% Mizar problem: s1_catalg_1,catalg_1,1678,10 
include('Axioms/SET010^0.ax').
thf(n1_type, type, np__1: $i).
thf(n2_type, type, np__2: $i).
thf(n3_type, type, np__3: $i).
thf(f1_s1_catalg_1_type, type, f1_s1_catalg_1: $i).
thf(f2_s1_catalg_1_type, type, f2_s1_catalg_1: $i).
thf(f3_s1_catalg_1_type, type, f3_s1_catalg_1: $i > $i > $i).
thf(f4_s1_catalg_1_type, type, f4_s1_catalg_1: $i > $i > $i > $i > $i > $i).
thf(f5_s1_catalg_1_type, type, f5_s1_catalg_1: $i > $i).
thf(g1_msualg_1_type, type, g1_msualg_1: $i > $i > $i > $i > $i).
thf(g3_msualg_1_type, type, g3_msualg_1: $i > $i > $i > $i).
thf(k10_catalg_1_type, type, k10_catalg_1: $i > $i > $i > $i > $i).
thf(k10_finseq_1_type, type, k10_finseq_1: $i > $i > $i).
thf(k10_xtuple_0_type, type, k10_xtuple_0: $i > $i).
thf(k11_finseq_1_type, type, k11_finseq_1: $i > $i > $i > $i).
thf(k13_finseq_1_type, type, k13_finseq_1: $i > $i).
thf(k16_funcop_1_type, type, k16_funcop_1: $i > $i > $i).
thf(k18_funcop_1_type, type, k18_funcop_1: $i > $i > $i).
thf(k1_card_1_type, type, k1_card_1: $i > $i).
thf(k1_funct_1_type, type, k1_funct_1: $i > $i > $i).
thf(k1_msualg_1_type, type, k1_msualg_1: $i > $i > $i).
thf(k1_msualg_3_type, type, k1_msualg_3: $i > $i > $i > $i > $i > $i).
thf(k1_numbers_type, type, k1_numbers: $i).
thf(k1_relset_1_type, type, k1_relset_1: $i > $i > $i).
thf(k1_tarski_type, type, k1_tarski: $i > $i).
thf(k1_xboole_0_type, type, k1_xboole_0: $i).
thf(k1_xtuple_0_type, type, k1_xtuple_0: $i > $i).
thf(k1_zfmisc_1_type, type, k1_zfmisc_1: $i > $i).
thf(k2_catalg_1_type, type, k2_catalg_1: $i > $i).
thf(k2_finseq_4_type, type, k2_finseq_4: $i > $i > $i > $i).
thf(k2_funcop_1_type, type, k2_funcop_1: $i > $i > $i).
thf(k2_msualg_1_type, type, k2_msualg_1: $i > $i > $i).
thf(k2_relset_1_type, type, k2_relset_1: $i > $i > $i).
thf(k2_tarski_type, type, k2_tarski: $i > $i > $i).
thf(k2_xboole_0_type, type, k2_xboole_0: $i > $i > $i).
thf(k2_xtuple_0_type, type, k2_xtuple_0: $i > $i).
thf(k2_zfmisc_1_type, type, k2_zfmisc_1: $i > $i > $i).
thf(k3_catalg_1_type, type, k3_catalg_1: $i > $i).
thf(k3_finseq_1_type, type, k3_finseq_1: $i > $i).
thf(k3_finseq_2_type, type, k3_finseq_2: $i > $i).
thf(k3_funct_2_type, type, k3_funct_2: $i > $i > $i > $i > $i).
thf(k3_msualg_1_type, type, k3_msualg_1: $i > $i > $i > $i).
thf(k3_relat_1_type, type, k3_relat_1: $i > $i > $i).
thf(k4_card_3_type, type, k4_card_3: $i > $i).
thf(k4_finseq_2_type, type, k4_finseq_2: $i > $i > $i).
thf(k4_msualg_1_type, type, k4_msualg_1: $i > $i > $i > $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(k4_tarski_type, type, k4_tarski: $i > $i > $i).
thf(k5_catalg_1_type, type, k5_catalg_1: $i > $i).
thf(k5_finseq_1_type, type, k5_finseq_1: $i > $i).
thf(k5_msualg_1_type, type, k5_msualg_1: $i > $i > $i > $i).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(k6_catalg_1_type, type, k6_catalg_1: $i > $i > $i).
thf(k6_finseq_2_type, type, k6_finseq_2: $i > $i > $i).
thf(k6_numbers_type, type, k6_numbers: $i).
thf(k7_catalg_1_type, type, k7_catalg_1: $i > $i > $i > $i).
thf(k7_funcop_1_type, type, k7_funcop_1: $i > $i > $i).
thf(k8_catalg_1_type, type, k8_catalg_1: $i > $i > $i).
thf(k9_catalg_1_type, type, k9_catalg_1: $i > $i > $i > $i).
thf(k9_finseq_1_type, type, k9_finseq_1: $i > $i).
thf(k9_xtuple_0_type, type, k9_xtuple_0: $i > $i).
thf(u1_msualg_1_type, type, u1_msualg_1: $i > $i).
thf(u1_struct_0_type, type, u1_struct_0: $i > $i).
thf(u2_msualg_1_type, type, u2_msualg_1: $i > $i).
thf(u3_msualg_1_type, type, u3_msualg_1: $i > $i > $i).
thf(u4_msualg_1_type, type, u4_msualg_1: $i > $i > $i).
thf(u4_struct_0_type, type, u4_struct_0: $i > $i).
thf(l1_msualg_1_type, type, l1_msualg_1: $i > $o).
thf(l1_struct_0_type, type, l1_struct_0: $i > $o).
thf(l2_msualg_1_type, type, l2_msualg_1: $i > $i > $o).
thf(l3_msualg_1_type, type, l3_msualg_1: $i > $i > $o).
thf(l5_struct_0_type, type, l5_struct_0: $i > $o).
thf(m1_catalg_1_type, type, m1_catalg_1: $i > $i > $o).
thf(m1_finseq_1_type, type, m1_finseq_1: $i > $i > $o).
thf(m1_finseq_2_type, type, m1_finseq_2: $i > $i > $o).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(m2_finseq_1_type, type, m2_finseq_1: $i > $i > $o).
thf(m2_finseq_2_type, type, m2_finseq_2: $i > $i > $i > $o).
thf(m2_pboole_type, type, m2_pboole: $i > $i > $i > $i > $o).
thf(m2_subset_1_type, type, m2_subset_1: $i > $i > $i > $o).
thf(r1_tarski_type, type, r1_tarski: $i > $i > $o).
thf(v11_struct_0_type, type, v11_struct_0: $i > $o).
thf(v13_struct_0_type, type, v13_struct_0: $i > $i > $o).
thf(v14_struct_0_type, type, v14_struct_0: $i > $o).
thf(v15_struct_0_type, type, v15_struct_0: $i > $o).
thf(v1_card_1_type, type, v1_card_1: $i > $o).
thf(v1_finseq_1_type, type, v1_finseq_1: $i > $o).
thf(v1_finset_1_type, type, v1_finset_1: $i > $o).
thf(v1_funcop_1_type, type, v1_funcop_1: $i > $o).
thf(v1_funct_1_type, type, v1_funct_1: $i > $o).
thf(v1_funct_2_type, type, v1_funct_2: $i > $i > $i > $o).
thf(v1_instalg1_type, type, v1_instalg1: $i > $o).
thf(v1_msualg_1_type, type, v1_msualg_1: $i > $o).
thf(v1_ordinal1_type, type, v1_ordinal1: $i > $o).
thf(v1_partfun1_type, type, v1_partfun1: $i > $i > $o).
thf(v1_prob_2_type, type, v1_prob_2: $i > $o).
thf(v1_relat_1_type, type, v1_relat_1: $i > $o).
thf(v1_setfam_1_type, type, v1_setfam_1: $i > $o).
thf(v1_subset_1_type, type, v1_subset_1: $i > $i > $o).
thf(v1_xboole_0_type, type, v1_xboole_0: $i > $o).
thf(v1_xtuple_0_type, type, v1_xtuple_0: $i > $o).
thf(v1_zfmisc_1_type, type, v1_zfmisc_1: $i > $o).
thf(v2_catalg_1_type, type, v2_catalg_1: $i > $o).
thf(v2_finseq_1_type, type, v2_finseq_1: $i > $o).
thf(v2_finset_1_type, type, v2_finset_1: $i > $o).
thf(v2_funcop_1_type, type, v2_funcop_1: $i > $o).
thf(v2_funct_1_type, type, v2_funct_1: $i > $o).
thf(v2_ordinal1_type, type, v2_ordinal1: $i > $o).
thf(v2_relat_1_type, type, v2_relat_1: $i > $o).
thf(v2_struct_0_type, type, v2_struct_0: $i > $o).
thf(v2_xxreal_0_type, type, v2_xxreal_0: $i > $o).
thf(v3_card_1_type, type, v3_card_1: $i > $i > $o).
thf(v3_catalg_1_type, type, v3_catalg_1: $i > $o).
thf(v3_finseq_1_type, type, v3_finseq_1: $i > $o).
thf(v3_funct_1_type, type, v3_funct_1: $i > $o).
thf(v3_msualg_1_type, type, v3_msualg_1: $i > $i > $o).
thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o).
thf(v3_relat_1_type, type, v3_relat_1: $i > $o).
thf(v4_funct_1_type, type, v4_funct_1: $i > $o).
thf(v4_relat_1_type, type, v4_relat_1: $i > $i > $o).
thf(v5_ordinal1_type, type, v5_ordinal1: $i > $o).
thf(v5_relat_1_type, type, v5_relat_1: $i > $i > $o).
thf(v6_ordinal1_type, type, v6_ordinal1: $i > $o).
thf(v7_ordinal1_type, type, v7_ordinal1: $i > $o).
thf(v7_struct_0_type, type, v7_struct_0: $i > $o).
thf(v8_struct_0_type, type, v8_struct_0: $i > $o).
thf(abstractness_v1_msualg_1, axiom,  (! [A: $i] :  ( (l1_msualg_1 @ A)  =>  ( (v1_msualg_1 @ A)  =>  ( (= @ A)  @  ( ( ( (g1_msualg_1 @  (u1_struct_0 @ A) )  @  (u4_struct_0 @ A) )  @  (u1_msualg_1 @ A) )  @  (u2_msualg_1 @ A) ) ) ) ) ) , file(msualg_1, v1_msualg_1)).
thf(abstractness_v3_msualg_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_msualg_1 @ A) )  &  ( (l3_msualg_1 @ B)  @ A) )  =>  ( ( (v3_msualg_1 @ B)  @ A)  =>  ( (= @ B)  @  ( ( (g3_msualg_1 @ A)  @  ( (u3_msualg_1 @ A)  @ B) )  @  ( (u4_msualg_1 @ A)  @ B) ) ) ) ) ) , file(msualg_1, v3_msualg_1)).
thf(antisymmetry_r2_hidden, axiom,  (! [A: $i, B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ~ ( ( (r2_hidden @ B)  @ A) ) ) ) , file(hidden, r2_hidden)).
thf(cc10_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_finseq_1 @ B) ) ) ) ) , file(finseq_1, cc10_finseq_1)).
thf(cc10_ordinal1, axiom,  (! [A: $i] :  ( (v6_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v6_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc10_ordinal1)).
thf(cc10_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ( ~ ( (v2_struct_0 @ A) )  &  (v7_struct_0 @ A) )  =>  ( (v13_struct_0 @ A)  @ np__1) ) ) ) , file(struct_0, cc10_struct_0)).
thf(cc11_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_finseq_1 @ B) ) ) ) ) , file(finseq_1, cc11_finseq_1)).
thf(cc11_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ( (v13_struct_0 @ A)  @ np__1)  =>  ( ~ ( (v2_struct_0 @ A) )  &  (v7_struct_0 @ A) ) ) ) ) , file(struct_0, cc11_struct_0)).
thf(cc12_struct_0, axiom,  (! [A: $i] :  ( (l5_struct_0 @ A)  =>  ( ~ ( (v2_struct_0 @ A) )  =>  (v14_struct_0 @ A) ) ) ) , file(struct_0, cc12_struct_0)).
thf(cc13_struct_0, axiom,  (! [A: $i] :  ( (l5_struct_0 @ A)  =>  ( (v11_struct_0 @ A)  =>  (v14_struct_0 @ A) ) ) ) , file(struct_0, cc13_struct_0)).
thf(cc14_struct_0, axiom,  (! [A: $i] :  ( (l5_struct_0 @ A)  =>  ( ( (v2_struct_0 @ A)  &  (v14_struct_0 @ A) )  =>  (v11_struct_0 @ A) ) ) ) , file(struct_0, cc14_struct_0)).
thf(cc15_struct_0, axiom,  (! [A: $i] :  ( (l5_struct_0 @ A)  =>  ( ( ~ ( (v11_struct_0 @ A) )  &  (v14_struct_0 @ A) )  =>  ~ ( (v2_struct_0 @ A) ) ) ) ) , file(struct_0, cc15_struct_0)).
thf(cc16_struct_0, axiom,  (! [A: $i] :  ( (l5_struct_0 @ A)  =>  ( (v11_struct_0 @ A)  =>  (v15_struct_0 @ A) ) ) ) , file(struct_0, cc16_struct_0)).
thf(cc17_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v7_struct_0 @ A) )  =>  ~ ( (v2_struct_0 @ A) ) ) ) ) , file(struct_0, cc17_struct_0)).
thf(cc1_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v1_finseq_1 @ A) ) ) ) , file(finseq_1, cc1_finseq_1)).
thf(cc1_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v7_ordinal1 @ B) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  ( (k4_finseq_2 @ B)  @ A) )  =>  ( (v3_card_1 @ C)  @ B) ) ) ) ) , file(finseq_2, cc1_finseq_2)).
thf(cc1_funcop_1, axiom,  (! [A: $i] :  ( (v4_funct_1 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) )  =>  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_funcop_1 @ B) ) ) ) ) ) ) , file(funcop_1, cc1_funcop_1)).
