% Mizar ND problem: t1_funct_3,funct_3,29,28 
fof(dh_c1_1__funct_3,definition,
    ( ! [A] : 
        ( r1_tarski(c1_1__funct_3,A)
       => k6_relat_1(c1_1__funct_3) = k7_relat_1(k6_relat_1(A),c1_1__funct_3) )
   => ! [B,C] : 
        ( r1_tarski(B,C)
       => k6_relat_1(B) = k7_relat_1(k6_relat_1(C),B) ) ),
    introduced(definition,[new_symbol(c1_1__funct_3),file(funct_3,c1_1__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c1_1__funct_3)]).

fof(dh_c2_1__funct_3,definition,
    ( ( r1_tarski(c1_1__funct_3,c2_1__funct_3)
     => k6_relat_1(c1_1__funct_3) = k7_relat_1(k6_relat_1(c2_1__funct_3),c1_1__funct_3) )
   => ! [A] : 
        ( r1_tarski(c1_1__funct_3,A)
       => k6_relat_1(c1_1__funct_3) = k7_relat_1(k6_relat_1(A),c1_1__funct_3) ) ),
    introduced(definition,[new_symbol(c2_1__funct_3),file(funct_3,c2_1__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c2_1__funct_3)]).

fof(e1_1__funct_3,assumption,(
    r1_tarski(c1_1__funct_3,c2_1__funct_3) ),
    introduced(assumption,[file(funct_3,e1_1__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,e1_1__funct_3)]).

fof(rc3_relat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc3_relat_1)]).

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(fc12_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]).

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

fof(fc4_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc4_relat_1)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t2_boole,theorem,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    [interesting(0.9),axiom,file(boole,t2_boole)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc1_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,cc1_relat_1)]).

fof(cc2_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(rc1_relat_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

fof(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc2_relat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc2_relat_1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

fof(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

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_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

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

fof(fc1_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k3_xboole_0(A,B)) ) ),
    file(relat_1,fc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc1_relat_1)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

fof(commutativity_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(idempotence_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(dt_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_1),
    [interesting(0.9),axiom,file(relat_1,k6_relat_1)]).

fof(dt_c1_1__funct_3,assumption,(
    $true ),
    introduced(assumption,[file(funct_3,c1_1__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c1_1__funct_3)]).

fof(dt_c2_1__funct_3,assumption,(
    $true ),
    introduced(assumption,[file(funct_3,c2_1__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c2_1__funct_3)]).

fof(fc2_funct_1,theorem,(
    ! [A] : 
      ( v1_relat_1(k6_relat_1(A))
      & v1_funct_1(k6_relat_1(A)) ) ),
    file(funct_1,fc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc2_funct_1)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t28_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k3_xboole_0(A,B) = A ) ),
    file(xboole_1,t28_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t28_xboole_1)]).

fof(e1_1_1__funct_3,plain,(
    k6_relat_1(c1_1__funct_3) = k6_relat_1(k3_xboole_0(c2_1__funct_3,c1_1__funct_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__funct_3,dt_c2_1__funct_3,e1_1__funct_3])],[rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc3_funct_1,t1_subset,t2_boole,t4_subset,t5_subset,cc1_funct_1,cc1_relat_1,cc2_funct_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_relat_1,fc1_subset_1,rc1_funct_1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,dt_k3_xboole_0,dt_k6_relat_1,dt_c1_1__funct_3,dt_c2_1__funct_3,fc2_funct_1,t3_subset,e1_1__funct_3,t28_xboole_1]),
    [interesting(0.65),file(funct_3,e1_1_1__funct_3),[file(funct_3,e1_1_1__funct_3)]]).

fof(fc1_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc1_funct_1)]).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    [interesting(0.9),axiom,file(relat_1,k5_relat_1)]).

fof(t43_funct_1,theorem,(
    ! [A,B] : k5_relat_1(k6_relat_1(B),k6_relat_1(A)) = k6_relat_1(k3_xboole_0(A,B)) ),
    file(funct_1,t43_funct_1),
    [interesting(0.9),axiom,file(funct_1,t43_funct_1)]).

fof(e2_1_1__funct_3,plain,(
    k6_relat_1(k3_xboole_0(c2_1__funct_3,c1_1__funct_3)) = k5_relat_1(k6_relat_1(c1_1__funct_3),k6_relat_1(c2_1__funct_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__funct_3,dt_c2_1__funct_3])],[fc1_funct_1,fc1_relat_1,rc1_funct_1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,dt_k3_xboole_0,dt_k5_relat_1,dt_k6_relat_1,dt_c1_1__funct_3,dt_c2_1__funct_3,fc2_funct_1,t43_funct_1]),
    [interesting(0.65),file(funct_3,e2_1_1__funct_3),[file(funct_3,e2_1_1__funct_3)]]).

fof(fc4_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B)) ) ) ),
    file(funct_1,fc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc4_funct_1)]).

