SET007 Axioms: SET007+866.ax


%------------------------------------------------------------------------------
% File     : SET007+866 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Propositional Calculus for Boolean Valued Functions. Part VIII
% 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    : bvfunc26 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   95 (   0 unit)
%            Number of atoms       :  446 ( 105 equality)
%            Maximal formula depth :   12 (   8 average)
%            Number of connectives :  438 (  87 ~  ;   0  |;  84  &)
%                                         (   4 <=>; 263 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    8 (   0 propositional; 1-4 arity)
%            Number of functors    :   22 (   1 constant; 0-3 arity)
%            Number of variables   :  293 (   0 singleton; 293 !;   0 ?)
%            Maximal term depth    :    5 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_bvfunc26,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_valuat_1(B) )
     => ( v1_relat_1(k1_bvfunc26(A,B))
        & v1_funct_1(k1_bvfunc26(A,B))
        & v1_valuat_1(k1_bvfunc26(A,B)) ) ) )).

fof(fc2_bvfunc26,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_valuat_1(B) )
     => ( v1_relat_1(k2_bvfunc26(A,B))
        & v1_funct_1(k2_bvfunc26(A,B))
        & v1_valuat_1(k2_bvfunc26(A,B)) ) ) )).

fof(d1_bvfunc26,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_valuat_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k1_bvfunc26(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) = k1_binari_5(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) )).

fof(d2_bvfunc26,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_valuat_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k2_bvfunc26(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) = k3_binari_5(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) )).

fof(d3_bvfunc26,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))
                 => ( D = k3_bvfunc26(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,A)
                       => k1_funct_1(D,E) = k1_binari_5(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) )).

fof(d4_bvfunc26,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))
                 => ( D = k4_bvfunc26(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,A)
                       => k1_funct_1(D,E) = k3_binari_5(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) )).

fof(t1_bvfunc26,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))
             => k3_bvfunc26(A,B,C) = k5_valuat_1(A,k6_valuat_1(A,B,C)) ) ) ) )).

fof(t2_bvfunc26,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))
             => k4_bvfunc26(A,B,C) = k5_valuat_1(A,k8_bvfunc_1(A,B,C)) ) ) ) )).

fof(t3_bvfunc26,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k3_bvfunc26(A,k19_bvfunc_1(A),B) = k5_valuat_1(A,B) ) ) )).

fof(t4_bvfunc26,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k3_bvfunc26(A,k18_bvfunc_1(A),B) = k19_bvfunc_1(A) ) ) )).

fof(t5_bvfunc26,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( k3_bvfunc26(A,k18_bvfunc_1(A),k18_bvfunc_1(A)) = k19_bvfunc_1(A)
        & k3_bvfunc26(A,k18_bvfunc_1(A),k19_bvfunc_1(A)) = k19_bvfunc_1(A)
        & k3_bvfunc26(A,k19_bvfunc_1(A),k19_bvfunc_1(A)) = k18_bvfunc_1(A) ) ) )).

fof(t6_bvfunc26,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( k3_bvfunc26(A,B,B) = k5_valuat_1(A,B)
            & k5_valuat_1(A,k3_bvfunc26(A,B,B)) = B ) ) ) )).

fof(t7_bvfunc26,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))
             => k5_valuat_1(A,k3_bvfunc26(A,B,C)) = k6_valuat_1(A,B,C) ) ) ) )).

fof(t8_bvfunc26,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( k3_bvfunc26(A,B,k5_valuat_1(A,B)) = k19_bvfunc_1(A)
            & k5_valuat_1(A,k3_bvfunc26(A,B,k5_valuat_1(A,B))) = k18_bvfunc_1(A) ) ) ) )).

fof(t9_bvfunc26,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))
                 => k3_bvfunc26(A,B,k6_valuat_1(A,C,D)) = k5_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D)) ) ) ) ) )).

fof(t10_bvfunc26,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))
                 => k3_bvfunc26(A,B,k6_valuat_1(A,C,D)) = k3_bvfunc26(A,k6_valuat_1(A,B,C),D) ) ) ) ) )).

fof(t11_bvfunc26,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))
                 => k3_bvfunc26(A,B,k8_bvfunc_1(A,C,D)) = k6_valuat_1(A,k5_valuat_1(A,k6_valuat_1(A,B,C)),k5_valuat_1(A,k6_valuat_1(A,B,D))) ) ) ) ) )).

fof(t12_bvfunc26,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))
                 => k3_bvfunc26(A,B,k9_bvfunc_1(A,C,D)) = k15_bvfunc_1(A,k6_valuat_1(A,B,C),k6_valuat_1(A,B,D)) ) ) ) ) )).

