% Mizar problem: t16_gate_1,gate_1,142,33 
fof(t16_gate_1,conjecture,(
    ! [A,B,C] : 
      ( ~ v1_xboole_0(k8_gate_1(A,B,C))
    <=> ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,dt_k1_gate_1,dt_k1_xboole_0,dt_k8_gate_1,fc1_xboole_0,rc1_xboole_0,rc2_xboole_0,t6_boole,t7_boole,t8_boole,d8_gate_1,t5_gate_1]),
    [file(gate_1,t16_gate_1)]).

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

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_k8_gate_1,axiom,(
    $true ),
    file(gate_1,k8_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),
    []).

fof(d8_gate_1,axiom,(
    ! [A,B,C] : 
      ( ~ ( ~ v1_xboole_0(A)
          & ~ v1_xboole_0(B)
          & ~ v1_xboole_0(C)
          & k8_gate_1(A,B,C) != k1_gate_1(k1_xboole_0) )
      & ( ~ ( ~ v1_xboole_0(A)
            & ~ v1_xboole_0(B)
            & ~ v1_xboole_0(C) )
       => k8_gate_1(A,B,C) = k1_xboole_0 ) ) ),
    file(gate_1,d8_gate_1),
    []).

fof(t5_gate_1,axiom,(
    ~ v1_xboole_0(k1_gate_1(k1_xboole_0)) ),
    file(gate_1,t5_gate_1),
    []).