SET007 Axioms: SET007+80.ax


%------------------------------------------------------------------------------
% File     : SET007+80 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Many-sorted 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    : pboole [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  235 (  20 unit)
%            Number of atoms       :  994 (  50 equality)
%            Maximal formula depth :   15 (   7 average)
%            Number of connectives :  802 (  43 ~  ;   3  |; 194  &)
%                                         (  35 <=>; 527 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   33 (   1 propositional; 0-4 arity)
%            Number of functors    :   44 (   9 constant; 0-4 arity)
%            Number of variables   :  717 (   0 singleton; 701 !;  16 ?)
%            Maximal term depth    :    5 (   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_pboole,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) )).

fof(rc2_pboole,axiom,(
    ! [A] :
    ? [B] :
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v3_relat_1(B)
      & v1_funct_1(B) ) )).

fof(rc3_pboole,axiom,(
    ! [A] :
    ? [B] :
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v2_relat_1(B)
      & v1_funct_1(B) ) )).

fof(cc1_pboole,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ( v2_relat_1(B)
           => ~ v3_relat_1(B) ) ) ) )).

fof(cc2_pboole,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ( v3_relat_1(B)
           => ~ v2_relat_1(B) ) ) ) )).

fof(rc4_pboole,axiom,(
    ! [A] :
    ? [B] :
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_funcop_1(B) ) )).

fof(cc3_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] :
          ( m3_pboole(D,A,B,C)
         => v1_funcop_1(D) ) ) )).

fof(fc1_pboole,axiom,(
    ! [A,B] :
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ( v1_relat_1(k6_pboole(A,B))
        & v2_relat_1(k6_pboole(A,B))
        & ~ v3_relat_1(k6_pboole(A,B))
        & v1_funct_1(k6_pboole(A,B)) ) ) )).

fof(fc2_pboole,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ~ v1_xboole_0(k1_funct_1(B,C)) ) )).

fof(rc5_pboole,axiom,(
    ! [A,B] :
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ? [C] :
          ( m4_pboole(C,A,B)
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C) ) ) )).

fof(fc3_pboole,axiom,(
    ! [A] :
      ( v1_relat_1(k1_pboole(A))
      & v3_relat_1(k1_pboole(A))
      & v1_funct_1(k1_pboole(A)) ) )).

fof(t1_pboole,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_relat_1(A)
       => v1_setfam_1(k2_relat_1(A)) ) ) )).

fof(t2_pboole,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v3_relat_1(A)
      <=> ( A = k1_xboole_0
          | k2_relat_1(A) = k1_tarski(k1_xboole_0) ) ) ) )).

fof(d1_pboole,axiom,(
    $true )).

fof(d2_pboole,axiom,(
    $true )).

fof(d3_pboole,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m1_pboole(B,A)
      <=> k1_relat_1(B) = A ) ) )).

fof(d4_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r1_pboole(A,B,C)
          <=> ! [D] :
                ( r2_hidden(D,A)
               => r2_hidden(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) )).

fof(d5_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
          <=> ! [D] :
                ( r2_hidden(D,A)
               => r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) )).

fof(t3_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( ! [D] :
                ( r2_hidden(D,A)
               => k1_funct_1(B,D) = k1_funct_1(C,D) )
           => B = C ) ) ) )).

fof(d6_pboole,axiom,(
    ! [A] : k1_pboole(A) = k2_funcop_1(A,k1_xboole_0) )).

fof(d7_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( D = k2_pboole(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k2_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) )).

fof(d8_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( D = k3_pboole(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) )).

fof(d9_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( D = k4_pboole(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k4_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) )).

fof(d10_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r4_pboole(A,B,C)
          <=> ! [D] :
                ~ ( r2_hidden(D,A)
                  & r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) )).

fof(d11_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r5_pboole(A,B,C)
          <=> ! [D] :
                ( r2_hidden(D,A)
               => r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) )).

fof(d12_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => k5_pboole(A,B,C) = k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B)) ) ) )).

fof(t4_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( r2_hidden(D,A)
             => k1_funct_1(k5_pboole(A,B,C),D) = k5_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) )).

fof(t5_pboole,axiom,(
    ! [A,B] : k1_funct_1(k1_pboole(B),A) = k1_xboole_0 )).

fof(t6_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ( ! [C] :
            ( r2_hidden(C,A)
           => k1_funct_1(B,C) = k1_xboole_0 )
       => B = k1_pboole(A) ) ) )).

fof(t7_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r1_pboole(A,B,C)
                  | r1_pboole(A,B,D) )
               => r1_pboole(A,B,k2_pboole(A,C,D)) ) ) ) ) )).

fof(t8_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r1_pboole(A,B,k3_pboole(A,C,D))
              <=> ( r1_pboole(A,B,C)
                  & r1_pboole(A,B,D) ) ) ) ) ) )).

