
          & v5_cohsp_1(C)
          & v6_cohsp_1(C)
          & v7_cohsp_1(C) ) ) )).

fof(rc8_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ? [B] :
          ( m1_pboole(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v4_cohsp_1(B)
          & v5_cohsp_1(B)
          & v6_cohsp_1(B)
          & v7_cohsp_1(B) ) ) )).

fof(cc7_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v8_cohsp_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_cohsp_1(A)
        & v6_cohsp_1(A) ) ) )).

fof(cc8_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v9_cohsp_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v7_cohsp_1(A)
        & v8_cohsp_1(A) ) ) )).

fof(cc9_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v10_cohsp_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v4_cohsp_1(A)
        & v5_cohsp_1(A)
        & v6_cohsp_1(A)
        & v9_cohsp_1(A) ) ) )).

fof(cc10_cohsp_1,axiom,(
    ! [A] :
      ( v3_cohsp_1(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ( v5_cohsp_1(B)
           => v8_cohsp_1(B) ) ) ) )).

fof(cc11_cohsp_1,axiom,(
    ! [A] :
      ( v2_finsub_1(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ( ( v7_cohsp_1(B)
              & v8_cohsp_1(B) )
           => v9_cohsp_1(B) ) ) ) )).

fof(cc12_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v4_cohsp_1(A)
        & v9_cohsp_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v4_cohsp_1(A)
        & v5_cohsp_1(A)
        & v6_cohsp_1(A)
        & v7_cohsp_1(A)
        & v8_cohsp_1(A)
        & v9_cohsp_1(A)
        & v10_cohsp_1(A) ) ) )).

fof(rc9_cohsp_1,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v4_cohsp_1(A)
      & v5_cohsp_1(A)
      & v6_cohsp_1(A)
      & v7_cohsp_1(A)
      & v8_cohsp_1(A)
      & v9_cohsp_1(A)
      & v10_cohsp_1(A) ) )).

fof(rc10_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ? [B] :
          ( m1_pboole(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v4_cohsp_1(B)
          & v5_cohsp_1(B)
          & v6_cohsp_1(B)
          & v7_cohsp_1(B)
          & v8_cohsp_1(B)
          & v9_cohsp_1(B)
          & v10_cohsp_1(B) ) ) )).

fof(rc11_cohsp_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A)
        & ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ? [C] :
          ( m1_relset_1(C,B,A)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,B,A)
          & v4_cohsp_1(C)
          & v5_cohsp_1(C)
          & v6_cohsp_1(C)
          & v7_cohsp_1(C)
          & v8_cohsp_1(C)
          & v9_cohsp_1(C)
          & v10_cohsp_1(C) ) ) )).

fof(fc6_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v8_cohsp_1(A) )
     => v3_cohsp_1(k1_relat_1(A)) ) )).

fof(fc7_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v9_cohsp_1(A) )
     => ( v2_finsub_1(k1_relat_1(A))
        & v3_cohsp_1(k1_relat_1(A)) ) ) )).

fof(fc8_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => v1_relat_1(k5_cohsp_1(A)) ) )).

fof(fc9_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => v1_relat_1(k7_cohsp_1(A)) ) )).

fof(fc10_cohsp_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A)
        & ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ( ~ v1_xboole_0(k9_cohsp_1(A,B))
        & v2_finsub_1(k9_cohsp_1(A,B))
        & v1_classes1(k9_cohsp_1(A,B))
        & v1_coh_sp(k9_cohsp_1(A,B))
        & v3_cohsp_1(k9_cohsp_1(A,B)) ) ) )).

fof(fc11_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => v1_relat_1(k10_cohsp_1(A)) ) )).

fof(fc12_cohsp_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A)
        & ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ( ~ v1_xboole_0(k12_cohsp_1(A,B))
        & v2_finsub_1(k12_cohsp_1(A,B))
        & v1_classes1(k12_cohsp_1(A,B))
        & v1_coh_sp(k12_cohsp_1(A,B))
        & v3_cohsp_1(k12_cohsp_1(A,B)) ) ) )).

fof(fc13_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ( ~ v1_xboole_0(k13_cohsp_1(A))
        & v2_finsub_1(k13_cohsp_1(A))
        & v1_classes1(k13_cohsp_1(A))
        & v1_coh_sp(k13_cohsp_1(A))
        & v3_cohsp_1(k13_cohsp_1(A)) ) ) )).

fof(fc14_cohsp_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A)
        & ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ( ~ v1_xboole_0(k15_cohsp_1(A,B))
        & v2_finsub_1(k15_cohsp_1(A,B))
        & v1_classes1(k15_cohsp_1(A,B))
        & v1_coh_sp(k15_cohsp_1(A,B))
        & v3_cohsp_1(k15_cohsp_1(A,B)) ) ) )).

fof(fc15_cohsp_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A)
        & ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ( ~ v1_xboole_0(k16_cohsp_1(A,B))
        & v2_finsub_1(k16_cohsp_1(A,B))
        & v1_classes1(k16_cohsp_1(A,B))
        & v1_coh_sp(k16_cohsp_1(A,B))
        & v3_cohsp_1(k16_cohsp_1(A,B)) ) ) )).

fof(fc16_cohsp_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A)
        & ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ~ v1_xboole_0(k17_cohsp_1(A,B)) ) )).

fof(fc17_cohsp_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A)
        & ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ( ~ v1_xboole_0(k17_cohsp_1(A,B))
        & v2_finsub_1(k17_cohsp_1(A,B))
        & v1_classes1(k17_cohsp_1(A,B))
        & v1_coh_sp(k17_cohsp_1(A,B))
        & v3_cohsp_1(k17_cohsp_1(A,B)) ) ) )).

fof(d1_cohsp_1,axiom,(
    ! [A] :
      ( v1_coh_sp(A)
    <=> ! [B] :
          ( ! [C,D] :
              ( ( r2_hidden(C,B)
                & r2_hidden(D,B) )
             => r2_hidden(k2_xboole_0(C,D),A) )
         => r2_hidden(k3_tarski(B),A) ) ) )).

fof(d2_cohsp_1,axiom,(
    ! [A] : k1_cohsp_1(A) = k2_coh_sp(A,k6_partfun1(A)) )).

