SET007 Axioms: SET007+618.ax


%------------------------------------------------------------------------------
% File     : SET007+618 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Propositional Calculus for Boolean Valued Functions. Part VI
% 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    : bvfunc10 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   27 (   0 unit)
%            Number of atoms       :  151 (  17 equality)
%            Maximal formula depth :   15 (  10 average)
%            Number of connectives :  151 (  27 ~  ;   0  |;   2  &)
%                                         (   0 <=>; 122 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    4 (   0 propositional; 1-4 arity)
%            Number of functors    :    7 (   1 constant; 0-3 arity)
%            Number of variables   :  120 (   0 singleton; 120 !;   0 ?)
%            Maximal term depth    :    7 (   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(t1_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k8_bvfunc_1(A,k8_bvfunc_1(A,k6_valuat_1(A,B,C),k6_valuat_1(A,C,D)),k6_valuat_1(A,D,B)) = k6_valuat_1(A,k6_valuat_1(A,k8_bvfunc_1(A,B,C),k8_bvfunc_1(A,C,D)),k8_bvfunc_1(A,D,B)) ) ) ) ) )).

fof(t2_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k8_bvfunc_1(A,k8_bvfunc_1(A,k6_valuat_1(A,B,k5_valuat_1(A,C)),k6_valuat_1(A,C,k5_valuat_1(A,D))),k6_valuat_1(A,D,k5_valuat_1(A,B))) = k8_bvfunc_1(A,k8_bvfunc_1(A,k6_valuat_1(A,C,k5_valuat_1(A,B)),k6_valuat_1(A,D,k5_valuat_1(A,C))),k6_valuat_1(A,B,k5_valuat_1(A,D))) ) ) ) ) )).

fof(t3_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k6_valuat_1(A,k6_valuat_1(A,k8_bvfunc_1(A,B,k5_valuat_1(A,C)),k8_bvfunc_1(A,C,k5_valuat_1(A,D))),k8_bvfunc_1(A,D,k5_valuat_1(A,B))) = k6_valuat_1(A,k6_valuat_1(A,k8_bvfunc_1(A,C,k5_valuat_1(A,B)),k8_bvfunc_1(A,D,k5_valuat_1(A,C))),k8_bvfunc_1(A,B,k5_valuat_1(A,D))) ) ) ) ) )).

fof(t4_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( ( k14_bvfunc_1(A,D,B) = k19_bvfunc_1(A)
                      & k14_bvfunc_1(A,D,C) = k19_bvfunc_1(A) )
                   => k14_bvfunc_1(A,D,k8_bvfunc_1(A,B,C)) = k19_bvfunc_1(A) ) ) ) ) ) )).

fof(t5_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( ( k14_bvfunc_1(A,B,D) = k19_bvfunc_1(A)
                      & k14_bvfunc_1(A,C,D) = k19_bvfunc_1(A) )
                   => k14_bvfunc_1(A,k6_valuat_1(A,B,C),D) = k19_bvfunc_1(A) ) ) ) ) ) )).

fof(t6_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => ! [F] :
                          ( m2_fraenkel(F,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                         => ! [G] :
                              ( m2_fraenkel(G,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                             => r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,D,E)),k14_bvfunc_1(A,F,G)),k8_bvfunc_1(A,k8_bvfunc_1(A,B,D),F)),k8_bvfunc_1(A,k8_bvfunc_1(A,C,E),G)) ) ) ) ) ) ) ) )).

fof(t7_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,D),k14_bvfunc_1(A,C,E)),k8_bvfunc_1(A,B,C)),k5_valuat_1(A,k6_valuat_1(A,D,E))) = k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,D,B),k14_bvfunc_1(A,E,C)),k8_bvfunc_1(A,D,E)),k5_valuat_1(A,k6_valuat_1(A,B,C))) ) ) ) ) ) )).

fof(t8_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => k6_valuat_1(A,k8_bvfunc_1(A,B,C),k8_bvfunc_1(A,D,E)) = k8_bvfunc_1(A,k8_bvfunc_1(A,k8_bvfunc_1(A,k6_valuat_1(A,B,D),k6_valuat_1(A,B,E)),k6_valuat_1(A,C,D)),k6_valuat_1(A,C,E)) ) ) ) ) ) )).

