% Mizar problem: t11_papdesaf,papdesaf,626,5 
fof(t11_papdesaf, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v7_struct_0(B))  &  (v2_analoaf(B) & l1_analoaf(B)) )  =>  (B=k2_analoaf(A) => v6_papdesaf(B)) ) ) ) ) ).
fof(abstractness_v1_analoaf, axiom,  (! [A] :  (l1_analoaf(A) =>  (v1_analoaf(A) => A=g1_analoaf(u1_struct_0(A), u1_analoaf(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(cc10_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_int_1(B)) ) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc11_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc12_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc13_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_membered(B)) ) ) ) ).
fof(cc14_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_membered(B)) ) ) ) ).
fof(cc15_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_membered(B)) ) ) ) ).
fof(cc16_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_membered(B)) ) ) ) ).
fof(cc17_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_membered(B)) ) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc18_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_membered(B)) ) ) ) ).
fof(cc19_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v7_membered(A)) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(A)) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(A)) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc6_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k3_rlvect_1, axiom,  (! [A, B, C] :  ( ( (v2_rlvect_1(A) & l1_algstr_0(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_rlvect_1(A, B, C)=k3_rlvect_1(A, C, B)) ) ).
fof(connectedness_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  =>  (r1_xxreal_0(A, B) | r1_xxreal_0(B, A)) ) ) ).
fof(d11_rlvect_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k5_algstr_0(A, B, C)=k1_algstr_0(A, B, k4_algstr_0(A, C))) ) ) ) ) ) ).
fof(d1_analoaf, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (r1_analoaf(A, B, C, D, E) <=>  ~ ( ( ~ (B=C)  &  ( ~ (D=E)  &  (! [F] :  (v1_xreal_0(F) =>  (! [G] :  (v1_xreal_0(G) =>  ~ ( ( ~ (r1_xxreal_0(F, k5_numbers))  &  ( ~ (r1_xxreal_0(G, k5_numbers))  & k1_rlvect_1(A, k5_algstr_0(A, C, B), F)=k1_rlvect_1(A, k5_algstr_0(A, E, D), G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_geomtrap, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (r1_geomtrap(A, B, C, D, E) <=>  (r1_analoaf(A, B, C, D, E) | r1_analoaf(A, B, C, E, D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_rlvect_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_rlvect_1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (v1_xreal_0(C) => k1_rlvect_1(A, B, C)=k1_binop_1(u1_rlvect_1(A), C, B)) ) ) ) ) ) ).
fof(d4_diraf, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_analoaf(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (r2_diraf(A, B, C, D, E) <=>  (r2_analoaf(A, B, C, D, E) | r2_analoaf(A, B, C, E, D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_diraf, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_analoaf(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r3_diraf(A, B, C, D) <=> r2_diraf(A, B, C, B, D)) ) ) ) ) ) ) ) ) ).
fof(d8_rlvect_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_rlvect_1(A))  =>  (v8_rlvect_1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k1_rlvect_1(A, B, 1)=B) ) ) ) ) ).
fof(dt_g1_analoaf, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), k2_zfmisc_1(A, A)))) =>  (v1_analoaf(g1_analoaf(A, B)) & l1_analoaf(g1_analoaf(A, B))) ) ) ).
fof(dt_k1_algstr_0, axiom,  (! [A, B, C] :  ( (l1_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_algstr_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_rlvect_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_rlvect_1(A))  &  (m1_subset_1(B, u1_struct_0(A)) & v1_xreal_0(C)) )  => m1_subset_1(k1_rlvect_1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_analoaf, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (v1_analoaf(k2_analoaf(A)) & l1_analoaf(k2_analoaf(A))) ) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_rlvect_1, axiom,  (! [A, B, C] :  ( ( (v2_rlvect_1(A) & l1_algstr_0(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k3_rlvect_1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k4_algstr_0, axiom,  (! [A, B] :  ( (l2_algstr_0(A) & m1_subset_1(B, u1_struct_0(A)))  => m1_subset_1(k4_algstr_0(A, B), u1_struct_0(A))) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A))) ) ).
fof(dt_k5_algstr_0, axiom,  (! [A, B, C] :  ( (l2_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k5_algstr_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k5_xcmplx_0(A))) ) ).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_analoaf, axiom,  (! [A] :  (l1_analoaf(A) => l1_struct_0(A)) ) ).
fof(dt_l1_rlvect_1, axiom,  (! [A] :  (l1_rlvect_1(A) => l2_algstr_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (l2_struct_0(A) & l1_algstr_0(A)) ) ) ).
fof(dt_l2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_analoaf, axiom,  (! [A] :  (l1_analoaf(A) => m1_subset_1(u1_analoaf(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)))))) ) ).