fof(d3_cohsp_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ( B = k2_cohsp_1(A)
      <=> ! [C] :
            ( r2_hidden(C,B)
          <=> ( r2_hidden(C,A)
              & v1_finset_1(C) ) ) ) ) )).

fof(t1_cohsp_1,axiom,(
    ! [A,B] :
      ( r2_hidden(B,k1_cohsp_1(A))
    <=> ~ ( B != k1_xboole_0
          & ! [C] :
              ~ ( B = k1_tarski(C)
                & r2_hidden(C,A) ) ) ) )).

fof(t2_cohsp_1,axiom,(
    ! [A] : k3_tarski(k1_cohsp_1(A)) = A )).

fof(t3_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_classes1(A)
        & v1_finset_1(A) )
     => k2_cohsp_1(A) = A ) )).

fof(t4_cohsp_1,axiom,(
    k1_coh_sp(k1_tarski(k1_xboole_0)) = k1_xboole_0 )).

fof(d4_cohsp_1,axiom,(
    ! [A] :
      ( v1_cohsp_1(A)
    <=> ! [B] :
          ( ( v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ? [C] :
              ( r1_tarski(k3_tarski(B),C)
              & r2_hidden(C,A) ) ) ) )).

fof(d5_cohsp_1,axiom,(
    ! [A] :
      ( v2_cohsp_1(A)
    <=> ! [B] :
          ( ( v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ? [C] :
              ( ! [D] :
                  ( r2_hidden(D,B)
                 => r1_tarski(C,D) )
              & r2_hidden(C,A) ) ) ) )).

fof(t5_cohsp_1,axiom,(
    ! [A] :
      ( v1_cohsp_1(A)
     => ! [B,C] :
          ~ ( r2_hidden(B,A)
            & r2_hidden(C,A)
            & ! [D] :
                ~ ( r1_tarski(k2_xboole_0(B,C),D)
                  & r2_hidden(D,A) ) ) ) )).

fof(t6_cohsp_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( ! [B,C] :
            ~ ( r2_hidden(B,A)
              & r2_hidden(C,A)
              & ! [D] :
                  ~ ( r1_tarski(k2_xboole_0(B,C),D)
                    & r2_hidden(D,A) ) )
       => v1_cohsp_1(A) ) ) )).

fof(t7_cohsp_1,axiom,(
    ! [A] :
      ( v2_cohsp_1(A)
     => ! [B,C] :
          ~ ( r2_hidden(B,A)
            & r2_hidden(C,A)
            & ! [D] :
                ~ ( r1_tarski(D,k3_xboole_0(B,C))
                  & r2_hidden(D,A) ) ) ) )).

fof(t8_cohsp_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( ! [B,C] :
            ~ ( r2_hidden(B,A)
              & r2_hidden(C,A)
              & ! [D] :
                  ~ ( r1_tarski(D,k3_xboole_0(B,C))
                    & r2_hidden(D,A) ) )
       => v2_cohsp_1(A) ) ) )).

fof(t9_cohsp_1,axiom,(
    ! [A] :
      ( v1_cohsp_1(k1_tarski(A))
      & v2_cohsp_1(k1_tarski(A)) ) )).

fof(t10_cohsp_1,axiom,(
    ! [A,B] : v1_cohsp_1(k1_enumset1(A,B,k2_xboole_0(A,B))) )).

fof(t11_cohsp_1,axiom,(
    ! [A,B] : v2_cohsp_1(k1_enumset1(A,B,k3_xboole_0(A,B))) )).

fof(t12_cohsp_1,axiom,(
    ! [A] :
      ( v1_cohsp_1(k5_finsub_1(A))
      & v2_cohsp_1(k5_finsub_1(A)) ) )).

fof(t13_cohsp_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ~ ( v1_cohsp_1(A)
            & r1_tarski(B,k3_tarski(A))
            & v1_finset_1(B)
            & ! [C] :
                ~ ( r2_hidden(C,A)
                  & r1_tarski(B,C) ) ) ) )).

fof(d6_cohsp_1,axiom,(
    $true )).

fof(d7_cohsp_1,axiom,(
    ! [A] :
      ( v3_cohsp_1(A)
    <=> ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_cohsp_1(B)
           => r2_hidden(k3_tarski(B),A) ) ) ) )).

fof(t14_cohsp_1,axiom,(
    $true )).

fof(t15_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( v1_cohsp_1(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => r2_hidden(k3_tarski(B),A) ) ) )).

fof(d8_cohsp_1,axiom,(
    ! [A,B] :
      ( r1_cohsp_1(A,B)
    <=> ! [C,D] :
          ( ( r2_hidden(C,B)
            & r2_hidden(D,B) )
         => ( r2_hidden(k3_xboole_0(C,D),A)
            & r2_hidden(k2_xboole_0(C,D),A) ) ) ) )).

fof(t16_cohsp_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( r1_cohsp_1(A,A)
       => ( v1_cohsp_1(A)
          & v2_cohsp_1(A) ) ) ) )).

fof(d9_cohsp_1,axiom,(
    ! [A,B,C] :
      ( r2_cohsp_1(A,B,C)
    <=> r1_cohsp_1(A,k2_tarski(B,C)) ) )).

fof(t17_cohsp_1,axiom,(
    ! [A,B,C] :
      ( r2_cohsp_1(A,B,C)
    <=> ( r2_hidden(B,A)
        & r2_hidden(C,A)
        & r2_hidden(k3_xboole_0(B,C),A)
        & r2_hidden(k2_xboole_0(B,C),A) ) ) )).

fof(d10_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v4_cohsp_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(k1_relat_1(A)))
           => ( r2_hidden(k3_tarski(B),k1_relat_1(A))
             => k1_funct_1(A,k3_tarski(B)) = k3_tarski(k9_relat_1(A,B)) ) ) ) ) )).

fof(d11_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v5_cohsp_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(k1_relat_1(A)))
           => ( ( v1_cohsp_1(B)
                & r2_hidden(k3_tarski(B),k1_relat_1(A)) )
             => k1_funct_1(A,k3_tarski(B)) = k3_tarski(k9_relat_1(A,B)) ) ) ) ) )).

fof(d12_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v6_cohsp_1(A)
      <=> ! [B,C] :
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & r1_tarski(B,C) )
           => r1_tarski(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) )).

