% Mizar problem: t50_wellord1,wellord1,859,52 
fof(t50_wellord1,conjecture,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r4_wellord1(A,B)
           => r4_wellord1(B,A) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d8_wellord1,dt_k2_funct_1,rc1_funct_1,t49_wellord1]),
    [file(wellord1,t50_wellord1)]).

fof(d8_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r4_wellord1(A,B)
          <=> ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & r3_wellord1(A,B,C) ) ) ) ) ),
    file(wellord1,d8_wellord1),
    []).

fof(dt_k2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_1(A))
        & v1_funct_1(k2_funct_1(A)) ) ) ),
    file(funct_1,k2_funct_1),
    []).

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

fof(t49_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r3_wellord1(A,B,C)
               => r3_wellord1(B,A,k2_funct_1(C)) ) ) ) ) ),
    file(wellord1,t49_wellord1),
    []).