SET007 Axioms: SET007+6.ax


%------------------------------------------------------------------------------
% File     : SET007+6 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Some Basic Properties of Sets
% 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    : zfmisc_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  150 (  52 unit)
%            Number of atoms       :  343 ( 159 equality)
%            Maximal formula depth :   13 (   5 average)
%            Number of connectives :  281 (  88 ~  ;  17  |;  90  &)
%                                         (  25 <=>;  61 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    8 (   1 propositional; 0-2 arity)
%            Number of functors    :   13 (   1 constant; 0-4 arity)
%            Number of variables   :  371 (   0 singleton; 368 !;   3 ?)
%            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(fc1_zfmisc_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k4_tarski(A,B)) )).

fof(d1_zfmisc_1,axiom,(
    ! [A,B] :
      ( B = k1_zfmisc_1(A)
    <=> ! [C] :
          ( r2_hidden(C,B)
        <=> r1_tarski(C,A) ) ) )).

fof(d2_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( C = k2_zfmisc_1(A,B)
    <=> ! [D] :
          ( r2_hidden(D,C)
        <=> ? [E,F] :
              ( r2_hidden(E,A)
              & r2_hidden(F,B)
              & D = k4_tarski(E,F) ) ) ) )).

fof(d3_zfmisc_1,axiom,(
    ! [A,B,C] : k3_zfmisc_1(A,B,C) = k2_zfmisc_1(k2_zfmisc_1(A,B),C) )).

fof(d4_zfmisc_1,axiom,(
    ! [A,B,C,D] : k4_zfmisc_1(A,B,C,D) = k2_zfmisc_1(k3_zfmisc_1(A,B,C),D) )).

fof(t1_zfmisc_1,axiom,(
    k1_zfmisc_1(k1_xboole_0) = k1_tarski(k1_xboole_0) )).

fof(t2_zfmisc_1,axiom,(
    k3_tarski(k1_xboole_0) = k1_xboole_0 )).

fof(t3_zfmisc_1,axiom,(
    $true )).

fof(t4_zfmisc_1,axiom,(
    $true )).

fof(t5_zfmisc_1,axiom,(
    $true )).

fof(t6_zfmisc_1,axiom,(
    ! [A,B] :
      ( r1_tarski(k1_tarski(A),k1_tarski(B))
     => A = B ) )).

fof(t7_zfmisc_1,axiom,(
    $true )).

fof(t8_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( k1_tarski(A) = k2_tarski(B,C)
     => A = B ) )).

fof(t9_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( k1_tarski(A) = k2_tarski(B,C)
     => B = C ) )).

fof(t10_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ~ ( k2_tarski(A,B) = k2_tarski(C,D)
        & A != C
        & A != D ) )).

fof(t11_zfmisc_1,axiom,(
    $true )).

fof(t12_zfmisc_1,axiom,(
    ! [A,B] : r1_tarski(k1_tarski(A),k2_tarski(A,B)) )).

fof(t13_zfmisc_1,axiom,(
    ! [A,B] :
      ( k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A)
     => A = B ) )).

fof(t14_zfmisc_1,axiom,(
    ! [A,B] : k2_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k2_tarski(A,B) )).

fof(t15_zfmisc_1,axiom,(
    $true )).

fof(t16_zfmisc_1,axiom,(
    ! [A,B] :
      ~ ( r1_xboole_0(k1_tarski(A),k1_tarski(B))
        & A = B ) )).

fof(t17_zfmisc_1,axiom,(
    ! [A,B] :
      ( A != B
     => r1_xboole_0(k1_tarski(A),k1_tarski(B)) ) )).

fof(t18_zfmisc_1,axiom,(
    ! [A,B] :
      ( k3_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A)
     => A = B ) )).

fof(t19_zfmisc_1,axiom,(
    ! [A,B] : k3_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_tarski(A) )).

fof(t20_zfmisc_1,axiom,(
    ! [A,B] :
      ( k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A)
    <=> A != B ) )).

