% Mizar ND problem: t1_amistd_2,amistd_2,74,51 
fof(dh_c1_3__amistd_2,definition,
    ( ( ( v1_relat_1(c1_3__amistd_2)
        & v1_funct_1(c1_3__amistd_2) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ( r2_tarski(k1_relat_1(c1_3__amistd_2),k1_relat_1(A))
          <=> r2_tarski(c1_3__amistd_2,A) ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C) )
           => ( r2_tarski(k1_relat_1(B),k1_relat_1(C))
            <=> r2_tarski(B,C) ) ) ) ),
    introduced(definition,[new_symbol(c1_3__amistd_2),file(amistd_2,c1_3__amistd_2)]),
    [interesting(0.8),axiom,file(amistd_2,c1_3__amistd_2)]).

fof(dh_c2_3__amistd_2,definition,
    ( ( ( v1_relat_1(c2_3__amistd_2)
        & v1_funct_1(c2_3__amistd_2) )
     => ( r2_tarski(k1_relat_1(c1_3__amistd_2),k1_relat_1(c2_3__amistd_2))
      <=> r2_tarski(c1_3__amistd_2,c2_3__amistd_2) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( r2_tarski(k1_relat_1(c1_3__amistd_2),k1_relat_1(A))
        <=> r2_tarski(c1_3__amistd_2,A) ) ) ),
    introduced(definition,[new_symbol(c2_3__amistd_2),file(amistd_2,c2_3__amistd_2)]),
    [interesting(0.8),axiom,file(amistd_2,c2_3__amistd_2)]).

fof(e1_3_1__amistd_2,assumption,(
    r2_tarski(k1_relat_1(c1_3__amistd_2),k1_relat_1(c2_3__amistd_2)) ),
    introduced(assumption,[file(amistd_2,e1_3_1__amistd_2)]),
    [interesting(0.65),axiom,file(amistd_2,e1_3_1__amistd_2)]).

fof(cc1_amistd_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_relat_1(A)
        & v1_setfam_1(A) ) ) ),
    file(amistd_1,cc1_amistd_1),
    [interesting(0.9),axiom,file(amistd_1,cc1_amistd_1)]).

fof(symmetry_r2_wellord2,theorem,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
     => r2_wellord2(B,A) ) ),
    file(wellord2,r2_wellord2),
    [interesting(0.9),axiom,file(wellord2,r2_wellord2)]).

fof(reflexivity_r2_wellord2,theorem,(
    ! [A,B] : r2_wellord2(A,A) ),
    file(wellord2,r2_wellord2),
    [interesting(0.9),axiom,file(wellord2,r2_wellord2)]).

fof(redefinition_r2_wellord2,definition,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> r2_tarski(A,B) ) ),
    file(wellord2,r2_wellord2),
    [interesting(0.9),axiom,file(wellord2,r2_wellord2)]).

fof(dt_k1_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    [interesting(0.9),axiom,file(card_1,k1_card_1)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_c1_3__amistd_2,assumption,
    ( v1_relat_1(c1_3__amistd_2)
    & v1_funct_1(c1_3__amistd_2) ),
    introduced(assumption,[file(amistd_2,c1_3__amistd_2)]),
    [interesting(0.8),axiom,file(amistd_2,c1_3__amistd_2)]).

fof(dt_c2_3__amistd_2,assumption,
    ( v1_relat_1(c2_3__amistd_2)
    & v1_funct_1(c2_3__amistd_2) ),
    introduced(assumption,[file(amistd_2,c2_3__amistd_2)]),
    [interesting(0.8),axiom,file(amistd_2,c2_3__amistd_2)]).

fof(t21_card_1,theorem,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> k1_card_1(A) = k1_card_1(B) ) ),
    file(card_1,t21_card_1),
    [interesting(0.9),axiom,file(card_1,t21_card_1)]).

