SET007 Axioms: SET007+10.ax


%------------------------------------------------------------------------------
% File     : SET007+10 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Relations and Their Basic Properties
% 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    : relat_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  234 (  46 unit)
%            Number of atoms       :  630 ( 124 equality)
%            Maximal formula depth :   13 (   5 average)
%            Number of connectives :  415 (  19 ~  ;   1  |;  68  &)
%                                         (  36 <=>; 291 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   10 (   1 propositional; 0-2 arity)
%            Number of functors    :   20 (   3 constant; 0-2 arity)
%            Number of variables   :  462 (   0 singleton; 451 !;  11 ?)
%            Maximal term depth    :    5 (   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(rc1_relat_1,axiom,(
    ? [A] :
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) )).

fof(fc1_relat_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k3_xboole_0(A,B)) ) )).

fof(fc2_relat_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k2_xboole_0(A,B)) ) )).

fof(fc3_relat_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k4_xboole_0(A,B)) ) )).

fof(cc1_relat_1,axiom,(
    ! [A] :
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) )).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) )).

fof(rc2_relat_1,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) )).

fof(fc5_relat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) )).

fof(fc6_relat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) )).

fof(fc7_relat_1,axiom,(
    ! [A] :
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) )).

fof(fc8_relat_1,axiom,(
    ! [A] :
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) )).

fof(fc9_relat_1,axiom,(
    ! [A,B] :
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(A,B))
        & v1_relat_1(k5_relat_1(A,B)) ) ) )).

fof(fc10_relat_1,axiom,(
    ! [A,B] :
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(B,A))
        & v1_relat_1(k5_relat_1(B,A)) ) ) )).

fof(fc11_relat_1,axiom,(
    ! [A] :
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k4_relat_1(A))
        & v1_relat_1(k4_relat_1(A)) ) ) )).

fof(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) )).

fof(rc3_relat_1,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v3_relat_1(A) ) )).

fof(fc13_relat_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v3_relat_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v3_relat_1(k7_relat_1(A,B)) ) ) )).

fof(d1_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
    <=> ! [B] :
          ~ ( r2_hidden(B,A)
            & ! [C,D] : B != k4_tarski(C,D) ) ) )).

fof(t1_relat_1,axiom,(
    $true )).

fof(t2_relat_1,axiom,(
    $true )).

fof(t3_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ( r1_tarski(A,B)
       => v1_relat_1(A) ) ) )).

fof(t4_relat_1,axiom,(
    ! [A,B] : v1_relat_1(k1_tarski(k4_tarski(A,B))) )).

fof(t5_relat_1,axiom,(
    ! [A,B,C,D] : v1_relat_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) )).

fof(t6_relat_1,axiom,(
    ! [A,B] : v1_relat_1(k2_zfmisc_1(A,B)) )).

fof(d2_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ( A = B
          <=> ! [C,D] :
                ( r2_hidden(k4_tarski(C,D),A)
              <=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) )).

fof(d3_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
          <=> ! [C,D] :
                ( r2_hidden(k4_tarski(C,D),A)
               => r2_hidden(k4_tarski(C,D),B) ) ) ) ) )).

fof(t7_relat_1,axiom,(
    $true )).

fof(t8_relat_1,axiom,(
    $true )).

fof(t9_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => v1_relat_1(k3_xboole_0(A,B)) ) )).

fof(t10_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => v1_relat_1(k4_xboole_0(B,A)) ) )).

fof(d4_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( B = k1_relat_1(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ? [D] : r2_hidden(k4_tarski(C,D),A) ) ) ) )).

fof(t11_relat_1,axiom,(
    $true )).

fof(t12_relat_1,axiom,(
    $true )).

fof(t13_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => k1_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) ) ) )).

fof(t14_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => r1_tarski(k1_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) ) ) )).

fof(t15_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => r1_tarski(k4_xboole_0(k1_relat_1(A),k1_relat_1(B)),k1_relat_1(k4_xboole_0(A,B))) ) ) )).

