SET007 Axioms: SET007+151.ax


%------------------------------------------------------------------------------
% File     : SET007+151 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Series of Positive Real Numbers. Measure Theory
% 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    : supinf_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  130 (   3 unit)
%            Number of atoms       :  977 ( 158 equality)
%            Maximal formula depth :   22 (   9 average)
%            Number of connectives : 1079 ( 232 ~  ;   4  |; 482  &)
%                                         (  40 <=>; 321 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   28 (   0 propositional; 1-3 arity)
%            Number of functors    :   37 (   9 constant; 0-5 arity)
%            Number of variables   :  330 (   0 singleton; 312 !;  18 ?)
%            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(fc1_supinf_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
     => ~ v1_xboole_0(k5_supinf_2(A,B)) ) )).

fof(fc2_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ~ v1_xboole_0(k6_supinf_2(A)) ) )).

fof(cc1_supinf_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
     => ! [C] :
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B)
              & v3_supinf_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,A,B)
              & v1_supinf_2(C,A,B)
              & v2_supinf_2(C,A,B) ) ) ) ) )).

fof(cc2_supinf_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
     => ! [C] :
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B)
              & v1_supinf_2(C,A,B)
              & v2_supinf_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,A,B)
              & v3_supinf_2(C,A,B) ) ) ) ) )).

fof(rc1_supinf_2,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
      & ~ v1_xboole_0(A)
      & v1_card_4(A) ) )).

fof(rc2_supinf_2,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
      & ~ v1_xboole_0(A)
      & v1_card_4(A)
      & v5_supinf_2(A) ) )).

fof(d1_supinf_2,axiom,(
    k1_supinf_2 = np__0 )).

fof(d2_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( ( r2_hidden(A,k6_supinf_1)
                    & r2_hidden(B,k6_supinf_1) )
                 => ( C = k2_supinf_2(A,B)
                  <=> ? [D] :
                        ( m1_subset_1(D,k1_numbers)
                        & ? [E] :
                            ( m1_subset_1(E,k1_numbers)
                            & A = D
                            & B = E
                            & C = k3_real_1(D,E) ) ) ) )
                & ( ( ( A = k4_supinf_1
                      & B != k5_supinf_1 )
                    | ( B = k4_supinf_1
                      & A != k5_supinf_1 ) )
                 => ( C = k2_supinf_2(A,B)
                  <=> C = k4_supinf_1 ) )
                & ( ( ( A = k5_supinf_1
                      & B != k4_supinf_1 )
                    | ( B = k5_supinf_1
                      & A != k4_supinf_1 ) )
                 => ( C = k2_supinf_2(A,B)
                  <=> C = k5_supinf_1 ) )
                & ~ ( ~ ( r2_hidden(A,k6_supinf_1)
                        & r2_hidden(B,k6_supinf_1) )
                    & ~ ( A = k4_supinf_1
                        & B != k5_supinf_1 )
                    & ~ ( B = k4_supinf_1
                        & A != k5_supinf_1 )
                    & ~ ( A = k5_supinf_1
                        & B != k4_supinf_1 )
                    & ~ ( B = k5_supinf_1
                        & A != k4_supinf_1 )
                    & ~ ( C = k2_supinf_2(A,B)
                      <=> C = k1_supinf_2 ) ) ) ) ) ) )).

fof(t1_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( ( A = C
                      & B = D )
                   => k2_supinf_2(A,B) = k3_real_1(C,D) ) ) ) ) ) )).

fof(t2_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ~ ( ~ r2_hidden(A,k6_supinf_1)
          & A != k4_supinf_1
          & A != k5_supinf_1 ) ) )).

fof(d3_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( ( r2_hidden(A,k6_supinf_1)
             => ( B = k3_supinf_2(A)
              <=> ? [C] :
                    ( m1_subset_1(C,k1_numbers)
                    & A = C
                    & B = k1_real_1(C) ) ) )
            & ( A = k4_supinf_1
             => ( B = k3_supinf_2(A)
              <=> B = k5_supinf_1 ) )
            & ~ ( ~ r2_hidden(A,k6_supinf_1)
                & A != k4_supinf_1
                & ~ ( B = k3_supinf_2(A)
                  <=> B = k4_supinf_1 ) ) ) ) ) )).

fof(d4_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => k4_supinf_2(A,B) = k2_supinf_2(A,k3_supinf_2(B)) ) ) )).

fof(t3_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( A = B
           => k3_supinf_2(A) = k1_real_1(B) ) ) ) )).

fof(t4_supinf_2,axiom,(
    k3_supinf_2(k5_supinf_1) = k4_supinf_1 )).

fof(t5_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( ( A = C
                      & B = D )
                   => k4_supinf_2(A,B) = k5_real_1(C,D) ) ) ) ) ) )).

