SET007 Axioms: SET007+799.ax


%------------------------------------------------------------------------------
% File     : SET007+799 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Basic Properties of Rough Sets and Rough Membership Function
% 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    : roughs_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  125 (   1 unit)
%            Number of atoms       :  769 (  55 equality)
%            Maximal formula depth :   14 (   7 average)
%            Number of connectives :  776 ( 132 ~  ;   0  |; 358  &)
%                                         (  27 <=>; 259 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   45 (   1 propositional; 0-3 arity)
%            Number of functors    :   48 (   5 constant; 0-4 arity)
%            Number of variables   :  305 (   0 singleton; 290 !;  15 ?)
%            Maximal term depth    :    6 (   2 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(fc1_roughs_1,axiom,(
    ! [A] :
      ( v1_orders_2(g1_orders_2(A,k6_partfun1(A)))
      & v2_orders_2(g1_orders_2(A,k6_partfun1(A)))
      & v3_orders_2(g1_orders_2(A,k6_partfun1(A)))
      & v4_orders_2(g1_orders_2(A,k6_partfun1(A)))
      & v1_orders_3(g1_orders_2(A,k6_partfun1(A))) ) )).

fof(fc2_roughs_1,axiom,(
    ! [A] :
      ( ~ v1_realset1(A)
     => ( ~ v3_struct_0(g1_orders_2(A,k1_eqrel_1(A)))
        & v1_orders_2(g1_orders_2(A,k1_eqrel_1(A)))
        & ~ v1_roughs_1(g1_orders_2(A,k1_eqrel_1(A))) ) ) )).

fof(cc1_roughs_1,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( v2_orders_2(A)
          & ~ v1_orders_3(A) )
       => ( ~ v3_realset2(A)
          & v2_orders_2(A) ) ) ) )).

fof(cc2_roughs_1,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( v3_realset2(A)
          & v2_orders_2(A) )
       => v1_orders_3(A) ) ) )).

fof(cc3_roughs_1,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_orders_3(A)
       => v1_roughs_1(A) ) ) )).

fof(cc4_roughs_1,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ~ v1_roughs_1(A)
       => ~ v1_orders_3(A) ) ) )).

fof(rc1_roughs_1,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & ~ v1_orders_3(A)
      & ~ v1_roughs_1(A) ) )).

fof(cc5_roughs_1,axiom,(
    ! [A] :
      ( ( v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_prob_2(A) ) ) )).

fof(rc2_roughs_1,axiom,(
    ! [A] :
    ? [B] :
      ( m1_finseq_1(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B)
      & v1_prob_2(B) ) )).

fof(rc3_roughs_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_finseq_1(B,A)
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finset_1(B)
          & v1_finseq_1(B)
          & v1_prob_2(B) ) ) )).

fof(fc3_roughs_1,axiom,(
    ! [A,B] :
      ( ( v1_finset_1(A)
        & m1_relset_1(B,A,A) )
     => ( v6_group_1(g1_orders_2(A,B))
        & v1_orders_2(g1_orders_2(A,B)) ) ) )).

fof(cc6_roughs_1,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v2_roughs_1(A)
       => v3_roughs_1(A) ) ) )).

fof(fc4_roughs_1,axiom,(
    ! [A] :
      ( v1_orders_2(g1_orders_2(A,k6_partfun1(A)))
      & v2_orders_2(g1_orders_2(A,k6_partfun1(A)))
      & v3_orders_2(g1_orders_2(A,k6_partfun1(A)))
      & v4_orders_2(g1_orders_2(A,k6_partfun1(A)))
      & v1_orders_3(g1_orders_2(A,k6_partfun1(A)))
      & v1_roughs_1(g1_orders_2(A,k6_partfun1(A)))
      & v2_roughs_1(g1_orders_2(A,k6_partfun1(A)))
      & v3_roughs_1(g1_orders_2(A,k6_partfun1(A))) ) )).

fof(rc4_roughs_1,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v6_group_1(A)
      & v1_orders_3(A)
      & v1_roughs_1(A)
      & v2_roughs_1(A)
      & v3_roughs_1(A) ) )).

