% Mizar problem: s2_matrix15,matrix15,4073,8 
include('Axioms/SET010^1.ax').
thf(n0_type, type, np__0: $i).
thf(n1_type, type, np__1: $i).
thf(f1_s2_matrix15_type, type, f1_s2_matrix15: $i).
thf(f2_s2_matrix15_type, type, f2_s2_matrix15: $i).
thf(f3_s2_matrix15_type, type, f3_s2_matrix15: $i).
thf(f4_s2_matrix15_type, type, f4_s2_matrix15: $i).
thf(f5_s2_matrix15_type, type, f5_s2_matrix15: $i).
thf(f6_s2_matrix15_type, type, f6_s2_matrix15: $i).
thf(f7_s2_matrix15_type, type, f7_s2_matrix15: $i > $i > $i > $i > $i).
thf(k10_funcop_1_type, type, k10_funcop_1: $i > $i > $i > $i > $i > $i).
thf(k10_fvsum_1_type, type, k10_fvsum_1: $i > $i > $i > $i > $i).
thf(k10_xtuple_0_type, type, k10_xtuple_0: $i > $i).
thf(k11_algstr_0_type, type, k11_algstr_0: $i > $i > $i).
thf(k12_matrix_1_type, type, k12_matrix_1: $i > $i > $i).
thf(k13_finseq_1_type, type, k13_finseq_1: $i > $i).
thf(k14_finseq_1_type, type, k14_finseq_1: $i > $i).
thf(k1_algstr_0_type, type, k1_algstr_0: $i > $i > $i > $i).
thf(k1_binop_1_type, type, k1_binop_1: $i > $i > $i > $i).
thf(k1_card_1_type, type, k1_card_1: $i > $i).
thf(k1_finseq_1_type, type, k1_finseq_1: $i > $i).
thf(k1_finseq_2_type, type, k1_finseq_2: $i > $i).
thf(k1_finseqop_type, type, k1_finseqop: $i > $i > $i > $i > $i > $i > $i).
thf(k1_funct_1_type, type, k1_funct_1: $i > $i > $i).
thf(k1_fvsum_1_type, type, k1_fvsum_1: $i > $i > $i).
thf(k1_group_1_type, type, k1_group_1: $i > $i).
thf(k1_matrix13_type, type, k1_matrix13: $i > $i > $i > $i > $i > $i > $i).
thf(k1_matrix_1_type, type, k1_matrix_1: $i > $i).
thf(k1_nat_1_type, type, k1_nat_1: $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_zfmisc_1_type, type, k1_zfmisc_1: $i > $i).
thf(k2_finseq_1_type, type, k2_finseq_1: $i > $i).
thf(k2_finseq_2_type, type, k2_finseq_2: $i > $i > $i).
thf(k2_funcop_1_type, type, k2_funcop_1: $i > $i > $i).
thf(k2_matrix_1_type, type, k2_matrix_1: $i > $i).
thf(k2_nat_1_type, type, k2_nat_1: $i > $i > $i).
thf(k2_tarski_type, type, k2_tarski: $i > $i > $i).
thf(k2_xcmplx_0_type, type, k2_xcmplx_0: $i > $i > $i).
thf(k2_zfmisc_1_type, type, k2_zfmisc_1: $i > $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_funcop_1_type, type, k3_funcop_1: $i > $i > $i > $i).
thf(k3_funct_2_type, type, k3_funct_2: $i > $i > $i > $i > $i).
thf(k3_fvsum_1_type, type, k3_fvsum_1: $i > $i > $i > $i).
thf(k3_matrix11_type, type, k3_matrix11: $i > $i > $i > $i > $i > $i > $i).
thf(k3_matrix_1_type, type, k3_matrix_1: $i > $i > $i > $i > $i).
thf(k3_numbers_type, type, k3_numbers: $i).
thf(k3_relat_1_type, type, k3_relat_1: $i > $i > $i).
thf(k3_rlvect_1_type, type, k3_rlvect_1: $i > $i > $i > $i).
thf(k4_algstr_0_type, type, k4_algstr_0: $i > $i > $i).
thf(k4_finseq_1_type, type, k4_finseq_1: $i > $i).
thf(k4_finseq_2_type, type, k4_finseq_2: $i > $i > $i).
thf(k4_finseqop_type, type, k4_finseqop: $i > $i > $i > $i > $i).
thf(k4_fvsum_1_type, type, k4_fvsum_1: $i > $i > $i > $i > $i).
thf(k4_numbers_type, type, k4_numbers: $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(k4_relat_1_type, type, k4_relat_1: $i > $i).
thf(k4_struct_0_type, type, k4_struct_0: $i > $i).
thf(k4_tarski_type, type, k4_tarski: $i > $i > $i).
thf(k4_xcmplx_0_type, type, k4_xcmplx_0: $i > $i).
thf(k5_algstr_0_type, type, k5_algstr_0: $i > $i > $i > $i).
thf(k5_binop_1_type, type, k5_binop_1: $i > $i > $i > $i > $i).
thf(k5_card_1_type, type, k5_card_1: $i > $i).
thf(k5_finseq_2_type, type, k5_finseq_2: $i > $i > $i > $i).
thf(k5_funcop_1_type, type, k5_funcop_1: $i > $i > $i > $i).
thf(k5_matrix13_type, type, k5_matrix13: $i > $i).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(k5_struct_0_type, type, k5_struct_0: $i > $i).
thf(k6_algstr_0_type, type, k6_algstr_0: $i > $i > $i > $i).
thf(k6_matrix13_type, type, k6_matrix13: $i > $i > $i > $i > $i).
thf(k6_matrix_1_type, type, k6_matrix_1: $i > $i > $i > $i).
thf(k6_numbers_type, type, k6_numbers: $i).
thf(k6_partfun1_type, type, k6_partfun1: $i > $i).
thf(k6_xcmplx_0_type, type, k6_xcmplx_0: $i > $i > $i).
thf(k7_funcop_1_type, type, k7_funcop_1: $i > $i > $i).
thf(k7_partfun1_type, type, k7_partfun1: $i > $i > $i > $i).
thf(k8_group_1_type, type, k8_group_1: $i > $i > $i > $i).
thf(k8_matrix13_type, type, k8_matrix13: $i > $i > $i).
thf(k8_matrix_1_type, type, k8_matrix_1: $i > $i > $i > $i).
thf(k9_fvsum_1_type, type, k9_fvsum_1: $i > $i > $i > $i).
thf(k9_xtuple_0_type, type, k9_xtuple_0: $i > $i).
thf(u1_algstr_0_type, type, u1_algstr_0: $i > $i).
thf(u1_struct_0_type, type, u1_struct_0: $i > $i).
thf(u2_algstr_0_type, type, u2_algstr_0: $i > $i).
thf(l1_algstr_0_type, type, l1_algstr_0: $i > $o).
thf(l1_struct_0_type, type, l1_struct_0: $i > $o).
thf(l2_algstr_0_type, type, l2_algstr_0: $i > $o).
thf(l2_struct_0_type, type, l2_struct_0: $i > $o).
thf(l3_algstr_0_type, type, l3_algstr_0: $i > $o).
thf(l3_struct_0_type, type, l3_struct_0: $i > $o).
thf(l4_algstr_0_type, type, l4_algstr_0: $i > $o).
thf(l4_struct_0_type, type, l4_struct_0: $i > $o).
thf(l5_algstr_0_type, type, l5_algstr_0: $i > $o).
thf(l6_algstr_0_type, type, l6_algstr_0: $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_matrix_1_type, type, m1_matrix_1: $i > $i > $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_subset_1_type, type, m2_subset_1: $i > $i > $i > $o).
thf(p1_s2_matrix15_type, type, p1_s2_matrix15: $i > $i > $o).
thf(r1_tarski_type, type, r1_tarski: $i > $i > $o).
thf(r1_xxreal_0_type, type, r1_xxreal_0: $i > $i > $o).
thf(v13_algstr_0_type, type, v13_algstr_0: $i > $o).
thf(v13_struct_0_type, type, v13_struct_0: $i > $i > $o).
thf(v1_algstr_1_type, type, v1_algstr_1: $i > $o).
thf(v1_binop_1_type, type, v1_binop_1: $i > $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_group_1_type, type, v1_group_1: $i > $o).
thf(v1_int_1_type, type, v1_int_1: $i > $o).
thf(v1_matrix_1_type, type, v1_matrix_1: $i > $o).
thf(v1_membered_type, type, v1_membered: $i > $o).
thf(v1_ordinal1_type, type, v1_ordinal1: $i > $o).
thf(v1_partfun1_type, type, v1_partfun1: $i > $i > $o).
thf(v1_pre_poly_type, type, v1_pre_poly: $i > $o).
thf(v1_rat_1_type, type, v1_rat_1: $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_valued_0_type, type, v1_valued_0: $i > $o).
thf(v1_vectsp_1_type, type, v1_vectsp_1: $i > $o).
thf(v1_xboole_0_type, type, v1_xboole_0: $i > $o).
thf(v1_xcmplx_0_type, type, v1_xcmplx_0: $i > $o).
thf(v1_xreal_0_type, type, v1_xreal_0: $i > $o).
thf(v1_xxreal_0_type, type, v1_xxreal_0: $i > $o).
thf(v1_zfmisc_1_type, type, v1_zfmisc_1: $i > $o).
thf(v2_binop_1_type, type, v2_binop_1: $i > $i > $o).
thf(v2_card_1_type, type, v2_card_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_matrix_1_type, type, v2_matrix_1: $i > $i > $o).
thf(v2_membered_type, type, v2_membered: $i > $o).
thf(v2_ordinal1_type, type, v2_ordinal1: $i > $o).
thf(v2_relat_1_type, type, v2_relat_1: $i > $o).
thf(v2_rlvect_1_type, type, v2_rlvect_1: $i > $o).
thf(v2_setfam_1_type, type, v2_setfam_1: $i > $o).
thf(v2_struct_0_type, type, v2_struct_0: $i > $o).
thf(v2_valued_0_type, type, v2_valued_0: $i > $o).
thf(v2_vectsp_1_type, type, v2_vectsp_1: $i > $o).
thf(v2_xxreal_0_type, type, v2_xxreal_0: $i > $o).
thf(v33_algstr_0_type, type, v33_algstr_0: $i > $o).
thf(v3_card_1_type, type, v3_card_1: $i > $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_group_1_type, type, v3_group_1: $i > $o).
thf(v3_membered_type, type, v3_membered: $i > $o).
thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o).
thf(v3_relat_1_type, type, v3_relat_1: $i > $o).
thf(v3_rlvect_1_type, type, v3_rlvect_1: $i > $o).
thf(v3_valued_0_type, type, v3_valued_0: $i > $o).
thf(v3_vectsp_1_type, type, v3_vectsp_1: $i > $o).
thf(v3_xxreal_0_type, type, v3_xxreal_0: $i > $o).
thf(v4_funct_1_type, type, v4_funct_1: $i > $o).
thf(v4_membered_type, type, v4_membered: $i > $o).
thf(v4_relat_1_type, type, v4_relat_1: $i > $i > $o).
thf(v4_rlvect_1_type, type, v4_rlvect_1: $i > $o).
thf(v4_valued_0_type, type, v4_valued_0: $i > $o).
thf(v4_vectsp_1_type, type, v4_vectsp_1: $i > $o).
thf(v5_finset_1_type, type, v5_finset_1: $i > $o).
thf(v5_group_1_type, type, v5_group_1: $i > $o).
thf(v5_membered_type, type, v5_membered: $i > $o).
thf(v5_ordinal1_type, type, v5_ordinal1: $i > $o).
thf(v5_relat_1_type, type, v5_relat_1: $i > $i > $o).
thf(v5_valued_0_type, type, v5_valued_0: $i > $o).
thf(v5_vectsp_1_type, type, v5_vectsp_1: $i > $o).
thf(v6_membered_type, type, v6_membered: $i > $o).
thf(v6_ordinal1_type, type, v6_ordinal1: $i > $o).
thf(v6_struct_0_type, type, v6_struct_0: $i > $o).
thf(v6_valued_0_type, type, v6_valued_0: $i > $o).
thf(v6_vectsp_1_type, type, v6_vectsp_1: $i > $o).
thf(v7_ordinal1_type, type, v7_ordinal1: $i > $o).
thf(v7_struct_0_type, type, v7_struct_0: $i > $o).
thf(v7_valued_0_type, type, v7_valued_0: $i > $o).
thf(v8_struct_0_type, type, v8_struct_0: $i > $o).
thf(v8_valued_0_type, type, v8_valued_0: $i > $o).
thf(v9_struct_0_type, type, v9_struct_0: $i > $i > $o).
thf(antisymmetry_r2_hidden, axiom,  (! [A: $i, B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ~ ( ( (r2_hidden @ B)  @ A) ) ) ) , file(hidden, r2_hidden)).
thf(cc10_card_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_zfmisc_1 @ A) )  =>  ( (v3_card_1 @ A)  @ np__1) ) ) , file(card_1, cc10_card_1)).
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(cc10_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_valued_0 @ B) ) ) ) ) , file(valued_0, cc10_valued_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(cc11_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v2_valued_0 @ B) ) ) ) ) , file(valued_0, cc11_valued_0)).
thf(cc12_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  ( (v5_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) ) ) ) ) , file(finseq_1, cc12_finseq_1)).
thf(cc12_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_valued_0 @ B) ) ) ) ) , file(valued_0, cc12_valued_0)).
thf(cc13_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v5_relat_1 @ B)  @ k3_numbers) ) ) ) ) , file(valued_0, cc13_valued_0)).
thf(cc14_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v5_relat_1 @ B)  @ k4_numbers) ) ) ) ) , file(valued_0, cc14_valued_0)).
thf(cc15_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_valued_0 @ B) ) ) ) ) , file(valued_0, cc15_valued_0)).
thf(cc16_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_valued_0 @ C) ) ) ) ) , file(valued_0, cc16_valued_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(cc17_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v2_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v2_valued_0 @ C) ) ) ) ) , file(valued_0, cc17_valued_0)).
thf(cc18_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v3_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v3_valued_0 @ C) ) ) ) ) , file(valued_0, cc18_valued_0)).
thf(cc19_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v4_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v5_relat_1 @ C)  @ k3_numbers) ) ) ) ) , file(valued_0, cc19_valued_0)).
thf(cc1_card_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(card_1, cc1_card_1)).
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_finset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_finset_1 @ A) ) ) , file(finset_1, cc1_finset_1)).
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_fvsum_1, axiom,  (! [A: $i] :  ( (l2_algstr_0 @ A)  =>  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v2_rlvect_1 @ A)  &  (v4_rlvect_1 @ A) ) )  =>  ( ~ ( (v2_struct_0 @ A) )  &  (v1_algstr_1 @ A) ) ) ) ) , file(fvsum_1, cc1_fvsum_1)).
thf(cc1_matrlin, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_finseq_1 @ B)  @  (k3_finseq_2 @ A) )  =>  ( (v1_matrix_1 @ B)  =>  ( (v1_matrix_1 @ B)  &  (v1_pre_poly @ B) ) ) ) ) ) ) , file(matrlin, cc1_matrlin)).
thf(cc1_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v3_ordinal1 @ A)  &  (v7_ordinal1 @ A) ) ) ) , file(nat_1, cc1_nat_1)).
thf(cc1_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) ) ) ) , file(ordinal1, cc1_ordinal1)).
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_setfam_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_setfam_1 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(setfam_1, cc1_setfam_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_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) ) ) ) , file(valued_0, cc1_valued_0)).
thf(cc1_vectsp_1, axiom,  (! [A: $i] :  ( (l6_algstr_0 @ A)  =>  ( ( ~ ( (v2_struct_0 @ A) )  &  (v5_vectsp_1 @ A) )  =>  ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_vectsp_1 @ A)  &  (v2_vectsp_1 @ A) ) ) ) ) ) , file(vectsp_1, cc1_vectsp_1)).
thf(cc1_xreal_0, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc1_xreal_0)).
thf(cc20_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v5_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v5_relat_1 @ C)  @ k4_numbers) ) ) ) ) , file(valued_0, cc20_valued_0)).
thf(cc21_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v6_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v4_valued_0 @ C) ) ) ) ) , file(valued_0, cc21_valued_0)).
thf(cc22_valued_0, axiom,  (! [A: $i] :  ( ( (v1_zfmisc_1 @ A)  &  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_valued_0 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  ( (v5_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) ) ) ) ) , file(valued_0, cc22_valued_0)).
thf(cc23_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v5_valued_0 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v7_valued_0 @ A) ) ) ) ) ) , file(valued_0, cc23_valued_0)).
thf(cc24_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v8_valued_0 @ A) ) ) ) ) ) , file(valued_0, cc24_valued_0)).
thf(cc2_card_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_card_1 @ A) ) ) , file(card_1, cc2_card_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_finset_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_finset_1 @ B) ) ) ) ) , file(finset_1, cc2_finset_1)).
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_nat_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  ~ ( (v3_xxreal_0 @ A) ) ) ) , file(nat_1, cc2_nat_1)).
thf(cc2_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) )  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc2_ordinal1)).