fof(t9_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r1_pboole(A,B,C)
                  & r2_pboole(A,C,D) )
               => r1_pboole(A,B,D) ) ) ) ) )).

fof(t10_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r1_pboole(A,B,C)
                  & r1_pboole(A,B,D) )
               => r4_pboole(A,C,D) ) ) ) ) )).

fof(t11_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ~ ( r4_pboole(A,B,C)
              & ! [D] :
                  ( m1_pboole(D,A)
                 => ~ ( r1_pboole(A,D,B)
                      & r1_pboole(A,D,C) ) ) ) ) ) )).

fof(t12_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r1_pboole(A,B,k4_pboole(A,C,D))
               => r1_pboole(A,B,C) ) ) ) ) )).

fof(d13_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,B,C)
          <=> ( r2_pboole(A,B,C)
              & r2_pboole(A,C,B) ) ) ) ) )).

fof(t13_pboole,axiom,(
    $true )).

fof(t14_pboole,axiom,(
    $true )).

fof(t15_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r2_pboole(A,B,C)
                  & r2_pboole(A,C,D) )
               => r2_pboole(A,B,D) ) ) ) ) )).

fof(t16_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,k2_pboole(A,B,C))
            & r2_pboole(A,C,k2_pboole(A,B,C)) ) ) ) )).

fof(t17_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r2_pboole(A,k3_pboole(A,B,C),B)
            & r2_pboole(A,k3_pboole(A,B,C),C) ) ) ) )).

fof(t18_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r2_pboole(A,B,C)
                  & r2_pboole(A,D,C) )
               => r2_pboole(A,k2_pboole(A,B,D),C) ) ) ) ) )).

fof(t19_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r2_pboole(A,B,C)
                  & r2_pboole(A,B,D) )
               => r2_pboole(A,B,k3_pboole(A,C,D)) ) ) ) ) )).

fof(t20_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r2_pboole(A,B,C)
               => ( r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,D))
                  & r2_pboole(A,k2_pboole(A,D,B),k2_pboole(A,D,C)) ) ) ) ) ) )).

fof(t21_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r2_pboole(A,B,C)
               => ( r2_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,D))
                  & r2_pboole(A,k3_pboole(A,D,B),k3_pboole(A,D,C)) ) ) ) ) ) )).

fof(t22_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ! [E] :
                  ( m1_pboole(E,A)
                 => ( ( r2_pboole(A,B,C)
                      & r2_pboole(A,D,E) )
                   => r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,E)) ) ) ) ) ) )).

fof(t23_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ! [E] :
                  ( m1_pboole(E,A)
                 => ( ( r2_pboole(A,B,C)
                      & r2_pboole(A,D,E) )
                   => r2_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,E)) ) ) ) ) ) )).

fof(t24_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
           => ( r6_pboole(A,k2_pboole(A,B,C),C)
              & r6_pboole(A,k2_pboole(A,C,B),C) ) ) ) ) )).

fof(t25_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
           => ( r6_pboole(A,k3_pboole(A,B,C),B)
              & r6_pboole(A,k3_pboole(A,C,B),B) ) ) ) ) )).

fof(t26_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => r2_pboole(A,k3_pboole(A,B,C),k2_pboole(A,B,D)) ) ) ) )).

fof(t27_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r2_pboole(A,B,C)
               => r6_pboole(A,k2_pboole(A,B,k3_pboole(A,D,C)),k3_pboole(A,k2_pboole(A,B,D),C)) ) ) ) ) )).

fof(t28_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,B,k2_pboole(A,C,D))
              <=> ( r2_pboole(A,C,B)
                  & r2_pboole(A,D,B)
                  & ! [E] :
                      ( m1_pboole(E,A)
                     => ( ( r2_pboole(A,C,E)
                          & r2_pboole(A,D,E) )
                       => r2_pboole(A,B,E) ) ) ) ) ) ) ) )).

fof(t29_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,B,k3_pboole(A,C,D))
              <=> ( r2_pboole(A,B,C)
                  & r2_pboole(A,B,D)
                  & ! [E] :
                      ( m1_pboole(E,A)
                     => ( ( r2_pboole(A,E,C)
                          & r2_pboole(A,E,D) )
                       => r2_pboole(A,E,B) ) ) ) ) ) ) ) )).

fof(t30_pboole,axiom,(
    $true )).

fof(t31_pboole,axiom,(
    $true )).

fof(t32_pboole,axiom,(
    $true )).

fof(t33_pboole,axiom,(
    $true )).

fof(t34_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,B,k2_pboole(A,C,D))) ) ) ) )).

fof(t35_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,B,k3_pboole(A,C,D))) ) ) ) )).

fof(t36_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k3_pboole(A,B,k2_pboole(A,B,C)),B)
            & r6_pboole(A,k3_pboole(A,k2_pboole(A,B,C),B),B)
            & r6_pboole(A,k3_pboole(A,B,k2_pboole(A,C,B)),B)
            & r6_pboole(A,k3_pboole(A,k2_pboole(A,C,B),B),B) ) ) ) )).

