% Mizar problem: t3_gate_4,gate_4,291,5 
fof(t3_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] :  (v1_xboole_0(L1) =>  (v1_xboole_0(A) |  ( ( ~ (v1_xboole_0(Z))  & v1_xboole_0(k4_gate_1(M1, Y)))  |  ( ( ~ (v1_xboole_0(k4_gate_1(M1, Y)))  & v1_xboole_0(Z))  |  ( ( ~ (v1_xboole_0(A1))  & v1_xboole_0(k4_gate_1(N, k2_gate_1(B, Z))))  |  ( ( ~ (v1_xboole_0(k4_gate_1(N, k2_gate_1(B, Z))))  & v1_xboole_0(A1))  |  ( ( ~ (v1_xboole_0(B1))  & v1_xboole_0(k4_gate_1(O, k2_gate_1(C, Z))))  |  ( ( ~ (v1_xboole_0(k4_gate_1(O, k2_gate_1(C, Z))))  & v1_xboole_0(B1))  |  ( ( ~ (v1_xboole_0(C1))  & v1_xboole_0(k4_gate_1(P, k2_gate_1(D, Z))))  |  ( ( ~ (v1_xboole_0(k4_gate_1(P, k2_gate_1(D, Z))))  & v1_xboole_0(C1))  |  ( ( ~ (v1_xboole_0(D1))  & v1_xboole_0(k4_gate_1(Q, k2_gate_1(E, Z))))  |  ( ( ~ (v1_xboole_0(k4_gate_1(Q, k2_gate_1(E, Z))))  & v1_xboole_0(D1))  |  ( ( ~ (v1_xboole_0(E1))  & v1_xboole_0(k4_gate_1(R, k2_gate_1(F, Z))))  |  ( ( ~ (v1_xboole_0(k4_gate_1(R, k2_gate_1(F, Z))))  & v1_xboole_0(E1))  |  ( ( ~ (v1_xboole_0(F1))  & v1_xboole_0(k4_gate_1(S, k2_gate_1(G, Z))))  |  ( ( ~ (v1_xboole_0(k4_gate_1(S, k2_gate_1(G, Z))))  & v1_xboole_0(F1))  |  ( ( ~ (v1_xboole_0(G1))  & v1_xboole_0(k4_gate_1(T, k2_gate_1(H, Z))))  |  ( ( ~ (v1_xboole_0(k4_gate_1(T, k2_gate_1(H, Z))))  & v1_xboole_0(G1))  |  ( ( ~ (v1_xboole_0(H1))  & v1_xboole_0(k4_gate_1(U, k2_gate_1(I, Z))))  |  ( ( ~ (v1_xboole_0(k4_gate_1(U, k2_gate_1(I, Z))))  & v1_xboole_0(H1))  |  ( ( ~ (v1_xboole_0(I1))  & v1_xboole_0(k4_gate_1(V, k2_gate_1(J, Z))))  |  ( ( ~ (v1_xboole_0(k4_gate_1(V, k2_gate_1(J, Z))))  & v1_xboole_0(I1))  |  ( ( ~ (v1_xboole_0(J1))  & v1_xboole_0(k4_gate_1(W, k2_gate_1(K, Z))))  |  ( ( ~ (v1_xboole_0(k4_gate_1(W, k2_gate_1(K, Z))))  & v1_xboole_0(J1))  |  ( ( ~ (v1_xboole_0(K1))  & v1_xboole_0(k4_gate_1(X, k2_gate_1(L, Z))))  |  ( ( ~ (v1_xboole_0(k4_gate_1(X, k2_gate_1(L, Z))))  & v1_xboole_0(K1))  |  ( ~ ( ( ~ (v1_xboole_0(K1))  & v1_xboole_0(k4_gate_1(k4_gate_1(X, k2_gate_1(L, Y)), k4_gate_1(L1, k2_gate_1(L, M1))))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(k4_gate_1(X, k2_gate_1(L, Y)), k4_gate_1(L1, k2_gate_1(L, M1)))))  & v1_xboole_0(K1)) )  &  ( ~ ( ( ~ (v1_xboole_0(J1))  & v1_xboole_0(k4_gate_1(k4_gate_1(W, k2_gate_1(K, Y)), k4_gate_1(L1, k2_gate_1(K, M1))))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(k4_gate_1(W, k2_gate_1(K, Y)), k4_gate_1(L1, k2_gate_1(K, M1)))))  & v1_xboole_0(J1)) )  &  ( ~ ( ( ~ (v1_xboole_0(I1))  & v1_xboole_0(k4_gate_1(k4_gate_1(V, k2_gate_1(J, Y)), k4_gate_1(L1, k2_gate_1(J, M1))))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(k4_gate_1(V, k2_gate_1(J, Y)), k4_gate_1(L1, k2_gate_1(J, M1)))))  & v1_xboole_0(I1)) )  &  ( ~ ( ( ~ (v1_xboole_0(H1))  & v1_xboole_0(k4_gate_1(k4_gate_1(U, k2_gate_1(I, Y)), k4_gate_1(L1, k2_gate_1(I, M1))))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(k4_gate_1(U, k2_gate_1(I, Y)), k4_gate_1(L1, k2_gate_1(I, M1)))))  & v1_xboole_0(H1)) )  &  ( ~ ( ( ~ (v1_xboole_0(G1))  & v1_xboole_0(k4_gate_1(k4_gate_1(T, k2_gate_1(H, Y)), k4_gate_1(L1, k2_gate_1(H, M1))))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(k4_gate_1(T, k2_gate_1(H, Y)), k4_gate_1(L1, k2_gate_1(H, M1)))))  & v1_xboole_0(G1)) )  &  ( ~ ( ( ~ (v1_xboole_0(F1))  & v1_xboole_0(k4_gate_1(k4_gate_1(S, k2_gate_1(G, Y)), k4_gate_1(L1, k2_gate_1(G, M1))))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(k4_gate_1(S, k2_gate_1(G, Y)), k4_gate_1(L1, k2_gate_1(G, M1)))))  & v1_xboole_0(F1)) )  &  ( ~ ( ( ~ (v1_xboole_0(E1))  & v1_xboole_0(k4_gate_1(k4_gate_1(R, k2_gate_1(F, Y)), k4_gate_1(L1, k2_gate_1(F, M1))))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(k4_gate_1(R, k2_gate_1(F, Y)), k4_gate_1(L1, k2_gate_1(F, M1)))))  & v1_xboole_0(E1)) )  &  ( ~ ( ( ~ (v1_xboole_0(D1))  & v1_xboole_0(k4_gate_1(k4_gate_1(Q, k2_gate_1(E, Y)), k4_gate_1(L1, k2_gate_1(E, M1))))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(k4_gate_1(Q, k2_gate_1(E, Y)), k4_gate_1(L1, k2_gate_1(E, M1)))))  & v1_xboole_0(D1)) )  &  ( ~ ( ( ~ (v1_xboole_0(C1))  & v1_xboole_0(k4_gate_1(k4_gate_1(P, k2_gate_1(D, Y)), k4_gate_1(L1, k2_gate_1(D, M1))))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(k4_gate_1(P, k2_gate_1(D, Y)), k4_gate_1(L1, k2_gate_1(D, M1)))))  & v1_xboole_0(C1)) )  &  ( ~ ( ( ~ (v1_xboole_0(B1))  & v1_xboole_0(k4_gate_1(k4_gate_1(O, k2_gate_1(C, Y)), k4_gate_1(L1, k2_gate_1(C, M1))))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(k4_gate_1(O, k2_gate_1(C, Y)), k4_gate_1(L1, k2_gate_1(C, M1)))))  & v1_xboole_0(B1)) )  &  ( ~ ( ( ~ (v1_xboole_0(A1))  & v1_xboole_0(k4_gate_1(k4_gate_1(N, k2_gate_1(B, Y)), k4_gate_1(L1, k2_gate_1(B, M1))))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(k4_gate_1(N, k2_gate_1(B, Y)), k4_gate_1(L1, k2_gate_1(B, M1)))))  & v1_xboole_0(A1)) )  &  ( ~ ( ( ~ (v1_xboole_0(Z))  & v1_xboole_0(k4_gate_1(k4_gate_1(L1, k2_gate_1(A, Y)), k4_gate_1(L1, k2_gate_1(A, M1))))) )  &  ~ ( ( ~ (v1_xboole_0(k4_gate_1(k4_gate_1(L1, k2_gate_1(A, Y)), k4_gate_1(L1, k2_gate_1(A, M1)))))  & v1_xboole_0(Z)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(commutativity_k2_gate_1, axiom,  (! [A, B] : k2_gate_1(A, B)=k2_gate_1(B, A)) ).
fof(commutativity_k4_gate_1, axiom,  (! [A, B] : k4_gate_1(A, B)=k4_gate_1(B, A)) ).
fof(dt_k2_gate_1, axiom, $true).
fof(dt_k4_gate_1, axiom, $true).
fof(fc3_gate_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_gate_1(A, B))) ) ) ).
fof(fc4_gate_1, axiom,  (! [A, B] :  (v1_xboole_0(A) => v1_xboole_0(k2_gate_1(A, B))) ) ).
fof(fc7_gate_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k4_gate_1(A, B))) ) ) ).
fof(fc8_gate_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_xboole_0(B))  => v1_xboole_0(k4_gate_1(A, B))) ) ).
fof(fc9_gate_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  => v1_xboole_0(k4_gate_1(A, B))) ) ).