fof(d5_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( B = k2_relat_1(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ? [D] : r2_hidden(k4_tarski(D,C),A) ) ) ) )).

fof(t16_relat_1,axiom,(
    $true )).

fof(t17_relat_1,axiom,(
    $true )).

fof(t18_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ~ ( r2_hidden(A,k1_relat_1(B))
          & ! [C] : ~ r2_hidden(C,k2_relat_1(B)) ) ) )).

fof(t19_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ~ ( r2_hidden(A,k2_relat_1(B))
          & ! [C] : ~ r2_hidden(C,k1_relat_1(B)) ) ) )).

fof(t20_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r2_hidden(k4_tarski(A,B),C)
       => ( r2_hidden(A,k1_relat_1(C))
          & r2_hidden(B,k2_relat_1(C)) ) ) ) )).

fof(t21_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => r1_tarski(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))) ) )).

fof(t22_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => k3_xboole_0(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))) = A ) )).

fof(t23_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( C = k1_tarski(k4_tarski(A,B))
       => ( k1_relat_1(C) = k1_tarski(A)
          & k2_relat_1(C) = k1_tarski(B) ) ) ) )).

fof(t24_relat_1,axiom,(
    ! [A,B,C,D,E] :
      ( v1_relat_1(E)
     => ( E = k2_tarski(k4_tarski(A,B),k4_tarski(C,D))
       => ( k1_relat_1(E) = k2_tarski(A,C)
          & k2_relat_1(E) = k2_tarski(B,D) ) ) ) )).

fof(t25_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
           => ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
              & r1_tarski(k2_relat_1(A),k2_relat_1(B)) ) ) ) ) )).

fof(t26_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => k2_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) )).

fof(t27_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => r1_tarski(k2_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k2_relat_1(A),k2_relat_1(B))) ) ) )).

fof(t28_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => r1_tarski(k4_xboole_0(k2_relat_1(A),k2_relat_1(B)),k2_relat_1(k4_xboole_0(A,B))) ) ) )).

fof(d6_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)) ) )).

fof(t29_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( r1_tarski(k1_relat_1(A),k3_relat_1(A))
        & r1_tarski(k2_relat_1(A),k3_relat_1(A)) ) ) )).

fof(t30_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r2_hidden(k4_tarski(A,B),C)
       => ( r2_hidden(A,k3_relat_1(C))
          & r2_hidden(B,k3_relat_1(C)) ) ) ) )).

fof(t31_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
           => r1_tarski(k3_relat_1(A),k3_relat_1(B)) ) ) ) )).

fof(t32_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( C = k1_tarski(k4_tarski(A,B))
       => k3_relat_1(C) = k2_tarski(A,B) ) ) )).

fof(t33_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => k3_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k3_relat_1(A),k3_relat_1(B)) ) ) )).

fof(t34_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => r1_tarski(k3_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k3_relat_1(A),k3_relat_1(B))) ) ) )).

fof(d7_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ( B = k4_relat_1(A)
          <=> ! [C,D] :
                ( r2_hidden(k4_tarski(C,D),B)
              <=> r2_hidden(k4_tarski(D,C),A) ) ) ) ) )).

fof(t35_relat_1,axiom,(
    $true )).

fof(t36_relat_1,axiom,(
    $true )).

fof(t37_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( k2_relat_1(A) = k1_relat_1(k4_relat_1(A))
        & k1_relat_1(A) = k2_relat_1(k4_relat_1(A)) ) ) )).

fof(t38_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => k3_relat_1(A) = k3_relat_1(k4_relat_1(A)) ) )).

fof(t39_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => k4_relat_1(k3_xboole_0(A,B)) = k3_xboole_0(k4_relat_1(A),k4_relat_1(B)) ) ) )).

fof(t40_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => k4_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k4_relat_1(A),k4_relat_1(B)) ) ) )).