fof(t21_zfmisc_1,axiom,(
    ! [A,B] :
      ( k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_xboole_0
     => A = B ) )).

fof(t22_zfmisc_1,axiom,(
    ! [A,B] : k4_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_xboole_0 )).

fof(t23_zfmisc_1,axiom,(
    ! [A,B] :
      ( A != B
     => k4_xboole_0(k2_tarski(A,B),k1_tarski(B)) = k1_tarski(A) ) )).

fof(t24_zfmisc_1,axiom,(
    ! [A,B] :
      ( r1_tarski(k1_tarski(A),k1_tarski(B))
     => A = B ) )).

fof(t25_zfmisc_1,axiom,(
    ! [A,B,C] :
      ~ ( r1_tarski(k1_tarski(A),k2_tarski(B,C))
        & A != B
        & A != C ) )).

fof(t26_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( r1_tarski(k2_tarski(A,B),k1_tarski(C))
     => A = C ) )).

fof(t27_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( r1_tarski(k2_tarski(A,B),k1_tarski(C))
     => k2_tarski(A,B) = k1_tarski(C) ) )).

fof(t28_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ~ ( r1_tarski(k2_tarski(A,B),k2_tarski(C,D))
        & A != C
        & A != D ) )).

fof(t29_zfmisc_1,axiom,(
    ! [A,B] :
      ( A != B
     => k5_xboole_0(k1_tarski(A),k1_tarski(B)) = k2_tarski(A,B) ) )).

fof(t30_zfmisc_1,axiom,(
    ! [A] : k1_zfmisc_1(k1_tarski(A)) = k2_tarski(k1_xboole_0,k1_tarski(A)) )).

fof(t31_zfmisc_1,axiom,(
    ! [A] : k3_tarski(k1_tarski(A)) = A )).

fof(t32_zfmisc_1,axiom,(
    ! [A,B] : k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B))) = k2_tarski(A,B) )).

fof(t33_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) )).

fof(t34_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D)))
    <=> ( A = C
        & B = D ) ) )).

fof(t35_zfmisc_1,axiom,(
    ! [A,B] : k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_tarski(A,B)) )).

fof(t36_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( k2_zfmisc_1(k1_tarski(A),k2_tarski(B,C)) = k2_tarski(k4_tarski(A,B),k4_tarski(A,C))
      & k2_zfmisc_1(k2_tarski(A,B),k1_tarski(C)) = k2_tarski(k4_tarski(A,C),k4_tarski(B,C)) ) )).

fof(t37_zfmisc_1,axiom,(
    ! [A,B] :
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) )).

fof(t38_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( r1_tarski(k2_tarski(A,B),C)
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,C) ) ) )).

fof(t39_zfmisc_1,axiom,(
    ! [A,B] :
      ( r1_tarski(A,k1_tarski(B))
    <=> ( A = k1_xboole_0
        | A = k1_tarski(B) ) ) )).

fof(t40_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( r1_tarski(A,B)
     => ( r2_hidden(C,A)
        | r1_tarski(A,k4_xboole_0(B,k1_tarski(C))) ) ) )).

fof(t41_zfmisc_1,axiom,(
    ! [A,B] :
      ~ ( A != k1_tarski(B)
        & A != k1_xboole_0
        & ! [C] :
            ~ ( r2_hidden(C,A)
              & C != B ) ) )).

fof(t42_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( r1_tarski(A,k2_tarski(B,C))
    <=> ~ ( A != k1_xboole_0
          & A != k1_tarski(B)
          & A != k1_tarski(C)
          & A != k2_tarski(B,C) ) ) )).

fof(t43_zfmisc_1,axiom,(
    ! [A,B,C] :
      ~ ( k1_tarski(A) = k2_xboole_0(B,C)
        & ~ ( B = k1_tarski(A)
            & C = k1_tarski(A) )
        & ~ ( B = k1_xboole_0
            & C = k1_tarski(A) )
        & ~ ( B = k1_tarski(A)
            & C = k1_xboole_0 ) ) )).