fof(t6_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ( A != k4_supinf_1
       => ( k4_supinf_2(k4_supinf_1,A) = k4_supinf_1
          & k4_supinf_2(A,k4_supinf_1) = k5_supinf_1 ) ) ) )).

fof(t7_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ( A != k5_supinf_1
       => ( k4_supinf_2(k5_supinf_1,A) = k5_supinf_1
          & k4_supinf_2(A,k5_supinf_1) = k4_supinf_1 ) ) ) )).

fof(t8_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ~ ( k2_supinf_2(A,B) = k4_supinf_1
              & A != k4_supinf_1
              & B != k4_supinf_1 ) ) ) )).

fof(t9_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ~ ( k2_supinf_2(A,B) = k5_supinf_1
              & A != k5_supinf_1
              & B != k5_supinf_1 ) ) ) )).

fof(t10_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ~ ( k4_supinf_2(A,B) = k4_supinf_1
              & A != k4_supinf_1
              & B != k5_supinf_1 ) ) ) )).

fof(t11_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ~ ( k4_supinf_2(A,B) = k5_supinf_1
              & A != k5_supinf_1
              & B != k4_supinf_1 ) ) ) )).

fof(t12_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ~ ( ~ ( A = k4_supinf_1
                  & B = k5_supinf_1 )
              & ~ ( A = k5_supinf_1
                  & B = k4_supinf_1 )
              & r2_hidden(k2_supinf_2(A,B),k6_supinf_1)
              & ~ ( r2_hidden(A,k6_supinf_1)
                  & r2_hidden(B,k6_supinf_1) ) ) ) ) )).

fof(t13_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ~ ( ~ ( A = k4_supinf_1
                  & B = k4_supinf_1 )
              & ~ ( A = k5_supinf_1
                  & B = k5_supinf_1 )
              & r2_hidden(k4_supinf_2(A,B),k6_supinf_1)
              & ~ ( r2_hidden(A,k6_supinf_1)
                  & r2_hidden(B,k6_supinf_1) ) ) ) ) )).

fof(t14_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ! [D] :
                  ( m1_subset_1(D,k3_supinf_1)
                 => ~ ( ~ ( A = k4_supinf_1
                          & C = k5_supinf_1 )
                      & ~ ( A = k5_supinf_1
                          & C = k4_supinf_1 )
                      & ~ ( B = k4_supinf_1
                          & D = k5_supinf_1 )
                      & ~ ( B = k5_supinf_1
                          & D = k4_supinf_1 )
                      & r1_supinf_1(A,B)
                      & r1_supinf_1(C,D)
                      & ~ r1_supinf_1(k2_supinf_2(A,C),k2_supinf_2(B,D)) ) ) ) ) ) )).

fof(t15_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ! [D] :
                  ( m1_subset_1(D,k3_supinf_1)
                 => ~ ( ~ ( A = k4_supinf_1
                          & D = k4_supinf_1 )
                      & ~ ( A = k5_supinf_1
                          & D = k5_supinf_1 )
                      & ~ ( B = k4_supinf_1
                          & C = k4_supinf_1 )
                      & ~ ( B = k5_supinf_1
                          & C = k5_supinf_1 )
                      & r1_supinf_1(A,B)
                      & r1_supinf_1(C,D)
                      & ~ r1_supinf_1(k4_supinf_2(A,D),k4_supinf_2(B,C)) ) ) ) ) ) )).

fof(t16_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( r1_supinf_1(A,B)
          <=> r1_supinf_1(k3_supinf_2(B),k3_supinf_2(A)) ) ) ) )).

fof(t17_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( ~ ( ~ r1_supinf_1(B,A)
                & r1_supinf_1(k3_supinf_2(A),k3_supinf_2(B)) )
            & ~ ( ~ r1_supinf_1(k3_supinf_2(A),k3_supinf_2(B))
                & r1_supinf_1(B,A) ) ) ) ) )).

fof(t18_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ( k2_supinf_2(A,k1_supinf_2) = A
        & k2_supinf_2(k1_supinf_2,A) = A ) ) )).

fof(t19_supinf_2,axiom,
    ( ~ r1_supinf_1(k1_supinf_2,k5_supinf_1)
    & ~ r1_supinf_1(k4_supinf_1,k1_supinf_2) )).

fof(t20_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( r1_supinf_1(k1_supinf_2,C)
                  & r1_supinf_1(k1_supinf_2,A)
                  & B = k2_supinf_2(A,C) )
               => r1_supinf_1(A,B) ) ) ) ) )).

fof(t21_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ( r2_hidden(A,k5_numbers)
       => r1_supinf_1(k1_supinf_2,A) ) ) )).