fof(t9_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => ! [F] :
                          ( m2_fraenkel(F,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                         => k8_bvfunc_1(A,k6_valuat_1(A,B,C),k6_valuat_1(A,k6_valuat_1(A,D,E),F)) = k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k8_bvfunc_1(A,B,D),k8_bvfunc_1(A,B,E)),k8_bvfunc_1(A,B,F)),k8_bvfunc_1(A,C,D)),k8_bvfunc_1(A,C,E)),k8_bvfunc_1(A,C,F)) ) ) ) ) ) ) )).

fof(t10_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,D,E)) = k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,k6_valuat_1(A,k6_valuat_1(A,C,D),E)),k14_bvfunc_1(A,C,k6_valuat_1(A,D,E))),k14_bvfunc_1(A,D,E)) ) ) ) ) ) )).

fof(t11_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,D),k14_bvfunc_1(A,C,E)),k8_bvfunc_1(A,B,C)),k8_bvfunc_1(A,D,E)) ) ) ) ) ) )).

fof(t12_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,k6_valuat_1(A,B,C),k5_valuat_1(A,D)),B),D),k5_valuat_1(A,C)) ) ) ) ) )).

fof(t13_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => ! [F] :
                          ( m2_fraenkel(F,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                         => ! [G] :
                              ( m2_fraenkel(G,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                             => k14_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),k8_bvfunc_1(A,k8_bvfunc_1(A,E,F),G)) = k14_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k5_valuat_1(A,E),k5_valuat_1(A,F)),D),k8_bvfunc_1(A,k8_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)),G)) ) ) ) ) ) ) ) )).

fof(t14_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,D,B)) = k8_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),k6_valuat_1(A,k6_valuat_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)),k5_valuat_1(A,D))) ) ) ) ) )).

fof(t15_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,D,B)),k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D)) = k6_valuat_1(A,k6_valuat_1(A,B,C),D) ) ) ) ) )).

fof(t16_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k8_bvfunc_1(A,B,C),k8_bvfunc_1(A,C,D)),k8_bvfunc_1(A,D,B)),k5_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D))) = k8_bvfunc_1(A,k8_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k5_valuat_1(A,B),C),D),k6_valuat_1(A,k6_valuat_1(A,B,k5_valuat_1(A,C)),D)),k6_valuat_1(A,k6_valuat_1(A,B,C),k5_valuat_1(A,D))) ) ) ) ) )).

fof(t17_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,B,k6_valuat_1(A,C,D))) ) ) ) ) )).

fof(t18_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,k8_bvfunc_1(A,B,C),D)) ) ) ) ) )).

fof(t19_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,B,k8_bvfunc_1(A,C,D))) ) ) ) ) )).

fof(t20_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,B,k8_bvfunc_1(A,C,k5_valuat_1(A,D)))) ) ) ) ) )).

fof(t21_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,C,k8_bvfunc_1(A,D,B))) ) ) ) ) )).

fof(t22_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,C,k8_bvfunc_1(A,D,k5_valuat_1(A,B)))) ) ) ) ) )).

fof(t23_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,k8_bvfunc_1(A,D,B)))) ) ) ) ) )).

fof(t24_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k6_valuat_1(A,k14_bvfunc_1(A,B,k8_bvfunc_1(A,C,k5_valuat_1(A,D))),k14_bvfunc_1(A,C,D))) ) ) ) ) )).

fof(t25_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k6_valuat_1(A,k14_bvfunc_1(A,B,k8_bvfunc_1(A,C,D)),k14_bvfunc_1(A,C,k8_bvfunc_1(A,D,B)))) ) ) ) ) )).

fof(t26_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k6_valuat_1(A,k14_bvfunc_1(A,B,k8_bvfunc_1(A,C,k5_valuat_1(A,D))),k14_bvfunc_1(A,C,k8_bvfunc_1(A,D,B)))) ) ) ) ) )).

fof(t27_bvfunc10,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k6_valuat_1(A,k14_bvfunc_1(A,B,k8_bvfunc_1(A,C,k5_valuat_1(A,D))),k14_bvfunc_1(A,C,k8_bvfunc_1(A,D,k5_valuat_1(A,B))))) ) ) ) ) )).
%------------------------------------------------------------------------------