fof(t41_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => k4_relat_1(k4_xboole_0(A,B)) = k4_xboole_0(k4_relat_1(A),k4_relat_1(B)) ) ) )).

fof(d8_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ! [C] :
              ( v1_relat_1(C)
             => ( C = k5_relat_1(A,B)
              <=> ! [D,E] :
                    ( r2_hidden(k4_tarski(D,E),C)
                  <=> ? [F] :
                        ( r2_hidden(k4_tarski(D,F),A)
                        & r2_hidden(k4_tarski(F,E),B) ) ) ) ) ) ) )).

fof(t42_relat_1,axiom,(
    $true )).

fof(t43_relat_1,axiom,(
    $true )).

fof(t44_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => r1_tarski(k1_relat_1(k5_relat_1(A,B)),k1_relat_1(A)) ) ) )).

fof(t45_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => r1_tarski(k2_relat_1(k5_relat_1(A,B)),k2_relat_1(B)) ) ) )).

fof(t46_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ( r1_tarski(k2_relat_1(A),k1_relat_1(B))
           => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) )).

fof(t47_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ( r1_tarski(k1_relat_1(A),k2_relat_1(B))
           => k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(A) ) ) ) )).

fof(t48_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ! [C] :
              ( v1_relat_1(C)
             => ( r1_tarski(A,B)
               => r1_tarski(k5_relat_1(C,A),k5_relat_1(C,B)) ) ) ) ) )).

fof(t49_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ! [C] :
              ( v1_relat_1(C)
             => ( r1_tarski(A,B)
               => r1_tarski(k5_relat_1(A,C),k5_relat_1(B,C)) ) ) ) ) )).

fof(t50_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ! [C] :
              ( v1_relat_1(C)
             => ! [D] :
                  ( v1_relat_1(D)
                 => ( ( r1_tarski(A,B)
                      & r1_tarski(C,D) )
                   => r1_tarski(k5_relat_1(A,C),k5_relat_1(B,D)) ) ) ) ) ) )).

fof(t51_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ! [C] :
              ( v1_relat_1(C)
             => k5_relat_1(A,k2_xboole_0(B,C)) = k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)) ) ) ) )).

fof(t52_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ! [C] :
              ( v1_relat_1(C)
             => r1_tarski(k5_relat_1(A,k3_xboole_0(B,C)),k3_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C))) ) ) ) )).

fof(t53_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ! [C] :
              ( v1_relat_1(C)
             => r1_tarski(k4_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)),k5_relat_1(A,k4_xboole_0(B,C))) ) ) ) )).

fof(t54_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => k4_relat_1(k5_relat_1(A,B)) = k5_relat_1(k4_relat_1(B),k4_relat_1(A)) ) ) )).

fof(t55_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ! [C] :
              ( v1_relat_1(C)
             => k5_relat_1(k5_relat_1(A,B),C) = k5_relat_1(A,k5_relat_1(B,C)) ) ) ) )).

fof(t56_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( ! [B,C] : ~ r2_hidden(k4_tarski(B,C),A)
       => A = k1_xboole_0 ) ) )).

fof(t57_relat_1,axiom,(
    $true )).

fof(t58_relat_1,axiom,(
    $true )).

fof(t59_relat_1,axiom,(
    $true )).

fof(t60_relat_1,axiom,
    ( k1_relat_1(k1_xboole_0) = k1_xboole_0
    & k2_relat_1(k1_xboole_0) = k1_xboole_0 )).

fof(t61_relat_1,axiom,(
    $true )).

fof(t62_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( k5_relat_1(k1_xboole_0,A) = k1_xboole_0
        & k5_relat_1(A,k1_xboole_0) = k1_xboole_0 ) ) )).

fof(t63_relat_1,axiom,(
    $true )).

fof(t64_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( ( k1_relat_1(A) = k1_xboole_0
          | k2_relat_1(A) = k1_xboole_0 )
       => A = k1_xboole_0 ) ) )).