fof(d5_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k3_supinf_1))
             => ( C = k5_supinf_2(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k3_supinf_1)
                   => ( r2_hidden(D,C)
                    <=> ? [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                          & ? [F] :
                              ( m1_subset_1(F,k3_supinf_1)
                              & r2_hidden(E,A)
                              & r2_hidden(F,B)
                              & D = k2_supinf_2(E,F) ) ) ) ) ) ) ) ) )).

fof(d6_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ( B = k6_supinf_2(A)
          <=> ! [C] :
                ( m1_subset_1(C,k3_supinf_1)
               => ( r2_hidden(C,B)
                <=> ? [D] :
                      ( m1_subset_1(D,k3_supinf_1)
                      & r2_hidden(D,A)
                      & C = k3_supinf_2(D) ) ) ) ) ) ) )).

fof(t22_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => k6_supinf_2(k6_supinf_2(A)) = A ) )).

fof(t23_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( r2_hidden(B,A)
          <=> r2_hidden(k3_supinf_2(B),k6_supinf_2(A)) ) ) ) )).

fof(t24_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ( r1_tarski(A,B)
          <=> r1_tarski(k6_supinf_2(A),k6_supinf_2(B)) ) ) ) )).

fof(t25_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ( r2_hidden(A,k6_supinf_1)
      <=> r2_hidden(k3_supinf_2(A),k6_supinf_1) ) ) )).

fof(t26_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ~ ( ~ ( r2_hidden(k5_supinf_1,A)
                  & r2_hidden(k4_supinf_1,B) )
              & ~ ( r2_hidden(k4_supinf_1,A)
                  & r2_hidden(k5_supinf_1,B) )
              & ~ ( k9_supinf_1(A) = k4_supinf_1
                  & k9_supinf_1(B) = k5_supinf_1 )
              & ~ ( k9_supinf_1(A) = k5_supinf_1
                  & k9_supinf_1(B) = k4_supinf_1 )
              & ~ r1_supinf_1(k9_supinf_1(k5_supinf_2(A,B)),k2_supinf_2(k9_supinf_1(A),k9_supinf_1(B))) ) ) ) )).

fof(t27_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ~ ( ~ ( r2_hidden(k5_supinf_1,A)
                  & r2_hidden(k4_supinf_1,B) )
              & ~ ( r2_hidden(k4_supinf_1,A)
                  & r2_hidden(k5_supinf_1,B) )
              & ~ ( k10_supinf_1(A) = k4_supinf_1
                  & k10_supinf_1(B) = k5_supinf_1 )
              & ~ ( k10_supinf_1(A) = k5_supinf_1
                  & k10_supinf_1(B) = k4_supinf_1 )
              & ~ r1_supinf_1(k2_supinf_2(k10_supinf_1(A),k10_supinf_1(B)),k10_supinf_1(k5_supinf_2(A,B))) ) ) ) )).

fof(t28_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ( ( v4_supinf_1(A)
              & v4_supinf_1(B) )
           => r1_supinf_1(k9_supinf_1(k5_supinf_2(A,B)),k2_supinf_2(k9_supinf_1(A),k9_supinf_1(B))) ) ) ) )).

fof(t29_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ( ( v5_supinf_1(A)
              & v5_supinf_1(B) )
           => r1_supinf_1(k2_supinf_2(k10_supinf_1(A),k10_supinf_1(B)),k10_supinf_1(k5_supinf_2(A,B))) ) ) ) )).

fof(t30_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( m1_supinf_1(B,A)
          <=> m2_supinf_1(k3_supinf_2(B),k6_supinf_2(A)) ) ) ) )).

fof(t31_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( m2_supinf_1(B,A)
          <=> m1_supinf_1(k3_supinf_2(B),k6_supinf_2(A)) ) ) ) )).

fof(t32_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => k10_supinf_1(k6_supinf_2(A)) = k3_supinf_2(k9_supinf_1(A)) ) )).

fof(t33_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => k9_supinf_1(k6_supinf_2(A)) = k3_supinf_2(k10_supinf_1(A)) ) )).

fof(d7_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => k8_supinf_2(A,B,C) = k9_supinf_1(k7_supinf_2(A,B,C)) ) ) ) )).

fof(d8_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => k9_supinf_2(A,B,C) = k10_supinf_1(k7_supinf_2(A,B,C)) ) ) ) )).

fof(d9_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k3_supinf_1)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,C)
                        & m2_relset_1(E,A,C) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,k5_supinf_2(B,C))
                            & m2_relset_1(F,A,k5_supinf_2(B,C)) )
                         => ( F = k11_supinf_2(A,B,C,D,E)
                          <=> ! [G] :
                                ( m1_subset_1(G,A)
                               => k10_supinf_2(A,k5_supinf_2(B,C),F,G) = k2_supinf_2(k10_supinf_2(A,B,D,G),k10_supinf_2(A,C,E,G)) ) ) ) ) ) ) ) ) )).