fof(t44_zfmisc_1,axiom,(
    ! [A,B,C] :
      ~ ( k1_tarski(A) = k2_xboole_0(B,C)
        & B != C
        & B != k1_xboole_0
        & C != k1_xboole_0 ) )).

fof(t45_zfmisc_1,axiom,(
    ! [A,B] :
      ( r1_tarski(k2_xboole_0(k1_tarski(A),B),B)
     => r2_hidden(A,B) ) )).

fof(t46_zfmisc_1,axiom,(
    ! [A,B] :
      ( r2_hidden(A,B)
     => k2_xboole_0(k1_tarski(A),B) = B ) )).

fof(t47_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( r1_tarski(k2_xboole_0(k2_tarski(A,B),C),C)
     => r2_hidden(A,C) ) )).

fof(t48_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( ( r2_hidden(A,B)
        & r2_hidden(C,B) )
     => k2_xboole_0(k2_tarski(A,C),B) = B ) )).

fof(t49_zfmisc_1,axiom,(
    ! [A,B] : k2_xboole_0(k1_tarski(A),B) != k1_xboole_0 )).

fof(t50_zfmisc_1,axiom,(
    ! [A,B,C] : k2_xboole_0(k2_tarski(A,B),C) != k1_xboole_0 )).

fof(t51_zfmisc_1,axiom,(
    ! [A,B] :
      ( k3_xboole_0(A,k1_tarski(B)) = k1_tarski(B)
     => r2_hidden(B,A) ) )).

fof(t52_zfmisc_1,axiom,(
    ! [A,B] :
      ( r2_hidden(A,B)
     => k3_xboole_0(B,k1_tarski(A)) = k1_tarski(A) ) )).

fof(t53_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( ( r2_hidden(A,B)
        & r2_hidden(C,B) )
     => k3_xboole_0(k2_tarski(A,C),B) = k2_tarski(A,C) ) )).

fof(t54_zfmisc_1,axiom,(
    ! [A,B] :
      ~ ( r1_xboole_0(k1_tarski(A),B)
        & r2_hidden(A,B) ) )).

fof(t55_zfmisc_1,axiom,(
    ! [A,B,C] :
      ~ ( r1_xboole_0(k2_tarski(A,B),C)
        & r2_hidden(A,C) ) )).

fof(t56_zfmisc_1,axiom,(
    ! [A,B] :
      ( ~ r2_hidden(A,B)
     => r1_xboole_0(k1_tarski(A),B) ) )).

fof(t57_zfmisc_1,axiom,(
    ! [A,B,C] :
      ~ ( ~ r2_hidden(A,B)
        & ~ r2_hidden(C,B)
        & ~ r1_xboole_0(k2_tarski(A,C),B) ) )).

fof(t58_zfmisc_1,axiom,(
    ! [A,B] :
      ( r1_xboole_0(k1_tarski(A),B)
      | k3_xboole_0(k1_tarski(A),B) = k1_tarski(A) ) )).

fof(t59_zfmisc_1,axiom,(
    ! [A,B,C] :
      ~ ( k3_xboole_0(k2_tarski(A,B),C) = k1_tarski(A)
        & r2_hidden(B,C)
        & A != B ) )).

fof(t60_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( r2_hidden(A,B)
     => ( ( r2_hidden(C,B)
          & A != C )
        | k3_xboole_0(k2_tarski(A,C),B) = k1_tarski(A) ) ) )).

fof(t61_zfmisc_1,axiom,(
    $true )).

fof(t62_zfmisc_1,axiom,(
    $true )).

fof(t63_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( k3_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B)
     => r2_hidden(A,C) ) )).

fof(t64_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( r2_hidden(A,k4_xboole_0(B,k1_tarski(C)))
    <=> ( r2_hidden(A,B)
        & A != C ) ) )).