fof(t65_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( k1_relat_1(A) = k1_xboole_0
      <=> k2_relat_1(A) = k1_xboole_0 ) ) )).

fof(t66_relat_1,axiom,(
    k4_relat_1(k1_xboole_0) = k1_xboole_0 )).

fof(t67_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ( r1_xboole_0(k2_relat_1(A),k1_relat_1(B))
           => k5_relat_1(A,B) = k1_xboole_0 ) ) ) )).

fof(d9_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v2_relat_1(A)
      <=> ~ r2_hidden(k1_xboole_0,k2_relat_1(A)) ) ) )).

fof(d10_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ( B = k6_relat_1(A)
      <=> ! [C,D] :
            ( r2_hidden(k4_tarski(C,D),B)
          <=> ( r2_hidden(C,A)
              & C = D ) ) ) ) )).

fof(t68_relat_1,axiom,(
    $true )).

fof(t69_relat_1,axiom,(
    $true )).

fof(t70_relat_1,axiom,(
    $true )).

fof(t71_relat_1,axiom,(
    ! [A] :
      ( k1_relat_1(k6_relat_1(A)) = A
      & k2_relat_1(k6_relat_1(A)) = A ) )).

fof(t72_relat_1,axiom,(
    ! [A] : k4_relat_1(k6_relat_1(A)) = k6_relat_1(A) )).

fof(t73_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ( ! [C] :
            ( r2_hidden(C,A)
           => r2_hidden(k4_tarski(C,C),B) )
       => r1_tarski(k6_relat_1(A),B) ) ) )).

fof(t74_relat_1,axiom,(
    ! [A,B,C,D] :
      ( v1_relat_1(D)
     => ( r2_hidden(k4_tarski(A,B),k5_relat_1(k6_relat_1(C),D))
      <=> ( r2_hidden(A,C)
          & r2_hidden(k4_tarski(A,B),D) ) ) ) )).

fof(t75_relat_1,axiom,(
    ! [A,B,C,D] :
      ( v1_relat_1(D)
     => ( r2_hidden(k4_tarski(A,B),k5_relat_1(D,k6_relat_1(C)))
      <=> ( r2_hidden(B,C)
          & r2_hidden(k4_tarski(A,B),D) ) ) ) )).

fof(t76_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ( r1_tarski(k5_relat_1(B,k6_relat_1(A)),B)
        & r1_tarski(k5_relat_1(k6_relat_1(A),B),B) ) ) )).

fof(t77_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ( r1_tarski(k1_relat_1(B),A)
       => k5_relat_1(k6_relat_1(A),B) = B ) ) )).

fof(t78_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A ) )).

fof(t79_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ( r1_tarski(k2_relat_1(B),A)
       => k5_relat_1(B,k6_relat_1(A)) = B ) ) )).

fof(t80_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => k5_relat_1(A,k6_relat_1(k2_relat_1(A))) = A ) )).

fof(t81_relat_1,axiom,(
    k6_relat_1(k1_xboole_0) = k1_xboole_0 )).

fof(t82_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => ! [D] :
              ( v1_relat_1(D)
             => ( ( k1_relat_1(B) = A
                  & r1_tarski(k2_relat_1(C),A)
                  & k5_relat_1(C,B) = k6_relat_1(k1_relat_1(D))
                  & k5_relat_1(B,D) = k6_relat_1(A) )
               => D = C ) ) ) ) )).

fof(d11_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B,C] :
          ( v1_relat_1(C)
         => ( C = k7_relat_1(A,B)
          <=> ! [D,E] :
                ( r2_hidden(k4_tarski(D,E),C)
              <=> ( r2_hidden(D,B)
                  & r2_hidden(k4_tarski(D,E),A) ) ) ) ) ) )).

fof(t83_relat_1,axiom,(
    $true )).

fof(t84_relat_1,axiom,(
    $true )).

