% Mizar problem: t29_e_siec,e_siec,751,5 
fof(t29_e_siec, conjecture,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  =>  (k3_relat_1(k15_e_siec(A), k15_e_siec(A))=k15_e_siec(A) &  (k3_relat_1(k15_e_siec(A), k16_e_siec(A))=k15_e_siec(A) &  (k3_relat_1(k16_e_siec(A), k15_e_siec(A))=k16_e_siec(A) & k3_relat_1(k16_e_siec(A), k16_e_siec(A))=k16_e_siec(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(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
fof(cc4_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(A)) ) ) ).
fof(cc7_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v4_relat_1(B, A)) ) ) ) ) ) ).
fof(cc8_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v5_relat_1(B, A)) ) ) ) ) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(d17_e_siec, axiom,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  => k15_e_siec(A)=k2_xboole_0(k2_relat_1(k4_xboole_0(u2_e_siec(A), k4_relat_1(u1_struct_0(A)))), k4_relat_1(k4_xboole_0(u1_struct_0(A), k10_xtuple_0(u2_e_siec(A)))))) ) ).
fof(d18_e_siec, axiom,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  => k16_e_siec(A)=k2_xboole_0(k2_relat_1(k4_xboole_0(u1_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(dt_k10_xtuple_0, axiom, $true).
fof(dt_k15_e_siec, axiom,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  => v1_relat_1(k15_e_siec(A))) ) ).
fof(dt_k16_e_siec, axiom,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  => v1_relat_1(k16_e_siec(A))) ) ).
fof(dt_k1_sysrel, axiom,  (! [A] :  (v1_relat_1(A) => v1_relat_1(k1_sysrel(A))) ) ).
fof(dt_k1_xboole_0, 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_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_k9_xtuple_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(fc10_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc11_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc12_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(A, B)) & v1_relat_1(k3_relat_1(A, B))) ) ) ).
fof(fc13_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(B, A)) & v1_relat_1(k3_relat_1(B, A))) ) ) ).
fof(fc14_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A))) ) ) ).
fof(fc15_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v2_relat_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_relat_1(k3_relat_1(A, B))) ) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
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(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc8_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k9_xtuple_0(A))) ) ) ).
fof(fc9_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k10_xtuple_0(A))) ) ) ).
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(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_e_siec, axiom,  (? [A] :  (l1_e_siec(A) & v2_e_siec(A)) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(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(rd1_relat_1, axiom,  (! [A] : k9_xtuple_0(k4_relat_1(A))=A) ).
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(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(t12_sysrel, axiom,  (! [A] : k3_relat_1(k4_relat_1(A), k4_relat_1(A))=k4_relat_1(A)) ).
fof(t13_e_siec, axiom,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  =>  (k10_xtuple_0(u1_e_siec(A))=k10_xtuple_0(k1_sysrel(u1_e_siec(A))) &  (k10_xtuple_0(u1_e_siec(A))=k9_xtuple_0(k1_sysrel(u1_e_siec(A))) &  (k10_xtuple_0(u2_e_siec(A))=k10_xtuple_0(k1_sysrel(u2_e_siec(A))) &  (k10_xtuple_0(u2_e_siec(A))=k9_xtuple_0(k1_sysrel(u2_e_siec(A))) & k10_xtuple_0(u1_e_siec(A))=k10_xtuple_0(u2_e_siec(A))) ) ) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t23_e_siec, axiom,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  =>  (k3_relat_1(k4_relat_1(k4_xboole_0(u1_struct_0(A), k10_xtuple_0(u2_e_siec(A)))), k4_xboole_0(u2_e_siec(A), k4_relat_1(u1_struct_0(A))))=k4_xboole_0(u2_e_siec(A), k4_relat_1(u1_struct_0(A))) & k3_relat_1(k4_relat_1(k4_xboole_0(u1_struct_0(A), k10_xtuple_0(u1_e_siec(A)))), k4_xboole_0(u1_e_siec(A), k4_relat_1(u1_struct_0(A))))=k4_xboole_0(u1_e_siec(A), k4_relat_1(u1_struct_0(A)))) ) ) ).
fof(t24_e_siec, axiom,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  =>  (k3_relat_1(k4_xboole_0(u2_e_siec(A), k4_relat_1(u1_struct_0(A))), k4_xboole_0(u2_e_siec(A), k4_relat_1(u1_struct_0(A))))=k1_xboole_0 &  (k3_relat_1(k4_xboole_0(u1_e_siec(A), k4_relat_1(u1_struct_0(A))), k4_xboole_0(u1_e_siec(A), k4_relat_1(u1_struct_0(A))))=k1_xboole_0 &  (k3_relat_1(k4_xboole_0(u2_e_siec(A), k4_relat_1(u1_struct_0(A))), k4_xboole_0(u1_e_siec(A), k4_relat_1(u1_struct_0(A))))=k1_xboole_0 & k3_relat_1(k4_xboole_0(u1_e_siec(A), k4_relat_1(u1_struct_0(A))), k4_xboole_0(u2_e_siec(A), k4_relat_1(u1_struct_0(A))))=k1_xboole_0) ) ) ) ) ).
fof(t27_e_siec, axiom,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  =>  (k3_relat_1(k4_xboole_0(u2_e_siec(A), k4_relat_1(u1_struct_0(A))), k4_relat_1(k4_xboole_0(u1_struct_0(A), k10_xtuple_0(u2_e_siec(A)))))=k1_xboole_0 & k3_relat_1(k4_xboole_0(u1_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)))))=k1_xboole_0) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t32_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (v1_relat_1(B) =>  (! [C] :  (v1_relat_1(C) => k3_relat_1(A, k2_xboole_0(C, B))=k2_xboole_0(k3_relat_1(A, C), k3_relat_1(A, B))) ) ) ) ) ) ).
fof(t35_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (v1_relat_1(B) => k2_relat_1(k3_relat_1(A, B))=k3_relat_1(k2_relat_1(B), k2_relat_1(A))) ) ) ) ).
fof(t3_boole, axiom,  (! [A] : k4_xboole_0(A, k1_xboole_0)=A) ).
fof(t4_boole, axiom,  (! [A] : k4_xboole_0(k1_xboole_0, A)=k1_xboole_0) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_sysrel, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (v1_relat_1(B) =>  (! [C] :  (v1_relat_1(C) => k3_relat_1(k2_xboole_0(A, B), C)=k2_xboole_0(k3_relat_1(A, C), k3_relat_1(B, C))) ) ) ) ) ) ).
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)) ) ) ) ) ).
