% Mizar problem: t1_gate_4,gate_4,64,5 
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(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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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))) ) ).
