SET007 Axioms: SET007+119.ax


%------------------------------------------------------------------------------
% File     : SET007+119 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Infimum and Supremum of the Set of Real Numbers
% 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_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  179 (  65 unit)
%            Number of atoms       :  619 (  71 equality)
%            Maximal formula depth :   14 (   5 average)
%            Number of connectives :  539 (  99 ~  ;   5  |; 129  &)
%                                         (  27 <=>; 279 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   20 (   1 propositional; 0-2 arity)
%            Number of functors    :   22 (   7 constant; 0-3 arity)
%            Number of variables   :  244 (   0 singleton; 223 !;  21 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_supinf_1,axiom,(
    ? [A] : v1_supinf_1(A) )).

fof(rc2_supinf_1,axiom,(
    ? [A] : v2_supinf_1(A) )).

fof(rc3_supinf_1,axiom,(
    ? [A] : v3_supinf_1(A) )).

fof(cc1_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => v3_supinf_1(A) ) )).

fof(cc2_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_supinf_1(A) ) ) )).

fof(fc1_supinf_1,axiom,(
    ~ v1_xboole_0(k3_supinf_1) )).

fof(fc2_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ~ v1_xboole_0(k7_supinf_1(A)) ) )).

fof(fc3_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ~ v1_xboole_0(k8_supinf_1(A)) ) )).

fof(fc4_supinf_1,axiom,(
    ! [A] :
      ( m3_supinf_1(A,k3_supinf_1)
     => ~ v1_xboole_0(k13_supinf_1(A)) ) )).

fof(fc5_supinf_1,axiom,(
    ! [A] :
      ( m3_supinf_1(A,k3_supinf_1)
     => ~ v1_xboole_0(k14_supinf_1(A)) ) )).

fof(d1_supinf_1,axiom,(
    k1_supinf_1 = k1_numbers )).

fof(t1_supinf_1,axiom,(
    $true )).

fof(t2_supinf_1,axiom,(
    ~ r2_hidden(k1_supinf_1,k1_numbers) )).

fof(d2_supinf_1,axiom,(
    ! [A] :
      ( v1_supinf_1(A)
    <=> A = k1_supinf_1 ) )).

fof(t3_supinf_1,axiom,(
    $true )).

fof(t4_supinf_1,axiom,(
    v1_supinf_1(k1_supinf_1) )).

fof(d3_supinf_1,axiom,(
    k2_supinf_1 = k1_tarski(k1_numbers) )).

fof(t5_supinf_1,axiom,(
    $true )).

fof(t6_supinf_1,axiom,(
    ~ r2_hidden(k2_supinf_1,k1_numbers) )).

fof(d4_supinf_1,axiom,(
    ! [A] :
      ( v2_supinf_1(A)
    <=> A = k2_supinf_1 ) )).

fof(t7_supinf_1,axiom,(
    $true )).

fof(t8_supinf_1,axiom,(
    v2_supinf_1(k2_supinf_1) )).

fof(d5_supinf_1,axiom,(
    ! [A] :
      ( v3_supinf_1(A)
    <=> r2_hidden(A,k2_xboole_0(k1_numbers,k2_tarski(k2_supinf_1,k1_supinf_1))) ) )).

fof(d6_supinf_1,axiom,(
    k3_supinf_1 = k2_xboole_0(k1_numbers,k2_tarski(k2_supinf_1,k1_supinf_1)) )).

fof(t9_supinf_1,axiom,(
    $true )).

fof(t10_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => m1_subset_1(A,k3_supinf_1) ) )).

fof(t11_supinf_1,axiom,(
    ! [A] :
      ( ( A = k2_supinf_1
        | A = k1_supinf_1 )
     => m1_subset_1(A,k3_supinf_1) ) )).

fof(t12_supinf_1,axiom,(
    $true )).

fof(t13_supinf_1,axiom,(
    $true )).

fof(t14_supinf_1,axiom,(
    k5_supinf_1 != k4_supinf_1 )).