thf(cc1_funct_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_funct_1 @ A) ) ) , file(funct_1, cc1_funct_1)).
thf(cc1_funct_2, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_partfun1 @ C)  @ A)  =>  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) , file(funct_2, cc1_funct_2)).
thf(cc1_msafree1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v3_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  =>  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v1_prob_2 @ B) ) ) ) ) ) ) ) , file(msafree1, cc1_msafree1)).
thf(cc1_mssubfam, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v3_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  =>  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v2_finset_1 @ B) ) ) ) ) ) ) ) , file(mssubfam, cc1_mssubfam)).
thf(cc1_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) ) ) ) , file(ordinal1, cc1_ordinal1)).
thf(cc1_pboole, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  =>  ( (v1_relat_1 @ B)  &  ( ~ ( (v3_relat_1 @ B) )  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) ) ) , file(pboole, cc1_pboole)).
thf(cc1_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_relat_1 @ A) ) ) , file(relat_1, cc1_relat_1)).
thf(cc1_relset_1, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_relat_1 @ C) ) ) ) , file(relset_1, cc1_relset_1)).
thf(cc1_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v2_struct_0 @ A)  =>  (v7_struct_0 @ A) ) ) ) , file(struct_0, cc1_struct_0)).
thf(cc1_subset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_xboole_0 @ B) ) ) ) ) , file(subset_1, cc1_subset_1)).
thf(cc2_catalg_1, axiom,  (! [A: $i] :  ( (l1_msualg_1 @ A)  =>  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_instalg1 @ A)  &  (v2_catalg_1 @ A) ) )  =>  ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (v1_instalg1 @ A) ) ) ) ) ) , file(catalg_1, cc2_catalg_1)).
thf(cc2_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) ) ) , file(finseq_1, cc2_finseq_1)).
thf(cc2_finseq_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (v4_funct_1 @ B) ) ) ) , file(finseq_2, cc2_finseq_2)).
thf(cc2_funcop_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_funcop_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_funcop_1 @ A) ) ) ) ) , file(funcop_1, cc2_funcop_1)).
thf(cc2_funct_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_funct_1 @ A) ) ) ) ) , file(funct_1, cc2_funct_1)).
thf(cc2_funct_2, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  =>  ( (v1_partfun1 @ C)  @ A) ) ) ) ) ) , file(funct_2, cc2_funct_2)).
thf(cc2_instalg1, axiom,  (! [A: $i] :  ( (l1_msualg_1 @ A)  =>  ( ~ ( (v2_struct_0 @ A) )  =>  (v1_instalg1 @ A) ) ) ) , file(instalg1, cc2_instalg1)).
thf(cc2_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) )  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc2_ordinal1)).
thf(cc2_pboole, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v3_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  =>  ( (v1_relat_1 @ B)  &  ( ~ ( (v2_relat_1 @ B) )  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) ) ) , file(pboole, cc2_pboole)).
thf(cc2_relat_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_relat_1 @ B) ) ) ) ) , file(relat_1, cc2_relat_1)).
thf(cc2_relset_1, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v5_relat_1 @ C)  @ B) ) ) ) ) , file(relset_1, cc2_relset_1)).
thf(cc2_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v7_struct_0 @ A) )  =>  ~ ( (v2_struct_0 @ A) ) ) ) ) , file(struct_0, cc2_struct_0)).
thf(cc2_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( ~ ( ( (v1_subset_1 @ B)  @ A) )  =>  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) ) , file(subset_1, cc2_subset_1)).
thf(cc3_catalg_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_catalg_1 @ B)  @ A)  =>  (v2_catalg_1 @ B) ) ) ) , file(catalg_1, cc3_catalg_1)).
thf(cc3_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  =>  ( (v5_relat_1 @ B)  @ A) ) ) ) , file(finseq_1, cc3_finseq_1)).
thf(cc3_finseq_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (v3_finseq_1 @ B) ) ) ) , file(finseq_2, cc3_finseq_2)).
thf(cc3_funcop_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_xboole_0 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_funcop_1 @ A) ) ) ) ) , file(funcop_1, cc3_funcop_1)).
thf(cc3_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_funct_1 @ B) ) ) ) ) , file(funct_1, cc3_funct_1)).
thf(cc3_funct_2, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ B) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  =>  ( (v1_partfun1 @ C)  @ A) ) ) ) ) ) , file(funct_2, cc3_funct_2)).
thf(cc3_instalg1, axiom,  (! [A: $i] :  ( (l1_msualg_1 @ A)  =>  ( (v11_struct_0 @ A)  =>  (v1_instalg1 @ A) ) ) ) , file(instalg1, cc3_instalg1)).
thf(cc3_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc3_ordinal1)).
thf(cc3_pboole, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (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: $i] :  ( ( ( ( (m2_pboole @ D)  @ A)  @ B)  @ C)  =>  (v1_funcop_1 @ D) ) ) ) ) , file(pboole, cc3_pboole)).
thf(cc3_relat_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v3_relat_1 @ A) ) ) ) , file(relat_1, cc3_relat_1)).
thf(cc3_relset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc3_relset_1)).
thf(cc3_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v1_xboole_0 @ B)  =>  ( (v1_subset_1 @ B)  @ A) ) ) ) ) ) , file(subset_1, cc3_subset_1)).
thf(cc4_catalg_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_catalg_1 @ B)  @ A)  =>  ~ ( (v2_struct_0 @ B) ) ) ) ) ) , file(catalg_1, cc4_catalg_1)).
thf(cc4_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v1_finseq_1 @ A) ) ) ) , file(finseq_1, cc4_finseq_1)).
thf(cc4_funct_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_funct_1 @ A) ) ) ) ) , file(funct_1, cc4_funct_1)).
thf(cc4_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) )  =>  ( ( ( (v1_funct_2 @ B)  @ A)  @ A)  =>  ( (v1_partfun1 @ B)  @ A) ) ) ) ) , file(funct_2, cc4_funct_2)).
thf(cc4_instalg1, axiom,  (! [A: $i] :  ( (l1_msualg_1 @ A)  =>  ( ( (v2_struct_0 @ A)  &  (v1_instalg1 @ A) )  =>  (v11_struct_0 @ A) ) ) ) , file(instalg1, cc4_instalg1)).
thf(cc4_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v5_ordinal1 @ A) ) ) , file(ordinal1, cc4_ordinal1)).
thf(cc4_pboole, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  =>  ( (v1_relat_1 @ B)  &  ( ~ ( (v3_relat_1 @ B) )  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) ) ) , file(pboole, cc4_pboole)).
thf(cc4_relat_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v2_relat_1 @ A) ) ) ) , file(relat_1, cc4_relat_1)).
thf(cc4_relset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) )  =>  (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc4_relset_1)).
thf(cc4_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v2_struct_0 @ A)  =>  ( (v2_struct_0 @ A)  &  (v8_struct_0 @ A) ) ) ) ) , file(struct_0, cc4_struct_0)).
thf(cc4_subset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ~ ( ( (v1_subset_1 @ B)  @ A) ) ) ) ) ) , file(subset_1, cc4_subset_1)).
thf(cc5_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) ) ) ) ) , file(finseq_1, cc5_finseq_1)).
thf(cc5_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ~ ( (v3_funct_1 @ A) ) ) )  =>  ( ~ ( (v1_zfmisc_1 @ A) )  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) ) ) , file(funct_1, cc5_funct_1)).
thf(cc5_instalg1, axiom,  (! [A: $i] :  ( (l1_msualg_1 @ A)  =>  ( ( ~ ( (v11_struct_0 @ A) )  &  (v1_instalg1 @ A) )  =>  ~ ( (v2_struct_0 @ A) ) ) ) ) , file(instalg1, cc5_instalg1)).
thf(cc5_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v3_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc5_ordinal1)).
thf(cc5_pboole, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) )  =>  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) ) ) , file(pboole, cc5_pboole)).
thf(cc5_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ B) )  =>  ( (v4_relat_1 @ C)  @ A) ) ) ) ) , file(relat_1, cc5_relat_1)).
thf(cc5_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v8_struct_0 @ A) )  =>  ( ~ ( (v2_struct_0 @ A) )  &  ~ ( (v8_struct_0 @ A) ) ) ) ) ) , file(struct_0, cc5_struct_0)).
thf(cc5_subset_1, axiom,  (! [A: $i] :  ( (v1_zfmisc_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_zfmisc_1 @ B) ) ) ) ) , file(subset_1, cc5_subset_1)).
thf(cc6_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) , file(finseq_1, cc6_finseq_1)).
thf(cc6_funct_1, axiom,  (! [A: $i] :  ( ( (v1_zfmisc_1 @ A)  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_funct_1 @ A) ) ) ) ) , file(funct_1, cc6_funct_1)).
thf(cc6_ordinal1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc6_ordinal1)).
thf(cc6_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ B) )  =>  ( (v5_relat_1 @ C)  @ A) ) ) ) ) , file(relat_1, cc6_relat_1)).
thf(cc6_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v7_struct_0 @ A)  =>  (v8_struct_0 @ A) ) ) ) , file(struct_0, cc6_struct_0)).
thf(cc7_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) , file(finseq_1, cc7_finseq_1)).
thf(cc7_funct_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v4_funct_1 @ A) ) ) , file(funct_1, cc7_funct_1)).
thf(cc7_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc7_ordinal1)).
thf(cc7_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( (v1_xboole_0 @ B)  &  ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) ) ) ) ) ) ) , file(relat_1, cc7_relat_1)).
thf(cc7_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v8_struct_0 @ A) )  =>  ~ ( (v7_struct_0 @ A) ) ) ) ) , file(struct_0, cc7_struct_0)).
thf(cc8_finseq_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v3_finseq_1 @ A) ) ) , file(finseq_1, cc8_finseq_1)).
thf(cc8_funct_1, axiom,  (! [A: $i] :  ( (v4_funct_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) ) ) ) ) ) , file(funct_1, cc8_funct_1)).
thf(cc8_funct_2, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_funct_1 @ C)  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) )  =>  ( (v1_funct_1 @ C)  &  ( ~ ( (v1_xboole_0 @ C) )  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) ) ) ) , file(funct_2, cc8_funct_2)).
thf(cc8_ordinal1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc8_ordinal1)).
thf(cc8_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  =>  ( (v1_xboole_0 @ B)  &  ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) ) ) ) ) ) ) , file(relat_1, cc8_relat_1)).
thf(cc8_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v2_struct_0 @ A)  =>  ( (v13_struct_0 @ A)  @ k1_xboole_0) ) ) ) , file(struct_0, cc8_struct_0)).
thf(cc9_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (v4_funct_1 @ A) ) ) , file(finseq_1, cc9_finseq_1)).
thf(cc9_funct_1, axiom,  (! [A: $i] :  ( (v4_funct_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_funct_1 @ B) ) ) ) ) , file(funct_1, cc9_funct_1)).
thf(cc9_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_ordinal1 @ A) ) ) , file(ordinal1, cc9_ordinal1)).
thf(cc9_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ( (v13_struct_0 @ A)  @ k1_xboole_0)  =>  (v2_struct_0 @ A) ) ) ) , file(struct_0, cc9_struct_0)).
thf(commutativity_k2_tarski, axiom,  (! [A: $i, B: $i] :  ( (= @  ( (k2_tarski @ A)  @ B) )  @  ( (k2_tarski @ B)  @ A) ) ) , file(tarski, k2_tarski)).
thf(commutativity_k2_xboole_0, axiom,  (! [A: $i, B: $i] :  ( (= @  ( (k2_xboole_0 @ A)  @ B) )  @  ( (k2_xboole_0 @ B)  @ A) ) ) , file(xboole_0, k2_xboole_0)).
thf(d10_catalg_1, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( (= @  ( ( (k7_catalg_1 @ A)  @ B)  @ C) )  @  ( (k4_tarski @ np__2)  @  ( ( (k11_finseq_1 @ A)  @ B)  @ C) ) ) ) ) ) , file(catalg_1, d10_catalg_1)).
thf(d15_pboole, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v1_funct_1 @ C)  &  ( (v1_partfun1 @ C)  @ A) ) ) )  =>  (! [D: $i] :  ( ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @ A)  &  ( (v1_funct_1 @ D)  &  ( (v1_partfun1 @ D)  @ A) ) ) )  =>  ( ( ( ( (m2_pboole @ D)  @ A)  @ B)  @ C)  <=>  (! [E: $i] :  ( ( (r2_hidden @ E)  @ A)  =>  ( (v1_funct_1 @  ( (k1_funct_1 @ D)  @ E) )  &  ( ( ( (v1_funct_2 @  ( (k1_funct_1 @ D)  @ E) )  @  ( (k1_funct_1 @ B)  @ E) )  @  ( (k1_funct_1 @ C)  @ E) )  &  ( (m1_subset_1 @  ( (k1_funct_1 @ D)  @ E) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k1_funct_1 @ B)  @ E) )  @  ( (k1_funct_1 @ C)  @ E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(pboole, d15_pboole)).
thf(d18_relat_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( (v1_relat_1 @ B)  =>  ( ( (v4_relat_1 @ B)  @ A)  <=>  ( (r1_tarski @  (k9_xtuple_0 @ B) )  @ A) ) ) ) ) , file(relat_1, d18_relat_1)).
thf(d1_msualg_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u4_struct_0 @ A) )  =>  ( (= @  ( (k1_msualg_1 @ A)  @ B) )  @  ( ( ( (k3_funct_2 @  (u4_struct_0 @ A) )  @  (k3_finseq_2 @  (u1_struct_0 @ A) ) )  @  (u1_msualg_1 @ A) )  @ B) ) ) ) ) ) , file(msualg_1, d1_msualg_1)).
thf(d1_tarski, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (= @ B)  @  (k1_tarski @ A) )  <=>  (! [C: $i] :  ( ( (r2_hidden @ C)  @ B)  <=>  ( (= @ C)  @ A) ) ) ) ) ) , file(tarski, d1_tarski)).