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_setfam_1, axiom,  (! [A: $i] :  ( ~ ( (v2_setfam_1 @ A) )  =>  ~ ( (v1_xboole_0 @ A) ) ) ) , file(setfam_1, cc2_setfam_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_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) ) ) ) , file(valued_0, cc2_valued_0)).
thf(cc2_vectsp_1, axiom,  (! [A: $i] :  ( (l6_algstr_0 @ A)  =>  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_vectsp_1 @ A)  &  (v2_vectsp_1 @ A) ) )  =>  ( ~ ( (v2_struct_0 @ A) )  &  (v5_vectsp_1 @ A) ) ) ) ) , file(vectsp_1, cc2_vectsp_1)).
thf(cc2_xreal_0, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc2_xreal_0)).
thf(cc2_xxreal_0, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_xxreal_0 @ A) ) ) , file(xxreal_0, cc2_xxreal_0)).
thf(cc30_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k1_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc30_valued_0)).
thf(cc31_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k5_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, cc31_valued_0)).
thf(cc3_card_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_card_1 @ A) ) ) , file(card_1, cc3_card_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_finset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_finset_1 @ A)  =>  (! [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_funct_2 @ C)  @ A)  @ B)  &  (v1_finset_1 @ C) ) ) ) ) ) ) ) , file(finset_1, cc3_finset_1)).
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_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v7_ordinal1 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) , file(nat_1, cc3_nat_1)).
thf(cc3_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc3_ordinal1)).
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_setfam_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_setfam_1 @ A) )  =>  ~ ( (v2_setfam_1 @ A) ) ) ) , file(setfam_1, cc3_setfam_1)).
thf(cc3_struct_0, axiom,  (! [A: $i] :  ( (l4_struct_0 @ A)  =>  ( ~ ( (v6_struct_0 @ A) )  =>  ~ ( (v7_struct_0 @ A) ) ) ) ) , file(struct_0, cc3_struct_0)).
thf(cc3_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc3_valued_0)).
thf(cc3_vectsp_1, axiom,  (! [A: $i] :  ( (l4_algstr_0 @ A)  =>  ( ( ~ ( (v2_struct_0 @ A) )  &  (v4_vectsp_1 @ A) )  =>  ( ~ ( (v2_struct_0 @ A) )  &  ( (v3_vectsp_1 @ A)  &  (v6_vectsp_1 @ A) ) ) ) ) ) , file(vectsp_1, cc3_vectsp_1)).
thf(cc3_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xcmplx_0 @ A) ) ) , file(xreal_0, cc3_xreal_0)).
thf(cc3_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) )  =>  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc3_xxreal_0)).
thf(cc4_card_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v1_finset_1 @ A) ) ) , file(card_1, cc4_card_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_finset_1, axiom,  (! [A: $i] :  ( (v1_zfmisc_1 @ A)  =>  (v1_finset_1 @ A) ) ) , file(finset_1, cc4_finset_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_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v5_ordinal1 @ A) ) ) , file(ordinal1, cc4_ordinal1)).
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_setfam_1, axiom,  (! [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  =>  ~ ( (v2_setfam_1 @ A) ) ) ) , file(setfam_1, cc4_setfam_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_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc4_valued_0)).
thf(cc4_vectsp_1, axiom,  (! [A: $i] :  ( (l4_algstr_0 @ A)  =>  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v3_vectsp_1 @ A)  &  (v6_vectsp_1 @ A) ) )  =>  ( ~ ( (v2_struct_0 @ A) )  &  (v1_group_1 @ A) ) ) ) ) , file(vectsp_1, cc4_vectsp_1)).
thf(cc4_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xxreal_0 @ A) ) ) , file(xreal_0, cc4_xreal_0)).
thf(cc4_xxreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) )  =>  ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc4_xxreal_0)).
thf(cc5_card_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_finset_1 @ A) ) ) , file(card_1, cc5_card_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_finset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  ~ ( (v1_zfmisc_1 @ A) ) ) ) , file(finset_1, cc5_finset_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_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v3_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc5_ordinal1)).
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_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) ) ) ) , file(valued_0, cc5_valued_0)).
thf(cc5_vectsp_1, axiom,  (! [A: $i] :  ( (l4_algstr_0 @ A)  =>  ( ( ~ ( (v2_struct_0 @ A) )  &  (v4_vectsp_1 @ A) )  =>  ( ~ ( (v2_struct_0 @ A) )  &  (v1_group_1 @ A) ) ) ) ) , file(vectsp_1, cc5_vectsp_1)).
thf(cc5_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) )  =>  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v2_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc5_xxreal_0)).
thf(cc6_card_1, axiom,  (! [A: $i] :  ( ( (v3_ordinal1 @ A)  &  (v1_finset_1 @ A) )  =>  (v7_ordinal1 @ A) ) ) , file(card_1, cc6_card_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_finset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v5_finset_1 @ A) ) ) , file(finset_1, cc6_finset_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(cc6_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) ) ) ) , file(valued_0, cc6_valued_0)).
thf(cc6_vectsp_1, axiom,  (! [A: $i] :  ( (l4_algstr_0 @ A)  =>  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v5_group_1 @ A)  &  (v6_vectsp_1 @ A) ) )  =>  ( ~ ( (v2_struct_0 @ A) )  &  (v3_vectsp_1 @ A) ) ) ) ) , file(vectsp_1, cc6_vectsp_1)).
thf(cc6_xxreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v2_xxreal_0 @ A) ) ) )  =>  ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc6_xxreal_0)).
thf(cc7_card_1, axiom,  (! [A: $i] :  ( ( (v3_card_1 @ A)  @ k1_xboole_0)  =>  (v1_xboole_0 @ A) ) ) , file(card_1, cc7_card_1)).
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_finset_1, axiom,  (! [A: $i] :  ( (v5_finset_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_finset_1 @ B) ) ) ) ) , file(finset_1, cc7_finset_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(cc7_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) ) ) ) , file(valued_0, cc7_valued_0)).
thf(cc7_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_xxreal_0 @ A) )  =>  ( (v1_xxreal_0 @ A)  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc7_xxreal_0)).
thf(cc8_card_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ( (v3_card_1 @ A)  @ k1_xboole_0) ) ) , file(card_1, cc8_card_1)).
thf(cc8_finseq_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v3_finseq_1 @ A) ) ) , file(finseq_1, cc8_finseq_1)).
thf(cc8_finset_1, axiom,  (! [A: $i] :  ( (v5_finset_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v5_finset_1 @ B) ) ) ) ) , file(finset_1, cc8_finset_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(cc8_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc8_valued_0)).
thf(cc8_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ A) ) ) )  =>  ( (v1_xboole_0 @ A)  &  (v1_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc8_xxreal_0)).
thf(cc9_card_1, axiom,  (! [A: $i] :  ( ( (v3_card_1 @ A)  @ np__1)  =>  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_zfmisc_1 @ A) ) ) ) , file(card_1, cc9_card_1)).
thf(cc9_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (v4_funct_1 @ A) ) ) , file(finseq_1, cc9_finseq_1)).
thf(cc9_finset_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v2_finset_1 @ A) ) ) ) , file(finset_1, cc9_finset_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(cc9_valued_0, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, cc9_valued_0)).
thf(commutativity_k1_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (m1_subset_1 @ B)  @ k5_numbers) )  =>  ( (= @  ( (k1_nat_1 @ A)  @ B) )  @  ( (k1_nat_1 @ B)  @ A) ) ) ) , file(nat_1, k1_nat_1)).
thf(commutativity_k2_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  (v7_ordinal1 @ B) )  =>  ( (= @  ( (k2_nat_1 @ A)  @ B) )  @  ( (k2_nat_1 @ B)  @ A) ) ) ) , file(nat_1, k2_nat_1)).
thf(commutativity_k2_tarski, axiom,  (! [A: $i, B: $i] :  ( (= @  ( (k2_tarski @ A)  @ B) )  @  ( (k2_tarski @ B)  @ A) ) ) , file(tarski, k2_tarski)).
thf(commutativity_k2_xcmplx_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k2_xcmplx_0 @ A)  @ B) )  @  ( (k2_xcmplx_0 @ B)  @ A) ) ) ) , file(xcmplx_0, k2_xcmplx_0)).
thf(commutativity_k3_rlvect_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v2_rlvect_1 @ A)  &  (l1_algstr_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( (= @  ( ( (k3_rlvect_1 @ A)  @ B)  @ C) )  @  ( ( (k3_rlvect_1 @ A)  @ C)  @ B) ) ) ) , file(rlvect_1, k3_rlvect_1)).
thf(commutativity_k8_group_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v5_group_1 @ A)  &  (l3_algstr_0 @ A) ) )  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( (= @  ( ( (k8_group_1 @ A)  @ B)  @ C) )  @  ( ( (k8_group_1 @ A)  @ C)  @ B) ) ) ) , file(group_1, k8_group_1)).
thf(connectedness_r1_xxreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v1_xxreal_0 @ B) )  =>  ( ( (r1_xxreal_0 @ A)  @ B)  |  ( (r1_xxreal_0 @ B)  @ A) ) ) ) , file(xxreal_0, r1_xxreal_0)).
thf(d10_vectsp_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v33_algstr_0 @ A)  &  ( (v3_group_1 @ A)  &  ( (v5_group_1 @ A)  &  ( (v4_vectsp_1 @ A)  &  (l6_algstr_0 @ A) ) ) ) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  ( ~ ( ( (= @ B)  @  (k4_struct_0 @ A) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  =>  ( ( (= @ C)  @  ( (k11_algstr_0 @ A)  @ B) )  <=>  ( (= @  ( ( (k8_group_1 @ A)  @ C)  @ B) )  @  (k5_struct_0 @ A) ) ) ) ) ) ) ) ) ) , file(vectsp_1, d10_vectsp_1)).
thf(d11_matrix_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l6_algstr_0 @ A) )  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  (! [C: $i] :  ( ( ( ( (m1_matrix_1 @ C)  @  (u1_struct_0 @ A) )  @ B)  @ B)  =>  ( ( (= @ C)  @  ( (k12_matrix_1 @ A)  @ B) )  <=>  ( (! [D: $i] :  ( (v7_ordinal1 @ D)  =>  ( ( (r2_hidden @  ( (k4_tarski @ D)  @ D) )  @  (k2_matrix_1 @ C) )  =>  ( (= @  ( ( ( (k3_matrix_1 @  (u1_struct_0 @ A) )  @ C)  @ D)  @ D) )  @  (k5_struct_0 @ A) ) ) ) )  &  (! [D: $i] :  ( (v7_ordinal1 @ D)  =>  (! [E: $i] :  ( (v7_ordinal1 @ E)  =>  ( ( (r2_hidden @  ( (k4_tarski @ D)  @ E) )  @  (k2_matrix_1 @ C) )  =>  ( ( (= @ D)  @ E)  |  ( (= @  ( ( ( (k3_matrix_1 @  (u1_struct_0 @ A) )  @ C)  @ D)  @ E) )  @  (k4_struct_0 @ A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(matrix_1, d11_matrix_1)).
thf(d12_ordinal1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  <=>  ( (r2_hidden @ A)  @ k4_ordinal1) ) ) , file(ordinal1, d12_ordinal1)).
thf(d13_finseq_1, axiom,  (! [A: $i] :  ( (? [B: $i] :  ( (v7_ordinal1 @ B)  &  ( (r1_tarski @ A)  @  (k2_finseq_1 @ B) ) ) )  =>  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @ k5_numbers)  =>  ( ( (= @ B)  @  (k14_finseq_1 @ A) )  <=>  ( ( (= @  (k10_xtuple_0 @ B) )  @ A)  &  (! [C: $i] :  ( (v7_ordinal1 @ C)  =>  (! [D: $i] :  ( (v7_ordinal1 @ D)  =>  (! [E: $i] :  ( (v7_ordinal1 @ E)  =>  (! [F: $i] :  ( (v7_ordinal1 @ F)  =>  ~ ( ( ( (r1_xxreal_0 @ np__1)  @ C)  &  ( ~ ( ( (r1_xxreal_0 @ D)  @ C) )  &  ( ( (r1_xxreal_0 @ D)  @  (k3_finseq_1 @ B) )  &  ( ( (= @ E)  @  ( (k1_funct_1 @ B)  @ C) )  &  ( ( (= @ F)  @  ( (k1_funct_1 @ B)  @ D) )  &  ( (r1_xxreal_0 @ F)  @ E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(finseq_1, d13_finseq_1)).
thf(d14_algstr_0, axiom,  (! [A: $i] :  ( (l2_algstr_0 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  =>  ( (= @  ( ( (k5_algstr_0 @ A)  @ B)  @ C) )  @  ( ( (k1_algstr_0 @ A)  @ B)  @  ( (k4_algstr_0 @ A)  @ C) ) ) ) ) ) ) ) ) , file(algstr_0, d14_algstr_0)).
thf(d14_matrix_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l2_struct_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_matrix_1 @ B)  &  ( (m2_finseq_1 @ B)  @  (k3_finseq_2 @  (u1_struct_0 @ A) ) ) )  =>  ( ( (v2_matrix_1 @ B)  @ A)  <=>  (! [C: $i] :  ( (v7_ordinal1 @ C)  =>  (! [D: $i] :  ( (v7_ordinal1 @ D)  =>  ( ( (r2_hidden @  ( (k4_tarski @ C)  @ D) )  @  (k2_matrix_1 @ B) )  =>  ( ( (= @  ( ( ( (k3_matrix_1 @  (u1_struct_0 @ A) )  @ B)  @ C)  @ D) )  @  (k4_struct_0 @ A) )  |  ( (= @ C)  @ D) ) ) ) ) ) ) ) ) ) ) ) , file(matrix_1, d14_matrix_1)).
thf(d18_algstr_0, axiom,  (! [A: $i] :  ( (l3_algstr_0 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  =>  ( (= @  ( ( (k6_algstr_0 @ A)  @ B)  @ C) )  @  ( ( ( (k5_binop_1 @  (u1_struct_0 @ A) )  @  (u2_algstr_0 @ A) )  @ B)  @ C) ) ) ) ) ) ) ) , file(algstr_0, d18_algstr_0)).
thf(d1_algstr_0, axiom,  (! [A: $i] :  ( (l1_algstr_0 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  =>  ( (= @  ( ( (k1_algstr_0 @ A)  @ B)  @ C) )  @  ( ( ( (k5_binop_1 @  (u1_struct_0 @ A) )  @  (u1_algstr_0 @ A) )  @ B)  @ C) ) ) ) ) ) ) ) , file(algstr_0, d1_algstr_0)).
thf(d1_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (= @  (k1_finseq_1 @ A) )  @  ( ( (replSep1 @  (^ [B: $i] :  ( ( (m2_subset_1 @ B)  @ k1_numbers)  @ k5_numbers) ) )  @  (^ [B: $i] : B) )  @  (^ [B: $i] :  ( ( (r1_xxreal_0 @ np__1)  @ B)  &  ( (r1_xxreal_0 @ B)  @ A) ) ) ) ) ) ) , file(finseq_1, d1_finseq_1)).
thf(d1_finseq_2, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (= @  (k1_finseq_2 @ A) )  @  (k6_partfun1 @  (k2_finseq_1 @ A) ) ) ) ) , file(finseq_2, d1_finseq_2)).
thf(d1_fvsum_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l3_algstr_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  ( (= @  ( (k1_fvsum_1 @ A)  @ B) )  @  ( ( ( ( (k10_funcop_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) )  @  (u2_algstr_0 @ A) )  @ B)  @  (k6_partfun1 @  (u1_struct_0 @ A) ) ) ) ) ) ) ) , file(fvsum_1, d1_fvsum_1)).
thf(d1_matrix13, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_matrix_1 @ B)  &  ( (m2_finseq_1 @ B)  @  (k3_finseq_2 @ A) ) )  =>  (! [C: $i] :  ( (v7_ordinal1 @ C)  =>  (! [D: $i] :  ( (v7_ordinal1 @ D)  =>  (! [E: $i] :  ( ( ( (m2_finseq_2 @ E)  @ k5_numbers)  @  ( (k4_finseq_2 @ C)  @ k5_numbers) )  =>  (! [F: $i] :  ( ( ( (m2_finseq_2 @ F)  @ k5_numbers)  @  ( (k4_finseq_2 @ D)  @ k5_numbers) )  =>  (! [G: $i] :  ( ( ( ( (m1_matrix_1 @ G)  @ A)  @ C)  @ D)  =>  ( ( (= @ G)  @  ( ( ( ( ( (k1_matrix13 @ A)  @ B)  @ C)  @ D)  @ E)  @ F) )  <=>  (! [H: $i] :  ( (v7_ordinal1 @ H)  =>  (! [I: $i] :  ( (v7_ordinal1 @ I)  =>  ( ( (r2_hidden @  ( (k4_tarski @ H)  @ I) )  @  (k2_matrix_1 @ G) )  =>  ( (= @  ( ( ( (k3_matrix_1 @ A)  @ G)  @ H)  @ I) )  @  ( ( ( (k3_matrix_1 @ A)  @ B)  @  ( (k1_funct_1 @ E)  @ H) )  @  ( (k1_funct_1 @ F)  @ I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(matrix13, d1_matrix13)).
thf(d2_finseq_2, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (= @  ( (k2_finseq_2 @ A)  @ B) )  @  ( (k7_funcop_1 @  (k2_finseq_1 @ A) )  @ B) ) ) ) ) , file(finseq_2, d2_finseq_2)).
thf(d2_matrix13, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_matrix_1 @ B)  &  ( (m2_finseq_1 @ B)  @  (k3_finseq_2 @ A) ) )  =>  (! [C: $i] :  ( ( (v1_finset_1 @ C)  &  ( (v1_setfam_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ k5_numbers) ) ) )  =>  (! [D: $i] :  ( ( (v1_finset_1 @ D)  &  ( (v1_setfam_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @ k5_numbers) ) ) )  =>  ( (= @  ( ( ( (k6_matrix13 @ A)  @ B)  @ C)  @ D) )  @  ( ( ( ( ( (k1_matrix13 @ A)  @ B)  @  (k5_card_1 @ C) )  @  (k5_card_1 @ D) )  @  (k5_matrix13 @ C) )  @  (k5_matrix13 @ D) ) ) ) ) ) ) ) ) ) ) , file(matrix13, d2_matrix13)).