fof(t34_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k3_supinf_1)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,C)
                        & m2_relset_1(E,A,C) )
                     => r1_tarski(k7_supinf_2(A,k5_supinf_2(B,C),k11_supinf_2(A,B,C,D,E)),k5_supinf_2(k7_supinf_2(A,B,D),k7_supinf_2(A,C,E))) ) ) ) ) ) )).

fof(t35_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k3_supinf_1)) )
             => ~ ( ~ ( r2_hidden(k5_supinf_1,B)
                      & r2_hidden(k4_supinf_1,C) )
                  & ~ ( r2_hidden(k4_supinf_1,B)
                      & r2_hidden(k5_supinf_1,C) )
                  & ? [D] :
                      ( v1_funct_1(D)
                      & v1_funct_2(D,A,B)
                      & m2_relset_1(D,A,B)
                      & ? [E] :
                          ( v1_funct_1(E)
                          & v1_funct_2(E,A,C)
                          & m2_relset_1(E,A,C)
                          & ~ ( k8_supinf_2(A,B,D) = k4_supinf_1
                              & k8_supinf_2(A,C,E) = k5_supinf_1 )
                          & ~ ( k8_supinf_2(A,B,D) = k5_supinf_1
                              & k8_supinf_2(A,C,E) = k4_supinf_1 )
                          & ~ r1_supinf_1(k8_supinf_2(A,k5_supinf_2(B,C),k11_supinf_2(A,B,C,D,E)),k2_supinf_2(k8_supinf_2(A,B,D),k8_supinf_2(A,C,E))) ) ) ) ) ) ) )).

fof(t36_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k3_supinf_1)) )
             => ~ ( ~ ( r2_hidden(k5_supinf_1,B)
                      & r2_hidden(k4_supinf_1,C) )
                  & ~ ( r2_hidden(k4_supinf_1,B)
                      & r2_hidden(k5_supinf_1,C) )
                  & ? [D] :
                      ( v1_funct_1(D)
                      & v1_funct_2(D,A,B)
                      & m2_relset_1(D,A,B)
                      & ? [E] :
                          ( v1_funct_1(E)
                          & v1_funct_2(E,A,C)
                          & m2_relset_1(E,A,C)
                          & ~ ( k9_supinf_2(A,B,D) = k4_supinf_1
                              & k9_supinf_2(A,C,E) = k5_supinf_1 )
                          & ~ ( k9_supinf_2(A,B,D) = k5_supinf_1
                              & k9_supinf_2(A,C,E) = k4_supinf_1 )
                          & ~ r1_supinf_1(k2_supinf_2(k9_supinf_2(A,B,D),k9_supinf_2(A,C,E)),k9_supinf_2(A,k5_supinf_2(B,C),k11_supinf_2(A,B,C,D,E))) ) ) ) ) ) ) )).

fof(d10_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,k6_supinf_2(B))
                    & m2_relset_1(D,A,k6_supinf_2(B)) )
                 => ( D = k12_supinf_2(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,A)
                       => k10_supinf_2(A,k6_supinf_2(B),D,E) = k3_supinf_2(k10_supinf_2(A,B,C,E)) ) ) ) ) ) ) )).

fof(t37_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => k7_supinf_2(A,k6_supinf_2(B),k12_supinf_2(A,B,C)) = k6_supinf_2(k7_supinf_2(A,B,C)) ) ) ) )).

fof(t38_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( k9_supinf_2(A,k6_supinf_2(B),k12_supinf_2(A,B,C)) = k3_supinf_2(k8_supinf_2(A,B,C))
                & k8_supinf_2(A,k6_supinf_2(B),k12_supinf_2(A,B,C)) = k3_supinf_2(k9_supinf_2(A,B,C)) ) ) ) ) )).

fof(d11_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v1_supinf_2(C,A,B)
              <=> ~ r1_supinf_1(k4_supinf_1,k8_supinf_2(A,B,C)) ) ) ) ) )).

fof(d12_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v2_supinf_2(C,A,B)
              <=> ~ r1_supinf_1(k9_supinf_2(A,B,C),k5_supinf_1) ) ) ) ) )).

fof(d13_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v3_supinf_2(C,A,B)
              <=> ( v1_supinf_2(C,A,B)
                  & v2_supinf_2(C,A,B) ) ) ) ) ) )).

fof(t39_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v3_supinf_2(C,A,B)
              <=> ( ~ r1_supinf_1(k4_supinf_1,k8_supinf_2(A,B,C))
                  & ~ r1_supinf_1(k9_supinf_2(A,B,C),k5_supinf_1) ) ) ) ) ) )).