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    [interesting(0.9),axiom,file(relat_1,k7_relat_1)]).

fof(t94_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k7_relat_1(B,A) = k5_relat_1(k6_relat_1(A),B) ) ),
    file(relat_1,t94_relat_1),
    [interesting(0.9),axiom,file(relat_1,t94_relat_1)]).

fof(e3_1_1__funct_3,plain,(
    k5_relat_1(k6_relat_1(c1_1__funct_3),k6_relat_1(c2_1__funct_3)) = k7_relat_1(k6_relat_1(c2_1__funct_3),c1_1__funct_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__funct_3,dt_c2_1__funct_3])],[fc1_funct_1,fc4_funct_1,rc1_funct_1,dt_k5_relat_1,dt_k6_relat_1,dt_k7_relat_1,dt_c1_1__funct_3,dt_c2_1__funct_3,fc2_funct_1,t94_relat_1]),
    [interesting(0.65),file(funct_3,e3_1_1__funct_3),[file(funct_3,e3_1_1__funct_3)]]).

fof(e2_1__funct_3,plain,(
    k6_relat_1(c1_1__funct_3) = k7_relat_1(k6_relat_1(c2_1__funct_3),c1_1__funct_3) ),
    inference(iterative_eq,[status(thm),assumptions([e1_1__funct_3,dt_c1_1__funct_3,dt_c2_1__funct_3])],[e1_1_1__funct_3,e2_1_1__funct_3,e3_1_1__funct_3]),
    [interesting(0.8),file(funct_3,e2_1__funct_3),[file(funct_3,e2_1__funct_3)]]).

fof(i4_1__funct_3,theorem,(
    $true ),
    introduced(tautology,[file(funct_3,i4_1__funct_3)]),
    [interesting(0.8),trivial,file(funct_3,i4_1__funct_3)]).

fof(i3_1__funct_3,plain,(
    k6_relat_1(c1_1__funct_3) = k7_relat_1(k6_relat_1(c2_1__funct_3),c1_1__funct_3) ),
    inference(conclusion,[status(thm),assumptions([e1_1__funct_3,dt_c1_1__funct_3,dt_c2_1__funct_3])],[e2_1__funct_3,i4_1__funct_3]),
    [interesting(0.8),file(funct_3,i3_1__funct_3),[file(funct_3,i3_1__funct_3)]]).

fof(i2_1__funct_3,plain,
    ( r1_tarski(c1_1__funct_3,c2_1__funct_3)
   => k6_relat_1(c1_1__funct_3) = k7_relat_1(k6_relat_1(c2_1__funct_3),c1_1__funct_3) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__funct_3,dt_c2_1__funct_3]),discharge_asm(discharge,[e1_1__funct_3])],[e1_1__funct_3,i3_1__funct_3]),
    [interesting(0.8),file(funct_3,i2_1__funct_3),[file(funct_3,i2_1__funct_3)]]).

fof(i2_1_tmp__funct_3,plain,
    ( r1_tarski(c1_1__funct_3,c2_1__funct_3)
   => k6_relat_1(c1_1__funct_3) = k7_relat_1(k6_relat_1(c2_1__funct_3),c1_1__funct_3) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__funct_3]),discharge_asm(discharge,[dt_c2_1__funct_3])],[dt_c2_1__funct_3,i2_1__funct_3]),
    [interesting(0.8),i1_1__funct_3]).

fof(i1_1__funct_3,plain,(
    ! [A] : 
      ( r1_tarski(c1_1__funct_3,A)
     => k6_relat_1(c1_1__funct_3) = k7_relat_1(k6_relat_1(A),c1_1__funct_3) ) ),
    inference(let,[status(thm),assumptions([dt_c1_1__funct_3])],[i2_1_tmp__funct_3,dh_c2_1__funct_3]),
    [interesting(0.8),file(funct_3,i1_1__funct_3),[file(funct_3,i1_1__funct_3)]]).

fof(i1_1_tmp__funct_3,plain,(
    ! [A] : 
      ( r1_tarski(c1_1__funct_3,A)
     => k6_relat_1(c1_1__funct_3) = k7_relat_1(k6_relat_1(A),c1_1__funct_3) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_1__funct_3])],[dt_c1_1__funct_3,i1_1__funct_3]),
    [interesting(1),t1_funct_3]).

fof(t1_funct_3,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k6_relat_1(A) = k7_relat_1(k6_relat_1(B),A) ) ),
    inference(let,[status(thm),assumptions([])],[i1_1_tmp__funct_3,dh_c1_1__funct_3]),
    [interesting(1),file(funct_3,t1_funct_3),[file(funct_3,t1_funct_3)]]).