fof(dt_u1_rlvect_1, axiom,  (! [A] :  (l1_rlvect_1(A) =>  (v1_funct_1(u1_rlvect_1(A)) &  (v1_funct_2(u1_rlvect_1(A), k2_zfmisc_1(k1_numbers, u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u1_rlvect_1(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers, u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_algstr_0, axiom,  (? [A] : l1_algstr_0(A)) ).
fof(existence_l1_analoaf, axiom,  (? [A] : l1_analoaf(A)) ).
fof(existence_l1_rlvect_1, axiom,  (? [A] : l1_rlvect_1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_algstr_0, axiom,  (? [A] : l2_algstr_0(A)) ).
fof(existence_l2_struct_0, axiom,  (? [A] : l2_struct_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc15_xreal_0, axiom,  (! [A] :  ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v3_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc16_xreal_0, axiom,  (! [A] :  ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v2_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc27_xreal_0, axiom,  (! [A] :  ( (v2_xxreal_0(A) & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) & v2_xxreal_0(k5_xcmplx_0(A))) ) ) ).
fof(fc28_xreal_0, axiom,  (! [A] :  ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) &  ~ (v2_xxreal_0(k5_xcmplx_0(A))) ) ) ) ).
fof(fc29_xreal_0, axiom,  (! [A] :  ( (v3_xxreal_0(A) & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) & v3_xxreal_0(k5_xcmplx_0(A))) ) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc30_xreal_0, axiom,  (! [A] :  ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) &  ~ (v3_xxreal_0(k5_xcmplx_0(A))) ) ) ) ).
fof(fc3_membered, axiom, v3_membered(k1_numbers)).
fof(fc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A))) ) ) ).
fof(fc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A))) ) ) ).
fof(fc56_membered, axiom, v7_membered(k1_numbers)).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc6_membered, axiom, v6_membered(k4_ordinal1)).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(free_g1_analoaf, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), k2_zfmisc_1(A, A)))) =>  (! [C, D] :  (g1_analoaf(A, B)=g1_analoaf(C, D) =>  (A=C & B=D) ) ) ) ) ).
fof(involutiveness_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A))=A) ) ).
fof(involutiveness_k5_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k5_xcmplx_0(k5_xcmplx_0(A))=A) ) ).
fof(l18_papdesaf, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ~ ( ( ~ (B=C)  &  ( ~ (D=C)  &  (r1_analoaf(A, B, C, C, D) &  (! [E] :  (v1_xreal_0(E) =>  ~ ( (k5_algstr_0(A, C, B)=k1_rlvect_1(A, k5_algstr_0(A, D, C), E) &  ~ (r1_xxreal_0(E, k5_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc20_struct_0, axiom,  (? [A] :  (l2_struct_0(A) &  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(A)) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc4_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(redefinition_k3_rlvect_1, axiom,  (! [A, B, C] :  ( ( (v2_rlvect_1(A) & l1_algstr_0(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_rlvect_1(A, B, C)=k1_algstr_0(A, B, C)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
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(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(rqLessOrEqual__r1_xxreal_0__r0_r0, axiom, r1_xxreal_0(0, 0)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r1, axiom, r1_xxreal_0(0, 1)).
fof(rqLessOrEqual__r1_xxreal_0__r0_rm1, axiom,  ~ (r1_xxreal_0(0, k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_r0, axiom,  ~ (r1_xxreal_0(1, 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom, r1_xxreal_0(1, 1)).
fof(rqLessOrEqual__r1_xxreal_0__r1_rm1, axiom,  ~ (r1_xxreal_0(1, k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__rm1_r0, axiom, r1_xxreal_0(k4_xcmplx_0(1), 0)).
fof(rqLessOrEqual__r1_xxreal_0__rm1_r1, axiom, r1_xxreal_0(k4_xcmplx_0(1), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rm1, axiom, r1_xxreal_0(k4_xcmplx_0(1), k4_xcmplx_0(1))).
fof(rqRealNeg__k4_xcmplx_0__r0_r0, axiom, k4_xcmplx_0(0)=0).
fof(rqRealNeg__k4_xcmplx_0__r1_rm1, axiom, k4_xcmplx_0(1)=k4_xcmplx_0(1)).
fof(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom, k4_xcmplx_0(k4_xcmplx_0(1))=1).