thf(d2_funcop_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( (= @  ( (k2_funcop_1 @ A)  @ B) )  @  ( (k2_zfmisc_1 @ A)  @  (k1_tarski @ B) ) ) ) ) , file(funcop_1, d2_funcop_1)).
thf(d2_msualg_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u4_struct_0 @ A) )  =>  ( (= @  ( (k2_msualg_1 @ A)  @ B) )  @  ( ( ( (k3_funct_2 @  (u4_struct_0 @ A) )  @  (u1_struct_0 @ A) )  @  (u2_msualg_1 @ A) )  @ B) ) ) ) ) ) , file(msualg_1, d2_msualg_1)).
thf(d2_partfun1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( ( (v1_partfun1 @ B)  @ A)  <=>  ( (= @  ( (k1_relset_1 @ A)  @ B) )  @ A) ) ) ) ) , file(partfun1, d2_partfun1)).
thf(d2_xboole_0, axiom,  ( (= @ k1_xboole_0)  @  (eps @  (^ [A: $i] :  (v1_xboole_0 @ A) ) ) ) , file(xboole_0, d2_xboole_0)).
thf(d3_catalg_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_msualg_1 @ B)  &  (l1_msualg_1 @ B) )  =>  ( ( (= @ B)  @  (k2_catalg_1 @ A) )  <=>  ( ( (= @  (u1_struct_0 @ B) )  @  ( (k2_zfmisc_1 @  (k1_tarski @ k6_numbers) )  @  ( (k4_finseq_2 @ np__2)  @ A) ) )  &  ( ( (= @  (u4_struct_0 @ B) )  @  ( (k2_xboole_0 @  ( (k2_zfmisc_1 @  (k1_tarski @ np__1) )  @  ( (k4_finseq_2 @ np__1)  @ A) ) )  @  ( (k2_zfmisc_1 @  (k1_tarski @ np__2) )  @  ( (k4_finseq_2 @ np__3)  @ A) ) ) )  &  ( (! [C: $i] :  ( ( (r2_hidden @ C)  @ A)  =>  ( ( (= @  ( (k1_funct_1 @  (u1_msualg_1 @ B) )  @  ( (k4_tarski @ np__1)  @  (k9_finseq_1 @ C) ) ) )  @ k1_xboole_0)  &  ( (= @  ( (k1_funct_1 @  (u2_msualg_1 @ B) )  @  ( (k4_tarski @ np__1)  @  (k9_finseq_1 @ C) ) ) )  @  ( (k4_tarski @ k6_numbers)  @  ( (k10_finseq_1 @ C)  @ C) ) ) ) ) )  &  (! [C: $i] :  (! [D: $i] :  (! [E: $i] :  ( ( ( (r2_hidden @ C)  @ A)  &  ( ( (r2_hidden @ D)  @ A)  &  ( (r2_hidden @ E)  @ A) ) )  =>  ( ( (= @  ( (k1_funct_1 @  (u1_msualg_1 @ B) )  @  ( (k4_tarski @ np__2)  @  ( ( (k11_finseq_1 @ C)  @ D)  @ E) ) ) )  @  ( (k10_finseq_1 @  ( (k4_tarski @ k6_numbers)  @  ( (k10_finseq_1 @ D)  @ E) ) )  @  ( (k4_tarski @ k6_numbers)  @  ( (k10_finseq_1 @ C)  @ D) ) ) )  &  ( (= @  ( (k1_funct_1 @  (u2_msualg_1 @ B) )  @  ( (k4_tarski @ np__2)  @  ( ( (k11_finseq_1 @ C)  @ D)  @ E) ) ) )  @  ( (k4_tarski @ k6_numbers)  @  ( (k10_finseq_1 @ C)  @ E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(catalg_1, d3_catalg_1)).
thf(d4_msualg_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u4_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (l3_msualg_1 @ C)  @ A)  =>  ( (= @  ( ( (k3_msualg_1 @ A)  @ B)  @ C) )  @  ( (k1_funct_1 @  ( (k3_relat_1 @  (u1_msualg_1 @ A) )  @  ( (k6_finseq_2 @  (u1_struct_0 @ A) )  @  ( (u3_msualg_1 @ A)  @ C) ) ) )  @ B) ) ) ) ) ) ) ) , file(msualg_1, d4_msualg_1)).
thf(d5_finseq_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (k3_finseq_2 @ A) )  &  ( (v1_funct_1 @ C)  &  ( (v1_partfun1 @ C)  @  (k3_finseq_2 @ A) ) ) ) )  =>  ( ( (= @ C)  @  ( (k6_finseq_2 @ A)  @ B) )  <=>  (! [D: $i] :  ( ( ( (m2_finseq_2 @ D)  @ A)  @  (k3_finseq_2 @ A) )  =>  ( (= @  ( (k1_funct_1 @ C)  @ D) )  @  (k4_card_3 @  ( (k3_relat_1 @ D)  @ B) ) ) ) ) ) ) ) ) ) ) , file(finseq_2, d5_finseq_2)).
thf(d5_msualg_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u4_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (l3_msualg_1 @ C)  @ A)  =>  ( (= @  ( ( (k4_msualg_1 @ A)  @ B)  @ C) )  @  ( (k1_funct_1 @  ( (k3_relat_1 @  (u2_msualg_1 @ A) )  @  ( (u3_msualg_1 @ A)  @ C) ) )  @ B) ) ) ) ) ) ) ) , file(msualg_1, d5_msualg_1)).
thf(d5_tarski, axiom,  (! [A: $i] :  (! [B: $i] :  ( (= @  ( (k4_tarski @ A)  @ B) )  @  ( (k2_tarski @  ( (k2_tarski @ A)  @ B) )  @  (k1_tarski @ A) ) ) ) ) , file(tarski, d5_tarski)).
thf(d6_msualg_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u4_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (l3_msualg_1 @ C)  @ A)  =>  ( (= @  ( ( (k5_msualg_1 @ A)  @ B)  @ C) )  @  ( (k1_funct_1 @  ( (u4_msualg_1 @ A)  @ C) )  @ B) ) ) ) ) ) ) ) , file(msualg_1, d6_msualg_1)).
thf(d8_catalg_1, axiom,  (! [A: $i] :  ( (= @  (k5_catalg_1 @ A) )  @  ( (k4_tarski @ np__1)  @  (k9_finseq_1 @ A) ) ) ) , file(catalg_1, d8_catalg_1)).
thf(d9_catalg_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( (= @  ( (k6_catalg_1 @ A)  @ B) )  @  ( (k4_tarski @ k6_numbers)  @  ( (k10_finseq_1 @ A)  @ B) ) ) ) ) , file(catalg_1, d9_catalg_1)).
thf(d9_funcop_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( (= @  ( (k16_funcop_1 @ A)  @ B) )  @  ( (k7_funcop_1 @  (k1_tarski @ A) )  @ B) ) ) ) , file(funcop_1, d9_funcop_1)).
thf(dt_f1_s1_catalg_1, axiom,  ~ ( (v1_xboole_0 @ f1_s1_catalg_1) ) , file(catalg_1, f1_s1_catalg_1)).
thf(dt_f2_s1_catalg_1, axiom,  ~ ( (v1_xboole_0 @ f2_s1_catalg_1) ) , file(catalg_1, f2_s1_catalg_1)).
thf(dt_f3_s1_catalg_1, axiom, $true, file(catalg_1, f3_s1_catalg_1)).
thf(dt_f4_s1_catalg_1, axiom, $true, file(catalg_1, f4_s1_catalg_1)).
thf(dt_f5_s1_catalg_1, axiom, $true, file(catalg_1, f5_s1_catalg_1)).
thf(dt_g1_msualg_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ B)  @  (k3_finseq_2 @ A) )  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @  (k3_finseq_2 @ A) ) ) ) ) )  &  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ B)  @ A)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) ) ) ) )  =>  ( (v1_msualg_1 @  ( ( ( (g1_msualg_1 @ A)  @ B)  @ C)  @ D) )  &  (l1_msualg_1 @  ( ( ( (g1_msualg_1 @ A)  @ B)  @ C)  @ D) ) ) ) ) , file(msualg_1, g1_msualg_1)).
thf(dt_g3_msualg_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_msualg_1 @ A) )  &  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @  (u1_struct_0 @ A) ) ) ) )  &  ( ( ( (m2_pboole @ C)  @  (u4_struct_0 @ A) )  @  ( (k3_relat_1 @  (u1_msualg_1 @ A) )  @  ( (k6_finseq_2 @  (u1_struct_0 @ A) )  @ B) ) )  @  ( (k3_relat_1 @  (u2_msualg_1 @ A) )  @ B) ) ) )  =>  ( ( (v3_msualg_1 @  ( ( (g3_msualg_1 @ A)  @ B)  @ C) )  @ A)  &  ( (l3_msualg_1 @  ( ( (g3_msualg_1 @ A)  @ B)  @ C) )  @ A) ) ) ) , file(msualg_1, g3_msualg_1)).
thf(dt_k10_catalg_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @ A)  &  ( ( (m1_subset_1 @ C)  @ A)  &  ( (m1_subset_1 @ D)  @ A) ) ) )  =>  ( (m1_subset_1 @  ( ( ( (k10_catalg_1 @ A)  @ B)  @ C)  @ D) )  @  (u4_struct_0 @  (k3_catalg_1 @ A) ) ) ) ) , file(catalg_1, k10_catalg_1)).
thf(dt_k10_finseq_1, axiom, $true, file(finseq_1, k10_finseq_1)).
thf(dt_k10_xtuple_0, axiom, $true, file(xtuple_0, k10_xtuple_0)).
thf(dt_k11_finseq_1, axiom, $true, file(finseq_1, k11_finseq_1)).
thf(dt_k13_finseq_1, axiom, $true, file(finseq_1, k13_finseq_1)).
thf(dt_k16_funcop_1, axiom, $true, file(funcop_1, k16_funcop_1)).
thf(dt_k18_funcop_1, axiom,  (! [A: $i, B: $i] :  ( (v1_funct_1 @  ( (k18_funcop_1 @ A)  @ B) )  &  ( ( ( (v1_funct_2 @  ( (k18_funcop_1 @ A)  @ B) )  @  (k1_tarski @ A) )  @  (k1_tarski @ B) )  &  ( (m1_subset_1 @  ( (k18_funcop_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_tarski @ A) )  @  (k1_tarski @ B) ) ) ) ) ) ) , file(funcop_1, k18_funcop_1)).
thf(dt_k1_card_1, axiom,  (! [A: $i] :  (v1_card_1 @  (k1_card_1 @ A) ) ) , file(card_1, k1_card_1)).
thf(dt_k1_funct_1, axiom, $true, file(funct_1, k1_funct_1)).
thf(dt_k1_msualg_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  &  ( (m1_subset_1 @ B)  @  (u4_struct_0 @ A) ) )  =>  ( ( (m2_finseq_2 @  ( (k1_msualg_1 @ A)  @ B) )  @  (u1_struct_0 @ A) )  @  (k3_finseq_2 @  (u1_struct_0 @ A) ) ) ) ) , file(msualg_1, k1_msualg_1)).
thf(dt_k1_msualg_3, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (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) ) ) )  &  ( ( ( ( (m2_pboole @ D)  @ A)  @ B)  @ C)  &  ( (m1_subset_1 @ E)  @ A) ) ) ) )  =>  ( (v1_funct_1 @  ( ( ( ( (k1_msualg_3 @ A)  @ B)  @ C)  @ D)  @ E) )  &  ( ( ( (v1_funct_2 @  ( ( ( ( (k1_msualg_3 @ A)  @ B)  @ C)  @ D)  @ E) )  @  ( (k1_funct_1 @ B)  @ E) )  @  ( (k1_funct_1 @ C)  @ E) )  &  ( (m1_subset_1 @  ( ( ( ( (k1_msualg_3 @ A)  @ B)  @ C)  @ D)  @ E) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k1_funct_1 @ B)  @ E) )  @  ( (k1_funct_1 @ C)  @ E) ) ) ) ) ) ) ) , file(msualg_3, k1_msualg_3)).
thf(dt_k1_numbers, axiom, $true, file(numbers, k1_numbers)).
thf(dt_k1_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( (m1_subset_1 @  ( (k1_relset_1 @ A)  @ B) )  @  (k1_zfmisc_1 @ A) ) ) ) , file(relset_1, k1_relset_1)).
thf(dt_k1_tarski, axiom, $true, file(tarski, k1_tarski)).
thf(dt_k1_xboole_0, axiom, $true, file(xboole_0, k1_xboole_0)).
thf(dt_k1_xtuple_0, axiom, $true, file(xtuple_0, k1_xtuple_0)).
thf(dt_k1_zfmisc_1, axiom, $true, file(zfmisc_1, k1_zfmisc_1)).
thf(dt_k2_catalg_1, axiom,  (! [A: $i] :  ( (v1_msualg_1 @  (k2_catalg_1 @ A) )  &  (l1_msualg_1 @  (k2_catalg_1 @ A) ) ) ) , file(catalg_1, k2_catalg_1)).
thf(dt_k2_finseq_4, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @ A)  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ( (m2_finseq_1 @  ( ( (k2_finseq_4 @ A)  @ B)  @ C) )  @ A) ) ) , file(finseq_4, k2_finseq_4)).
thf(dt_k2_funcop_1, axiom, $true, file(funcop_1, k2_funcop_1)).
thf(dt_k2_msualg_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  &  ( (m1_subset_1 @ B)  @  (u4_struct_0 @ A) ) )  =>  ( (m1_subset_1 @  ( (k2_msualg_1 @ A)  @ B) )  @  (u1_struct_0 @ A) ) ) ) , file(msualg_1, k2_msualg_1)).
thf(dt_k2_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  =>  ( (m1_subset_1 @  ( (k2_relset_1 @ A)  @ B) )  @  (k1_zfmisc_1 @ A) ) ) ) , file(relset_1, k2_relset_1)).
thf(dt_k2_tarski, axiom, $true, file(tarski, k2_tarski)).
thf(dt_k2_xboole_0, axiom, $true, file(xboole_0, k2_xboole_0)).
