SET007 Axioms: SET007+569.ax


%------------------------------------------------------------------------------
% File     : SET007+569 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : A Theory of Boolean Valued Functions and Partitions
% 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    : bvfunc_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  133 (   7 unit)
%            Number of atoms       :  655 ( 129 equality)
%            Maximal formula depth :   18 (   7 average)
%            Number of connectives :  626 ( 104 ~  ;   1  |; 219  &)
%                                         (  24 <=>; 278 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   22 (   1 propositional; 0-4 arity)
%            Number of functors    :   58 (   8 constant; 0-4 arity)
%            Number of variables   :  360 (   0 singleton; 354 !;   6 ?)
%            Maximal term depth    :    4 (   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_bvfunc_1,axiom,(
    ! [A,B] :
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k1_bvfunc_1(A,B)) ) )).

fof(fc2_bvfunc_1,axiom,(
    ! [A,B] :
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k2_bvfunc_1(A,B)) ) )).

fof(cc1_bvfunc_1,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) )).

fof(fc3_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(k3_bvfunc_1(A))
      & v1_fraenkel(k3_bvfunc_1(A)) ) )).

fof(cc2_bvfunc_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k3_bvfunc_1(A))
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_valuat_1(B) ) ) )).

fof(fc4_bvfunc_1,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(k6_bvfunc_1(A,B))
        & v1_funct_1(k6_bvfunc_1(A,B))
        & v1_valuat_1(k6_bvfunc_1(A,B)) ) ) )).

fof(fc5_bvfunc_1,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(k7_bvfunc_1(A,B))
        & v1_funct_1(k7_bvfunc_1(A,B))
        & v1_valuat_1(k7_bvfunc_1(A,B)) ) ) )).

fof(fc6_bvfunc_1,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(k12_bvfunc_1(A,B))
        & v1_funct_1(k12_bvfunc_1(A,B))
        & v1_valuat_1(k12_bvfunc_1(A,B)) ) ) )).

fof(fc7_bvfunc_1,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(k13_bvfunc_1(A,B))
        & v1_funct_1(k13_bvfunc_1(A,B))
        & v1_valuat_1(k13_bvfunc_1(A,B)) ) ) )).

fof(fc8_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( v1_relat_1(k18_bvfunc_1(A))
        & v1_funct_1(k18_bvfunc_1(A))
        & v1_funct_2(k18_bvfunc_1(A),A,k6_margrel1)
        & v5_seqm_3(k18_bvfunc_1(A))
        & v1_valuat_1(k18_bvfunc_1(A)) ) ) )).

fof(fc9_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( v1_relat_1(k19_bvfunc_1(A))
        & v1_funct_1(k19_bvfunc_1(A))
        & v1_funct_2(k19_bvfunc_1(A),A,k6_margrel1)
        & v5_seqm_3(k19_bvfunc_1(A))
        & v1_valuat_1(k19_bvfunc_1(A)) ) ) )).

fof(rc1_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_funct_2(B,A,k6_margrel1)
          & v5_seqm_3(B)
          & v1_valuat_1(B) ) ) )).

fof(d1_bvfunc_1,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_bvfunc_1(A,B) = k1_binarith(k9_margrel1(A),B) ) ) )).

fof(d2_bvfunc_1,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k2_bvfunc_1(A,B) = k9_margrel1(k2_binarith(A,B)) ) ) )).

fof(d3_bvfunc_1,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ( r1_xreal_0(A,B)
          <=> k1_bvfunc_1(A,B) = k8_margrel1 ) ) ) )).

fof(d4_bvfunc_1,axiom,(
    ! [A] : k3_bvfunc_1(A) = k1_fraenkel(A,k6_margrel1) )).

fof(d5_bvfunc_1,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 = k6_bvfunc_1(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_binarith(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) )).

fof(d6_bvfunc_1,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 = k7_bvfunc_1(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) = k2_binarith(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) )).

