% Mizar problem: t41_gate_1,gate_1,757,38 
fof(t41_gate_1, conjecture,  (! [A] :  (! [B] :  ( ~ (v1_xboole_0(k34_gate_1(A, B)))  <=>  ( ~ ( (v1_xboole_0(A) & v1_xboole_0(B)) )  &  ~ ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) ) ) ) ) ) ) ).
fof(commutativity_k34_gate_1, axiom,  (! [A, B] : k34_gate_1(A, B)=k34_gate_1(B, A)) ).
fof(dt_k1_gate_1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k34_gate_1, axiom, $true).
fof(fc1_gate_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v1_xboole_0(k1_gate_1(A))) ) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc2_gate_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  => v1_xboole_0(k1_gate_1(A))) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(d34_gate_1, axiom,  (! [A] :  (! [B] :  ( ~ ( ( ~ ( (v1_xboole_0(A) & v1_xboole_0(B)) )  &  ( ~ ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) ) )  &  ~ (k34_gate_1(A, B)=k1_gate_1(k1_xboole_0)) ) ) )  &  ( ~ ( ( ~ ( (v1_xboole_0(A) & v1_xboole_0(B)) )  &  ~ ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) ) ) ) )  => k34_gate_1(A, B)=k1_xboole_0) ) ) ) ).
