% Mizar ND problem: t8_binari_6,binari_6,75,23 
fof(dh_c1_8__binari_6,definition,
    ( ( v2_margrel1(c1_8__binari_6)
     => k2_bvfunc_1(k7_margrel1,c1_8__binari_6) = k9_margrel1(c1_8__binari_6) )
   => ! [A] : 
        ( v2_margrel1(A)
       => k2_bvfunc_1(k7_margrel1,A) = k9_margrel1(A) ) ),
    introduced(definition,[new_symbol(c1_8__binari_6),file(binari_6,c1_8__binari_6)]),
    [interesting(0.8),axiom,file(binari_6,c1_8__binari_6)]).

fof(commutativity_k2_tarski,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(commutativity_k2_binarith,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k2_binarith(A,B) = k2_binarith(B,A) ) ),
    file(binarith,k2_binarith),
    [interesting(0.9),axiom,file(binarith,k2_binarith)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_k2_binarith,axiom,(
    $true ),
    file(binarith,k2_binarith),
    [interesting(0.9),axiom,file(binarith,k2_binarith)]).

fof(dt_k6_margrel1,axiom,(
    $true ),
    file(margrel1,k6_margrel1),
    [interesting(0.9),axiom,file(margrel1,k6_margrel1)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(cc1_bvfunc_1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(bvfunc_1,cc1_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,cc1_bvfunc_1)]).

fof(cc1_margrel1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => v2_margrel1(A) ) ),
    file(margrel1,cc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,cc1_margrel1)]).

fof(fc2_binarith,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k2_binarith(A,B)) ) ),
    file(binarith,fc2_binarith),
    [interesting(0.9),axiom,file(binarith,fc2_binarith)]).

fof(fc2_bvfunc_1,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k2_bvfunc_1(A,B)) ) ),
    file(bvfunc_1,fc2_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,fc2_bvfunc_1)]).

fof(fc3_margrel1,theorem,(
    ~ v1_xboole_0(k6_margrel1) ),
    file(margrel1,fc3_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc3_margrel1)]).

fof(fc4_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => v2_margrel1(k9_margrel1(A)) ) ),
    file(margrel1,fc4_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc4_margrel1)]).

fof(rc2_margrel1,theorem,(
    ? [A] : v2_margrel1(A) ),
    file(margrel1,rc2_margrel1),
    [interesting(0.9),axiom,file(margrel1,rc2_margrel1)]).

fof(d12_margrel1,definition,(
    k6_margrel1 = k2_tarski(0,1) ),
    file(margrel1,d12_margrel1),
    [interesting(0.9),axiom,file(margrel1,d12_margrel1)]).

fof(commutativity_k2_bvfunc_1,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k2_bvfunc_1(A,B) = k2_bvfunc_1(B,A) ) ),
    file(bvfunc_1,k2_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k2_bvfunc_1)]).

fof(involutiveness_k9_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k9_margrel1(A)) = A ) ),
    file(margrel1,k9_margrel1),
    [interesting(0.9),axiom,file(margrel1,k9_margrel1)]).

fof(dt_k2_bvfunc_1,axiom,(
    $true ),
    file(bvfunc_1,k2_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k2_bvfunc_1)]).

fof(dt_k7_margrel1,axiom,(
    m1_subset_1(k7_margrel1,k6_margrel1) ),
    file(margrel1,k7_margrel1),
    [interesting(0.9),axiom,file(margrel1,k7_margrel1)]).

fof(dt_k9_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => v2_margrel1(k9_margrel1(A)) ) ),
    file(margrel1,k9_margrel1),
    [interesting(0.9),axiom,file(margrel1,k9_margrel1)]).

fof(dt_c1_8__binari_6,assumption,(
    v2_margrel1(c1_8__binari_6) ),
    introduced(assumption,[file(binari_6,c1_8__binari_6)]),
    [interesting(0.8),axiom,file(binari_6,c1_8__binari_6)]).

fof(d2_bvfunc_1,definition,(
    ! [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),
    [interesting(0.9),axiom,file(bvfunc_1,d2_bvfunc_1)]).

fof(d13_margrel1,definition,(
    k7_margrel1 = 0 ),
    file(margrel1,d13_margrel1),
    [interesting(0.9),axiom,file(margrel1,d13_margrel1)]).

fof(commutativity_k1_binarith,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k1_binarith(A,B) = k1_binarith(B,A) ) ),
    file(binarith,k1_binarith),
    [interesting(0.9),axiom,file(binarith,k1_binarith)]).

fof(dt_k1_binarith,axiom,(
    $true ),
    file(binarith,k1_binarith),
    [interesting(0.9),axiom,file(binarith,k1_binarith)]).

fof(fc1_binarith,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k1_binarith(A,B)) ) ),
    file(binarith,fc1_binarith),
    [interesting(0.9),axiom,file(binarith,fc1_binarith)]).

