% Mizar problem: t35_binarith,binarith,463,37 
fof(t35_binarith,conjecture,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k2_binarith(A,k10_margrel1(k9_margrel1(A),B)) = k1_binarith(A,B) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k10_margrel1,commutativity_k1_binarith,commutativity_k2_binarith,d1_binarith,d2_binarith,dt_k10_margrel1,dt_k1_binarith,dt_k2_binarith,dt_k9_margrel1,fc1_binarith,fc2_binarith,fc4_margrel1,fc5_margrel1,involutiveness_k9_margrel1,rc2_margrel1,t16_binarith,t25_binarith,t26_binarith,t40_margrel1,t52_margrel1,t9_binarith]),
    [file(binarith,t35_binarith)]).

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(d1_binarith,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k1_binarith(A,B) = k9_margrel1(k10_margrel1(k9_margrel1(A),k9_margrel1(B))) ) ) ),
    file(binarith,d1_binarith),
    []).

fof(d2_binarith,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k2_binarith(A,B) = k1_binarith(k10_margrel1(k9_margrel1(A),B),k10_margrel1(A,k9_margrel1(B))) ) ) ),
    file(binarith,d2_binarith),
    []).

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_k9_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => v2_margrel1(k9_margrel1(A)) ) ),
    file(margrel1,k9_margrel1),
    []).

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

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

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(t16_binarith,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => k10_margrel1(A,A) = A ) ),
    file(binarith,t16_binarith),
    []).

fof(t25_binarith,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k10_margrel1(A,k1_binarith(A,B)) = A ) ) ),
    file(binarith,t25_binarith),
    []).

fof(t26_binarith,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k1_binarith(A,k10_margrel1(k9_margrel1(A),B)) = k1_binarith(A,B) ) ) ),
    file(binarith,t26_binarith),
    []).

fof(t40_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k9_margrel1(A)) = A ) ),
    file(margrel1,t40_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),
    []).

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),
    []).