fof(e2_3_1__amistd_2,plain,(
    k1_card_1(k1_relat_1(c1_3__amistd_2)) = k1_card_1(k1_relat_1(c2_3__amistd_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__amistd_2,dt_c2_3__amistd_2,e1_3_1__amistd_2])],[cc1_amistd_1,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_card_1,dt_k1_relat_1,dt_c1_3__amistd_2,dt_c2_3__amistd_2,e1_3_1__amistd_2,t21_card_1]),
    [interesting(0.65),file(amistd_2,e2_3_1__amistd_2),[file(amistd_2,e2_3_1__amistd_2)]]).

fof(t21_pre_circ,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k1_card_1(A) = k1_card_1(k1_relat_1(A)) ) ),
    file(pre_circ,t21_pre_circ),
    [interesting(0.9),axiom,file(pre_circ,t21_pre_circ)]).

fof(e1_3__amistd_2,plain,
    ( k1_card_1(c1_3__amistd_2) = k1_card_1(k1_relat_1(c1_3__amistd_2))
    & k1_card_1(c2_3__amistd_2) = k1_card_1(k1_relat_1(c2_3__amistd_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__amistd_2,dt_c2_3__amistd_2])],[dt_k1_card_1,dt_k1_relat_1,dt_c1_3__amistd_2,dt_c2_3__amistd_2,cc1_amistd_1,t21_pre_circ]),
    [interesting(0.8),file(amistd_2,e1_3__amistd_2),[file(amistd_2,e1_3__amistd_2)]]).

fof(e3_3_1__amistd_2,plain,(
    r2_tarski(c1_3__amistd_2,c2_3__amistd_2) ),
    inference(mizar_by,[status(thm),assumptions([e1_3_1__amistd_2,dt_c1_3__amistd_2,dt_c2_3__amistd_2])],[cc1_amistd_1,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_card_1,dt_k1_relat_1,dt_c1_3__amistd_2,dt_c2_3__amistd_2,e2_3_1__amistd_2,e1_3__amistd_2,t21_card_1]),
    [interesting(0.65),file(amistd_2,e3_3_1__amistd_2),[file(amistd_2,e3_3_1__amistd_2)]]).

fof(i2_3_1__amistd_2,theorem,(
    $true ),
    introduced(tautology,[file(amistd_2,i2_3_1__amistd_2)]),
    [interesting(0.65),trivial,file(amistd_2,i2_3_1__amistd_2)]).

fof(i1_3_1__amistd_2,plain,(
    r2_tarski(c1_3__amistd_2,c2_3__amistd_2) ),
    inference(conclusion,[status(thm),assumptions([e1_3_1__amistd_2,dt_c1_3__amistd_2,dt_c2_3__amistd_2])],[e3_3_1__amistd_2,i2_3_1__amistd_2]),
    [interesting(0.65),file(amistd_2,i1_3_1__amistd_2),[file(amistd_2,i1_3_1__amistd_2)]]).

fof(e2_3__amistd_2,plain,
    ( r2_tarski(k1_relat_1(c1_3__amistd_2),k1_relat_1(c2_3__amistd_2))
   => r2_tarski(c1_3__amistd_2,c2_3__amistd_2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__amistd_2,dt_c2_3__amistd_2]),discharge_asm(discharge,[e1_3_1__amistd_2])],[e1_3_1__amistd_2,i1_3_1__amistd_2]),
    [interesting(0.8),file(amistd_2,e2_3__amistd_2),[file(amistd_2,e2_3__amistd_2)]]).

fof(e3_3__amistd_2,assumption,(
    r2_tarski(c1_3__amistd_2,c2_3__amistd_2) ),
    introduced(assumption,[file(amistd_2,e3_3__amistd_2)]),
    [interesting(0.8),axiom,file(amistd_2,e3_3__amistd_2)]).