fof(rc5_roughs_1,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v6_group_1(A)
      & ~ v1_orders_3(A)
      & ~ v1_roughs_1(A)
      & v2_roughs_1(A)
      & v3_roughs_1(A) ) )).

fof(fc5_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(u1_orders_2(A))
        & v1_relat_2(u1_orders_2(A))
        & v3_relat_2(u1_orders_2(A))
        & v1_partfun1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(fc6_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(u1_orders_2(A))
        & v1_relat_2(u1_orders_2(A))
        & v3_relat_2(u1_orders_2(A))
        & v8_relat_2(u1_orders_2(A))
        & v1_partfun1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(rc6_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v4_roughs_1(B,A) ) ) )).

fof(fc7_roughs_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_roughs_1(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ~ v4_roughs_1(k3_roughs_1(A,B),A) ) )).

fof(fc8_roughs_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_roughs_1(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ~ v4_roughs_1(k4_roughs_1(A,B),A) ) )).

fof(rc7_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v1_roughs_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v4_roughs_1(B,A) ) ) )).

fof(fc9_roughs_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v3_roughs_1(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k1_card_1(k6_eqrel_1(u1_struct_0(A),u1_orders_2(A),B)))
        & v1_card_1(k1_card_1(k6_eqrel_1(u1_struct_0(A),u1_orders_2(A),B))) ) ) )).

fof(cc7_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_orders_3(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ v4_roughs_1(B,A) ) ) )).

fof(t1_roughs_1,axiom,(
    ! [A] :
      ( r1_tarski(k1_eqrel_1(A),k6_partfun1(A))
     => v1_realset1(A) ) )).

fof(d1_roughs_1,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_roughs_1(A)
      <=> r1_tarski(u1_orders_2(A),k6_partfun1(u1_struct_0(A))) ) ) )).

fof(t2_roughs_1,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & l1_orders_2(A) )
     => r1_tarski(k6_partfun1(u1_struct_0(A)),u1_orders_2(A)) ) )).

fof(t3_roughs_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => r1_tarski(k6_partfun1(A),B) ) )).

fof(t4_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v1_roughs_1(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_subset_1(B,u1_struct_0(A))
          & ? [C] :
              ( m1_subset_1(C,u1_struct_0(A))
              & B != C
              & r2_hidden(k4_tarski(B,C),u1_orders_2(A)) ) ) ) )).

fof(t5_roughs_1,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,A)
     => ! [C] :
          ( m2_finseq_1(C,A)
         => k3_card_3(k8_finseq_1(A,B,C)) = k2_xboole_0(k3_card_3(B),k3_card_3(C)) ) ) )).

fof(t6_roughs_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( v1_prob_2(B)
              & r1_tarski(A,B) )
           => v1_prob_2(A) ) ) ) )).

fof(t7_roughs_1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_2(D)
        & v3_relat_2(D)
        & v1_partfun1(D,A,A)
        & m2_relset_1(D,A,A) )
     => ( r2_hidden(B,k6_eqrel_1(A,D,C))
       => r2_hidden(C,k6_eqrel_1(A,D,B)) ) ) )).

fof(d2_roughs_1,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v2_roughs_1(A)
      <=> ( v3_relat_2(u1_orders_2(A))
          & v8_relat_2(u1_orders_2(A))
          & v1_partfun1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A))
          & m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ) ) )).

fof(d3_roughs_1,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v3_roughs_1(A)
      <=> ( v1_relat_2(u1_orders_2(A))
          & v3_relat_2(u1_orders_2(A))
          & v1_partfun1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A))
          & m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ) ) )).

fof(d6_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k5_roughs_1(A,B) = k6_subset_1(u1_struct_0(A),k4_roughs_1(A,B),k3_roughs_1(A,B)) ) ) )).

fof(d7_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_roughs_1(B,A)
          <=> k5_roughs_1(A,B) != k1_xboole_0 ) ) ) )).