fof(t37_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k2_pboole(A,B,k3_pboole(A,B,C)),B)
            & r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),B),B)
            & r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,B)),B)
            & r6_pboole(A,k2_pboole(A,k3_pboole(A,C,B),B),B) ) ) ) )).

fof(t38_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => r6_pboole(A,k3_pboole(A,B,k2_pboole(A,C,D)),k2_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))) ) ) ) )).

fof(t39_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,D)),k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D)))
                & r6_pboole(A,k2_pboole(A,k3_pboole(A,C,D),B),k3_pboole(A,k2_pboole(A,C,B),k2_pboole(A,D,B))) ) ) ) ) )).

fof(t40_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D)),B)
               => r2_pboole(A,B,k2_pboole(A,C,D)) ) ) ) ) )).

fof(t41_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D)),B)
               => r2_pboole(A,k3_pboole(A,C,D),B) ) ) ) ) )).

fof(t42_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => r6_pboole(A,k2_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k3_pboole(A,C,D)),k3_pboole(A,D,B)),k3_pboole(A,k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,C,D)),k2_pboole(A,D,B))) ) ) ) )).

fof(t43_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r2_pboole(A,k2_pboole(A,B,C),D)
               => ( r2_pboole(A,B,D)
                  & r2_pboole(A,C,D) ) ) ) ) ) )).

fof(t44_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r2_pboole(A,B,k3_pboole(A,C,D))
               => ( r2_pboole(A,B,C)
                  & r2_pboole(A,B,D) ) ) ) ) ) )).

fof(t45_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,D)))
                & r6_pboole(A,k2_pboole(A,B,k2_pboole(A,C,D)),k2_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D))) ) ) ) ) )).

fof(t46_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,D)))
                & r6_pboole(A,k3_pboole(A,B,k3_pboole(A,C,D)),k3_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))) ) ) ) ) )).

fof(t47_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k2_pboole(A,B,k2_pboole(A,B,C)),k2_pboole(A,B,C))
            & r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),C),k2_pboole(A,B,C)) ) ) ) )).

fof(t48_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k3_pboole(A,B,k3_pboole(A,B,C)),k3_pboole(A,B,C))
            & r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),C),k3_pboole(A,B,C)) ) ) ) )).

fof(t49_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => r2_pboole(A,k1_pboole(A),B) ) )).

fof(t50_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ( r2_pboole(A,B,k1_pboole(A))
       => r6_pboole(A,B,k1_pboole(A)) ) ) )).

fof(t51_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r2_pboole(A,B,C)
                  & r2_pboole(A,B,D)
                  & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) )
               => r6_pboole(A,B,k1_pboole(A)) ) ) ) ) )).

fof(t52_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r2_pboole(A,B,C)
                  & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) )
               => r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A)) ) ) ) ) )).

fof(t53_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ( r6_pboole(A,k2_pboole(A,B,k1_pboole(A)),B)
        & r6_pboole(A,k2_pboole(A,k1_pboole(A),B),B) ) ) )).

fof(t54_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k2_pboole(A,B,C),k1_pboole(A))
           => ( r6_pboole(A,B,k1_pboole(A))
              & r6_pboole(A,C,k1_pboole(A)) ) ) ) ) )).

fof(t55_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ( r6_pboole(A,k3_pboole(A,B,k1_pboole(A)),k1_pboole(A))
        & r6_pboole(A,k3_pboole(A,k1_pboole(A),B),k1_pboole(A)) ) ) )).

fof(t56_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r2_pboole(A,B,k2_pboole(A,C,D))
                  & r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A)) )
               => r2_pboole(A,B,C) ) ) ) ) )).

fof(t57_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( ( r2_pboole(A,B,C)
              & r6_pboole(A,k3_pboole(A,C,B),k1_pboole(A)) )
           => r6_pboole(A,B,k1_pboole(A)) ) ) ) )).

fof(t58_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k4_pboole(A,B,C),k1_pboole(A))
          <=> r2_pboole(A,B,C) ) ) ) )).

fof(t59_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r2_pboole(A,B,C)
               => r2_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D)) ) ) ) ) )).

fof(t60_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r2_pboole(A,B,C)
               => r2_pboole(A,k4_pboole(A,D,C),k4_pboole(A,D,B)) ) ) ) ) )).

fof(t61_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ! [E] :
                  ( m1_pboole(E,A)
                 => ( ( r2_pboole(A,B,C)
                      & r2_pboole(A,D,E) )
                   => r2_pboole(A,k4_pboole(A,B,E),k4_pboole(A,C,D)) ) ) ) ) ) )).

fof(t62_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r2_pboole(A,k4_pboole(A,B,C),B) ) ) )).

fof(t63_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,k4_pboole(A,C,B))
           => r6_pboole(A,B,k1_pboole(A)) ) ) ) )).