fof(d7_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( ( ( r2_hidden(A,k1_numbers)
                & r2_hidden(B,k1_numbers) )
             => ( r1_supinf_1(A,B)
              <=> ? [C] :
                    ( m1_subset_1(C,k1_numbers)
                    & ? [D] :
                        ( m1_subset_1(D,k1_numbers)
                        & C = A
                        & D = B
                        & r1_xreal_0(C,D) ) ) ) )
            & ( ~ ( r2_hidden(A,k1_numbers)
                  & r2_hidden(B,k1_numbers) )
             => ( r1_supinf_1(A,B)
              <=> ( A = k5_supinf_1
                  | B = k4_supinf_1 ) ) ) ) ) ) )).

fof(t15_supinf_1,axiom,(
    $true )).

fof(t16_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( ( m1_subset_1(A,k1_numbers)
              & m1_subset_1(B,k1_numbers) )
           => ( r1_supinf_1(A,B)
            <=> ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & C = A
                      & D = B
                      & r1_xreal_0(C,D) ) ) ) ) ) ) )).

fof(t17_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ~ ( r2_hidden(A,k1_numbers)
          & r1_supinf_1(A,k5_supinf_1) ) ) )).

fof(t18_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ~ ( r2_hidden(A,k1_numbers)
          & r1_supinf_1(k4_supinf_1,A) ) ) )).

fof(t19_supinf_1,axiom,(
    ~ r1_supinf_1(k4_supinf_1,k5_supinf_1) )).

fof(t20_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => r1_supinf_1(A,k4_supinf_1) ) )).

fof(t21_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => r1_supinf_1(k5_supinf_1,A) ) )).

fof(t22_supinf_1,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(B,A) )
           => A = B ) ) ) )).

fof(t23_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ( r1_supinf_1(A,k5_supinf_1)
       => A = k5_supinf_1 ) ) )).

fof(t24_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ( r1_supinf_1(k4_supinf_1,A)
       => A = k4_supinf_1 ) ) )).

fof(t25_supinf_1,axiom,(
    $true )).

fof(t26_supinf_1,axiom,(
    ~ v1_xboole_0(k3_supinf_1) )).

fof(t27_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
    <=> r2_hidden(A,k3_supinf_1) ) )).

fof(t28_supinf_1,axiom,(
    $true )).

fof(t29_supinf_1,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(A,B)
                  & r1_supinf_1(B,C) )
               => r1_supinf_1(A,C) ) ) ) ) )).

fof(t30_supinf_1,axiom,(
    $true )).

fof(t31_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ( r2_hidden(A,k1_numbers)
       => ( ~ r1_supinf_1(A,k5_supinf_1)
          & ~ r1_supinf_1(k4_supinf_1,A) ) ) ) )).

fof(d8_supinf_1,axiom,(
    $true )).

fof(d9_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( m1_supinf_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k3_supinf_1)
               => ( r2_hidden(C,A)
                 => r1_supinf_1(C,B) ) ) ) ) ) )).

fof(t32_supinf_1,axiom,(
    $true )).

fof(t33_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => m1_supinf_1(k4_supinf_1,A) ) )).

fof(t34_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ( r1_tarski(A,B)
           => ! [C] :
                ( m1_subset_1(C,k3_supinf_1)
               => ( m1_supinf_1(C,B)
                 => m1_supinf_1(C,A) ) ) ) ) ) )).

fof(d10_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( m2_supinf_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k3_supinf_1)
               => ( r2_hidden(C,A)
                 => r1_supinf_1(B,C) ) ) ) ) ) )).

fof(t35_supinf_1,axiom,(
    $true )).

fof(t36_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => m2_supinf_1(k5_supinf_1,A) ) )).

fof(t37_supinf_1,axiom,(
    $true )).

fof(t38_supinf_1,axiom,(
    $true )).

fof(t39_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ( r1_tarski(A,B)
           => ! [C] :
                ( m1_subset_1(C,k3_supinf_1)
               => ( m2_supinf_1(C,B)
                 => m2_supinf_1(C,A) ) ) ) ) ) )).

fof(t40_supinf_1,axiom,(
    $true )).

fof(t41_supinf_1,axiom,(
    m1_supinf_1(k4_supinf_1,k6_supinf_1) )).

fof(t42_supinf_1,axiom,(
    m2_supinf_1(k5_supinf_1,k6_supinf_1) )).

fof(d11_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ( v4_supinf_1(A)
      <=> ? [B] :
            ( m1_supinf_1(B,A)
            & r2_hidden(B,k6_supinf_1) ) ) ) )).

fof(t43_supinf_1,axiom,(
    $true )).

