% Mizar problem: t4_gate_4,gate_4,646,50 
fof(t4_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,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1] : 
      ( v1_xboole_0(X1)
     => ( v1_xboole_0(A)
        | v1_xboole_0(Q)
        | ( ~ v1_xboole_0(H1)
          & v1_xboole_0(k4_gate_1(Y1,G1)) )
        | ( ~ v1_xboole_0(k4_gate_1(Y1,G1))
          & v1_xboole_0(H1) )
        | ( ~ v1_xboole_0(I1)
          & v1_xboole_0(k4_gate_1(R,k2_gate_1(B,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(R,k2_gate_1(B,H1)))
          & v1_xboole_0(I1) )
        | ( ~ v1_xboole_0(J1)
          & v1_xboole_0(k4_gate_1(S,k2_gate_1(C,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(S,k2_gate_1(C,H1)))
          & v1_xboole_0(J1) )
        | ( ~ v1_xboole_0(K1)
          & v1_xboole_0(k4_gate_1(T,k2_gate_1(D,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(T,k2_gate_1(D,H1)))
          & v1_xboole_0(K1) )
        | ( ~ v1_xboole_0(L1)
          & v1_xboole_0(k4_gate_1(U,k2_gate_1(E,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(U,k2_gate_1(E,H1)))
          & v1_xboole_0(L1) )
        | ( ~ v1_xboole_0(M1)
          & v1_xboole_0(k4_gate_1(V,k2_gate_1(F,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(V,k2_gate_1(F,H1)))
          & v1_xboole_0(M1) )
        | ( ~ v1_xboole_0(N1)
          & v1_xboole_0(k4_gate_1(W,k2_gate_1(G,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(W,k2_gate_1(G,H1)))
          & v1_xboole_0(N1) )
        | ( ~ v1_xboole_0(O1)
          & v1_xboole_0(k4_gate_1(X,k2_gate_1(H,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(X,k2_gate_1(H,H1)))
          & v1_xboole_0(O1) )
        | ( ~ v1_xboole_0(P1)
          & v1_xboole_0(k4_gate_1(Y,k2_gate_1(I,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(Y,k2_gate_1(I,H1)))
          & v1_xboole_0(P1) )
        | ( ~ v1_xboole_0(Q1)
          & v1_xboole_0(k4_gate_1(Z,k2_gate_1(J,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(Z,k2_gate_1(J,H1)))
          & v1_xboole_0(Q1) )
        | ( ~ v1_xboole_0(R1)
          & v1_xboole_0(k4_gate_1(A1,k2_gate_1(K,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(A1,k2_gate_1(K,H1)))
          & v1_xboole_0(R1) )
        | ( ~ v1_xboole_0(S1)
          & v1_xboole_0(k4_gate_1(B1,k2_gate_1(L,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(B1,k2_gate_1(L,H1)))
          & v1_xboole_0(S1) )
        | ( ~ v1_xboole_0(T1)
          & v1_xboole_0(k4_gate_1(C1,k2_gate_1(M,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(C1,k2_gate_1(M,H1)))
          & v1_xboole_0(T1) )
        | ( ~ v1_xboole_0(U1)
          & v1_xboole_0(k4_gate_1(D1,k2_gate_1(N,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(D1,k2_gate_1(N,H1)))
          & v1_xboole_0(U1) )
        | ( ~ v1_xboole_0(V1)
          & v1_xboole_0(k4_gate_1(E1,k2_gate_1(O,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(E1,k2_gate_1(O,H1)))
          & v1_xboole_0(V1) )
        | ( ~ v1_xboole_0(W1)
          & v1_xboole_0(k4_gate_1(F1,k2_gate_1(P,H1))) )
        | ( ~ v1_xboole_0(k4_gate_1(F1,k2_gate_1(P,H1)))
          & v1_xboole_0(W1) )
        | ( ~ ( ~ v1_xboole_0(W1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(F1,k2_gate_1(P,G1)),k4_gate_1(X1,k2_gate_1(P,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(F1,k2_gate_1(P,G1)),k4_gate_1(X1,k2_gate_1(P,Y1))))
              & v1_xboole_0(W1) )
          & ~ ( ~ v1_xboole_0(V1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(E1,k2_gate_1(O,G1)),k4_gate_1(X1,k2_gate_1(O,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(E1,k2_gate_1(O,G1)),k4_gate_1(X1,k2_gate_1(O,Y1))))
              & v1_xboole_0(V1) )
          & ~ ( ~ v1_xboole_0(U1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(D1,k2_gate_1(N,G1)),k4_gate_1(X1,k2_gate_1(N,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(D1,k2_gate_1(N,G1)),k4_gate_1(X1,k2_gate_1(N,Y1))))
