SET007 Axioms: SET007+187.ax


%------------------------------------------------------------------------------
% File     : SET007+187 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Some Basic Properties of 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    : pzfmisc1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   93 (   4 unit)
%            Number of atoms       :  453 (  14 equality)
%            Maximal formula depth :   16 (   8 average)
%            Number of connectives :  398 (  38 ~  ;  13  |;  66  &)
%                                         (  13 <=>; 268 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   14 (   1 propositional; 0-3 arity)
%            Number of functors    :   16 (   1 constant; 0-3 arity)
%            Number of variables   :  317 (   0 singleton; 317 !;   0 ?)
%            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(fc1_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ( v1_relat_1(k1_pzfmisc1(A,B))
        & v2_relat_1(k1_pzfmisc1(A,B))
        & v1_funct_1(k1_pzfmisc1(A,B))
        & v1_pre_circ(k1_pzfmisc1(A,B),A) ) ) )).

fof(fc2_pzfmisc1,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k2_pzfmisc1(A,B,C))
        & v2_relat_1(k2_pzfmisc1(A,B,C))
        & v1_funct_1(k2_pzfmisc1(A,B,C))
        & v1_pre_circ(k2_pzfmisc1(A,B,C),A) ) ) )).

fof(t1_pzfmisc1,axiom,(
    ! [A,B,C,D] :
      ( m1_pboole(D,A)
     => ( r2_hidden(B,A)
       => k1_relat_1(k1_funct_4(D,k3_cqc_lang(B,C))) = A ) ) )).

fof(t2_pzfmisc1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( A = k1_xboole_0
       => m1_pboole(A,k1_xboole_0) ) ) )).

fof(t3_pzfmisc1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ~ ( v3_relat_1(B)
              & v2_relat_1(B) ) ) ) )).

fof(d1_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( C = k1_pzfmisc1(A,B)
          <=> ! [D] :
                ( r2_hidden(D,A)
               => k1_funct_1(C,D) = k1_tarski(k1_funct_1(B,D)) ) ) ) ) )).

fof(d2_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( D = k2_pzfmisc1(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k2_tarski(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) )).

fof(t4_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,B,k1_pzfmisc1(A,C))
          <=> ! [D] :
                ( m1_pboole(D,A)
               => ( r1_pboole(A,D,B)
                <=> r6_pboole(A,D,C) ) ) ) ) ) )).

fof(t5_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ! [E] :
                    ( m1_pboole(E,A)
                   => ( r1_pboole(A,E,B)
                    <=> ( r6_pboole(A,E,C)
                        | r6_pboole(A,E,D) ) ) )
               => r6_pboole(A,B,k2_pzfmisc1(A,C,D)) ) ) ) ) )).

fof(t6_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,B,k2_pzfmisc1(A,C,D))
               => ! [E] :
                    ( m1_pboole(E,A)
                   => ( ( r6_pboole(A,E,C)
                        | r6_pboole(A,E,D) )
                     => r1_pboole(A,E,B) ) ) ) ) ) ) )).

fof(t7_pzfmisc1,axiom,(
    $true )).

fof(t8_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r1_pboole(A,B,k1_pzfmisc1(A,C))
           => r6_pboole(A,B,C) ) ) ) )).

fof(t9_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => r1_pboole(A,B,k1_pzfmisc1(A,B)) ) )).

fof(t10_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r6_pboole(A,B,C)
                  | r6_pboole(A,B,D) )
               => r1_pboole(A,B,k2_pzfmisc1(A,C,D)) ) ) ) ) )).

fof(t11_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k2_pzfmisc1(A,B,C)) ) ) )).

fof(t12_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => r6_pboole(A,k2_pzfmisc1(A,B,B),k1_pzfmisc1(A,B)) ) )).

fof(t13_pzfmisc1,axiom,(
    $true )).

fof(t14_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r2_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C))
           => r6_pboole(A,B,C) ) ) ) )).

fof(t15_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C))
           => r6_pboole(A,B,C) ) ) ) )).

fof(t16_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,C,D))
               => ( r6_pboole(A,B,C)
                  & r6_pboole(A,B,D) ) ) ) ) ) )).