thf(dt_k2_xtuple_0, axiom, $true, file(xtuple_0, k2_xtuple_0)).
thf(dt_k2_zfmisc_1, axiom, $true, file(zfmisc_1, k2_zfmisc_1)).
thf(dt_k3_catalg_1, axiom,  (! [A: $i] :  ( (v1_msualg_1 @  (k3_catalg_1 @ A) )  &  ( (m1_catalg_1 @  (k3_catalg_1 @ A) )  @ A) ) ) , file(catalg_1, k3_catalg_1)).
thf(dt_k3_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( ( (m2_subset_1 @  (k3_finseq_1 @ A) )  @ k1_numbers)  @ k5_numbers) ) ) , file(finseq_1, k3_finseq_1)).
thf(dt_k3_finseq_2, axiom,  (! [A: $i] :  ( (m1_finseq_2 @  (k3_finseq_2 @ A) )  @ A) ) , file(finseq_2, k3_finseq_2)).
thf(dt_k3_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (m1_subset_1 @ D)  @ A) ) )  =>  ( (m1_subset_1 @  ( ( ( (k3_funct_2 @ A)  @ B)  @ C)  @ D) )  @ B) ) ) , file(funct_2, k3_funct_2)).
thf(dt_k3_msualg_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  &  ( ( (m1_subset_1 @ B)  @  (u4_struct_0 @ A) )  &  ( (l3_msualg_1 @ C)  @ A) ) )  =>  ( (m1_subset_1 @  ( ( (k3_msualg_1 @ A)  @ B)  @ C) )  @  (k10_xtuple_0 @  ( (k6_finseq_2 @  (u1_struct_0 @ A) )  @  ( (u3_msualg_1 @ A)  @ C) ) ) ) ) ) , file(msualg_1, k3_msualg_1)).
thf(dt_k3_relat_1, axiom,  (! [A: $i, B: $i] :  (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) ) ) , file(relat_1, k3_relat_1)).
thf(dt_k4_card_3, axiom, $true, file(card_3, k4_card_3)).
thf(dt_k4_finseq_2, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ A)  =>  ( (m1_finseq_2 @  ( (k4_finseq_2 @ A)  @ B) )  @ B) ) ) , file(finseq_2, k4_finseq_2)).
thf(dt_k4_msualg_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  &  ( ( (m1_subset_1 @ B)  @  (u4_struct_0 @ A) )  &  ( (l3_msualg_1 @ C)  @ A) ) )  =>  ( (m1_subset_1 @  ( ( (k4_msualg_1 @ A)  @ B)  @ C) )  @  (k10_xtuple_0 @  ( (u3_msualg_1 @ A)  @ C) ) ) ) ) , file(msualg_1, k4_msualg_1)).
thf(dt_k4_ordinal1, axiom, $true, file(ordinal1, k4_ordinal1)).
thf(dt_k4_tarski, axiom, $true, file(tarski, k4_tarski)).
thf(dt_k5_catalg_1, axiom, $true, file(catalg_1, k5_catalg_1)).
thf(dt_k5_finseq_1, axiom, $true, file(finseq_1, k5_finseq_1)).
thf(dt_k5_msualg_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  &  ( ( (m1_subset_1 @ B)  @  (u4_struct_0 @ A) )  &  ( (l3_msualg_1 @ C)  @ A) ) )  =>  ( (v1_funct_1 @  ( ( (k5_msualg_1 @ A)  @ B)  @ C) )  &  ( ( ( (v1_funct_2 @  ( ( (k5_msualg_1 @ A)  @ B)  @ C) )  @  ( ( (k3_msualg_1 @ A)  @ B)  @ C) )  @  ( ( (k4_msualg_1 @ A)  @ B)  @ C) )  &  ( (m1_subset_1 @  ( ( (k5_msualg_1 @ A)  @ B)  @ C) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( ( (k3_msualg_1 @ A)  @ B)  @ C) )  @  ( ( (k4_msualg_1 @ A)  @ B)  @ C) ) ) ) ) ) ) ) , file(msualg_1, k5_msualg_1)).
thf(dt_k5_numbers, axiom,  ( (m1_subset_1 @ k5_numbers)  @  (k1_zfmisc_1 @ k1_numbers) ) , file(numbers, k5_numbers)).
thf(dt_k6_catalg_1, axiom, $true, file(catalg_1, k6_catalg_1)).
thf(dt_k6_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) )  =>  ( (v1_relat_1 @  ( (k6_finseq_2 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (k6_finseq_2 @ A)  @ B) )  @  (k3_finseq_2 @ A) )  &  ( (v1_funct_1 @  ( (k6_finseq_2 @ A)  @ B) )  &  ( (v1_partfun1 @  ( (k6_finseq_2 @ A)  @ B) )  @  (k3_finseq_2 @ A) ) ) ) ) ) ) , file(finseq_2, k6_finseq_2)).
thf(dt_k6_numbers, axiom,  ( ( (m2_subset_1 @ k6_numbers)  @ k1_numbers)  @ k5_numbers) , file(numbers, k6_numbers)).
thf(dt_k7_catalg_1, axiom, $true, file(catalg_1, k7_catalg_1)).
thf(dt_k7_funcop_1, axiom,  (! [A: $i, B: $i] :  ( (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) ) ) ) ) ) ) , file(funcop_1, k7_funcop_1)).
thf(dt_k8_catalg_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ B)  @ A) )  =>  ( (m1_subset_1 @  ( (k8_catalg_1 @ A)  @ B) )  @  (u4_struct_0 @  (k3_catalg_1 @ A) ) ) ) ) , file(catalg_1, k8_catalg_1)).
thf(dt_k9_catalg_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @ A)  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ( (m1_subset_1 @  ( ( (k9_catalg_1 @ A)  @ B)  @ C) )  @  (u1_struct_0 @  (k3_catalg_1 @ A) ) ) ) ) , file(catalg_1, k9_catalg_1)).
thf(dt_k9_finseq_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @  (k9_finseq_1 @ A) )  &  (v1_funct_1 @  (k9_finseq_1 @ A) ) ) ) , file(finseq_1, k9_finseq_1)).
thf(dt_k9_xtuple_0, axiom, $true, file(xtuple_0, k9_xtuple_0)).
thf(dt_l1_msualg_1, axiom,  (! [A: $i] :  ( (l1_msualg_1 @ A)  =>  (l5_struct_0 @ A) ) ) , file(msualg_1, l1_msualg_1)).
thf(dt_l1_struct_0, axiom, $true, file(struct_0, l1_struct_0)).
thf(dt_l2_msualg_1, axiom, $true, file(msualg_1, l2_msualg_1)).
thf(dt_l3_msualg_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_msualg_1 @ A) )  =>  (! [B: $i] :  ( ( (l3_msualg_1 @ B)  @ A)  =>  ( (l2_msualg_1 @ B)  @ A) ) ) ) ) , file(msualg_1, l3_msualg_1)).
thf(dt_l5_struct_0, axiom,  (! [A: $i] :  ( (l5_struct_0 @ A)  =>  (l1_struct_0 @ A) ) ) , file(struct_0, l5_struct_0)).
thf(dt_m1_catalg_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_catalg_1 @ B)  @ A)  =>  ( (v1_instalg1 @ B)  &  (l1_msualg_1 @ B) ) ) ) ) , file(catalg_1, m1_catalg_1)).
thf(dt_m1_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  =>  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) ) ) ) ) , file(finseq_1, m1_finseq_1)).
thf(dt_m1_finseq_2, axiom, $true, file(finseq_2, m1_finseq_2)).
thf(dt_m1_subset_1, axiom, $true, file(subset_1, m1_subset_1)).
thf(dt_m2_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @ A)  =>  ( (v1_funct_1 @ B)  &  ( (v1_finseq_1 @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ A) ) ) ) ) ) ) ) , file(finseq_1, m2_finseq_1)).
thf(dt_m2_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (! [C: $i] :  ( ( ( (m2_finseq_2 @ C)  @ A)  @ B)  =>  ( (m2_finseq_1 @ C)  @ A) ) ) ) ) , file(finseq_2, m2_finseq_2)).
thf(dt_m2_pboole, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (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: $i] :  ( ( ( ( (m2_pboole @ D)  @ A)  @ B)  @ C)  =>  ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @ A)  &  ( (v1_funct_1 @ D)  &  ( (v1_partfun1 @ D)  @ A) ) ) ) ) ) ) ) , file(pboole, m2_pboole)).
thf(dt_m2_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) ) ) )  =>  (! [C: $i] :  ( ( ( (m2_subset_1 @ C)  @ A)  @ B)  =>  ( (m1_subset_1 @ C)  @ A) ) ) ) ) , file(subset_1, m2_subset_1)).
thf(dt_u1_msualg_1, axiom,  (! [A: $i] :  ( (l1_msualg_1 @ A)  =>  ( (v1_funct_1 @  (u1_msualg_1 @ A) )  &  ( ( ( (v1_funct_2 @  (u1_msualg_1 @ A) )  @  (u4_struct_0 @ A) )  @  (k3_finseq_2 @  (u1_struct_0 @ A) ) )  &  ( (m1_subset_1 @  (u1_msualg_1 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u4_struct_0 @ A) )  @  (k3_finseq_2 @  (u1_struct_0 @ A) ) ) ) ) ) ) ) ) , file(msualg_1, u1_msualg_1)).
thf(dt_u1_struct_0, axiom, $true, file(struct_0, u1_struct_0)).
thf(dt_u2_msualg_1, axiom,  (! [A: $i] :  ( (l1_msualg_1 @ A)  =>  ( (v1_funct_1 @  (u2_msualg_1 @ A) )  &  ( ( ( (v1_funct_2 @  (u2_msualg_1 @ A) )  @  (u4_struct_0 @ A) )  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @  (u2_msualg_1 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u4_struct_0 @ A) )  @  (u1_struct_0 @ A) ) ) ) ) ) ) ) , file(msualg_1, u2_msualg_1)).
thf(dt_u3_msualg_1, axiom,  (! [A: $i, B: $i] :  ( ( (l1_struct_0 @ A)  &  ( (l2_msualg_1 @ B)  @ A) )  =>  ( (v1_relat_1 @  ( (u3_msualg_1 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (u3_msualg_1 @ A)  @ B) )  @  (u1_struct_0 @ A) )  &  ( (v1_funct_1 @  ( (u3_msualg_1 @ A)  @ B) )  &  ( (v1_partfun1 @  ( (u3_msualg_1 @ A)  @ B) )  @  (u1_struct_0 @ A) ) ) ) ) ) ) , file(msualg_1, u3_msualg_1)).
thf(dt_u4_msualg_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_msualg_1 @ A) )  &  ( (l3_msualg_1 @ B)  @ A) )  =>  ( ( ( (m2_pboole @  ( (u4_msualg_1 @ A)  @ B) )  @  (u4_struct_0 @ A) )  @  ( (k3_relat_1 @  (u1_msualg_1 @ A) )  @  ( (k6_finseq_2 @  (u1_struct_0 @ A) )  @  ( (u3_msualg_1 @ A)  @ B) ) ) )  @  ( (k3_relat_1 @  (u2_msualg_1 @ A) )  @  ( (u3_msualg_1 @ A)  @ B) ) ) ) ) , file(msualg_1, u4_msualg_1)).
thf(dt_u4_struct_0, axiom, $true, file(struct_0, u4_struct_0)).
thf(existence_l1_msualg_1, axiom,  (? [A: $i] :  (l1_msualg_1 @ A) ) , file(msualg_1, l1_msualg_1)).
thf(existence_l1_struct_0, axiom,  (? [A: $i] :  (l1_struct_0 @ A) ) , file(struct_0, l1_struct_0)).
thf(existence_l2_msualg_1, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  (? [B: $i] :  ( (l2_msualg_1 @ B)  @ A) ) ) ) , file(msualg_1, l2_msualg_1)).
thf(existence_l3_msualg_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_msualg_1 @ A) )  =>  (? [B: $i] :  ( (l3_msualg_1 @ B)  @ A) ) ) ) , file(msualg_1, l3_msualg_1)).
thf(existence_l5_struct_0, axiom,  (? [A: $i] :  (l5_struct_0 @ A) ) , file(struct_0, l5_struct_0)).
thf(existence_m1_catalg_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_catalg_1 @ B)  @ A) ) ) , file(catalg_1, m1_catalg_1)).
thf(existence_m1_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_finseq_1 @ B)  @ A) ) ) , file(finseq_1, m1_finseq_1)).
thf(existence_m1_finseq_2, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_finseq_2 @ B)  @ A) ) ) , file(finseq_2, m1_finseq_2)).
thf(existence_m1_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_subset_1 @ B)  @ A) ) ) , file(subset_1, m1_subset_1)).
thf(existence_m2_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m2_finseq_1 @ B)  @ A) ) ) , file(finseq_1, m2_finseq_1)).
thf(existence_m2_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (? [C: $i] :  ( ( (m2_finseq_2 @ C)  @ A)  @ B) ) ) ) , file(finseq_2, m2_finseq_2)).
thf(existence_m2_pboole, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (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: $i] :  ( ( ( (m2_pboole @ D)  @ A)  @ B)  @ C) ) ) ) , file(pboole, m2_pboole)).
thf(existence_m2_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) ) ) )  =>  (? [C: $i] :  ( ( (m2_subset_1 @ C)  @ A)  @ B) ) ) ) , file(subset_1, m2_subset_1)).
thf(fc10_catalg_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v11_struct_0 @ A) )  &  ( (v3_catalg_1 @ A)  &  (l1_msualg_1 @ A) ) )  &  ( (m1_subset_1 @ B)  @  (u4_struct_0 @ A) ) )  =>  (v1_finseq_1 @  (k2_xtuple_0 @ B) ) ) ) , file(catalg_1, fc10_catalg_1)).
thf(fc10_finseq_1, axiom,  (! [A: $i, B: $i] :  (v1_finseq_1 @  ( (k10_finseq_1 @ A)  @ B) ) ) , file(finseq_1, fc10_finseq_1)).
