% Mizar problem: t14_altcat_3,altcat_3,597,5 
fof(t14_altcat_3, conjecture,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_setfam_1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k7_altcat_1(A))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k7_altcat_1(A))) =>  ( ~ (k1_altcat_1(k7_altcat_1(A), B, C)=k1_xboole_0)  =>  (! [D] :  (m1_subset_1(D, k1_altcat_1(k7_altcat_1(A), B, C)) =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, B, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) )  =>  (E=D =>  (v5_altcat_3(D, k7_altcat_1(A), B, C) <=> v2_funct_2(E, C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(abstractness_v6_altcat_1, axiom,  (! [A] :  (l2_altcat_1(A) =>  (v6_altcat_1(A) => A=g2_altcat_1(u1_struct_0(A), u1_altcat_1(A), u2_altcat_1(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_altcat_1, axiom,  (! [A] :  (l2_altcat_1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_altcat_1(A) &  (v8_altcat_1(A) & v9_altcat_1(A)) ) )  =>  ( ~ (v2_struct_0(A))  & v10_altcat_1(A)) ) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_setfam_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_setfam_1(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc1_zfmisc_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_zfmisc_1(A)) ) ).
fof(cc2_altcat_1, axiom,  (! [A] :  (l2_altcat_1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_altcat_1(A) &  (v10_altcat_1(A) & v12_altcat_1(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v8_altcat_1(A) & v9_altcat_1(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_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_setfam_1, axiom,  (! [A] :  ( ~ (v2_setfam_1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc2_zfmisc_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v1_xboole_0(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_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc3_setfam_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_setfam_1(A))  =>  ~ (v2_setfam_1(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_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
fof(cc4_setfam_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v2_setfam_1(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(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(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(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(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d14_altcat_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v6_altcat_1(B) &  (v10_altcat_1(B) & l2_altcat_1(B)) ) )  =>  (B=k7_altcat_1(A) <=>  (u1_struct_0(B)=A &  (! [C] :  (m1_subset_1(C, u1_struct_0(B)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(B)) => k1_altcat_1(B, C, D)=k1_funct_2(C, D)) ) ) ) ) ) ) ) ) ) ).
fof(d19_relat_1, axiom,  (! [A] :  (! [B] :  (v1_relat_1(B) =>  (v5_relat_1(B, A) <=> r1_tarski(k10_xtuple_0(B), A)) ) ) ) ).
fof(d1_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( ( ~ (B=k1_xboole_0)  =>  (v1_funct_2(C, A, B) <=> A=k1_relset_1(A, C)) )  &  (B=k1_xboole_0 =>  (v1_funct_2(C, A, B) <=> C=k1_xboole_0) ) ) ) ) ) ) ).
fof(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d2_altcat_1, axiom,  (! [A] :  (l1_altcat_1(A) =>  (v2_altcat_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)) =>  ~ ( ( ~ (k1_altcat_1(A, B, C)=k1_xboole_0)  &  ( ~ (k1_altcat_1(A, C, D)=k1_xboole_0)  & k1_altcat_1(A, B, D)=k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k1_funct_2(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (? [E] :  ( (v1_relat_1(E) & v1_funct_1(E))  &  (D=E &  (k9_xtuple_0(E)=A & r1_tarski(k10_xtuple_0(E), B)) ) ) ) ) ) ) ) ) ) ).
fof(d3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (B=k10_xtuple_0(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (? [D] :  (r2_hidden(D, k9_xtuple_0(A)) & C=k1_funct_1(A, D)) ) ) ) ) ) ) ) ).
fof(d3_funct_2, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v2_funct_2(B, A) <=> k2_relset_1(A, B)=A) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d5_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k4_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) &  ~ (r2_hidden(D, B)) ) ) ) ) ) ) ) ).
fof(d8_altcat_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_altcat_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, k1_altcat_1(A, B, C)) =>  (v5_altcat_3(D, A, B, C) <=>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  ( ~ (k1_altcat_1(A, C, E)=k1_xboole_0)  =>  (! [F] :  (m1_subset_1(F, k1_altcat_1(A, C, E)) =>  (! [G] :  (m1_subset_1(G, k1_altcat_1(A, C, E)) =>  (k5_altcat_1(A, B, C, E, D, F)=k5_altcat_1(A, B, C, E, D, G) => F=G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_funcop_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ( (A=B => k14_funcop_1(A, B, C, D)=C)  &  ( ~ (A=B)  => k14_funcop_1(A, B, C, D)=D) ) ) ) ) ) ).