fof(t17_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,C,D))
               => r6_pboole(A,C,D) ) ) ) ) )).

fof(t18_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r2_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,B,C))
            & r2_pboole(A,k1_pzfmisc1(A,C),k2_pzfmisc1(A,B,C)) ) ) ) )).

fof(t19_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( ( r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pzfmisc1(A,B))
              | r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pzfmisc1(A,C)) )
           => r6_pboole(A,B,C) ) ) ) )).

fof(t20_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,B,C)),k2_pzfmisc1(A,B,C)) ) ) )).

fof(t21_pzfmisc1,axiom,(
    $true )).

fof(t22_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ~ ( ~ v1_xboole_0(A)
              & r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pboole(A))
              & B = C ) ) ) )).

fof(t23_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( ( r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pzfmisc1(A,B))
              | r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pzfmisc1(A,C)) )
           => r6_pboole(A,B,C) ) ) ) )).

fof(t24_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,B,C)),k1_pzfmisc1(A,B))
            & r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,C),k2_pzfmisc1(A,B,C)),k1_pzfmisc1(A,C)) ) ) ) )).

fof(t25_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ~ ( ~ v1_xboole_0(A)
              & r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pzfmisc1(A,B))
              & B = C ) ) ) )).

fof(t26_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pboole(A))
           => r6_pboole(A,B,C) ) ) ) )).

fof(t27_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,B,C)),k1_pboole(A))
            & r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,C),k2_pzfmisc1(A,B,C)),k1_pboole(A)) ) ) ) )).

fof(t28_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r2_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C))
           => r6_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)) ) ) ) )).

fof(t29_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r2_pboole(A,k2_pzfmisc1(A,B,C),k1_pzfmisc1(A,D))
               => ( r6_pboole(A,B,D)
                  & r6_pboole(A,C,D) ) ) ) ) ) )).

fof(t30_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r2_pboole(A,k2_pzfmisc1(A,B,C),k1_pzfmisc1(A,D))
               => r6_pboole(A,k2_pzfmisc1(A,B,C),k1_pzfmisc1(A,D)) ) ) ) ) )).

fof(t31_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => r6_pboole(A,k1_mboolean(A,k1_pzfmisc1(A,B)),k2_pzfmisc1(A,k1_pboole(A),k1_pzfmisc1(A,B))) ) )).

fof(t32_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => r2_pboole(A,k1_pzfmisc1(A,B),k1_mboolean(A,B)) ) )).

fof(t33_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => r6_pboole(A,k2_mboolean(A,k1_pzfmisc1(A,B)),B) ) )).

fof(t34_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r6_pboole(A,k2_mboolean(A,k2_pzfmisc1(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C))),k2_pzfmisc1(A,B,C)) ) ) )).

fof(t35_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => r6_pboole(A,k2_mboolean(A,k2_pzfmisc1(A,B,C)),k2_pboole(A,B,C)) ) ) )).

fof(t36_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r2_pboole(A,k1_pzfmisc1(A,B),C)
          <=> r1_pboole(A,B,C) ) ) ) )).

fof(t37_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r2_pboole(A,k2_pzfmisc1(A,B,C),D)
              <=> ( r1_pboole(A,B,D)
                  & r1_pboole(A,C,D) ) ) ) ) ) )).

fof(t38_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ~ ( ~ r6_pboole(A,B,k1_pboole(A))
                    & ~ r6_pboole(A,B,k1_pzfmisc1(A,C))
                    & ~ r6_pboole(A,B,k1_pzfmisc1(A,D))
                    & ~ r6_pboole(A,B,k2_pzfmisc1(A,C,D)) )
               => r2_pboole(A,B,k2_pzfmisc1(A,C,D)) ) ) ) ) )).

fof(t39_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ( r1_pboole(A,B,C)
                  | r6_pboole(A,B,D) )
               => r1_pboole(A,B,k2_pboole(A,C,k1_pzfmisc1(A,D))) ) ) ) ) )).