thf(fc10_funcop_1, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ B) )  =>  (v2_relat_1 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(funcop_1, fc10_funcop_1)).
thf(fc10_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  (v1_setfam_1 @  (k10_xtuple_0 @ A) ) ) ) , file(funct_1, fc10_funct_1)).
thf(fc10_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_xboole_0 @  (k9_xtuple_0 @ A) ) ) ) , file(relat_1, fc10_relat_1)).
thf(fc10_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) , file(subset_1, fc10_subset_1)).
thf(fc11_finseq_1, axiom,  (! [A: $i, B: $i, C: $i] :  (v1_finseq_1 @  ( ( (k11_finseq_1 @ A)  @ B)  @ C) ) ) , file(finseq_1, fc11_finseq_1)).
thf(fc11_funcop_1, axiom,  (! [A: $i, B: $i] :  ( (v1_relat_1 @  ( (k16_funcop_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k16_funcop_1 @ A)  @ B) ) ) ) , file(funcop_1, fc11_funcop_1)).
thf(fc11_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) )  &  ( (m1_subset_1 @ B)  @  (k9_xtuple_0 @ A) ) )  =>  ~ ( (v1_xboole_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) ) , file(funct_1, fc11_funct_1)).
thf(fc11_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_xboole_0 @  (k10_xtuple_0 @ A) ) ) ) , file(relat_1, fc11_relat_1)).
thf(fc12_finseq_1, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k13_finseq_1 @ A) ) ) ) , file(finseq_1, fc12_finseq_1)).
thf(fc12_funcop_1, axiom,  (! [A: $i, B: $i] :  (v2_funct_1 @  ( (k16_funcop_1 @ A)  @ B) ) ) , file(funcop_1, fc12_funcop_1)).
thf(fc12_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_funct_1 @ A) ) )  =>  (v1_zfmisc_1 @  (k10_xtuple_0 @ A) ) ) ) , file(funct_1, fc12_funct_1)).
thf(fc12_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ B) )  =>  ( (v1_xboole_0 @  ( (k3_relat_1 @ A)  @ B) )  &  (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(relat_1, fc12_relat_1)).
thf(fc13_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ~ ( (v3_funct_1 @ A) ) ) )  =>  ~ ( (v1_zfmisc_1 @  (k10_xtuple_0 @ A) ) ) ) ) , file(funct_1, fc13_funct_1)).
thf(fc13_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ B) )  =>  ( (v1_xboole_0 @  ( (k3_relat_1 @ B)  @ A) )  &  (v1_relat_1 @  ( (k3_relat_1 @ B)  @ A) ) ) ) ) , file(relat_1, fc13_relat_1)).
thf(fc13_struct_0, axiom,  (! [A: $i] :  ( ( (v11_struct_0 @ A)  &  (l5_struct_0 @ A) )  =>  (v1_xboole_0 @  (u4_struct_0 @ A) ) ) ) , file(struct_0, fc13_struct_0)).
thf(fc14_funcop_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) )  =>  (v1_funcop_1 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(funcop_1, fc14_funcop_1)).
thf(fc14_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (v4_funct_1 @  (k1_tarski @ A) ) ) ) , file(funct_1, fc14_funct_1)).
thf(fc14_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v11_struct_0 @ A) )  &  (l5_struct_0 @ A) )  =>  ~ ( (v1_xboole_0 @  (u4_struct_0 @ A) ) ) ) ) , file(struct_0, fc14_struct_0)).
thf(fc15_funcop_1, axiom,  (! [A: $i, B: $i] :  (v3_funct_1 @  ( (k2_funcop_1 @ A)  @ B) ) ) , file(funcop_1, fc15_funcop_1)).
thf(fc15_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) ) )  =>  (v4_funct_1 @  ( (k2_tarski @ A)  @ B) ) ) ) , file(funct_1, fc15_funct_1)).
thf(fc15_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (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) ) ) ) ) , file(relat_1, fc15_relat_1)).
thf(fc16_finseq_1, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k5_finseq_1 @ A) ) ) ) , file(finseq_1, fc16_finseq_1)).
thf(fc17_funcop_1, axiom,  (! [A: $i, B: $i] :  ( (v4_relat_1 @  ( (k2_funcop_1 @ A)  @ B) )  @ A) ) , file(funcop_1, fc17_funcop_1)).
thf(fc17_funct_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (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) ) ) ) ) , file(funct_1, fc17_funct_1)).
thf(fc18_funcop_1, axiom,  (! [A: $i, B: $i] :  ( (v4_relat_1 @  ( (k16_funcop_1 @ A)  @ B) )  @  (k1_tarski @ A) ) ) , file(funcop_1, fc18_funcop_1)).
thf(fc18_funct_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_zfmisc_1 @ A) )  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ~ ( (v1_zfmisc_1 @  (k9_xtuple_0 @ A) ) ) ) ) , file(funct_1, fc18_funct_1)).
thf(fc19_finseq_1, axiom,  (! [A: $i, B: $i] :  ~ ( (v1_xboole_0 @  ( (k10_finseq_1 @ A)  @ B) ) ) ) , file(finseq_1, fc19_finseq_1)).
thf(fc19_funcop_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) )  =>  (v1_funcop_1 @  ( (k16_funcop_1 @ A)  @ B) ) ) ) , file(funcop_1, fc19_funcop_1)).
thf(fc19_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v3_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  (v1_xboole_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(funct_1, fc19_funct_1)).
thf(fc19_struct_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_card_1 @ A)  &  ( ( (v13_struct_0 @ B)  @ A)  &  (l1_struct_0 @ B) ) )  =>  ( (v3_card_1 @  (u1_struct_0 @ B) )  @ A) ) ) , file(struct_0, fc19_struct_0)).
thf(fc1_funcop_1, axiom,  (! [A: $i, B: $i] :  ( (v1_relat_1 @  ( (k2_funcop_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(funcop_1, fc1_funcop_1)).
thf(fc1_funct_1, axiom,  (! [A: $i, B: $i] :  (v1_funct_1 @  (k1_tarski @  ( (k4_tarski @ A)  @ B) ) ) ) , file(funct_1, fc1_funct_1)).
thf(fc1_msafree1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  =>  ~ ( (v1_xboole_0 @  (k10_xtuple_0 @ B) ) ) ) ) , file(msafree1, fc1_msafree1)).
thf(fc1_pboole, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @ B)  &  ( (v1_funct_1 @ D)  &  ( (v1_partfun1 @ D)  @ B) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ C)  @ D) )  &  ( ( (v4_relat_1 @  ( (k3_relat_1 @ C)  @ D) )  @ A)  &  ( (v1_funct_1 @  ( (k3_relat_1 @ C)  @ D) )  &  ( (v1_partfun1 @  ( (k3_relat_1 @ C)  @ D) )  @ A) ) ) ) ) ) , file(pboole, fc1_pboole)).
thf(fc1_relset_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  &  ( (v1_relat_1 @ C)  &  ( (v4_relat_1 @ C)  @ A) ) )  =>  ( (v4_relat_1 @  ( (k2_xboole_0 @ B)  @ C) )  @ A) ) ) , file(relset_1, fc1_relset_1)).
thf(fc1_struct_0, axiom,  (! [A: $i] :  ( ( (v2_struct_0 @ A)  &  (l1_struct_0 @ A) )  =>  (v1_xboole_0 @  (u1_struct_0 @ A) ) ) ) , file(struct_0, fc1_struct_0)).
thf(fc1_subset_1, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k1_zfmisc_1 @ A) ) ) ) , file(subset_1, fc1_subset_1)).
thf(fc1_xboole_0, axiom,  (v1_xboole_0 @ k1_xboole_0) , file(xboole_0, fc1_xboole_0)).
thf(fc1_xtuple_0, axiom,  (! [A: $i, B: $i] :  (v1_xtuple_0 @  ( (k4_tarski @ A)  @ B) ) ) , file(xtuple_0, fc1_xtuple_0)).
thf(fc20_finseq_1, axiom,  (! [A: $i, B: $i, C: $i] :  ~ ( (v1_xboole_0 @  ( ( (k11_finseq_1 @ A)  @ B)  @ C) ) ) ) , file(finseq_1, fc20_finseq_1)).
thf(fc20_funcop_1, axiom,  (! [A: $i, B: $i] :  ( (v1_relat_1 @  ( (k2_funcop_1 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (k2_funcop_1 @ A)  @ B) )  @ A)  &  ( (v1_funct_1 @  ( (k2_funcop_1 @ A)  @ B) )  &  ( (v1_partfun1 @  ( (k2_funcop_1 @ A)  @ B) )  @ A) ) ) ) ) , file(funcop_1, fc20_funcop_1)).
thf(fc20_struct_0, axiom,  (! [A: $i] :  ( ( (v15_struct_0 @ A)  &  (l5_struct_0 @ A) )  =>  (v1_zfmisc_1 @  (u4_struct_0 @ A) ) ) ) , file(struct_0, fc20_struct_0)).
thf(fc21_funcop_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ C)  @ A) )  =>  ( (v5_relat_1 @  ( (k16_funcop_1 @ B)  @ C) )  @ A) ) ) , file(funcop_1, fc21_funcop_1)).
thf(fc21_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v15_struct_0 @ A) )  &  (l5_struct_0 @ A) )  =>  ~ ( (v1_zfmisc_1 @  (u4_struct_0 @ A) ) ) ) ) , file(struct_0, fc21_struct_0)).
thf(fc22_finseq_1, axiom,  (! [A: $i] :  (v4_funct_1 @  (k13_finseq_1 @ A) ) ) , file(finseq_1, fc22_finseq_1)).
thf(fc22_funcop_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ C)  @ B) )  =>  ( (v5_relat_1 @  ( (k2_funcop_1 @ A)  @ C) )  @ B) ) ) , file(funcop_1, fc22_funcop_1)).
thf(fc23_funcop_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ B)  @ A) )  =>  ( (v4_relat_1 @  ( (k16_funcop_1 @ B)  @ C) )  @ A) ) ) , file(funcop_1, fc23_funcop_1)).
thf(fc24_finseq_1, axiom,  (! [A: $i] :  ( (v3_card_1 @  (k5_finseq_1 @ A) )  @ np__1) ) , file(finseq_1, fc24_finseq_1)).
thf(fc24_relat_1, axiom,  (! [A: $i] :  ( ( (v1_zfmisc_1 @ A)  &  (v1_relat_1 @ A) )  =>  (v1_zfmisc_1 @  (k9_xtuple_0 @ A) ) ) ) , file(relat_1, fc24_relat_1)).
thf(fc25_finseq_1, axiom,  (! [A: $i, B: $i] :  ( (v3_card_1 @  ( (k10_finseq_1 @ A)  @ B) )  @ np__2) ) , file(finseq_1, fc25_finseq_1)).
thf(fc25_relat_1, axiom,  (! [A: $i] :  ( ( (v1_zfmisc_1 @ A)  &  (v1_relat_1 @ A) )  =>  (v1_zfmisc_1 @  (k10_xtuple_0 @ A) ) ) ) , file(relat_1, fc25_relat_1)).
thf(fc26_finseq_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( (v3_card_1 @  ( ( (k11_finseq_1 @ A)  @ B)  @ C) )  @ np__3) ) , file(finseq_1, fc26_finseq_1)).
thf(fc27_finseq_1, axiom,  (! [A: $i] :  (v3_finseq_1 @  (k13_finseq_1 @ A) ) ) , file(finseq_1, fc27_finseq_1)).
thf(fc29_finseq_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v3_finseq_1 @ A)  &  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) ) )  =>  (v1_finseq_1 @  ( (k1_funct_1 @ B)  @ C) ) ) ) , file(finseq_1, fc29_finseq_1)).
thf(fc29_relat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (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) ) ) ) , file(relat_1, fc29_relat_1)).
thf(fc2_catalg_1, axiom,  (! [A: $i] :  ( (v1_msualg_1 @  (k2_catalg_1 @ A) )  &  (v1_instalg1 @  (k2_catalg_1 @ A) ) ) ) , file(catalg_1, fc2_catalg_1)).
thf(fc2_funcop_1, axiom,  (! [A: $i] :  (v1_xboole_0 @  ( (k2_funcop_1 @ k1_xboole_0)  @ A) ) ) , file(funcop_1, fc2_funcop_1)).
thf(fc2_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (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) ) ) ) ) , file(funct_1, fc2_funct_1)).
thf(fc2_pboole, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ~ ( (v1_xboole_0 @  ( (k1_funct_1 @ B)  @ C) ) ) ) ) , file(pboole, fc2_pboole)).
thf(fc2_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  ~ ( (v1_xboole_0 @  (u1_struct_0 @ A) ) ) ) ) , file(struct_0, fc2_struct_0)).
thf(fc2_xboole_0, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k1_tarski @ A) ) ) ) , file(xboole_0, fc2_xboole_0)).
thf(fc30_relat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (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) ) ) ) , file(relat_1, fc30_relat_1)).
thf(fc3_catalg_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  ( ~ ( (v2_struct_0 @  (k2_catalg_1 @ A) ) )  &  ( ~ ( (v11_struct_0 @  (k2_catalg_1 @ A) ) )  &  (v1_msualg_1 @  (k2_catalg_1 @ A) ) ) ) ) ) , file(catalg_1, fc3_catalg_1)).
thf(fc3_funcop_1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ B)  =>  (v1_xboole_0 @  ( (k2_funcop_1 @ B)  @ A) ) ) ) , file(funcop_1, fc3_funcop_1)).
thf(fc3_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_relat_1 @ B) )  =>  (v1_relat_1 @  ( (k2_xboole_0 @ A)  @ B) ) ) ) , file(relat_1, fc3_relat_1)).
thf(fc3_xboole_0, axiom,  (! [A: $i, B: $i] :  ~ ( (v1_xboole_0 @  ( (k2_tarski @ A)  @ B) ) ) ) , file(xboole_0, fc3_xboole_0)).
thf(fc4_catalg_1, axiom,  (! [A: $i] :  ( (v1_msualg_1 @  (k2_catalg_1 @ A) )  &  (v3_catalg_1 @  (k2_catalg_1 @ A) ) ) ) , file(catalg_1, fc4_catalg_1)).