fof(t40_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v1_supinf_2(C,A,B)
              <=> v2_supinf_2(k12_supinf_2(A,B,C),A,k6_supinf_2(B)) ) ) ) ) )).

fof(t41_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v2_supinf_2(C,A,B)
              <=> v1_supinf_2(k12_supinf_2(A,B,C),A,k6_supinf_2(B)) ) ) ) ) )).

fof(t42_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v3_supinf_2(C,A,B)
              <=> v3_supinf_2(k12_supinf_2(A,B,C),A,k6_supinf_2(B)) ) ) ) ) )).

fof(t43_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ( r1_supinf_1(k5_supinf_1,k10_supinf_2(A,B,C,D))
                    & r1_supinf_1(k10_supinf_2(A,B,C,D),k4_supinf_1) ) ) ) ) ) )).

fof(t44_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ( r1_tarski(B,k6_supinf_1)
                   => ( ~ r1_supinf_1(k10_supinf_2(A,B,C,D),k5_supinf_1)
                      & ~ r1_supinf_1(k4_supinf_1,k10_supinf_2(A,B,C,D)) ) ) ) ) ) ) )).

fof(t45_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ( r1_supinf_1(k9_supinf_2(A,B,C),k10_supinf_2(A,B,C,D))
                    & r1_supinf_1(k10_supinf_2(A,B,C,D),k8_supinf_2(A,B,C)) ) ) ) ) ) )).

fof(t46_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( r1_tarski(B,k6_supinf_1)
               => ( v1_supinf_2(C,A,B)
                <=> r2_hidden(k8_supinf_2(A,B,C),k6_supinf_1) ) ) ) ) ) )).

fof(t47_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( r1_tarski(B,k6_supinf_1)
               => ( v2_supinf_2(C,A,B)
                <=> r2_hidden(k9_supinf_2(A,B,C),k6_supinf_1) ) ) ) ) ) )).

fof(t48_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( r1_tarski(B,k6_supinf_1)
               => ( v3_supinf_2(C,A,B)
                <=> ( r2_hidden(k9_supinf_2(A,B,C),k6_supinf_1)
                    & r2_hidden(k8_supinf_2(A,B,C),k6_supinf_1) ) ) ) ) ) ) )).

fof(t49_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k3_supinf_1)) )
             => ( ( r1_tarski(B,k6_supinf_1)
                  & r1_tarski(C,k6_supinf_1) )
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,A,B)
                      & m2_relset_1(D,A,B) )
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,A,C)
                          & m2_relset_1(E,A,C) )
                       => ( ( v1_supinf_2(D,A,B)
                            & v1_supinf_2(E,A,C) )
                         => v1_supinf_2(k11_supinf_2(A,B,C,D,E),A,k5_supinf_2(B,C)) ) ) ) ) ) ) ) )).

fof(t50_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k3_supinf_1)) )
             => ( ( r1_tarski(B,k6_supinf_1)
                  & r1_tarski(C,k6_supinf_1) )
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,A,B)
                      & m2_relset_1(D,A,B) )
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,A,C)
                          & m2_relset_1(E,A,C) )
                       => ( ( v2_supinf_2(D,A,B)
                            & v2_supinf_2(E,A,C) )
                         => v2_supinf_2(k11_supinf_2(A,B,C,D,E),A,k5_supinf_2(B,C)) ) ) ) ) ) ) ) )).

fof(t51_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k3_supinf_1)) )
             => ( ( r1_tarski(B,k6_supinf_1)
                  & r1_tarski(C,k6_supinf_1) )
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,A,B)
                      & m2_relset_1(D,A,B) )
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,A,C)
                          & m2_relset_1(E,A,C) )
                       => ( ( v3_supinf_2(D,A,B)
                            & v3_supinf_2(E,A,C) )
                         => v3_supinf_2(k11_supinf_2(A,B,C,D,E),A,k5_supinf_2(B,C)) ) ) ) ) ) ) ) )).

fof(t52_supinf_2,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k3_supinf_1)
      & m2_relset_1(A,k5_numbers,k3_supinf_1)
      & v2_funct_1(A)
      & k5_numbers = k2_relat_1(A)
      & ~ v1_xboole_0(k2_relat_1(A))
      & m1_subset_1(k2_relat_1(A),k1_zfmisc_1(k3_supinf_1)) ) )).

fof(d14_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_card_4(B)
          <=> ~ ( ~ v1_xboole_0(B)
                & ! [C] :
                    ( ( v1_funct_1(C)
                      & v1_funct_2(C,k5_numbers,A)
                      & m2_relset_1(C,k5_numbers,A) )
                   => B != k2_relat_1(C) ) ) ) ) ) )).

fof(d15_supinf_2,axiom,(
    ! [A] :
      ( v5_supinf_2(A)
    <=> ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( r2_hidden(B,A)
           => r1_supinf_1(k1_supinf_2,B) ) ) ) )).