fof(t40_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r2_pboole(A,k2_pboole(A,B,k1_pzfmisc1(A,C)),D)
              <=> ( r1_pboole(A,C,D)
                  & r2_pboole(A,B,D) ) ) ) ) ) )).

fof(t41_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),C),C)
           => r1_pboole(A,B,C) ) ) ) )).

fof(t42_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r1_pboole(A,B,C)
           => r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),C),C) ) ) ) )).

fof(t43_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k2_pboole(A,k2_pzfmisc1(A,B,C),D),D)
              <=> ( r1_pboole(A,B,D)
                  & r1_pboole(A,C,D) ) ) ) ) ) )).

fof(t44_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ~ ( ~ v1_xboole_0(A)
              & k2_pboole(A,k1_pzfmisc1(A,B),C) = k1_pboole(A) ) ) ) )).

fof(t45_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ~ ( ~ v1_xboole_0(A)
                  & k2_pboole(A,k2_pzfmisc1(A,B,C),D) = k1_pboole(A) ) ) ) ) )).

fof(t46_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k3_pboole(A,B,k1_pzfmisc1(A,C)),k1_pzfmisc1(A,C))
           => r1_pboole(A,C,B) ) ) ) )).

fof(t47_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r1_pboole(A,B,C)
           => r6_pboole(A,k3_pboole(A,C,k1_pzfmisc1(A,B)),k1_pzfmisc1(A,B)) ) ) ) )).

fof(t48_pzfmisc1,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,D,C) )
              <=> r6_pboole(A,k3_pboole(A,k2_pzfmisc1(A,B,D),C),k2_pzfmisc1(A,B,D)) ) ) ) ) )).

fof(t49_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ~ ( ~ v1_xboole_0(A)
              & r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,B),C),k1_pboole(A))
              & r1_pboole(A,B,C) ) ) ) )).

fof(t50_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k3_pboole(A,k2_pzfmisc1(A,B,C),D),k1_pboole(A))
               => ( v1_xboole_0(A)
                  | ( ~ r1_pboole(A,B,D)
                    & ~ r1_pboole(A,C,D) ) ) ) ) ) ) )).

fof(t51_pzfmisc1,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,k1_pzfmisc1(A,D)))
               => r1_pboole(A,B,C) ) ) ) ) )).

fof(t52_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ~ ( ~ v1_xboole_0(A)
                  & r1_pboole(A,B,k4_pboole(A,C,k1_pzfmisc1(A,D)))
                  & B = D ) ) ) ) )).

fof(t53_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ~ ( ~ v1_xboole_0(A)
              & r6_pboole(A,k4_pboole(A,B,k1_pzfmisc1(A,C)),B)
              & r1_pboole(A,C,B) ) ) ) )).

fof(t54_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ~ ( ~ v1_xboole_0(A)
              & r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,B),C),k1_pzfmisc1(A,B))
              & r1_pboole(A,B,C) ) ) ) )).

fof(t55_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,B),C),k1_pboole(A))
          <=> r1_pboole(A,B,C) ) ) ) )).

fof(t56_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ~ ( ~ v1_xboole_0(A)
                  & r6_pboole(A,k4_pboole(A,k2_pzfmisc1(A,B,C),D),k1_pzfmisc1(A,B))
                  & r1_pboole(A,B,D) ) ) ) ) )).

fof(t57_pzfmisc1,axiom,(
    $true )).

fof(t58_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k4_pboole(A,k2_pzfmisc1(A,B,C),D),k2_pzfmisc1(A,B,C))
               => ( v1_xboole_0(A)
                  | ( ~ r1_pboole(A,B,D)
                    & ~ r1_pboole(A,C,D) ) ) ) ) ) ) )).

fof(t59_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k4_pboole(A,k2_pzfmisc1(A,B,C),D),k1_pboole(A))
              <=> ( r1_pboole(A,B,D)
                  & r1_pboole(A,C,D) ) ) ) ) ) )).

