% Mizar problem: t41_borsuk_5,borsuk_5,741,23 
fof(t41_borsuk_5,conjecture,(
    ! [A] : 
      ( v1_rat_1(A)
     => ! [B] : 
          ( ( v1_xreal_0(B)
            & ~ v1_rat_1(B) )
         => ~ v1_rat_1(k6_xcmplx_0(B,A)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_rat_1,cc2_xreal_0,commutativity_k2_xcmplx_0,dt_k2_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,fc16_rat_1,fc1_xreal_0,fc2_rat_1,fc3_rat_1,fc3_xreal_0,fc5_xreal_0,involutiveness_k4_xcmplx_0,rc1_xreal_0,rc2_borsuk_5,rc2_rat_1,t38_borsuk_5]),
    [file(borsuk_5,t41_borsuk_5)]).

fof(cc1_rat_1,axiom,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(rat_1,cc1_rat_1),
    []).

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

fof(commutativity_k2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(dt_k4_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k4_xcmplx_0(A)) ) ),
    file(xcmplx_0,k4_xcmplx_0),
    []).

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

fof(fc16_rat_1,axiom,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & v1_rat_1(k4_xcmplx_0(A)) ) ) ),
    file(rat_1,fc16_rat_1),
    []).

fof(fc1_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc1_xreal_0),
    []).

fof(fc2_rat_1,axiom,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_rat_1(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v1_rat_1(k2_xcmplx_0(A,B)) ) ) ),
    file(rat_1,fc2_rat_1),
    []).

fof(fc3_rat_1,axiom,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_rat_1(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v1_rat_1(k6_xcmplx_0(A,B)) ) ) ),
    file(rat_1,fc3_rat_1),
    []).

fof(fc3_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc3_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(involutiveness_k4_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ),
    file(xcmplx_0,k4_xcmplx_0),
    []).

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

fof(rc2_borsuk_5,axiom,(
    ? [A] : 
      ( v1_xreal_0(A)
      & v1_xcmplx_0(A)
      & ~ v1_rat_1(A) ) ),
    file(borsuk_5,rc2_borsuk_5),
    []).

fof(rc2_rat_1,axiom,(
    ? [A] : v1_rat_1(A) ),
    file(rat_1,rc2_rat_1),
    []).

fof(t38_borsuk_5,axiom,(
    ! [A] : 
      ( v1_rat_1(A)
     => ! [B] : 
          ( ( v1_xreal_0(B)
            & ~ v1_rat_1(B) )
         => ~ v1_rat_1(k2_xcmplx_0(A,B)) ) ) ),
    file(borsuk_5,t38_borsuk_5),
    []).