fof(d13_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v7_cohsp_1(A)
      <=> ! [B,C] :
            ( r2_cohsp_1(k1_relat_1(A),B,C)
           => k1_funct_1(A,k3_xboole_0(B,C)) = k3_xboole_0(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) )).

fof(t18_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v4_cohsp_1(A)
       => ! [B,C] :
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & r2_hidden(k2_xboole_0(B,C),k1_relat_1(A)) )
           => k1_funct_1(A,k2_xboole_0(B,C)) = k2_xboole_0(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) )).

fof(t19_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v4_cohsp_1(A)
       => k1_funct_1(A,k1_xboole_0) = k1_xboole_0 ) ) )).

fof(d14_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v8_cohsp_1(A)
      <=> ( v3_cohsp_1(k1_relat_1(A))
          & v5_cohsp_1(A) ) ) ) )).

fof(d15_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v9_cohsp_1(A)
      <=> ( v2_finsub_1(k1_relat_1(A))
          & v8_cohsp_1(A)
          & v7_cohsp_1(A) ) ) ) )).

fof(d16_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v10_cohsp_1(A)
      <=> ( v9_cohsp_1(A)
          & v4_cohsp_1(A) ) ) ) )).

fof(t20_cohsp_1,axiom,(
    ! [A] : k3_tarski(k5_finsub_1(A)) = A )).

fof(t21_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v8_cohsp_1(A) )
     => ( v1_classes1(k1_relat_1(A))
       => ! [B] :
            ( r2_hidden(B,k1_relat_1(A))
           => k1_funct_1(A,B) = k3_tarski(k9_relat_1(A,k5_finsub_1(B))) ) ) ) )).

fof(t22_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_classes1(k1_relat_1(A))
       => ( v8_cohsp_1(A)
        <=> ( v3_cohsp_1(k1_relat_1(A))
            & v6_cohsp_1(A)
            & ! [B,C] :
                ~ ( r2_hidden(B,k1_relat_1(A))
                  & r2_hidden(C,k1_funct_1(A,B))
                  & ! [D] :
                      ~ ( v1_finset_1(D)
                        & r1_tarski(D,B)
                        & r2_hidden(C,k1_funct_1(A,D)) ) ) ) ) ) ) )).

fof(t23_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ( v1_classes1(k1_relat_1(A))
          & v3_cohsp_1(k1_relat_1(A)) )
       => ( v9_cohsp_1(A)
        <=> ( v6_cohsp_1(A)
            & ! [B,C] :
                ~ ( r2_hidden(B,k1_relat_1(A))
                  & r2_hidden(C,k1_funct_1(A,B))
                  & ! [D] :
                      ~ ( v1_finset_1(D)
                        & r1_tarski(D,B)
                        & r2_hidden(C,k1_funct_1(A,D))
                        & ! [E] :
                            ( ( r1_tarski(E,B)
                              & r2_hidden(C,k1_funct_1(A,E)) )
                           => r1_tarski(D,E) ) ) ) ) ) ) ) )).

fof(t24_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ( v1_classes1(k1_relat_1(A))
          & v3_cohsp_1(k1_relat_1(A)) )
       => ( v10_cohsp_1(A)
        <=> ( v6_cohsp_1(A)
            & ! [B,C] :
                ~ ( r2_hidden(B,k1_relat_1(A))
                  & r2_hidden(C,k1_funct_1(A,B))
                  & ! [D] :
                      ~ ( r2_hidden(D,B)
                        & r2_hidden(C,k1_funct_1(A,k1_tarski(D)))
                        & ! [E] :
                            ( ( r1_tarski(E,B)
                              & r2_hidden(C,k1_funct_1(A,E)) )
                           => r2_hidden(D,E) ) ) ) ) ) ) ) )).

fof(d17_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( B = k5_cohsp_1(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ? [D] :
                  ( v1_finset_1(D)
                  & ? [E] :
                      ( C = k4_tarski(D,E)
                      & r2_hidden(D,k1_relat_1(A))
                      & r2_hidden(E,k1_funct_1(A,D)) ) ) ) ) ) )).

fof(t25_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] :
          ( r2_hidden(k4_tarski(B,C),k5_cohsp_1(A))
        <=> ( v1_finset_1(B)
            & r2_hidden(B,k1_relat_1(A))
            & r2_hidden(C,k1_funct_1(A,B)) ) ) ) )).

fof(t26_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v6_cohsp_1(A) )
     => ! [B,C] :
          ( ( r2_hidden(C,k1_relat_1(A))
            & r1_tarski(B,C)
            & v1_finset_1(C) )
         => ! [D] :
              ( r2_hidden(k4_tarski(B,D),k5_cohsp_1(A))
             => r2_hidden(k4_tarski(C,D),k5_cohsp_1(A)) ) ) ) )).

fof(t27_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E,F] :
                      ( ( r2_hidden(k4_tarski(D,E),k6_cohsp_1(A,B,C))
                        & r2_hidden(k4_tarski(D,F),k6_cohsp_1(A,B,C)) )
                     => r2_hidden(k2_tarski(E,F),B) ) ) ) ) ) )).

fof(t28_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v6_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ( r2_hidden(k2_xboole_0(D,E),A)
                       => ! [F,G] :
                            ( ( r2_hidden(k4_tarski(D,F),k6_cohsp_1(A,B,C))
                              & r2_hidden(k4_tarski(E,G),k6_cohsp_1(A,B,C)) )
                           => r2_hidden(k2_tarski(F,G),B) ) ) ) ) ) ) ) )).

fof(t29_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v8_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & v8_cohsp_1(D)
                    & m2_relset_1(D,A,B) )
                 => ( k6_cohsp_1(A,B,C) = k6_cohsp_1(A,B,D)
                   => C = D ) ) ) ) ) )).

fof(t30_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k3_tarski(B))))
             => ~ ( ! [D] :
                      ( r2_hidden(D,C)
                     => v1_finset_1(k1_mcart_1(D)) )
                  & ! [D] :
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,A) )
                     => ! [E] :
                          ( ( v1_finset_1(E)
                            & m1_subset_1(E,A) )
                         => ( r1_tarski(D,E)
                           => ! [F] :
                                ( r2_hidden(k4_tarski(D,F),C)
                               => r2_hidden(k4_tarski(E,F),C) ) ) ) )
                  & ! [D] :
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,A) )
                     => ! [E,F] :
                          ( ( r2_hidden(k4_tarski(D,E),C)
                            & r2_hidden(k4_tarski(D,F),C) )
                         => r2_hidden(k2_tarski(E,F),B) ) )
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,A,B)
                        & v8_cohsp_1(D)
                        & m2_relset_1(D,A,B) )
                     => C != k6_cohsp_1(A,B,D) ) ) ) ) ) )).

