% Mizar problem: t99_zfmisc_1,zfmisc_1,1454,5 
fof(t99_zfmisc_1, conjecture,  (! [A] :  (! [B] :  (! [C] :  (k2_zfmisc_1(k3_xboole_0(A, B), C)=k3_xboole_0(k2_zfmisc_1(A, C), k2_zfmisc_1(B, C)) & k2_zfmisc_1(C, k3_xboole_0(A, B))=k3_xboole_0(k2_zfmisc_1(C, A), k2_zfmisc_1(C, 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_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, A)) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, 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(d4_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k3_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) & r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(d5_tarski, axiom,  (! [A] :  (! [B] : k4_tarski(A, B)=k2_tarski(k2_tarski(A, B), k1_tarski(A))) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k4_tarski, 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(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc3_xboole_0, axiom,  (! [A, B] :  ~ (v1_xboole_0(k2_tarski(A, B))) ) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(l110_zfmisc_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] :  (! [F] :  ( (r1_tarski(A, k2_zfmisc_1(C, E)) &  (r1_tarski(B, k2_zfmisc_1(D, F)) &  (! [G] :  (! [H] :  (r2_hidden(k4_tarski(G, H), A) <=> r2_hidden(k4_tarski(G, H), B)) ) ) ) )  => A=B) ) ) ) ) ) ) ).
fof(l46_zfmisc_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (r2_hidden(k4_tarski(A, B), k2_zfmisc_1(C, D)) <=>  (r2_hidden(A, C) & r2_hidden(B, D)) ) ) ) ) ) ).
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(t17_xboole_1, axiom,  (! [A] :  (! [B] : r1_tarski(k3_xboole_0(A, B), A)) ) ).
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(t88_zfmisc_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (r2_hidden(k4_tarski(A, B), k2_zfmisc_1(C, D)) => r2_hidden(k4_tarski(B, A), k2_zfmisc_1(D, C))) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