fof(t64_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => r6_pboole(A,k4_pboole(A,B,B),k1_pboole(A)) ) )).

fof(t65_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => r6_pboole(A,k4_pboole(A,B,k1_pboole(A)),B) ) )).

fof(t66_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => r6_pboole(A,k4_pboole(A,k1_pboole(A),B),k1_pboole(A)) ) )).

fof(t67_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k4_pboole(A,B,k2_pboole(A,B,C)),k1_pboole(A))
            & r6_pboole(A,k4_pboole(A,B,k2_pboole(A,C,B)),k1_pboole(A)) ) ) ) )).

fof(t68_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => r6_pboole(A,k3_pboole(A,B,k4_pboole(A,C,D)),k4_pboole(A,k3_pboole(A,B,C),D)) ) ) ) )).

fof(t69_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k3_pboole(A,k4_pboole(A,B,C),C),k1_pboole(A))
            & r6_pboole(A,k3_pboole(A,C,k4_pboole(A,B,C)),k1_pboole(A)) ) ) ) )).

fof(t70_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => r6_pboole(A,k4_pboole(A,B,k4_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,C),k3_pboole(A,B,D))) ) ) ) )).

fof(t71_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k2_pboole(A,k4_pboole(A,B,C),k3_pboole(A,B,C)),B)
            & r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k4_pboole(A,B,C)),B) ) ) ) )).

fof(t72_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
           => ( r6_pboole(A,C,k2_pboole(A,B,k4_pboole(A,C,B)))
              & r6_pboole(A,C,k2_pboole(A,k4_pboole(A,C,B),B)) ) ) ) ) )).

fof(t73_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k2_pboole(A,B,k4_pboole(A,C,B)),k2_pboole(A,B,C))
            & r6_pboole(A,k2_pboole(A,k4_pboole(A,C,B),B),k2_pboole(A,C,B)) ) ) ) )).

fof(t74_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r6_pboole(A,k4_pboole(A,B,k4_pboole(A,B,C)),k3_pboole(A,B,C)) ) ) )).

fof(t75_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => r6_pboole(A,k4_pboole(A,B,k3_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,B,D))) ) ) ) )).

fof(t76_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k4_pboole(A,B,k3_pboole(A,B,C)),k4_pboole(A,B,C))
            & r6_pboole(A,k4_pboole(A,B,k3_pboole(A,C,B)),k4_pboole(A,B,C)) ) ) ) )).

fof(t77_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A))
          <=> r6_pboole(A,k4_pboole(A,B,C),B) ) ) ) )).

fof(t78_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D))) ) ) ) )).

fof(t79_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => r6_pboole(A,k4_pboole(A,k4_pboole(A,B,C),D),k4_pboole(A,B,k2_pboole(A,C,D))) ) ) ) )).

fof(t80_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => r6_pboole(A,k4_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D))) ) ) ) )).

fof(t81_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),C),k4_pboole(A,B,C)) ) ) )).

fof(t82_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r2_pboole(A,B,k2_pboole(A,C,D))
               => ( r2_pboole(A,k4_pboole(A,B,C),D)
                  & r2_pboole(A,k4_pboole(A,B,D),C) ) ) ) ) ) )).

fof(t83_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),k3_pboole(A,B,C)),k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B))) ) ) )).

fof(t84_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r6_pboole(A,k4_pboole(A,k4_pboole(A,B,C),C),k4_pboole(A,B,C)) ) ) )).

fof(t85_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => r6_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k3_pboole(A,k4_pboole(A,B,C),k4_pboole(A,B,D))) ) ) ) )).

fof(t86_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B))
           => r6_pboole(A,B,C) ) ) ) )).

fof(t87_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => r6_pboole(A,k3_pboole(A,B,k4_pboole(A,C,D)),k4_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))) ) ) ) )).

fof(t88_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r2_pboole(A,k4_pboole(A,B,C),D)
               => r2_pboole(A,B,k2_pboole(A,C,D)) ) ) ) ) )).

fof(t89_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r2_pboole(A,k4_pboole(A,B,C),k5_pboole(A,B,C)) ) ) )).

fof(t90_pboole,axiom,(
    $true )).

fof(t91_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ( r6_pboole(A,k5_pboole(A,B,k1_pboole(A)),B)
        & r6_pboole(A,k5_pboole(A,k1_pboole(A),B),B) ) ) )).

fof(t92_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => r6_pboole(A,k5_pboole(A,B,B),k1_pboole(A)) ) )).

fof(t93_pboole,axiom,(
    $true )).

fof(t94_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r6_pboole(A,k2_pboole(A,B,C),k2_pboole(A,k5_pboole(A,B,C),k3_pboole(A,B,C))) ) ) )).

fof(t95_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r6_pboole(A,k5_pboole(A,B,C),k4_pboole(A,k2_pboole(A,B,C),k3_pboole(A,B,C))) ) ) )).