fof(d7_bvfunc_1,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 = k8_bvfunc_1(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,A)
                       => k8_funct_2(A,k6_margrel1,D,E) = k3_binarith(k8_funct_2(A,k6_margrel1,B,E),k8_funct_2(A,k6_margrel1,C,E)) ) ) ) ) ) ) )).

fof(d8_bvfunc_1,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 = k9_bvfunc_1(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,A)
                       => k8_funct_2(A,k6_margrel1,D,E) = k4_binarith(k8_funct_2(A,k6_margrel1,B,E),k8_funct_2(A,k6_margrel1,C,E)) ) ) ) ) ) ) )).

fof(d9_bvfunc_1,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 = k12_bvfunc_1(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_bvfunc_1(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) )).

fof(d10_bvfunc_1,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 = k13_bvfunc_1(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) = k2_bvfunc_1(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) )).

fof(d11_bvfunc_1,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 = k14_bvfunc_1(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,A)
                       => k8_funct_2(A,k6_margrel1,D,E) = k1_binarith(k9_margrel1(k1_funct_1(B,E)),k1_funct_1(C,E)) ) ) ) ) ) ) )).

fof(d12_bvfunc_1,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 = k15_bvfunc_1(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,A)
                       => k8_funct_2(A,k6_margrel1,D,E) = k9_margrel1(k2_binarith(k1_funct_1(B,E),k1_funct_1(C,E))) ) ) ) ) ) ) )).

fof(d13_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( B = k18_bvfunc_1(A)
          <=> ! [C] :
                ( m1_subset_1(C,A)
               => k1_funct_1(B,C) = k7_margrel1 ) ) ) ) )).

fof(d14_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( B = k19_bvfunc_1(A)
          <=> ! [C] :
                ( m1_subset_1(C,A)
               => k1_funct_1(B,C) = k8_margrel1 ) ) ) ) )).

fof(t1_bvfunc_1,axiom,(
    $true )).

fof(t2_bvfunc_1,axiom,(
    $true )).

fof(t3_bvfunc_1,axiom,(
    $true )).

fof(t4_bvfunc_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A) )
     => k3_valuat_1(k3_valuat_1(A)) = A ) )).

fof(t5_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( k5_valuat_1(A,k19_bvfunc_1(A)) = k18_bvfunc_1(A)
            & k5_valuat_1(A,k18_bvfunc_1(A)) = k19_bvfunc_1(A) ) ) ) )).

fof(t6_bvfunc_1,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,B) = B ) ) ) )).

fof(t7_bvfunc_1,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,B,C),D) = k6_valuat_1(A,B,k6_valuat_1(A,C,D)) ) ) ) ) )).

fof(t8_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k6_valuat_1(A,B,k18_bvfunc_1(A)) = k18_bvfunc_1(A) ) ) )).

fof(t9_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k6_valuat_1(A,B,k19_bvfunc_1(A)) = B ) ) )).

fof(t10_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k8_bvfunc_1(A,B,B) = B ) ) )).

fof(t11_bvfunc_1,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,B,C),D) = k8_bvfunc_1(A,B,k8_bvfunc_1(A,C,D)) ) ) ) ) )).

fof(t12_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k8_bvfunc_1(A,B,k18_bvfunc_1(A)) = B ) ) )).

fof(t13_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k8_bvfunc_1(A,B,k19_bvfunc_1(A)) = k19_bvfunc_1(A) ) ) )).

fof(t14_bvfunc_1,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,k6_valuat_1(A,B,C),D) = k6_valuat_1(A,k8_bvfunc_1(A,B,D),k8_bvfunc_1(A,C,D)) ) ) ) ) )).

fof(t15_bvfunc_1,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,k8_bvfunc_1(A,B,C),D) = k8_bvfunc_1(A,k6_valuat_1(A,B,D),k6_valuat_1(A,C,D)) ) ) ) ) )).

fof(t16_bvfunc_1,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,k8_bvfunc_1(A,B,C)) = k6_valuat_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)) ) ) ) )).

fof(t17_bvfunc_1,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,k6_valuat_1(A,B,C)) = k8_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)) ) ) ) )).