fof(d16_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_card_4(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k3_supinf_1)
            & m2_relset_1(B,k5_numbers,k3_supinf_1) )
         => ( m1_supinf_2(B,A)
          <=> A = k2_relat_1(B) ) ) ) )).

fof(t53_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_card_4(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_supinf_2(B,A)
         => ? [C] :
              ( v1_funct_1(C)
              & v1_funct_2(C,k5_numbers,k3_supinf_1)
              & m2_relset_1(C,k5_numbers,k3_supinf_1)
              & k13_supinf_2(C,np__0) = k13_supinf_2(B,np__0)
              & ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,k3_supinf_1)
                     => ( E = k13_supinf_2(C,D)
                       => k13_supinf_2(C,k1_nat_1(D,np__1)) = k2_supinf_2(E,k13_supinf_2(B,k1_nat_1(D,np__1))) ) ) ) ) ) ) )).

fof(d17_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_card_4(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_supinf_2(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k3_supinf_1)
                & m2_relset_1(C,k5_numbers,k3_supinf_1) )
             => ( C = k14_supinf_2(A,B)
              <=> ( k13_supinf_2(C,np__0) = k13_supinf_2(B,np__0)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( E = k13_supinf_2(C,D)
                           => k13_supinf_2(C,k1_nat_1(D,np__1)) = k2_supinf_2(E,k13_supinf_2(B,k1_nat_1(D,np__1))) ) ) ) ) ) ) ) ) )).

fof(t54_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_card_4(A)
        & v5_supinf_2(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_supinf_2(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => r1_supinf_1(k1_supinf_2,k13_supinf_2(B,C)) ) ) ) )).

fof(t55_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_card_4(A)
        & v5_supinf_2(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_supinf_2(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_supinf_1(k13_supinf_2(k14_supinf_2(A,B),C),k13_supinf_2(k14_supinf_2(A,B),k1_nat_1(C,np__1)))
                & r1_supinf_1(k1_supinf_2,k13_supinf_2(k14_supinf_2(A,B),C)) ) ) ) ) )).

fof(t56_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_card_4(A)
        & v5_supinf_2(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_supinf_2(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => r1_supinf_1(k13_supinf_2(k14_supinf_2(A,B),C),k13_supinf_2(k14_supinf_2(A,B),k1_nat_1(C,D))) ) ) ) ) )).

fof(d18_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_card_4(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ( m2_supinf_2(B,A)
          <=> ? [C] :
                ( m1_supinf_2(C,A)
                & B = k2_relat_1(k14_supinf_2(A,C)) ) ) ) ) )).

fof(d19_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_card_4(A)
        & v5_supinf_2(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_supinf_2(B,A)
         => k16_supinf_2(A,B) = k9_supinf_1(k15_supinf_2(k14_supinf_2(A,B))) ) ) )).

fof(d20_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_card_4(A)
        & v5_supinf_2(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_supinf_2(B,A)
         => ( r1_supinf_2(A,B)
          <=> r2_hidden(k16_supinf_2(A,B),k6_supinf_1) ) ) ) )).

fof(t57_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ( ~ v1_xboole_0(k15_supinf_2(A))
        & v1_card_4(k15_supinf_2(A))
        & m1_subset_1(k15_supinf_2(A),k1_zfmisc_1(k3_supinf_1)) ) ) )).

fof(d21_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k3_supinf_1)
            & m2_relset_1(B,k5_numbers,k3_supinf_1) )
         => ( B = k18_supinf_2(A)
          <=> ! [C] :
                ( m1_supinf_2(C,k17_supinf_2(A))
               => ( C = A
                 => B = k14_supinf_2(k17_supinf_2(A),C) ) ) ) ) ) )).

fof(d22_supinf_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k3_supinf_1)
        & m2_relset_1(B,A,k3_supinf_1) )
     => ( v6_supinf_2(B,A)
      <=> v5_supinf_2(k2_relat_1(B)) ) ) )).

fof(d23_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => k19_supinf_2(A) = k9_supinf_1(k17_supinf_2(k18_supinf_2(A))) ) )).

fof(t58_supinf_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k3_supinf_1)
            & m2_relset_1(B,A,k3_supinf_1) )
         => ( v6_supinf_2(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,A)
               => r1_supinf_1(k1_supinf_2,k8_funct_2(A,k3_supinf_1,B,C)) ) ) ) ) )).

fof(t59_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( v6_supinf_2(A,k5_numbers)
           => ( r1_supinf_1(k13_supinf_2(k18_supinf_2(A),B),k13_supinf_2(k18_supinf_2(A),k1_nat_1(B,np__1)))
              & r1_supinf_1(k1_supinf_2,k13_supinf_2(k18_supinf_2(A),B)) ) ) ) ) )).