thf(d2_matrix_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  (! [C: $i] :  ( (v7_ordinal1 @ C)  =>  (! [D: $i] :  ( ( (v1_matrix_1 @ D)  &  ( (m2_finseq_1 @ D)  @  (k3_finseq_2 @ A) ) )  =>  ( ( ( ( (m1_matrix_1 @ D)  @ A)  @ B)  @ C)  <=>  ( ( (= @  (k3_finseq_1 @ D) )  @ B)  &  (! [E: $i] :  ( ( (m2_finseq_1 @ E)  @ A)  =>  ( ( (r2_hidden @ E)  @  (k10_xtuple_0 @ D) )  =>  ( (= @  (k3_finseq_1 @ E) )  @ C) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(matrix_1, d2_matrix_1)).
thf(d2_xboole_0, axiom,  ( (= @ k1_xboole_0)  @  (eps @  (^ [A: $i] :  (v1_xboole_0 @ A) ) ) ) , file(xboole_0, d2_xboole_0)).
thf(d3_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  (! [B: $i] :  ( ( ( (m2_subset_1 @ B)  @ k1_numbers)  @ k5_numbers)  =>  ( ( (= @ B)  @  (k3_finseq_1 @ A) )  <=>  ( (= @  (k2_finseq_1 @ B) )  @  (k9_xtuple_0 @ A) ) ) ) ) ) ) , file(finseq_1, d3_finseq_1)).
thf(d3_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (! [B: $i] :  ( ( (= @ B)  @  (k10_xtuple_0 @ A) )  <=>  (! [C: $i] :  ( ( (r2_hidden @ C)  @ B)  <=>  (? [D: $i] :  ( ( (r2_hidden @ D)  @  (k9_xtuple_0 @ A) )  &  ( (= @ C)  @  ( (k1_funct_1 @ A)  @ D) ) ) ) ) ) ) ) ) ) , file(funct_1, d3_funct_1)).
thf(d3_fvsum_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l2_algstr_0 @ A) )  =>  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @  (u1_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (m2_finseq_1 @ C)  @  (u1_struct_0 @ A) )  =>  ( (= @  ( ( (k3_fvsum_1 @ A)  @ B)  @ C) )  @  ( ( ( ( ( (k1_finseqop @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) )  @  (u1_algstr_0 @ A) )  @ B)  @ C) ) ) ) ) ) ) ) , file(fvsum_1, d3_fvsum_1)).
thf(d3_matrix11, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  (! [C: $i] :  ( (v7_ordinal1 @ C)  =>  (! [D: $i] :  ( ~ ( (v1_xboole_0 @ D) )  =>  (! [E: $i] :  ( ( ( ( (m1_matrix_1 @ E)  @ D)  @ B)  @ C)  =>  (! [F: $i] :  ( ( (m2_finseq_1 @ F)  @ D)  =>  (! [G: $i] :  ( ( ( ( (m1_matrix_1 @ G)  @ D)  @ B)  @ C)  =>  ( ( ( (= @  (k3_finseq_1 @ F) )  @  (k1_matrix_1 @ E) )  =>  ( ( (= @ G)  @  ( ( ( ( ( (k3_matrix11 @ A)  @ B)  @ C)  @ D)  @ E)  @ F) )  <=>  ( ( (= @  (k3_finseq_1 @ G) )  @  (k3_finseq_1 @ E) )  &  ( ( (= @  (k1_matrix_1 @ G) )  @  (k1_matrix_1 @ E) )  &  (! [H: $i] :  ( (v7_ordinal1 @ H)  =>  (! [I: $i] :  ( (v7_ordinal1 @ I)  =>  ( ( (r2_hidden @  ( (k4_tarski @ H)  @ I) )  @  (k2_matrix_1 @ E) )  =>  ( ( ~ ( ( (= @ H)  @ A) )  =>  ( (= @  ( ( ( (k3_matrix_1 @ D)  @ G)  @ H)  @ I) )  @  ( ( ( (k3_matrix_1 @ D)  @ E)  @ H)  @ I) ) )  &  ( ( (= @ H)  @ A)  =>  ( (= @  ( ( ( (k3_matrix_1 @ D)  @ G)  @ A)  @ I) )  @  ( (k1_funct_1 @ F)  @ I) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ~ ( ( (= @  (k3_finseq_1 @ F) )  @  (k1_matrix_1 @ E) ) )  =>  ( ( (= @ G)  @  ( ( ( ( ( (k3_matrix11 @ A)  @ B)  @ C)  @ D)  @ E)  @ F) )  <=>  ( (= @ G)  @ E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(matrix11, d3_matrix11)).
thf(d3_rlvect_1, axiom,  (! [A: $i] :  ( (l1_algstr_0 @ A)  =>  ( (v3_rlvect_1 @ A)  <=>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @  (u1_struct_0 @ A) )  =>  ( (= @  ( ( (k1_algstr_0 @ A)  @  ( ( (k1_algstr_0 @ A)  @ B)  @ C) )  @ D) )  @  ( ( (k1_algstr_0 @ A)  @ B)  @  ( ( (k1_algstr_0 @ A)  @ C)  @ D) ) ) ) ) ) ) ) ) ) ) ) , file(rlvect_1, d3_rlvect_1)).
thf(d4_finseq_2, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (= @  ( (k4_finseq_2 @ A)  @ B) )  @  ( ( (replSep1 @  (^ [C: $i] :  ( ( (m2_finseq_2 @ C)  @ B)  @  (k3_finseq_2 @ B) ) ) )  @  (^ [C: $i] : C) )  @  (^ [C: $i] :  ( (= @  (k3_finseq_1 @ C) )  @ A) ) ) ) ) ) ) , file(finseq_2, d4_finseq_2)).
thf(d4_matrix_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v1_matrix_1 @ A) ) ) )  =>  ( (= @  (k2_matrix_1 @ A) )  @  ( (k2_zfmisc_1 @  (k4_finseq_1 @ A) )  @  (k2_finseq_1 @  (k1_matrix_1 @ A) ) ) ) ) ) , file(matrix_1, d4_matrix_1)).
thf(d4_rlvect_1, axiom,  (! [A: $i] :  ( (l2_algstr_0 @ A)  =>  ( (v4_rlvect_1 @ A)  <=>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  ( (= @  ( ( (k1_algstr_0 @ A)  @ B)  @  (k4_struct_0 @ A) ) )  @ B) ) ) ) ) ) , file(rlvect_1, d4_rlvect_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_fvsum_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l3_algstr_0 @ A) )  =>  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @  (u1_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  =>  ( (= @  ( ( (k9_fvsum_1 @ A)  @ B)  @ C) )  @  ( ( ( (k4_finseqop @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) )  @ B)  @  ( (k1_fvsum_1 @ A)  @ C) ) ) ) ) ) ) ) ) , file(fvsum_1, d6_fvsum_1)).
thf(d6_partfun1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) )  =>  (! [C: $i] :  ( ( (r2_hidden @ C)  @  (k9_xtuple_0 @ B) )  =>  ( (= @  ( ( (k7_partfun1 @ A)  @ B)  @ C) )  @  ( (k1_funct_1 @ B)  @ C) ) ) ) ) ) ) , file(partfun1, d6_partfun1)).
thf(d7_card_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v3_card_1 @ B)  @ A)  <=>  ( (= @  (k1_card_1 @ B) )  @ A) ) ) ) , file(card_1, d7_card_1)).
thf(d7_matrix_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_matrix_1 @ B)  &  ( (m2_finseq_1 @ B)  @  (k3_finseq_2 @ A) ) )  =>  (! [C: $i] :  ( (v7_ordinal1 @ C)  =>  (! [D: $i] :  ( ( (m2_finseq_1 @ D)  @ A)  =>  ( ( (= @ D)  @  ( ( (k6_matrix_1 @ A)  @ B)  @ C) )  <=>  ( ( (= @  (k3_finseq_1 @ D) )  @  (k1_matrix_1 @ B) )  &  (! [E: $i] :  ( (v7_ordinal1 @ E)  =>  ( ( (r2_hidden @ E)  @  (k2_finseq_1 @  (k1_matrix_1 @ B) ) )  =>  ( (= @  ( (k1_funct_1 @ D)  @ E) )  @  ( ( ( (k3_matrix_1 @ A)  @ B)  @ C)  @ E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(matrix_1, d7_matrix_1)).
thf(dt_f1_s2_matrix15, axiom,  ( ~ ( (v2_struct_0 @ f1_s2_matrix15) )  &  ( ~ ( (v6_struct_0 @ f1_s2_matrix15) )  &  ( (v13_algstr_0 @ f1_s2_matrix15)  &  ( (v33_algstr_0 @ f1_s2_matrix15)  &  ( (v3_group_1 @ f1_s2_matrix15)  &  ( (v5_group_1 @ f1_s2_matrix15)  &  ( (v4_vectsp_1 @ f1_s2_matrix15)  &  ( (v5_vectsp_1 @ f1_s2_matrix15)  &  ( (v2_rlvect_1 @ f1_s2_matrix15)  &  ( (v3_rlvect_1 @ f1_s2_matrix15)  &  ( (v4_rlvect_1 @ f1_s2_matrix15)  &  (l6_algstr_0 @ f1_s2_matrix15) ) ) ) ) ) ) ) ) ) ) ) , file(matrix15, f1_s2_matrix15)).
thf(dt_f2_s2_matrix15, axiom,  (v7_ordinal1 @ f2_s2_matrix15) , file(matrix15, f2_s2_matrix15)).
thf(dt_f3_s2_matrix15, axiom,  (v7_ordinal1 @ f3_s2_matrix15) , file(matrix15, f3_s2_matrix15)).
thf(dt_f4_s2_matrix15, axiom,  (v7_ordinal1 @ f4_s2_matrix15) , file(matrix15, f4_s2_matrix15)).
thf(dt_f5_s2_matrix15, axiom,  ( ( ( (m1_matrix_1 @ f5_s2_matrix15)  @  (u1_struct_0 @ f1_s2_matrix15) )  @ f2_s2_matrix15)  @ f3_s2_matrix15) , file(matrix15, f5_s2_matrix15)).
thf(dt_f6_s2_matrix15, axiom,  ( ( ( (m1_matrix_1 @ f6_s2_matrix15)  @  (u1_struct_0 @ f1_s2_matrix15) )  @ f2_s2_matrix15)  @ f4_s2_matrix15) , file(matrix15, f6_s2_matrix15)).
thf(dt_f7_s2_matrix15, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_matrix_1 @  ( ( ( (f7_s2_matrix15 @ A)  @ B)  @ C)  @ D) )  @  (u1_struct_0 @ f1_s2_matrix15) )  @ f2_s2_matrix15)  @ f4_s2_matrix15) ) , file(matrix15, f7_s2_matrix15)).
thf(dt_k10_funcop_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) )  &  ( ( (m1_subset_1 @ D)  @ A)  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ B)  @ A)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( ( ( ( (k10_funcop_1 @ A)  @ B)  @ C)  @ D)  @ E) )  &  ( ( ( (v1_funct_2 @  ( ( ( ( (k10_funcop_1 @ A)  @ B)  @ C)  @ D)  @ E) )  @ B)  @ A)  &  ( (m1_subset_1 @  ( ( ( ( (k10_funcop_1 @ A)  @ B)  @ C)  @ D)  @ E) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) ) ) ) ) ) , file(funcop_1, k10_funcop_1)).
thf(dt_k10_fvsum_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  ( ( ~ ( (v2_struct_0 @ B) )  &  (l3_algstr_0 @ B) )  &  ( ( (m1_subset_1 @ C)  @  ( (k4_finseq_2 @ A)  @  (u1_struct_0 @ B) ) )  &  ( (m1_subset_1 @ D)  @  (u1_struct_0 @ B) ) ) ) )  =>  ( ( (m2_finseq_2 @  ( ( ( (k10_fvsum_1 @ A)  @ B)  @ C)  @ D) )  @  (u1_struct_0 @ B) )  @  ( (k4_finseq_2 @ A)  @  (u1_struct_0 @ B) ) ) ) ) , file(fvsum_1, k10_fvsum_1)).
thf(dt_k10_xtuple_0, axiom, $true, file(xtuple_0, k10_xtuple_0)).
thf(dt_k11_algstr_0, axiom,  (! [A: $i, B: $i] :  ( ( (l5_algstr_0 @ A)  &  ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) ) )  =>  ( (m1_subset_1 @  ( (k11_algstr_0 @ A)  @ B) )  @  (u1_struct_0 @ A) ) ) ) , file(algstr_0, k11_algstr_0)).
thf(dt_k12_matrix_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l6_algstr_0 @ A) )  &  (v7_ordinal1 @ B) )  =>  ( ( ( (m1_matrix_1 @  ( (k12_matrix_1 @ A)  @ B) )  @  (u1_struct_0 @ A) )  @ B)  @ B) ) ) , file(matrix_1, k12_matrix_1)).
thf(dt_k13_finseq_1, axiom, $true, file(finseq_1, k13_finseq_1)).
thf(dt_k14_finseq_1, axiom,  (! [A: $i] :  ( (m2_finseq_1 @  (k14_finseq_1 @ A) )  @ k5_numbers) ) , file(finseq_1, k14_finseq_1)).
thf(dt_k1_algstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (l1_algstr_0 @ A)  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( (m1_subset_1 @  ( ( (k1_algstr_0 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ A) ) ) ) , file(algstr_0, k1_algstr_0)).
thf(dt_k1_binop_1, axiom, $true, file(binop_1, k1_binop_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_finseq_1, axiom, $true, file(finseq_1, k1_finseq_1)).
thf(dt_k1_finseq_2, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v1_relat_1 @  (k1_finseq_2 @ A) )  &  ( (v1_funct_1 @  (k1_finseq_2 @ A) )  &  (v1_finseq_1 @  (k1_finseq_2 @ A) ) ) ) ) ) , file(finseq_2, k1_finseq_2)).
thf(dt_k1_finseqop, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( ~ ( (v1_xboole_0 @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @  ( (k2_zfmisc_1 @ A)  @ B) )  @ C)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ C) ) ) ) )  &  ( ( (m1_finseq_1 @ E)  @ A)  &  ( (m1_finseq_1 @ F)  @ B) ) ) ) ) )  =>  ( (m2_finseq_1 @  ( ( ( ( ( (k1_finseqop @ A)  @ B)  @ C)  @ D)  @ E)  @ F) )  @ C) ) ) , file(finseqop, k1_finseqop)).
thf(dt_k1_funct_1, axiom, $true, file(funct_1, k1_funct_1)).
thf(dt_k1_fvsum_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l3_algstr_0 @ A) )  &  ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) ) )  =>  ( (v1_funct_1 @  ( (k1_fvsum_1 @ A)  @ B) )  &  ( ( ( (v1_funct_2 @  ( (k1_fvsum_1 @ A)  @ B) )  @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @  ( (k1_fvsum_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) ) ) ) ) ) ) , file(fvsum_1, k1_fvsum_1)).
thf(dt_k1_group_1, axiom,  (! [A: $i] :  ( (l3_algstr_0 @ A)  =>  ( (m1_subset_1 @  (k1_group_1 @ A) )  @  (u1_struct_0 @ A) ) ) ) , file(group_1, k1_group_1)).
thf(dt_k1_matrix13, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_matrix_1 @ B)  &  ( (m1_finseq_1 @ B)  @  (k3_finseq_2 @ A) ) )  &  ( (v7_ordinal1 @ C)  &  ( (v7_ordinal1 @ D)  &  ( ( (m1_subset_1 @ E)  @  ( (k4_finseq_2 @ C)  @ k5_numbers) )  &  ( (m1_subset_1 @ F)  @  ( (k4_finseq_2 @ D)  @ k5_numbers) ) ) ) ) ) )  =>  ( ( ( (m1_matrix_1 @  ( ( ( ( ( (k1_matrix13 @ A)  @ B)  @ C)  @ D)  @ E)  @ F) )  @ A)  @ C)  @ D) ) ) , file(matrix13, k1_matrix13)).
thf(dt_k1_matrix_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v1_matrix_1 @ A) ) ) )  =>  ( (m1_subset_1 @  (k1_matrix_1 @ A) )  @ k5_numbers) ) ) , file(matrix_1, k1_matrix_1)).
thf(dt_k1_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (m1_subset_1 @ B)  @ k5_numbers) )  =>  ( ( (m2_subset_1 @  ( (k1_nat_1 @ A)  @ B) )  @ k1_numbers)  @ k5_numbers) ) ) , file(nat_1, k1_nat_1)).