fof(d15_bvfunc_1,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))
             => ( r1_bvfunc_1(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,A)
                   => ( k1_funct_1(B,D) = k8_margrel1
                     => k1_funct_1(C,D) = k8_margrel1 ) ) ) ) ) ) )).

fof(t18_bvfunc_1,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,B,C)
                        & r1_bvfunc_1(A,C,B) )
                     => B = C )
                    & ( ( r1_bvfunc_1(A,B,C)
                        & r1_bvfunc_1(A,C,D) )
                     => r1_bvfunc_1(A,B,D) ) ) ) ) ) ) )).

fof(t19_bvfunc_1,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,C) = k19_bvfunc_1(A)
              <=> r1_bvfunc_1(A,B,C) ) ) ) ) )).

fof(t20_bvfunc_1,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,C) = k19_bvfunc_1(A)
              <=> B = C ) ) ) ) )).

fof(t21_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( r1_bvfunc_1(A,k18_bvfunc_1(A),B)
            & r1_bvfunc_1(A,B,k19_bvfunc_1(A)) ) ) ) )).

fof(d16_bvfunc_1,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] :
                      ( m1_subset_1(D,A)
                     => k1_funct_1(B,D) = k8_margrel1 )
                 => ( C = k20_bvfunc_1(A,B)
                  <=> C = k19_bvfunc_1(A) ) )
                & ( ~ ! [D] :
                        ( m1_subset_1(D,A)
                       => k1_funct_1(B,D) = k8_margrel1 )
                 => ( C = k20_bvfunc_1(A,B)
                  <=> C = k18_bvfunc_1(A) ) ) ) ) ) ) )).

fof(d17_bvfunc_1,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] :
                      ( m1_subset_1(D,A)
                     => k1_funct_1(B,D) = k7_margrel1 )
                 => ( C = k21_bvfunc_1(A,B)
                  <=> C = k18_bvfunc_1(A) ) )
                & ( ~ ! [D] :
                        ( m1_subset_1(D,A)
                       => k1_funct_1(B,D) = k7_margrel1 )
                 => ( C = k21_bvfunc_1(A,B)
                  <=> C = k19_bvfunc_1(A) ) ) ) ) ) ) )).

fof(t22_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( k5_valuat_1(A,k20_bvfunc_1(A,B)) = k21_bvfunc_1(A,k5_valuat_1(A,B))
            & k5_valuat_1(A,k21_bvfunc_1(A,B)) = k20_bvfunc_1(A,k5_valuat_1(A,B)) ) ) ) )).

fof(t23_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( k20_bvfunc_1(A,k18_bvfunc_1(A)) = k18_bvfunc_1(A)
        & k20_bvfunc_1(A,k19_bvfunc_1(A)) = k19_bvfunc_1(A)
        & k21_bvfunc_1(A,k18_bvfunc_1(A)) = k18_bvfunc_1(A)
        & k21_bvfunc_1(A,k19_bvfunc_1(A)) = k19_bvfunc_1(A) ) ) )).

fof(t24_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v5_seqm_3(B)
            & m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) )
         => ( B = k18_bvfunc_1(A)
            | B = k19_bvfunc_1(A) ) ) ) )).

fof(t25_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v5_seqm_3(B)
            & m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) )
         => ( k20_bvfunc_1(A,B) = B
            & k21_bvfunc_1(A,B) = B ) ) ) )).

fof(t26_bvfunc_1,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))
             => ( k20_bvfunc_1(A,k6_valuat_1(A,B,C)) = k6_valuat_1(A,k20_bvfunc_1(A,B),k20_bvfunc_1(A,C))
                & k21_bvfunc_1(A,k8_bvfunc_1(A,B,C)) = k8_bvfunc_1(A,k21_bvfunc_1(A,B),k21_bvfunc_1(A,C)) ) ) ) ) )).

