% Mizar problem: t3_conmetr,conmetr,156,5 
fof(t3_conmetr, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_analmetr(A) & l2_analmetr(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  ~ ( (v5_analmetr(B, A) &  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) =>  ~ ( (r2_hidden(C, D) & r10_analmetr(A, B, D)) ) ) ) ) ) ) ) ) ) ) ) ).
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(cc1_analmetr, axiom,  (! [A] :  (l2_analmetr(A) =>  ( ( ~ (v2_struct_0(A))  & v4_analmetr(A))  =>  ( ~ (v2_struct_0(A))  & v3_analmetr(A)) ) ) ) ).
fof(commutativity_k2_aff_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k2_aff_1(A, B, C)=k2_aff_1(A, C, B)) ) ).
fof(d12_analmetr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_analmetr(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v5_analmetr(B, A) <=>  (? [C] :  (m1_subset_1(C, u1_struct_0(A)) &  (? [D] :  (m1_subset_1(D, u1_struct_0(A)) &  ( ~ (C=D)  & B=k3_analmetr(A, C, D)) ) ) ) ) ) ) ) ) ) ).
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_aff_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_aff_1(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_aff_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k2_aff_1(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_analmetr, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l2_analmetr(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k3_analmetr(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_l1_analmetr, axiom,  (! [A] :  (l1_analmetr(A) => l1_struct_0(A)) ) ).
fof(dt_l1_analoaf, axiom,  (! [A] :  (l1_analoaf(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_analmetr, axiom,  (! [A] :  (l2_analmetr(A) =>  (l1_analoaf(A) & l1_analmetr(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_struct_0, axiom, $true).
fof(existence_l1_analmetr, axiom,  (? [A] : l1_analmetr(A)) ).
fof(existence_l1_analoaf, axiom,  (? [A] : l1_analoaf(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_analmetr, axiom,  (? [A] : l2_analmetr(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc2_analmetr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_analmetr(A))  =>  ( ~ (v2_struct_0(g1_analoaf(u1_struct_0(A), u1_analoaf(A))))  & v1_analoaf(g1_analoaf(u1_struct_0(A), u1_analoaf(A)))) ) ) ).
fof(fc3_analmetr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_analmetr(A) & l2_analmetr(A)) )  =>  ( ~ (v7_struct_0(g1_analoaf(u1_struct_0(A), u1_analoaf(A))))  &  (v1_analoaf(g1_analoaf(u1_struct_0(A), u1_analoaf(A))) & v1_diraf(g1_analoaf(u1_struct_0(A), u1_analoaf(A)))) ) ) ) ).
fof(fc4_analmetr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_analmetr(A) & l2_analmetr(A)) )  =>  ( ~ (v7_struct_0(g1_analoaf(u1_struct_0(A), u1_analoaf(A))))  &  (v1_analoaf(g1_analoaf(u1_struct_0(A), u1_analoaf(A))) &  (v1_diraf(g1_analoaf(u1_struct_0(A), u1_analoaf(A))) & v2_diraf(g1_analoaf(u1_struct_0(A), u1_analoaf(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(irreflexivity_r10_analmetr, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_analmetr(A) & l2_analmetr(A)) )  &  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) )  =>  ~ (r10_analmetr(A, B, B)) ) ) ).
fof(rc3_analmetr, axiom,  (? [A] :  (l2_analmetr(A) &  ~ (v2_struct_0(A)) ) ) ).
fof(rc4_analmetr, axiom,  (? [A] :  (l1_analmetr(A) &  ~ (v2_struct_0(A)) ) ) ).
fof(redefinition_k2_aff_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k2_aff_1(A, B, C)=k1_aff_1(A, B, C)) ) ).
fof(redefinition_r10_analmetr, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_analmetr(A) & l2_analmetr(A)) )  &  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) )  =>  (r10_analmetr(A, B, C) <=> r7_analmetr(A, B, C)) ) ) ).
