% Mizar problem: t27_binari_5,binari_5,369,61 
fof(t27_binari_5,conjecture,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ! [C] : 
              ( v2_margrel1(C)
             => ( ( k2_bvfunc_1(A,B) = k8_margrel1
                  & k2_bvfunc_1(B,C) = k8_margrel1 )
               => k2_bvfunc_1(A,C) = k8_margrel1 ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_bvfunc_1,cc1_margrel1,commutativity_k2_bvfunc_1,dt_k1_bvfunc_1,dt_k2_bvfunc_1,dt_k6_margrel1,dt_k8_margrel1,dt_m1_subset_1,existence_m1_subset_1,fc1_bvfunc_1,fc2_bvfunc_1,fc3_margrel1,rc2_margrel1,t1_subset,t24_binari_5,t26_binari_5,t2_subset]),
    [file(binari_5,t27_binari_5)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

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(cc1_margrel1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => v2_margrel1(A) ) ),
    file(margrel1,cc1_margrel1),
    []).

fof(commutativity_k2_bvfunc_1,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k2_bvfunc_1(A,B) = k2_bvfunc_1(B,A) ) ),
    file(bvfunc_1,k2_bvfunc_1),
    []).

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

fof(dt_k2_bvfunc_1,axiom,(
    $true ),
    file(bvfunc_1,k2_bvfunc_1),
    []).

fof(dt_k6_margrel1,axiom,(
    $true ),
    file(margrel1,k6_margrel1),
    []).

fof(dt_k8_margrel1,axiom,(
    m1_subset_1(k8_margrel1,k6_margrel1) ),
    file(margrel1,k8_margrel1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

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(fc2_bvfunc_1,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k2_bvfunc_1(A,B)) ) ),
    file(bvfunc_1,fc2_bvfunc_1),
    []).

fof(fc3_margrel1,axiom,(
    ~ v1_xboole_0(k6_margrel1) ),
    file(margrel1,fc3_margrel1),
    []).

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

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t24_binari_5,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ( k2_bvfunc_1(A,B) = k8_margrel1
          <=> ( k1_bvfunc_1(A,B) = k8_margrel1
              & k1_bvfunc_1(B,A) = k8_margrel1 ) ) ) ) ),
    file(binari_5,t24_binari_5),
    []).

fof(t26_binari_5,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ! [C] : 
              ( v2_margrel1(C)
             => ( ( k1_bvfunc_1(A,B) = k8_margrel1
                  & k1_bvfunc_1(B,C) = k8_margrel1 )
               => k1_bvfunc_1(A,C) = k8_margrel1 ) ) ) ) ),
    file(binari_5,t26_binari_5),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).