fof(t85_relat_1,axiom,(
    $true )).

fof(t86_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r2_hidden(A,k1_relat_1(k7_relat_1(C,B)))
      <=> ( r2_hidden(A,B)
          & r2_hidden(A,k1_relat_1(C)) ) ) ) )).

fof(t87_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => r1_tarski(k1_relat_1(k7_relat_1(B,A)),A) ) )).

fof(t88_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => r1_tarski(k7_relat_1(B,A),B) ) )).

fof(t89_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)) ) )).

fof(t90_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A) ) )).

fof(t91_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ( r1_tarski(A,k1_relat_1(B))
       => k1_relat_1(k7_relat_1(B,A)) = A ) ) )).

fof(t92_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => r1_tarski(k5_relat_1(k7_relat_1(B,A),C),k5_relat_1(B,C)) ) ) )).

fof(t93_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => r1_tarski(k5_relat_1(B,k7_relat_1(C,A)),k5_relat_1(B,C)) ) ) )).

fof(t94_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => k7_relat_1(B,A) = k5_relat_1(k6_relat_1(A),B) ) )).

fof(t95_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ( k7_relat_1(B,A) = k1_xboole_0
      <=> r1_xboole_0(k1_relat_1(B),A) ) ) )).

fof(t96_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => k7_relat_1(B,A) = k3_xboole_0(B,k2_zfmisc_1(A,k2_relat_1(B))) ) )).

fof(t97_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ( r1_tarski(k1_relat_1(B),A)
       => k7_relat_1(B,A) = B ) ) )).

fof(t98_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => k7_relat_1(A,k1_relat_1(A)) = A ) )).

fof(t99_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) ) )).

fof(t100_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,k3_xboole_0(A,B)) ) )).

fof(t101_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => k7_relat_1(k7_relat_1(B,A),A) = k7_relat_1(B,A) ) )).

fof(t102_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A) ) ) )).

fof(t103_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => k7_relat_1(k7_relat_1(C,B),A) = k7_relat_1(C,A) ) ) )).

fof(t104_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => r1_tarski(k7_relat_1(C,A),k7_relat_1(C,B)) ) ) )).

fof(t105_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => ( r1_tarski(B,C)
           => r1_tarski(k7_relat_1(B,A),k7_relat_1(C,A)) ) ) ) )).

fof(t106_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ! [D] :
          ( v1_relat_1(D)
         => ( ( r1_tarski(C,D)
              & r1_tarski(A,B) )
           => r1_tarski(k7_relat_1(C,A),k7_relat_1(D,B)) ) ) ) )).

fof(t107_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => k7_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) ) )).

fof(t108_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => k7_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) ) )).

fof(t109_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => k7_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) ) )).

fof(t110_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => k7_relat_1(A,k1_xboole_0) = k1_xboole_0 ) )).

fof(t111_relat_1,axiom,(
    ! [A] : k7_relat_1(k1_xboole_0,A) = k1_xboole_0 )).

fof(t112_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => k7_relat_1(k5_relat_1(B,C),A) = k5_relat_1(k7_relat_1(B,A),C) ) ) )).

fof(d12_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => ( C = k8_relat_1(A,B)
          <=> ! [D,E] :
                ( r2_hidden(k4_tarski(D,E),C)
              <=> ( r2_hidden(E,A)
                  & r2_hidden(k4_tarski(D,E),B) ) ) ) ) ) )).

fof(t113_relat_1,axiom,(
    $true )).

fof(t114_relat_1,axiom,(
    $true )).

fof(t115_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r2_hidden(A,k2_relat_1(k8_relat_1(B,C)))
      <=> ( r2_hidden(A,B)
          & r2_hidden(A,k2_relat_1(C)) ) ) ) )).

fof(t116_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => r1_tarski(k2_relat_1(k8_relat_1(A,B)),A) ) )).

fof(t117_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => r1_tarski(k8_relat_1(A,B),B) ) )).

