% Mizar problem: t43_binari_6,binari_6,410,52 
fof(t43_binari_6,conjecture,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ! [C] : 
              ( v2_margrel1(C)
             => ( k1_binari_5(A,k1_binari_5(B,C)) = k10_margrel1(k1_binarith(k9_margrel1(A),B),k1_binarith(k9_margrel1(A),C))
                & k1_binari_5(A,k1_binari_5(B,C)) = k10_margrel1(k1_bvfunc_1(A,B),k1_bvfunc_1(A,C)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_bvfunc_1,commutativity_k10_margrel1,commutativity_k1_binari_5,commutativity_k1_binarith,d1_binari_5,d1_bvfunc_1,dt_k10_margrel1,dt_k1_binari_5,dt_k1_binarith,dt_k1_bvfunc_1,dt_k9_margrel1,fc1_binari_5,fc1_binarith,fc1_bvfunc_1,fc4_margrel1,fc5_margrel1,involutiveness_k9_margrel1,rc2_margrel1,t23_binarith,t40_margrel1,t9_binarith]),
    [file(binari_6,t43_binari_6)]).

fof(cc1_bvfunc_1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(bvfunc_1,cc1_bvfunc_1),
    []).

fof(commutativity_k10_margrel1,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k10_margrel1(A,B) = k10_margrel1(B,A) ) ),
    file(margrel1,k10_margrel1),
    []).

fof(commutativity_k1_binari_5,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k1_binari_5(A,B) = k1_binari_5(B,A) ) ),
    file(binari_5,k1_binari_5),
    []).

fof(commutativity_k1_binarith,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k1_binarith(A,B) = k1_binarith(B,A) ) ),
    file(binarith,k1_binarith),
    []).

fof(d1_binari_5,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k1_binari_5(A,B) = k9_margrel1(k10_margrel1(A,B)) ) ) ),
    file(binari_5,d1_binari_5),
    []).

fof(d1_bvfunc_1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k1_bvfunc_1(A,B) = k1_binarith(k9_margrel1(A),B) ) ) ),
    file(bvfunc_1,d1_bvfunc_1),
    []).

fof(dt_k10_margrel1,axiom,(
    $true ),
    file(margrel1,k10_margrel1),
    []).

fof(dt_k1_binari_5,axiom,(
    $true ),
    file(binari_5,k1_binari_5),
    []).

fof(dt_k1_binarith,axiom,(
    $true ),
    file(binarith,k1_binarith),
    []).

fof(dt_k1_bvfunc_1,axiom,(
    $true ),
    file(bvfunc_1,k1_bvfunc_1),
    []).

fof(dt_k9_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => v2_margrel1(k9_margrel1(A)) ) ),
    file(margrel1,k9_margrel1),
    []).

fof(fc1_binari_5,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => ( v4_ordinal2(k1_binari_5(A,B))
        & v1_xcmplx_0(k1_binari_5(A,B))
        & v2_margrel1(k1_binari_5(A,B))
        & v1_xreal_0(k1_binari_5(A,B)) ) ) ),
    file(binari_5,fc1_binari_5),
    []).

fof(fc1_binarith,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k1_binarith(A,B)) ) ),
    file(binarith,fc1_binarith),
    []).

fof(fc1_bvfunc_1,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k1_bvfunc_1(A,B)) ) ),
    file(bvfunc_1,fc1_bvfunc_1),
    []).

fof(fc4_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => v2_margrel1(k9_margrel1(A)) ) ),
    file(margrel1,fc4_margrel1),
    []).

fof(fc5_margrel1,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k10_margrel1(A,B)) ) ),
    file(margrel1,fc5_margrel1),
    []).

fof(involutiveness_k9_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k9_margrel1(A)) = A ) ),
    file(margrel1,k9_margrel1),
    []).

fof(rc2_margrel1,axiom,(
    ? [A] : v2_margrel1(A) ),
    file(margrel1,rc2_margrel1),
    []).

fof(t23_binarith,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ! [C] : 
              ( v2_margrel1(C)
             => k1_binarith(A,k10_margrel1(B,C)) = k10_margrel1(k1_binarith(A,B),k1_binarith(A,C)) ) ) ) ),
    file(binarith,t23_binarith),
    []).

fof(t40_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k9_margrel1(A)) = A ) ),
    file(margrel1,t40_margrel1),
    []).

fof(t9_binarith,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k9_margrel1(k10_margrel1(A,B)) = k1_binarith(k9_margrel1(A),k9_margrel1(B)) ) ) ),
    file(binarith,t9_binarith),
    []).