% Mizar problem: t46_binari_5,binari_5,1561,57 
fof(t46_binari_5,conjecture,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ! [C] : 
              ( v2_margrel1(C)
             => k1_bvfunc_1(k1_bvfunc_1(A,k1_bvfunc_1(B,C)),k1_bvfunc_1(B,k1_bvfunc_1(A,C))) = k8_margrel1 ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_bvfunc_1,cc1_margrel1,commutativity_k10_margrel1,commutativity_k1_binarith,d1_bvfunc_1,dt_k10_margrel1,dt_k1_binarith,dt_k1_bvfunc_1,dt_k6_margrel1,dt_k7_margrel1,dt_k8_margrel1,dt_k9_margrel1,dt_m1_subset_1,existence_m1_subset_1,fc1_binarith,fc1_bvfunc_1,fc3_margrel1,fc4_margrel1,fc5_margrel1,involutiveness_k9_margrel1,rc2_margrel1,t10_binarith,t19_binarith,t1_subset,t20_binarith,t23_binarith,t2_subset,t39_margrel1,t40_margrel1,t41_margrel1,t50_margrel1,t52_margrel1]),
    [file(binari_5,t46_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_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(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_binarith,axiom,(
    $true ),
    file(binarith,k1_binarith),
    []).

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

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

fof(dt_k7_margrel1,axiom,(
    m1_subset_1(k7_margrel1,k6_margrel1) ),
    file(margrel1,k7_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(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(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(t19_binarith,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => k1_binarith(A,k8_margrel1) = k8_margrel1 ) ),
    file(binarith,t19_binarith),
    []).

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

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

fof(t39_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( A = k7_margrel1
        | A = k8_margrel1 ) ) ),
    file(margrel1,t39_margrel1),
    []).

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

fof(t41_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( ( A = k7_margrel1
         => k9_margrel1(A) = k8_margrel1 )
        & ( k9_margrel1(A) = k8_margrel1
         => A = k7_margrel1 )
        & ( A = k8_margrel1
         => k9_margrel1(A) = k7_margrel1 )
        & ( k9_margrel1(A) = k7_margrel1
         => A = k8_margrel1 ) ) ) ),
    file(margrel1,t41_margrel1),
    []).

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

fof(t52_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ! [C] : 
              ( v2_margrel1(C)
             => k10_margrel1(A,k10_margrel1(B,C)) = k10_margrel1(k10_margrel1(A,B),C) ) ) ) ),
    file(margrel1,t52_margrel1),
    []).