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(symmetry_r10_analmetr, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_analmetr(A) & l2_analmetr(A)) )  &  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) )  =>  (r10_analmetr(A, B, C) => r10_analmetr(A, C, B)) ) ) ).
fof(t15_aff_1, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r2_tarski(B, k2_aff_1(A, B, C)) & r2_tarski(C, k2_aff_1(A, B, C))) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t39_analmetr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_analmetr(A))  =>  (v4_analmetr(A) <=>  ( ~ ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => B=C) ) ) ) )  &  (! [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] :  (m1_subset_1(G, u1_struct_0(A)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(A)) =>  (r2_analoaf(A, B, C, C, B) &  (r2_analoaf(A, B, C, D, D) &  ( ~ ( (r2_analoaf(A, B, C, F, G) &  (r2_analoaf(A, B, C, H, I) &  ( ~ (r2_analoaf(A, F, G, H, I))  &  ~ (B=C) ) ) ) )  &  ( (r2_analoaf(A, B, C, B, D) => r2_analoaf(A, C, B, C, D))  &  ( (? [J] :  (m1_subset_1(J, u1_struct_0(A)) &  (r2_analoaf(A, B, C, D, J) & r2_analoaf(A, B, D, C, J)) ) )  &  ( ~ ( (! [J] :  (m1_subset_1(J, u1_struct_0(A)) =>  (! [K] :  (m1_subset_1(K, u1_struct_0(A)) =>  (! [L] :  (m1_subset_1(L, u1_struct_0(A)) => r2_analoaf(A, J, K, J, L)) ) ) ) ) ) )  &  ( (? [J] :  (m1_subset_1(J, u1_struct_0(A)) &  (r2_analoaf(A, B, C, D, J) &  ~ (D=J) ) ) )  &  ( ~ ( (r2_analoaf(A, B, C, C, E) &  ( ~ (C=B)  &  (! [J] :  (m1_subset_1(J, u1_struct_0(A)) =>  ~ ( (r2_analoaf(A, D, C, C, J) & r2_analoaf(A, D, B, E, J)) ) ) ) ) ) )  &  ( (r4_analmetr(A, B, C, B, C) => B=C)  &  (r4_analmetr(A, B, C, D, D) &  ( (r4_analmetr(A, B, C, D, E) =>  (r4_analmetr(A, B, C, E, D) & r4_analmetr(A, D, E, B, C)) )  &  ( ~ ( (r4_analmetr(A, B, C, F, G) &  (r2_analoaf(A, B, C, H, I) &  ( ~ (r4_analmetr(A, F, G, H, I))  &  ~ (B=C) ) ) ) )  &  ( ~ ( (r4_analmetr(A, B, C, F, G) &  (r4_analmetr(A, B, C, H, I) &  ( ~ (r2_analoaf(A, F, G, H, I))  &  ~ (B=C) ) ) ) )  &  ( (? [J] :  (m1_subset_1(J, u1_struct_0(A)) &  (r4_analmetr(A, B, C, D, J) &  ~ (D=J) ) ) )  &  ~ ( ( ~ (r2_analoaf(A, B, C, D, E))  &  (! [J] :  (m1_subset_1(J, u1_struct_0(A)) =>  ~ ( (r2_analoaf(A, B, C, B, J) & r2_analoaf(A, D, E, D, J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t41_analmetr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_analmetr(A) & l2_analmetr(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(g1_analoaf(u1_struct_0(A), u1_analoaf(A)))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(g1_analoaf(u1_struct_0(A), u1_analoaf(A)))) =>  ( (B=D & C=E)  => k3_analmetr(A, B, C)=k2_aff_1(g1_analoaf(u1_struct_0(A), u1_analoaf(A)), D, E)) ) ) ) ) ) ) ) ) ) ) ).
fof(t45_analmetr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_analmetr(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (r7_analmetr(A, B, C) <=>  (? [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] :  (m1_subset_1(G, u1_struct_0(A)) &  ( ~ (D=E)  &  ( ~ (F=G)  &  (B=k3_analmetr(A, D, E) &  (C=k3_analmetr(A, F, G) & r4_analmetr(A, D, E, F, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