fof(t118_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)) ) )).

fof(t119_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => k2_relat_1(k8_relat_1(A,B)) = k3_xboole_0(k2_relat_1(B),A) ) )).

fof(t120_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ( r1_tarski(A,k2_relat_1(B))
       => k2_relat_1(k8_relat_1(A,B)) = A ) ) )).

fof(t121_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => r1_tarski(k5_relat_1(k8_relat_1(A,B),C),k5_relat_1(B,C)) ) ) )).

fof(t122_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => r1_tarski(k5_relat_1(B,k8_relat_1(A,C)),k5_relat_1(B,C)) ) ) )).

fof(t123_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => k8_relat_1(A,B) = k5_relat_1(B,k6_relat_1(A)) ) )).

fof(t124_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => k8_relat_1(A,B) = k3_xboole_0(B,k2_zfmisc_1(k1_relat_1(B),A)) ) )).

fof(t125_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ( r1_tarski(k2_relat_1(B),A)
       => k8_relat_1(A,B) = B ) ) )).

fof(t126_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => k8_relat_1(k2_relat_1(A),A) = A ) )).

fof(t127_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(k3_xboole_0(A,B),C) ) )).

fof(t128_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => k8_relat_1(A,k8_relat_1(A,B)) = k8_relat_1(A,B) ) )).

fof(t129_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => k8_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,C) ) ) )).

fof(t130_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(A,C) ) ) )).

fof(t131_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => r1_tarski(k8_relat_1(A,C),k8_relat_1(B,C)) ) ) )).

fof(t132_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => ( r1_tarski(B,C)
           => r1_tarski(k8_relat_1(A,B),k8_relat_1(A,C)) ) ) ) )).

fof(t133_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ! [D] :
          ( v1_relat_1(D)
         => ( ( r1_tarski(C,D)
              & r1_tarski(A,B) )
           => r1_tarski(k8_relat_1(A,C),k8_relat_1(B,D)) ) ) ) )).

fof(t134_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => k8_relat_1(k2_xboole_0(A,B),C) = k2_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) ) )).

fof(t135_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => k8_relat_1(k3_xboole_0(A,B),C) = k3_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) ) )).

fof(t136_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => k8_relat_1(k4_xboole_0(A,B),C) = k4_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) ) )).

fof(t137_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => k8_relat_1(k1_xboole_0,A) = k1_xboole_0 ) )).

fof(t138_relat_1,axiom,(
    ! [A] : k8_relat_1(A,k1_xboole_0) = k1_xboole_0 )).

fof(t139_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => k8_relat_1(A,k5_relat_1(B,C)) = k5_relat_1(B,k8_relat_1(A,C)) ) ) )).

fof(t140_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => k7_relat_1(k8_relat_1(A,C),B) = k8_relat_1(A,k7_relat_1(C,B)) ) )).

fof(d13_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B,C] :
          ( C = k9_relat_1(A,B)
        <=> ! [D] :
              ( r2_hidden(D,C)
            <=> ? [E] :
                  ( r2_hidden(k4_tarski(E,D),A)
                  & r2_hidden(E,B) ) ) ) ) )).

fof(t141_relat_1,axiom,(
    $true )).

fof(t142_relat_1,axiom,(
    $true )).

fof(t143_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r2_hidden(A,k9_relat_1(C,B))
      <=> ? [D] :
            ( r2_hidden(D,k1_relat_1(C))
            & r2_hidden(k4_tarski(D,A),C)
            & r2_hidden(D,B) ) ) ) )).

fof(t144_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => r1_tarski(k9_relat_1(B,A),k2_relat_1(B)) ) )).

fof(t145_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => k9_relat_1(B,A) = k9_relat_1(B,k3_xboole_0(k1_relat_1(B),A)) ) )).

fof(t146_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A) ) )).