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_zfmisc_1, axiom, $true, file(zfmisc_1, k1_zfmisc_1)).
thf(dt_k2_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (m1_subset_1 @  (k2_finseq_1 @ A) )  @  (k1_zfmisc_1 @ k5_numbers) ) ) ) , file(finseq_1, k2_finseq_1)).
thf(dt_k2_finseq_2, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v1_relat_1 @  ( (k2_finseq_2 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k2_finseq_2 @ A)  @ B) )  &  (v1_finseq_1 @  ( (k2_finseq_2 @ A)  @ B) ) ) ) ) ) , file(finseq_2, k2_finseq_2)).
thf(dt_k2_funcop_1, axiom, $true, file(funcop_1, k2_funcop_1)).
thf(dt_k2_matrix_1, axiom, $true, file(matrix_1, k2_matrix_1)).
thf(dt_k2_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  (v7_ordinal1 @ B) )  =>  ( ( (m2_subset_1 @  ( (k2_nat_1 @ A)  @ B) )  @ k1_numbers)  @ k5_numbers) ) ) , file(nat_1, k2_nat_1)).
thf(dt_k2_tarski, axiom, $true, file(tarski, k2_tarski)).
thf(dt_k2_xcmplx_0, axiom, $true, file(xcmplx_0, k2_xcmplx_0)).
thf(dt_k2_zfmisc_1, axiom, $true, file(zfmisc_1, k2_zfmisc_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_funcop_1, axiom, $true, file(funcop_1, k3_funcop_1)).
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_fvsum_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l2_algstr_0 @ A) )  &  ( ( (m1_finseq_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_finseq_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( (m2_finseq_1 @  ( ( (k3_fvsum_1 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ A) ) ) ) , file(fvsum_1, k3_fvsum_1)).
thf(dt_k3_matrix11, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (v7_ordinal1 @ B)  &  ( (v7_ordinal1 @ C)  &  ( ~ ( (v1_xboole_0 @ D) )  &  ( ( ( ( (m1_matrix_1 @ E)  @ D)  @ B)  @ C)  &  ( (m1_finseq_1 @ F)  @ D) ) ) ) ) )  =>  ( ( ( (m1_matrix_1 @  ( ( ( ( ( (k3_matrix11 @ A)  @ B)  @ C)  @ D)  @ E)  @ F) )  @ D)  @ B)  @ C) ) ) , file(matrix11, k3_matrix11)).
thf(dt_k3_matrix_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (v1_matrix_1 @ B)  &  ( (m1_finseq_1 @ B)  @  (k3_finseq_2 @ A) ) )  &  ( (v7_ordinal1 @ C)  &  (v7_ordinal1 @ D) ) )  =>  ( (m1_subset_1 @  ( ( ( (k3_matrix_1 @ A)  @ B)  @ C)  @ D) )  @ A) ) ) , file(matrix_1, k3_matrix_1)).
thf(dt_k3_numbers, axiom, $true, file(numbers, k3_numbers)).
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_k3_rlvect_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v2_rlvect_1 @ A)  &  (l1_algstr_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( (m1_subset_1 @  ( ( (k3_rlvect_1 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ A) ) ) ) , file(rlvect_1, k3_rlvect_1)).
thf(dt_k4_algstr_0, axiom,  (! [A: $i, B: $i] :  ( ( (l2_algstr_0 @ A)  &  ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) ) )  =>  ( (m1_subset_1 @  ( (k4_algstr_0 @ A)  @ B) )  @  (u1_struct_0 @ A) ) ) ) , file(algstr_0, k4_algstr_0)).
thf(dt_k4_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (m1_subset_1 @  (k4_finseq_1 @ A) )  @  (k1_zfmisc_1 @ k5_numbers) ) ) ) , file(finseq_1, k4_finseq_1)).
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_finseqop, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_finseq_1 @ C)  @ A)  &  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (m2_finseq_1 @  ( ( ( (k4_finseqop @ A)  @ B)  @ C)  @ D) )  @ B) ) ) , file(finseqop, k4_finseqop)).
thf(dt_k4_fvsum_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  ( ( ~ ( (v2_struct_0 @ B) )  &  (l2_algstr_0 @ B) )  &  ( ( (m1_subset_1 @ C)  @  ( (k4_finseq_2 @ A)  @  (u1_struct_0 @ B) ) )  &  ( (m1_subset_1 @ D)  @  ( (k4_finseq_2 @ A)  @  (u1_struct_0 @ B) ) ) ) ) )  =>  ( ( (m2_finseq_2 @  ( ( ( (k4_fvsum_1 @ A)  @ B)  @ C)  @ D) )  @  (u1_struct_0 @ B) )  @  ( (k4_finseq_2 @ A)  @  (u1_struct_0 @ B) ) ) ) ) , file(fvsum_1, k4_fvsum_1)).
thf(dt_k4_numbers, axiom, $true, file(numbers, k4_numbers)).
thf(dt_k4_ordinal1, axiom, $true, file(ordinal1, k4_ordinal1)).
thf(dt_k4_relat_1, axiom,  (! [A: $i] :  (v1_relat_1 @  (k4_relat_1 @ A) ) ) , file(relat_1, k4_relat_1)).
thf(dt_k4_struct_0, axiom,  (! [A: $i] :  ( (l2_struct_0 @ A)  =>  ( (m1_subset_1 @  (k4_struct_0 @ A) )  @  (u1_struct_0 @ A) ) ) ) , file(struct_0, k4_struct_0)).
thf(dt_k4_tarski, axiom, $true, file(tarski, k4_tarski)).
thf(dt_k4_xcmplx_0, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) ) ) ) , file(xcmplx_0, k4_xcmplx_0)).
thf(dt_k5_algstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (l2_algstr_0 @ A)  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( (m1_subset_1 @  ( ( (k5_algstr_0 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ A) ) ) ) , file(algstr_0, k5_algstr_0)).
thf(dt_k5_binop_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) )  &  ( ( (m1_subset_1 @ C)  @ A)  &  ( (m1_subset_1 @ D)  @ A) ) )  =>  ( (m1_subset_1 @  ( ( ( (k5_binop_1 @ A)  @ B)  @ C)  @ D) )  @ A) ) ) , file(binop_1, k5_binop_1)).
thf(dt_k5_card_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  ( (m1_subset_1 @  (k5_card_1 @ A) )  @ k4_ordinal1) ) ) , file(card_1, k5_card_1)).
thf(dt_k5_finseq_2, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v7_ordinal1 @ B)  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ( ( (m2_finseq_2 @  ( ( (k5_finseq_2 @ A)  @ B)  @ C) )  @ A)  @  ( (k4_finseq_2 @ B)  @ A) ) ) ) , file(finseq_2, k5_finseq_2)).
thf(dt_k5_funcop_1, axiom, $true, file(funcop_1, k5_funcop_1)).
thf(dt_k5_matrix13, axiom,  (! [A: $i] :  ( ( (v1_finset_1 @ A)  &  ( (v1_setfam_1 @ A)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k5_numbers) ) ) )  =>  ( ( (m2_finseq_2 @  (k5_matrix13 @ A) )  @ k5_numbers)  @  ( (k4_finseq_2 @  (k5_card_1 @ A) )  @ k5_numbers) ) ) ) , file(matrix13, k5_matrix13)).
thf(dt_k5_numbers, axiom,  ( (m1_subset_1 @ k5_numbers)  @  (k1_zfmisc_1 @ k1_numbers) ) , file(numbers, k5_numbers)).
thf(dt_k5_struct_0, axiom,  (! [A: $i] :  ( (l3_struct_0 @ A)  =>  ( (m1_subset_1 @  (k5_struct_0 @ A) )  @  (u1_struct_0 @ A) ) ) ) , file(struct_0, k5_struct_0)).
thf(dt_k6_algstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (l3_algstr_0 @ A)  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( (m1_subset_1 @  ( ( (k6_algstr_0 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ A) ) ) ) , file(algstr_0, k6_algstr_0)).
thf(dt_k6_matrix13, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_matrix_1 @ B)  &  ( (m1_finseq_1 @ B)  @  (k3_finseq_2 @ A) ) )  &  ( ( (v1_finset_1 @ C)  &  ( (v1_setfam_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ k5_numbers) ) ) )  &  ( (v1_finset_1 @ D)  &  ( (v1_setfam_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @ k5_numbers) ) ) ) ) ) )  =>  ( ( ( (m1_matrix_1 @  ( ( ( (k6_matrix13 @ A)  @ B)  @ C)  @ D) )  @ A)  @  (k5_card_1 @ C) )  @  (k5_card_1 @ D) ) ) ) , file(matrix13, k6_matrix13)).
thf(dt_k6_matrix_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_matrix_1 @ B)  &  ( (m1_finseq_1 @ B)  @  (k3_finseq_2 @ A) ) )  &  (v7_ordinal1 @ C) ) )  =>  ( (m2_finseq_1 @  ( ( (k6_matrix_1 @ A)  @ B)  @ C) )  @ A) ) ) , file(matrix_1, k6_matrix_1)).
thf(dt_k6_numbers, axiom,  ( ( (m2_subset_1 @ k6_numbers)  @ k1_numbers)  @ k5_numbers) , file(numbers, k6_numbers)).
thf(dt_k6_partfun1, axiom,  (! [A: $i] :  ( ( (v1_partfun1 @  (k6_partfun1 @ A) )  @ A)  &  ( (m1_subset_1 @  (k6_partfun1 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) , file(partfun1, k6_partfun1)).
thf(dt_k6_xcmplx_0, axiom, $true, file(xcmplx_0, k6_xcmplx_0)).
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_k7_partfun1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) )  =>  ( (m1_subset_1 @  ( ( (k7_partfun1 @ A)  @ B)  @ C) )  @ A) ) ) , file(partfun1, k7_partfun1)).
thf(dt_k8_group_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v5_group_1 @ A)  &  (l3_algstr_0 @ A) ) )  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( (m1_subset_1 @  ( ( (k8_group_1 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ A) ) ) ) , file(group_1, k8_group_1)).
thf(dt_k8_matrix13, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v6_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v33_algstr_0 @ A)  &  ( (v3_group_1 @ A)  &  ( (v5_group_1 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v4_vectsp_1 @ A)  &  ( (v5_vectsp_1 @ A)  &  (l6_algstr_0 @ A) ) ) ) ) ) ) ) ) ) ) )  &  ( (v1_matrix_1 @ B)  &  ( (m1_finseq_1 @ B)  @  (k3_finseq_2 @  (u1_struct_0 @ A) ) ) ) )  =>  ( (m1_subset_1 @  ( (k8_matrix13 @ A)  @ B) )  @ k5_numbers) ) ) , file(matrix13, k8_matrix13)).
thf(dt_k8_matrix_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_matrix_1 @ B)  &  ( (m1_finseq_1 @ B)  @  (k3_finseq_2 @ A) ) )  &  (v7_ordinal1 @ C) ) )  =>  ( ( (m2_finseq_2 @  ( ( (k8_matrix_1 @ A)  @ B)  @ C) )  @ A)  @  ( (k4_finseq_2 @  (k1_matrix_1 @ B) )  @ A) ) ) ) , file(matrix_1, k8_matrix_1)).
thf(dt_k9_fvsum_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l3_algstr_0 @ A) )  &  ( ( (m1_finseq_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( (m2_finseq_1 @  ( ( (k9_fvsum_1 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ A) ) ) ) , file(fvsum_1, k9_fvsum_1)).
thf(dt_k9_xtuple_0, axiom, $true, file(xtuple_0, k9_xtuple_0)).
thf(dt_l1_algstr_0, axiom,  (! [A: $i] :  ( (l1_algstr_0 @ A)  =>  (l1_struct_0 @ A) ) ) , file(algstr_0, l1_algstr_0)).
thf(dt_l1_struct_0, axiom, $true, file(struct_0, l1_struct_0)).
thf(dt_l2_algstr_0, axiom,  (! [A: $i] :  ( (l2_algstr_0 @ A)  =>  ( (l2_struct_0 @ A)  &  (l1_algstr_0 @ A) ) ) ) , file(algstr_0, l2_algstr_0)).
thf(dt_l2_struct_0, axiom,  (! [A: $i] :  ( (l2_struct_0 @ A)  =>  (l1_struct_0 @ A) ) ) , file(struct_0, l2_struct_0)).
thf(dt_l3_algstr_0, axiom,  (! [A: $i] :  ( (l3_algstr_0 @ A)  =>  (l1_struct_0 @ A) ) ) , file(algstr_0, l3_algstr_0)).
thf(dt_l3_struct_0, axiom,  (! [A: $i] :  ( (l3_struct_0 @ A)  =>  (l1_struct_0 @ A) ) ) , file(struct_0, l3_struct_0)).
thf(dt_l4_algstr_0, axiom,  (! [A: $i] :  ( (l4_algstr_0 @ A)  =>  ( (l3_struct_0 @ A)  &  (l3_algstr_0 @ A) ) ) ) , file(algstr_0, l4_algstr_0)).
thf(dt_l4_struct_0, axiom,  (! [A: $i] :  ( (l4_struct_0 @ A)  =>  ( (l2_struct_0 @ A)  &  (l3_struct_0 @ A) ) ) ) , file(struct_0, l4_struct_0)).
thf(dt_l5_algstr_0, axiom,  (! [A: $i] :  ( (l5_algstr_0 @ A)  =>  ( (l4_algstr_0 @ A)  &  (l4_struct_0 @ A) ) ) ) , file(algstr_0, l5_algstr_0)).
thf(dt_l6_algstr_0, axiom,  (! [A: $i] :  ( (l6_algstr_0 @ A)  =>  ( (l2_algstr_0 @ A)  &  (l5_algstr_0 @ A) ) ) ) , file(algstr_0, l6_algstr_0)).
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_matrix_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v7_ordinal1 @ B)  &  (v7_ordinal1 @ C) ) )  =>  (! [D: $i] :  ( ( ( ( (m1_matrix_1 @ D)  @ A)  @ B)  @ C)  =>  ( (v1_matrix_1 @ D)  &  ( (m2_finseq_1 @ D)  @  (k3_finseq_2 @ A) ) ) ) ) ) ) , file(matrix_1, m1_matrix_1)).
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_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_algstr_0, axiom,  (! [A: $i] :  ( (l1_algstr_0 @ A)  =>  ( (v1_funct_1 @  (u1_algstr_0 @ A) )  &  ( ( ( (v1_funct_2 @  (u1_algstr_0 @ A) )  @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @  (u1_algstr_0 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) ) ) ) ) ) ) ) , file(algstr_0, u1_algstr_0)).
thf(dt_u1_struct_0, axiom, $true, file(struct_0, u1_struct_0)).
thf(dt_u2_algstr_0, axiom,  (! [A: $i] :  ( (l3_algstr_0 @ A)  =>  ( (v1_funct_1 @  (u2_algstr_0 @ A) )  &  ( ( ( (v1_funct_2 @  (u2_algstr_0 @ A) )  @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @  (u2_algstr_0 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) ) ) ) ) ) ) ) , file(algstr_0, u2_algstr_0)).
thf(existence_l1_algstr_0, axiom,  (? [A: $i] :  (l1_algstr_0 @ A) ) , file(algstr_0, l1_algstr_0)).
thf(existence_l1_struct_0, axiom,  (? [A: $i] :  (l1_struct_0 @ A) ) , file(struct_0, l1_struct_0)).
thf(existence_l2_algstr_0, axiom,  (? [A: $i] :  (l2_algstr_0 @ A) ) , file(algstr_0, l2_algstr_0)).
thf(existence_l2_struct_0, axiom,  (? [A: $i] :  (l2_struct_0 @ A) ) , file(struct_0, l2_struct_0)).
thf(existence_l3_algstr_0, axiom,  (? [A: $i] :  (l3_algstr_0 @ A) ) , file(algstr_0, l3_algstr_0)).
thf(existence_l3_struct_0, axiom,  (? [A: $i] :  (l3_struct_0 @ A) ) , file(struct_0, l3_struct_0)).
thf(existence_l4_algstr_0, axiom,  (? [A: $i] :  (l4_algstr_0 @ A) ) , file(algstr_0, l4_algstr_0)).
thf(existence_l4_struct_0, axiom,  (? [A: $i] :  (l4_struct_0 @ A) ) , file(struct_0, l4_struct_0)).
thf(existence_l5_algstr_0, axiom,  (? [A: $i] :  (l5_algstr_0 @ A) ) , file(algstr_0, l5_algstr_0)).
thf(existence_l6_algstr_0, axiom,  (? [A: $i] :  (l6_algstr_0 @ A) ) , file(algstr_0, l6_algstr_0)).
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_matrix_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v7_ordinal1 @ B)  &  (v7_ordinal1 @ C) ) )  =>  (? [D: $i] :  ( ( ( (m1_matrix_1 @ D)  @ A)  @ B)  @ C) ) ) ) , file(matrix_1, m1_matrix_1)).
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_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_card_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_finset_1 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_finset_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) , file(card_1, fc10_card_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_nat_1, axiom,  (! [A: $i, B: $i] :  ( (v3_ordinal1 @ A)  =>  (v5_ordinal1 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(nat_1, fc10_nat_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_struct_0, axiom,  (! [A: $i] :  ( (l2_struct_0 @ A)  =>  ( (v9_struct_0 @  (k4_struct_0 @ A) )  @ A) ) ) , file(struct_0, fc10_struct_0)).
thf(fc10_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v2_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc10_xreal_0)).
thf(fc11_card_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_finset_1 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_finset_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) ) ) ) , file(card_1, fc11_card_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_funct_2, axiom,  (! [A: $i] :  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  ( ( (v4_relat_1 @  (k4_relat_1 @ A) )  @ A)  &  ( (v1_funct_1 @  (k4_relat_1 @ A) )  &  ( (v1_partfun1 @  (k4_relat_1 @ A) )  @ A) ) ) ) ) , file(funct_2, fc11_funct_2)).