fof(t31_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v8_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => k8_funct_2(A,B,C,D) = k9_relat_1(k6_cohsp_1(A,B,C),k3_cohsp_1(A,D)) ) ) ) ) )).

fof(d18_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( B = k7_cohsp_1(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ? [D,E] :
                  ( C = k4_tarski(D,E)
                  & r2_hidden(D,k1_relat_1(A))
                  & r2_hidden(E,k1_funct_1(A,D))
                  & ! [F] :
                      ( ( r2_hidden(F,k1_relat_1(A))
                        & r1_tarski(F,D)
                        & r2_hidden(E,k1_funct_1(A,F)) )
                     => D = F ) ) ) ) ) )).

fof(t32_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] :
          ( r2_hidden(k4_tarski(B,C),k7_cohsp_1(A))
        <=> ( r2_hidden(B,k1_relat_1(A))
            & r2_hidden(C,k1_funct_1(A,B))
            & ! [D] :
                ( ( r2_hidden(D,k1_relat_1(A))
                  & r1_tarski(D,B)
                  & r2_hidden(C,k1_funct_1(A,D)) )
               => B = D ) ) ) ) )).

fof(t33_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v8_cohsp_1(A) )
     => ( v1_classes1(k1_relat_1(A))
       => r1_tarski(k7_cohsp_1(A),k5_cohsp_1(A)) ) ) )).

fof(t34_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v8_cohsp_1(A) )
     => ( v1_classes1(k1_relat_1(A))
       => ! [B,C] :
            ( r2_hidden(k4_tarski(B,C),k7_cohsp_1(A))
           => v1_finset_1(B) ) ) ) )).

fof(t35_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v6_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D,E] :
                  ( r2_hidden(k2_xboole_0(D,E),A)
                 => ! [F,G] :
                      ( ( r2_hidden(k4_tarski(D,F),k8_cohsp_1(A,B,C))
                        & r2_hidden(k4_tarski(E,G),k8_cohsp_1(A,B,C)) )
                     => r2_hidden(k2_tarski(F,G),B) ) ) ) ) ) )).

fof(t36_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v7_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D,E] :
                  ( r2_hidden(k2_xboole_0(D,E),A)
                 => ! [F] :
                      ( ( r2_hidden(k4_tarski(D,F),k8_cohsp_1(A,B,C))
                        & r2_hidden(k4_tarski(E,F),k8_cohsp_1(A,B,C)) )
                     => D = E ) ) ) ) ) )).

fof(t37_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v9_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & v9_cohsp_1(D)
                    & m2_relset_1(D,A,B) )
                 => ( r1_tarski(k8_cohsp_1(A,B,C),k8_cohsp_1(A,B,D))
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => r1_tarski(k8_funct_2(A,B,C,E),k8_funct_2(A,B,D,E)) ) ) ) ) ) ) )).

fof(t38_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v9_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & v9_cohsp_1(D)
                    & m2_relset_1(D,A,B) )
                 => ( k8_cohsp_1(A,B,C) = k8_cohsp_1(A,B,D)
                   => C = D ) ) ) ) ) )).

fof(t39_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k3_tarski(B))))
             => ~ ( ! [D] :
                      ( r2_hidden(D,C)
                     => v1_finset_1(k1_mcart_1(D)) )
                  & ! [D] :
                      ( m1_subset_1(D,A)
                     => ! [E] :
                          ( m1_subset_1(E,A)
                         => ( r2_hidden(k2_xboole_0(D,E),A)
                           => ! [F,G] :
                                ( ( r2_hidden(k4_tarski(D,F),C)
                                  & r2_hidden(k4_tarski(E,G),C) )
                               => r2_hidden(k2_tarski(F,G),B) ) ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,A)
                     => ! [E] :
                          ( m1_subset_1(E,A)
                         => ( r2_hidden(k2_xboole_0(D,E),A)
                           => ! [F] :
                                ( ( r2_hidden(k4_tarski(D,F),C)
                                  & r2_hidden(k4_tarski(E,F),C) )
                               => D = E ) ) ) )
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,A,B)
                        & v9_cohsp_1(D)
                        & m2_relset_1(D,A,B) )
                     => C != k8_cohsp_1(A,B,D) ) ) ) ) ) )).

fof(t40_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v9_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => k8_funct_2(A,B,C,D) = k9_relat_1(k8_cohsp_1(A,B,C),k3_cohsp_1(A,D)) ) ) ) ) )).

fof(t41_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v9_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( r2_hidden(E,k8_funct_2(A,B,C,D))
                    <=> ? [F] :
                          ( m1_subset_1(F,A)
                          & r2_hidden(k4_tarski(F,E),k8_cohsp_1(A,B,C))
                          & r1_tarski(F,D) ) ) ) ) ) ) )).

fof(t42_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ? [C] :
              ( v1_funct_1(C)
              & v1_funct_2(C,A,B)
              & v9_cohsp_1(C)
              & m2_relset_1(C,A,B)
              & k8_cohsp_1(A,B,C) = k1_xboole_0 ) ) ) )).

fof(t43_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_finset_1(C)
                & m1_subset_1(C,A) )
             => ! [D] :
                  ~ ( r2_hidden(D,k3_tarski(B))
                    & ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,A,B)
                          & v9_cohsp_1(E)
                          & m2_relset_1(E,A,B) )
                       => k8_cohsp_1(A,B,E) != k1_tarski(k4_tarski(C,D)) ) ) ) ) ) )).

fof(t44_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D,E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,A,B)
                    & v9_cohsp_1(E)
                    & m2_relset_1(E,A,B) )
                 => ( k8_cohsp_1(A,B,E) = k1_tarski(k4_tarski(C,D))
                   => ! [F] :
                        ( m1_subset_1(F,A)
                       => ( ( r1_tarski(C,F)
                           => k8_funct_2(A,B,E,F) = k1_tarski(D) )
                          & ( ~ r1_tarski(C,F)
                           => k8_funct_2(A,B,E,F) = k1_xboole_0 ) ) ) ) ) ) ) ) )).