fof(dt_g2_altcat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, k2_zfmisc_1(A, A)) &  (v1_funct_1(B) & v1_partfun1(B, k2_zfmisc_1(A, A))) ) )  & m2_pboole(C, k3_zfmisc_1(A, A, A), k3_altcat_1(A, B, B), k2_altcat_1(A, B)))  =>  (v6_altcat_1(g2_altcat_1(A, B, C)) & l2_altcat_1(g2_altcat_1(A, B, C))) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k14_funcop_1, axiom, $true).
fof(dt_k16_funcop_1, axiom,  (! [A, B, C, D, E] :  ( (m1_subset_1(D, A) & m1_subset_1(E, A))  => m1_subset_1(k16_funcop_1(A, B, C, D, E), A)) ) ).
fof(dt_k1_altcat_1, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_funct_2, axiom, $true).
fof(dt_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => m1_subset_1(k1_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_altcat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, k2_zfmisc_1(A, A)) &  (v1_funct_1(B) & v1_partfun1(B, k2_zfmisc_1(A, A))) ) )  =>  (v1_relat_1(k2_altcat_1(A, B)) &  (v4_relat_1(k2_altcat_1(A, B), k3_zfmisc_1(A, A, A)) &  (v1_funct_1(k2_altcat_1(A, B)) & v1_partfun1(k2_altcat_1(A, B), k3_zfmisc_1(A, A, A))) ) ) ) ) ).
fof(dt_k2_funcop_1, axiom, $true).
fof(dt_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => m1_subset_1(k2_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_altcat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, k2_zfmisc_1(A, A)) &  (v1_funct_1(B) & v1_partfun1(B, k2_zfmisc_1(A, A))) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, k2_zfmisc_1(A, A)) &  (v1_funct_1(C) & v1_partfun1(C, k2_zfmisc_1(A, A))) ) ) )  =>  (v1_relat_1(k3_altcat_1(A, B, C)) &  (v4_relat_1(k3_altcat_1(A, B, C), k3_zfmisc_1(A, A, A)) &  (v1_funct_1(k3_altcat_1(A, B, C)) & v1_partfun1(k3_altcat_1(A, B, C), k3_zfmisc_1(A, A, A))) ) ) ) ) ).
fof(dt_k3_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k3_zfmisc_1, axiom, $true).
fof(dt_k4_xboole_0, axiom, $true).
fof(dt_k5_altcat_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ( ~ (v2_struct_0(A))  & l2_altcat_1(A))  &  (m1_subset_1(B, u1_struct_0(A)) &  (m1_subset_1(C, u1_struct_0(A)) &  (m1_subset_1(D, u1_struct_0(A)) &  (m1_subset_1(E, k1_altcat_1(A, B, C)) & m1_subset_1(F, k1_altcat_1(A, C, D))) ) ) ) )  => m1_subset_1(k5_altcat_1(A, B, C, D, E, F), k1_altcat_1(A, B, D))) ) ).
fof(dt_k6_subset_1, axiom,  (! [A, B] : m1_subset_1(k6_subset_1(A, B), k1_zfmisc_1(A))) ).
fof(dt_k7_altcat_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v2_struct_0(k7_altcat_1(A)))  &  (v6_altcat_1(k7_altcat_1(A)) &  (v10_altcat_1(k7_altcat_1(A)) & l2_altcat_1(k7_altcat_1(A))) ) ) ) ) ).
fof(dt_k7_funcop_1, axiom,  (! [A, B] :  (v1_funct_1(k7_funcop_1(A, B)) &  (v1_funct_2(k7_funcop_1(A, B), A, k1_tarski(B)) & m1_subset_1(k7_funcop_1(A, B), k1_zfmisc_1(k2_zfmisc_1(A, k1_tarski(B))))) ) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_l1_altcat_1, axiom,  (! [A] :  (l1_altcat_1(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_altcat_1, axiom,  (! [A] :  (l2_altcat_1(A) => l1_altcat_1(A)) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m2_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  =>  (! [D] :  (m2_pboole(D, A, B, C) =>  (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) & v1_partfun1(D, A)) ) ) ) ) ) ) ).
fof(dt_o_1_0_altcat_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  => m1_subset_1(o_1_0_altcat_3(A), A)) ) ).
fof(dt_o_2_1_altcat_3, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_setfam_1(A))  & m1_subset_1(B, u1_struct_0(k7_altcat_1(A))))  => m1_subset_1(o_2_1_altcat_3(A, B), B)) ) ).
fof(dt_u1_altcat_1, axiom,  (! [A] :  (l1_altcat_1(A) =>  (v1_relat_1(u1_altcat_1(A)) &  (v4_relat_1(u1_altcat_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))) &  (v1_funct_1(u1_altcat_1(A)) & v1_partfun1(u1_altcat_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)))) ) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_altcat_1, axiom,  (! [A] :  (l2_altcat_1(A) => m2_pboole(u2_altcat_1(A), k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A)), k3_altcat_1(u1_struct_0(A), u1_altcat_1(A), u1_altcat_1(A)), k2_altcat_1(u1_struct_0(A), u1_altcat_1(A)))) ) ).
fof(existence_l1_altcat_1, axiom,  (? [A] : l1_altcat_1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_altcat_1, axiom,  (? [A] : l2_altcat_1(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  =>  (? [D] : m2_pboole(D, A, B, C)) ) ) ).