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(fc11_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v6_struct_0 @ A) )  &  (l4_struct_0 @ A) )  =>  ~ ( ( (v9_struct_0 @  (k5_struct_0 @ A) )  @ A) ) ) ) , file(struct_0, fc11_struct_0)).
thf(fc11_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc11_xreal_0)).
thf(fc12_finseq_1, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k13_finseq_1 @ A) ) ) ) , file(finseq_1, fc12_finseq_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(fc12_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k2_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc12_xreal_0)).
thf(fc13_card_1, axiom,  (! [A: $i] :  ( (v3_card_1 @  (k1_tarski @ A) )  @ np__1) ) , file(card_1, fc13_card_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_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc13_xreal_0)).
thf(fc14_card_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_card_1 @ A)  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v3_card_1 @ B)  @ A) ) ) )  =>  ( (v3_card_1 @  (k9_xtuple_0 @ B) )  @ A) ) ) , file(card_1, fc14_card_1)).
thf(fc14_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_finset_1 @ A)  &  (v1_finset_1 @ B) )  =>  (v1_finset_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(finset_1, fc14_finset_1)).
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_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k2_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc14_xreal_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(fc15_xreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  =>  ( (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) )  &  ~ ( (v3_xxreal_0 @  (k4_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc15_xreal_0)).
thf(fc16_xreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  =>  ( (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) )  &  ~ ( (v2_xxreal_0 @  (k4_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc16_xreal_0)).
thf(fc17_finset_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  (v1_finset_1 @  (k1_zfmisc_1 @ A) ) ) ) , file(finset_1, fc17_finset_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(fc17_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v3_xxreal_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc17_xreal_0)).
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(fc18_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v2_xxreal_0 @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) ) , file(xreal_0, fc18_xreal_0)).
thf(fc19_finset_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_finset_1 @ A) )  =>  (v1_finset_1 @  (k9_xtuple_0 @ A) ) ) ) , file(finset_1, fc19_finset_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(fc19_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc19_xreal_0)).
thf(fc1_card_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ( (v1_xboole_0 @  (k1_card_1 @ A) )  &  (v1_card_1 @  (k1_card_1 @ A) ) ) ) ) , file(card_1, fc1_card_1)).
thf(fc1_finseq_1, axiom,  (! [A: $i] :  ( ( (v7_ordinal1 @ A)  &  (v1_xboole_0 @ A) )  =>  (v1_xboole_0 @  (k1_finseq_1 @ A) ) ) ) , file(finseq_1, fc1_finseq_1)).
thf(fc1_finseq_2, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v1_relat_1 @  (k1_finseq_2 @ A) )  &  ( (v1_funct_1 @  (k1_finseq_2 @ A) )  &  ( ( (v3_card_1 @  (k1_finseq_2 @ A) )  @ A)  &  (v1_finseq_1 @  (k1_finseq_2 @ A) ) ) ) ) ) ) , file(finseq_2, fc1_finseq_2)).
thf(fc1_finset_1, axiom,  (! [A: $i] :  (v1_finset_1 @  (k1_tarski @ A) ) ) , file(finset_1, fc1_finset_1)).
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_fvsum_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v2_rlvect_1 @ A)  &  (l2_algstr_0 @ A) ) )  =>  ( (v1_funct_1 @  (u1_algstr_0 @ A) )  &  ( ( ( (v1_funct_2 @  (u1_algstr_0 @ A) )  @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) )  &  ( (v1_binop_1 @  (u1_algstr_0 @ A) )  @  (u1_struct_0 @ A) ) ) ) ) ) , file(fvsum_1, fc1_fvsum_1)).
thf(fc1_matrix13, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_setfam_1 @  (k1_finseq_1 @ A) ) ) ) , file(matrix13, fc1_matrix13)).
thf(fc1_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  (v7_ordinal1 @ B) )  =>  (v7_ordinal1 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(nat_1, fc1_nat_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_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) )  =>  (v1_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc1_valued_0)).
thf(fc1_xboole_0, axiom,  (v1_xboole_0 @ k1_xboole_0) , file(xboole_0, fc1_xboole_0)).
thf(fc20_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finset_1 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ B)  @ A) )  &  (v1_finset_1 @  ( (k3_relat_1 @ B)  @ A) ) ) ) ) , file(finset_1, fc20_finset_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_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc20_xreal_0)).
thf(fc21_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc21_xreal_0)).
thf(fc22_finseq_1, axiom,  (! [A: $i] :  (v4_funct_1 @  (k13_finseq_1 @ A) ) ) , file(finseq_1, fc22_finseq_1)).
thf(fc22_finset_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_finset_1 @ A) )  =>  (v1_finset_1 @  (k10_xtuple_0 @ A) ) ) ) , file(finset_1, fc22_finset_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(fc22_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc22_xreal_0)).
thf(fc23_finseq_1, axiom,  (! [A: $i] :  ( ( (v7_ordinal1 @ A)  &  ~ ( (v1_xboole_0 @ A) ) )  =>  ~ ( (v1_xboole_0 @  (k1_finseq_1 @ A) ) ) ) ) , file(finseq_1, fc23_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_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(fc27_finseq_1, axiom,  (! [A: $i] :  (v3_finseq_1 @  (k13_finseq_1 @ A) ) ) , file(finseq_1, fc27_finseq_1)).
thf(fc28_relat_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  ( ( (v4_relat_1 @  (k4_relat_1 @ A) )  @ A)  &  ( (v5_relat_1 @  (k4_relat_1 @ A) )  @ A) ) ) ) , file(relat_1, fc28_relat_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_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  ( ~ ( (v1_xboole_0 @  (k1_card_1 @ A) ) )  &  (v1_card_1 @  (k1_card_1 @ A) ) ) ) ) , file(card_1, fc2_card_1)).
thf(fc2_finseq_1, axiom,  (! [A: $i] :  ( ( (v7_ordinal1 @ A)  &  ~ ( (v1_xboole_0 @ A) ) )  =>  ~ ( (v1_xboole_0 @  (k1_finseq_1 @ A) ) ) ) ) , file(finseq_1, fc2_finseq_1)).
thf(fc2_finseq_2, axiom,  ( (v1_relat_1 @  (k1_finseq_2 @ k6_numbers) )  &  ( (v1_funct_1 @  (k1_finseq_2 @ k6_numbers) )  &  ( (v1_xboole_0 @  (k1_finseq_2 @ k6_numbers) )  &  (v1_finseq_1 @  (k1_finseq_2 @ k6_numbers) ) ) ) ) , file(finseq_2, fc2_finseq_2)).
thf(fc2_finset_1, axiom,  (! [A: $i, B: $i] :  (v1_finset_1 @  ( (k2_tarski @ A)  @ B) ) ) , file(finset_1, fc2_finset_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_fvsum_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v3_rlvect_1 @ A)  &  (l2_algstr_0 @ A) ) )  =>  ( (v1_funct_1 @  (u1_algstr_0 @ A) )  &  ( ( ( (v1_funct_2 @  (u1_algstr_0 @ A) )  @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) )  &  ( (v2_binop_1 @  (u1_algstr_0 @ A) )  @  (u1_struct_0 @ A) ) ) ) ) ) , file(fvsum_1, fc2_fvsum_1)).
thf(fc2_setfam_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (v1_setfam_1 @  (k1_tarski @ A) ) ) ) , file(setfam_1, fc2_setfam_1)).
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_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) )  =>  (v2_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc2_valued_0)).
thf(fc2_xboole_0, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k1_tarski @ A) ) ) ) , file(xboole_0, fc2_xboole_0)).
thf(fc30_finset_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  (v5_finset_1 @  (k1_tarski @ A) ) ) ) , file(finset_1, fc30_finset_1)).
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(fc31_finset_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  (v5_finset_1 @  (k1_zfmisc_1 @ A) ) ) ) , file(finset_1, fc31_finset_1)).
thf(fc32_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_finset_1 @ A)  &  (v1_finset_1 @ B) )  =>  (v5_finset_1 @  ( (k2_tarski @ A)  @ B) ) ) ) , file(finset_1, fc32_finset_1)).
thf(fc35_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finset_1 @ A) ) )  =>  (v1_finset_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(finset_1, fc35_finset_1)).
thf(fc36_finset_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v2_finset_1 @ A) )  =>  (v5_finset_1 @  (k10_xtuple_0 @ A) ) ) ) , file(finset_1, fc36_finset_1)).
thf(fc3_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_finset_1 @  (k1_finseq_1 @ A) ) ) ) , file(finseq_1, fc3_finseq_1)).
thf(fc3_finseq_2, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_finseq_1 @  ( (k2_funcop_1 @  (k2_finseq_1 @ A) )  @ B) ) ) ) , file(finseq_2, fc3_finseq_2)).
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_funct_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  (v1_funct_1 @  (k4_relat_1 @ A) ) ) ) , file(funct_1, fc3_funct_1)).
thf(fc3_fvsum_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v5_group_1 @ A)  &  (l3_algstr_0 @ A) ) )  =>  ( (v1_funct_1 @  (u2_algstr_0 @ A) )  &  ( ( ( (v1_funct_2 @  (u2_algstr_0 @ A) )  @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) )  &  ( (v1_binop_1 @  (u2_algstr_0 @ A) )  @  (u1_struct_0 @ A) ) ) ) ) ) , file(fvsum_1, fc3_fvsum_1)).
thf(fc3_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v7_ordinal1 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) , file(nat_1, fc3_nat_1)).
thf(fc3_setfam_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  (v1_setfam_1 @  ( (k2_tarski @ A)  @ B) ) ) ) , file(setfam_1, fc3_setfam_1)).
thf(fc3_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  (v3_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc3_valued_0)).
thf(fc3_xboole_0, axiom,  (! [A: $i, B: $i] :  ~ ( (v1_xboole_0 @  ( (k2_tarski @ A)  @ B) ) ) ) , file(xboole_0, fc3_xboole_0)).
thf(fc3_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  ( (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) )  &  (v1_xreal_0 @  (k4_xcmplx_0 @ A) ) ) ) ) , file(xreal_0, fc3_xreal_0)).
thf(fc49_valued_0, axiom,  (! [A: $i] :  ( (v1_membered @ A)  =>  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  (v1_valued_0 @  (k4_relat_1 @ A) ) ) ) ) , file(valued_0, fc49_valued_0)).
thf(fc4_card_1, axiom,  (v1_card_1 @ k4_ordinal1) , file(card_1, fc4_card_1)).
thf(fc4_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v3_card_1 @  (k1_finseq_1 @ A) )  @ A) ) ) , file(finseq_1, fc4_finseq_1)).
thf(fc4_finseq_2, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v1_relat_1 @  ( (k2_finseq_2 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k2_finseq_2 @ A)  @ B) )  &  ( ( (v3_card_1 @  ( (k2_finseq_2 @ A)  @ B) )  @ A)  &  (v1_finseq_1 @  ( (k2_finseq_2 @ A)  @ B) ) ) ) ) ) ) , file(finseq_2, fc4_finseq_2)).
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_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  (v2_funct_1 @  (k4_relat_1 @ A) ) ) ) , file(funct_1, fc4_funct_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_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v7_ordinal1 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (k2_xcmplx_0 @ B)  @ A) ) ) ) ) , file(nat_1, fc4_nat_1)).
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_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  (v4_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc4_valued_0)).
thf(fc50_valued_0, axiom,  (! [A: $i] :  ( (v2_membered @ A)  =>  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  (v2_valued_0 @  (k4_relat_1 @ A) ) ) ) ) , file(valued_0, fc50_valued_0)).
thf(fc51_valued_0, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  (v3_valued_0 @  (k4_relat_1 @ A) ) ) ) ) , file(valued_0, fc51_valued_0)).
thf(fc52_valued_0, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  ( (v5_relat_1 @  (k4_relat_1 @ A) )  @ k3_numbers) ) ) ) , file(valued_0, fc52_valued_0)).
thf(fc53_valued_0, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  ( (v5_relat_1 @  (k4_relat_1 @ A) )  @ k4_numbers) ) ) ) , file(valued_0, fc53_valued_0)).
thf(fc54_valued_0, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  (v4_valued_0 @  (k4_relat_1 @ A) ) ) ) ) , file(valued_0, fc54_valued_0)).
thf(fc55_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  (v1_valued_0 @ B) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v1_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc55_valued_0)).
thf(fc56_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  (v2_valued_0 @ B) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v2_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc56_valued_0)).
thf(fc57_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  (v3_valued_0 @ B) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v3_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc57_valued_0)).
thf(fc58_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ k3_numbers) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  ( (v5_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  @ k3_numbers) ) ) ) , file(valued_0, fc58_valued_0)).
thf(fc59_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ k4_numbers) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  ( (v5_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  @ k4_numbers) ) ) ) , file(valued_0, fc59_valued_0)).
thf(fc5_card_1, axiom,  (v2_card_1 @ k4_ordinal1) , file(card_1, fc5_card_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_funcop_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) )  &  ( (v1_relat_1 @ C)  &  (v1_funct_1 @ C) ) ) )  =>  ( (v1_relat_1 @  ( ( (k3_funcop_1 @ A)  @ B)  @ C) )  &  (v1_funct_1 @  ( ( (k3_funcop_1 @ A)  @ B)  @ C) ) ) ) ) , file(funcop_1, fc5_funcop_1)).
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_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  (v5_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc5_valued_0)).
thf(fc5_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  (v1_xreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc5_xreal_0)).
thf(fc60_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  (v4_valued_0 @ B) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v4_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc60_valued_0)).
thf(fc61_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  (v1_xcmplx_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc61_valued_0)).
thf(fc62_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_valued_0 @ A) ) )  =>  (v1_xxreal_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc62_valued_0)).
thf(fc63_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  =>  (v1_xreal_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc63_valued_0)).
thf(fc64_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  (v1_funct_1 @ A) ) )  =>  (v1_rat_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc64_valued_0)).
thf(fc65_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k4_numbers)  &  (v1_funct_1 @ A) ) )  =>  (v1_int_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc65_valued_0)).
thf(fc66_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v4_valued_0 @ A) ) )  =>  (v7_ordinal1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc66_valued_0)).
thf(fc67_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_xcmplx_0 @ B)  =>  (v1_valued_0 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc67_valued_0)).
thf(fc68_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_xxreal_0 @ B)  =>  (v2_valued_0 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc68_valued_0)).
thf(fc69_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_xreal_0 @ B)  =>  (v3_valued_0 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc69_valued_0)).
thf(fc6_card_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  ( (v1_finset_1 @  (k1_card_1 @ A) )  &  (v1_card_1 @  (k1_card_1 @ A) ) ) ) ) , file(card_1, fc6_card_1)).
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(fc6_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  (v6_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc6_valued_0)).
thf(fc70_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_rat_1 @ B)  =>  ( (v5_relat_1 @  ( (k2_funcop_1 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_0, fc70_valued_0)).
thf(fc71_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_int_1 @ B)  =>  ( (v5_relat_1 @  ( (k2_funcop_1 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_0, fc71_valued_0)).
thf(fc72_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ B)  =>  (v4_valued_0 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc72_valued_0)).
thf(fc7_card_1, axiom,  ~ ( (v1_finset_1 @ k4_ordinal1) ) , file(card_1, fc7_card_1)).
thf(fc7_finseq_2, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v1_relat_1 @  ( (k2_finseq_2 @ A)  @ k6_numbers) )  &  ( (v3_relat_1 @  ( (k2_finseq_2 @ A)  @ k6_numbers) )  &  ( (v1_funct_1 @  ( (k2_finseq_2 @ A)  @ k6_numbers) )  &  (v1_finseq_1 @  ( (k2_finseq_2 @ A)  @ k6_numbers) ) ) ) ) ) ) , file(finseq_2, fc7_finseq_2)).
thf(fc7_funcop_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( (v1_relat_1 @ C)  &  (v1_funct_1 @ C) ) )  =>  ( (v1_relat_1 @  ( ( (k5_funcop_1 @ A)  @ B)  @ C) )  &  (v1_funct_1 @  ( ( (k5_funcop_1 @ A)  @ B)  @ C) ) ) ) ) , file(funcop_1, fc7_funcop_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_relset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  ( ~ ( (v1_xboole_0 @  (k4_relat_1 @ A) ) )  &  (v1_relat_1 @  (k4_relat_1 @ A) ) ) ) ) , file(relset_1, fc7_relset_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(fc7_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  (v1_xreal_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc7_xreal_0)).
thf(fc85_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_membered @ B)  =>  (v1_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc85_valued_0)).
thf(fc86_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v2_membered @ B)  =>  (v2_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc86_valued_0)).
thf(fc87_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v3_membered @ B)  =>  (v3_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc87_valued_0)).
thf(fc88_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v4_membered @ B)  =>  ( (v5_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_0, fc88_valued_0)).
thf(fc89_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v5_membered @ B)  =>  ( (v5_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_0, fc89_valued_0)).
thf(fc8_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  ( ~ ( (v1_finset_1 @  (k1_card_1 @ A) ) )  &  (v1_card_1 @  (k1_card_1 @ A) ) ) ) ) , file(card_1, fc8_card_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_nat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k5_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k5_numbers) ) ) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k5_numbers)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ B) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ C) )  &  ( ( (v4_relat_1 @  ( (k3_relat_1 @ A)  @ C) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( (k3_relat_1 @ A)  @ C) )  @ B)  &  (v1_funct_1 @  ( (k3_relat_1 @ A)  @ C) ) ) ) ) ) ) , file(nat_1, fc8_nat_1)).
