% Mizar problem: t6_gate_1,gate_1,135,33 
fof(t6_gate_1, conjecture,  (! [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))) ) ) ) ) ).
fof(commutativity_k4_gate_1, axiom,  (! [A, B] : k4_gate_1(A, B)=k4_gate_1(B, A)) ).
fof(dt_k4_gate_1, axiom, $true).
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))) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