thf(fc4_funcop_1, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ B) )  =>  ~ ( (v1_xboole_0 @  ( (k2_funcop_1 @ B)  @ A) ) ) ) ) , file(funcop_1, fc4_funcop_1)).
thf(fc4_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ A)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ D)  @ C) )  &  ( ( (v1_funct_2 @  ( (k3_relat_1 @ D)  @ C) )  @ A)  @ B) ) ) ) , file(funct_2, fc4_funct_2)).
thf(fc4_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v5_ordinal1 @ A) ) )  =>  (v3_ordinal1 @  (k9_xtuple_0 @ A) ) ) ) , file(ordinal1, fc4_ordinal1)).
thf(fc4_relset_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  &  ( (v1_relat_1 @ C)  &  ( (v5_relat_1 @ C)  @ A) ) )  =>  ( (v5_relat_1 @  ( (k2_xboole_0 @ B)  @ C) )  @ A) ) ) , file(relset_1, fc4_relset_1)).
thf(fc4_xboole_0, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  ~ ( (v1_xboole_0 @  ( (k2_xboole_0 @ A)  @ B) ) ) ) ) , file(xboole_0, fc4_xboole_0)).
thf(fc4_xtuple_0, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_xboole_0 @  (k9_xtuple_0 @ A) ) ) ) , file(xtuple_0, fc4_xtuple_0)).
thf(fc5_catalg_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_instalg1 @ A)  &  ( (v2_catalg_1 @ A)  &  (l1_msualg_1 @ A) ) ) )  &  ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) ) )  =>  ( (v1_relat_1 @  (k2_xtuple_0 @ B) )  &  (v1_funct_1 @  (k2_xtuple_0 @ B) ) ) ) ) , file(catalg_1, fc5_catalg_1)).
thf(fc5_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (k4_finseq_2 @ A)  @ B) ) ) ) ) , file(finseq_2, fc5_finseq_2)).
thf(fc5_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ B)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ B) ) ) ) )  &  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ D)  @ C) )  &  ( ( (v1_funct_2 @  ( (k3_relat_1 @ D)  @ C) )  @ A)  @ B) ) ) ) , file(funct_2, fc5_funct_2)).
thf(fc5_relat_1, axiom,  (! [A: $i, B: $i] :  (v1_relat_1 @  (k1_tarski @  ( (k4_tarski @ A)  @ B) ) ) ) , file(relat_1, fc5_relat_1)).
thf(fc5_xboole_0, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  ~ ( (v1_xboole_0 @  ( (k2_xboole_0 @ B)  @ A) ) ) ) ) , file(xboole_0, fc5_xboole_0)).
thf(fc5_xtuple_0, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_xboole_0 @  (k10_xtuple_0 @ A) ) ) ) , file(xtuple_0, fc5_xtuple_0)).
thf(fc6_catalg_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v3_catalg_1 @ A)  &  (l1_msualg_1 @ A) ) )  &  ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) ) )  =>  ( (v1_relat_1 @  (k2_xtuple_0 @ B) )  &  (v1_funct_1 @  (k2_xtuple_0 @ B) ) ) ) ) , file(catalg_1, fc6_catalg_1)).
thf(fc6_finseq_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @  (k5_finseq_1 @ A) )  &  (v1_funct_1 @  (k5_finseq_1 @ A) ) ) ) , file(finseq_1, fc6_finseq_1)).
thf(fc6_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  =>  ( (v1_relat_1 @  ( (k6_finseq_2 @ A)  @ B) )  &  ( (v2_relat_1 @  ( (k6_finseq_2 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (k6_finseq_2 @ A)  @ B) )  @  (k3_finseq_2 @ A) )  &  ( (v1_funct_1 @  ( (k6_finseq_2 @ A)  @ B) )  &  ( (v1_partfun1 @  ( (k6_finseq_2 @ A)  @ B) )  @  (k3_finseq_2 @ A) ) ) ) ) ) ) ) , file(finseq_2, fc6_finseq_2)).
thf(fc6_ordinal1, axiom,  ( ~ ( (v1_xboole_0 @ k4_ordinal1) )  &  (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1)).
thf(fc6_relat_1, axiom,  (! [A: $i, B: $i] :  (v1_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) , file(relat_1, fc6_relat_1)).
thf(fc6_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v7_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  ~ ( (v1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) ) , file(struct_0, fc6_struct_0)).
thf(fc7_catalg_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v11_struct_0 @ A) )  &  ( (v3_catalg_1 @ A)  &  (l1_msualg_1 @ A) ) )  &  ( (m1_subset_1 @ B)  @  (u4_struct_0 @ A) ) )  =>  ( (v1_relat_1 @  (k2_xtuple_0 @ B) )  &  (v1_funct_1 @  (k2_xtuple_0 @ B) ) ) ) ) , file(catalg_1, fc7_catalg_1)).
thf(fc7_finseq_1, axiom,  (! [A: $i] :  (v1_finseq_1 @  (k5_finseq_1 @ A) ) ) , file(finseq_1, fc7_finseq_1)).
thf(fc7_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (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) ) ) ) ) , file(funct_1, fc7_funct_1)).
thf(fc7_relat_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  (v1_relat_1 @  ( (k2_tarski @  ( (k4_tarski @ A)  @ B) )  @  ( (k4_tarski @ C)  @ D) ) ) ) , file(relat_1, fc7_relat_1)).
thf(fc7_struct_0, axiom,  (! [A: $i] :  ( ( (v7_struct_0 @ A)  &  (l1_struct_0 @ A) )  =>  (v1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) , file(struct_0, fc7_struct_0)).
thf(fc8_catalg_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_instalg1 @ A)  &  ( (v2_catalg_1 @ A)  &  (l1_msualg_1 @ A) ) ) )  &  ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) ) )  =>  (v1_finseq_1 @  (k2_xtuple_0 @ B) ) ) ) , file(catalg_1, fc8_catalg_1)).
thf(fc8_finseq_1, axiom,  (! [A: $i, B: $i] :  ( (v1_relat_1 @  ( (k10_finseq_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k10_finseq_1 @ A)  @ B) ) ) ) , file(finseq_1, fc8_finseq_1)).
thf(fc8_funcop_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_funcop_1 @ A) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) ) , file(funcop_1, fc8_funcop_1)).
thf(fc8_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ B)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ C) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ D)  @ E) )  &  ( ( (v1_funct_2 @  ( (k3_relat_1 @ D)  @ E) )  @ A)  @ C) ) ) ) , file(funct_2, fc8_funct_2)).
thf(fc8_relat_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_relat_1 @ A) )  =>  ~ ( (v1_xboole_0 @  (k9_xtuple_0 @ A) ) ) ) ) , file(relat_1, fc8_relat_1)).
thf(fc8_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ C) ) )  =>  (v1_relat_1 @  (k9_xtuple_0 @ D) ) ) ) , file(relset_1, fc8_relset_1)).
thf(fc8_struct_0, axiom,  (! [A: $i] :  ( ( (v8_struct_0 @ A)  &  (l1_struct_0 @ A) )  =>  (v1_finset_1 @  (u1_struct_0 @ A) ) ) ) , file(struct_0, fc8_struct_0)).
thf(fc9_catalg_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v3_catalg_1 @ A)  &  (l1_msualg_1 @ A) ) )  &  ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) ) )  =>  (v1_finseq_1 @  (k2_xtuple_0 @ B) ) ) ) , file(catalg_1, fc9_catalg_1)).
thf(fc9_finseq_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( (v1_relat_1 @  ( ( (k11_finseq_1 @ A)  @ B)  @ C) )  &  (v1_funct_1 @  ( ( (k11_finseq_1 @ A)  @ B)  @ C) ) ) ) , file(finseq_1, fc9_finseq_1)).
thf(fc9_funcop_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_funcop_1 @ A) ) )  &  ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ B)  @ A) )  &  (v1_funcop_1 @  ( (k3_relat_1 @ B)  @ A) ) ) ) ) , file(funcop_1, fc9_funcop_1)).
thf(fc9_relat_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_relat_1 @ A) )  =>  ~ ( (v1_xboole_0 @  (k10_xtuple_0 @ A) ) ) ) ) , file(relat_1, fc9_relat_1)).
thf(fc9_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @  ( (k2_zfmisc_1 @ B)  @ C) ) ) )  =>  (v1_relat_1 @  (k10_xtuple_0 @ D) ) ) ) , file(relset_1, fc9_relset_1)).
thf(fc9_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v8_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  ~ ( (v1_finset_1 @  (u1_struct_0 @ A) ) ) ) ) , file(struct_0, fc9_struct_0)).
thf(free_g1_msualg_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ B)  @  (k3_finseq_2 @ A) )  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @  (k3_finseq_2 @ A) ) ) ) ) )  &  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ B)  @ A)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) ) ) ) )  =>  (! [E: $i, F: $i, G: $i, H: $i] :  ( ( (= @  ( ( ( (g1_msualg_1 @ A)  @ B)  @ C)  @ D) )  @  ( ( ( (g1_msualg_1 @ E)  @ F)  @ G)  @ H) )  =>  ( ( (= @ A)  @ E)  &  ( ( (= @ B)  @ F)  &  ( ( (= @ C)  @ G)  &  ( (= @ D)  @ H) ) ) ) ) ) ) ) , file(msualg_1, g1_msualg_1)).
thf(free_g3_msualg_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_msualg_1 @ A) )  &  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @  (u1_struct_0 @ A) ) ) ) )  &  ( ( ( (m2_pboole @ C)  @  (u4_struct_0 @ A) )  @  ( (k3_relat_1 @  (u1_msualg_1 @ A) )  @  ( (k6_finseq_2 @  (u1_struct_0 @ A) )  @ B) ) )  @  ( (k3_relat_1 @  (u2_msualg_1 @ A) )  @ B) ) ) )  =>  (! [D: $i, E: $i, F: $i] :  ( ( (= @  ( ( (g3_msualg_1 @ A)  @ B)  @ C) )  @  ( ( (g3_msualg_1 @ D)  @ E)  @ F) )  =>  ( ( (= @ A)  @ D)  &  ( ( (= @ B)  @ E)  &  ( (= @ C)  @ F) ) ) ) ) ) ) , file(msualg_1, g3_msualg_1)).
thf(idempotence_k2_xboole_0, axiom,  (! [A: $i, B: $i] :  ( (= @  ( (k2_xboole_0 @ A)  @ A) )  @ A) ) , file(xboole_0, k2_xboole_0)).
thf(projectivity_k1_card_1, axiom,  (! [A: $i] :  ( (= @  (k1_card_1 @  (k1_card_1 @ A) ) )  @  (k1_card_1 @ A) ) ) , file(card_1, k1_card_1)).
thf(projectivity_k3_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (= @  (k3_finseq_1 @  (k3_finseq_1 @ A) ) )  @  (k3_finseq_1 @ A) ) ) ) , file(finseq_1, k3_finseq_1)).
thf(rc1_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) ) ) ) ) ) ) , file(finseq_1, rc1_finseq_1)).
thf(rc1_finseq_2, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  &  ~ ( (v1_xboole_0 @ B) ) ) ) ) , file(finseq_2, rc1_finseq_2)).
thf(rc1_funcop_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_funcop_1 @ A) ) ) ) , file(funcop_1, rc1_funcop_1)).
thf(rc1_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) , file(funct_1, rc1_funct_1)).
thf(rc1_funct_2, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( ( (v5_relat_1 @ C)  @ B)  &  ( (v1_funct_1 @ C)  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) ) ) ) , file(funct_2, rc1_funct_2)).
thf(rc1_instalg1, axiom,  (? [A: $i] :  ( (l1_msualg_1 @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  ~ ( (v11_struct_0 @ A) ) ) ) ) , file(instalg1, rc1_instalg1)).
thf(rc1_msafree1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v1_prob_2 @ B) ) ) ) ) ) ) , file(msafree1, rc1_msafree1)).
thf(rc1_msualg_1, axiom,  (? [A: $i] :  ( (l1_msualg_1 @ A)  &  (v1_msualg_1 @ A) ) ) , file(msualg_1, rc1_msualg_1)).
thf(rc1_ordinal1, axiom,  (? [A: $i] :  (v3_ordinal1 @ A) ) , file(ordinal1, rc1_ordinal1)).
thf(rc1_pboole, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) , file(pboole, rc1_pboole)).
thf(rc1_relat_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_relat_1 @ A) ) ) , file(relat_1, rc1_relat_1)).
thf(rc1_relset_1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( ( (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) ) ) ) ) ) ) , file(relset_1, rc1_relset_1)).
thf(rc1_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(subset_1, rc1_subset_1)).
thf(rc1_xboole_0, axiom,  (? [A: $i] :  (v1_xboole_0 @ A) ) , file(xboole_0, rc1_xboole_0)).
thf(rc1_xtuple_0, axiom,  (? [A: $i] :  (v1_xtuple_0 @ A) ) , file(xtuple_0, rc1_xtuple_0)).
thf(rc21_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_zfmisc_1 @ B) ) ) ) ) ) , file(struct_0, rc21_struct_0)).
thf(rc22_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v7_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ~ ( (v1_zfmisc_1 @ B) ) ) ) ) ) , file(struct_0, rc22_struct_0)).
thf(rc23_struct_0, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (? [B: $i] :  ( (l1_struct_0 @ B)  &  ( (v13_struct_0 @ B)  @ A) ) ) ) ) , file(struct_0, rc23_struct_0)).
thf(rc25_struct_0, axiom,  (? [A: $i] :  ( (l5_struct_0 @ A)  &  ~ ( (v15_struct_0 @ A) ) ) ) , file(struct_0, rc25_struct_0)).
thf(rc2_catalg_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ~ ( (v3_relat_1 @ A) )  &  (v1_funct_1 @ A) ) ) ) , file(catalg_1, rc2_catalg_1)).
thf(rc2_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_xboole_0 @ B)  &  ( (v1_finset_1 @ B)  &  (v1_finseq_1 @ B) ) ) ) ) ) ) ) ) ) , file(finseq_1, rc2_finseq_1)).