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(fc90_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v6_membered @ B)  =>  (v4_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc90_valued_0)).
thf(fc91_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v5_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v5_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v5_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc91_valued_0)).
thf(fc92_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v7_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v7_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v7_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc92_valued_0)).
thf(fc93_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v6_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v5_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc93_valued_0)).
thf(fc94_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v8_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v8_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v7_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc94_valued_0)).
thf(fc95_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v5_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v6_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc95_valued_0)).
thf(fc96_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v5_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ B)  @ A) )  &  (v6_valued_0 @  ( (k3_relat_1 @ B)  @ A) ) ) ) ) , file(valued_0, fc96_valued_0)).
thf(fc97_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v8_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v7_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v8_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc97_valued_0)).
thf(fc98_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v8_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v7_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ B)  @ A) )  &  (v8_valued_0 @  ( (k3_relat_1 @ B)  @ A) ) ) ) ) , file(valued_0, fc98_valued_0)).
thf(fc99_valued_0, axiom,  (! [A: $i] :  ( (v2_membered @ A)  =>  ( (v1_funct_1 @  (k4_relat_1 @ A) )  &  ( ( ( (v1_funct_2 @  (k4_relat_1 @ A) )  @ A)  @ A)  &  (v5_valued_0 @  (k4_relat_1 @ A) ) ) ) ) ) , file(valued_0, fc99_valued_0)).
thf(fc9_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  ~ ( (v1_finset_1 @  (k1_zfmisc_1 @ A) ) ) ) ) , file(card_1, fc9_card_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_nat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k5_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k5_numbers) ) ) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k5_numbers)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ B) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ C) )  &  ( (v1_partfun1 @  ( (k3_relat_1 @ A)  @ C) )  @ k5_numbers) ) ) ) , file(nat_1, fc9_nat_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(fc9_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v3_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc9_xreal_0)).
thf(ie1_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (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) ) ) ) )  &  ( (m1_subset_1 @ D)  @ A) ) ) )  =>  ( (= @  ( ( (k7_partfun1 @ B)  @ C)  @ D) )  @  ( ( ( (k3_funct_2 @ A)  @ B)  @ C)  @ D) ) ) ) , file(funct_2, ie1_funct_2)).
thf(ie6_vectsp_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v4_vectsp_1 @ A)  &  (l4_algstr_0 @ A) ) )  =>  ( (= @  (k1_group_1 @ A) )  @  (k5_struct_0 @ A) ) ) ) , file(vectsp_1, ie6_vectsp_1)).
thf(involutiveness_k4_xcmplx_0, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ A) ) )  @ A) ) ) , file(xcmplx_0, k4_xcmplx_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(projectivity_k5_card_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  ( (= @  (k5_card_1 @  (k5_card_1 @ A) ) )  @  (k5_card_1 @ A) ) ) ) , file(card_1, k5_card_1)).
thf(rc11_vectsp_1, axiom,  (? [A: $i] :  ( (l4_algstr_0 @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  (v4_vectsp_1 @ A) ) ) ) , file(vectsp_1, rc11_vectsp_1)).
thf(rc17_struct_0, axiom,  (! [A: $i] :  ( (l2_struct_0 @ A)  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (v9_struct_0 @ B)  @ A) ) ) ) ) , file(struct_0, rc17_struct_0)).
thf(rc19_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v7_struct_0 @ A) )  &  (l2_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ~ ( ( (v9_struct_0 @ B)  @ A) ) ) ) ) ) , file(struct_0, rc19_struct_0)).
thf(rc1_card_1, axiom,  (? [A: $i] :  (v1_card_1 @ A) ) , file(card_1, rc1_card_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_finset_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_finset_1 @ A) ) ) , file(finset_1, rc1_finset_1)).
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_matrix13, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k5_numbers) )  &  ( (v1_xboole_0 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_setfam_1 @ A) ) ) ) ) , file(matrix13, rc1_matrix13)).
thf(rc1_nat_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  ( (v3_ordinal1 @ A)  &  ( (v7_ordinal1 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v1_xreal_0 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_card_1 @ A) ) ) ) ) ) ) ) ) ) ) , file(nat_1, rc1_nat_1)).
thf(rc1_ordinal1, axiom,  (? [A: $i] :  (v3_ordinal1 @ A) ) , file(ordinal1, rc1_ordinal1)).
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_setfam_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_setfam_1 @ A) ) ) , file(setfam_1, rc1_setfam_1)).
thf(rc1_valued_0, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, rc1_valued_0)).
thf(rc1_vectsp_9, 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(vectsp_9, rc1_vectsp_9)).
thf(rc1_xboole_0, axiom,  (? [A: $i] :  (v1_xboole_0 @ A) ) , file(xboole_0, rc1_xboole_0)).
thf(rc1_xreal_0, axiom,  (? [A: $i] :  (v1_xreal_0 @ A) ) , file(xreal_0, rc1_xreal_0)).
thf(rc1_xxreal_0, axiom,  (? [A: $i] :  (v1_xxreal_0 @ A) ) , file(xxreal_0, rc1_xxreal_0)).
thf(rc20_struct_0, axiom,  (? [A: $i] :  ( (l2_struct_0 @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  (v7_struct_0 @ A) ) ) ) , file(struct_0, rc20_struct_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(rc2_card_1, axiom,  (? [A: $i] :  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  ( (v3_ordinal1 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_card_1 @ A) ) ) ) ) ) , file(card_1, rc2_card_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_finset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_finset_1 @ B) ) ) ) ) ) , file(finset_1, rc2_finset_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_matrix13, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k5_numbers) )  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_finset_1 @ A)  &  (v1_setfam_1 @ A) ) ) ) ) , file(matrix13, rc2_matrix13)).
thf(rc2_nat_1, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k1_numbers) )  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_ordinal1 @ A) ) ) ) , file(nat_1, rc2_nat_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_relat_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  (v2_relat_1 @ A) ) ) , file(relat_1, rc2_relat_1)).
thf(rc2_setfam_1, axiom,  (? [A: $i] :  ~ ( (v2_setfam_1 @ A) ) ) , file(setfam_1, rc2_setfam_1)).
thf(rc2_valued_0, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  ( ( (v5_relat_1 @ A)  @ k4_numbers)  &  ( (v1_funct_1 @ A)  &  ( (v3_funct_1 @ A)  &  (v4_valued_0 @ A) ) ) ) ) ) ) ) , file(valued_0, rc2_valued_0)).
thf(rc2_vectsp_1, axiom,  (? [A: $i] :  ( (l5_algstr_0 @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  (v4_vectsp_1 @ A) ) ) ) , file(vectsp_1, rc2_vectsp_1)).
thf(rc2_xboole_0, axiom,  (? [A: $i] :  ~ ( (v1_xboole_0 @ A) ) ) , file(xboole_0, rc2_xboole_0)).
thf(rc2_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc2_xreal_0)).
thf(rc2_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) ) ) , file(xxreal_0, rc2_xxreal_0)).
thf(rc3_card_1, axiom,  (? [A: $i] :  ~ ( (v1_finset_1 @ A) ) ) , file(card_1, rc3_card_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_finset_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) ) ) , file(finset_1, rc3_finset_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_matrix13, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v6_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v33_algstr_0 @ A)  &  ( (v3_group_1 @ A)  &  ( (v5_group_1 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v4_vectsp_1 @ A)  &  ( (v5_vectsp_1 @ A)  &  (l6_algstr_0 @ A) ) ) ) ) ) ) ) ) ) ) )  =>  (? [B: $i] :  ( ( (m1_finseq_1 @ B)  @  (k3_finseq_2 @  (u1_struct_0 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (k3_finseq_2 @  (u1_struct_0 @ A) ) )  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v1_finseq_1 @ B)  &  ( (v2_finseq_1 @ B)  &  ( (v1_funcop_1 @ B)  &  ( (v2_funcop_1 @ B)  &  ( (v1_matrix_1 @ B)  &  ( (v2_matrix_1 @ B)  @ A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(matrix13, rc3_matrix13)).
thf(rc3_nat_1, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  ( (v3_ordinal1 @ A)  &  ( (v7_ordinal1 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v1_xreal_0 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_card_1 @ A) ) ) ) ) ) ) ) ) ) ) ) , file(nat_1, rc3_nat_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_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_setfam_1, axiom,  (! [A: $i] :  ( ~ ( (v2_setfam_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  &  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(setfam_1, rc3_setfam_1)).
thf(rc3_valued_0, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k5_numbers) ) )  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( ( (v1_partfun1 @ A)  @ k5_numbers)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k5_numbers)  &  ( (v1_valued_0 @ A)  &  ( (v2_valued_0 @ A)  &  ( (v3_valued_0 @ A)  &  ( (v4_valued_0 @ A)  &  (v5_valued_0 @ A) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(valued_0, rc3_valued_0)).
thf(rc3_vectsp_1, axiom,  (? [A: $i] :  ( (l3_algstr_0 @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  ( (v3_group_1 @ A)  &  (v5_group_1 @ A) ) ) ) ) , file(vectsp_1, rc3_vectsp_1)).
thf(rc3_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc3_xreal_0)).
thf(rc3_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) ) ) , file(xxreal_0, rc3_xxreal_0)).
thf(rc4_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( (v1_finset_1 @ B) ) ) ) ) ) , file(card_1, rc4_card_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_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_valued_0, 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)  &  ( (v3_funct_1 @ B)  &  ( ( (v1_funct_2 @ B)  @ k5_numbers)  @ A) ) ) ) ) ) ) ) ) , file(valued_0, rc4_valued_0)).
thf(rc4_vectsp_1, axiom,  (? [A: $i] :  ( (l4_algstr_0 @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_group_1 @ A)  &  ( (v3_group_1 @ A)  &  (v5_group_1 @ A) ) ) ) ) ) , file(vectsp_1, rc4_vectsp_1)).
thf(rc4_xreal_0, axiom,  (? [A: $i] :  ( (v1_xboole_0 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc4_xreal_0)).
thf(rc4_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xboole_0 @ A)  &  (v1_xxreal_0 @ A) ) ) , file(xxreal_0, rc4_xxreal_0)).
thf(rc5_card_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (? [B: $i] :  ( (v3_card_1 @ B)  @ A) ) ) ) , file(card_1, rc5_card_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_finset_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)  &  (v1_finset_1 @ C) ) ) ) ) ) ) , file(finset_1, rc5_finset_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_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v7_ordinal1 @ A) ) ) , file(ordinal1, rc5_ordinal1)).
thf(rc5_valued_0, axiom,  (! [A: $i] :  ( ~ ( (v2_setfam_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ A) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ k5_numbers)  &  ( ( (v1_funct_2 @ B)  @ k5_numbers)  @ A) ) ) ) ) ) ) ) ) ) ) ) , file(valued_0, rc5_valued_0)).
thf(rc6_card_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v3_card_1 @ B)  @ A) ) ) ) ) ) , file(card_1, rc6_card_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_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  (? [C: $i] :  ( ~ ( (v1_xboole_0 @ C) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( ( (v5_relat_1 @ C)  @ B)  &  ( (v1_funct_1 @ C)  &  (v1_finset_1 @ C) ) ) ) ) ) ) ) ) , file(finset_1, rc6_finset_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_valued_0, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v4_valued_0 @ B) ) ) ) ) ) ) , file(valued_0, rc6_valued_0)).
thf(rc7_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( (v3_card_1 @ B)  @ np__1) ) ) ) ) , file(card_1, rc7_card_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_finset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( ~ ( (v1_zfmisc_1 @ B) )  &  (v1_finset_1 @ B) ) ) ) ) ) , file(finset_1, rc7_finset_1)).
thf(rc7_funct_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v4_funct_1 @ A) ) ) , file(funct_1, rc7_funct_1)).
thf(rc8_finseq_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_finseq_1 @ A) ) ) , file(finseq_1, rc8_finseq_1)).
thf(rc8_finset_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_finset_1 @ A)  &  (v5_finset_1 @ A) ) ) ) , file(finset_1, rc8_finset_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_finset_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finset_1 @ A) ) ) ) ) , file(finset_1, rc9_finset_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_relat_1, axiom,  (! [A: $i] :  ( (= @  (k9_xtuple_0 @  (k4_relat_1 @ A) ) )  @ A) ) , file(relat_1, rd1_relat_1)).
thf(rd2_relat_1, axiom,  (! [A: $i] :  ( (= @  (k10_xtuple_0 @  (k4_relat_1 @ A) ) )  @ A) ) , file(relat_1, rd2_relat_1)).
thf(redefinition_k10_funcop_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) )  &  ( ( (m1_subset_1 @ D)  @ A)  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ B)  @ A)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) ) ) ) ) ) )  =>  ( (= @  ( ( ( ( (k10_funcop_1 @ A)  @ B)  @ C)  @ D)  @ E) )  @  ( ( (k5_funcop_1 @ C)  @ D)  @ E) ) ) ) , file(funcop_1, k10_funcop_1)).
thf(redefinition_k10_fvsum_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  ( ( ~ ( (v2_struct_0 @ B) )  &  (l3_algstr_0 @ B) )  &  ( ( (m1_subset_1 @ C)  @  ( (k4_finseq_2 @ A)  @  (u1_struct_0 @ B) ) )  &  ( (m1_subset_1 @ D)  @  (u1_struct_0 @ B) ) ) ) )  =>  ( (= @  ( ( ( (k10_fvsum_1 @ A)  @ B)  @ C)  @ D) )  @  ( ( (k9_fvsum_1 @ B)  @ C)  @ D) ) ) ) , file(fvsum_1, k10_fvsum_1)).
thf(redefinition_k1_finseqop, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( ~ ( (v1_xboole_0 @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @  ( (k2_zfmisc_1 @ A)  @ B) )  @ C)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ C) ) ) ) )  &  ( ( (m1_finseq_1 @ E)  @ A)  &  ( (m1_finseq_1 @ F)  @ B) ) ) ) ) )  =>  ( (= @  ( ( ( ( ( (k1_finseqop @ A)  @ B)  @ C)  @ D)  @ E)  @ F) )  @  ( ( (k3_funcop_1 @ D)  @ E)  @ F) ) ) ) , file(finseqop, k1_finseqop)).
thf(redefinition_k1_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (m1_subset_1 @ B)  @ k5_numbers) )  =>  ( (= @  ( (k1_nat_1 @ A)  @ B) )  @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(nat_1, k1_nat_1)).
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_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (= @  (k2_finseq_1 @ A) )  @  (k1_finseq_1 @ A) ) ) ) , file(finseq_1, k2_finseq_1)).
thf(redefinition_k2_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  (v7_ordinal1 @ B) )  =>  ( (= @  ( (k2_nat_1 @ A)  @ B) )  @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(nat_1, k2_nat_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_k3_rlvect_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v2_rlvect_1 @ A)  &  (l1_algstr_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( (= @  ( ( (k3_rlvect_1 @ A)  @ B)  @ C) )  @  ( ( (k1_algstr_0 @ A)  @ B)  @ C) ) ) ) , file(rlvect_1, k3_rlvect_1)).
thf(redefinition_k4_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (= @  (k4_finseq_1 @ A) )  @  (k9_xtuple_0 @ A) ) ) ) , file(finseq_1, k4_finseq_1)).
thf(redefinition_k4_finseqop, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_finseq_1 @ C)  @ A)  &  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (= @  ( ( ( (k4_finseqop @ A)  @ B)  @ C)  @ D) )  @  ( (k3_relat_1 @ C)  @ D) ) ) ) , file(finseqop, k4_finseqop)).
thf(redefinition_k4_fvsum_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  ( ( ~ ( (v2_struct_0 @ B) )  &  (l2_algstr_0 @ B) )  &  ( ( (m1_subset_1 @ C)  @  ( (k4_finseq_2 @ A)  @  (u1_struct_0 @ B) ) )  &  ( (m1_subset_1 @ D)  @  ( (k4_finseq_2 @ A)  @  (u1_struct_0 @ B) ) ) ) ) )  =>  ( (= @  ( ( ( (k4_fvsum_1 @ A)  @ B)  @ C)  @ D) )  @  ( ( (k3_fvsum_1 @ B)  @ C)  @ D) ) ) ) , file(fvsum_1, k4_fvsum_1)).
thf(redefinition_k5_binop_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) )  &  ( ( (m1_subset_1 @ C)  @ A)  &  ( (m1_subset_1 @ D)  @ A) ) )  =>  ( (= @  ( ( ( (k5_binop_1 @ A)  @ B)  @ C)  @ D) )  @  ( ( (k1_binop_1 @ B)  @ C)  @ D) ) ) ) , file(binop_1, k5_binop_1)).
thf(redefinition_k5_card_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  ( (= @  (k5_card_1 @ A) )  @  (k1_card_1 @ A) ) ) ) , file(card_1, k5_card_1)).
thf(redefinition_k5_finseq_2, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v7_ordinal1 @ B)  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ( (= @  ( ( (k5_finseq_2 @ A)  @ B)  @ C) )  @  ( (k2_finseq_2 @ B)  @ C) ) ) ) , file(finseq_2, k5_finseq_2)).
thf(redefinition_k5_matrix13, axiom,  (! [A: $i] :  ( ( (v1_finset_1 @ A)  &  ( (v1_setfam_1 @ A)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k5_numbers) ) ) )  =>  ( (= @  (k5_matrix13 @ A) )  @  (k14_finseq_1 @ A) ) ) ) , file(matrix13, k5_matrix13)).
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_k6_partfun1, axiom,  (! [A: $i] :  ( (= @  (k6_partfun1 @ A) )  @  (k4_relat_1 @ A) ) ) , file(partfun1, k6_partfun1)).