fof(t65_zfmisc_1,axiom,(
    ! [A,B] :
      ( k4_xboole_0(A,k1_tarski(B)) = A
    <=> ~ r2_hidden(B,A) ) )).

fof(t66_zfmisc_1,axiom,(
    ! [A,B] :
      ~ ( k4_xboole_0(A,k1_tarski(B)) = k1_xboole_0
        & A != k1_xboole_0
        & A != k1_tarski(B) ) )).

fof(t67_zfmisc_1,axiom,(
    ! [A,B] :
      ( k4_xboole_0(k1_tarski(A),B) = k1_tarski(A)
    <=> ~ r2_hidden(A,B) ) )).

fof(t68_zfmisc_1,axiom,(
    ! [A,B] :
      ( k4_xboole_0(k1_tarski(A),B) = k1_xboole_0
    <=> r2_hidden(A,B) ) )).

fof(t69_zfmisc_1,axiom,(
    ! [A,B] :
      ( k4_xboole_0(k1_tarski(A),B) = k1_xboole_0
      | k4_xboole_0(k1_tarski(A),B) = k1_tarski(A) ) )).

fof(t70_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( k4_xboole_0(k2_tarski(A,B),C) = k1_tarski(A)
    <=> ( ~ r2_hidden(A,C)
        & ( r2_hidden(B,C)
          | A = B ) ) ) )).

fof(t71_zfmisc_1,axiom,(
    $true )).

fof(t72_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( k4_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B)
    <=> ( ~ r2_hidden(A,C)
        & ~ r2_hidden(B,C) ) ) )).

fof(t73_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( k4_xboole_0(k2_tarski(A,B),C) = k1_xboole_0
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,C) ) ) )).

fof(t74_zfmisc_1,axiom,(
    ! [A,B,C] :
      ~ ( k4_xboole_0(k2_tarski(A,B),C) != k1_xboole_0
        & k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(A)
        & k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(B)
        & k4_xboole_0(k2_tarski(A,B),C) != k2_tarski(A,B) ) )).

fof(t75_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( k4_xboole_0(A,k2_tarski(B,C)) = k1_xboole_0
    <=> ~ ( A != k1_xboole_0
          & A != k1_tarski(B)
          & A != k1_tarski(C)
          & A != k2_tarski(B,C) ) ) )).

fof(t76_zfmisc_1,axiom,(
    $true )).

fof(t77_zfmisc_1,axiom,(
    $true )).

fof(t78_zfmisc_1,axiom,(
    $true )).

fof(t79_zfmisc_1,axiom,(
    ! [A,B] :
      ( r1_tarski(A,B)
     => r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)) ) )).

fof(t80_zfmisc_1,axiom,(
    ! [A] : r1_tarski(k1_tarski(A),k1_zfmisc_1(A)) )).

fof(t81_zfmisc_1,axiom,(
    ! [A,B] : r1_tarski(k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)),k1_zfmisc_1(k2_xboole_0(A,B))) )).

fof(t82_zfmisc_1,axiom,(
    ! [A,B] :
      ( k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) = k1_zfmisc_1(k2_xboole_0(A,B))
     => r3_xboole_0(A,B) ) )).

fof(t83_zfmisc_1,axiom,(
    ! [A,B] : k1_zfmisc_1(k3_xboole_0(A,B)) = k3_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) )).

fof(t84_zfmisc_1,axiom,(
    ! [A,B] : r1_tarski(k1_zfmisc_1(k4_xboole_0(A,B)),k2_xboole_0(k1_tarski(k1_xboole_0),k4_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)))) )).

fof(t85_zfmisc_1,axiom,(
    $true )).

fof(t86_zfmisc_1,axiom,(
    ! [A,B] : r1_tarski(k2_xboole_0(k1_zfmisc_1(k4_xboole_0(A,B)),k1_zfmisc_1(k4_xboole_0(B,A))),k1_zfmisc_1(k5_xboole_0(A,B))) )).

fof(t87_zfmisc_1,axiom,(
    $true )).