fof(commutativity_k10_margrel1,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k10_margrel1(A,B) = k10_margrel1(B,A) ) ),
    file(margrel1,k10_margrel1),
    [interesting(0.9),axiom,file(margrel1,k10_margrel1)]).

fof(dt_k10_margrel1,axiom,(
    $true ),
    file(margrel1,k10_margrel1),
    [interesting(0.9),axiom,file(margrel1,k10_margrel1)]).

fof(dt_k1_bvfunc_1,axiom,(
    $true ),
    file(bvfunc_1,k1_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k1_bvfunc_1)]).

fof(fc1_bvfunc_1,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k1_bvfunc_1(A,B)) ) ),
    file(bvfunc_1,fc1_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,fc1_bvfunc_1)]).

fof(fc5_margrel1,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k10_margrel1(A,B)) ) ),
    file(margrel1,fc5_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc5_margrel1)]).

fof(d1_bvfunc_1,definition,(
    ! [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),
    [interesting(0.9),axiom,file(bvfunc_1,d1_bvfunc_1)]).

fof(t23_binari_5,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k2_bvfunc_1(A,B) = k10_margrel1(k1_bvfunc_1(A,B),k1_bvfunc_1(B,A)) ) ) ),
    file(binari_5,t23_binari_5),
    [interesting(0.9),axiom,file(binari_5,t23_binari_5)]).

fof(e1_8_1__binari_6,plain,(
    k2_bvfunc_1(k7_margrel1,c1_8__binari_6) = k10_margrel1(k1_bvfunc_1(k7_margrel1,c1_8__binari_6),k1_bvfunc_1(c1_8__binari_6,k7_margrel1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__binari_6])],[commutativity_k2_tarski,dt_k2_tarski,commutativity_k1_binarith,commutativity_k2_binarith,involutiveness_k9_margrel1,existence_m1_subset_1,dt_k1_binarith,dt_k2_binarith,dt_k6_margrel1,dt_k9_margrel1,dt_m1_subset_1,cc1_margrel1,fc1_binarith,fc2_binarith,fc3_margrel1,fc4_margrel1,d12_margrel1,commutativity_k10_margrel1,commutativity_k2_bvfunc_1,dt_k10_margrel1,dt_k1_bvfunc_1,dt_k2_bvfunc_1,dt_k7_margrel1,dt_c1_8__binari_6,cc1_bvfunc_1,fc1_bvfunc_1,fc2_bvfunc_1,fc5_margrel1,rc2_margrel1,d1_bvfunc_1,d2_bvfunc_1,d13_margrel1,t23_binari_5]),
    [interesting(0.65),file(binari_6,e1_8_1__binari_6),[file(binari_6,e1_8_1__binari_6)]]).

fof(dt_k8_margrel1,axiom,(
    m1_subset_1(k8_margrel1,k6_margrel1) ),
    file(margrel1,k8_margrel1),
    [interesting(0.9),axiom,file(margrel1,k8_margrel1)]).

fof(d14_margrel1,definition,(
    k8_margrel1 = 1 ),
    file(margrel1,d14_margrel1),
    [interesting(0.9),axiom,file(margrel1,d14_margrel1)]).

fof(t2_binari_6,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k1_bvfunc_1(k7_margrel1,A) = k8_margrel1 ) ),
    file(binari_6,t2_binari_6),
    [interesting(0.9),axiom,file(binari_6,t2_binari_6)]).

fof(e2_8_1__binari_6,plain,(
    k10_margrel1(k1_bvfunc_1(k7_margrel1,c1_8__binari_6),k1_bvfunc_1(c1_8__binari_6,k7_margrel1)) = k10_margrel1(k8_margrel1,k1_bvfunc_1(c1_8__binari_6,k7_margrel1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__binari_6])],[commutativity_k2_tarski,dt_k2_tarski,commutativity_k1_binarith,involutiveness_k9_margrel1,existence_m1_subset_1,dt_k1_binarith,dt_k6_margrel1,dt_k9_margrel1,dt_m1_subset_1,cc1_margrel1,fc1_binarith,fc3_margrel1,fc4_margrel1,d12_margrel1,commutativity_k10_margrel1,dt_k10_margrel1,dt_k1_bvfunc_1,dt_k7_margrel1,dt_k8_margrel1,dt_c1_8__binari_6,cc1_bvfunc_1,fc1_bvfunc_1,fc5_margrel1,rc2_margrel1,d1_bvfunc_1,d13_margrel1,d14_margrel1,t2_binari_6]),
    [interesting(0.65),file(binari_6,e2_8_1__binari_6),[file(binari_6,e2_8_1__binari_6)]]).

fof(t7_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k1_binarith(A,k7_margrel1) = A ) ),
    file(binarith,t7_binarith),
    [interesting(0.9),axiom,file(binarith,t7_binarith)]).