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(fc14_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v4_funct_1(k1_tarski(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_altcat_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, k2_zfmisc_1(A, A)) &  (v1_funct_1(B) & v1_partfun1(B, k2_zfmisc_1(A, A))) ) )  & m2_pboole(C, k3_zfmisc_1(A, A, A), k3_altcat_1(A, B, B), k2_altcat_1(A, B))) )  =>  ( ~ (v2_struct_0(g2_altcat_1(A, B, C)))  & v6_altcat_1(g2_altcat_1(A, B, C))) ) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_zfmisc_1, axiom,  (! [A] : v1_zfmisc_1(k1_tarski(A))) ).
fof(fc2_altcat_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v2_struct_0(k7_altcat_1(A)))  &  (v2_altcat_1(k7_altcat_1(A)) &  (v6_altcat_1(k7_altcat_1(A)) &  (v10_altcat_1(k7_altcat_1(A)) &  (v11_altcat_1(k7_altcat_1(A)) & v12_altcat_1(k7_altcat_1(A))) ) ) ) ) ) ) ).
fof(fc2_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v1_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc2_setfam_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  => v1_setfam_1(k1_tarski(A))) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc2_zfmisc_1, axiom,  (! [A, B] :  (v1_xboole_0(B) => v1_xboole_0(k2_zfmisc_1(A, B))) ) ).
fof(fc3_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  => v4_relat_1(k4_xboole_0(B, C), A)) ) ).
fof(fc3_zfmisc_1, axiom,  (! [A, B] :  (v1_xboole_0(A) => v1_xboole_0(k2_zfmisc_1(A, B))) ) ).
fof(fc4_zfmisc_1, axiom,  (! [A, B] :  ( (v1_zfmisc_1(A) & v1_zfmisc_1(B))  => v1_zfmisc_1(k2_zfmisc_1(A, B))) ) ).
fof(fc6_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k4_xboole_0(B, C), A)) ) ).
fof(fc7_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v2_funct_1(B)) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))) => v1_relat_1(k9_xtuple_0(D))) ) ).
fof(fc9_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k2_zfmisc_1(B, C)))) => v1_relat_1(k10_xtuple_0(D))) ) ).
fof(free_g2_altcat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, k2_zfmisc_1(A, A)) &  (v1_funct_1(B) & v1_partfun1(B, k2_zfmisc_1(A, A))) ) )  & m2_pboole(C, k3_zfmisc_1(A, A, A), k3_altcat_1(A, B, B), k2_altcat_1(A, B)))  =>  (! [D, E, F] :  (g2_altcat_1(A, B, C)=g2_altcat_1(D, E, F) =>  (A=D &  (B=E & C=F) ) ) ) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_setfam_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_setfam_1(A)) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_zfmisc_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ).
fof(rc2_altcat_1, axiom,  (? [A] :  (l2_altcat_1(A) & v6_altcat_1(A)) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_setfam_1, axiom,  (? [A] :  ~ (v2_setfam_1(A)) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_zfmisc_1, axiom,  (? [A] :  ~ (v1_zfmisc_1(A)) ) ).
fof(rc3_altcat_1, axiom,  (? [A] :  (l2_altcat_1(A) &  ( ~ (v2_struct_0(A))  & v6_altcat_1(A)) ) ) ).
fof(rc3_setfam_1, axiom,  (! [A] :  ( ~ (v2_setfam_1(A))  =>  (? [B] :  (m1_subset_1(B, A) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc5_altcat_1, axiom,  (? [A] :  (l2_altcat_1(A) &  ( ~ (v2_struct_0(A))  &  (v6_altcat_1(A) & v10_altcat_1(A)) ) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc6_altcat_1, axiom,  (? [A] :  (l2_altcat_1(A) &  ( ~ (v2_struct_0(A))  &  (v2_altcat_1(A) &  (v6_altcat_1(A) &  (v11_altcat_1(A) & v12_altcat_1(A)) ) ) ) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(redefinition_k16_funcop_1, axiom,  (! [A, B, C, D, E] :  ( (m1_subset_1(D, A) & m1_subset_1(E, A))  => k16_funcop_1(A, B, C, D, E)=k14_funcop_1(B, C, D, E)) ) ).
fof(redefinition_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k1_relset_1(A, B)=k9_xtuple_0(B)) ) ).
fof(redefinition_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => k2_relset_1(A, B)=k10_xtuple_0(B)) ) ).
fof(redefinition_k6_subset_1, axiom,  (! [A, B] : k6_subset_1(A, B)=k4_xboole_0(A, B)) ).
fof(redefinition_k7_funcop_1, axiom,  (! [A, B] : k7_funcop_1(A, B)=k2_funcop_1(A, B)) ).