fof(t96_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => r6_pboole(A,k4_pboole(A,k5_pboole(A,B,C),D),k2_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k4_pboole(A,C,k2_pboole(A,B,D)))) ) ) ) )).

fof(t97_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => r6_pboole(A,k4_pboole(A,B,k5_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k3_pboole(A,k3_pboole(A,B,C),D))) ) ) ) )).

fof(t98_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => r6_pboole(A,k5_pboole(A,k5_pboole(A,B,C),D),k5_pboole(A,B,k5_pboole(A,C,D))) ) ) ) )).

fof(t99_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r2_pboole(A,k4_pboole(A,B,C),D)
                  & r2_pboole(A,k4_pboole(A,C,B),D) )
               => r2_pboole(A,k5_pboole(A,B,C),D) ) ) ) ) )).

fof(t100_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r6_pboole(A,k2_pboole(A,B,C),k5_pboole(A,B,k4_pboole(A,C,B))) ) ) )).

fof(t101_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r6_pboole(A,k3_pboole(A,B,C),k5_pboole(A,B,k4_pboole(A,B,C))) ) ) )).

fof(t102_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r6_pboole(A,k4_pboole(A,B,C),k5_pboole(A,B,k3_pboole(A,B,C))) ) ) )).

fof(t103_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r6_pboole(A,k4_pboole(A,B,C),k5_pboole(A,C,k2_pboole(A,C,B))) ) ) )).

fof(t104_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r6_pboole(A,k2_pboole(A,B,C),k5_pboole(A,k5_pboole(A,B,C),k3_pboole(A,B,C))) ) ) )).

fof(t105_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r6_pboole(A,k3_pboole(A,B,C),k5_pboole(A,k5_pboole(A,B,C),k2_pboole(A,B,C))) ) ) )).

fof(t106_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r4_pboole(A,B,C)
                  | r4_pboole(A,B,D) )
               => r4_pboole(A,B,k2_pboole(A,C,D)) ) ) ) ) )).

fof(t107_pboole,axiom,(
    $true )).

fof(t108_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r4_pboole(A,B,C)
                  & r2_pboole(A,C,D) )
               => r4_pboole(A,B,D) ) ) ) ) )).

fof(t109_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r4_pboole(A,B,C)
                  & r2_pboole(A,B,D) )
               => r4_pboole(A,D,C) ) ) ) ) )).

fof(t110_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ! [E] :
                  ( m1_pboole(E,A)
                 => ( ( r2_pboole(A,B,C)
                      & r2_pboole(A,D,E)
                      & r4_pboole(A,B,D) )
                   => r4_pboole(A,C,E) ) ) ) ) ) )).

fof(t111_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r4_pboole(A,B,k3_pboole(A,C,D))
               => ( r4_pboole(A,B,C)
                  & r4_pboole(A,B,D) ) ) ) ) ) )).

fof(t112_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r4_pboole(A,B,C)
                  & r2_pboole(A,B,D) )
               => r4_pboole(A,B,k3_pboole(A,C,D)) ) ) ) ) )).

fof(t113_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r4_pboole(A,B,k4_pboole(A,C,D))
               => r4_pboole(A,B,C) ) ) ) ) )).

fof(t114_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ~ ( ~ r4_pboole(A,B,C)
                  & r4_pboole(A,k3_pboole(A,D,B),k3_pboole(A,D,C)) ) ) ) ) )).

fof(t115_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r4_pboole(A,B,k4_pboole(A,C,D))
               => r4_pboole(A,C,k4_pboole(A,B,D)) ) ) ) ) )).

fof(t116_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ~ ( ~ r5_pboole(A,B,C)
                  & r2_pboole(A,C,D)
                  & r5_pboole(A,B,D) ) ) ) ) )).

fof(t117_pboole,axiom,(
    $true )).

fof(t118_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r5_pboole(A,B,k4_pboole(A,C,B)) ) ) )).

fof(t119_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r5_pboole(A,k3_pboole(A,B,C),k4_pboole(A,B,C)) ) ) )).

fof(t120_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r5_pboole(A,k3_pboole(A,B,C),k5_pboole(A,B,C)) ) ) )).

fof(t121_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r5_pboole(A,B,C)
           => r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A)) ) ) ) )).

fof(t122_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ~ ( B != k1_pboole(A)
          & r5_pboole(A,B,B) ) ) )).

fof(t123_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r2_pboole(A,B,C)
                  & r2_pboole(A,B,D)
                  & r5_pboole(A,C,D) )
               => r6_pboole(A,B,k1_pboole(A)) ) ) ) ) )).

fof(t124_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ! [E] :
                  ( m1_pboole(E,A)
                 => ( ( r6_pboole(A,k2_pboole(A,B,C),k2_pboole(A,D,E))
                      & r5_pboole(A,D,B)
                      & r5_pboole(A,E,C) )
                   => ( r6_pboole(A,D,C)
                      & r6_pboole(A,E,B) ) ) ) ) ) ) )).