fof(t60_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( ~ ( ~ r6_pboole(A,B,k1_pboole(A))
                    & ~ r6_pboole(A,B,k1_pzfmisc1(A,C))
                    & ~ r6_pboole(A,B,k1_pzfmisc1(A,D))
                    & ~ r6_pboole(A,B,k2_pzfmisc1(A,C,D)) )
               => r6_pboole(A,k4_pboole(A,B,k2_pzfmisc1(A,C,D)),k1_pboole(A)) ) ) ) ) )).

fof(t61_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( ( r6_pboole(A,B,k1_pboole(A))
              | r6_pboole(A,C,k1_pboole(A)) )
           => r6_pboole(A,k11_pboole(A,B,C),k1_pboole(A)) ) ) ) )).

fof(t62_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( ( v2_relat_1(B)
              & v2_relat_1(C)
              & r6_pboole(A,k11_pboole(A,B,C),k11_pboole(A,C,B)) )
           => r6_pboole(A,B,C) ) ) ) )).

fof(t63_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k11_pboole(A,B,B),k11_pboole(A,C,C))
           => r6_pboole(A,B,C) ) ) ) )).

fof(t64_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( v2_relat_1(B)
               => ( ( ~ r2_pboole(A,k11_pboole(A,C,B),k11_pboole(A,D,B))
                    & ~ r2_pboole(A,k11_pboole(A,B,C),k11_pboole(A,B,D)) )
                  | r2_pboole(A,C,D) ) ) ) ) ) )).

fof(t65_pzfmisc1,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,k11_pboole(A,B,D),k11_pboole(A,C,D))
                  & r2_pboole(A,k11_pboole(A,D,B),k11_pboole(A,D,C)) ) ) ) ) ) )).

fof(t66_pzfmisc1,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,k11_pboole(A,B,D),k11_pboole(A,C,E)) ) ) ) ) ) )).

fof(t67_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k11_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,D)))
                & r6_pboole(A,k11_pboole(A,D,k2_pboole(A,B,C)),k2_pboole(A,k11_pboole(A,D,B),k11_pboole(A,D,C))) ) ) ) ) )).

fof(t68_pzfmisc1,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,k11_pboole(A,k2_pboole(A,B,C),k2_pboole(A,D,E)),k2_pboole(A,k2_pboole(A,k2_pboole(A,k11_pboole(A,B,D),k11_pboole(A,B,E)),k11_pboole(A,C,D)),k11_pboole(A,C,E))) ) ) ) ) )).

fof(t69_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k11_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,D)))
                & r6_pboole(A,k11_pboole(A,D,k3_pboole(A,B,C)),k3_pboole(A,k11_pboole(A,D,B),k11_pboole(A,D,C))) ) ) ) ) )).

fof(t70_pzfmisc1,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,k11_pboole(A,k3_pboole(A,B,C),k3_pboole(A,D,E)),k3_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,E))) ) ) ) ) )).

fof(t71_pzfmisc1,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) )
                   => r6_pboole(A,k3_pboole(A,k11_pboole(A,B,E),k11_pboole(A,C,D)),k11_pboole(A,B,D)) ) ) ) ) ) )).

fof(t72_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k11_pboole(A,k4_pboole(A,B,C),D),k4_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,D)))
                & r6_pboole(A,k11_pboole(A,D,k4_pboole(A,B,C)),k4_pboole(A,k11_pboole(A,D,B),k11_pboole(A,D,C))) ) ) ) ) )).

fof(t73_pzfmisc1,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,k4_pboole(A,k11_pboole(A,B,C),k11_pboole(A,D,E)),k2_pboole(A,k11_pboole(A,k4_pboole(A,B,D),C),k11_pboole(A,B,k4_pboole(A,C,E)))) ) ) ) ) )).

fof(t74_pzfmisc1,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,k3_pboole(A,B,C),k1_pboole(A))
                      | r6_pboole(A,k3_pboole(A,D,E),k1_pboole(A)) )
                   => r6_pboole(A,k3_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,E)),k1_pboole(A)) ) ) ) ) ) )).

fof(t75_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( v2_relat_1(B)
           => ( v2_relat_1(k11_pboole(A,k1_pzfmisc1(A,C),B))
              & v2_relat_1(k11_pboole(A,B,k1_pzfmisc1(A,C))) ) ) ) ) )).