fof(t13_bvfunc26,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))
                 => ( k3_bvfunc26(A,B,k3_bvfunc26(A,C,D)) = k8_bvfunc_1(A,k5_valuat_1(A,B),k6_valuat_1(A,C,D))
                    & k3_bvfunc26(A,B,k3_bvfunc26(A,C,D)) = k14_bvfunc_1(A,B,k6_valuat_1(A,C,D)) ) ) ) ) ) )).

fof(t14_bvfunc26,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))
                 => ( k3_bvfunc26(A,B,k4_bvfunc26(A,C,D)) = k8_bvfunc_1(A,k8_bvfunc_1(A,k5_valuat_1(A,B),C),D)
                    & k3_bvfunc26(A,B,k4_bvfunc26(A,C,D)) = k14_bvfunc_1(A,B,k8_bvfunc_1(A,C,D)) ) ) ) ) ) )).

fof(t15_bvfunc26,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))
                 => k3_bvfunc26(A,B,k15_bvfunc_1(A,C,D)) = k14_bvfunc_1(A,B,k9_bvfunc_1(A,C,D)) ) ) ) ) )).

fof(t16_bvfunc26,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))
             => k3_bvfunc26(A,B,k6_valuat_1(A,B,C)) = k3_bvfunc26(A,B,C) ) ) ) )).

fof(t17_bvfunc26,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))
             => k3_bvfunc26(A,B,k8_bvfunc_1(A,B,C)) = k6_valuat_1(A,k5_valuat_1(A,B),k5_valuat_1(A,k6_valuat_1(A,B,C))) ) ) ) )).

fof(t18_bvfunc26,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))
             => k3_bvfunc26(A,B,k15_bvfunc_1(A,B,C)) = k14_bvfunc_1(A,B,k9_bvfunc_1(A,B,C)) ) ) ) )).

fof(t19_bvfunc26,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))
             => ( k3_bvfunc26(A,B,k3_bvfunc26(A,B,C)) = k8_bvfunc_1(A,k5_valuat_1(A,B),C)
                & k3_bvfunc26(A,B,k3_bvfunc26(A,B,C)) = k14_bvfunc_1(A,B,C) ) ) ) ) )).

fof(t20_bvfunc26,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))
             => k3_bvfunc26(A,B,k4_bvfunc26(A,B,C)) = k19_bvfunc_1(A) ) ) ) )).

fof(t21_bvfunc26,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))
             => k3_bvfunc26(A,B,k15_bvfunc_1(A,B,C)) = k8_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)) ) ) ) )).

fof(t22_bvfunc26,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))
             => k6_valuat_1(A,B,C) = k3_bvfunc26(A,k3_bvfunc26(A,B,C),k3_bvfunc26(A,B,C)) ) ) ) )).

fof(t23_bvfunc26,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))
                 => k3_bvfunc26(A,k3_bvfunc26(A,B,C),k3_bvfunc26(A,B,D)) = k6_valuat_1(A,B,k8_bvfunc_1(A,C,D)) ) ) ) ) )).

fof(t24_bvfunc26,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))
                 => k3_bvfunc26(A,B,k14_bvfunc_1(A,C,D)) = k6_valuat_1(A,k8_bvfunc_1(A,k5_valuat_1(A,B),C),k5_valuat_1(A,k6_valuat_1(A,B,D))) ) ) ) ) )).

fof(t25_bvfunc26,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))
             => k3_bvfunc26(A,B,k14_bvfunc_1(A,B,C)) = k5_valuat_1(A,k6_valuat_1(A,B,C)) ) ) ) )).

fof(t26_bvfunc26,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k4_bvfunc26(A,k19_bvfunc_1(A),B) = k18_bvfunc_1(A) ) ) )).

fof(t27_bvfunc26,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k4_bvfunc26(A,k18_bvfunc_1(A),B) = k5_valuat_1(A,B) ) ) )).

fof(t28_bvfunc26,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( k4_bvfunc26(A,k18_bvfunc_1(A),k18_bvfunc_1(A)) = k19_bvfunc_1(A)
        & k4_bvfunc26(A,k18_bvfunc_1(A),k19_bvfunc_1(A)) = k18_bvfunc_1(A)
        & k4_bvfunc26(A,k19_bvfunc_1(A),k19_bvfunc_1(A)) = k18_bvfunc_1(A) ) ) )).

fof(t29_bvfunc26,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( k4_bvfunc26(A,B,B) = k5_valuat_1(A,B)
            & k5_valuat_1(A,k4_bvfunc26(A,B,B)) = B ) ) ) )).