fof(e3_8_1__binari_6,plain,(
    k10_margrel1(k8_margrel1,k1_bvfunc_1(c1_8__binari_6,k7_margrel1)) = k10_margrel1(k8_margrel1,k9_margrel1(c1_8__binari_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__binari_6])],[commutativity_k2_tarski,dt_k2_tarski,existence_m1_subset_1,dt_k6_margrel1,dt_m1_subset_1,cc1_margrel1,fc3_margrel1,d12_margrel1,commutativity_k10_margrel1,commutativity_k1_binarith,involutiveness_k9_margrel1,dt_k10_margrel1,dt_k1_binarith,dt_k1_bvfunc_1,dt_k7_margrel1,dt_k8_margrel1,dt_k9_margrel1,dt_c1_8__binari_6,cc1_bvfunc_1,fc1_binarith,fc1_bvfunc_1,fc4_margrel1,fc5_margrel1,rc2_margrel1,d1_bvfunc_1,d13_margrel1,d14_margrel1,t7_binarith]),
    [interesting(0.65),file(binari_6,e3_8_1__binari_6),[file(binari_6,e3_8_1__binari_6)]]).

fof(t50_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k10_margrel1(k8_margrel1,A) = A ) ),
    file(margrel1,t50_margrel1),
    [interesting(0.9),axiom,file(margrel1,t50_margrel1)]).

fof(e4_8_1__binari_6,plain,(
    k10_margrel1(k8_margrel1,k9_margrel1(c1_8__binari_6)) = k9_margrel1(c1_8__binari_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__binari_6])],[commutativity_k2_tarski,dt_k2_tarski,existence_m1_subset_1,dt_k6_margrel1,dt_m1_subset_1,cc1_margrel1,fc3_margrel1,d12_margrel1,commutativity_k10_margrel1,involutiveness_k9_margrel1,dt_k10_margrel1,dt_k8_margrel1,dt_k9_margrel1,dt_c1_8__binari_6,cc1_bvfunc_1,fc4_margrel1,fc5_margrel1,rc2_margrel1,d14_margrel1,t50_margrel1]),
    [interesting(0.65),file(binari_6,e4_8_1__binari_6),[file(binari_6,e4_8_1__binari_6)]]).

fof(e1_8__binari_6,plain,(
    k2_bvfunc_1(k7_margrel1,c1_8__binari_6) = k9_margrel1(c1_8__binari_6) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_8__binari_6])],[e1_8_1__binari_6,e2_8_1__binari_6,e3_8_1__binari_6,e4_8_1__binari_6]),
    [interesting(0.8),file(binari_6,e1_8__binari_6),[file(binari_6,e1_8__binari_6)]]).

fof(e2_8__binari_6,plain,(
    k2_bvfunc_1(k7_margrel1,c1_8__binari_6) = k9_margrel1(c1_8__binari_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__binari_6])],[commutativity_k2_tarski,dt_k2_tarski,commutativity_k2_binarith,existence_m1_subset_1,dt_k2_binarith,dt_k6_margrel1,dt_m1_subset_1,cc1_bvfunc_1,cc1_margrel1,fc2_binarith,fc2_bvfunc_1,fc3_margrel1,fc4_margrel1,rc2_margrel1,d12_margrel1,commutativity_k2_bvfunc_1,involutiveness_k9_margrel1,dt_k2_bvfunc_1,dt_k7_margrel1,dt_k9_margrel1,dt_c1_8__binari_6,d2_bvfunc_1,d13_margrel1,e1_8__binari_6]),
    [interesting(0.8),file(binari_6,e2_8__binari_6),[file(binari_6,e2_8__binari_6)]]).

fof(i2_8__binari_6,theorem,(
    $true ),
    introduced(tautology,[file(binari_6,i2_8__binari_6)]),
    [interesting(0.8),trivial,file(binari_6,i2_8__binari_6)]).

fof(i1_8__binari_6,plain,(
    k2_bvfunc_1(k7_margrel1,c1_8__binari_6) = k9_margrel1(c1_8__binari_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_8__binari_6])],[e2_8__binari_6,i2_8__binari_6]),
    [interesting(0.8),file(binari_6,i1_8__binari_6),[file(binari_6,i1_8__binari_6)]]).

fof(i1_8_tmp__binari_6,plain,
    ( v2_margrel1(c1_8__binari_6)
   => k2_bvfunc_1(k7_margrel1,c1_8__binari_6) = k9_margrel1(c1_8__binari_6) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_8__binari_6])],[dt_c1_8__binari_6,i1_8__binari_6]),
    [interesting(1),t8_binari_6]).

fof(t8_binari_6,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k2_bvfunc_1(k7_margrel1,A) = k9_margrel1(A) ) ),
    inference(let,[status(thm),assumptions([])],[i1_8_tmp__binari_6,dh_c1_8__binari_6]),
    [interesting(1),file(binari_6,t8_binari_6),[file(binari_6,t8_binari_6)]]).