% Mizar problem: t9_zf_colla,zf_colla,400,5 
fof(t9_zf_colla, conjecture,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  &  (k9_xtuple_0(B)=A &  (! [C] :  (m1_subset_1(C, A) => k1_funct_1(B, C)=k7_relat_1(B, C)) ) ) ) ) ) ) ).
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_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc11_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_membered(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_membered(B)) ) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc15_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_membered(B)) ) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc16_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_membered(B)) ) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_membered(B)) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc18_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_membered(B)) ) ) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v7_membered(A)) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(A)) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(A)) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(connectedness_r1_ordinal1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  =>  (r1_ordinal1(A, B) | r1_ordinal1(B, A)) ) ) ).
fof(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d2_ordinal1, axiom,  (! [A] :  (v1_ordinal1(A) <=>  (! [B] :  (r2_tarski(B, A) => r1_tarski(B, A)) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d6_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (! [C] :  (C=k7_relat_1(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (? [E] :  (r2_hidden(E, k9_xtuple_0(A)) &  (r2_hidden(E, B) & D=k1_funct_1(A, E)) ) ) ) ) ) ) ) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zf_colla, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
fof(dt_k7_relat_1, axiom, $true).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(A))) ) ) ).
fof(fc10_relset_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(k9_xtuple_0(A)))) )  =>  ( ~ (v1_xboole_0(k5_relat_1(A, B)))  & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc11_relset_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(k9_xtuple_0(A)))) )  =>  ~ (v1_xboole_0(k7_relat_1(A, B))) ) ) ).
fof(fc12_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc13_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ~ (v1_zfmisc_1(k10_xtuple_0(A))) ) ) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  ( (v4_funct_1(A) &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ) ).
fof(fc18_funct_1, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  ~ (v1_zfmisc_1(k9_xtuple_0(A))) ) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc4_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc5_ordinal1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  & v3_ordinal1(B))  =>  (v1_relat_1(k5_relat_1(A, B)) &  (v5_relat_1(k5_relat_1(A, B), k10_xtuple_0(A)) & v5_ordinal1(k5_relat_1(A, B))) ) ) ) ).
fof(fc8_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_funct_1(k5_relat_1(A, B))) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(A)) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc4_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(redefinition_r1_ordinal1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  =>  (r1_ordinal1(A, B) <=> r1_tarski(A, B)) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_ordinal1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => r1_ordinal1(A, A)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(s1_classes1__e3_10_3__zf_colla, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & v3_ordinal1(B))  =>  ( (! [C] :  ~ ( (r2_hidden(C, k1_zf_colla(A, B)) &  (! [D] :  ~ ( (? [E] :  (? [F] :  (E=C &  (F=D &  (! [G] :  (r2_hidden(G, F) <=>  (? [H] :  (m1_subset_1(H, A) &  (? [I] :  (v3_ordinal1(I) &  (? [J] :  ( (v1_relat_1(J) & v1_funct_1(J))  &  (r2_tarski(H, E) &  (r2_tarski(I, B) &  (r2_tarski(H, k1_zf_colla(A, I)) &  ( (k9_xtuple_0(J)=k1_zf_colla(A, I) &  (! [K] :  (m1_subset_1(K, A) =>  (r2_tarski(K, k1_zf_colla(A, I)) => k1_funct_1(J, K)=k7_relat_1(J, K)) ) ) )  & G=k1_funct_1(J, H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  &  (k9_xtuple_0(C)=k1_zf_colla(A, B) &  (! [D] :  (r2_hidden(D, k1_zf_colla(A, B)) =>  (? [L] :  (? [M] :  (L=D &  (M=k1_funct_1(C, D) &  (! [N] :  (r2_hidden(N, M) <=>  (? [O] :  (m1_subset_1(O, A) &  (? [P] :  (v3_ordinal1(P) &  (? [Q] :  ( (v1_relat_1(Q) & v1_funct_1(Q))  &  (r2_tarski(O, L) &  (r2_tarski(P, B) &  (r2_tarski(O, k1_zf_colla(A, P)) &  ( (k9_xtuple_0(Q)=k1_zf_colla(A, P) &  (! [R] :  (m1_subset_1(R, A) =>  (r2_tarski(R, k1_zf_colla(A, P)) => k1_funct_1(Q, R)=k7_relat_1(Q, R)) ) ) )  & N=k1_funct_1(Q, O)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(s1_tarski__e5_10_3_1__zf_colla, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (v3_ordinal1(B) & m1_subset_1(C, A)) )  =>  ( (! [D] :  (! [E] :  (! [F] :  ( ( (? [G] :  (v3_ordinal1(G) &  (? [H] :  ( (v1_relat_1(H) & v1_funct_1(H))  &  (r2_tarski(G, B) &  (r2_hidden(D, k1_zf_colla(A, G)) &  ( (k9_xtuple_0(H)=k1_zf_colla(A, G) &  (! [I] :  (m1_subset_1(I, A) =>  (r2_tarski(I, k1_zf_colla(A, G)) => k1_funct_1(H, I)=k7_relat_1(H, I)) ) ) )  & E=k1_funct_1(H, D)) ) ) ) ) ) )  &  (? [J] :  (v3_ordinal1(J) &  (? [K] :  ( (v1_relat_1(K) & v1_funct_1(K))  &  (r2_tarski(J, B) &  (r2_hidden(D, k1_zf_colla(A, J)) &  ( (k9_xtuple_0(K)=k1_zf_colla(A, J) &  (! [L] :  (m1_subset_1(L, A) =>  (r2_tarski(L, k1_zf_colla(A, J)) => k1_funct_1(K, L)=k7_relat_1(K, L)) ) ) )  & F=k1_funct_1(K, D)) ) ) ) ) ) ) )  => E=F) ) ) )  =>  (? [D] :  (! [E] :  (r2_hidden(E, D) <=>  (? [F] :  (r2_hidden(F, C) &  (? [M] :  (v3_ordinal1(M) &  (? [N] :  ( (v1_relat_1(N) & v1_funct_1(N))  &  (r2_tarski(M, B) &  (r2_hidden(F, k1_zf_colla(A, M)) &  ( (k9_xtuple_0(N)=k1_zf_colla(A, M) &  (! [O] :  (m1_subset_1(O, A) =>  (r2_tarski(O, k1_zf_colla(A, M)) => k1_funct_1(N, O)=k7_relat_1(N, O)) ) ) )  & E=k1_funct_1(N, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(s2_ordinal1__e3_10__zf_colla, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( (! [B] :  (v3_ordinal1(B) =>  ( (! [C] :  (v3_ordinal1(C) =>  (r2_tarski(C, B) =>  (! [D] :  ( (v1_relat_1(D) & v1_funct_1(D))  =>  (! [E] :  ( (v1_relat_1(E) & v1_funct_1(E))  =>  ( ( (k9_xtuple_0(D)=k1_zf_colla(A, C) &  (! [F] :  (m1_subset_1(F, A) =>  (r2_tarski(F, k1_zf_colla(A, C)) => k1_funct_1(D, F)=k7_relat_1(D, F)) ) ) )  &  (k9_xtuple_0(E)=k1_zf_colla(A, C) &  (! [F] :  (m1_subset_1(F, A) =>  (r2_tarski(F, k1_zf_colla(A, C)) => k1_funct_1(E, F)=k7_relat_1(E, F)) ) ) ) )  => D=E) ) ) ) ) ) ) )  =>  (! [G] :  ( (v1_relat_1(G) & v1_funct_1(G))  =>  (! [H] :  ( (v1_relat_1(H) & v1_funct_1(H))  =>  ( ( (k9_xtuple_0(G)=k1_zf_colla(A, B) &  (! [I] :  (m1_subset_1(I, A) =>  (r2_tarski(I, k1_zf_colla(A, B)) => k1_funct_1(G, I)=k7_relat_1(G, I)) ) ) )  &  (k9_xtuple_0(H)=k1_zf_colla(A, B) &  (! [I] :  (m1_subset_1(I, A) =>  (r2_tarski(I, k1_zf_colla(A, B)) => k1_funct_1(H, I)=k7_relat_1(H, I)) ) ) ) )  => G=H) ) ) ) ) ) ) )  =>  (! [B] :  (v3_ordinal1(B) =>  (! [J] :  ( (v1_relat_1(J) & v1_funct_1(J))  =>  (! [K] :  ( (v1_relat_1(K) & v1_funct_1(K))  =>  ( ( (k9_xtuple_0(J)=k1_zf_colla(A, B) &  (! [L] :  (m1_subset_1(L, A) =>  (r2_tarski(L, k1_zf_colla(A, B)) => k1_funct_1(J, L)=k7_relat_1(J, L)) ) ) )  &  (k9_xtuple_0(K)=k1_zf_colla(A, B) &  (! [L] :  (m1_subset_1(L, A) =>  (r2_tarski(L, k1_zf_colla(A, B)) => k1_funct_1(K, L)=k7_relat_1(K, L)) ) ) ) )  => J=K) ) ) ) ) ) ) ) ) ) ).
fof(s2_ordinal1__e5_10__zf_colla, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( (! [B] :  (v3_ordinal1(B) =>  ( (! [C] :  (v3_ordinal1(C) =>  (r2_tarski(C, B) =>  (? [D] :  ( (v1_relat_1(D) & v1_funct_1(D))  &  (k9_xtuple_0(D)=k1_zf_colla(A, C) &  (! [E] :  (m1_subset_1(E, A) =>  (r2_tarski(E, k1_zf_colla(A, C)) => k1_funct_1(D, E)=k7_relat_1(D, E)) ) ) ) ) ) ) ) )  =>  (? [F] :  ( (v1_relat_1(F) & v1_funct_1(F))  &  (k9_xtuple_0(F)=k1_zf_colla(A, B) &  (! [G] :  (m1_subset_1(G, A) =>  (r2_tarski(G, k1_zf_colla(A, B)) => k1_funct_1(F, G)=k7_relat_1(F, G)) ) ) ) ) ) ) ) )  =>  (! [B] :  (v3_ordinal1(B) =>  (? [H] :  ( (v1_relat_1(H) & v1_funct_1(H))  &  (k9_xtuple_0(H)=k1_zf_colla(A, B) &  (! [I] :  (m1_subset_1(I, A) =>  (r2_tarski(I, k1_zf_colla(A, B)) => k1_funct_1(H, I)=k7_relat_1(H, I)) ) ) ) ) ) ) ) ) ) ) ).