fof(t45_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v9_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k8_cohsp_1(A,B,C)))
                 => ? [E] :
                      ( v1_funct_1(E)
                      & v1_funct_2(E,A,B)
                      & v9_cohsp_1(E)
                      & m2_relset_1(E,A,B)
                      & k8_cohsp_1(A,B,E) = D ) ) ) ) ) )).

fof(t46_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ~ ( ! [D,E] :
                    ~ ( r2_hidden(D,C)
                      & r2_hidden(E,C)
                      & ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,B)
                            & v9_cohsp_1(F)
                            & m2_relset_1(F,A,B) )
                         => k2_xboole_0(D,E) != k8_cohsp_1(A,B,F) ) )
                & ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,A,B)
                      & v9_cohsp_1(D)
                      & m2_relset_1(D,A,B) )
                   => k3_tarski(C) != k8_cohsp_1(A,B,D) ) ) ) ) )).

fof(d19_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( C = k9_cohsp_1(A,B)
            <=> ! [D] :
                  ( r2_hidden(D,C)
                <=> ? [E] :
                      ( v1_funct_1(E)
                      & v1_funct_2(E,A,B)
                      & v9_cohsp_1(E)
                      & m2_relset_1(E,A,B)
                      & D = k8_cohsp_1(A,B,E) ) ) ) ) ) )).

fof(t47_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v9_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => r1_tarski(k8_cohsp_1(A,B,C),k2_zfmisc_1(k2_cohsp_1(A),k3_tarski(B))) ) ) ) )).

fof(t48_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => k3_tarski(k9_cohsp_1(A,B)) = k2_zfmisc_1(k2_cohsp_1(A),k3_tarski(B)) ) ) )).

fof(t49_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_finset_1(C)
                & m1_subset_1(C,A) )
             => ! [D] :
                  ( ( v1_finset_1(D)
                    & m1_subset_1(D,A) )
                 => ! [E,F] :
                      ( r2_hidden(k4_tarski(k4_tarski(C,E),k4_tarski(D,F)),k1_coh_sp(k9_cohsp_1(A,B)))
                    <=> ( ( ~ r2_hidden(k2_xboole_0(C,D),A)
                          & r2_hidden(E,k3_tarski(B))
                          & r2_hidden(F,k3_tarski(B)) )
                        | ( r2_hidden(k4_tarski(E,F),k1_coh_sp(B))
                          & ( E = F
                           => C = D ) ) ) ) ) ) ) ) )).

fof(t50_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v9_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ( v10_cohsp_1(C)
              <=> ! [D,E] :
                    ~ ( r2_hidden(k4_tarski(D,E),k8_cohsp_1(A,B,C))
                      & ! [F] : D != k1_tarski(F) ) ) ) ) ) )).

fof(d20_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( B = k10_cohsp_1(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ? [D,E] :
                  ( C = k4_tarski(D,E)
                  & r2_hidden(k4_tarski(k1_tarski(D),E),k7_cohsp_1(A)) ) ) ) ) )).

fof(t51_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] :
          ( r2_hidden(k4_tarski(B,C),k10_cohsp_1(A))
        <=> r2_hidden(k4_tarski(k1_tarski(B),C),k7_cohsp_1(A)) ) ) )).

fof(t52_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( k1_funct_1(A,k1_xboole_0) = k1_xboole_0
       => ! [B,C] :
            ( ( r2_hidden(k1_tarski(B),k1_relat_1(A))
              & r2_hidden(C,k1_funct_1(A,k1_tarski(B))) )
           => r2_hidden(k4_tarski(B,C),k10_cohsp_1(A)) ) ) ) )).

fof(t53_cohsp_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] :
          ( r2_hidden(k4_tarski(B,C),k10_cohsp_1(A))
         => ( r2_hidden(k1_tarski(B),k1_relat_1(A))
            & r2_hidden(C,k1_funct_1(A,k1_tarski(B))) ) ) ) )).

fof(d21_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( C = k12_cohsp_1(A,B)
            <=> ! [D] :
                  ( r2_hidden(D,C)
                <=> ? [E] :
                      ( v1_funct_1(E)
                      & v1_funct_2(E,A,B)
                      & v10_cohsp_1(E)
                      & m2_relset_1(E,A,B)
                      & D = k11_cohsp_1(A,B,E) ) ) ) ) ) )).

fof(t54_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v6_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D,E] :
                  ( r2_hidden(k2_tarski(D,E),A)
                 => ! [F,G] :
                      ( ( r2_hidden(k4_tarski(D,F),k11_cohsp_1(A,B,C))
                        & r2_hidden(k4_tarski(E,G),k11_cohsp_1(A,B,C)) )
                     => r2_hidden(k2_tarski(F,G),B) ) ) ) ) ) )).

fof(t55_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v7_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D,E] :
                  ( r2_hidden(k2_tarski(D,E),A)
                 => ! [F] :
                      ( ( r2_hidden(k4_tarski(D,F),k11_cohsp_1(A,B,C))
                        & r2_hidden(k4_tarski(E,F),k11_cohsp_1(A,B,C)) )
                     => D = E ) ) ) ) ) )).

fof(t56_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v10_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & v10_cohsp_1(D)
                    & m2_relset_1(D,A,B) )
                 => ( k11_cohsp_1(A,B,C) = k11_cohsp_1(A,B,D)
                   => C = D ) ) ) ) ) )).

fof(t57_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k3_tarski(A),k3_tarski(B))))
             => ~ ( ! [D,E] :
                      ( r2_hidden(k2_tarski(D,E),A)
                     => ! [F,G] :
                          ( ( r2_hidden(k4_tarski(D,F),C)
                            & r2_hidden(k4_tarski(E,G),C) )
                         => r2_hidden(k2_tarski(F,G),B) ) )
                  & ! [D,E] :
                      ( r2_hidden(k2_tarski(D,E),A)
                     => ! [F] :
                          ( ( r2_hidden(k4_tarski(D,F),C)
                            & r2_hidden(k4_tarski(E,F),C) )
                         => D = E ) )
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,A,B)
                        & v10_cohsp_1(D)
                        & m2_relset_1(D,A,B) )
                     => C != k11_cohsp_1(A,B,D) ) ) ) ) ) )).