fof(t27_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( ( v5_seqm_3(C)
                & m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) )
             => ( k20_bvfunc_1(A,k14_bvfunc_1(A,C,B)) = k14_bvfunc_1(A,C,k20_bvfunc_1(A,B))
                & k20_bvfunc_1(A,k14_bvfunc_1(A,B,C)) = k14_bvfunc_1(A,k21_bvfunc_1(A,B),C) ) ) ) ) )).

fof(t28_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( ( v5_seqm_3(C)
                & m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) )
             => ( k20_bvfunc_1(A,k8_bvfunc_1(A,C,B)) = k8_bvfunc_1(A,C,k20_bvfunc_1(A,B))
                & k21_bvfunc_1(A,k6_valuat_1(A,C,B)) = k6_valuat_1(A,C,k21_bvfunc_1(A,B))
                & k21_bvfunc_1(A,k6_valuat_1(A,B,C)) = k6_valuat_1(A,k21_bvfunc_1(A,B),C) ) ) ) ) )).

fof(t29_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,A)
             => r1_xreal_0(k1_funct_1(k20_bvfunc_1(A,B),C),k1_funct_1(B,C)) ) ) ) )).

fof(t30_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,A)
             => r1_xreal_0(k1_funct_1(B,C),k1_funct_1(k21_bvfunc_1(A,B),C)) ) ) ) )).

fof(d18_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ( r2_bvfunc_1(A,B,C)
              <=> ! [D] :
                    ( r2_hidden(D,C)
                   => ! [E,F] :
                        ( ( r2_hidden(E,D)
                          & r2_hidden(F,D) )
                       => k1_funct_1(B,E) = k1_funct_1(B,F) ) ) ) ) ) ) )).

fof(t31_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => r2_bvfunc_1(A,B,k3_pua2mss1(A)) ) ) )).

fof(t32_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v5_seqm_3(B)
            & m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) )
         => r2_bvfunc_1(A,B,k6_partit1(A)) ) ) )).

fof(d19_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( D = k23_bvfunc_1(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,A)
                       => ( ( ! [F] :
                                ( m1_subset_1(F,A)
                               => ( r2_hidden(F,k22_bvfunc_1(A,E,C))
                                 => k1_funct_1(B,F) = k8_margrel1 ) )
                           => k1_funct_1(D,E) = k8_margrel1 )
                          & ( ? [F] :
                                ( m1_subset_1(F,A)
                                & r2_hidden(F,k22_bvfunc_1(A,E,C))
                                & k1_funct_1(B,F) != k8_margrel1 )
                           => k1_funct_1(D,E) = k7_margrel1 ) ) ) ) ) ) ) ) )).

fof(d20_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( D = k24_bvfunc_1(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,A)
                       => ( ( ? [F] :
                                ( m1_subset_1(F,A)
                                & r2_hidden(F,k22_bvfunc_1(A,E,C))
                                & k1_funct_1(B,F) = k8_margrel1 )
                           => k1_funct_1(D,E) = k8_margrel1 )
                          & ( ! [F] :
                                ( m1_subset_1(F,A)
                               => ~ ( r2_hidden(F,k22_bvfunc_1(A,E,C))
                                    & k1_funct_1(B,F) = k8_margrel1 ) )
                           => k1_funct_1(D,E) = k7_margrel1 ) ) ) ) ) ) ) ) )).

fof(t33_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => r2_bvfunc_1(A,k23_bvfunc_1(A,B,C),C) ) ) ) )).

fof(t34_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => r2_bvfunc_1(A,k24_bvfunc_1(A,B,C),C) ) ) ) )).

fof(t35_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => r1_bvfunc_1(A,k23_bvfunc_1(A,B,C),B) ) ) ) )).

fof(t36_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => r1_bvfunc_1(A,B,k24_bvfunc_1(A,B,C)) ) ) ) )).

fof(t37_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => k5_valuat_1(A,k23_bvfunc_1(A,B,C)) = k24_bvfunc_1(A,k5_valuat_1(A,B),C) ) ) ) )).

fof(t38_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k23_bvfunc_1(A,B,k6_partit1(A)) = k20_bvfunc_1(A,B) ) ) )).

