% Mizar problem: t2_gate_4,gate_4,165,5 
fof(t2_gate_4, conjecture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~ ( ( ~ (v1_xboole_0(Q))  &  ( ~ ( ( ~ (v1_xboole_0(H1))  & v1_xboole_0(k4_gate_1(X1, k2_gate_1(A, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(X1, k2_gate_1(A, G1))))  & v1_xboole_0(H1)) )  &  ( ~ ( ( ~ (v1_xboole_0(I1))  & v1_xboole_0(k4_gate_1(R, k2_gate_1(B, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(R, k2_gate_1(B, G1))))  & v1_xboole_0(I1)) )  &  ( ~ ( ( ~ (v1_xboole_0(J1))  & v1_xboole_0(k4_gate_1(S, k2_gate_1(C, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(S, k2_gate_1(C, G1))))  & v1_xboole_0(J1)) )  &  ( ~ ( ( ~ (v1_xboole_0(K1))  & v1_xboole_0(k4_gate_1(T, k2_gate_1(D, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(T, k2_gate_1(D, G1))))  & v1_xboole_0(K1)) )  &  ( ~ ( ( ~ (v1_xboole_0(L1))  & v1_xboole_0(k4_gate_1(U, k2_gate_1(E, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(U, k2_gate_1(E, G1))))  & v1_xboole_0(L1)) )  &  ( ~ ( ( ~ (v1_xboole_0(M1))  & v1_xboole_0(k4_gate_1(V, k2_gate_1(F, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(V, k2_gate_1(F, G1))))  & v1_xboole_0(M1)) )  &  ( ~ ( ( ~ (v1_xboole_0(N1))  & v1_xboole_0(k4_gate_1(W, k2_gate_1(G, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(W, k2_gate_1(G, G1))))  & v1_xboole_0(N1)) )  &  ( ~ ( ( ~ (v1_xboole_0(O1))  & v1_xboole_0(k4_gate_1(X, k2_gate_1(H, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(X, k2_gate_1(H, G1))))  & v1_xboole_0(O1)) )  &  ( ~ ( ( ~ (v1_xboole_0(P1))  & v1_xboole_0(k4_gate_1(Y, k2_gate_1(I, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(Y, k2_gate_1(I, G1))))  & v1_xboole_0(P1)) )  &  ( ~ ( ( ~ (v1_xboole_0(Q1))  & v1_xboole_0(k4_gate_1(Z, k2_gate_1(J, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(Z, k2_gate_1(J, G1))))  & v1_xboole_0(Q1)) )  &  ( ~ ( ( ~ (v1_xboole_0(R1))  & v1_xboole_0(k4_gate_1(A1, k2_gate_1(K, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(A1, k2_gate_1(K, G1))))  & v1_xboole_0(R1)) )  &  ( ~ ( ( ~ (v1_xboole_0(S1))  & v1_xboole_0(k4_gate_1(B1, k2_gate_1(L, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(B1, k2_gate_1(L, G1))))  & v1_xboole_0(S1)) )  &  ( ~ ( ( ~ (v1_xboole_0(T1))  & v1_xboole_0(k4_gate_1(C1, k2_gate_1(M, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(C1, k2_gate_1(M, G1))))  & v1_xboole_0(T1)) )  &  ( ~ ( ( ~ (v1_xboole_0(U1))  & v1_xboole_0(k4_gate_1(D1, k2_gate_1(N, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(D1, k2_gate_1(N, G1))))  & v1_xboole_0(U1)) )  &  ( ~ ( ( ~ (v1_xboole_0(V1))  & v1_xboole_0(k4_gate_1(E1, k2_gate_1(O, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(E1, k2_gate_1(O, G1))))  & v1_xboole_0(V1)) )  &  ( ~ ( ( ~ (v1_xboole_0(W1))  & v1_xboole_0(k4_gate_1(F1, k2_gate_1(P, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(F1, k2_gate_1(P, G1))))  & v1_xboole_0(W1)) )  &  ~ ( ( ~ ( ( ~ (v1_xboole_0(G1))  & v1_xboole_0(k2_gate_1(Q, G1))) )  &  ( ~ ( ( ~ (v1_xboole_0(k2_gate_1(Q, G1)))  & v1_xboole_0(G1)) )  &  ( ~ ( ( ~ (v1_xboole_0(F1))  & v1_xboole_0(k4_gate_1(W1, k2_gate_1(P, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(W1, k2_gate_1(P, G1))))  & v1_xboole_0(F1)) )  &  ( ~ ( ( ~ (v1_xboole_0(E1))  & v1_xboole_0(k4_gate_1(V1, k2_gate_1(O, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(V1, k2_gate_1(O, G1))))  & v1_xboole_0(E1)) )  &  ( ~ ( ( ~ (v1_xboole_0(D1))  & v1_xboole_0(k4_gate_1(U1, k2_gate_1(N, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(U1, k2_gate_1(N, G1))))  & v1_xboole_0(D1)) )  &  ( ~ ( ( ~ (v1_xboole_0(C1))  & v1_xboole_0(k4_gate_1(T1, k2_gate_1(M, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(T1, k2_gate_1(M, G1))))  & v1_xboole_0(C1)) )  &  ( ~ ( ( ~ (v1_xboole_0(B1))  & v1_xboole_0(k4_gate_1(S1, k2_gate_1(L, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(S1, k2_gate_1(L, G1))))  & v1_xboole_0(B1)) )  &  ( ~ ( ( ~ (v1_xboole_0(A1))  & v1_xboole_0(k4_gate_1(R1, k2_gate_1(K, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(R1, k2_gate_1(K, G1))))  & v1_xboole_0(A1)) )  &  ( ~ ( ( ~ (v1_xboole_0(Z))  & v1_xboole_0(k4_gate_1(Q1, k2_gate_1(J, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(Q1, k2_gate_1(J, G1))))  & v1_xboole_0(Z)) )  &  ( ~ ( ( ~ (v1_xboole_0(Y))  & v1_xboole_0(k4_gate_1(P1, k2_gate_1(I, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(P1, k2_gate_1(I, G1))))  & v1_xboole_0(Y)) )  &  ( ~ ( ( ~ (v1_xboole_0(X))  & v1_xboole_0(k4_gate_1(O1, k2_gate_1(H, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(O1, k2_gate_1(H, G1))))  & v1_xboole_0(X)) )  &  ( ~ ( ( ~ (v1_xboole_0(W))  & v1_xboole_0(k4_gate_1(N1, k2_gate_1(G, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(N1, k2_gate_1(G, G1))))  & v1_xboole_0(W)) )  &  ( ~ ( ( ~ (v1_xboole_0(V))  & v1_xboole_0(k4_gate_1(M1, k2_gate_1(F, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(M1, k2_gate_1(F, G1))))  & v1_xboole_0(V)) )  &  ( ~ ( ( ~ (v1_xboole_0(U))  & v1_xboole_0(k4_gate_1(L1, k2_gate_1(E, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(L1, k2_gate_1(E, G1))))  & v1_xboole_0(U)) )  &  ( ~ ( ( ~ (v1_xboole_0(T))  & v1_xboole_0(k4_gate_1(K1, k2_gate_1(D, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(K1, k2_gate_1(D, G1))))  & v1_xboole_0(T)) )  &  ( ~ ( ( ~ (v1_xboole_0(S))  & v1_xboole_0(k4_gate_1(J1, k2_gate_1(C, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(J1, k2_gate_1(C, G1))))  & v1_xboole_0(S)) )  &  ( ~ ( ( ~ (v1_xboole_0(R))  & v1_xboole_0(k4_gate_1(I1, k2_gate_1(B, G1)))) )  &  ( ~ ( ( ~ (v1_xboole_0(k4_gate_1(I1, k2_gate_1(B, G1))))  & v1_xboole_0(R)) )  &  ( ~ ( ( ~ (v1_xboole_0(X1))  & v1_xboole_0(k4_gate_1(H1, k2_gate_1(A, G1)))) )  &  ~ ( ( ~ (v1_xboole_0(k4_gate_1(H1, k2_gate_1(A, G1))))  & v1_xboole_0(X1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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))) ) ).