fof(t88_zfmisc_1,axiom,(
    $true )).

fof(t89_zfmisc_1,axiom,(
    $true )).

fof(t90_zfmisc_1,axiom,(
    $true )).

fof(t91_zfmisc_1,axiom,(
    $true )).

fof(t92_zfmisc_1,axiom,(
    ! [A,B] :
      ( r2_hidden(A,B)
     => r1_tarski(A,k3_tarski(B)) ) )).

fof(t93_zfmisc_1,axiom,(
    ! [A,B] : k3_tarski(k2_tarski(A,B)) = k2_xboole_0(A,B) )).

fof(t94_zfmisc_1,axiom,(
    ! [A,B] :
      ( ! [C] :
          ( r2_hidden(C,A)
         => r1_tarski(C,B) )
     => r1_tarski(k3_tarski(A),B) ) )).

fof(t95_zfmisc_1,axiom,(
    ! [A,B] :
      ( r1_tarski(A,B)
     => r1_tarski(k3_tarski(A),k3_tarski(B)) ) )).

fof(t96_zfmisc_1,axiom,(
    ! [A,B] : k3_tarski(k2_xboole_0(A,B)) = k2_xboole_0(k3_tarski(A),k3_tarski(B)) )).

fof(t97_zfmisc_1,axiom,(
    ! [A,B] : r1_tarski(k3_tarski(k3_xboole_0(A,B)),k3_xboole_0(k3_tarski(A),k3_tarski(B))) )).

fof(t98_zfmisc_1,axiom,(
    ! [A,B] :
      ( ! [C] :
          ( r2_hidden(C,A)
         => r1_xboole_0(C,B) )
     => r1_xboole_0(k3_tarski(A),B) ) )).

fof(t99_zfmisc_1,axiom,(
    ! [A] : k3_tarski(k1_zfmisc_1(A)) = A )).

fof(t100_zfmisc_1,axiom,(
    ! [A] : r1_tarski(A,k1_zfmisc_1(k3_tarski(A))) )).

fof(t101_zfmisc_1,axiom,(
    ! [A,B] :
      ( ! [C,D] :
          ( ( r2_hidden(C,k2_xboole_0(A,B))
            & r2_hidden(D,k2_xboole_0(A,B)) )
         => ( C = D
            | r1_xboole_0(C,D) ) )
     => k3_tarski(k3_xboole_0(A,B)) = k3_xboole_0(k3_tarski(A),k3_tarski(B)) ) )).

fof(t102_zfmisc_1,axiom,(
    ! [A,B,C] :
      ~ ( r2_hidden(A,k2_zfmisc_1(B,C))
        & ! [D,E] : k4_tarski(D,E) != A ) )).

fof(t103_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ~ ( r1_tarski(A,k2_zfmisc_1(B,C))
        & r2_hidden(D,A)
        & ! [E,F] :
            ~ ( r2_hidden(E,B)
              & r2_hidden(F,C)
              & D = k4_tarski(E,F) ) ) )).

fof(t104_zfmisc_1,axiom,(
    ! [A,B,C,D,E] :
      ~ ( r2_hidden(A,k3_xboole_0(k2_zfmisc_1(B,C),k2_zfmisc_1(D,E)))
        & ! [F,G] :
            ~ ( A = k4_tarski(F,G)
              & r2_hidden(F,k3_xboole_0(B,D))
              & r2_hidden(G,k3_xboole_0(C,E)) ) ) )).

fof(t105_zfmisc_1,axiom,(
    ! [A,B] : r1_tarski(k2_zfmisc_1(A,B),k1_zfmisc_1(k1_zfmisc_1(k2_xboole_0(A,B)))) )).

fof(t106_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) )).

fof(t107_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
     => r2_hidden(k4_tarski(B,A),k2_zfmisc_1(D,C)) ) )).