fof(t39_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k24_bvfunc_1(A,B,k6_partit1(A)) = k21_bvfunc_1(A,B) ) ) )).

fof(t40_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k23_bvfunc_1(A,B,k3_pua2mss1(A)) = B ) ) )).

fof(t41_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k24_bvfunc_1(A,B,k3_pua2mss1(A)) = B ) ) )).

fof(t42_bvfunc_1,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] :
                  ( m1_eqrel_1(D,A)
                 => k23_bvfunc_1(A,k6_valuat_1(A,B,C),D) = k6_valuat_1(A,k23_bvfunc_1(A,B,D),k23_bvfunc_1(A,C,D)) ) ) ) ) )).

fof(t43_bvfunc_1,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] :
                  ( m1_eqrel_1(D,A)
                 => k24_bvfunc_1(A,k8_bvfunc_1(A,B,C),D) = k8_bvfunc_1(A,k24_bvfunc_1(A,B,D),k24_bvfunc_1(A,C,D)) ) ) ) ) )).

fof(t44_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => r2_bvfunc_1(A,B,k25_bvfunc_1(A,B)) ) ) )).

fof(t45_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ( r2_bvfunc_1(A,B,C)
               => r1_setfam_1(C,k25_bvfunc_1(A,B)) ) ) ) ) )).

fof(s1_bvfunc_1,axiom,(
    ! [A] :
      ( m2_fraenkel(A,f1_s1_bvfunc_1,k6_margrel1,k1_fraenkel(f1_s1_bvfunc_1,k6_margrel1))
     => ! [B] :
          ( m2_fraenkel(B,f1_s1_bvfunc_1,k6_margrel1,k1_fraenkel(f1_s1_bvfunc_1,k6_margrel1))
         => ( ( ! [C] :
                  ( m1_subset_1(C,f1_s1_bvfunc_1)
                 => k1_funct_1(A,C) = f4_s1_bvfunc_1(C,f2_s1_bvfunc_1,f3_s1_bvfunc_1) )
              & ! [C] :
                  ( m1_subset_1(C,f1_s1_bvfunc_1)
                 => k1_funct_1(B,C) = f4_s1_bvfunc_1(C,f2_s1_bvfunc_1,f3_s1_bvfunc_1) ) )
           => A = B ) ) ) )).

fof(s2_bvfunc_1,axiom,(
    ! [A] :
      ( m2_fraenkel(A,f1_s2_bvfunc_1,k6_margrel1,k1_fraenkel(f1_s2_bvfunc_1,k6_margrel1))
     => ! [B] :
          ( m2_fraenkel(B,f1_s2_bvfunc_1,k6_margrel1,k1_fraenkel(f1_s2_bvfunc_1,k6_margrel1))
         => ( ( ! [C] :
                  ( m1_subset_1(C,f1_s2_bvfunc_1)
                 => k1_funct_1(A,C) = f2_s2_bvfunc_1(C) )
              & ! [C] :
                  ( m1_subset_1(C,f1_s2_bvfunc_1)
                 => k1_funct_1(B,C) = f2_s2_bvfunc_1(C) ) )
           => A = B ) ) ) )).

fof(dt_m1_bvfunc_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A) )
     => ! [C] :
          ( m1_bvfunc_1(C,A,B)
         => m1_subset_1(C,k1_zfmisc_1(A)) ) ) )).

fof(existence_m1_bvfunc_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A) )
     => ? [C] : m1_bvfunc_1(C,A,B) ) )).

fof(redefinition_m1_bvfunc_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A) )
     => ! [C] :
          ( m1_bvfunc_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) )).

fof(reflexivity_r1_bvfunc_1,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)) )
     => r1_bvfunc_1(A,B,B) ) )).

fof(dt_k1_bvfunc_1,axiom,(
    $true )).

fof(dt_k2_bvfunc_1,axiom,(
    $true )).

fof(commutativity_k2_bvfunc_1,axiom,(
    ! [A,B] :
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k2_bvfunc_1(A,B) = k2_bvfunc_1(B,A) ) )).

