% Mizar problem: t1_gate_3,gate_3,39,5 
fof(t1_gate_3, conjecture,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] :  (! [F] :  (! [G] :  (! [H] :  (! [I] :  (! [J] :  (! [K] :  (! [L] :  ~ ( ( ~ ( ( ~ (v1_xboole_0(A))  & v1_xboole_0(k2_gate_1(k1_gate_1(J), k1_gate_1(I)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k2_gate_1(k1_gate_1(J), k1_gate_1(I))))  & v1_xboole_0(A)) )  &  ( ~ ( ( ~ (v1_xboole_0(B))  & v1_xboole_0(k2_gate_1(k1_gate_1(J), I))) )  &  ( ~ ( ( ~ (v1_xboole_0(k2_gate_1(k1_gate_1(J), I)))  & v1_xboole_0(B)) )  &  ( ~ ( ( ~ (v1_xboole_0(C))  & v1_xboole_0(k2_gate_1(J, k1_gate_1(I)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k2_gate_1(J, k1_gate_1(I))))  & v1_xboole_0(C)) )  &  ( ~ ( ( ~ (v1_xboole_0(D))  & v1_xboole_0(k2_gate_1(J, I))) )  &  ( ~ ( ( ~ (v1_xboole_0(k2_gate_1(J, I)))  & v1_xboole_0(D)) )  &  ( ~ ( ( ~ (v1_xboole_0(E))  & v1_xboole_0(k2_gate_1(k1_gate_1(L), k1_gate_1(K)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k2_gate_1(k1_gate_1(L), k1_gate_1(K))))  & v1_xboole_0(E)) )  &  ( ~ ( ( ~ (v1_xboole_0(F))  & v1_xboole_0(k2_gate_1(k1_gate_1(L), K))) )  &  ( ~ ( ( ~ (v1_xboole_0(k2_gate_1(k1_gate_1(L), K)))  & v1_xboole_0(F)) )  &  ( ~ ( ( ~ (v1_xboole_0(G))  & v1_xboole_0(k2_gate_1(L, k1_gate_1(K)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k2_gate_1(L, k1_gate_1(K))))  & v1_xboole_0(G)) )  &  ( ~ ( ( ~ (v1_xboole_0(H))  & v1_xboole_0(k2_gate_1(L, K))) )  &  ( ~ ( ( ~ (v1_xboole_0(k2_gate_1(L, K)))  & v1_xboole_0(H)) )  &  ( ~ ( ( ~ (v1_xboole_0(K))  & v1_xboole_0(k1_gate_1(J))) )  &  ( ~ ( ( ~ (v1_xboole_0(k1_gate_1(J)))  & v1_xboole_0(K)) )  &  ( ~ ( ( ~ (v1_xboole_0(L))  & v1_xboole_0(I)) )  &  ( ~ ( ( ~ (v1_xboole_0(I))  & v1_xboole_0(L)) )  &  ~ ( ( ~ ( ( ~ (v1_xboole_0(F))  & v1_xboole_0(A)) )  &  ( ~ ( ( ~ (v1_xboole_0(A))  & v1_xboole_0(F)) )  &  ( ~ ( ( ~ (v1_xboole_0(H))  & v1_xboole_0(B)) )  &  ( ~ ( ( ~ (v1_xboole_0(B))  & v1_xboole_0(H)) )  &  ( ~ ( ( ~ (v1_xboole_0(G))  & v1_xboole_0(D)) )  &  ( ~ ( ( ~ (v1_xboole_0(D))  & v1_xboole_0(G)) )  &  ( ~ ( ( ~ (v1_xboole_0(E))  & v1_xboole_0(C)) )  &  ~ ( ( ~ (v1_xboole_0(C))  & v1_xboole_0(E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(commutativity_k2_gate_1, axiom,  (! [A, B] : k2_gate_1(A, B)=k2_gate_1(B, A)) ).
fof(dt_k1_gate_1, axiom, $true).
fof(dt_k2_gate_1, axiom, $true).
fof(fc1_gate_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v1_xboole_0(k1_gate_1(A))) ) ) ).
fof(fc2_gate_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  => v1_xboole_0(k1_gate_1(A))) ) ).
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))) ) ).
