% Mizar problem: t3_gate_2,gate_2,155,37 
fof(t3_gate_2,conjecture,(
    ! [A,B,C,D] : 
      ( ~ ( v1_xboole_0(k2_gate_1(A,B))
          & v1_xboole_0(k3_gate_1(k1_gate_1(A),k1_gate_1(B))) )
      & ( ~ v1_xboole_0(k3_gate_1(k1_gate_1(A),k1_gate_1(B)))
       => v1_xboole_0(k2_gate_1(A,B)) )
      & ~ ( ~ v1_xboole_0(k3_gate_1(A,B))
          & ~ v1_xboole_0(k3_gate_1(C,B))
          & v1_xboole_0(k3_gate_1(k2_gate_1(A,C),B)) )
      & ( ~ v1_xboole_0(k3_gate_1(k2_gate_1(A,C),B))
       => ( ~ v1_xboole_0(k3_gate_1(A,B))
          & ~ v1_xboole_0(k3_gate_1(C,B)) ) )
      & ~ ( ~ v1_xboole_0(k3_gate_1(A,B))
          & ~ v1_xboole_0(k3_gate_1(C,B))
          & ~ v1_xboole_0(k3_gate_1(D,B))
          & v1_xboole_0(k3_gate_1(k8_gate_1(A,C,D),B)) )
      & ( ~ v1_xboole_0(k3_gate_1(k8_gate_1(A,C,D),B))
       => ( ~ v1_xboole_0(k3_gate_1(A,B))
          & ~ v1_xboole_0(k3_gate_1(C,B))
          & ~ v1_xboole_0(k3_gate_1(D,B)) ) )
      & ~ ( ~ v1_xboole_0(k3_gate_1(A,B))
          & ~ ( ~ v1_xboole_0(A)
              & v1_xboole_0(C) )
          & ~ ( ~ v1_xboole_0(C)
              & v1_xboole_0(A) )
          & v1_xboole_0(k3_gate_1(C,B)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,dt_k1_gate_1,dt_k1_xboole_0,dt_k2_gate_1,dt_k3_gate_1,dt_k8_gate_1,t16_gate_1,t4_gate_1,t6_boole,t6_gate_1,t7_boole,t7_gate_1,t8_boole]),
    [file(gate_2,t3_gate_2)]).

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_k2_gate_1,axiom,(
    $true ),
    file(gate_1,k2_gate_1),
    []).

fof(dt_k3_gate_1,axiom,(
    $true ),
    file(gate_1,k3_gate_1),
    []).

fof(dt_k8_gate_1,axiom,(
    $true ),
    file(gate_1,k8_gate_1),
    []).

fof(t16_gate_1,axiom,(
    ! [A,B,C] : 
      ( ~ v1_xboole_0(k8_gate_1(A,B,C))
    <=> ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C) ) ) ),
    file(gate_1,t16_gate_1),
    []).

fof(t4_gate_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_gate_1(A))
    <=> v1_xboole_0(A) ) ),
    file(gate_1,t4_gate_1),
    []).

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

fof(t6_gate_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_gate_1(A,B))
    <=> ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) ) ) ),
    file(gate_1,t6_gate_1),
    []).

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

fof(t7_gate_1,axiom,(
    ! [A,B] : 
      ( ~ ( ~ v1_xboole_0(k3_gate_1(A,B))
          & v1_xboole_0(A)
          & v1_xboole_0(B) )
      & ~ ( ~ ( v1_xboole_0(A)
              & v1_xboole_0(B) )
          & v1_xboole_0(k3_gate_1(A,B)) ) ) ),
    file(gate_1,t7_gate_1),
    []).

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