fof(dt_k3_bvfunc_1,axiom,(
    $true )).

fof(dt_k4_bvfunc_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_bvfunc_1(A)) )
     => m1_subset_1(k4_bvfunc_1(A,B),k3_bvfunc_1(A)) ) )).

fof(redefinition_k4_bvfunc_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_bvfunc_1(A)) )
     => k4_bvfunc_1(A,B) = k3_valuat_1(B) ) )).

fof(dt_k5_bvfunc_1,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_bvfunc_1(A,B,C),k3_bvfunc_1(A)) ) )).

fof(commutativity_k5_bvfunc_1,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_bvfunc_1(A,B,C) = k5_bvfunc_1(A,C,B) ) )).

fof(redefinition_k5_bvfunc_1,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_bvfunc_1(A,B,C) = k4_valuat_1(B,C) ) )).

fof(dt_k6_bvfunc_1,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(k6_bvfunc_1(A,B))
        & v1_funct_1(k6_bvfunc_1(A,B)) ) ) )).

fof(commutativity_k6_bvfunc_1,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) )
     => k6_bvfunc_1(A,B) = k6_bvfunc_1(B,A) ) )).

fof(dt_k7_bvfunc_1,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(k7_bvfunc_1(A,B))
        & v1_funct_1(k7_bvfunc_1(A,B)) ) ) )).

fof(commutativity_k7_bvfunc_1,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) )
     => k7_bvfunc_1(A,B) = k7_bvfunc_1(B,A) ) )).

fof(dt_k8_bvfunc_1,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(k8_bvfunc_1(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) )).

fof(commutativity_k8_bvfunc_1,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)) )
     => k8_bvfunc_1(A,B,C) = k8_bvfunc_1(A,C,B) ) )).

fof(redefinition_k8_bvfunc_1,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)) )
     => k8_bvfunc_1(A,B,C) = k6_bvfunc_1(B,C) ) )).

fof(dt_k9_bvfunc_1,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(k9_bvfunc_1(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) )).

fof(commutativity_k9_bvfunc_1,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)) )
     => k9_bvfunc_1(A,B,C) = k9_bvfunc_1(A,C,B) ) )).

fof(redefinition_k9_bvfunc_1,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)) )
     => k9_bvfunc_1(A,B,C) = k7_bvfunc_1(B,C) ) )).

fof(dt_k10_bvfunc_1,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(k10_bvfunc_1(A,B,C),k3_bvfunc_1(A)) ) )).

fof(commutativity_k10_bvfunc_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_bvfunc_1(A))
        & m1_subset_1(C,k3_bvfunc_1(A)) )
     => k10_bvfunc_1(A,B,C) = k10_bvfunc_1(A,C,B) ) )).

fof(redefinition_k10_bvfunc_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_bvfunc_1(A))
        & m1_subset_1(C,k3_bvfunc_1(A)) )
     => k10_bvfunc_1(A,B,C) = k6_bvfunc_1(B,C) ) )).

fof(dt_k11_bvfunc_1,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(k11_bvfunc_1(A,B,C),k3_bvfunc_1(A)) ) )).

fof(commutativity_k11_bvfunc_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_bvfunc_1(A))
        & m1_subset_1(C,k3_bvfunc_1(A)) )
     => k11_bvfunc_1(A,B,C) = k11_bvfunc_1(A,C,B) ) )).

fof(redefinition_k11_bvfunc_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_bvfunc_1(A))
        & m1_subset_1(C,k3_bvfunc_1(A)) )
     => k11_bvfunc_1(A,B,C) = k7_bvfunc_1(B,C) ) )).

fof(dt_k12_bvfunc_1,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(k12_bvfunc_1(A,B))
        & v1_funct_1(k12_bvfunc_1(A,B)) ) ) )).

fof(dt_k13_bvfunc_1,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(k13_bvfunc_1(A,B))
        & v1_funct_1(k13_bvfunc_1(A,B)) ) ) )).

fof(commutativity_k13_bvfunc_1,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) )
     => k13_bvfunc_1(A,B) = k13_bvfunc_1(B,A) ) )).

