% Mizar problem: t1_gate_4,gate_4,66,23 
fof(t1_gate_4,conjecture,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1] : ~ ( ~ v1_xboole_0(A)
      & ~ v1_xboole_0(M)
      & ~ ( ~ v1_xboole_0(Z)
          & v1_xboole_0(k4_gate_1(L1,k2_gate_1(A,Y))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(L1,k2_gate_1(A,Y)))
          & v1_xboole_0(Z) )
      & ~ ( ~ v1_xboole_0(A1)
          & v1_xboole_0(k4_gate_1(N,k2_gate_1(B,Y))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(N,k2_gate_1(B,Y)))
          & v1_xboole_0(A1) )
      & ~ ( ~ v1_xboole_0(B1)
          & v1_xboole_0(k4_gate_1(O,k2_gate_1(C,Y))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(O,k2_gate_1(C,Y)))
          & v1_xboole_0(B1) )
      & ~ ( ~ v1_xboole_0(C1)
          & v1_xboole_0(k4_gate_1(P,k2_gate_1(D,Y))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(P,k2_gate_1(D,Y)))
          & v1_xboole_0(C1) )
      & ~ ( ~ v1_xboole_0(D1)
          & v1_xboole_0(k4_gate_1(Q,k2_gate_1(E,Y))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(Q,k2_gate_1(E,Y)))
          & v1_xboole_0(D1) )
      & ~ ( ~ v1_xboole_0(E1)
          & v1_xboole_0(k4_gate_1(R,k2_gate_1(F,Y))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(R,k2_gate_1(F,Y)))
          & v1_xboole_0(E1) )
      & ~ ( ~ v1_xboole_0(F1)
          & v1_xboole_0(k4_gate_1(S,k2_gate_1(G,Y))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(S,k2_gate_1(G,Y)))
          & v1_xboole_0(F1) )
      & ~ ( ~ v1_xboole_0(G1)
          & v1_xboole_0(k4_gate_1(T,k2_gate_1(H,Y))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(T,k2_gate_1(H,Y)))
          & v1_xboole_0(G1) )
      & ~ ( ~ v1_xboole_0(H1)
          & v1_xboole_0(k4_gate_1(U,k2_gate_1(I,Y))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(U,k2_gate_1(I,Y)))
          & v1_xboole_0(H1) )
      & ~ ( ~ v1_xboole_0(I1)
          & v1_xboole_0(k4_gate_1(V,k2_gate_1(J,Y))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(V,k2_gate_1(J,Y)))
          & v1_xboole_0(I1) )
      & ~ ( ~ v1_xboole_0(J1)
          & v1_xboole_0(k4_gate_1(W,k2_gate_1(K,Y))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(W,k2_gate_1(K,Y)))
          & v1_xboole_0(J1) )
      & ~ ( ~ v1_xboole_0(K1)
          & v1_xboole_0(k4_gate_1(X,k2_gate_1(L,Y))) )
      & ~ ( ~ v1_xboole_0(k4_gate_1(X,k2_gate_1(L,Y)))
          & v1_xboole_0(K1) )
      & ~ ( ~ ( ~ v1_xboole_0(Y)
              & v1_xboole_0(k2_gate_1(M,Y)) )
          & ~ ( ~ v1_xboole_0(k2_gate_1(M,Y))
              & v1_xboole_0(Y) )
          & ~ ( ~ v1_xboole_0(X)
              & v1_xboole_0(k4_gate_1(K1,k2_gate_1(L,Y))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(K1,k2_gate_1(L,Y)))
              & v1_xboole_0(X) )
          & ~ ( ~ v1_xboole_0(W)
              & v1_xboole_0(k4_gate_1(J1,k2_gate_1(K,Y))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(J1,k2_gate_1(K,Y)))
              & v1_xboole_0(W) )
          & ~ ( ~ v1_xboole_0(V)
              & v1_xboole_0(k4_gate_1(I1,k2_gate_1(J,Y))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(I1,k2_gate_1(J,Y)))
              & v1_xboole_0(V) )
          & ~ ( ~ v1_xboole_0(U)
              & v1_xboole_0(k4_gate_1(H1,k2_gate_1(I,Y))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(H1,k2_gate_1(I,Y)))
              & v1_xboole_0(U) )
          & ~ ( ~ v1_xboole_0(T)
              & v1_xboole_0(k4_gate_1(G1,k2_gate_1(H,Y))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(G1,k2_gate_1(H,Y)))
              & v1_xboole_0(T) )
          & ~ ( ~ v1_xboole_0(S)
              & v1_xboole_0(k4_gate_1(F1,k2_gate_1(G,Y))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(F1,k2_gate_1(G,Y)))
              & v1_xboole_0(S) )
          & ~ ( ~ v1_xboole_0(R)
              & v1_xboole_0(k4_gate_1(E1,k2_gate_1(F,Y))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(E1,k2_gate_1(F,Y)))
              & v1_xboole_0(R) )
          & ~ ( ~ v1_xboole_0(Q)
              & v1_xboole_0(k4_gate_1(D1,k2_gate_1(E,Y))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(D1,k2_gate_1(E,Y)))
              & v1_xboole_0(Q) )
          & ~ ( ~ v1_xboole_0(P)
              & v1_xboole_0(k4_gate_1(C1,k2_gate_1(D,Y))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(C1,k2_gate_1(D,Y)))
              & v1_xboole_0(P) )
          & ~ ( ~ v1_xboole_0(O)
              & v1_xboole_0(k4_gate_1(B1,k2_gate_1(C,Y))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(B1,k2_gate_1(C,Y)))
              & v1_xboole_0(O) )
          & ~ ( ~ v1_xboole_0(N)
              & v1_xboole_0(k4_gate_1(A1,k2_gate_1(B,Y))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(A1,k2_gate_1(B,Y)))
              & v1_xboole_0(N) )
          & ~ ( ~ v1_xboole_0(L1)
              & v1_xboole_0(k4_gate_1(Z,k2_gate_1(A,Y))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(Z,k2_gate_1(A,Y)))
              & v1_xboole_0(L1) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_k2_gate_1,dt_k4_gate_1,t6_gate_1,t8_gate_1]),
    [file(gate_4,t1_gate_4)]).

fof(dt_k2_gate_1,axiom,(
    $true ),
    file(gate_1,k2_gate_1),
    []).

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

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(t8_gate_1,axiom,(
    ! [A,B] : 
      ( ~ ( ~ v1_xboole_0(k4_gate_1(A,B))
          & ~ ( ~ v1_xboole_0(A)
              & v1_xboole_0(B) )
          & ~ ( v1_xboole_0(A)
              & ~ v1_xboole_0(B) ) )
      & ~ ( ( ( ~ v1_xboole_0(A)
              & v1_xboole_0(B) )
            | ( v1_xboole_0(A)
              & ~ v1_xboole_0(B) ) )
          & v1_xboole_0(k4_gate_1(A,B)) ) ) ),
    file(gate_1,t8_gate_1),
    []).