fof(t147_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => r1_tarski(k9_relat_1(B,A),k9_relat_1(B,k1_relat_1(B))) ) )).

fof(t148_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => k2_relat_1(k7_relat_1(B,A)) = k9_relat_1(B,A) ) )).

fof(t149_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => k9_relat_1(A,k1_xboole_0) = k1_xboole_0 ) )).

fof(t150_relat_1,axiom,(
    ! [A] : k9_relat_1(k1_xboole_0,A) = k1_xboole_0 )).

fof(t151_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ( k9_relat_1(B,A) = k1_xboole_0
      <=> r1_xboole_0(k1_relat_1(B),A) ) ) )).

fof(t152_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ~ ( A != k1_xboole_0
          & r1_tarski(A,k1_relat_1(B))
          & k9_relat_1(B,A) = k1_xboole_0 ) ) )).

fof(t153_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => k9_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) ) )).

fof(t154_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => r1_tarski(k9_relat_1(C,k3_xboole_0(A,B)),k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))) ) )).

fof(t155_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => r1_tarski(k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)),k9_relat_1(C,k4_xboole_0(A,B))) ) )).

fof(t156_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) ) ) )).

fof(t157_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => ( r1_tarski(B,C)
           => r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A)) ) ) ) )).

fof(t158_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ! [D] :
          ( v1_relat_1(D)
         => ( ( r1_tarski(C,D)
              & r1_tarski(A,B) )
           => r1_tarski(k9_relat_1(C,A),k9_relat_1(D,B)) ) ) ) )).

fof(t159_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => k9_relat_1(k5_relat_1(B,C),A) = k9_relat_1(C,k9_relat_1(B,A)) ) ) )).

fof(t160_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => k2_relat_1(k5_relat_1(A,B)) = k9_relat_1(B,k2_relat_1(A)) ) ) )).

fof(t161_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => r1_tarski(k9_relat_1(k7_relat_1(C,A),B),k9_relat_1(C,B)) ) )).

fof(t162_relat_1,axiom,(
    $true )).

fof(t163_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => r1_tarski(k3_xboole_0(k1_relat_1(B),A),k9_relat_1(k4_relat_1(B),k9_relat_1(B,A))) ) )).

fof(d14_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B,C] :
          ( C = k10_relat_1(A,B)
        <=> ! [D] :
              ( r2_hidden(D,C)
            <=> ? [E] :
                  ( r2_hidden(k4_tarski(D,E),A)
                  & r2_hidden(E,B) ) ) ) ) )).

fof(t164_relat_1,axiom,(
    $true )).

fof(t165_relat_1,axiom,(
    $true )).

fof(t166_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r2_hidden(A,k10_relat_1(C,B))
      <=> ? [D] :
            ( r2_hidden(D,k2_relat_1(C))
            & r2_hidden(k4_tarski(A,D),C)
            & r2_hidden(D,B) ) ) ) )).

fof(t167_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => r1_tarski(k10_relat_1(B,A),k1_relat_1(B)) ) )).

fof(t168_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => k10_relat_1(B,A) = k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)) ) )).

fof(t169_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => k10_relat_1(A,k2_relat_1(A)) = k1_relat_1(A) ) )).

fof(t170_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => r1_tarski(k10_relat_1(B,A),k10_relat_1(B,k2_relat_1(B))) ) )).

fof(t171_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => k10_relat_1(A,k1_xboole_0) = k1_xboole_0 ) )).

fof(t172_relat_1,axiom,(
    ! [A] : k10_relat_1(k1_xboole_0,A) = k1_xboole_0 )).

fof(t173_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ( k10_relat_1(B,A) = k1_xboole_0
      <=> r1_xboole_0(k2_relat_1(B),A) ) ) )).

fof(t174_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ~ ( A != k1_xboole_0
          & r1_tarski(A,k2_relat_1(B))
          & k10_relat_1(B,A) = k1_xboole_0 ) ) )).