fof(t44_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ( ( r1_tarski(A,B)
              & v4_supinf_1(B) )
           => v4_supinf_1(A) ) ) ) )).

fof(t45_supinf_1,axiom,(
    ~ v4_supinf_1(k6_supinf_1) )).

fof(d12_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ( v5_supinf_1(A)
      <=> ? [B] :
            ( m2_supinf_1(B,A)
            & r2_hidden(B,k6_supinf_1) ) ) ) )).

fof(t46_supinf_1,axiom,(
    $true )).

fof(t47_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ( ( r1_tarski(A,B)
              & v5_supinf_1(B) )
           => v5_supinf_1(A) ) ) ) )).

fof(t48_supinf_1,axiom,(
    ~ v5_supinf_1(k6_supinf_1) )).

fof(d13_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ( v6_supinf_1(A)
      <=> ( v4_supinf_1(A)
          & v5_supinf_1(A) ) ) ) )).

fof(t49_supinf_1,axiom,(
    $true )).

fof(t50_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ( ( r1_tarski(A,B)
              & v6_supinf_1(B) )
           => v6_supinf_1(A) ) ) ) )).

fof(t51_supinf_1,axiom,(
    ! [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,k3_supinf_1)
             => ( r2_hidden(C,B)
              <=> m1_supinf_1(C,A) ) ) ) ) )).

fof(d14_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ( B = k7_supinf_1(A)
          <=> ! [C] :
                ( m1_subset_1(C,k3_supinf_1)
               => ( r2_hidden(C,B)
                <=> m1_supinf_1(C,A) ) ) ) ) ) )).

fof(t52_supinf_1,axiom,(
    $true )).

fof(t53_supinf_1,axiom,(
    $true )).

fof(t54_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ( r1_tarski(A,B)
           => ! [C] :
                ( m1_subset_1(C,k3_supinf_1)
               => ( r2_hidden(C,k7_supinf_1(B))
                 => r2_hidden(C,k7_supinf_1(A)) ) ) ) ) ) )).

fof(t55_supinf_1,axiom,(
    ! [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,k3_supinf_1)
             => ( r2_hidden(C,B)
              <=> m2_supinf_1(C,A) ) ) ) ) )).

fof(d15_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ( B = k8_supinf_1(A)
          <=> ! [C] :
                ( m1_subset_1(C,k3_supinf_1)
               => ( r2_hidden(C,B)
                <=> m2_supinf_1(C,A) ) ) ) ) ) )).

fof(t56_supinf_1,axiom,(
    $true )).

fof(t57_supinf_1,axiom,(
    $true )).

fof(t58_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ( r1_tarski(A,B)
           => ! [C] :
                ( m1_subset_1(C,k3_supinf_1)
               => ( r2_hidden(C,k8_supinf_1(B))
                 => r2_hidden(C,k8_supinf_1(A)) ) ) ) ) ) )).

fof(t59_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ~ ( v4_supinf_1(A)
          & A != k1_tarski(k5_supinf_1)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ~ ( r2_hidden(B,A)
                  & B != k5_supinf_1 ) ) ) ) )).

fof(t60_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ~ ( v5_supinf_1(A)
          & A != k1_tarski(k4_supinf_1)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ~ ( r2_hidden(B,A)
                  & B != k4_supinf_1 ) ) ) ) )).

fof(t61_supinf_1,axiom,(
    $true )).

fof(t62_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ~ ( v4_supinf_1(A)
          & A != k1_tarski(k5_supinf_1)
          & ! [B] :
              ( m1_subset_1(B,k3_supinf_1)
             => ~ ( m1_supinf_1(B,A)
                  & ! [C] :
                      ( m1_subset_1(C,k3_supinf_1)
                     => ( m1_supinf_1(C,A)
                       => r1_supinf_1(B,C) ) ) ) ) ) ) )).

fof(t63_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ~ ( v5_supinf_1(A)
          & A != k1_tarski(k4_supinf_1)
          & ! [B] :
              ( m1_subset_1(B,k3_supinf_1)
             => ~ ( m2_supinf_1(B,A)
                  & ! [C] :
                      ( m1_subset_1(C,k3_supinf_1)
                     => ( m2_supinf_1(C,A)
                       => r1_supinf_1(C,B) ) ) ) ) ) ) )).