fof(t60_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ( v6_supinf_2(A,k5_numbers)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r1_supinf_1(k13_supinf_2(k18_supinf_2(A),B),k13_supinf_2(k18_supinf_2(A),k1_nat_1(B,C))) ) ) ) ) )).

fof(t61_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k3_supinf_1)
            & m2_relset_1(B,k5_numbers,k3_supinf_1) )
         => ( ( v6_supinf_2(A,k5_numbers)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => r1_supinf_1(k13_supinf_2(A,C),k13_supinf_2(B,C)) ) )
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r1_supinf_1(k13_supinf_2(k18_supinf_2(A),C),k13_supinf_2(k18_supinf_2(B),C)) ) ) ) ) )).

fof(t62_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k3_supinf_1)
            & m2_relset_1(B,k5_numbers,k3_supinf_1) )
         => ( ( v6_supinf_2(A,k5_numbers)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => r1_supinf_1(k13_supinf_2(A,C),k13_supinf_2(B,C)) ) )
           => r1_supinf_1(k19_supinf_2(A),k19_supinf_2(B)) ) ) ) )).

fof(t63_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ( k13_supinf_2(k18_supinf_2(A),np__0) = k13_supinf_2(A,np__0)
        & ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m1_subset_1(C,k3_supinf_1)
               => ( C = k13_supinf_2(k18_supinf_2(A),B)
                 => k13_supinf_2(k18_supinf_2(A),k1_nat_1(B,np__1)) = k2_supinf_2(C,k13_supinf_2(A,k1_nat_1(B,np__1))) ) ) ) ) ) )).

fof(t64_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ( v6_supinf_2(A,k5_numbers)
       => ( ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => k13_supinf_2(A,B) != k4_supinf_1 )
          | k19_supinf_2(A) = k4_supinf_1 ) ) ) )).

fof(d24_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ( v7_supinf_2(A)
      <=> r2_hidden(k19_supinf_2(A),k6_supinf_1) ) ) )).

fof(t65_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ~ ( v6_supinf_2(A,k5_numbers)
          & ? [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
              & k13_supinf_2(A,B) = k4_supinf_1 )
          & v7_supinf_2(A) ) ) )).

fof(t66_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k3_supinf_1)
            & m2_relset_1(B,k5_numbers,k3_supinf_1) )
         => ( ( v6_supinf_2(A,k5_numbers)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => r1_supinf_1(k13_supinf_2(A,C),k13_supinf_2(B,C)) )
              & v7_supinf_2(B) )
           => v7_supinf_2(A) ) ) ) )).

fof(t67_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ( v6_supinf_2(A,k5_numbers)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(B,C)
                   => k13_supinf_2(A,C) = k1_supinf_2 ) )
             => k19_supinf_2(A) = k13_supinf_2(k18_supinf_2(A),B) ) ) ) ) )).

fof(t68_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ( ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => r2_hidden(k13_supinf_2(A,B),k6_supinf_1) )
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => r2_hidden(k13_supinf_2(k18_supinf_2(A),B),k6_supinf_1) ) ) ) )).

fof(t69_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ( v6_supinf_2(A,k5_numbers)
       => ( ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ~ ( ! [C] :
                      ( m2_subset_1(C,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(B,C)
                       => k13_supinf_2(A,C) = k1_supinf_2 ) )
                  & ! [C] :
                      ( m2_subset_1(C,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(C,B)
                          & k13_supinf_2(A,C) = k4_supinf_1 ) ) ) )
          | v7_supinf_2(A) ) ) ) )).

fof(dt_m1_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_card_4(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_supinf_2(B,A)
         => ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k3_supinf_1)
            & m2_relset_1(B,k5_numbers,k3_supinf_1) ) ) ) )).

fof(existence_m1_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_card_4(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ? [B] : m1_supinf_2(B,A) ) )).

fof(dt_m2_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_card_4(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m2_supinf_2(B,A)
         => ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) ) ) ) )).

fof(existence_m2_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_card_4(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ? [B] : m2_supinf_2(B,A) ) )).

fof(redefinition_v4_supinf_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ( v4_supinf_2(B,A)
      <=> v1_card_4(B) ) ) )).

fof(dt_k1_supinf_2,axiom,(
    m1_subset_1(k1_supinf_2,k3_supinf_1) )).

fof(dt_k2_supinf_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k2_supinf_2(A,B),k3_supinf_1) ) )).

fof(commutativity_k2_supinf_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => k2_supinf_2(A,B) = k2_supinf_2(B,A) ) )).

fof(dt_k3_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => m1_subset_1(k3_supinf_2(A),k3_supinf_1) ) )).