fof(t125_pboole,axiom,(
    $true )).

fof(t126_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r5_pboole(A,B,C)
           => r6_pboole(A,k4_pboole(A,B,C),B) ) ) ) )).

fof(t127_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r5_pboole(A,B,C)
           => r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),C),B) ) ) ) )).

fof(t128_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k4_pboole(A,B,C),B)
           => r5_pboole(A,B,C) ) ) ) )).

fof(t129_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r5_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B)) ) ) )).

fof(d14_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r7_pboole(A,B,C)
          <=> ! [D] :
                ( m1_pboole(D,A)
               => ( r1_pboole(A,D,B)
                 => r1_pboole(A,D,C) ) ) ) ) ) )).

fof(t130_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
           => r7_pboole(A,B,C) ) ) ) )).

fof(t131_pboole,axiom,(
    $true )).

fof(t132_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r7_pboole(A,B,C)
                  & r7_pboole(A,C,D) )
               => r7_pboole(A,B,D) ) ) ) ) )).

fof(t133_pboole,axiom,(
    r1_pboole(k1_xboole_0,k1_pboole(k1_xboole_0),k1_pboole(k1_xboole_0)) )).

fof(t134_pboole,axiom,(
    ! [A] :
      ( m1_pboole(A,k1_xboole_0)
     => A = k1_xboole_0 ) )).

fof(t135_pboole,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ! [C] :
              ( m1_pboole(C,A)
             => ~ ( r4_pboole(A,B,C)
                  & r5_pboole(A,B,C) ) ) ) ) )).

fof(t136_pboole,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ~ r3_pboole(A,B,k1_pboole(A)) ) ) )).

fof(t137_pboole,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ! [C] :
              ( m1_pboole(C,A)
             => ! [D] :
                  ( m1_pboole(D,A)
                 => ~ ( r3_pboole(A,B,C)
                      & r3_pboole(A,B,D)
                      & k3_pboole(A,C,D) = k1_pboole(A) ) ) ) ) ) )).

fof(t138_pboole,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ( ~ r4_pboole(A,B,k1_pboole(A))
            & ~ r4_pboole(A,k1_pboole(A),B) ) ) ) )).

fof(t139_pboole,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ! [C] :
              ( m1_pboole(C,A)
             => ~ ( r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A))
                  & r4_pboole(A,B,C) ) ) ) ) )).

fof(t140_pboole,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ~ ( r4_pboole(A,B,B)
              & B = k1_pboole(A) ) ) ) )).

fof(d15_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ( v3_relat_1(B)
      <=> ! [C] :
            ( r2_hidden(C,A)
           => v1_xboole_0(k1_funct_1(B,C)) ) ) ) )).

fof(d16_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ( v2_relat_1(B)
      <=> ! [C] :
            ~ ( r2_hidden(C,A)
              & v1_xboole_0(k1_funct_1(B,C)) ) ) ) )).

fof(t141_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ( v3_relat_1(B)
      <=> r6_pboole(A,B,k1_pboole(A)) ) ) )).

fof(t142_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( ( v3_relat_1(B)
              & r2_pboole(A,C,B) )
           => v3_relat_1(C) ) ) ) )).

fof(t143_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( ( v2_relat_1(B)
              & r2_pboole(A,B,C) )
           => v2_relat_1(C) ) ) ) )).

fof(t144_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( ( v2_relat_1(B)
              & r7_pboole(A,B,C) )
           => r2_pboole(A,B,C) ) ) ) )).

fof(t145_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( ( v2_relat_1(B)
              & r7_pboole(A,B,C) )
           => v2_relat_1(C) ) ) ) )).

fof(t146_pboole,axiom,(
    ! [A,B] :
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ? [C] :
          ( m1_pboole(C,A)
          & r1_pboole(A,C,B) ) ) )).

fof(t147_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ( ! [D] :
                ( m1_pboole(D,A)
               => ( r1_pboole(A,D,C)
                <=> r1_pboole(A,D,B) ) )
           => r6_pboole(A,C,B) ) ) ) )).

fof(t148_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( ( v2_relat_1(D)
                & m1_pboole(D,A) )
             => ( ! [E] :
                    ( m1_pboole(E,A)
                   => ( r1_pboole(A,E,D)
                    <=> ( r1_pboole(A,E,B)
                        & r1_pboole(A,E,C) ) ) )
               => r6_pboole(A,D,k3_pboole(A,B,C)) ) ) ) ) )).

fof(t149_pboole,axiom,(
    ! [A,B] :
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ~ r2_hidden(k1_xboole_0,k2_relat_1(B)) ) )).

fof(t150_pboole,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ! [C] :
              ( m1_subset_1(C,k2_relat_1(B))
             => ? [D] :
                  ( r2_hidden(D,A)
                  & C = k1_funct_1(B,D) ) ) ) ) )).