fof(t64_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ( A = k1_tarski(k5_supinf_1)
       => v4_supinf_1(A) ) ) )).

fof(t65_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ( A = k1_tarski(k4_supinf_1)
       => v5_supinf_1(A) ) ) )).

fof(t66_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ~ ( A = k1_tarski(k5_supinf_1)
          & ! [B] :
              ( m1_subset_1(B,k3_supinf_1)
             => ~ ( m1_supinf_1(B,A)
                  & ! [C] :
                      ( m1_subset_1(C,k3_supinf_1)
                     => ( m1_supinf_1(C,A)
                       => r1_supinf_1(B,C) ) ) ) ) ) ) )).

fof(t67_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ~ ( A = k1_tarski(k4_supinf_1)
          & ! [B] :
              ( m1_subset_1(B,k3_supinf_1)
             => ~ ( m2_supinf_1(B,A)
                  & ! [C] :
                      ( m1_subset_1(C,k3_supinf_1)
                     => ( m2_supinf_1(C,A)
                       => r1_supinf_1(C,B) ) ) ) ) ) ) )).

fof(t68_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ~ ( v4_supinf_1(A)
          & ! [B] :
              ( m1_subset_1(B,k3_supinf_1)
             => ~ ( m1_supinf_1(B,A)
                  & ! [C] :
                      ( m1_subset_1(C,k3_supinf_1)
                     => ( m1_supinf_1(C,A)
                       => r1_supinf_1(B,C) ) ) ) ) ) ) )).

fof(t69_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ~ ( v5_supinf_1(A)
          & ! [B] :
              ( m1_subset_1(B,k3_supinf_1)
             => ~ ( m2_supinf_1(B,A)
                  & ! [C] :
                      ( m1_subset_1(C,k3_supinf_1)
                     => ( m2_supinf_1(C,A)
                       => r1_supinf_1(C,B) ) ) ) ) ) ) )).

fof(t70_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ( ~ v4_supinf_1(A)
       => ! [B] :
            ( m1_subset_1(B,k3_supinf_1)
           => ( m1_supinf_1(B,A)
             => B = k4_supinf_1 ) ) ) ) )).

fof(t71_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ( ~ v5_supinf_1(A)
       => ! [B] :
            ( m1_subset_1(B,k3_supinf_1)
           => ( m2_supinf_1(B,A)
             => B = k5_supinf_1 ) ) ) ) )).

fof(t72_supinf_1,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)
          & ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ( m1_supinf_1(C,A)
               => r1_supinf_1(B,C) ) ) ) ) )).

fof(t73_supinf_1,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)
          & ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ( m2_supinf_1(C,A)
               => r1_supinf_1(C,B) ) ) ) ) )).

fof(d16_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( B = k9_supinf_1(A)
          <=> ( m1_supinf_1(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k3_supinf_1)
                 => ( m1_supinf_1(C,A)
                   => r1_supinf_1(B,C) ) ) ) ) ) ) )).

fof(t74_supinf_1,axiom,(
    $true )).

fof(t75_supinf_1,axiom,(
    $true )).

fof(t76_supinf_1,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)
           => r1_supinf_1(B,k9_supinf_1(A)) ) ) ) )).

fof(d17_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( B = k10_supinf_1(A)
          <=> ( m2_supinf_1(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k3_supinf_1)
                 => ( m2_supinf_1(C,A)
                   => r1_supinf_1(C,B) ) ) ) ) ) ) )).

fof(t77_supinf_1,axiom,(
    $true )).

fof(t78_supinf_1,axiom,(
    $true )).

fof(t79_supinf_1,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)
           => r1_supinf_1(k10_supinf_1(A),B) ) ) ) )).

fof(t80_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_supinf_1(B,A)
         => ( r2_hidden(B,A)
           => B = k9_supinf_1(A) ) ) ) )).

fof(t81_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m2_supinf_1(B,A)
         => ( r2_hidden(B,A)
           => B = k10_supinf_1(A) ) ) ) )).

fof(t82_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ( k9_supinf_1(A) = k10_supinf_1(k7_supinf_1(A))
        & k10_supinf_1(A) = k9_supinf_1(k8_supinf_1(A)) ) ) )).

fof(t83_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ( v4_supinf_1(A)
       => ( A = k1_tarski(k5_supinf_1)
          | r2_hidden(k9_supinf_1(A),k6_supinf_1) ) ) ) )).

