% Mizar problem: t165_real_2,real_2,283,49 
fof(t165_real_2,conjecture,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,k6_xcmplx_0(B,C))
                 => r1_xreal_0(C,k6_xcmplx_0(B,A)) )
                & ( r1_xreal_0(k6_xcmplx_0(B,C),A)
                 => r1_xreal_0(k6_xcmplx_0(B,A),C) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[rc1_xreal_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_k6_xcmplx_0,cc2_xreal_0,fc5_xreal_0,t13_xreal_1,t14_xreal_1]),
    [file(real_2,t165_real_2)]).

fof(rc1_xreal_0,axiom,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    []).

fof(reflexivity_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(connectedness_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(dt_k6_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k6_xcmplx_0),
    []).

fof(cc2_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    []).

fof(fc5_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc5_xreal_0),
    []).

fof(t13_xreal_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r1_xreal_0(A,k6_xcmplx_0(B,C))
               => r1_xreal_0(C,k6_xcmplx_0(B,A)) ) ) ) ) ),
    file(xreal_1,t13_xreal_1),
    []).

fof(t14_xreal_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r1_xreal_0(k6_xcmplx_0(A,B),C)
               => r1_xreal_0(k6_xcmplx_0(A,C),B) ) ) ) ) ),
    file(xreal_1,t14_xreal_1),
    []).