fof(t30_bvfunc26,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))
             => k5_valuat_1(A,k4_bvfunc26(A,B,C)) = k8_bvfunc_1(A,B,C) ) ) ) )).

fof(t31_bvfunc26,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( k4_bvfunc26(A,B,k5_valuat_1(A,B)) = k18_bvfunc_1(A)
            & k5_valuat_1(A,k4_bvfunc26(A,B,k5_valuat_1(A,B))) = k19_bvfunc_1(A) ) ) ) )).

fof(t32_bvfunc26,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))
             => k6_valuat_1(A,k5_valuat_1(A,B),k9_bvfunc_1(A,B,C)) = k6_valuat_1(A,k5_valuat_1(A,B),C) ) ) ) )).

fof(t33_bvfunc26,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))
                 => k4_bvfunc26(A,B,k6_valuat_1(A,C,D)) = k8_bvfunc_1(A,k5_valuat_1(A,k8_bvfunc_1(A,B,C)),k5_valuat_1(A,k8_bvfunc_1(A,B,D))) ) ) ) ) )).

fof(t34_bvfunc26,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))
                 => k4_bvfunc26(A,B,k8_bvfunc_1(A,C,D)) = k5_valuat_1(A,k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D)) ) ) ) ) )).

fof(t35_bvfunc26,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))
                 => k4_bvfunc26(A,B,k15_bvfunc_1(A,C,D)) = k6_valuat_1(A,k5_valuat_1(A,B),k9_bvfunc_1(A,C,D)) ) ) ) ) )).

fof(t36_bvfunc26,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))
                 => k4_bvfunc26(A,B,k14_bvfunc_1(A,C,D)) = k6_valuat_1(A,k6_valuat_1(A,k5_valuat_1(A,B),C),k5_valuat_1(A,D)) ) ) ) ) )).

fof(t37_bvfunc26,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))
                 => k4_bvfunc26(A,B,k3_bvfunc26(A,C,D)) = k6_valuat_1(A,k6_valuat_1(A,k5_valuat_1(A,B),C),D) ) ) ) ) )).

fof(t38_bvfunc26,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))
                 => k4_bvfunc26(A,B,k4_bvfunc26(A,C,D)) = k6_valuat_1(A,k5_valuat_1(A,B),k8_bvfunc_1(A,C,D)) ) ) ) ) )).

fof(t39_bvfunc26,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))
             => k4_bvfunc26(A,B,k6_valuat_1(A,B,C)) = k5_valuat_1(A,k6_valuat_1(A,B,k8_bvfunc_1(A,B,C))) ) ) ) )).

fof(t40_bvfunc26,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))
             => k4_bvfunc26(A,B,k8_bvfunc_1(A,B,C)) = k5_valuat_1(A,k8_bvfunc_1(A,B,C)) ) ) ) )).

fof(t41_bvfunc26,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))
             => k4_bvfunc26(A,B,k15_bvfunc_1(A,B,C)) = k6_valuat_1(A,k5_valuat_1(A,B),C) ) ) ) )).

fof(t42_bvfunc26,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))
             => k4_bvfunc26(A,B,k14_bvfunc_1(A,B,C)) = k18_bvfunc_1(A) ) ) ) )).

fof(t43_bvfunc26,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))
             => k4_bvfunc26(A,B,k3_bvfunc26(A,B,C)) = k18_bvfunc_1(A) ) ) ) )).

fof(t44_bvfunc26,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))
             => k4_bvfunc26(A,B,k4_bvfunc26(A,B,C)) = k6_valuat_1(A,k5_valuat_1(A,B),C) ) ) ) )).

fof(t45_bvfunc26,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => k15_bvfunc_1(A,k18_bvfunc_1(A),k18_bvfunc_1(A)) = k19_bvfunc_1(A) ) )).

fof(t46_bvfunc26,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => k15_bvfunc_1(A,k18_bvfunc_1(A),k19_bvfunc_1(A)) = k18_bvfunc_1(A) ) )).

fof(t47_bvfunc26,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => k15_bvfunc_1(A,k19_bvfunc_1(A),k19_bvfunc_1(A)) = k19_bvfunc_1(A) ) )).

fof(t48_bvfunc26,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( k15_bvfunc_1(A,B,B) = k19_bvfunc_1(A)
            & k5_valuat_1(A,k15_bvfunc_1(A,B,B)) = k18_bvfunc_1(A) ) ) ) )).

fof(t49_bvfunc26,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))
             => k15_bvfunc_1(A,B,k8_bvfunc_1(A,B,C)) = k8_bvfunc_1(A,B,k5_valuat_1(A,C)) ) ) ) )).