fof(t8_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( r2_hidden(C,k3_roughs_1(A,B))
             => r1_tarski(k6_eqrel_1(u1_struct_0(A),u1_orders_2(A),C),B) ) ) ) )).

fof(t9_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_tarski(k6_eqrel_1(u1_struct_0(A),u1_orders_2(A),C),B)
               => r2_hidden(C,k3_roughs_1(A,B)) ) ) ) ) )).

fof(t10_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ~ ( r2_hidden(C,k4_roughs_1(A,B))
                & r1_xboole_0(k6_eqrel_1(u1_struct_0(A),u1_orders_2(A),C),B) ) ) ) )).

fof(t11_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ~ r1_xboole_0(k6_eqrel_1(u1_struct_0(A),u1_orders_2(A),C),B)
               => r2_hidden(C,k4_roughs_1(A,B)) ) ) ) ) )).

fof(t12_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(k3_roughs_1(A,B),B) ) ) )).

fof(t13_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(B,k4_roughs_1(A,B)) ) ) )).

fof(t14_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(k3_roughs_1(A,B),k4_roughs_1(A,B)) ) ) )).

fof(t15_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ~ v4_roughs_1(B,A)
          <=> k3_roughs_1(A,B) = B ) ) ) )).

fof(t16_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ~ v4_roughs_1(B,A)
          <=> k4_roughs_1(A,B) = B ) ) ) )).

fof(t17_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( B = k3_roughs_1(A,B)
          <=> B = k4_roughs_1(A,B) ) ) ) )).

fof(t18_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => k3_roughs_1(A,k1_pre_topc(A)) = k1_xboole_0 ) )).

fof(t19_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => k4_roughs_1(A,k1_pre_topc(A)) = k1_xboole_0 ) )).

fof(t20_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => k3_roughs_1(A,k2_pre_topc(A)) = k2_pre_topc(A) ) )).

fof(t21_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => k4_roughs_1(A,k2_pre_topc(A)) = k2_pre_topc(A) ) )).

fof(t22_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k3_roughs_1(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k3_roughs_1(A,B),k3_roughs_1(A,C)) ) ) ) )).

fof(t23_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k4_roughs_1(A,k4_subset_1(u1_struct_0(A),B,C)) = k4_subset_1(u1_struct_0(A),k4_roughs_1(A,B),k4_roughs_1(A,C)) ) ) ) )).

fof(t24_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(B,C)
               => r1_tarski(k3_roughs_1(A,B),k3_roughs_1(A,C)) ) ) ) ) )).

fof(t25_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(B,C)
               => r1_tarski(k4_roughs_1(A,B),k4_roughs_1(A,C)) ) ) ) ) )).

fof(t26_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_tarski(k4_subset_1(u1_struct_0(A),k3_roughs_1(A,B),k3_roughs_1(A,C)),k3_roughs_1(A,k4_subset_1(u1_struct_0(A),B,C))) ) ) ) )).

fof(t27_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_tarski(k4_roughs_1(A,k5_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),k4_roughs_1(A,B),k4_roughs_1(A,C))) ) ) ) )).

fof(t28_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k3_roughs_1(A,k3_subset_1(u1_struct_0(A),B)) = k3_subset_1(u1_struct_0(A),k4_roughs_1(A,B)) ) ) )).

fof(t29_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_roughs_1(A,k3_subset_1(u1_struct_0(A),B)) = k3_subset_1(u1_struct_0(A),k3_roughs_1(A,B)) ) ) )).

fof(t30_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_roughs_1(A,k3_roughs_1(A,k4_roughs_1(A,B))) = k4_roughs_1(A,B) ) ) )).

fof(t31_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k3_roughs_1(A,k4_roughs_1(A,k3_roughs_1(A,B))) = k3_roughs_1(A,B) ) ) )).

fof(t32_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k5_roughs_1(A,B) = k5_roughs_1(A,k3_subset_1(u1_struct_0(A),B)) ) ) )).

fof(t33_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k3_roughs_1(A,k3_roughs_1(A,B)) = k3_roughs_1(A,B) ) ) )).