              & v1_xboole_0(U1) )
          & ~ ( ~ v1_xboole_0(T1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(C1,k2_gate_1(M,G1)),k4_gate_1(X1,k2_gate_1(M,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(C1,k2_gate_1(M,G1)),k4_gate_1(X1,k2_gate_1(M,Y1))))
              & v1_xboole_0(T1) )
          & ~ ( ~ v1_xboole_0(S1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(B1,k2_gate_1(L,G1)),k4_gate_1(X1,k2_gate_1(L,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(B1,k2_gate_1(L,G1)),k4_gate_1(X1,k2_gate_1(L,Y1))))
              & v1_xboole_0(S1) )
          & ~ ( ~ v1_xboole_0(R1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(A1,k2_gate_1(K,G1)),k4_gate_1(X1,k2_gate_1(K,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(A1,k2_gate_1(K,G1)),k4_gate_1(X1,k2_gate_1(K,Y1))))
              & v1_xboole_0(R1) )
          & ~ ( ~ v1_xboole_0(Q1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(Z,k2_gate_1(J,G1)),k4_gate_1(X1,k2_gate_1(J,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(Z,k2_gate_1(J,G1)),k4_gate_1(X1,k2_gate_1(J,Y1))))
              & v1_xboole_0(Q1) )
          & ~ ( ~ v1_xboole_0(P1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(Y,k2_gate_1(I,G1)),k4_gate_1(X1,k2_gate_1(I,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(Y,k2_gate_1(I,G1)),k4_gate_1(X1,k2_gate_1(I,Y1))))
              & v1_xboole_0(P1) )
          & ~ ( ~ v1_xboole_0(O1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(X,k2_gate_1(H,G1)),k4_gate_1(X1,k2_gate_1(H,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(X,k2_gate_1(H,G1)),k4_gate_1(X1,k2_gate_1(H,Y1))))
              & v1_xboole_0(O1) )
          & ~ ( ~ v1_xboole_0(N1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(W,k2_gate_1(G,G1)),k4_gate_1(X1,k2_gate_1(G,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(W,k2_gate_1(G,G1)),k4_gate_1(X1,k2_gate_1(G,Y1))))
              & v1_xboole_0(N1) )
          & ~ ( ~ v1_xboole_0(M1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(V,k2_gate_1(F,G1)),k4_gate_1(X1,k2_gate_1(F,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(V,k2_gate_1(F,G1)),k4_gate_1(X1,k2_gate_1(F,Y1))))
              & v1_xboole_0(M1) )
          & ~ ( ~ v1_xboole_0(L1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(U,k2_gate_1(E,G1)),k4_gate_1(X1,k2_gate_1(E,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(U,k2_gate_1(E,G1)),k4_gate_1(X1,k2_gate_1(E,Y1))))
              & v1_xboole_0(L1) )
          & ~ ( ~ v1_xboole_0(K1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(T,k2_gate_1(D,G1)),k4_gate_1(X1,k2_gate_1(D,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(T,k2_gate_1(D,G1)),k4_gate_1(X1,k2_gate_1(D,Y1))))
              & v1_xboole_0(K1) )
          & ~ ( ~ v1_xboole_0(J1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(S,k2_gate_1(C,G1)),k4_gate_1(X1,k2_gate_1(C,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(S,k2_gate_1(C,G1)),k4_gate_1(X1,k2_gate_1(C,Y1))))
              & v1_xboole_0(J1) )
          & ~ ( ~ v1_xboole_0(I1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(R,k2_gate_1(B,G1)),k4_gate_1(X1,k2_gate_1(B,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(R,k2_gate_1(B,G1)),k4_gate_1(X1,k2_gate_1(B,Y1))))
              & v1_xboole_0(I1) )
          & ~ ( ~ v1_xboole_0(H1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(X1,k2_gate_1(A,G1)),k4_gate_1(X1,k2_gate_1(A,Y1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(X1,k2_gate_1(A,G1)),k4_gate_1(X1,k2_gate_1(A,Y1))))
              & v1_xboole_0(H1) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_k2_gate_1,dt_k4_gate_1,t6_gate_1,t8_gate_1]),
    [file(gate_4,t4_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),
    []).