% Mizar problem: t8_xboole_0,xboole_0,335,5 
fof(t8_xboole_0, conjecture,  (! [A] :  (! [B] :  ~ ( (r2_xboole_0(A, B) &  (! [C] :  ~ ( (r2_hidden(C, B) & r1_tarski(A, k4_xboole_0(B, k1_tarski(C)))) ) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_xboole_0, axiom,  (! [A, B] :  (r2_xboole_0(A, B) =>  ~ (r2_xboole_0(B, A)) ) ) ).
fof(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d5_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k4_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) &  ~ (r2_hidden(D, B)) ) ) ) ) ) ) ) ).
fof(d8_xboole_0, axiom,  (! [A] :  (! [B] :  (r2_xboole_0(A, B) <=>  (r1_tarski(A, B) &  ~ (A=B) ) ) ) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k4_xboole_0, axiom, $true).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(irreflexivity_r2_xboole_0, axiom,  (! [A, B] :  ~ (r2_xboole_0(A, A)) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(t6_xboole_0, axiom,  (! [A] :  (! [B] :  ~ ( (r2_xboole_0(A, B) &  (! [C] :  ~ ( (r2_hidden(C, B) &  ~ (r2_hidden(C, A)) ) ) ) ) ) ) ) ).