fof(t34_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k3_roughs_1(A,k3_roughs_1(A,B)) = k4_roughs_1(A,k3_roughs_1(A,B)) ) ) )).

fof(t35_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_roughs_1(A,k4_roughs_1(A,B)) = k4_roughs_1(A,B) ) ) )).

fof(t36_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_roughs_1(A,k4_roughs_1(A,B)) = k3_roughs_1(A,k4_roughs_1(A,B)) ) ) )).

fof(t37_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C,D] :
              ( ( r2_hidden(C,k4_roughs_1(A,B))
                & r2_hidden(k4_tarski(C,D),u1_orders_2(A)) )
             => r2_hidden(D,k4_roughs_1(A,B)) ) ) ) )).

fof(d8_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_roughs_1(C,A,B)
            <=> C = k4_tarski(k3_roughs_1(A,B),k4_roughs_1(A,B)) ) ) ) )).

fof(d9_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),k1_numbers)
                & m2_relset_1(C,u1_struct_0(A),k1_numbers) )
             => ( C = k6_roughs_1(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),k1_numbers,C,D) = k6_real_1(k4_card_1(k5_subset_1(u1_struct_0(A),B,k6_eqrel_1(u1_struct_0(A),u1_orders_2(A),D))),k4_card_1(k6_eqrel_1(u1_struct_0(A),u1_orders_2(A),D))) ) ) ) ) ) )).

fof(t38_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_xreal_0(np__0,k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,B),C))
                & r1_xreal_0(k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,B),C),np__1) ) ) ) ) )).

fof(t39_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r2_hidden(k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,B),C),k1_rcomp_1(np__0,np__1)) ) ) ) )).

fof(t40_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,B),C) = np__1
              <=> r2_hidden(C,k3_roughs_1(A,B)) ) ) ) ) )).

fof(t41_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,B),C) = np__0
              <=> r2_hidden(C,k3_subset_1(u1_struct_0(A),k4_roughs_1(A,B))) ) ) ) ) )).

fof(t42_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( ~ r1_xreal_0(k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,B),C),np__0)
                  & ~ r1_xreal_0(np__1,k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,B),C)) )
              <=> r2_hidden(C,k5_roughs_1(A,B)) ) ) ) ) )).

fof(t43_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_orders_3(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ v4_roughs_1(B,A) ) ) )).

fof(t44_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v1_orders_3(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k6_roughs_1(A,B) = k5_funct_3(B,u1_struct_0(A)) ) ) )).

fof(t45_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C,D] :
              ( r2_hidden(k4_tarski(C,D),u1_orders_2(A))
             => k1_funct_1(k6_roughs_1(A,B),C) = k1_funct_1(k6_roughs_1(A,B),D) ) ) ) )).

fof(t46_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,k3_subset_1(u1_struct_0(A),B)),C) = k5_real_1(np__1,k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,B),C)) ) ) ) )).

fof(t47_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_tarski(B,C)
                   => r1_xreal_0(k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,B),D),k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,C),D)) ) ) ) ) ) )).

fof(t48_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r1_xreal_0(k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,B),D),k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,k4_subset_1(u1_struct_0(A),B,C)),D)) ) ) ) ) )).

fof(t49_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r1_xreal_0(k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,k5_subset_1(u1_struct_0(A),B,C)),D),k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,B),D)) ) ) ) ) )).

fof(t50_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r1_xreal_0(k4_square_1(k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,B),D),k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,C),D)),k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,k4_subset_1(u1_struct_0(A),B,C)),D)) ) ) ) ) )).

fof(t51_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_xboole_0(B,C)
                   => k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,k4_subset_1(u1_struct_0(A),B,C)),D) = k3_real_1(k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,B),D),k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,C),D)) ) ) ) ) ) )).

fof(t52_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r1_xreal_0(k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,k5_subset_1(u1_struct_0(A),B,C)),D),k3_square_1(k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,B),D),k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,C),D))) ) ) ) ) )).

