% Mizar problem: t9_gate_1,gate_1,83,5 
fof(t9_gate_1,conjecture,(
    ! [A] : 
      ( v1_xboole_0(k4_gate_1(A,A))
      & ~ ( ~ $true
          & v1_xboole_0(k4_gate_1(A,A)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d4_gate_1,dt_k1_gate_1,dt_k1_xboole_0,dt_k4_gate_1,fc1_xboole_0,rc1_xboole_0,rc2_xboole_0,t6_boole,t7_boole,t8_boole]),
    [file(gate_1,t9_gate_1)]).

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

fof(d4_gate_1,axiom,(
    ! [A,B] : 
      ( ( ( ( ~ v1_xboole_0(A)
            & v1_xboole_0(B) )
          | ( v1_xboole_0(A)
            & ~ v1_xboole_0(B) ) )
       => k4_gate_1(A,B) = k1_gate_1(k1_xboole_0) )
      & ~ ( ~ ( ~ v1_xboole_0(A)
              & v1_xboole_0(B) )
          & ~ ( v1_xboole_0(A)
              & ~ v1_xboole_0(B) )
          & k4_gate_1(A,B) != k1_xboole_0 ) ) ),
    file(gate_1,d4_gate_1),
    []).

fof(dt_k1_gate_1,axiom,(
    $true ),
    file(gate_1,k1_gate_1),
    []).

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

fof(dt_k4_gate_1,axiom,(
    $true ),
    file(gate_1,k4_gate_1),
    []).

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

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

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

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

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

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