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(s3_funct_1__e19_24_1_2_1_1_1_1__altcat_3, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v1_xboole_0(A))  & v1_setfam_1(A))  &  (m1_subset_1(B, u1_struct_0(k7_altcat_1(A))) &  (m1_subset_1(C, u1_struct_0(k7_altcat_1(A))) & m1_subset_1(E, C)) ) )  =>  (? [F] :  ( (v1_relat_1(F) & v1_funct_1(F))  &  (k9_xtuple_0(F)=B &  (! [G] :  (r2_hidden(G, B) => k1_funct_1(F, G)=k16_funcop_1(C, G, D, E, o_2_1_altcat_3(A, C))) ) ) ) ) ) ) ).
fof(t12_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(A, k9_xtuple_0(k3_relat_1(B, C))) => k1_funct_1(k3_relat_1(B, C), A)=k1_funct_1(C, k1_funct_1(B, A))) ) ) ) ) ) ).
fof(t131_zfmisc_1, axiom,  (! [A] :  ~ ( ( ~ (v1_xboole_0(A))  &  (v1_zfmisc_1(A) &  (! [B] :  ~ (A=k1_tarski(B)) ) ) ) ) ) ).
fof(t139_zfmisc_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  <=>  (! [B] :  ~ (v1_xboole_0(k4_xboole_0(A, k1_tarski(B)))) ) ) ) ).
fof(t13_funcop_1, axiom,  (! [A] :  (! [B] :  (k9_xtuple_0(k2_funcop_1(A, B))=A & r1_tarski(k10_xtuple_0(k2_funcop_1(A, B)), k1_tarski(B))) ) ) ).
fof(t13_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(A, k9_xtuple_0(B)) => k1_funct_1(k3_relat_1(B, C), A)=k1_funct_1(C, k1_funct_1(B, A))) ) ) ) ) ) ).
fof(t14_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(A, k10_xtuple_0(k3_relat_1(B, C))) => r2_hidden(A, k10_xtuple_0(C))) ) ) ) ) ) ).
fof(t16_altcat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_altcat_1(A) & l2_altcat_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)) =>  ~ ( ( ~ (k1_altcat_1(A, B, C)=k1_xboole_0)  &  ( ~ (k1_altcat_1(A, C, D)=k1_xboole_0)  &  ( ~ (k1_altcat_1(A, B, D)=k1_xboole_0)  &  (? [E] :  (m1_subset_1(E, k1_altcat_1(A, B, C)) &  (? [F] :  (m1_subset_1(F, k1_altcat_1(A, C, D)) &  (? [G] :  ( (v1_relat_1(G) & v1_funct_1(G))  &  (? [H] :  ( (v1_relat_1(H) & v1_funct_1(H))  &  (E=G &  (F=H &  ~ (k5_altcat_1(A, B, C, D, E, F)=k3_relat_1(G, H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t27_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (v1_relat_1(B) =>  (r1_tarski(k10_xtuple_0(B), k9_xtuple_0(A)) => k9_xtuple_0(k3_relat_1(B, A))=k9_xtuple_0(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(t33_zfmisc_1, axiom,  (! [A] :  (! [B] :  (r1_tarski(B, k1_tarski(A)) <=>  (B=k1_xboole_0 | B=k1_tarski(A)) ) ) ) ).
fof(t38_relat_1, axiom,  (k9_xtuple_0(k1_xboole_0)=k1_xboole_0 & k10_xtuple_0(k1_xboole_0)=k1_xboole_0) ).
fof(t3_boole, axiom,  (! [A] : k4_xboole_0(A, k1_xboole_0)=A) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t41_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  ( (k9_xtuple_0(A)=k1_xboole_0 | k10_xtuple_0(A)=k1_xboole_0)  => A=k1_xboole_0) ) ) ).
fof(t42_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (k9_xtuple_0(A)=k1_xboole_0 <=> k10_xtuple_0(A)=k1_xboole_0) ) ) ).
fof(t4_boole, axiom,  (! [A] : k4_xboole_0(k1_xboole_0, A)=k1_xboole_0) ).
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(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_funcop_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (r2_hidden(B, A) => k1_funct_1(k2_funcop_1(A, C), B)=C) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