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_group_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v5_group_1 @ A)  &  (l3_algstr_0 @ A) ) )  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( (= @  ( ( (k8_group_1 @ A)  @ B)  @ C) )  @  ( ( (k6_algstr_0 @ A)  @ B)  @ C) ) ) ) , file(group_1, k8_group_1)).
thf(redefinition_k8_matrix_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_matrix_1 @ B)  &  ( (m1_finseq_1 @ B)  @  (k3_finseq_2 @ A) ) )  &  (v7_ordinal1 @ C) ) )  =>  ( (= @  ( ( (k8_matrix_1 @ A)  @ B)  @ C) )  @  ( ( (k6_matrix_1 @ A)  @ B)  @ C) ) ) ) , file(matrix_1, k8_matrix_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(reflexivity_r1_xxreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v1_xxreal_0 @ B) )  =>  ( (r1_xxreal_0 @ A)  @ A) ) ) , file(xxreal_0, r1_xxreal_0)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r0, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r1, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r0_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__0)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r0, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @ np__0) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom,  ( (r1_xxreal_0 @ np__1)  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r1_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r0, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r0)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r1)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_rm1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r0_r0_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @ np__0) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r0_r0)).
thf(rqRealAdd__k2_xcmplx_0__r0_r1_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @ np__1) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r1_r1)).
thf(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r1_r0_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @ np__0) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r0_r1)).
thf(rqRealAdd__k2_xcmplx_0__r1_rm1_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm1_r0)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__0) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r1_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__1) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r1_r0)).
thf(rqRealDiff__k6_xcmplx_0__r0_r0_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__0) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r0_r0)).
thf(rqRealDiff__k6_xcmplx_0__r0_r1_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r1_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r0_rm1_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm1_r1)).
thf(rqRealDiff__k6_xcmplx_0__r1_r0_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__0) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r0_r1)).
thf(rqRealDiff__k6_xcmplx_0__r1_r1_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__1) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r1_r0)).
thf(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__0) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)).
thf(rqRealNeg__k4_xcmplx_0__r0_r0, axiom,  ( (= @  (k4_xcmplx_0 @ np__0) )  @ np__0) , file(arithm, rqRealNeg__k4_xcmplx_0__r0_r0)).
thf(rqRealNeg__k4_xcmplx_0__r1_rm1, axiom,  ( (= @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r1_rm1)).
thf(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom,  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__1) ) )  @ np__1) , file(arithm, rqRealNeg__k4_xcmplx_0__rm1_r1)).
thf(spc0_boole, axiom,  (v1_xboole_0 @ np__0) , file(boole, spc0_boole)).
thf(spc0_numerals, axiom,  ( ( ( (m2_subset_1 @ np__0)  @ k1_numbers)  @ k5_numbers)  &  ( ( (m1_subset_1 @ np__0)  @ k5_numbers)  &  ( (m1_subset_1 @ np__0)  @ k1_numbers) ) ) , file(numerals, spc0_numerals)).
thf(spc1_arithm, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k2_xcmplx_0 @ A)  @  (k4_xcmplx_0 @ B) ) )  @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(arithm, spc1_arithm)).
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(spc6_arithm, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_xcmplx_0 @ A)  &  ( (v1_xcmplx_0 @ B)  &  (v1_xcmplx_0 @ C) ) )  =>  ( (= @  ( (k2_xcmplx_0 @  ( (k2_xcmplx_0 @ A)  @ B) )  @ C) )  @  ( (k2_xcmplx_0 @ A)  @  ( (k2_xcmplx_0 @ B)  @ C) ) ) ) ) , file(arithm, spc6_arithm)).
thf(spc8_arithm, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ A) )  @  (k4_xcmplx_0 @ B) ) )  @  (k4_xcmplx_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) , file(arithm, spc8_arithm)).
thf(spc9_arithm, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ A) )  @  (k4_xcmplx_0 @ B) ) )  @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) , file(arithm, spc9_arithm)).
thf(t11_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ( (r1_xxreal_0 @ A)  @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) ) , file(nat_1, t11_nat_1)).
thf(t13_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ( ~ ( ( (r1_xxreal_0 @  ( (k1_nat_1 @ B)  @ np__1) )  @ A) )  <=>  ( (r1_xxreal_0 @ A)  @ B) ) ) ) ) ) , file(nat_1, t13_nat_1)).
thf(t17_matrix13, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  (! [C: $i] :  ( (v7_ordinal1 @ C)  =>  (! [D: $i] :  ( (v7_ordinal1 @ D)  =>  (! [E: $i] :  ( (v7_ordinal1 @ E)  =>  (! [F: $i] :  ( ( (v1_matrix_1 @ F)  &  ( (m2_finseq_1 @ F)  @  (k3_finseq_2 @ A) ) )  =>  (! [G: $i] :  ( ( ( (m2_finseq_2 @ G)  @ k5_numbers)  @  ( (k4_finseq_2 @ B)  @ k5_numbers) )  =>  (! [H: $i] :  ( ( ( (m2_finseq_2 @ H)  @ k5_numbers)  @  ( (k4_finseq_2 @ C)  @ k5_numbers) )  =>  ( ( (r1_tarski @  ( (k2_zfmisc_1 @  (k10_xtuple_0 @ G) )  @  (k10_xtuple_0 @ H) ) )  @  (k2_matrix_1 @ F) )  =>  ( ( (r2_hidden @  ( (k4_tarski @ D)  @ E) )  @  (k2_matrix_1 @  ( ( ( ( ( (k1_matrix13 @ A)  @ F)  @ B)  @ C)  @ G)  @ H) ) )  <=>  ( (r2_hidden @  ( (k4_tarski @  ( (k1_funct_1 @ G)  @ D) )  @  ( (k1_funct_1 @ H)  @ E) ) )  @  (k2_matrix_1 @ F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(matrix13, t17_matrix13)).
thf(t19_vectsp_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  (l2_algstr_0 @ A) ) ) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  =>  ( ( ( (= @  ( ( (k1_algstr_0 @ A)  @ B)  @  ( (k4_algstr_0 @ A)  @ C) ) )  @  (k4_struct_0 @ A) )  =>  ( (= @ B)  @ C) )  &  ( ( ( (= @ B)  @ C)  =>  ( (= @  ( ( (k1_algstr_0 @ A)  @ B)  @  ( (k4_algstr_0 @ A)  @ C) ) )  @  (k4_struct_0 @ A) ) )  &  ( ( ( (= @  ( ( (k5_algstr_0 @ A)  @ B)  @ C) )  @  (k4_struct_0 @ A) )  =>  ( (= @ B)  @ C) )  &  ( ( (= @ B)  @ C)  =>  ( (= @  ( ( (k5_algstr_0 @ A)  @ B)  @ C) )  @  (k4_struct_0 @ A) ) ) ) ) ) ) ) ) ) ) ) , file(vectsp_1, t19_vectsp_1)).
thf(t1_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k2_xcmplx_0 @ A)  @ k6_numbers) )  @ A) ) ) , file(arithm, t1_arithm)).
thf(t1_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ( ( (r2_hidden @ A)  @  (k2_finseq_1 @ B) )  <=>  ( ( (r1_xxreal_0 @ np__1)  @ A)  &  ( (r1_xxreal_0 @ A)  @ B) ) ) ) ) ) ) , file(finseq_1, t1_finseq_1)).
thf(t1_numerals, axiom,  ( (m1_subset_1 @ k1_xboole_0)  @ k4_ordinal1) , file(numerals, t1_numerals)).
thf(t1_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( ( (r1_xxreal_0 @ A)  @ B)  &  (v2_xxreal_0 @ A) )  =>  (v2_xxreal_0 @ B) ) ) ) ) ) , file(real, t1_real)).
thf(t1_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ( (m1_subset_1 @ A)  @ B) ) ) ) , file(subset, t1_subset)).
thf(t23_matrix_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  (! [C: $i] :  ( ~ ( (v1_xboole_0 @ C) )  =>  ( ~ ( ( (r1_xxreal_0 @ A)  @ k1_xboole_0) )  =>  (! [D: $i] :  ( ( ( ( (m1_matrix_1 @ D)  @ C)  @ A)  @ B)  =>  ( ( (= @  (k3_finseq_1 @ D) )  @ A)  &  ( ( (= @  (k1_matrix_1 @ D) )  @ B)  &  ( (= @  (k2_matrix_1 @ D) )  @  ( (k2_zfmisc_1 @  (k2_finseq_1 @ A) )  @  (k2_finseq_1 @ B) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(matrix_1, t23_matrix_1)).
thf(t24_matrix_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ~ ( (v1_xboole_0 @ B) )  =>  (! [C: $i] :  ( ( ( ( (m1_matrix_1 @ C)  @ B)  @ A)  @ A)  =>  ( ( (= @  (k3_finseq_1 @ C) )  @ A)  &  ( ( (= @  (k1_matrix_1 @ C) )  @ A)  &  ( (= @  (k2_matrix_1 @ C) )  @  ( (k2_zfmisc_1 @  (k2_finseq_1 @ A) )  @  (k2_finseq_1 @ A) ) ) ) ) ) ) ) ) ) ) , file(matrix_1, t24_matrix_1)).
thf(t25_matrix_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  (! [C: $i] :  ( ~ ( (v1_xboole_0 @ C) )  =>  (! [D: $i] :  ( ( ( ( (m1_matrix_1 @ D)  @ C)  @ A)  @ B)  =>  ( ( (= @  (k3_finseq_1 @ D) )  @ A)  &  ( (= @  (k2_matrix_1 @ D) )  @  ( (k2_zfmisc_1 @  (k2_finseq_1 @ A) )  @  (k2_finseq_1 @  (k1_matrix_1 @ D) ) ) ) ) ) ) ) ) ) ) ) ) , file(matrix_1, t25_matrix_1)).
thf(t25_vectsp_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v6_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v33_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v3_group_1 @ A)  &  ( (v5_group_1 @ A)  &  ( (v4_vectsp_1 @ A)  &  ( (v5_vectsp_1 @ A)  &  (l6_algstr_0 @ A) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  ( ~ ( ( (= @ B)  @  (k4_struct_0 @ A) ) )  =>  ( ~ ( ( (= @  ( (k11_algstr_0 @ A)  @ B) )  @  (k4_struct_0 @ A) ) )  &  ~ ( ( (= @  ( (k4_algstr_0 @ A)  @  ( (k11_algstr_0 @ A)  @ B) ) )  @  (k4_struct_0 @ A) ) ) ) ) ) ) ) ) , file(vectsp_1, t25_vectsp_1)).
thf(t26_matrix_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  (! [C: $i] :  ( ~ ( (v1_xboole_0 @ C) )  =>  (! [D: $i] :  ( ( ( ( (m1_matrix_1 @ D)  @ C)  @ A)  @ B)  =>  (! [E: $i] :  ( ( ( ( (m1_matrix_1 @ E)  @ C)  @ A)  @ B)  =>  ( (= @  (k2_matrix_1 @ D) )  @  (k2_matrix_1 @ E) ) ) ) ) ) ) ) ) ) ) ) , file(matrix_1, t26_matrix_1)).
thf(t27_matrix_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  (! [C: $i] :  ( ~ ( (v1_xboole_0 @ C) )  =>  (! [D: $i] :  ( ( ( ( (m1_matrix_1 @ D)  @ C)  @ A)  @ B)  =>  (! [E: $i] :  ( ( ( ( (m1_matrix_1 @ E)  @ C)  @ A)  @ B)  =>  ( (! [F: $i] :  ( (v7_ordinal1 @ F)  =>  (! [G: $i] :  ( (v7_ordinal1 @ G)  =>  ( ( (r2_hidden @  ( (k4_tarski @ F)  @ G) )  @  (k2_matrix_1 @ D) )  =>  ( (= @  ( ( ( (k3_matrix_1 @ C)  @ D)  @ F)  @ G) )  @  ( ( ( (k3_matrix_1 @ C)  @ E)  @ F)  @ G) ) ) ) ) ) )  =>  ( (= @ D)  @ E) ) ) ) ) ) ) ) ) ) ) ) , file(matrix_1, t27_matrix_1)).
thf(t28_matrix11, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  (! [C: $i] :  ( ~ ( (v1_xboole_0 @ C) )  =>  (! [D: $i] :  ( (v7_ordinal1 @ D)  =>  (! [E: $i] :  ( ( ( ( (m1_matrix_1 @ E)  @ C)  @ B)  @ A)  =>  (! [F: $i] :  ( ( (m2_finseq_1 @ F)  @ C)  =>  (! [G: $i] :  ( (v7_ordinal1 @ G)  =>  ( ( (r2_hidden @ G)  @  (k2_finseq_1 @ B) )  =>  ( ( ( ( (= @ G)  @ D)  &  ( (= @  (k3_finseq_1 @ F) )  @  (k1_matrix_1 @ E) ) )  =>  ( (= @  ( ( (k8_matrix_1 @ C)  @  ( ( ( ( ( (k3_matrix11 @ D)  @ B)  @ A)  @ C)  @ E)  @ F) )  @ G) )  @ F) )  &  ( ~ ( ( (= @ G)  @ D) )  =>  ( (= @  ( ( (k8_matrix_1 @ C)  @  ( ( ( ( ( (k3_matrix11 @ D)  @ B)  @ A)  @ C)  @ E)  @ F) )  @ G) )  @  ( ( (k8_matrix_1 @ C)  @ E)  @ G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(matrix11, t28_matrix11)).
thf(t2_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( ( (r1_xxreal_0 @ A)  @ B)  &  (v3_xxreal_0 @ B) )  =>  (v3_xxreal_0 @ A) ) ) ) ) ) , file(real, t2_real)).
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(t3_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ( (r1_xxreal_0 @ A)  @ B)  &  ( ~ ( (v3_xxreal_0 @ A) )  &  (v3_xxreal_0 @ B) ) ) ) ) ) ) ) , file(real, t3_real)).
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(t40_finseq_3, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v1_finset_1 @ B)  =>  ( ( (r1_tarski @ B)  @  (k2_finseq_1 @ A) )  =>  ( (= @  ( (k1_relset_1 @ k5_numbers)  @  (k14_finseq_1 @ B) ) )  @  (k2_finseq_1 @  (k5_card_1 @ B) ) ) ) ) ) ) ) , file(finseq_3, t40_finseq_3)).
thf(t48_finseq_3, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (= @  (k14_finseq_1 @  (k2_finseq_1 @ A) ) )  @  (k1_finseq_2 @ A) ) ) ) , file(finseq_3, t48_finseq_3)).
thf(t49_finseq_2, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k2_finseq_1 @ A) )  =>  ( (= @  ( (k1_funct_1 @  (k1_finseq_2 @ A) )  @ B) )  @ B) ) ) ) ) , file(finseq_2, t49_finseq_2)).
thf(t4_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k6_xcmplx_0 @ A)  @ k6_numbers) )  @ A) ) ) , file(arithm, t4_arithm)).
thf(t4_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ( (r1_xxreal_0 @ A)  @ B)  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v2_xxreal_0 @ A) ) ) ) ) ) ) ) , file(real, t4_real)).
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(t51_fvsum_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ k5_numbers)  =>  (! [C: $i] :  ( ( ~ ( (v2_struct_0 @ C) )  &  (l3_algstr_0 @ C) )  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @  (u1_struct_0 @ C) )  =>  (! [E: $i] :  ( ( (m1_subset_1 @ E)  @  (u1_struct_0 @ C) )  =>  (! [F: $i] :  ( ( ( (m2_finseq_2 @ F)  @  (u1_struct_0 @ C) )  @  ( (k4_finseq_2 @ B)  @  (u1_struct_0 @ C) ) )  =>  ( ( ( (r2_hidden @ A)  @  (k2_finseq_1 @ B) )  &  ( (= @ D)  @  ( (k1_funct_1 @ F)  @ A) ) )  =>  ( (= @  ( (k1_funct_1 @  ( ( ( (k10_fvsum_1 @ B)  @ C)  @ F)  @ E) )  @ A) )  @  ( ( (k6_algstr_0 @ C)  @ E)  @ D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(fvsum_1, t51_fvsum_1)).
thf(t55_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (= @  (k5_card_1 @  (k2_finseq_1 @ A) ) )  @  (k5_card_1 @ A) ) ) ) , file(finseq_1, t55_finseq_1)).
thf(t55_fvsum_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( (v5_vectsp_1 @ B)  &  (l6_algstr_0 @ B) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ B) )  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @  (u1_struct_0 @ B) )  =>  (! [E: $i] :  ( ( ( (m2_finseq_2 @ E)  @  (u1_struct_0 @ B) )  @  ( (k4_finseq_2 @ A)  @  (u1_struct_0 @ B) ) )  =>  ( (= @  ( ( ( (k10_fvsum_1 @ A)  @ B)  @ E)  @  ( ( (k1_algstr_0 @ B)  @ C)  @ D) ) )  @  ( ( ( (k4_fvsum_1 @ A)  @ B)  @  ( ( ( (k10_fvsum_1 @ A)  @ B)  @ E)  @ C) )  @  ( ( ( (k10_fvsum_1 @ A)  @ B)  @ E)  @ D) ) ) ) ) ) ) ) ) ) ) ) ) , file(fvsum_1, t55_fvsum_1)).
thf(t57_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (= @  (k5_card_1 @  (k2_finseq_1 @ A) ) )  @ A) ) ) , file(finseq_1, t57_finseq_1)).
thf(t57_fvsum_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( (v5_group_1 @ B)  &  ( (v5_vectsp_1 @ B)  &  ( (v6_vectsp_1 @ B)  &  (l6_algstr_0 @ B) ) ) ) )  =>  (! [C: $i] :  ( ( ( (m2_finseq_2 @ C)  @  (u1_struct_0 @ B) )  @  ( (k4_finseq_2 @ A)  @  (u1_struct_0 @ B) ) )  =>  ( (= @  ( ( ( (k10_fvsum_1 @ A)  @ B)  @ C)  @  (k5_struct_0 @ B) ) )  @ C) ) ) ) ) ) ) , file(fvsum_1, t57_fvsum_1)).
thf(t5_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  <=>  ( (r1_tarski @  (k2_finseq_1 @ A) )  @  (k2_finseq_1 @ B) ) ) ) ) ) ) , file(finseq_1, t5_finseq_1)).
thf(t5_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  =>  ( (v1_xboole_0 @ B)  |  ( (v3_xxreal_0 @ A)  |  (v2_xxreal_0 @ B) ) ) ) ) ) ) ) , file(real, t5_real)).