fof(d10_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m2_finseq_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,k1_numbers)
                 => ( D = k7_roughs_1(A,B,C)
                  <=> ( k4_relset_1(k5_numbers,k1_numbers,D) = k4_relset_1(k5_numbers,k1_zfmisc_1(u1_struct_0(A)),B)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( r2_hidden(E,k4_relset_1(k5_numbers,k1_zfmisc_1(u1_struct_0(A)),B))
                           => k1_funct_1(D,E) = k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,k1_roughs_1(u1_struct_0(A),B,E)),C) ) ) ) ) ) ) ) ) )).

fof(t53_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m2_finseq_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => k7_roughs_1(A,k8_finseq_1(k1_zfmisc_1(u1_struct_0(A)),B,k12_finseq_1(k1_zfmisc_1(u1_struct_0(A)),D)),C) = k8_finseq_1(k1_numbers,k7_roughs_1(A,B,C),k12_finseq_1(k1_numbers,k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,D),C))) ) ) ) ) )).

fof(t54_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,k1_pre_topc(A)),B) = np__0 ) ) )).

fof(t55_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_prob_2(C)
                & m2_finseq_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => k8_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,k2_roughs_1(u1_struct_0(A),C)),B) = k15_rvsum_1(k7_roughs_1(A,C,B)) ) ) ) )).

fof(d11_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_roughs_1(A,B,C)
              <=> r1_tarski(k3_roughs_1(A,B),k3_roughs_1(A,C)) ) ) ) ) )).

fof(d12_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_roughs_1(A,B,C)
              <=> r1_tarski(k4_roughs_1(A,B),k4_roughs_1(A,C)) ) ) ) ) )).

fof(d13_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r3_roughs_1(A,B,C)
              <=> ( r1_roughs_1(A,B,C)
                  & r2_roughs_1(A,B,C) ) ) ) ) ) )).

fof(t59_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( r1_roughs_1(A,B,C)
                      & r1_roughs_1(A,C,D) )
                   => r1_roughs_1(A,B,D) ) ) ) ) ) )).

fof(t60_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( r2_roughs_1(A,B,C)
                      & r2_roughs_1(A,C,D) )
                   => r2_roughs_1(A,B,D) ) ) ) ) ) )).

fof(t61_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( r3_roughs_1(A,B,C)
                      & r3_roughs_1(A,C,D) )
                   => r3_roughs_1(A,B,D) ) ) ) ) ) )).

fof(d14_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r4_roughs_1(A,B,C)
              <=> k3_roughs_1(A,B) = k3_roughs_1(A,C) ) ) ) ) )).

fof(d15_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r5_roughs_1(A,B,C)
              <=> k4_roughs_1(A,B) = k4_roughs_1(A,C) ) ) ) ) )).

fof(d16_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r6_roughs_1(A,B,C)
              <=> ( k3_roughs_1(A,B) = k3_roughs_1(A,C)
                  & k4_roughs_1(A,B) = k4_roughs_1(A,C) ) ) ) ) ) )).

fof(d17_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r4_roughs_1(A,B,C)
              <=> ( r1_roughs_1(A,B,C)
                  & r1_roughs_1(A,C,B) ) ) ) ) ) )).

fof(d18_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r5_roughs_1(A,B,C)
              <=> ( r2_roughs_1(A,B,C)
                  & r2_roughs_1(A,C,B) ) ) ) ) ) )).

fof(d19_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r6_roughs_1(A,B,C)
              <=> ( r4_roughs_1(A,B,C)
                  & r5_roughs_1(A,B,C) ) ) ) ) ) )).

fof(dt_m1_roughs_1,axiom,(
    $true )).

fof(existence_m1_roughs_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_roughs_1(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ? [C] : m1_roughs_1(C,A,B) ) )).

fof(symmetry_r4_roughs_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r4_roughs_1(A,B,C)
       => r4_roughs_1(A,C,B) ) ) )).

fof(reflexivity_r4_roughs_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => r4_roughs_1(A,B,B) ) )).

fof(symmetry_r5_roughs_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r5_roughs_1(A,B,C)
       => r5_roughs_1(A,C,B) ) ) )).