fof(s2_ordinal1__e6_10_3__zf_colla, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (v3_ordinal1(B) &  (v1_relat_1(C) & v1_funct_1(C)) ) )  =>  ( (! [D] :  (v3_ordinal1(D) =>  ( (! [E] :  (v3_ordinal1(E) =>  (r2_tarski(E, D) =>  (r1_ordinal1(E, B) =>  (k9_xtuple_0(k5_relat_1(C, k1_zf_colla(A, E)))=k1_zf_colla(A, E) &  (! [F] :  (m1_subset_1(F, A) =>  (r2_tarski(F, k1_zf_colla(A, E)) => k1_funct_1(k5_relat_1(C, k1_zf_colla(A, E)), F)=k7_relat_1(k5_relat_1(C, k1_zf_colla(A, E)), F)) ) ) ) ) ) ) )  =>  (r1_ordinal1(D, B) =>  (k9_xtuple_0(k5_relat_1(C, k1_zf_colla(A, D)))=k1_zf_colla(A, D) &  (! [G] :  (m1_subset_1(G, A) =>  (r2_tarski(G, k1_zf_colla(A, D)) => k1_funct_1(k5_relat_1(C, k1_zf_colla(A, D)), G)=k7_relat_1(k5_relat_1(C, k1_zf_colla(A, D)), G)) ) ) ) ) ) ) )  =>  (! [D] :  (v3_ordinal1(D) =>  (r1_ordinal1(D, B) =>  (k9_xtuple_0(k5_relat_1(C, k1_zf_colla(A, D)))=k1_zf_colla(A, D) &  (! [H] :  (m1_subset_1(H, A) =>  (r2_tarski(H, k1_zf_colla(A, D)) => k1_funct_1(k5_relat_1(C, k1_zf_colla(A, D)), H)=k7_relat_1(k5_relat_1(C, k1_zf_colla(A, D)), H)) ) ) ) ) ) ) ) ) ) ).
fof(t128_relat_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (v1_relat_1(C) => r1_tarski(k7_relat_1(k5_relat_1(C, A), B), k7_relat_1(C, B))) ) ) ) ).
fof(t12_ordinal1, axiom,  (! [A] :  (v1_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (! [C] :  (v3_ordinal1(C) =>  ( (r1_tarski(A, B) & r2_tarski(B, C))  => r2_tarski(A, C)) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  ( (k9_xtuple_0(A)=k9_xtuple_0(B) &  (! [C] :  (r2_hidden(C, k9_xtuple_0(A)) => k1_funct_1(A, C)=k1_funct_1(B, C)) ) )  => A=B) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t49_funct_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(B, A) => k1_funct_1(k5_relat_1(C, A), B)=k1_funct_1(C, B)) ) ) ) ) ).
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(t4_zf_colla, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (v3_ordinal1(B) =>  (! [C] :  (v3_ordinal1(C) =>  (r1_ordinal1(B, C) => r1_tarski(k1_zf_colla(A, B), k1_zf_colla(A, C))) ) ) ) ) ) ) ).
fof(t51_funct_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r1_tarski(A, B) =>  (k5_relat_1(k5_relat_1(C, A), B)=k5_relat_1(C, A) & k5_relat_1(k5_relat_1(C, B), A)=k5_relat_1(C, A)) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t62_relat_1, axiom,  (! [A] :  (! [B] :  (v1_relat_1(B) =>  (r1_tarski(A, k9_xtuple_0(B)) => k9_xtuple_0(k5_relat_1(B, A))=A) ) ) ) ).
fof(t68_relat_1, axiom,  (! [A] :  (! [B] :  (v1_relat_1(B) =>  (r1_tarski(k9_xtuple_0(B), A) => k5_relat_1(B, A)=B) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_zf_colla, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (v3_ordinal1(B) =>  (! [C] :  (m1_subset_1(C, A) =>  (! [D] :  (m1_subset_1(D, A) =>  ( (r2_tarski(D, C) & r2_tarski(C, k1_zf_colla(A, B)))  =>  (r2_tarski(D, k1_zf_colla(A, B)) &  (? [E] :  (v3_ordinal1(E) &  (r2_tarski(E, B) & r2_tarski(D, k1_zf_colla(A, E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_zf_colla, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (v3_ordinal1(B) => r1_tarski(k1_zf_colla(A, B), A)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_zf_colla, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v3_ordinal1(B) & A=k1_zf_colla(A, B)) ) ) ) ).