fof(t108_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ( ! [E,F] :
          ( r2_hidden(k4_tarski(E,F),k2_zfmisc_1(A,B))
        <=> r2_hidden(k4_tarski(E,F),k2_zfmisc_1(C,D)) )
     => k2_zfmisc_1(A,B) = k2_zfmisc_1(C,D) ) )).

fof(t109_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ( ( r1_tarski(A,k2_zfmisc_1(B,C))
        & ! [E,F] :
            ( r2_hidden(k4_tarski(E,F),A)
           => r2_hidden(k4_tarski(E,F),D) ) )
     => r1_tarski(A,D) ) )).

fof(t110_zfmisc_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( r1_tarski(A,k2_zfmisc_1(B,C))
        & r1_tarski(D,k2_zfmisc_1(E,F))
        & ! [G,H] :
            ( r2_hidden(k4_tarski(G,H),A)
          <=> r2_hidden(k4_tarski(G,H),D) ) )
     => A = D ) )).

fof(t111_zfmisc_1,axiom,(
    ! [A,B] :
      ( ( ! [C] :
            ~ ( r2_hidden(C,A)
              & ! [D,E] : C != k4_tarski(D,E) )
        & ! [C,D] :
            ( r2_hidden(k4_tarski(C,D),A)
           => r2_hidden(k4_tarski(C,D),B) ) )
     => r1_tarski(A,B) ) )).

fof(t112_zfmisc_1,axiom,(
    ! [A,B] :
      ( ( ! [C] :
            ~ ( r2_hidden(C,A)
              & ! [D,E] : C != k4_tarski(D,E) )
        & ! [C] :
            ~ ( r2_hidden(C,B)
              & ! [D,E] : C != k4_tarski(D,E) )
        & ! [C,D] :
            ( r2_hidden(k4_tarski(C,D),A)
          <=> r2_hidden(k4_tarski(C,D),B) ) )
     => A = B ) )).

fof(t113_zfmisc_1,axiom,(
    ! [A,B] :
      ( k2_zfmisc_1(A,B) = k1_xboole_0
    <=> ( A = k1_xboole_0
        | B = k1_xboole_0 ) ) )).

fof(t114_zfmisc_1,axiom,(
    ! [A,B] :
      ( k2_zfmisc_1(A,B) = k2_zfmisc_1(B,A)
     => ( A = k1_xboole_0
        | B = k1_xboole_0
        | A = B ) ) )).

fof(t115_zfmisc_1,axiom,(
    ! [A,B] :
      ( k2_zfmisc_1(A,A) = k2_zfmisc_1(B,B)
     => A = B ) )).

fof(t116_zfmisc_1,axiom,(
    ! [A] :
      ( r1_tarski(A,k2_zfmisc_1(A,A))
     => A = k1_xboole_0 ) )).

fof(t117_zfmisc_1,axiom,(
    ! [A,B,C] :
      ~ ( A != k1_xboole_0
        & ( r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(C,A))
          | r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(A,C)) )
        & ~ r1_tarski(B,C) ) )).

fof(t118_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( r1_tarski(A,B)
     => ( r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C))
        & r1_tarski(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) ) )).

fof(t119_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) )).

fof(t120_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( k2_zfmisc_1(k2_xboole_0(A,B),C) = k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C))
      & k2_zfmisc_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) )).

fof(t121_zfmisc_1,axiom,(
    ! [A,B,C,D] : k2_zfmisc_1(k2_xboole_0(A,B),k2_xboole_0(C,D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(A,D)),k2_zfmisc_1(B,C)),k2_zfmisc_1(B,D)) )).

fof(t122_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( k2_zfmisc_1(k3_xboole_0(A,B),C) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C))
      & k2_zfmisc_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) )).

fof(t123_zfmisc_1,axiom,(
    ! [A,B,C,D] : k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(C,D)) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) )).

fof(t124_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => k3_xboole_0(k2_zfmisc_1(A,D),k2_zfmisc_1(B,C)) = k2_zfmisc_1(A,C) ) )).

