% Mizar problem: t10_gate_1,gate_1,180,65 
fof(t10_gate_1, conjecture,  (! [A] :  (! [B] :  ( ~ (v1_xboole_0(k5_gate_1(A, B)))  <=>  ( ~ ( ( ~ (v1_xboole_0(A))  & v1_xboole_0(B)) )  &  ~ ( ( ~ (v1_xboole_0(B))  & v1_xboole_0(A)) ) ) ) ) ) ).
fof(commutativity_k5_gate_1, axiom,  (! [A, B] : k5_gate_1(A, B)=k5_gate_1(B, A)) ).
fof(dt_k5_gate_1, axiom, $true).
fof(fc10_gate_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) &  ~ (v1_xboole_0(B)) )  => v1_xboole_0(k5_gate_1(A, B))) ) ).
fof(fc11_gate_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_xboole_0(B))  =>  ~ (v1_xboole_0(k5_gate_1(A, B))) ) ) ).
fof(fc12_gate_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k5_gate_1(A, B))) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
