% Mizar problem: t13_gate_1,gate_1,237,67 
fof(t13_gate_1, conjecture,  (! [A] :  (! [B] :  ( ~ (v1_xboole_0(k7_gate_1(A, B)))  <=>  (v1_xboole_0(A) & v1_xboole_0(B)) ) ) ) ).
fof(commutativity_k7_gate_1, axiom,  (! [A, B] : k7_gate_1(A, B)=k7_gate_1(B, A)) ).
fof(dt_k7_gate_1, axiom, $true).
fof(fc15_gate_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_xboole_0(B))  =>  ~ (v1_xboole_0(k7_gate_1(A, B))) ) ) ).
fof(fc16_gate_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  => v1_xboole_0(k7_gate_1(A, B))) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