fof(t58_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v10_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => k8_funct_2(A,B,C,D) = k9_relat_1(k11_cohsp_1(A,B,C),D) ) ) ) ) )).

fof(t59_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ? [C] :
              ( v1_funct_1(C)
              & v1_funct_2(C,A,B)
              & v10_cohsp_1(C)
              & m2_relset_1(C,A,B)
              & k11_cohsp_1(A,B,C) = k1_xboole_0 ) ) ) )).

fof(t60_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C,D] :
              ~ ( r2_hidden(C,k3_tarski(A))
                & r2_hidden(D,k3_tarski(B))
                & ! [E] :
                    ( ( v1_funct_1(E)
                      & v1_funct_2(E,A,B)
                      & v10_cohsp_1(E)
                      & m2_relset_1(E,A,B) )
                   => k11_cohsp_1(A,B,E) != k1_tarski(k4_tarski(C,D)) ) ) ) ) )).

fof(t61_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C,D] :
              ( ( r2_hidden(C,k3_tarski(A))
                & r2_hidden(D,k3_tarski(B)) )
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,A,B)
                    & v10_cohsp_1(E)
                    & m2_relset_1(E,A,B) )
                 => ( k11_cohsp_1(A,B,E) = k1_tarski(k4_tarski(C,D))
                   => ! [F] :
                        ( m1_subset_1(F,A)
                       => ( ( r2_hidden(C,F)
                           => k8_funct_2(A,B,E,F) = k1_tarski(D) )
                          & ( ~ r2_hidden(C,F)
                           => k8_funct_2(A,B,E,F) = k1_xboole_0 ) ) ) ) ) ) ) ) )).

fof(t62_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v10_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k11_cohsp_1(A,B,C)))
                 => ? [E] :
                      ( v1_funct_1(E)
                      & v1_funct_2(E,A,B)
                      & v10_cohsp_1(E)
                      & m2_relset_1(E,A,B)
                      & k11_cohsp_1(A,B,E) = D ) ) ) ) ) )).

fof(t63_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ~ ( ! [D,E] :
                    ~ ( r2_hidden(D,C)
                      & r2_hidden(E,C)
                      & ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,B)
                            & v10_cohsp_1(F)
                            & m2_relset_1(F,A,B) )
                         => k2_xboole_0(D,E) != k11_cohsp_1(A,B,F) ) )
                & ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,A,B)
                      & v10_cohsp_1(D)
                      & m2_relset_1(D,A,B) )
                   => k3_tarski(C) != k11_cohsp_1(A,B,D) ) ) ) ) )).

fof(t64_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => k3_tarski(k12_cohsp_1(A,B)) = k2_zfmisc_1(k3_tarski(A),k3_tarski(B)) ) ) )).

fof(t65_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C,D,E,F] :
              ( r2_hidden(k4_tarski(k4_tarski(C,E),k4_tarski(D,F)),k1_coh_sp(k12_cohsp_1(A,B)))
            <=> ( r2_hidden(C,k3_tarski(A))
                & r2_hidden(D,k3_tarski(A))
                & ( ( ~ r2_hidden(k4_tarski(C,D),k1_coh_sp(A))
                    & r2_hidden(E,k3_tarski(B))
                    & r2_hidden(F,k3_tarski(B)) )
                  | ( r2_hidden(k4_tarski(E,F),k1_coh_sp(B))
                    & ( E = F
                     => C = D ) ) ) ) ) ) ) )).

fof(t66_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( r2_hidden(B,k13_cohsp_1(A))
        <=> ( r1_tarski(B,k3_tarski(A))
            & ! [C] :
                ( m1_subset_1(C,A)
               => ? [D] : r1_tarski(k3_xboole_0(B,C),k1_tarski(D)) ) ) ) ) )).

fof(t67_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => k3_tarski(k13_cohsp_1(A)) = k3_tarski(A) ) )).

fof(t68_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B,C] :
          ~ ( B != C
            & r2_hidden(k2_tarski(B,C),A)
            & r2_hidden(k2_tarski(B,C),k13_cohsp_1(A)) ) ) )).

fof(t69_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B,C] :
          ( r1_tarski(k2_tarski(B,C),k3_tarski(A))
         => ( r2_hidden(k2_tarski(B,C),A)
            | r2_hidden(k2_tarski(B,C),k13_cohsp_1(A)) ) ) ) )).

fof(t70_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B,C] :
          ( r2_hidden(k4_tarski(B,C),k1_coh_sp(k13_cohsp_1(A)))
        <=> ( r2_hidden(B,k3_tarski(A))
            & r2_hidden(C,k3_tarski(A))
            & ~ ( B != C
                & r2_hidden(k4_tarski(B,C),k1_coh_sp(A)) ) ) ) ) )).

fof(t71_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => k13_cohsp_1(k13_cohsp_1(A)) = A ) )).

fof(t72_cohsp_1,axiom,(
    k13_cohsp_1(k1_tarski(k1_xboole_0)) = k1_tarski(k1_xboole_0) )).

fof(t73_cohsp_1,axiom,(
    ! [A] :
      ( k13_cohsp_1(k1_cohsp_1(A)) = k1_zfmisc_1(A)
      & k13_cohsp_1(k1_zfmisc_1(A)) = k1_cohsp_1(A) ) )).

fof(d23_cohsp_1,axiom,(
    ! [A,B] : k14_cohsp_1(A,B) = k3_card_3(k2_card_3(k10_finseq_1(A,B))) )).

fof(t74_cohsp_1,axiom,(
    ! [A,B] : k14_cohsp_1(A,B) = k2_xboole_0(k2_zfmisc_1(A,k1_tarski(np__1)),k2_zfmisc_1(B,k1_tarski(np__2))) )).

fof(t75_cohsp_1,axiom,(
    ! [A] :
      ( k14_cohsp_1(A,k1_xboole_0) = k2_zfmisc_1(A,k1_tarski(np__1))
      & k14_cohsp_1(k1_xboole_0,A) = k2_zfmisc_1(A,k1_tarski(np__2)) ) )).