fof(t50_bvfunc26,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,B,k3_bvfunc26(A,C,D)) = k8_bvfunc_1(A,k6_valuat_1(A,B,k5_valuat_1(A,C)),k6_valuat_1(A,B,k5_valuat_1(A,D))) ) ) ) ) )).

fof(t51_bvfunc26,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,B,k3_bvfunc26(A,C,D)) = k8_bvfunc_1(A,k8_bvfunc_1(A,B,k5_valuat_1(A,C)),k5_valuat_1(A,D)) ) ) ) ) )).

fof(t52_bvfunc26,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))
                 => k9_bvfunc_1(A,B,k3_bvfunc26(A,C,D)) = k8_bvfunc_1(A,k6_valuat_1(A,k5_valuat_1(A,B),k5_valuat_1(A,k6_valuat_1(A,C,D))),k6_valuat_1(A,k6_valuat_1(A,B,C),D)) ) ) ) ) )).

fof(t53_bvfunc26,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))
                 => k15_bvfunc_1(A,B,k3_bvfunc26(A,C,D)) = k8_bvfunc_1(A,k6_valuat_1(A,B,k5_valuat_1(A,k6_valuat_1(A,C,D))),k6_valuat_1(A,k6_valuat_1(A,k5_valuat_1(A,B),C),D)) ) ) ) ) )).

fof(t54_bvfunc26,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,k3_bvfunc26(A,C,D)) = k5_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D)) ) ) ) ) )).

fof(t55_bvfunc26,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))
                 => k4_bvfunc26(A,B,k3_bvfunc26(A,C,D)) = k5_valuat_1(A,k8_bvfunc_1(A,k8_bvfunc_1(A,B,k5_valuat_1(A,C)),k5_valuat_1(A,D))) ) ) ) ) )).

fof(t56_bvfunc26,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))
             => k6_valuat_1(A,B,k3_bvfunc26(A,B,C)) = k6_valuat_1(A,B,k5_valuat_1(A,C)) ) ) ) )).

fof(t57_bvfunc26,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))
             => k8_bvfunc_1(A,B,k3_bvfunc26(A,B,C)) = k19_bvfunc_1(A) ) ) ) )).

fof(t58_bvfunc26,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))
             => k9_bvfunc_1(A,B,k3_bvfunc26(A,B,C)) = k8_bvfunc_1(A,k5_valuat_1(A,B),C) ) ) ) )).

fof(t59_bvfunc26,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))
             => k15_bvfunc_1(A,B,k3_bvfunc26(A,B,C)) = k6_valuat_1(A,B,k5_valuat_1(A,C)) ) ) ) )).

fof(t60_bvfunc26,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))
             => k14_bvfunc_1(A,B,k3_bvfunc26(A,B,C)) = k5_valuat_1(A,k6_valuat_1(A,B,C)) ) ) ) )).

fof(t61_bvfunc26,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))
             => k4_bvfunc26(A,B,k3_bvfunc26(A,B,C)) = k18_bvfunc_1(A) ) ) ) )).

fof(t62_bvfunc26,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,B,k4_bvfunc26(A,C,D)) = k6_valuat_1(A,k6_valuat_1(A,B,k5_valuat_1(A,C)),k5_valuat_1(A,D)) ) ) ) ) )).

fof(t63_bvfunc26,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,B,k4_bvfunc26(A,C,D)) = k6_valuat_1(A,k8_bvfunc_1(A,B,k5_valuat_1(A,C)),k8_bvfunc_1(A,B,k5_valuat_1(A,D))) ) ) ) ) )).

fof(t64_bvfunc26,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))
                 => k9_bvfunc_1(A,B,k4_bvfunc26(A,C,D)) = k6_valuat_1(A,k8_bvfunc_1(A,B,k5_valuat_1(A,k8_bvfunc_1(A,C,D))),k8_bvfunc_1(A,k8_bvfunc_1(A,k5_valuat_1(A,B),C),D)) ) ) ) ) )).

fof(t65_bvfunc26,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))
                 => k15_bvfunc_1(A,B,k4_bvfunc26(A,C,D)) = k6_valuat_1(A,k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D),k8_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,k8_bvfunc_1(A,C,D)))) ) ) ) ) )).

fof(t66_bvfunc26,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,k4_bvfunc26(A,C,D)) = k5_valuat_1(A,k6_valuat_1(A,B,k8_bvfunc_1(A,C,D))) ) ) ) ) )).

