% Mizar problem: t40_xtuple_0,xtuple_0,828,5 
fof(t40_xtuple_0, conjecture,  (! [A] :  (! [B] : r1_tarski(k13_xtuple_0(k3_xboole_0(A, B)), k3_xboole_0(k13_xtuple_0(A), k13_xtuple_0(B)))) ) ).
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(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(d14_xtuple_0, axiom,  (! [A] : k11_xtuple_0(A)=k9_xtuple_0(k9_xtuple_0(A))) ).
fof(d16_xtuple_0, axiom,  (! [A] : k13_xtuple_0(A)=k9_xtuple_0(k11_xtuple_0(A))) ).
fof(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(dt_k11_xtuple_0, axiom, $true).
fof(dt_k13_xtuple_0, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc4_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc6_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k11_xtuple_0(A))) ) ).
fof(fc8_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k13_xtuple_0(A))) ) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
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(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(t16_xtuple_0, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) => r1_tarski(k13_xtuple_0(A), k13_xtuple_0(B))) ) ) ).
fof(t17_xboole_1, axiom,  (! [A] :  (! [B] : r1_tarski(k3_xboole_0(A, B), A)) ) ).
fof(t19_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r1_tarski(C, A) & r1_tarski(C, B))  => r1_tarski(C, k3_xboole_0(A, B))) ) ) ) ).
fof(t2_boole, axiom,  (! [A] : k3_xboole_0(A, k1_xboole_0)=k1_xboole_0) ).
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)) ) ) ) ) ).
