% Mizar problem: t59_binari_6,binari_6,582,29 
fof(t59_binari_6,conjecture,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k3_binari_5(A,k2_bvfunc_1(A,B)) = k10_margrel1(k9_margrel1(A),B) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_bvfunc_1,cc1_margrel1,commutativity_k10_margrel1,commutativity_k1_binarith,commutativity_k2_binarith,commutativity_k2_bvfunc_1,commutativity_k2_tarski,commutativity_k3_binari_5,d12_margrel1,d14_margrel1,d2_binari_5,d2_bvfunc_1,dt_k10_margrel1,dt_k1_binarith,dt_k2_binarith,dt_k2_bvfunc_1,dt_k2_tarski,dt_k3_binari_5,dt_k6_margrel1,dt_k8_margrel1,dt_k9_margrel1,dt_m1_subset_1,existence_m1_subset_1,fc1_binarith,fc2_binari_5,fc2_binarith,fc2_bvfunc_1,fc3_margrel1,fc4_margrel1,fc5_margrel1,involutiveness_k9_margrel1,rc2_margrel1,t10_binarith,t18_binarith,t19_binarith,t20_binarith,t21_binarith,t40_margrel1,t50_margrel1,t52_binari_6]),
    [file(binari_6,t59_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(cc1_margrel1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => v2_margrel1(A) ) ),
    file(margrel1,cc1_margrel1),
    []).

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

fof(commutativity_k2_binarith,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k2_binarith(A,B) = k2_binarith(B,A) ) ),
    file(binarith,k2_binarith),
    []).

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(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k3_binari_5,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k3_binari_5(A,B) = k3_binari_5(B,A) ) ),
    file(binari_5,k3_binari_5),
    []).

fof(d12_margrel1,axiom,(
    k6_margrel1 = k2_tarski(0,1) ),
    file(margrel1,d12_margrel1),
    []).

fof(d14_margrel1,axiom,(
    k8_margrel1 = 1 ),
    file(margrel1,d14_margrel1),
    []).

fof(d2_binari_5,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k3_binari_5(A,B) = k9_margrel1(k1_binarith(A,B)) ) ) ),
    file(binari_5,d2_binari_5),
    []).

fof(d2_bvfunc_1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k2_bvfunc_1(A,B) = k9_margrel1(k2_binarith(A,B)) ) ) ),
    file(bvfunc_1,d2_bvfunc_1),
    []).

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

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

fof(dt_k2_binarith,axiom,(
    $true ),
    file(binarith,k2_binarith),
    []).

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

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k3_binari_5,axiom,(
    $true ),
    file(binari_5,k3_binari_5),
    []).

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_k9_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => v2_margrel1(k9_margrel1(A)) ) ),
    file(margrel1,k9_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_binarith,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k1_binarith(A,B)) ) ),
    file(binarith,fc1_binarith),
    []).

fof(fc2_binari_5,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => ( v4_ordinal2(k3_binari_5(A,B))
        & v1_xcmplx_0(k3_binari_5(A,B))
        & v2_margrel1(k3_binari_5(A,B))
        & v1_xreal_0(k3_binari_5(A,B)) ) ) ),
    file(binari_5,fc2_binari_5),
    []).

fof(fc2_binarith,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k2_binarith(A,B)) ) ),
    file(binarith,fc2_binarith),
    []).

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(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(t10_binarith,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k9_margrel1(k1_binarith(A,B)) = k10_margrel1(k9_margrel1(A),k9_margrel1(B)) ) ) ),
    file(binarith,t10_binarith),
    []).

fof(t18_binarith,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => k1_binarith(A,k9_margrel1(A)) = k8_margrel1 ) ),
    file(binarith,t18_binarith),
    []).

fof(t19_binarith,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => k1_binarith(A,k8_margrel1) = k8_margrel1 ) ),
    file(binarith,t19_binarith),
    []).

fof(t20_binarith,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ! [C] : 
              ( v2_margrel1(C)
             => k1_binarith(k1_binarith(A,B),C) = k1_binarith(A,k1_binarith(B,C)) ) ) ) ),
    file(binarith,t20_binarith),
    []).

fof(t21_binarith,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => k1_binarith(A,A) = A ) ),
    file(binarith,t21_binarith),
    []).

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

fof(t50_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => k10_margrel1(k8_margrel1,A) = A ) ),
    file(margrel1,t50_margrel1),
    []).

fof(t52_binari_6,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ! [C] : 
              ( v2_margrel1(C)
             => k3_binari_5(A,k2_bvfunc_1(B,C)) = k9_margrel1(k10_margrel1(k1_binarith(k1_binarith(A,k9_margrel1(B)),C),k1_binarith(k1_binarith(A,k9_margrel1(C)),B))) ) ) ) ),
    file(binari_6,t52_binari_6),
    []).