fof(spc0_numerals, axiom, m1_subset_1(0, k4_ordinal1)).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(t10_papdesaf, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (v1_xreal_0(G) =>  ( (k5_algstr_0(A, B, C)=k1_rlvect_1(A, k5_algstr_0(A, E, B), G) &  (r1_geomtrap(A, B, D, B, F) & r1_geomtrap(A, C, D, E, F)) )  =>  (G=k5_numbers |  (r1_geomtrap(A, B, C, B, D) |  (F=k3_rlvect_1(A, E, k1_rlvect_1(A, k5_algstr_0(A, D, C), k5_xcmplx_0(k4_xcmplx_0(G)))) &  (F=k3_rlvect_1(A, B, k1_rlvect_1(A, k5_algstr_0(A, D, B), k5_xcmplx_0(k4_xcmplx_0(G)))) & k5_algstr_0(A, D, C)=k1_rlvect_1(A, k5_algstr_0(A, F, E), k4_xcmplx_0(G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t122_xreal_1, axiom,  (! [A] :  (v1_xreal_0(A) =>  ( ~ ( ( ~ (r1_xxreal_0(A, k5_numbers))  & r1_xxreal_0(k5_xcmplx_0(A), k5_numbers)) )  &  ~ ( ( ~ (r1_xxreal_0(k5_xcmplx_0(A), k5_numbers))  & r1_xxreal_0(A, k5_numbers)) ) ) ) ) ).
fof(t1_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v2_xxreal_0(A))  => v2_xxreal_0(B)) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t222_xcmplx_1, axiom,  (! [A] :  (v1_xcmplx_0(A) => k5_xcmplx_0(k4_xcmplx_0(A))=k4_xcmplx_0(k5_xcmplx_0(A))) ) ).
fof(t22_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (r2_diraf(A, B, C, D, E) =>  (r2_diraf(A, B, C, E, D) &  (r2_diraf(A, C, B, D, E) &  (r2_diraf(A, C, B, E, D) &  (r2_diraf(A, D, E, B, C) &  (r2_diraf(A, D, E, C, B) &  (r2_diraf(A, E, D, B, C) & r2_diraf(A, E, D, C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t24_rlvect_1, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v5_rlvect_1(B) &  (v6_rlvect_1(B) &  (v7_rlvect_1(B) &  (v8_rlvect_1(B) & l1_rlvect_1(B)) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_subset_1(C, u1_struct_0(B)) => k1_rlvect_1(B, k4_algstr_0(B, C), A)=k1_rlvect_1(B, C, k4_xcmplx_0(A))) ) ) ) ) ) ).
fof(t27_rlvect_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k5_algstr_0(A, B, k1_algstr_0(A, C, D))=k5_algstr_0(A, k5_algstr_0(A, B, D), C)) ) ) ) ) ) ) ) ).
fof(t2_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (r2_analoaf(A, B, C, D, E) =>  (r2_analoaf(A, C, B, E, D) &  (r2_analoaf(A, D, E, B, C) & r2_analoaf(A, E, D, C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_geomtrap, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(k2_analoaf(A))) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(k2_analoaf(A))) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(k2_analoaf(A))) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(k2_analoaf(A))) =>  ( (F=B &  (G=D &  (H=C & I=E) ) )  =>  (r2_analoaf(k2_analoaf(A), F, G, H, I) <=> r1_analoaf(A, B, D, C, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v3_xxreal_0(B))  => v3_xxreal_0(A)) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t31_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r3_diraf(A, B, B, C) &  (r3_diraf(A, B, C, C) & r3_diraf(A, B, C, B)) ) ) ) ) ) ) ) ).
fof(t32_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ( (r3_diraf(A, B, C, D) &  (r3_diraf(A, B, C, E) & r3_diraf(A, B, C, F)) )  =>  (B=C | r3_diraf(A, D, E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t33_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  ( (r3_diraf(A, B, C, D) & r2_diraf(A, B, C, D, E))  =>  (B=C | r3_diraf(A, B, C, E)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t33_rlvect_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k4_algstr_0(A, k5_algstr_0(A, B, C))=k1_algstr_0(A, C, k4_algstr_0(A, B))) ) ) ) ) ) ).
fof(t34_rlvect_1, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v5_rlvect_1(B) &  (v6_rlvect_1(B) &  (v7_rlvect_1(B) &  (v8_rlvect_1(B) & l1_rlvect_1(B)) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_subset_1(C, u1_struct_0(B)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(B)) => k1_rlvect_1(B, k5_algstr_0(B, C, D), A)=k5_algstr_0(B, k1_rlvect_1(B, C, A), k1_rlvect_1(B, D, A))) ) ) ) ) ) ) ) ).
fof(t3_papdesaf, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k2_analoaf(A))) <=> m1_subset_1(B, u1_struct_0(A))) ) ) ) ).
fof(t3_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v3_xxreal_0(A))  & v3_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_analoaf(A, B, B, C, D) & r2_analoaf(A, C, D, B, B)) ) ) ) ) ) ) ) ) ).
fof(t4_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v2_xxreal_0(B))  & v2_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t61_rlsub_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (B=k1_algstr_0(A, C, D) <=> C=k5_algstr_0(A, B, D)) ) ) ) ) ) ) ) ) ).
fof(t7_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(B)) ) ) ) ) ) ) ) ).
fof(t8_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v3_xxreal_0(B))  &  ~ (v2_xxreal_0(A)) ) ) ) ) ) ) ) ).