fof(t125_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( k2_zfmisc_1(k4_xboole_0(A,B),C) = k4_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C))
      & k2_zfmisc_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) )).

fof(t126_zfmisc_1,axiom,(
    ! [A,B,C,D] : k4_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) = k2_xboole_0(k2_zfmisc_1(k4_xboole_0(A,C),B),k2_zfmisc_1(A,k4_xboole_0(B,D))) )).

fof(t127_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ( ( r1_xboole_0(A,B)
        | r1_xboole_0(C,D) )
     => r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) )).

fof(t128_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D))
    <=> ( A = C
        & r2_hidden(B,D) ) ) )).

fof(t129_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D)))
    <=> ( r2_hidden(A,C)
        & B = D ) ) )).

fof(t130_zfmisc_1,axiom,(
    ! [A,B] :
      ( A != k1_xboole_0
     => ( k2_zfmisc_1(k1_tarski(B),A) != k1_xboole_0
        & k2_zfmisc_1(A,k1_tarski(B)) != k1_xboole_0 ) ) )).

fof(t131_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ( A != B
     => ( r1_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),D))
        & r1_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(D,k1_tarski(B))) ) ) )).

fof(t132_zfmisc_1,axiom,(
    ! [A,B,C] :
      ( k2_zfmisc_1(k2_tarski(A,B),C) = k2_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),C))
      & k2_zfmisc_1(C,k2_tarski(A,B)) = k2_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(C,k1_tarski(B))) ) )).

fof(t133_zfmisc_1,axiom,(
    $true )).

fof(t134_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ( k2_zfmisc_1(A,B) = k2_zfmisc_1(C,D)
     => ( A = k1_xboole_0
        | B = k1_xboole_0
        | ( A = C
          & B = D ) ) ) )).

fof(t135_zfmisc_1,axiom,(
    ! [A,B] :
      ( ( r1_tarski(A,k2_zfmisc_1(A,B))
        | r1_tarski(A,k2_zfmisc_1(B,A)) )
     => A = k1_xboole_0 ) )).

fof(t136_zfmisc_1,axiom,(
    ! [A] :
    ? [B] :
      ( r2_hidden(A,B)
      & ! [C,D] :
          ( ( r2_hidden(C,B)
            & r1_tarski(D,C) )
         => r2_hidden(D,B) )
      & ! [C] :
          ( r2_hidden(C,B)
         => r2_hidden(k1_zfmisc_1(C),B) )
      & ! [C] :
          ~ ( r1_tarski(C,B)
            & ~ r2_tarski(C,B)
            & ~ r2_hidden(C,B) ) ) )).

fof(t137_zfmisc_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( r2_hidden(A,k2_zfmisc_1(B,C))
        & r2_hidden(A,k2_zfmisc_1(D,E)) )
     => r2_hidden(A,k2_zfmisc_1(k3_xboole_0(B,D),k3_xboole_0(C,E))) ) )).

fof(t138_zfmisc_1,axiom,(
    ! [A,B,C,D] :
      ( r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))
     => ( k2_zfmisc_1(A,B) = k1_xboole_0
        | ( r1_tarski(A,C)
          & r1_tarski(B,D) ) ) ) )).

fof(t139_zfmisc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B,C,D] :
          ( ( r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))
            | r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C)) )
         => r1_tarski(B,D) ) ) )).

fof(t140_zfmisc_1,axiom,(
    ! [A,B] :
      ( r2_hidden(A,B)
     => k2_xboole_0(k4_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B ) )).

fof(t141_zfmisc_1,axiom,(
    ! [A,B] :
      ( ~ r2_hidden(A,B)
     => k4_xboole_0(k2_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B ) )).

fof(dt_k1_zfmisc_1,axiom,(
    $true )).

fof(dt_k2_zfmisc_1,axiom,(
    $true )).

fof(dt_k3_zfmisc_1,axiom,(
    $true )).

fof(dt_k4_zfmisc_1,axiom,(
    $true )).
%------------------------------------------------------------------------------