fof(t76_cohsp_1,axiom,(
    ! [A,B,C] :
      ( r2_hidden(C,k14_cohsp_1(A,B))
     => ( C = k4_tarski(k1_mcart_1(C),k2_mcart_1(C))
        & ( ( k2_mcart_1(C) = np__1
            & r2_hidden(k1_mcart_1(C),A) )
          | ( k2_mcart_1(C) = np__2
            & r2_hidden(k1_mcart_1(C),B) ) ) ) ) )).

fof(t77_cohsp_1,axiom,(
    ! [A,B,C] :
      ( r2_hidden(k4_tarski(C,np__1),k14_cohsp_1(A,B))
    <=> r2_hidden(C,A) ) )).

fof(t78_cohsp_1,axiom,(
    ! [A,B,C] :
      ( r2_hidden(k4_tarski(C,np__2),k14_cohsp_1(A,B))
    <=> r2_hidden(C,B) ) )).

fof(t79_cohsp_1,axiom,(
    ! [A,B,C,D] :
      ( r1_tarski(k14_cohsp_1(A,B),k14_cohsp_1(C,D))
    <=> ( r1_tarski(A,C)
        & r1_tarski(B,D) ) ) )).

fof(t80_cohsp_1,axiom,(
    ! [A,B,C] :
      ~ ( r1_tarski(C,k14_cohsp_1(A,B))
        & ! [D,E] :
            ~ ( C = k14_cohsp_1(D,E)
              & r1_tarski(D,A)
              & r1_tarski(E,B) ) ) )).

fof(t81_cohsp_1,axiom,(
    ! [A,B,C,D] :
      ( k14_cohsp_1(A,B) = k14_cohsp_1(C,D)
    <=> ( A = C
        & B = D ) ) )).

fof(t82_cohsp_1,axiom,(
    ! [A,B,C,D] : k2_xboole_0(k14_cohsp_1(A,B),k14_cohsp_1(C,D)) = k14_cohsp_1(k2_xboole_0(A,C),k2_xboole_0(B,D)) )).

fof(t83_cohsp_1,axiom,(
    ! [A,B,C,D] : k3_xboole_0(k14_cohsp_1(A,B),k14_cohsp_1(C,D)) = k14_cohsp_1(k3_xboole_0(A,C),k3_xboole_0(B,D)) )).

fof(t84_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( r2_hidden(C,k15_cohsp_1(A,B))
            <=> ? [D] :
                  ( m1_subset_1(D,A)
                  & ? [E] :
                      ( m1_subset_1(E,B)
                      & C = k14_cohsp_1(D,E) ) ) ) ) ) )).

fof(t85_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C,D] :
              ( r2_hidden(k14_cohsp_1(C,D),k15_cohsp_1(A,B))
            <=> ( r2_hidden(C,A)
                & r2_hidden(D,B) ) ) ) ) )).

fof(t86_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => k3_tarski(k15_cohsp_1(A,B)) = k14_cohsp_1(k3_tarski(A),k3_tarski(B)) ) ) )).

fof(t87_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C,D] :
              ( r2_hidden(k14_cohsp_1(C,D),k16_cohsp_1(A,B))
            <=> ( ( r2_hidden(C,A)
                  & D = k1_xboole_0 )
                | ( C = k1_xboole_0
                  & r2_hidden(D,B) ) ) ) ) ) )).

fof(t88_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ~ ( r2_hidden(C,k16_cohsp_1(A,B))
                & ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,B)
                       => ~ ( C = k14_cohsp_1(D,E)
                            & ( D = k1_xboole_0
                              | E = k1_xboole_0 ) ) ) ) ) ) ) )).

fof(t89_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => k3_tarski(k16_cohsp_1(A,B)) = k14_cohsp_1(k3_tarski(A),k3_tarski(B)) ) ) )).

fof(t90_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C,D] :
              ( r2_hidden(k4_tarski(k4_tarski(C,np__1),k4_tarski(D,np__1)),k1_coh_sp(k15_cohsp_1(A,B)))
            <=> r2_hidden(k4_tarski(C,D),k1_coh_sp(A)) ) ) ) )).

fof(t91_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C,D] :
              ( r2_hidden(k4_tarski(k4_tarski(C,np__2),k4_tarski(D,np__2)),k1_coh_sp(k15_cohsp_1(A,B)))
            <=> r2_hidden(k4_tarski(C,D),k1_coh_sp(B)) ) ) ) )).

fof(t92_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C,D] :
              ( ( r2_hidden(C,k3_tarski(A))
                & r2_hidden(D,k3_tarski(B)) )
             => ( r2_hidden(k4_tarski(k4_tarski(C,np__1),k4_tarski(D,np__2)),k1_coh_sp(k15_cohsp_1(A,B)))
                & r2_hidden(k4_tarski(k4_tarski(D,np__2),k4_tarski(C,np__1)),k1_coh_sp(k15_cohsp_1(A,B))) ) ) ) ) )).

fof(t93_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C,D] :
              ( r2_hidden(k4_tarski(k4_tarski(C,np__1),k4_tarski(D,np__1)),k1_coh_sp(k16_cohsp_1(A,B)))
            <=> r2_hidden(k4_tarski(C,D),k1_coh_sp(A)) ) ) ) )).

fof(t94_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C,D] :
              ( r2_hidden(k4_tarski(k4_tarski(C,np__2),k4_tarski(D,np__2)),k1_coh_sp(k16_cohsp_1(A,B)))
            <=> r2_hidden(k4_tarski(C,D),k1_coh_sp(B)) ) ) ) )).

fof(t95_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C,D] :
              ( ~ r2_hidden(k4_tarski(k4_tarski(C,np__1),k4_tarski(D,np__2)),k1_coh_sp(k16_cohsp_1(A,B)))
              & ~ r2_hidden(k4_tarski(k4_tarski(D,np__2),k4_tarski(C,np__1)),k1_coh_sp(k16_cohsp_1(A,B))) ) ) ) )).

fof(t96_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => k13_cohsp_1(k15_cohsp_1(A,B)) = k16_cohsp_1(k13_cohsp_1(A),k13_cohsp_1(B)) ) ) )).

fof(t97_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( r2_hidden(C,k17_cohsp_1(A,B))
            <=> ? [D] :
                  ( m1_subset_1(D,A)
                  & ? [E] :
                      ( m1_subset_1(E,B)
                      & r1_tarski(C,k2_zfmisc_1(D,E)) ) ) ) ) ) )).

