% Mizar problem: t10_xregular,xregular,489,5 
fof(t10_xregular, conjecture,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] :  (! [F] :  ~ ( (r2_tarski(A, B) &  (r2_tarski(B, C) &  (r2_tarski(C, D) &  (r2_tarski(D, E) &  (r2_tarski(E, F) & r2_tarski(F, A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(d4_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] :  (! [F] :  (! [G] :  (G=k4_enumset1(A, B, C, D, E, F) <=>  (! [H] :  (r2_hidden(H, G) <=>  ~ ( ( ~ (H=A)  &  ( ~ (H=B)  &  ( ~ (H=C)  &  ( ~ (H=D)  &  ( ~ (H=E)  &  ~ (H=F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k4_enumset1, axiom, $true).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(symmetry_r1_xboole_0, axiom,  (! [A, B] :  (r1_xboole_0(A, B) => r1_xboole_0(B, A)) ) ).
fof(t1_xregular, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (r2_tarski(B, A) & r1_xboole_0(B, A)) ) ) ) ).
fof(t3_xboole_0, axiom,  (! [A] :  (! [B] :  ( ~ ( ( ~ (r1_xboole_0(A, B))  &  (! [C] :  ~ ( (r2_hidden(C, A) & r2_hidden(C, B)) ) ) ) )  &  ~ ( ( (? [C] :  (r2_hidden(C, A) & r2_hidden(C, B)) )  & r1_xboole_0(A, B)) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