fof(involutiveness_k3_supinf_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => k3_supinf_2(k3_supinf_2(A)) = A ) )).

fof(dt_k4_supinf_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k4_supinf_2(A,B),k3_supinf_1) ) )).

fof(dt_k5_supinf_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
     => m1_subset_1(k5_supinf_2(A,B),k1_zfmisc_1(k3_supinf_1)) ) )).

fof(dt_k6_supinf_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => m1_subset_1(k6_supinf_2(A),k1_zfmisc_1(k3_supinf_1)) ) )).

fof(dt_k7_supinf_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => ( ~ v1_xboole_0(k7_supinf_2(A,B,C))
        & m1_subset_1(k7_supinf_2(A,B,C),k1_zfmisc_1(k3_supinf_1)) ) ) )).

fof(redefinition_k7_supinf_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k7_supinf_2(A,B,C) = k2_relat_1(C) ) )).

fof(dt_k8_supinf_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k8_supinf_2(A,B,C),k3_supinf_1) ) )).

fof(dt_k9_supinf_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k9_supinf_2(A,B,C),k3_supinf_1) ) )).

fof(dt_k10_supinf_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k10_supinf_2(A,B,C,D),k3_supinf_1) ) )).

fof(redefinition_k10_supinf_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k10_supinf_2(A,B,C,D) = k1_funct_1(C,D) ) )).

fof(dt_k11_supinf_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k3_supinf_1))
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,A,C)
        & m1_relset_1(E,A,C) )
     => ( v1_funct_1(k11_supinf_2(A,B,C,D,E))
        & v1_funct_2(k11_supinf_2(A,B,C,D,E),A,k5_supinf_2(B,C))
        & m2_relset_1(k11_supinf_2(A,B,C,D,E),A,k5_supinf_2(B,C)) ) ) )).

fof(dt_k12_supinf_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => ( v1_funct_1(k12_supinf_2(A,B,C))
        & v1_funct_2(k12_supinf_2(A,B,C),A,k6_supinf_2(B))
        & m2_relset_1(k12_supinf_2(A,B,C),A,k6_supinf_2(B)) ) ) )).

fof(dt_k13_supinf_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m1_relset_1(A,k5_numbers,k3_supinf_1)
        & m1_subset_1(B,k5_numbers) )
     => m1_subset_1(k13_supinf_2(A,B),k3_supinf_1) ) )).

fof(redefinition_k13_supinf_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m1_relset_1(A,k5_numbers,k3_supinf_1)
        & m1_subset_1(B,k5_numbers) )
     => k13_supinf_2(A,B) = k1_funct_1(A,B) ) )).

fof(dt_k14_supinf_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_card_4(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
        & m1_supinf_2(B,A) )
     => ( v1_funct_1(k14_supinf_2(A,B))
        & v1_funct_2(k14_supinf_2(A,B),k5_numbers,k3_supinf_1)
        & m2_relset_1(k14_supinf_2(A,B),k5_numbers,k3_supinf_1) ) ) )).

fof(dt_k15_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m1_relset_1(A,k5_numbers,k3_supinf_1) )
     => ( ~ v1_xboole_0(k15_supinf_2(A))
        & m1_subset_1(k15_supinf_2(A),k1_zfmisc_1(k3_supinf_1)) ) ) )).

fof(redefinition_k15_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m1_relset_1(A,k5_numbers,k3_supinf_1) )
     => k15_supinf_2(A) = k2_relat_1(A) ) )).

fof(dt_k16_supinf_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_card_4(A)
        & v5_supinf_2(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
        & m1_supinf_2(B,A) )
     => m1_subset_1(k16_supinf_2(A,B),k3_supinf_1) ) )).

fof(dt_k17_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m1_relset_1(A,k5_numbers,k3_supinf_1) )
     => ( ~ v1_xboole_0(k17_supinf_2(A))
        & v1_card_4(k17_supinf_2(A))
        & m1_subset_1(k17_supinf_2(A),k1_zfmisc_1(k3_supinf_1)) ) ) )).

fof(redefinition_k17_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m1_relset_1(A,k5_numbers,k3_supinf_1) )
     => k17_supinf_2(A) = k2_relat_1(A) ) )).

fof(dt_k18_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m1_relset_1(A,k5_numbers,k3_supinf_1) )
     => ( v1_funct_1(k18_supinf_2(A))
        & v1_funct_2(k18_supinf_2(A),k5_numbers,k3_supinf_1)
        & m2_relset_1(k18_supinf_2(A),k5_numbers,k3_supinf_1) ) ) )).

fof(dt_k19_supinf_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m1_relset_1(A,k5_numbers,k3_supinf_1) )
     => m1_subset_1(k19_supinf_2(A),k3_supinf_1) ) )).
%------------------------------------------------------------------------------