fof(reflexivity_r5_roughs_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => r5_roughs_1(A,B,B) ) )).

fof(symmetry_r6_roughs_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r6_roughs_1(A,B,C)
       => r6_roughs_1(A,C,B) ) ) )).

fof(reflexivity_r6_roughs_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => r6_roughs_1(A,B,B) ) )).

fof(dt_k1_roughs_1,axiom,(
    ! [A,B,C] :
      ( ( m1_finseq_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k5_numbers) )
     => m1_subset_1(k1_roughs_1(A,B,C),k1_zfmisc_1(A)) ) )).

fof(redefinition_k1_roughs_1,axiom,(
    ! [A,B,C] :
      ( ( m1_finseq_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k5_numbers) )
     => k1_roughs_1(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k2_roughs_1,axiom,(
    ! [A,B] :
      ( m1_finseq_1(B,k1_zfmisc_1(A))
     => m1_subset_1(k2_roughs_1(A,B),k1_zfmisc_1(A)) ) )).

fof(redefinition_k2_roughs_1,axiom,(
    ! [A,B] :
      ( m1_finseq_1(B,k1_zfmisc_1(A))
     => k2_roughs_1(A,B) = k3_card_3(B) ) )).

fof(dt_k3_roughs_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k3_roughs_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k4_roughs_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k4_roughs_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k5_roughs_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k5_roughs_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k6_roughs_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v3_roughs_1(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_funct_1(k6_roughs_1(A,B))
        & v1_funct_2(k6_roughs_1(A,B),u1_struct_0(A),k1_numbers)
        & m2_relset_1(k6_roughs_1(A,B),u1_struct_0(A),k1_numbers) ) ) )).

fof(dt_k7_roughs_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v3_roughs_1(A)
        & l1_orders_2(A)
        & m1_finseq_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m2_finseq_1(k7_roughs_1(A,B,C),k1_numbers) ) )).

fof(d4_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k3_roughs_1(A,B) = a_2_0_roughs_1(A,B) ) ) )).

fof(d5_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_roughs_1(A,B) = a_2_1_roughs_1(A,B) ) ) )).

fof(t56_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k3_roughs_1(A,B) = a_2_2_roughs_1(A,B) ) ) )).

fof(t57_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_roughs_1(A,B) = a_2_3_roughs_1(A,B) ) ) )).

fof(t58_roughs_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_roughs_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k5_roughs_1(A,B) = a_2_4_roughs_1(A,B) ) ) )).

fof(fraenkel_a_2_0_roughs_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v3_roughs_1(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_0_roughs_1(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & r1_tarski(k6_eqrel_1(u1_struct_0(B),u1_orders_2(B),D),C) ) ) ) )).

fof(fraenkel_a_2_1_roughs_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v3_roughs_1(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_1_roughs_1(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & ~ r1_xboole_0(k6_eqrel_1(u1_struct_0(B),u1_orders_2(B),D),C) ) ) ) )).

fof(fraenkel_a_2_2_roughs_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v6_group_1(B)
        & v2_roughs_1(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_2_roughs_1(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & k8_funct_2(u1_struct_0(B),k1_numbers,k6_roughs_1(B,C),D) = np__1 ) ) ) )).

fof(fraenkel_a_2_3_roughs_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v6_group_1(B)
        & v2_roughs_1(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_3_roughs_1(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & ~ r1_xreal_0(k8_funct_2(u1_struct_0(B),k1_numbers,k6_roughs_1(B,C),D),np__0) ) ) ) )).

fof(fraenkel_a_2_4_roughs_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v6_group_1(B)
        & v2_roughs_1(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_4_roughs_1(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & ~ r1_xreal_0(k8_funct_2(u1_struct_0(B),k1_numbers,k6_roughs_1(B,C),D),np__0)
            & ~ r1_xreal_0(np__1,k8_funct_2(u1_struct_0(B),k1_numbers,k6_roughs_1(B,C),D)) ) ) ) )).
%------------------------------------------------------------------------------