fof(t151_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( r2_hidden(C,A)
         => m1_subset_1(k1_funct_1(B,C),k2_relat_1(B)) ) ) )).

fof(d17_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( m2_pboole(C,A,B)
          <=> ! [D] :
                ( r2_hidden(D,A)
               => m1_subset_1(k1_funct_1(C,D),k1_funct_1(B,D)) ) ) ) ) )).

fof(d18_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( m3_pboole(D,A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,A)
                   => ( v1_funct_1(k1_funct_1(D,E))
                      & v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E))
                      & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) )).

fof(d19_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,k3_finseq_2(A))
         => ( C = k6_pboole(A,B)
          <=> ! [D] :
                ( m2_finseq_2(D,A,k3_finseq_2(A))
               => k1_funct_1(C,D) = k4_card_3(k5_relat_1(D,B)) ) ) ) ) )).

fof(d20_pboole,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k3_finseq_2(k1_tarski(A)))
        & m2_relset_1(B,k5_numbers,k3_finseq_2(k1_tarski(A))) )
     => ( B = k9_pboole(A)
      <=> ! [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
           => k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(A)),B,C) = k2_finseq_2(C,A) ) ) ) )).

fof(t152_pboole,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B,C] : k5_relat_1(k2_finseq_2(A,B),k2_funcop_1(k1_tarski(B),C)) = k2_finseq_2(A,C) ) )).

fof(t153_pboole,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C,D] :
              ( m1_pboole(D,k1_tarski(C))
             => ( D = k2_funcop_1(k1_tarski(C),A)
               => k1_funct_1(k7_pboole(k5_numbers,k3_finseq_2(k1_tarski(C)),k9_pboole(C),k6_pboole(k1_tarski(C),D)),B) = k1_funct_2(k2_finseq_1(B),A) ) ) ) ) )).

fof(d21_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( D = k11_pboole(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k2_zfmisc_1(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) )).

fof(d22_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( D = k12_pboole(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k1_funct_2(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) )).

fof(d23_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( m4_pboole(C,A,B)
          <=> r2_pboole(A,C,B) ) ) ) )).

fof(d24_pboole,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_funcop_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_funcop_1(C) )
             => ( C = k13_pboole(A,B)
              <=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] :
                      ( r2_hidden(D,k1_relat_1(C))
                     => k1_funct_1(C,D) = k5_relat_1(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) )).

fof(d25_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( ( v1_funcop_1(C)
            & m1_pboole(C,A) )
         => ! [D] :
              ( m1_pboole(D,A)
             => ( D = k14_pboole(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k9_relat_1(k1_funct_1(C,E),k1_funct_1(B,E)) ) ) ) ) ) )).

fof(s1_pboole,axiom,
    ( ! [A] :
        ~ ( r2_hidden(A,f1_s1_pboole)
          & f2_s1_pboole(A) = k1_xboole_0 )
   => ? [A] :
        ( m1_pboole(A,f1_s1_pboole)
        & ! [B] :
            ( r2_hidden(B,f1_s1_pboole)
           => r2_hidden(k1_funct_1(A,B),f2_s1_pboole(B)) ) ) )).

fof(s2_pboole,axiom,(
    ? [A] :
      ( m1_pboole(A,f1_s2_pboole)
      & ! [B] :
          ( r2_hidden(B,f1_s2_pboole)
         => ! [C] :
              ( r2_hidden(C,k1_funct_1(A,B))
            <=> ( r2_hidden(C,k1_funct_1(f2_s2_pboole,B))
                & p1_s2_pboole(B,C) ) ) ) ) )).

fof(s3_pboole,axiom,
    ( ! [A] :
        ~ ( r2_hidden(A,f1_s3_pboole)
          & ! [B] : ~ p1_s3_pboole(A,B) )
   => ? [A] :
        ( m1_pboole(A,f1_s3_pboole)
        & ! [B] :
            ( r2_hidden(B,f1_s3_pboole)
           => p1_s3_pboole(B,k1_funct_1(A,B)) ) ) )).

fof(s4_pboole,axiom,(
    ? [A] :
      ( m1_pboole(A,f1_s4_pboole)
      & ! [B] :
          ( r2_hidden(B,f1_s4_pboole)
         => k1_funct_1(A,B) = f2_s4_pboole(B) ) ) )).

fof(s5_pboole,axiom,(
    ? [A] :
      ( m1_pboole(A,f1_s5_pboole)
      & ! [B] :
          ( m1_subset_1(B,f1_s5_pboole)
         => k1_funct_1(A,B) = f2_s5_pboole(B) ) ) )).

fof(dt_m1_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) )).

fof(existence_m1_pboole,axiom,(
    ! [A] :
    ? [B] : m1_pboole(B,A) )).

fof(dt_m2_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m2_pboole(C,A,B)
         => m1_pboole(C,A) ) ) )).

fof(existence_m2_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ? [C] : m2_pboole(C,A,B) ) )).