fof(e4_3__amistd_2,plain,(
    k1_card_1(c1_3__amistd_2) = k1_card_1(c2_3__amistd_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__amistd_2,dt_c2_3__amistd_2,e3_3__amistd_2])],[cc1_amistd_1,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_card_1,dt_c1_3__amistd_2,dt_c2_3__amistd_2,e3_3__amistd_2,t21_card_1]),
    [interesting(0.8),file(amistd_2,e4_3__amistd_2),[file(amistd_2,e4_3__amistd_2)]]).

fof(e5_3__amistd_2,plain,(
    r2_tarski(k1_relat_1(c1_3__amistd_2),k1_relat_1(c2_3__amistd_2)) ),
    inference(mizar_by,[status(thm),assumptions([e3_3__amistd_2,dt_c1_3__amistd_2,dt_c2_3__amistd_2])],[cc1_amistd_1,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k1_card_1,dt_k1_relat_1,dt_c1_3__amistd_2,dt_c2_3__amistd_2,e4_3__amistd_2,e1_3__amistd_2,t21_card_1]),
    [interesting(0.8),file(amistd_2,e5_3__amistd_2),[file(amistd_2,e5_3__amistd_2)]]).

fof(i4_3__amistd_2,theorem,(
    $true ),
    introduced(tautology,[file(amistd_2,i4_3__amistd_2)]),
    [interesting(0.8),trivial,file(amistd_2,i4_3__amistd_2)]).

fof(i3_3__amistd_2,plain,(
    r2_tarski(k1_relat_1(c1_3__amistd_2),k1_relat_1(c2_3__amistd_2)) ),
    inference(conclusion,[status(thm),assumptions([e3_3__amistd_2,dt_c1_3__amistd_2,dt_c2_3__amistd_2])],[e5_3__amistd_2,i4_3__amistd_2]),
    [interesting(0.8),file(amistd_2,i3_3__amistd_2),[file(amistd_2,i3_3__amistd_2)]]).

fof(i2_3__amistd_2,plain,
    ( r2_tarski(c1_3__amistd_2,c2_3__amistd_2)
   => r2_tarski(k1_relat_1(c1_3__amistd_2),k1_relat_1(c2_3__amistd_2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__amistd_2,dt_c2_3__amistd_2]),discharge_asm(discharge,[e3_3__amistd_2])],[e3_3__amistd_2,i3_3__amistd_2]),
    [interesting(0.8),file(amistd_2,i2_3__amistd_2),[file(amistd_2,i2_3__amistd_2)]]).

fof(i1_3__amistd_2,plain,
    ( r2_tarski(k1_relat_1(c1_3__amistd_2),k1_relat_1(c2_3__amistd_2))
  <=> r2_tarski(c1_3__amistd_2,c2_3__amistd_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__amistd_2,dt_c2_3__amistd_2])],[e2_3__amistd_2,i2_3__amistd_2]),
    [interesting(0.8),file(amistd_2,i1_3__amistd_2),[file(amistd_2,i1_3__amistd_2)]]).

fof(i1_3_tmp__amistd_2,plain,
    ( ( v1_relat_1(c1_3__amistd_2)
      & v1_funct_1(c1_3__amistd_2)
      & v1_relat_1(c2_3__amistd_2)
      & v1_funct_1(c2_3__amistd_2) )
   => ( r2_tarski(k1_relat_1(c1_3__amistd_2),k1_relat_1(c2_3__amistd_2))
    <=> r2_tarski(c1_3__amistd_2,c2_3__amistd_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__amistd_2,dt_c2_3__amistd_2])],[dt_c1_3__amistd_2,dt_c2_3__amistd_2,i1_3__amistd_2]),
    [interesting(1),t1_amistd_2]).

fof(t1_amistd_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_tarski(k1_relat_1(A),k1_relat_1(B))
          <=> r2_tarski(A,B) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__amistd_2,dh_c1_3__amistd_2,dh_c2_3__amistd_2]),
    [interesting(1),file(amistd_2,t1_amistd_2),[file(amistd_2,t1_amistd_2)]]).