thf(rc2_funcop_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_funct_1 @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) ) ) ) , file(funcop_1, rc2_funcop_1)).
thf(rc2_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_funct_1 @ A) ) ) ) , file(funct_1, rc2_funct_1)).
thf(rc2_msualg_1, axiom,  (? [A: $i] :  ( (l1_msualg_1 @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  ( (v11_struct_0 @ A)  &  (v1_msualg_1 @ A) ) ) ) ) , file(msualg_1, rc2_msualg_1)).
thf(rc2_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  (v3_ordinal1 @ A) ) ) ) ) , file(ordinal1, rc2_ordinal1)).
thf(rc2_pboole, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v3_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) , file(pboole, rc2_pboole)).
thf(rc2_relat_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  (v2_relat_1 @ A) ) ) , file(relat_1, rc2_relat_1)).
thf(rc2_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  (v1_xboole_0 @ B) ) ) ) , file(subset_1, rc2_subset_1)).
thf(rc2_xboole_0, axiom,  (? [A: $i] :  ~ ( (v1_xboole_0 @ A) ) ) , file(xboole_0, rc2_xboole_0)).
thf(rc3_catalg_1, axiom,  (? [A: $i] :  ( (l1_msualg_1 @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_msualg_1 @ A)  &  ( (v1_instalg1 @ A)  &  (v2_catalg_1 @ A) ) ) ) ) ) , file(catalg_1, rc3_catalg_1)).
thf(rc3_finseq_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) , file(finseq_1, rc3_finseq_1)).
thf(rc3_funcop_1, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ B) )  =>  (? [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( ( (v5_relat_1 @ C)  @ B)  &  ( (v1_funct_1 @ C)  &  ( (v1_partfun1 @ C)  @ A) ) ) ) ) ) ) ) ) , file(funcop_1, rc3_funcop_1)).
thf(rc3_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) ) , file(funct_1, rc3_funct_1)).
thf(rc3_msualg_1, axiom,  (? [A: $i] :  ( (l1_msualg_1 @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (v1_msualg_1 @ A) ) ) ) ) , file(msualg_1, rc3_msualg_1)).
thf(rc3_ordinal1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v5_ordinal1 @ B) ) ) ) ) ) , file(ordinal1, rc3_ordinal1)).
thf(rc3_pboole, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) , file(pboole, rc3_pboole)).
thf(rc3_relat_1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v5_relat_1 @ C)  @ B) ) ) ) ) , file(relat_1, rc3_relat_1)).
thf(rc3_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( ( (v1_subset_1 @ B)  @ A) ) ) ) ) , file(subset_1, rc3_subset_1)).
thf(rc4_catalg_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_catalg_1 @ B)  @ A)  &  ( (v1_msualg_1 @ B)  &  ( (v1_instalg1 @ B)  &  (v2_catalg_1 @ B) ) ) ) ) ) , file(catalg_1, rc4_catalg_1)).
thf(rc4_finseq_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_finset_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) ) ) , file(finseq_1, rc4_finseq_1)).
thf(rc4_funcop_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) , file(funcop_1, rc4_funcop_1)).
thf(rc4_funct_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) ) ) , file(funct_1, rc4_funct_1)).
thf(rc4_ordinal1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(ordinal1, rc4_ordinal1)).
thf(rc4_pboole, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v1_funcop_1 @ B) ) ) ) ) ) ) , file(pboole, rc4_pboole)).
thf(rc4_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(struct_0, rc4_struct_0)).
thf(rc4_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( (v1_subset_1 @ B)  @ A) ) ) ) ) , file(subset_1, rc4_subset_1)).
thf(rc5_catalg_1, axiom,  (? [A: $i] :  ( (l1_msualg_1 @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_msualg_1 @ A)  &  ( (v1_instalg1 @ A)  &  ( (v2_catalg_1 @ A)  &  (v3_catalg_1 @ A) ) ) ) ) ) ) , file(catalg_1, rc5_catalg_1)).
thf(rc5_finseq_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_finset_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) ) ) ) , file(finseq_1, rc5_finseq_1)).
thf(rc5_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ~ ( (v3_funct_1 @ A) ) ) ) ) , file(funct_1, rc5_funct_1)).
thf(rc5_msualg_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_msualg_1 @ A) )  =>  (? [B: $i] :  ( ( (l3_msualg_1 @ B)  @ A)  &  ( (v3_msualg_1 @ B)  @ A) ) ) ) ) , file(msualg_1, rc5_msualg_1)).
thf(rc5_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v7_ordinal1 @ A) ) ) , file(ordinal1, rc5_ordinal1)).
thf(rc5_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_zfmisc_1 @ B) ) ) ) ) ) , file(subset_1, rc5_subset_1)).
thf(rc6_catalg_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_catalg_1 @ B)  @ A)  &  ( (v1_msualg_1 @ B)  &  ( (v1_instalg1 @ B)  &  ( (v2_catalg_1 @ B)  &  (v3_catalg_1 @ B) ) ) ) ) ) ) , file(catalg_1, rc6_catalg_1)).
thf(rc6_finseq_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_finset_1 @ B)  &  ( (v1_finseq_1 @ B)  &  (v2_finseq_1 @ B) ) ) ) ) ) ) ) ) ) ) ) , file(finseq_1, rc6_finseq_1)).
thf(rc6_funct_1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( ( (v5_relat_1 @ C)  @ B)  &  (v1_funct_1 @ C) ) ) ) ) ) , file(funct_1, rc6_funct_1)).
thf(rc6_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( (v1_zfmisc_1 @ B) ) ) ) ) ) , file(subset_1, rc6_subset_1)).
thf(rc7_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( ( (v3_card_1 @ B)  @ A)  &  ( (v1_finseq_1 @ B)  &  (v2_finseq_1 @ B) ) ) ) ) ) ) ) ) ) , file(finseq_1, rc7_finseq_1)).
thf(rc7_funct_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v4_funct_1 @ A) ) ) , file(funct_1, rc7_funct_1)).
thf(rc7_pboole, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [C: $i] :  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ B)  &  ( ( (v5_relat_1 @ C)  @ A)  &  ( (v1_funct_1 @ C)  &  ( (v1_partfun1 @ C)  @ B) ) ) ) ) ) ) ) , file(pboole, rc7_pboole)).
thf(rc8_finseq_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_finseq_1 @ A) ) ) , file(finseq_1, rc8_finseq_1)).
thf(rc9_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v1_finseq_1 @ B)  &  (v2_finseq_1 @ B) ) ) ) ) ) ) ) ) , file(finseq_1, rc9_finseq_1)).
thf(rc9_funct_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) ) ) ) ) , file(funct_1, rc9_funct_1)).
thf(rd1_xtuple_0, axiom,  (! [A: $i, B: $i] :  ( (= @  (k1_xtuple_0 @  ( (k4_tarski @ A)  @ B) ) )  @ A) ) , file(xtuple_0, rd1_xtuple_0)).
thf(rd2_xtuple_0, axiom,  (! [A: $i, B: $i] :  ( (= @  (k2_xtuple_0 @  ( (k4_tarski @ A)  @ B) ) )  @ B) ) , file(xtuple_0, rd2_xtuple_0)).
thf(rd3_xtuple_0, axiom,  (! [A: $i] :  ( (v1_xtuple_0 @ A)  =>  ( (= @  ( (k4_tarski @  (k1_xtuple_0 @ A) )  @  (k2_xtuple_0 @ A) ) )  @ A) ) ) , file(xtuple_0, rd3_xtuple_0)).
thf(redefinition_k10_catalg_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @ A)  &  ( ( (m1_subset_1 @ C)  @ A)  &  ( (m1_subset_1 @ D)  @ A) ) ) )  =>  ( (= @  ( ( ( (k10_catalg_1 @ A)  @ B)  @ C)  @ D) )  @  ( ( (k7_catalg_1 @ B)  @ C)  @ D) ) ) ) , file(catalg_1, k10_catalg_1)).
thf(redefinition_k18_funcop_1, axiom,  (! [A: $i, B: $i] :  ( (= @  ( (k18_funcop_1 @ A)  @ B) )  @  ( (k16_funcop_1 @ A)  @ B) ) ) , file(funcop_1, k18_funcop_1)).
thf(redefinition_k1_msualg_3, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (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) ) ) )  &  ( ( ( ( (m2_pboole @ D)  @ A)  @ B)  @ C)  &  ( (m1_subset_1 @ E)  @ A) ) ) ) )  =>  ( (= @  ( ( ( ( (k1_msualg_3 @ A)  @ B)  @ C)  @ D)  @ E) )  @  ( (k1_funct_1 @ D)  @ E) ) ) ) , file(msualg_3, k1_msualg_3)).
thf(redefinition_k1_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( (= @  ( (k1_relset_1 @ A)  @ B) )  @  (k9_xtuple_0 @ B) ) ) ) , file(relset_1, k1_relset_1)).
thf(redefinition_k2_finseq_4, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @ A)  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ( (= @  ( ( (k2_finseq_4 @ A)  @ B)  @ C) )  @  ( (k10_finseq_1 @ B)  @ C) ) ) ) , file(finseq_4, k2_finseq_4)).
thf(redefinition_k2_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  =>  ( (= @  ( (k2_relset_1 @ A)  @ B) )  @  (k10_xtuple_0 @ B) ) ) ) , file(relset_1, k2_relset_1)).
thf(redefinition_k3_catalg_1, axiom,  (! [A: $i] :  ( (= @  (k3_catalg_1 @ A) )  @  (k2_catalg_1 @ A) ) ) , file(catalg_1, k3_catalg_1)).
thf(redefinition_k3_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (= @  (k3_finseq_1 @ A) )  @  (k1_card_1 @ A) ) ) ) , file(finseq_1, k3_finseq_1)).
thf(redefinition_k3_finseq_2, axiom,  (! [A: $i] :  ( (= @  (k3_finseq_2 @ A) )  @  (k13_finseq_1 @ A) ) ) , file(finseq_2, k3_finseq_2)).
thf(redefinition_k3_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (m1_subset_1 @ D)  @ A) ) )  =>  ( (= @  ( ( ( (k3_funct_2 @ A)  @ B)  @ C)  @ D) )  @  ( (k1_funct_1 @ C)  @ D) ) ) ) , file(funct_2, k3_funct_2)).
thf(redefinition_k5_numbers, axiom,  ( (= @ k5_numbers)  @ k4_ordinal1) , file(numbers, k5_numbers)).
thf(redefinition_k6_numbers, axiom,  ( (= @ k6_numbers)  @ k1_xboole_0) , file(numbers, k6_numbers)).
thf(redefinition_k7_funcop_1, axiom,  (! [A: $i, B: $i] :  ( (= @  ( (k7_funcop_1 @ A)  @ B) )  @  ( (k2_funcop_1 @ A)  @ B) ) ) , file(funcop_1, k7_funcop_1)).
thf(redefinition_k8_catalg_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ B)  @ A) )  =>  ( (= @  ( (k8_catalg_1 @ A)  @ B) )  @  (k5_catalg_1 @ B) ) ) ) , file(catalg_1, k8_catalg_1)).
thf(redefinition_k9_catalg_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @ A)  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ( (= @  ( ( (k9_catalg_1 @ A)  @ B)  @ C) )  @  ( (k6_catalg_1 @ B)  @ C) ) ) ) , file(catalg_1, k9_catalg_1)).
thf(redefinition_k9_finseq_1, axiom,  (! [A: $i] :  ( (= @  (k9_finseq_1 @ A) )  @  (k5_finseq_1 @ A) ) ) , file(finseq_1, k9_finseq_1)).
thf(redefinition_m2_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @ A)  <=>  ( (m1_finseq_1 @ B)  @ A) ) ) ) , file(finseq_1, m2_finseq_1)).
thf(redefinition_m2_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (! [C: $i] :  ( ( ( (m2_finseq_2 @ C)  @ A)  @ B)  <=>  ( (m1_subset_1 @ C)  @ B) ) ) ) ) , file(finseq_2, m2_finseq_2)).
thf(redefinition_m2_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) ) ) )  =>  (! [C: $i] :  ( ( ( (m2_subset_1 @ C)  @ A)  @ B)  <=>  ( (m1_subset_1 @ C)  @ B) ) ) ) ) , file(subset_1, m2_subset_1)).
thf(reflexivity_r1_tarski, axiom,  (! [A: $i, B: $i] :  ( (r1_tarski @ A)  @ A) ) , file(tarski, r1_tarski)).
thf(spc1_boole, axiom,  ~ ( (v1_xboole_0 @ np__1) ) , file(boole, spc1_boole)).
thf(spc1_numerals, axiom,  ( ( (v2_xxreal_0 @ np__1)  &  ( ( (m2_subset_1 @ np__1)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__1)  @ k5_numbers)  &  ( (m1_subset_1 @ np__1)  @ k1_numbers) ) ) , file(numerals, spc1_numerals)).
thf(spc2_boole, axiom,  ~ ( (v1_xboole_0 @ np__2) ) , file(boole, spc2_boole)).
thf(spc2_numerals, axiom,  ( ( (v2_xxreal_0 @ np__2)  &  ( ( (m2_subset_1 @ np__2)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__2)  @ k5_numbers)  &  ( (m1_subset_1 @ np__2)  @ k1_numbers) ) ) , file(numerals, spc2_numerals)).
thf(spc3_boole, axiom,  ~ ( (v1_xboole_0 @ np__3) ) , file(boole, spc3_boole)).
thf(spc3_numerals, axiom,  ( ( (v2_xxreal_0 @ np__3)  &  ( ( (m2_subset_1 @ np__3)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__3)  @ k5_numbers)  &  ( (m1_subset_1 @ np__3)  @ k1_numbers) ) ) , file(numerals, spc3_numerals)).
thf(t10_card_3, axiom,  ( (= @  (k4_card_3 @ k1_xboole_0) )  @  (k1_tarski @ k1_xboole_0) ) , file(card_3, t10_card_3)).