fof(t175_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => k10_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) ) )).

fof(t176_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => r1_tarski(k10_relat_1(C,k3_xboole_0(A,B)),k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B))) ) )).

fof(t177_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => r1_tarski(k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)),k10_relat_1(C,k4_xboole_0(A,B))) ) )).

fof(t178_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) ) ) )).

fof(t179_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => ( r1_tarski(B,C)
           => r1_tarski(k10_relat_1(B,A),k10_relat_1(C,A)) ) ) ) )).

fof(t180_relat_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ! [D] :
          ( v1_relat_1(D)
         => ( ( r1_tarski(C,D)
              & r1_tarski(A,B) )
           => r1_tarski(k10_relat_1(C,A),k10_relat_1(D,B)) ) ) ) )).

fof(t181_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => k10_relat_1(k5_relat_1(B,C),A) = k10_relat_1(B,k10_relat_1(C,A)) ) ) )).

fof(t182_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => k1_relat_1(k5_relat_1(A,B)) = k10_relat_1(A,k1_relat_1(B)) ) ) )).

fof(t183_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => r1_tarski(k3_xboole_0(k2_relat_1(B),A),k10_relat_1(k4_relat_1(B),k10_relat_1(B,A))) ) )).

fof(d15_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v3_relat_1(A)
      <=> r1_tarski(k2_relat_1(A),k1_tarski(k1_xboole_0)) ) ) )).

fof(t184_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v3_relat_1(A)
      <=> ! [B] :
            ( r2_hidden(B,k2_relat_1(A))
           => B = k1_xboole_0 ) ) ) )).

fof(t185_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ! [C,D] :
              ( ( k7_relat_1(A,C) = k7_relat_1(B,C)
                & k7_relat_1(A,D) = k7_relat_1(B,D) )
             => k7_relat_1(A,k2_xboole_0(C,D)) = k7_relat_1(B,k2_xboole_0(C,D)) ) ) ) )).

fof(t186_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => ( ( r1_tarski(k1_relat_1(C),A)
              & r1_tarski(C,B) )
           => r1_tarski(C,k7_relat_1(B,A)) ) ) ) )).

fof(t187_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r1_xboole_0(B,k1_relat_1(A))
         => k7_relat_1(A,B) = k1_xboole_0 ) ) )).

fof(t188_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ! [C,D] :
              ( ( r1_tarski(C,D)
                & k7_relat_1(A,D) = k7_relat_1(B,D) )
             => k7_relat_1(A,C) = k7_relat_1(B,C) ) ) ) )).

fof(t189_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => k7_relat_1(A,k1_relat_1(B)) = k7_relat_1(A,k1_relat_1(k7_relat_1(B,k1_relat_1(A)))) ) ) )).

fof(t190_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ~ ( ~ v3_relat_1(k7_relat_1(B,A))
          & v3_relat_1(B) ) ) )).

fof(s1_relat_1,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & ! [B,C] :
          ( r2_hidden(k4_tarski(B,C),A)
        <=> ( r2_hidden(B,f1_s1_relat_1)
            & r2_hidden(C,f2_s1_relat_1)
            & p1_s1_relat_1(B,C) ) ) ) )).

fof(dt_k1_relat_1,axiom,(
    $true )).

fof(dt_k2_relat_1,axiom,(
    $true )).

fof(dt_k3_relat_1,axiom,(
    $true )).

fof(dt_k4_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => v1_relat_1(k4_relat_1(A)) ) )).

fof(involutiveness_k4_relat_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => k4_relat_1(k4_relat_1(A)) = A ) )).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) )).

fof(dt_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) )).

fof(dt_k7_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) )).

fof(dt_k8_relat_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => v1_relat_1(k8_relat_1(A,B)) ) )).

fof(dt_k9_relat_1,axiom,(
    $true )).

fof(dt_k10_relat_1,axiom,(
    $true )).
%------------------------------------------------------------------------------