fof(dt_k14_bvfunc_1,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(k14_bvfunc_1(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) )).

fof(redefinition_k14_bvfunc_1,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)) )
     => k14_bvfunc_1(A,B,C) = k12_bvfunc_1(B,C) ) )).

fof(dt_k15_bvfunc_1,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(k15_bvfunc_1(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) )).

fof(commutativity_k15_bvfunc_1,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)) )
     => k15_bvfunc_1(A,B,C) = k15_bvfunc_1(A,C,B) ) )).

fof(redefinition_k15_bvfunc_1,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)) )
     => k15_bvfunc_1(A,B,C) = k13_bvfunc_1(B,C) ) )).

fof(dt_k16_bvfunc_1,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(k16_bvfunc_1(A,B,C),k3_bvfunc_1(A)) ) )).

fof(redefinition_k16_bvfunc_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_bvfunc_1(A))
        & m1_subset_1(C,k3_bvfunc_1(A)) )
     => k16_bvfunc_1(A,B,C) = k12_bvfunc_1(B,C) ) )).

fof(dt_k17_bvfunc_1,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(k17_bvfunc_1(A,B,C),k3_bvfunc_1(A)) ) )).

fof(commutativity_k17_bvfunc_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_bvfunc_1(A))
        & m1_subset_1(C,k3_bvfunc_1(A)) )
     => k17_bvfunc_1(A,B,C) = k17_bvfunc_1(A,C,B) ) )).

fof(redefinition_k17_bvfunc_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_bvfunc_1(A))
        & m1_subset_1(C,k3_bvfunc_1(A)) )
     => k17_bvfunc_1(A,B,C) = k13_bvfunc_1(B,C) ) )).

fof(dt_k18_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => m2_fraenkel(k18_bvfunc_1(A),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) )).

fof(dt_k19_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => m2_fraenkel(k19_bvfunc_1(A),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) )).

fof(dt_k20_bvfunc_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1)) )
     => m2_fraenkel(k20_bvfunc_1(A,B),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) )).

fof(dt_k21_bvfunc_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1)) )
     => m2_fraenkel(k21_bvfunc_1(A,B),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) )).

fof(dt_k22_bvfunc_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_eqrel_1(C,A) )
     => m1_bvfunc_1(k22_bvfunc_1(A,B,C),A,C) ) )).

fof(redefinition_k22_bvfunc_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_eqrel_1(C,A) )
     => k22_bvfunc_1(A,B,C) = k1_t_1topsp(A,B,C) ) )).

fof(dt_k23_bvfunc_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_eqrel_1(C,A) )
     => m2_fraenkel(k23_bvfunc_1(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) )).

fof(dt_k24_bvfunc_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_eqrel_1(C,A) )
     => m2_fraenkel(k24_bvfunc_1(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) )).

fof(dt_k25_bvfunc_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1)) )
     => m1_eqrel_1(k25_bvfunc_1(A,B),A) ) )).

fof(d21_bvfunc_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k25_bvfunc_1(A,B) = k4_xboole_0(k2_tarski(a_2_0_bvfunc_1(A,B),a_2_1_bvfunc_1(A,B)),k1_tarski(k1_xboole_0)) ) ) )).

fof(fraenkel_a_2_0_bvfunc_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & m2_fraenkel(C,B,k6_margrel1,k1_fraenkel(B,k6_margrel1)) )
     => ( r2_hidden(A,a_2_0_bvfunc_1(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,B)
            & A = D
            & k8_funct_2(B,k6_margrel1,C,D) = k8_margrel1 ) ) ) )).

fof(fraenkel_a_2_1_bvfunc_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & m2_fraenkel(C,B,k6_margrel1,k1_fraenkel(B,k6_margrel1)) )
     => ( r2_hidden(A,a_2_1_bvfunc_1(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,B)
            & A = D
            & k8_funct_2(B,k6_margrel1,C,D) = k7_margrel1 ) ) ) )).
%------------------------------------------------------------------------------