fof(dt_m3_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] :
          ( m3_pboole(D,A,B,C)
         => m1_pboole(D,A) ) ) )).

fof(existence_m3_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ? [D] : m3_pboole(D,A,B,C) ) )).

fof(dt_m4_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m4_pboole(C,A,B)
         => m1_pboole(C,A) ) ) )).

fof(existence_m4_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ? [C] : m4_pboole(C,A,B) ) )).

fof(redefinition_v1_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ( v1_pboole(B,A)
      <=> v3_relat_1(B) ) ) )).

fof(redefinition_v2_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ( v2_pboole(B,A)
      <=> v2_relat_1(B) ) ) )).

fof(reflexivity_r2_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r2_pboole(A,B,B) ) )).

fof(antisymmetry_r3_pboole,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r3_pboole(A,B,C)
       => ~ r3_pboole(A,C,B) ) ) )).

fof(redefinition_r3_pboole,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r3_pboole(A,B,C)
      <=> r1_pboole(A,B,C) ) ) )).

fof(symmetry_r4_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r4_pboole(A,B,C)
       => r4_pboole(A,C,B) ) ) )).

fof(symmetry_r5_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r5_pboole(A,B,C)
       => r5_pboole(A,C,B) ) ) )).

fof(symmetry_r6_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
       => r6_pboole(A,C,B) ) ) )).

fof(reflexivity_r6_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r6_pboole(A,B,B) ) )).

fof(redefinition_r6_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
      <=> B = C ) ) )).

fof(reflexivity_r7_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r7_pboole(A,B,B) ) )).

fof(dt_k1_pboole,axiom,(
    ! [A] : m1_pboole(k1_pboole(A),A) )).

fof(dt_k2_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => m1_pboole(k2_pboole(A,B,C),A) ) )).

fof(commutativity_k2_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => k2_pboole(A,B,C) = k2_pboole(A,C,B) ) )).

fof(idempotence_k2_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => k2_pboole(A,B,B) = B ) )).

fof(dt_k3_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => m1_pboole(k3_pboole(A,B,C),A) ) )).

fof(commutativity_k3_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => k3_pboole(A,B,C) = k3_pboole(A,C,B) ) )).

fof(idempotence_k3_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => k3_pboole(A,B,B) = B ) )).

fof(dt_k4_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => m1_pboole(k4_pboole(A,B,C),A) ) )).

fof(dt_k5_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => m1_pboole(k5_pboole(A,B,C),A) ) )).

fof(commutativity_k5_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => k5_pboole(A,B,C) = k5_pboole(A,C,B) ) )).

fof(dt_k6_pboole,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => m1_pboole(k6_pboole(A,B),k3_finseq_2(A)) ) )).

fof(dt_k7_pboole,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_pboole(D,B) )
     => m1_pboole(k7_pboole(A,B,C,D),A) ) )).

fof(redefinition_k7_pboole,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_pboole(D,B) )
     => k7_pboole(A,B,C,D) = k5_relat_1(C,D) ) )).

fof(dt_k8_pboole,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & v2_relat_1(D)
        & m1_pboole(D,B) )
     => ( v2_relat_1(k8_pboole(A,B,C,D))
        & m1_pboole(k8_pboole(A,B,C,D),A) ) ) )).

fof(redefinition_k8_pboole,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & v2_relat_1(D)
        & m1_pboole(D,B) )
     => k8_pboole(A,B,C,D) = k5_relat_1(C,D) ) )).

fof(dt_k9_pboole,axiom,(
    ! [A] :
      ( v1_funct_1(k9_pboole(A))
      & v1_funct_2(k9_pboole(A),k5_numbers,k3_finseq_2(k1_tarski(A)))
      & m2_relset_1(k9_pboole(A),k5_numbers,k3_finseq_2(k1_tarski(A))) ) )).

fof(dt_k10_pboole,axiom,(
    ! [A,B] :
      ( v1_funct_1(k10_pboole(A,B))
      & v1_funct_2(k10_pboole(A,B),A,k1_tarski(B))
      & m2_relset_1(k10_pboole(A,B),A,k1_tarski(B)) ) )).

fof(redefinition_k10_pboole,axiom,(
    ! [A,B] : k10_pboole(A,B) = k2_funcop_1(A,B) )).

fof(dt_k11_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => m1_pboole(k11_pboole(A,B,C),A) ) )).

fof(dt_k12_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => m1_pboole(k12_pboole(A,B,C),A) ) )).

fof(dt_k13_pboole,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_funcop_1(B) )
     => ( v1_relat_1(k13_pboole(A,B))
        & v1_funct_1(k13_pboole(A,B))
        & v1_funcop_1(k13_pboole(A,B)) ) ) )).

fof(dt_k14_pboole,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & v1_funcop_1(C)
        & m1_pboole(C,A) )
     => m1_pboole(k14_pboole(A,B,C),A) ) )).
%------------------------------------------------------------------------------