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(t6_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  =>  ( (v1_xboole_0 @ A)  |  ( (v2_xxreal_0 @ B)  |  (v3_xxreal_0 @ A) ) ) ) ) ) ) ) , file(real, t6_real)).
thf(t6_vectsp_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v1_vectsp_1 @ A)  &  (l6_algstr_0 @ A) ) ) ) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  ( (= @  ( ( (k6_algstr_0 @ A)  @ B)  @  (k4_struct_0 @ A) ) )  @  (k4_struct_0 @ A) ) ) ) ) ) , file(vectsp_1, t6_vectsp_1)).
thf(t74_matrix13, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v6_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v33_algstr_0 @ A)  &  ( (v3_group_1 @ A)  &  ( (v5_group_1 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v4_vectsp_1 @ A)  &  ( (v5_vectsp_1 @ A)  &  (l6_algstr_0 @ A) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( (v1_matrix_1 @ B)  &  ( (m2_finseq_1 @ B)  @  (k3_finseq_2 @  (u1_struct_0 @ A) ) ) )  =>  ( ( (r1_xxreal_0 @  ( (k8_matrix13 @ A)  @ B) )  @  (k3_finseq_1 @ B) )  &  ( (r1_xxreal_0 @  ( (k8_matrix13 @ A)  @ B) )  @  (k1_matrix_1 @ B) ) ) ) ) ) ) , file(matrix13, t74_matrix13)).
thf(t7_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( ( (r2_hidden @ A)  @ B)  &  (v1_xboole_0 @ B) ) ) ) ) , file(boole, t7_boole)).
thf(t7_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ~ ( ( (r1_xxreal_0 @ A)  @ B) )  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ B) ) ) ) ) ) ) ) ) , file(real, t7_real)).
thf(t87_zfmisc_1, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  (! [D: $i] :  ( ( (r2_hidden @  ( (k4_tarski @ A)  @ B) )  @  ( (k2_zfmisc_1 @ C)  @ D) )  <=>  ( ( (r2_hidden @ A)  @ C)  &  ( (r2_hidden @ B)  @ D) ) ) ) ) ) ) , file(zfmisc_1, t87_zfmisc_1)).
thf(t8_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( (v1_xboole_0 @ A)  &  ( ~ ( ( (= @ A)  @ B) )  &  (v1_xboole_0 @ B) ) ) ) ) ) , file(boole, t8_boole)).
thf(t8_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ~ ( ( ( (r1_xxreal_0 @ A)  @  ( (k1_nat_1 @ B)  @ np__1) )  &  ( ~ ( ( (r1_xxreal_0 @ A)  @ B) )  &  ~ ( ( (= @ A)  @  ( (k1_nat_1 @ B)  @ np__1) ) ) ) ) ) ) ) ) ) , file(nat_1, t8_nat_1)).
thf(t8_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ~ ( ( (r1_xxreal_0 @ A)  @ B) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  ~ ( (v2_xxreal_0 @ A) ) ) ) ) ) ) ) ) , file(real, t8_real)).
thf(t92_matrix13, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  (! [C: $i] :  ( (v7_ordinal1 @ C)  =>  (! [D: $i] :  ( (v7_ordinal1 @ D)  =>  (! [E: $i] :  ( ( ~ ( (v2_struct_0 @ E) )  &  ( ~ ( (v6_struct_0 @ E) )  &  ( (v13_algstr_0 @ E)  &  ( (v33_algstr_0 @ E)  &  ( (v3_group_1 @ E)  &  ( (v5_group_1 @ E)  &  ( (v2_rlvect_1 @ E)  &  ( (v3_rlvect_1 @ E)  &  ( (v4_rlvect_1 @ E)  &  ( (v4_vectsp_1 @ E)  &  ( (v5_vectsp_1 @ E)  &  (l6_algstr_0 @ E) ) ) ) ) ) ) ) ) ) ) )  =>  (! [F: $i] :  ( ( (m1_subset_1 @ F)  @  (u1_struct_0 @ E) )  =>  (! [G: $i] :  ( ( ( ( (m1_matrix_1 @ G)  @  (u1_struct_0 @ E) )  @ A)  @ B)  =>  ( ( (r2_hidden @ C)  @  (k2_finseq_1 @  (k3_finseq_1 @ G) ) )  =>  ( ( ( (= @ D)  @ C)  &  ( (= @ F)  @  ( (k4_algstr_0 @ E)  @  (k1_group_1 @ E) ) ) )  |  ( (= @  ( (k8_matrix13 @ E)  @ G) )  @  ( (k8_matrix13 @ E)  @  ( ( ( ( ( (k3_matrix11 @ D)  @ A)  @ B)  @  (u1_struct_0 @ E) )  @ G)  @  ( ( ( (k4_fvsum_1 @  (k1_matrix_1 @ G) )  @ E)  @  ( ( (k8_matrix_1 @  (u1_struct_0 @ E) )  @ G)  @ D) )  @  ( ( ( (k10_fvsum_1 @  (k1_matrix_1 @ G) )  @ E)  @  ( ( (k8_matrix_1 @  (u1_struct_0 @ E) )  @ G)  @ C) )  @ F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(matrix13, t92_matrix13)).
thf(t96_zfmisc_1, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  (! [D: $i] :  ( ( ( (r1_tarski @ A)  @ B)  &  ( (r1_tarski @ C)  @ D) )  =>  ( (r1_tarski @  ( (k2_zfmisc_1 @ A)  @ C) )  @  ( (k2_zfmisc_1 @ B)  @ D) ) ) ) ) ) ) , file(zfmisc_1, t96_zfmisc_1)).
thf(s1_matrix15, axiom,  (! [A: $i > $i > $o] :  (! [B: $i > $i > $i > $i > $i] :  (! [C: $i] :  (! [D: $i] :  (! [E: $i] :  (! [F: $i] :  (! [G: $i] :  (! [H: $i] :  ( ( ( ~ ( (v2_struct_0 @ H) )  &  ( ~ ( (v6_struct_0 @ H) )  &  ( (v13_algstr_0 @ H)  &  ( (v33_algstr_0 @ H)  &  ( (v3_group_1 @ H)  &  ( (v5_group_1 @ H)  &  ( (v4_vectsp_1 @ H)  &  ( (v5_vectsp_1 @ H)  &  ( (v2_rlvect_1 @ H)  &  ( (v3_rlvect_1 @ H)  &  ( (v4_rlvect_1 @ H)  &  (l6_algstr_0 @ H) ) ) ) ) ) ) ) ) ) ) )  &  ( (v7_ordinal1 @ G)  &  ( (v7_ordinal1 @ F)  &  ( (v7_ordinal1 @ E)  &  ( ( ( ( (m1_matrix_1 @ D)  @  (u1_struct_0 @ H) )  @ G)  @ F)  &  ( ( ( ( (m1_matrix_1 @ C)  @  (u1_struct_0 @ H) )  @ G)  @ E)  &  (! [I: $i, J: $i, K: $i, L: $i] :  ( ( ( (m1_matrix_1 @  ( ( ( (B @ I)  @ J)  @ K)  @ L) )  @  (u1_struct_0 @ H) )  @ G)  @ E) ) ) ) ) ) ) )  =>  ( ( ( (A @ D)  @ C)  &  (! [M: $i] :  ( ( ( ( (m1_matrix_1 @ M)  @  (u1_struct_0 @ H) )  @ G)  @ F)  =>  (! [N: $i] :  ( ( ( ( (m1_matrix_1 @ N)  @  (u1_struct_0 @ H) )  @ G)  @ E)  =>  ( ( (A @ M)  @ N)  =>  (! [O: $i] :  ( (v7_ordinal1 @ O)  =>  (! [P: $i] :  ( (v7_ordinal1 @ P)  =>  ( ( (r2_hidden @ P)  @  (k4_finseq_1 @ M) )  =>  ( ( (= @ O)  @ P)  |  (! [Q: $i] :  ( ( (m1_subset_1 @ Q)  @  (u1_struct_0 @ H) )  =>  ( (A @  ( ( ( ( ( (k3_matrix11 @ O)  @ G)  @ F)  @  (u1_struct_0 @ H) )  @ M)  @  ( ( ( (k4_fvsum_1 @  (k1_matrix_1 @ M) )  @ H)  @  ( ( (k8_matrix_1 @  (u1_struct_0 @ H) )  @ M)  @ O) )  @  ( ( ( (k10_fvsum_1 @  (k1_matrix_1 @ M) )  @ H)  @  ( ( (k8_matrix_1 @  (u1_struct_0 @ H) )  @ M)  @ P) )  @ Q) ) ) )  @  ( ( ( (B @ N)  @ O)  @ P)  @ Q) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [M: $i] :  ( ( ( ( (m1_matrix_1 @ M)  @  (u1_struct_0 @ H) )  @ G)  @ F)  &  (? [N: $i] :  ( ( ( ( (m1_matrix_1 @ N)  @  (u1_struct_0 @ H) )  @ G)  @ E)  &  (? [O: $i] :  ( ( (v1_finset_1 @ O)  &  ( (v1_setfam_1 @ O)  &  ( (m1_subset_1 @ O)  @  (k1_zfmisc_1 @ k5_numbers) ) ) )  &  ( ( (r1_tarski @ O)  @  (k2_finseq_1 @ F) )  &  ( ( (= @  ( (k8_matrix13 @ H)  @ D) )  @  ( (k8_matrix13 @ H)  @ M) )  &  ( ( (= @  ( (k8_matrix13 @ H)  @ D) )  @  (k5_card_1 @ O) )  &  ( ( (A @ M)  @ N)  &  ( ( (v2_matrix_1 @  ( ( ( (k6_matrix13 @  (u1_struct_0 @ H) )  @ M)  @  (k2_finseq_1 @  (k5_card_1 @ O) ) )  @ O) )  @ H)  &  ( (! [P: $i] :  ( (v7_ordinal1 @ P)  =>  ~ ( ( ( (r2_hidden @ P)  @  (k2_finseq_1 @  (k5_card_1 @ O) ) )  &  ( (= @  ( ( ( (k3_matrix_1 @  (u1_struct_0 @ H) )  @ M)  @ P)  @  ( ( (k7_partfun1 @ k5_numbers)  @  (k5_matrix13 @ O) )  @ P) ) )  @  (k4_struct_0 @ H) ) ) ) ) )  &  ( (! [P: $i] :  ( (v7_ordinal1 @ P)  =>  ( ( (r2_hidden @ P)  @  (k4_finseq_1 @ M) )  =>  ( ( (r1_xxreal_0 @ P)  @  (k5_card_1 @ O) )  |  ( (= @  ( ( (k8_matrix_1 @  (u1_struct_0 @ H) )  @ M)  @ P) )  @  ( ( (k5_finseq_2 @  (u1_struct_0 @ H) )  @ F)  @  (k4_struct_0 @ H) ) ) ) ) ) )  &  (! [P: $i] :  ( (v7_ordinal1 @ P)  =>  (! [Q: $i] :  ( (v7_ordinal1 @ Q)  =>  ( ( ( (r2_hidden @ P)  @  (k2_finseq_1 @  (k5_card_1 @ O) ) )  &  ( (r2_hidden @ Q)  @  (k2_finseq_1 @  (k1_matrix_1 @ M) ) ) )  =>  ( ( (r1_xxreal_0 @  ( (k1_funct_1 @  (k5_matrix13 @ O) )  @ P) )  @ Q)  |  ( (= @  ( ( ( (k3_matrix_1 @  (u1_struct_0 @ H) )  @ M)  @ P)  @ Q) )  @  (k4_struct_0 @ H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(matrix15, s1_matrix15)).
thf(s2_nat_1, axiom,  (! [A: $i > $o] :  ( ( (A @ k6_numbers)  &  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ( (A @ B)  =>  (A @  ( (k1_nat_1 @ B)  @ np__1) ) ) ) ) )  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  (A @ B) ) ) ) ) , file(nat_1, s2_nat_1)).
thf(s2_matrix15, conjecture,  ( ( ( (p1_s2_matrix15 @ f5_s2_matrix15)  @ f6_s2_matrix15)  &  (! [A: $i] :  ( ( ( ( (m1_matrix_1 @ A)  @  (u1_struct_0 @ f1_s2_matrix15) )  @ f2_s2_matrix15)  @ f3_s2_matrix15)  =>  (! [B: $i] :  ( ( ( ( (m1_matrix_1 @ B)  @  (u1_struct_0 @ f1_s2_matrix15) )  @ f2_s2_matrix15)  @ f4_s2_matrix15)  =>  ( ( (p1_s2_matrix15 @ A)  @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ f1_s2_matrix15) )  =>  (! [D: $i] :  ( (v7_ordinal1 @ D)  =>  (! [E: $i] :  ( (v7_ordinal1 @ E)  =>  ( ( (r2_hidden @ E)  @  (k4_finseq_1 @ A) )  =>  ( ( ( (= @ D)  @ E)  &  ( (= @ C)  @  ( (k4_algstr_0 @ f1_s2_matrix15)  @  (k1_group_1 @ f1_s2_matrix15) ) ) )  |  ( (p1_s2_matrix15 @  ( ( ( ( ( (k3_matrix11 @ D)  @ f2_s2_matrix15)  @ f3_s2_matrix15)  @  (u1_struct_0 @ f1_s2_matrix15) )  @ A)  @  ( ( ( (k4_fvsum_1 @  (k1_matrix_1 @ A) )  @ f1_s2_matrix15)  @  ( ( (k8_matrix_1 @  (u1_struct_0 @ f1_s2_matrix15) )  @ A)  @ D) )  @  ( ( ( (k10_fvsum_1 @  (k1_matrix_1 @ A) )  @ f1_s2_matrix15)  @  ( ( (k8_matrix_1 @  (u1_struct_0 @ f1_s2_matrix15) )  @ A)  @ E) )  @ C) ) ) )  @  ( ( ( (f7_s2_matrix15 @ B)  @ D)  @ E)  @ C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [A: $i] :  ( ( ( ( (m1_matrix_1 @ A)  @  (u1_struct_0 @ f1_s2_matrix15) )  @ f2_s2_matrix15)  @ f3_s2_matrix15)  &  (? [B: $i] :  ( ( ( ( (m1_matrix_1 @ B)  @  (u1_struct_0 @ f1_s2_matrix15) )  @ f2_s2_matrix15)  @ f4_s2_matrix15)  &  (? [C: $i] :  ( ( (v1_finset_1 @ C)  &  ( (v1_setfam_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ k5_numbers) ) ) )  &  ( ( (r1_tarski @ C)  @  (k2_finseq_1 @ f3_s2_matrix15) )  &  ( ( (= @  ( (k8_matrix13 @ f1_s2_matrix15)  @ f5_s2_matrix15) )  @  ( (k8_matrix13 @ f1_s2_matrix15)  @ A) )  &  ( ( (= @  ( (k8_matrix13 @ f1_s2_matrix15)  @ f5_s2_matrix15) )  @  (k5_card_1 @ C) )  &  ( ( (p1_s2_matrix15 @ A)  @ B)  &  ( ( (= @  ( ( ( (k6_matrix13 @  (u1_struct_0 @ f1_s2_matrix15) )  @ A)  @  (k2_finseq_1 @  (k5_card_1 @ C) ) )  @ C) )  @  ( (k12_matrix_1 @ f1_s2_matrix15)  @  (k5_card_1 @ C) ) )  &  ( (! [D: $i] :  ( (v7_ordinal1 @ D)  =>  ( ( (r2_hidden @ D)  @  (k4_finseq_1 @ A) )  =>  ( ( (r1_xxreal_0 @ D)  @  (k5_card_1 @ C) )  |  ( (= @  ( ( (k8_matrix_1 @  (u1_struct_0 @ f1_s2_matrix15) )  @ A)  @ D) )  @  ( ( (k5_finseq_2 @  (u1_struct_0 @ f1_s2_matrix15) )  @ f3_s2_matrix15)  @  (k4_struct_0 @ f1_s2_matrix15) ) ) ) ) ) )  &  (! [D: $i] :  ( (v7_ordinal1 @ D)  =>  (! [E: $i] :  ( (v7_ordinal1 @ E)  =>  ( ( ( (r2_hidden @ D)  @  (k2_finseq_1 @  (k5_card_1 @ C) ) )  &  ( (r2_hidden @ E)  @  (k2_finseq_1 @  (k1_matrix_1 @ A) ) ) )  =>  ( ( (r1_xxreal_0 @  ( (k1_funct_1 @  (k5_matrix13 @ C) )  @ D) )  @ E)  |  ( (= @  ( ( ( (k3_matrix_1 @  (u1_struct_0 @ f1_s2_matrix15) )  @ A)  @ D)  @ E) )  @  (k4_struct_0 @ f1_s2_matrix15) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(matrix15, s2_matrix15)).
thf(sethood_m1_subset_1, axiom, ( ! [A: $i] :  ( sethood @ ( ^ [X: $i] : (m1_subset_1 @ X @ A) ) ) ) , file(subset_1, m1_subset_1)).