fof(t67_bvfunc26,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))
                 => k3_bvfunc26(A,B,k4_bvfunc26(A,C,D)) = k8_bvfunc_1(A,k8_bvfunc_1(A,k5_valuat_1(A,B),C),D) ) ) ) ) )).

fof(t68_bvfunc26,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))
             => k6_valuat_1(A,B,k4_bvfunc26(A,B,C)) = k18_bvfunc_1(A) ) ) ) )).

fof(t69_bvfunc26,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))
             => k8_bvfunc_1(A,B,k4_bvfunc26(A,B,C)) = k8_bvfunc_1(A,B,k5_valuat_1(A,C)) ) ) ) )).

fof(t70_bvfunc26,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))
             => k9_bvfunc_1(A,B,k4_bvfunc26(A,B,C)) = k8_bvfunc_1(A,B,k5_valuat_1(A,C)) ) ) ) )).

fof(t71_bvfunc26,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))
             => k15_bvfunc_1(A,B,k4_bvfunc26(A,B,C)) = k6_valuat_1(A,k5_valuat_1(A,B),C) ) ) ) )).

fof(t72_bvfunc26,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))
             => k14_bvfunc_1(A,B,k4_bvfunc26(A,B,C)) = k5_valuat_1(A,k8_bvfunc_1(A,B,k6_valuat_1(A,B,C))) ) ) ) )).

fof(t73_bvfunc26,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))
             => k3_bvfunc26(A,B,k4_bvfunc26(A,B,C)) = k19_bvfunc_1(A) ) ) ) )).

fof(dt_k1_bvfunc26,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_valuat_1(B) )
     => ( v1_relat_1(k1_bvfunc26(A,B))
        & v1_funct_1(k1_bvfunc26(A,B)) ) ) )).

fof(commutativity_k1_bvfunc26,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_valuat_1(B) )
     => k1_bvfunc26(A,B) = k1_bvfunc26(B,A) ) )).

fof(dt_k2_bvfunc26,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_valuat_1(B) )
     => ( v1_relat_1(k2_bvfunc26(A,B))
        & v1_funct_1(k2_bvfunc26(A,B)) ) ) )).

fof(commutativity_k2_bvfunc26,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_valuat_1(B) )
     => k2_bvfunc26(A,B) = k2_bvfunc26(B,A) ) )).

fof(dt_k3_bvfunc26,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
     => m2_fraenkel(k3_bvfunc26(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) )).

fof(commutativity_k3_bvfunc26,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
     => k3_bvfunc26(A,B,C) = k3_bvfunc26(A,C,B) ) )).

fof(redefinition_k3_bvfunc26,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
     => k3_bvfunc26(A,B,C) = k1_bvfunc26(B,C) ) )).

fof(dt_k4_bvfunc26,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
     => m2_fraenkel(k4_bvfunc26(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) )).

fof(commutativity_k4_bvfunc26,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
     => k4_bvfunc26(A,B,C) = k4_bvfunc26(A,C,B) ) )).

fof(redefinition_k4_bvfunc26,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
     => k4_bvfunc26(A,B,C) = k2_bvfunc26(B,C) ) )).

fof(dt_k5_bvfunc26,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_bvfunc_1(A))
        & m1_subset_1(C,k3_bvfunc_1(A)) )
     => m1_subset_1(k5_bvfunc26(A,B,C),k3_bvfunc_1(A)) ) )).

fof(commutativity_k5_bvfunc26,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_bvfunc_1(A))
        & m1_subset_1(C,k3_bvfunc_1(A)) )
     => k5_bvfunc26(A,B,C) = k5_bvfunc26(A,C,B) ) )).

fof(redefinition_k5_bvfunc26,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_bvfunc_1(A))
        & m1_subset_1(C,k3_bvfunc_1(A)) )
     => k5_bvfunc26(A,B,C) = k1_bvfunc26(B,C) ) )).

fof(dt_k6_bvfunc26,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_bvfunc_1(A))
        & m1_subset_1(C,k3_bvfunc_1(A)) )
     => m1_subset_1(k6_bvfunc26(A,B,C),k3_bvfunc_1(A)) ) )).

fof(commutativity_k6_bvfunc26,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_bvfunc_1(A))
        & m1_subset_1(C,k3_bvfunc_1(A)) )
     => k6_bvfunc26(A,B,C) = k6_bvfunc26(A,C,B) ) )).

fof(redefinition_k6_bvfunc26,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_bvfunc_1(A))
        & m1_subset_1(C,k3_bvfunc_1(A)) )
     => k6_bvfunc26(A,B,C) = k2_bvfunc26(B,C) ) )).
%------------------------------------------------------------------------------