fof(t76_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k11_pboole(A,k2_pzfmisc1(A,B,C),D),k2_pboole(A,k11_pboole(A,k1_pzfmisc1(A,B),D),k11_pboole(A,k1_pzfmisc1(A,C),D)))
                & r6_pboole(A,k11_pboole(A,D,k2_pzfmisc1(A,B,C)),k2_pboole(A,k11_pboole(A,D,k1_pzfmisc1(A,B)),k11_pboole(A,D,k1_pzfmisc1(A,C)))) ) ) ) ) )).

fof(t77_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ! [E] :
                  ( m1_pboole(E,A)
                 => ( ( v2_relat_1(B)
                      & v2_relat_1(C)
                      & r6_pboole(A,k11_pboole(A,B,C),k11_pboole(A,D,E)) )
                   => ( r6_pboole(A,B,D)
                      & r6_pboole(A,C,E) ) ) ) ) ) ) )).

fof(t78_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( ( r2_pboole(A,B,k11_pboole(A,B,C))
              | r2_pboole(A,B,k11_pboole(A,C,B)) )
           => r6_pboole(A,B,k1_pboole(A)) ) ) ) )).

fof(t79_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ! [E] :
                  ( m1_pboole(E,A)
                 => ! [F] :
                      ( m1_pboole(F,A)
                     => ( ( r1_pboole(A,B,k11_pboole(A,C,D))
                          & r1_pboole(A,B,k11_pboole(A,E,F)) )
                       => r1_pboole(A,B,k11_pboole(A,k3_pboole(A,C,E),k3_pboole(A,D,F))) ) ) ) ) ) ) )).

fof(t80_pzfmisc1,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,k11_pboole(A,B,C),k11_pboole(A,D,E))
                      & v2_relat_1(k11_pboole(A,B,C)) )
                   => ( r2_pboole(A,B,D)
                      & r2_pboole(A,C,E) ) ) ) ) ) ) )).

fof(t81_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
           => r2_pboole(A,k11_pboole(A,B,B),k11_pboole(A,C,C)) ) ) ) )).

fof(t82_pzfmisc1,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,k3_pboole(A,k11_pboole(A,B,C),k11_pboole(A,C,B)),k1_pboole(A)) ) ) ) )).

fof(t83_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ! [E] :
                  ( m1_pboole(E,A)
                 => ( v2_relat_1(B)
                   => ( ( ~ r2_pboole(A,k11_pboole(A,B,C),k11_pboole(A,D,E))
                        & ~ r2_pboole(A,k11_pboole(A,C,B),k11_pboole(A,E,D)) )
                      | r2_pboole(A,C,E) ) ) ) ) ) ) )).

fof(t84_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ! [E] :
                  ( m1_pboole(E,A)
                 => ! [F] :
                      ( m1_pboole(F,A)
                     => ! [G] :
                          ( m1_pboole(G,A)
                         => ( ( r2_pboole(A,B,k11_pboole(A,C,D))
                              & r2_pboole(A,E,k11_pboole(A,F,G)) )
                           => r2_pboole(A,k2_pboole(A,B,E),k11_pboole(A,k2_pboole(A,C,F),k2_pboole(A,D,G))) ) ) ) ) ) ) ) )).

fof(d3_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( r1_pzfmisc1(A,B,C)
          <=> ! [D] :
                ( ( r2_hidden(D,A)
                  & k1_funct_1(C,D) = k1_xboole_0 )
               => k1_funct_1(B,D) = k1_xboole_0 ) ) ) ) )).

fof(reflexivity_r1_pzfmisc1,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r1_pzfmisc1(A,B,B) ) )).

fof(dt_k1_pzfmisc1,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => m1_pboole(k1_pzfmisc1(A,B),A) ) )).

fof(dt_k2_pzfmisc1,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => m1_pboole(k2_pzfmisc1(A,B,C),A) ) )).

fof(commutativity_k2_pzfmisc1,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => k2_pzfmisc1(A,B,C) = k2_pzfmisc1(A,C,B) ) )).
%------------------------------------------------------------------------------