fof(t84_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ( v5_supinf_1(A)
       => ( A = k1_tarski(k4_supinf_1)
          | r2_hidden(k10_supinf_1(A),k6_supinf_1) ) ) ) )).

fof(t85_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => k9_supinf_1(k11_supinf_1(A)) = A ) )).

fof(t86_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => k10_supinf_1(k11_supinf_1(A)) = A ) )).

fof(t87_supinf_1,axiom,(
    $true )).

fof(t88_supinf_1,axiom,(
    $true )).

fof(t89_supinf_1,axiom,(
    $true )).

fof(t90_supinf_1,axiom,(
    $true )).

fof(t91_supinf_1,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_supinf_1(k9_supinf_1(A),k9_supinf_1(B)) ) ) ) )).

fof(t92_supinf_1,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(A,C)
                  & r1_supinf_1(B,C) )
               => r1_supinf_1(k9_supinf_1(k12_supinf_1(A,B)),C) ) ) ) ) )).

fof(t93_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( ( r1_supinf_1(A,B)
             => k9_supinf_1(k12_supinf_1(A,B)) = B )
            & ( r1_supinf_1(B,A)
             => k9_supinf_1(k12_supinf_1(A,B)) = A ) ) ) ) )).

fof(t94_supinf_1,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_supinf_1(k10_supinf_1(B),k10_supinf_1(A)) ) ) ) )).

fof(t95_supinf_1,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(C,A)
                  & r1_supinf_1(C,B) )
               => r1_supinf_1(C,k10_supinf_1(k12_supinf_1(A,B))) ) ) ) ) )).

fof(t96_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( ( r1_supinf_1(A,B)
             => k10_supinf_1(k12_supinf_1(A,B)) = A )
            & ( r1_supinf_1(B,A)
             => k10_supinf_1(k12_supinf_1(A,B)) = B ) ) ) ) )).

fof(t97_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( ? [C] :
                ( m1_subset_1(C,k3_supinf_1)
                & r2_hidden(C,A)
                & r1_supinf_1(B,C) )
           => r1_supinf_1(B,k9_supinf_1(A)) ) ) ) )).

fof(t98_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( ? [C] :
                ( m1_subset_1(C,k3_supinf_1)
                & r2_hidden(C,A)
                & r1_supinf_1(C,B) )
           => r1_supinf_1(k10_supinf_1(A),B) ) ) ) )).

fof(t99_supinf_1,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,k3_supinf_1)
               => ~ ( r2_hidden(C,A)
                    & ! [D] :
                        ( m1_subset_1(D,k3_supinf_1)
                       => ~ ( r2_hidden(D,B)
                            & r1_supinf_1(C,D) ) ) ) )
           => r1_supinf_1(k9_supinf_1(A),k9_supinf_1(B)) ) ) ) )).

fof(t100_supinf_1,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,k3_supinf_1)
               => ~ ( r2_hidden(C,B)
                    & ! [D] :
                        ( m1_subset_1(D,k3_supinf_1)
                       => ~ ( r2_hidden(D,A)
                            & r1_supinf_1(D,C) ) ) ) )
           => r1_supinf_1(k10_supinf_1(A),k10_supinf_1(B)) ) ) ) )).

fof(t101_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ! [C] :
              ( m1_supinf_1(C,A)
             => ! [D] :
                  ( m1_supinf_1(D,B)
                 => m1_supinf_1(k9_supinf_1(k12_supinf_1(C,D)),k4_subset_1(k3_supinf_1,A,B)) ) ) ) ) )).

fof(t102_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ! [C] :
              ( m2_supinf_1(C,A)
             => ! [D] :
                  ( m2_supinf_1(D,B)
                 => m2_supinf_1(k10_supinf_1(k12_supinf_1(C,D)),k4_subset_1(k3_supinf_1,A,B)) ) ) ) ) )).

fof(t103_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k3_supinf_1))
             => ! [D] :
                  ( m1_supinf_1(D,A)
                 => ! [E] :
                      ( m1_supinf_1(E,B)
                     => ( C = k5_subset_1(k3_supinf_1,A,B)
                       => m1_supinf_1(k10_supinf_1(k12_supinf_1(D,E)),C) ) ) ) ) ) ) )).