fof(t98_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] :
              ( m1_subset_1(C,k17_cohsp_1(A,B))
             => ( r2_hidden(k1_funct_5(C),A)
                & r2_hidden(k2_funct_5(C),B)
                & r1_tarski(C,k2_zfmisc_1(k1_funct_5(C),k2_funct_5(C))) ) ) ) ) )).

fof(t99_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => k3_tarski(k17_cohsp_1(A,B)) = k2_zfmisc_1(k3_tarski(A),k3_tarski(B)) ) ) )).

fof(t100_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C,D,E,F] :
              ( r2_hidden(k4_tarski(k4_tarski(C,E),k4_tarski(D,F)),k1_coh_sp(k17_cohsp_1(A,B)))
            <=> ( r2_hidden(k4_tarski(C,D),k1_coh_sp(A))
                & r2_hidden(k4_tarski(E,F),k1_coh_sp(B)) ) ) ) ) )).

fof(s1_cohsp_1,axiom,
    ( ( r2_hidden(f1_s1_cohsp_1,f2_s1_cohsp_1)
      & p1_s1_cohsp_1(f1_s1_cohsp_1)
      & v1_finset_1(f1_s1_cohsp_1) )
   => ? [A] :
        ( r2_hidden(A,f2_s1_cohsp_1)
        & p1_s1_cohsp_1(A)
        & ! [B] :
            ( ( r2_hidden(B,f2_s1_cohsp_1)
              & p1_s1_cohsp_1(B)
              & r1_tarski(B,A) )
           => B = A ) ) )).

fof(dt_k1_cohsp_1,axiom,(
    $true )).

fof(dt_k2_cohsp_1,axiom,(
    ! [A] : m1_subset_1(k2_cohsp_1(A),k1_zfmisc_1(A)) )).

fof(dt_k3_cohsp_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & m1_subset_1(B,A) )
     => ( ~ v1_xboole_0(k3_cohsp_1(A,B))
        & v4_finsub_1(k3_cohsp_1(A,B))
        & m1_subset_1(k3_cohsp_1(A,B),k1_zfmisc_1(A)) ) ) )).

fof(redefinition_k3_cohsp_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & m1_subset_1(B,A) )
     => k3_cohsp_1(A,B) = k5_finsub_1(B) ) )).

fof(dt_k4_cohsp_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v3_cohsp_1(A)
        & v1_cohsp_1(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => m1_subset_1(k4_cohsp_1(A,B),A) ) )).

fof(redefinition_k4_cohsp_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v3_cohsp_1(A)
        & v1_cohsp_1(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => k4_cohsp_1(A,B) = k3_tarski(B) ) )).

fof(dt_k5_cohsp_1,axiom,(
    $true )).

fof(dt_k6_cohsp_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k6_cohsp_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(A,k3_tarski(B)))) ) )).

fof(redefinition_k6_cohsp_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k6_cohsp_1(A,B,C) = k5_cohsp_1(C) ) )).

fof(dt_k7_cohsp_1,axiom,(
    $true )).

fof(dt_k8_cohsp_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k8_cohsp_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(A,k3_tarski(B)))) ) )).

fof(redefinition_k8_cohsp_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k8_cohsp_1(A,B,C) = k7_cohsp_1(C) ) )).

fof(dt_k9_cohsp_1,axiom,(
    $true )).

fof(dt_k10_cohsp_1,axiom,(
    $true )).

fof(dt_k11_cohsp_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k11_cohsp_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k3_tarski(A),k3_tarski(B)))) ) )).

fof(redefinition_k11_cohsp_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k11_cohsp_1(A,B,C) = k10_cohsp_1(C) ) )).

fof(dt_k12_cohsp_1,axiom,(
    $true )).

fof(dt_k13_cohsp_1,axiom,(
    $true )).

fof(dt_k14_cohsp_1,axiom,(
    $true )).

fof(dt_k15_cohsp_1,axiom,(
    $true )).

fof(dt_k16_cohsp_1,axiom,(
    $true )).

fof(dt_k17_cohsp_1,axiom,(
    $true )).

fof(d22_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => k13_cohsp_1(A) = a_1_0_cohsp_1(A) ) )).

fof(d24_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => k15_cohsp_1(A,B) = a_2_0_cohsp_1(A,B) ) ) )).

fof(d25_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => k16_cohsp_1(A,B) = k2_xboole_0(a_1_1_cohsp_1(A),a_1_2_cohsp_1(B)) ) ) )).

fof(d26_cohsp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => k17_cohsp_1(A,B) = k3_tarski(a_2_1_cohsp_1(A,B)) ) ) )).

fof(fraenkel_a_1_0_cohsp_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ( r2_hidden(A,a_1_0_cohsp_1(B))
      <=> ? [C] :
            ( m1_subset_1(C,k1_zfmisc_1(k3_tarski(B)))
            & A = C
            & ! [D] :
                ( m1_subset_1(D,B)
               => ? [E] : r1_tarski(k3_xboole_0(C,D),k1_tarski(E)) ) ) ) ) )).

fof(fraenkel_a_2_0_cohsp_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B)
        & ~ v1_xboole_0(C)
        & v1_classes1(C)
        & v1_coh_sp(C) )
     => ( r2_hidden(A,a_2_0_cohsp_1(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,B)
            & m1_subset_1(E,C)
            & A = k14_cohsp_1(D,E) ) ) ) )).

fof(fraenkel_a_1_1_cohsp_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ( r2_hidden(A,a_1_1_cohsp_1(B))
      <=> ? [C] :
            ( m1_subset_1(C,B)
            & A = k14_cohsp_1(C,k1_xboole_0) ) ) ) )).

fof(fraenkel_a_1_2_cohsp_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ( r2_hidden(A,a_1_2_cohsp_1(B))
      <=> ? [C] :
            ( m1_subset_1(C,B)
            & A = k14_cohsp_1(k1_xboole_0,C) ) ) ) )).

fof(fraenkel_a_2_1_cohsp_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B)
        & ~ v1_xboole_0(C)
        & v1_classes1(C)
        & v1_coh_sp(C) )
     => ( r2_hidden(A,a_2_1_cohsp_1(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,B)
            & m1_subset_1(E,C)
            & A = k1_zfmisc_1(k2_zfmisc_1(D,E)) ) ) ) )).
%------------------------------------------------------------------------------