% Mizar problem: t31_e_siec,e_siec,873,5 
fof(t31_e_siec, conjecture,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  =>  (r1_tarski(k17_e_siec(A), k2_zfmisc_1(k12_e_siec(A), k12_e_siec(A))) & r1_tarski(k14_e_siec(A), k2_zfmisc_1(k12_e_siec(A), k12_e_siec(A)))) ) ) ).
fof(cc2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc5_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v4_relat_1(C, A)) ) ) ) ).
fof(cc6_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v5_relat_1(C, A)) ) ) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(d14_e_siec, axiom,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  => k12_e_siec(A)=u1_struct_0(A)) ) ).
fof(d16_e_siec, axiom,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  => k14_e_siec(A)=k2_xboole_0(k2_xboole_0(k2_relat_1(u1_e_siec(A)), u2_e_siec(A)), k4_relat_1(u1_struct_0(A)))) ) ).
fof(d19_e_siec, axiom,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  => k17_e_siec(A)=k2_xboole_0(k4_xboole_0(k2_xboole_0(u1_e_siec(A), u2_e_siec(A)), k4_relat_1(u1_struct_0(A))), k4_relat_1(k4_xboole_0(u1_struct_0(A), k10_xtuple_0(u1_e_siec(A)))))) ) ).
fof(d1_e_siec, axiom,  (! [A] :  (l1_e_siec(A) =>  (v2_e_siec(A) <=>  (r1_tarski(u1_e_siec(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))) &  (r1_tarski(u2_e_siec(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))) &  (k3_relat_1(u1_e_siec(A), u1_e_siec(A))=u1_e_siec(A) &  (k3_relat_1(u1_e_siec(A), u2_e_siec(A))=u1_e_siec(A) &  (k3_relat_1(u2_e_siec(A), u2_e_siec(A))=u2_e_siec(A) & k3_relat_1(u2_e_siec(A), u1_e_siec(A))=u2_e_siec(A)) ) ) ) ) ) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k12_e_siec, axiom, $true).
fof(dt_k14_e_siec, axiom,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  => v1_relat_1(k14_e_siec(A))) ) ).
fof(dt_k17_e_siec, axiom,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  => v1_relat_1(k17_e_siec(A))) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => v1_relat_1(k2_relat_1(A))) ) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k4_relat_1, axiom,  (! [A] : v1_relat_1(k4_relat_1(A))) ).
fof(dt_k4_xboole_0, axiom, $true).
fof(dt_l1_e_siec, axiom,  (! [A] :  (l1_e_siec(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_e_siec, axiom,  (! [A] :  (l1_e_siec(A) => v1_relat_1(u1_e_siec(A))) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_e_siec, axiom,  (! [A] :  (l1_e_siec(A) => v1_relat_1(u2_e_siec(A))) ) ).
fof(existence_l1_e_siec, axiom,  (? [A] : l1_e_siec(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc28_relat_1, axiom,  (! [A] :  (v1_relat_1(k4_relat_1(A)) &  (v4_relat_1(k4_relat_1(A), A) & v5_relat_1(k4_relat_1(A), A)) ) ) ).
fof(fc29_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(C, B)) & v5_relat_1(k3_relat_1(C, B), A)) ) ) ).
fof(fc2_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k4_xboole_0(A, B))) ) ).
fof(fc30_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(B, C)) & v4_relat_1(k3_relat_1(B, C), A)) ) ) ).
fof(fc3_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k2_xboole_0(A, B))) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(involutiveness_k2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k2_relat_1(k2_relat_1(A))=A) ) ).
fof(rc2_e_siec, axiom,  (? [A] :  (l1_e_siec(A) & v2_e_siec(A)) ) ).
fof(rc3_e_siec, axiom,  (? [A] :  (l1_e_siec(A) & v3_e_siec(A)) ) ).
fof(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rd2_relat_1, axiom,  (! [A] : k10_xtuple_0(k4_relat_1(A))=A) ).
fof(rd3_relat_1, axiom,  (! [A] : k2_relat_1(k4_relat_1(A))=k4_relat_1(A)) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(t13_relset_1, axiom,  (! [A] : r1_tarski(k4_relat_1(A), k2_zfmisc_1(A, A))) ).
fof(t15_sysrel, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) => r1_tarski(k4_relat_1(A), k4_relat_1(B))) ) ) ).
fof(t1_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r1_tarski(A, B) & r1_tarski(B, C))  => r1_tarski(A, C)) ) ) ) ).
fof(t36_xboole_1, axiom,  (! [A] :  (! [B] : r1_tarski(k4_xboole_0(A, B), A)) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_sysrel, axiom,  (! [A] :  (! [B] :  (! [C] :  (v1_relat_1(C) =>  (r1_tarski(C, k2_zfmisc_1(A, B)) => r1_tarski(k2_relat_1(C), k2_zfmisc_1(B, A))) ) ) ) ) ).
fof(t8_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r1_tarski(A, C) & r1_tarski(B, C))  => r1_tarski(k2_xboole_0(A, B), C)) ) ) ) ).