fof(t104_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k3_supinf_1))
             => ! [D] :
                  ( m2_supinf_1(D,A)
                 => ! [E] :
                      ( m2_supinf_1(E,B)
                     => ( C = k5_subset_1(k3_supinf_1,A,B)
                       => m2_supinf_1(k9_supinf_1(k12_supinf_1(D,E)),C) ) ) ) ) ) ) )).

fof(t105_supinf_1,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)) )
         => k9_supinf_1(k4_subset_1(k3_supinf_1,A,B)) = k9_supinf_1(k12_supinf_1(k9_supinf_1(A),k9_supinf_1(B))) ) ) )).

fof(t106_supinf_1,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)) )
         => k10_supinf_1(k4_subset_1(k3_supinf_1,A,B)) = k10_supinf_1(k12_supinf_1(k10_supinf_1(A),k10_supinf_1(B))) ) ) )).

fof(t107_supinf_1,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] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k3_supinf_1)) )
             => ( C = k5_subset_1(k3_supinf_1,A,B)
               => r1_supinf_1(k9_supinf_1(C),k10_supinf_1(k12_supinf_1(k9_supinf_1(A),k9_supinf_1(B)))) ) ) ) ) )).

fof(t108_supinf_1,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] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k3_supinf_1)) )
             => ( C = k5_subset_1(k3_supinf_1,A,B)
               => r1_supinf_1(k9_supinf_1(k12_supinf_1(k10_supinf_1(A),k10_supinf_1(B))),k10_supinf_1(C)) ) ) ) ) )).

fof(d18_supinf_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m3_supinf_1(B,A)
        <=> ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
            & ! [C] :
                ( r2_hidden(C,B)
               => ~ v1_xboole_0(C) ) ) ) ) )).

fof(d19_supinf_1,axiom,(
    ! [A] :
      ( m3_supinf_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ( B = k13_supinf_1(A)
          <=> ! [C] :
                ( m1_subset_1(C,k3_supinf_1)
               => ( r2_hidden(C,B)
                <=> ? [D] :
                      ( ~ v1_xboole_0(D)
                      & m1_subset_1(D,k1_zfmisc_1(k3_supinf_1))
                      & r2_hidden(D,A)
                      & C = k9_supinf_1(D) ) ) ) ) ) ) )).

fof(t109_supinf_1,axiom,(
    $true )).

fof(t110_supinf_1,axiom,(
    $true )).

fof(t111_supinf_1,axiom,(
    $true )).

fof(t112_supinf_1,axiom,(
    ! [A] :
      ( m3_supinf_1(A,k3_supinf_1)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ( B = k3_tarski(A)
           => m1_supinf_1(k9_supinf_1(B),k13_supinf_1(A)) ) ) ) )).

fof(t113_supinf_1,axiom,(
    ! [A] :
      ( m3_supinf_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ( B = k3_tarski(A)
           => m1_supinf_1(k9_supinf_1(k13_supinf_1(A)),B) ) ) ) )).

fof(t114_supinf_1,axiom,(
    ! [A] :
      ( m3_supinf_1(A,k3_supinf_1)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ( B = k3_tarski(A)
           => k9_supinf_1(B) = k9_supinf_1(k13_supinf_1(A)) ) ) ) )).

fof(d20_supinf_1,axiom,(
    ! [A] :
      ( m3_supinf_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ( B = k14_supinf_1(A)
          <=> ! [C] :
                ( m1_subset_1(C,k3_supinf_1)
               => ( r2_hidden(C,B)
                <=> ? [D] :
                      ( ~ v1_xboole_0(D)
                      & m1_subset_1(D,k1_zfmisc_1(k3_supinf_1))
                      & r2_hidden(D,A)
                      & C = k10_supinf_1(D) ) ) ) ) ) ) )).

fof(t115_supinf_1,axiom,(
    $true )).

fof(t116_supinf_1,axiom,(
    $true )).

fof(t117_supinf_1,axiom,(
    ! [A] :
      ( m3_supinf_1(A,k3_supinf_1)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ( B = k3_tarski(A)
           => m2_supinf_1(k10_supinf_1(B),k14_supinf_1(A)) ) ) ) )).

fof(t118_supinf_1,axiom,(
    ! [A] :
      ( m3_supinf_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
         => ( B = k3_tarski(A)
           => m2_supinf_1(k10_supinf_1(k14_supinf_1(A)),B) ) ) ) )).