thf(t11_catalg_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (= @  (k5_catalg_1 @ A) )  @  (k5_catalg_1 @ B) )  =>  ( (= @ A)  @ B) ) ) ) , file(catalg_1, t11_catalg_1)).
thf(t124_finseq_3, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( (r2_hidden @ A)  @  (k4_card_3 @  ( (k10_finseq_1 @ B)  @ C) ) )  <=>  (? [D: $i] :  (? [E: $i] :  ( ( (r2_hidden @ D)  @ B)  &  ( ( (r2_hidden @ E)  @ C)  &  ( (= @ A)  @  ( (k10_finseq_1 @ D)  @ E) ) ) ) ) ) ) ) ) ) , file(finseq_3, t124_finseq_3)).
thf(t125_finseq_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (! [B: $i] :  (! [C: $i] :  ( ( ( (r2_hidden @ B)  @  (k9_xtuple_0 @ A) )  &  ( (r2_hidden @ C)  @  (k9_xtuple_0 @ A) ) )  =>  ( (= @  ( (k3_relat_1 @  ( (k10_finseq_1 @ B)  @ C) )  @ A) )  @  ( (k10_finseq_1 @  ( (k1_funct_1 @ A)  @ B) )  @  ( (k1_funct_1 @ A)  @ C) ) ) ) ) ) ) ) , file(finseq_2, t125_finseq_2)).
thf(t12_catalg_1, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  (! [D: $i] :  ( ( (= @  ( (k6_catalg_1 @ A)  @ C) )  @  ( (k6_catalg_1 @ B)  @ D) )  =>  ( ( (= @ A)  @ B)  &  ( (= @ C)  @ D) ) ) ) ) ) ) , file(catalg_1, t12_catalg_1)).
thf(t13_catalg_1, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  (! [D: $i] :  (! [E: $i] :  (! [F: $i] :  ( ( (= @  ( ( (k7_catalg_1 @ A)  @ C)  @ E) )  @  ( ( (k7_catalg_1 @ B)  @ D)  @ F) )  =>  ( ( (= @ A)  @ B)  &  ( ( (= @ C)  @ D)  &  ( (= @ E)  @ F) ) ) ) ) ) ) ) ) ) , file(catalg_1, t13_catalg_1)).
thf(t13_funcop_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (= @  (k9_xtuple_0 @  ( (k2_funcop_1 @ A)  @ B) ) )  @ A)  &  ( (r1_tarski @  (k10_xtuple_0 @  ( (k2_funcop_1 @ A)  @ B) ) )  @  (k1_tarski @ B) ) ) ) ) , file(funcop_1, t13_funcop_1)).
thf(t14_catalg_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_catalg_1 @ B)  @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ B) )  =>  (? [D: $i] :  ( ( (m1_subset_1 @ D)  @ A)  &  (? [E: $i] :  ( ( (m1_subset_1 @ E)  @ A)  &  ( (= @ C)  @  ( ( (k9_catalg_1 @ A)  @ D)  @ E) ) ) ) ) ) ) ) ) ) ) ) , file(catalg_1, t14_catalg_1)).
thf(t15_catalg_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u4_struct_0 @  (k3_catalg_1 @ A) ) )  =>  ( ( ( (= @  (k1_xtuple_0 @ B) )  @ np__1)  &  ( (= @  (k3_finseq_1 @  (k2_xtuple_0 @ B) ) )  @ np__1) )  |  ( ( (= @  (k1_xtuple_0 @ B) )  @ np__2)  &  ( (= @  (k3_finseq_1 @  (k2_xtuple_0 @ B) ) )  @ np__3) ) ) ) ) ) ) , file(catalg_1, t15_catalg_1)).
thf(t15_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  (! [D: $i] :  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  =>  (! [E: $i] :  ( ( (v1_relat_1 @ E)  &  (v1_funct_1 @ E) )  =>  ( ( (r2_hidden @ C)  @ A)  =>  ( ( (= @ B)  @ k1_xboole_0)  |  ( (= @  ( (k1_funct_1 @  ( (k3_relat_1 @ D)  @ E) )  @ C) )  @  ( (k1_funct_1 @ E)  @  ( (k1_funct_1 @ D)  @ C) ) ) ) ) ) ) ) ) ) ) ) , file(funct_2, t15_funct_2)).
thf(t16_catalg_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u4_struct_0 @  (k3_catalg_1 @ A) ) )  =>  ~ ( ( ( ( (= @  (k1_xtuple_0 @ B) )  @ np__1)  |  ( (= @  (k3_finseq_1 @  (k2_xtuple_0 @ B) ) )  @ np__1) )  &  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ A)  =>  ~ ( ( (= @ B)  @  ( (k8_catalg_1 @ A)  @ C) ) ) ) ) ) ) ) ) ) ) , file(catalg_1, t16_catalg_1)).
thf(t17_catalg_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u4_struct_0 @  (k3_catalg_1 @ A) ) )  =>  ~ ( ( ( ( (= @  (k1_xtuple_0 @ B) )  @ np__2)  |  ( (= @  (k3_finseq_1 @  (k2_xtuple_0 @ B) ) )  @ np__3) )  &  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ A)  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @ A)  =>  (! [E: $i] :  ( ( (m1_subset_1 @ E)  @ A)  =>  ~ ( ( (= @ B)  @  ( ( ( (k10_catalg_1 @ A)  @ C)  @ D)  @ E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(catalg_1, t17_catalg_1)).
thf(t1_boole, axiom,  (! [A: $i] :  ( (= @  ( (k2_xboole_0 @ A)  @ k1_xboole_0) )  @ A) ) , file(boole, t1_boole)).
thf(t1_numerals, axiom,  ( (m1_subset_1 @ k1_xboole_0)  @ k4_ordinal1) , file(numerals, t1_numerals)).
thf(t1_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ( (m1_subset_1 @ A)  @ B) ) ) ) , file(subset, t1_subset)).
thf(t1_xboole_1, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( ( (r1_tarski @ A)  @ B)  &  ( (r1_tarski @ B)  @ C) )  =>  ( (r1_tarski @ A)  @ C) ) ) ) ) , file(xboole_1, t1_xboole_1)).
thf(t2_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) )  =>  ( ( (r1_tarski @  (k10_xtuple_0 @ B) )  @ A)  =>  ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @  (k9_xtuple_0 @ B) )  @ A)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k9_xtuple_0 @ B) )  @ A) ) ) ) ) ) ) ) ) , file(funct_2, t2_funct_2)).
thf(t2_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @ B)  =>  ( (v1_xboole_0 @ B)  |  ( (r2_hidden @ A)  @ B) ) ) ) ) , file(subset, t2_subset)).
thf(t31_zfmisc_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (r1_tarski @  (k1_tarski @ A) )  @ B)  <=>  ( (r2_hidden @ A)  @ B) ) ) ) , file(zfmisc_1, t31_zfmisc_1)).
thf(t3_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ B) )  <=>  ( (r1_tarski @ A)  @ B) ) ) ) , file(subset, t3_subset)).
thf(t44_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( (v1_funct_1 @ C)  &  (v1_finseq_1 @ C) ) )  =>  ( ( (= @ C)  @  ( (k10_finseq_1 @ A)  @ B) )  <=>  ( ( (= @  (k3_finseq_1 @ C) )  @ np__2)  &  ( ( (= @  ( (k1_funct_1 @ C)  @ np__1) )  @ A)  &  ( (= @  ( (k1_funct_1 @ C)  @ np__2) )  @ B) ) ) ) ) ) ) ) , file(finseq_1, t44_finseq_1)).
thf(t4_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( ( (r2_hidden @ A)  @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) ) )  =>  ( (m1_subset_1 @ A)  @ C) ) ) ) ) , file(subset, t4_subset)).
thf(t5_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ~ ( ( ( (r2_hidden @ A)  @ B)  &  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) )  &  (v1_xboole_0 @ C) ) ) ) ) ) ) , file(subset, t5_subset)).
thf(t6_boole, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ( (= @ A)  @ k1_xboole_0) ) ) , file(boole, t6_boole)).
thf(t7_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( ( (r2_hidden @ A)  @ B)  &  (v1_xboole_0 @ B) ) ) ) ) , file(boole, t7_boole)).
thf(t7_funcop_1, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( (r2_hidden @ B)  @ A)  =>  ( (= @  ( (k1_funct_1 @  ( (k2_funcop_1 @ A)  @ C) )  @ B) )  @ C) ) ) ) ) , file(funcop_1, t7_funcop_1)).
thf(t7_mcart_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (= @  (k1_xtuple_0 @  ( (k4_tarski @ A)  @ B) ) )  @ A)  &  ( (= @  (k2_xtuple_0 @  ( (k4_tarski @ A)  @ B) ) )  @ B) ) ) ) , file(mcart_1, t7_mcart_1)).
thf(t8_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( (v1_xboole_0 @ A)  &  ( ~ ( ( (= @ A)  @ B) )  &  (v1_xboole_0 @ B) ) ) ) ) ) , file(boole, t8_boole)).
thf(s1_classes1, axiom,  (! [A: $i > $i > $o] :  (! [B: $i] :  ( (! [C: $i] :  ~ ( ( ( (r2_hidden @ C)  @ B)  &  (! [D: $i] :  ~ ( ( (A @ C)  @ D) ) ) ) ) )  =>  (? [C: $i] :  ( ( (v1_relat_1 @ C)  &  (v1_funct_1 @ C) )  &  ( ( (= @  (k9_xtuple_0 @ C) )  @ B)  &  (! [D: $i] :  ( ( (r2_hidden @ D)  @ B)  =>  ( (A @ D)  @  ( (k1_funct_1 @ C)  @ D) ) ) ) ) ) ) ) ) ) , file(classes1, s1_classes1)).
thf(s5_funct_1, axiom,  (! [A: $i > $i > $o] :  (! [B: $i] :  (! [C: $i] :  ( (! [D: $i] :  ~ ( ( ( (r2_hidden @ D)  @ C)  &  (! [E: $i] :  ~ ( ( ( (r2_hidden @ E)  @ B)  &  ( (A @ D)  @ E) ) ) ) ) ) )  =>  (? [D: $i] :  ( ( (v1_relat_1 @ D)  &  (v1_funct_1 @ D) )  &  ( ( (= @  (k9_xtuple_0 @ D) )  @ C)  &  ( ( (r1_tarski @  (k10_xtuple_0 @ D) )  @ B)  &  (! [E: $i] :  ( ( (r2_hidden @ E)  @ C)  =>  ( (A @ E)  @  ( (k1_funct_1 @ D)  @ E) ) ) ) ) ) ) ) ) ) ) ) , file(funct_1, s5_funct_1)).
thf(s1_catalg_1, conjecture,  ( ( (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ f1_s1_catalg_1)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ f1_s1_catalg_1)  =>  ( (r1_tarski @  ( (f3_s1_catalg_1 @ A)  @ B) )  @ f2_s1_catalg_1) ) ) ) )  &  ( (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ f1_s1_catalg_1)  =>  ( (r2_hidden @  (f5_s1_catalg_1 @ A) )  @  ( (f3_s1_catalg_1 @ A)  @ A) ) ) )  &  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ f1_s1_catalg_1)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ f1_s1_catalg_1)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ f1_s1_catalg_1)  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @ f2_s1_catalg_1)  =>  (! [E: $i] :  ( ( (m1_subset_1 @ E)  @ f2_s1_catalg_1)  =>  ( ( ( (r2_hidden @ D)  @  ( (f3_s1_catalg_1 @ A)  @ B) )  &  ( (r2_hidden @ E)  @  ( (f3_s1_catalg_1 @ B)  @ C) ) )  =>  ( (r2_hidden @  ( ( ( ( (f4_s1_catalg_1 @ A)  @ B)  @ C)  @ E)  @ D) )  @  ( (f3_s1_catalg_1 @ A)  @ C) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [A: $i] :  ( ( ( (v3_msualg_1 @ A)  @  (k3_catalg_1 @ f1_s1_catalg_1) )  &  ( (l3_msualg_1 @ A)  @  (k3_catalg_1 @ f1_s1_catalg_1) ) )  &  ( (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ f1_s1_catalg_1)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ f1_s1_catalg_1)  =>  ( (= @  ( (k1_funct_1 @  ( (u3_msualg_1 @  (k3_catalg_1 @ f1_s1_catalg_1) )  @ A) )  @  ( ( (k9_catalg_1 @ f1_s1_catalg_1)  @ B)  @ C) ) )  @  ( (f3_s1_catalg_1 @ B)  @ C) ) ) ) ) )  &  ( (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ f1_s1_catalg_1)  =>  ( (= @  ( (k1_funct_1 @  ( ( (k5_msualg_1 @  (k3_catalg_1 @ f1_s1_catalg_1) )  @  ( (k8_catalg_1 @ f1_s1_catalg_1)  @ B) )  @ A) )  @ k1_xboole_0) )  @  (f5_s1_catalg_1 @ B) ) ) )  &  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ f1_s1_catalg_1)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ f1_s1_catalg_1)  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @ f1_s1_catalg_1)  =>  (! [E: $i] :  ( ( (m1_subset_1 @ E)  @ f2_s1_catalg_1)  =>  (! [F: $i] :  ( ( (m1_subset_1 @ F)  @ f2_s1_catalg_1)  =>  ( ( ( (r2_hidden @ E)  @  ( (f3_s1_catalg_1 @ B)  @ C) )  &  ( (r2_hidden @ F)  @  ( (f3_s1_catalg_1 @ C)  @ D) ) )  =>  ( (= @  ( (k1_funct_1 @  ( ( (k5_msualg_1 @  (k3_catalg_1 @ f1_s1_catalg_1) )  @  ( ( ( (k10_catalg_1 @ f1_s1_catalg_1)  @ B)  @ C)  @ D) )  @ A) )  @  ( ( (k2_finseq_4 @ f2_s1_catalg_1)  @ F)  @ E) ) )  @  ( ( ( ( (f4_s1_catalg_1 @ B)  @ C)  @ D)  @ F)  @ E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(catalg_1, s1_catalg_1)).