fof(t119_supinf_1,axiom,(
    ! [A] :
      ( m3_supinf_1(A,k3_supinf_1)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ( B = k3_tarski(A)
           => k10_supinf_1(B) = k10_supinf_1(k14_supinf_1(A)) ) ) ) )).

fof(t120_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( A = C
                      & B = D )
                   => ( r1_xreal_0(C,D)
                    <=> r1_supinf_1(A,B) ) ) ) ) ) ) )).

fof(s1_supinf_1,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k2_xboole_0(k1_numbers,k2_tarski(k5_supinf_1,k4_supinf_1))))
      & ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( r2_hidden(B,A)
          <=> p1_s1_supinf_1(B) ) ) ) )).

fof(dt_m1_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m1_supinf_1(B,A)
         => m1_subset_1(B,k3_supinf_1) ) ) )).

fof(existence_m1_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ? [B] : m1_supinf_1(B,A) ) )).

fof(dt_m2_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] :
          ( m2_supinf_1(B,A)
         => m1_subset_1(B,k3_supinf_1) ) ) )).

fof(existence_m2_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ? [B] : m2_supinf_1(B,A) ) )).

fof(dt_m3_supinf_1,axiom,(
    $true )).

fof(existence_m3_supinf_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] : m3_supinf_1(B,A) ) )).

fof(reflexivity_r1_supinf_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => r1_supinf_1(A,A) ) )).

fof(connectedness_r1_supinf_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => ( r1_supinf_1(A,B)
        | r1_supinf_1(B,A) ) ) )).

fof(dt_k1_supinf_1,axiom,(
    $true )).

fof(dt_k2_supinf_1,axiom,(
    $true )).

fof(dt_k3_supinf_1,axiom,(
    $true )).

fof(dt_k4_supinf_1,axiom,(
    m1_subset_1(k4_supinf_1,k3_supinf_1) )).

fof(redefinition_k4_supinf_1,axiom,(
    k4_supinf_1 = k1_supinf_1 )).

fof(dt_k5_supinf_1,axiom,(
    m1_subset_1(k5_supinf_1,k3_supinf_1) )).

fof(redefinition_k5_supinf_1,axiom,(
    k5_supinf_1 = k2_supinf_1 )).

fof(dt_k6_supinf_1,axiom,
    ( ~ v1_xboole_0(k6_supinf_1)
    & m1_subset_1(k6_supinf_1,k1_zfmisc_1(k3_supinf_1)) )).

fof(redefinition_k6_supinf_1,axiom,(
    k6_supinf_1 = k1_numbers )).

fof(dt_k7_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => m1_subset_1(k7_supinf_1(A),k1_zfmisc_1(k3_supinf_1)) ) )).

fof(dt_k8_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => m1_subset_1(k8_supinf_1(A),k1_zfmisc_1(k3_supinf_1)) ) )).

fof(dt_k9_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => m1_subset_1(k9_supinf_1(A),k3_supinf_1) ) )).

fof(dt_k10_supinf_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => m1_subset_1(k10_supinf_1(A),k3_supinf_1) ) )).

fof(dt_k11_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => m1_subset_1(k11_supinf_1(A),k1_zfmisc_1(k3_supinf_1)) ) )).

fof(redefinition_k11_supinf_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => k11_supinf_1(A) = k1_tarski(A) ) )).

fof(dt_k12_supinf_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k12_supinf_1(A,B),k1_zfmisc_1(k3_supinf_1)) ) )).

fof(commutativity_k12_supinf_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => k12_supinf_1(A,B) = k12_supinf_1(B,A) ) )).

fof(redefinition_k12_supinf_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => k12_supinf_1(A,B) = k2_tarski(A,B) ) )).

fof(dt_k13_supinf_1,axiom,(
    ! [A] :
      ( m3_supinf_1(A,k3_supinf_1)
     => m1_subset_1(k13_supinf_1(A),k1_zfmisc_1(k3_supinf_1)) ) )).

fof(dt_k14_supinf_1,axiom,(
    ! [A] :
      ( m3_supinf_1(A,k3_supinf_1)
     => m1_subset_1(k14_supinf_1(A),k1_zfmisc_1(k3_supinf_1)) ) )).
%------------------------------------------------------------------------------