% Mizar problem: s1_msualg_6,msualg_6,1040,16 
include('Axioms/SET010^0.ax').
thf(n0_type, type, np__0: $i).
thf(n1_type, type, np__1: $i).
thf(n2_type, type, np__2: $i).
thf(f1_s1_msualg_6_type, type, f1_s1_msualg_6: $i).
thf(f2_s1_msualg_6_type, type, f2_s1_msualg_6: $i).
thf(k10_xtuple_0_type, type, k10_xtuple_0: $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_funct_1_type, type, k1_funct_1: $i > $i > $i).
thf(k1_nat_1_type, type, k1_nat_1: $i > $i > $i).
thf(k1_numbers_type, type, k1_numbers: $i).
thf(k1_partfun1_type, type, k1_partfun1: $i > $i > $i > $i > $i > $i > $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_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_msualg_6_type, type, k3_msualg_6: $i > $i).
thf(k3_relat_1_type, type, k3_relat_1: $i > $i > $i).
thf(k3_xcmplx_0_type, type, k3_xcmplx_0: $i > $i > $i).
thf(k4_finseq_1_type, type, k4_finseq_1: $i > $i).
thf(k4_funct_7_type, type, k4_funct_7: $i > $i > $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(k4_relat_1_type, type, k4_relat_1: $i > $i).
thf(k4_relset_1_type, type, k4_relset_1: $i > $i > $i > $i > $i > $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_finseq_1_type, type, k5_finseq_1: $i > $i).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(k5_relat_1_type, type, k5_relat_1: $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_finseq_1_type, type, k7_finseq_1: $i > $i > $i).
thf(k9_finseq_1_type, type, k9_finseq_1: $i > $i).
thf(k9_xtuple_0_type, type, k9_xtuple_0: $i > $i).
thf(u1_struct_0_type, type, u1_struct_0: $i > $i).
thf(u3_msualg_1_type, type, u3_msualg_1: $i > $i > $i).
thf(l1_msualg_1_type, type, l1_msualg_1: $i > $o).
thf(l1_struct_0_type, type, l1_struct_0: $i > $o).
thf(l2_msualg_1_type, type, l2_msualg_1: $i > $i > $o).
thf(l3_msualg_1_type, type, l3_msualg_1: $i > $i > $o).
thf(l5_struct_0_type, type, l5_struct_0: $i > $o).
thf(m1_rewrite1_type, type, m1_rewrite1: $i > $i > $o).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(m2_msualg_6_type, type, m2_msualg_6: $i > $i > $i > $i > $i > $o).
thf(m2_subset_1_type, type, m2_subset_1: $i > $i > $i > $o).
thf(p1_s1_msualg_6_type, type, p1_s1_msualg_6: $i > $i > $i > $o).
thf(r1_funct_2_type, type, r1_funct_2: $i > $i > $i > $i > $i > $i > $o).
thf(r1_msualg_6_type, type, r1_msualg_6: $i > $i > $i > $i > $i > $o).
thf(r1_rewrite1_type, type, r1_rewrite1: $i > $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(r2_funct_2_type, type, r2_funct_2: $i > $i > $i > $i > $o).
thf(r2_relset_1_type, type, r2_relset_1: $i > $i > $i > $i > $o).
thf(v10_rewrite1_type, type, v10_rewrite1: $i > $o).
thf(v11_struct_0_type, type, v11_struct_0: $i > $o).
thf(v13_struct_0_type, type, v13_struct_0: $i > $i > $o).
thf(v14_struct_0_type, type, v14_struct_0: $i > $o).
thf(v15_struct_0_type, type, v15_struct_0: $i > $o).
thf(v1_card_1_type, type, v1_card_1: $i > $o).
thf(v1_finseq_1_type, type, v1_finseq_1: $i > $o).
thf(v1_finset_1_type, type, v1_finset_1: $i > $o).
thf(v1_funcop_1_type, type, v1_funcop_1: $i > $o).
thf(v1_funct_1_type, type, v1_funct_1: $i > $o).
thf(v1_funct_2_type, type, v1_funct_2: $i > $i > $i > $o).
thf(v1_funct_7_type, type, v1_funct_7: $i > $o).
thf(v1_msualg_6_type, type, v1_msualg_6: $i > $i > $o).
thf(v1_ordinal1_type, type, v1_ordinal1: $i > $o).
thf(v1_partfun1_type, type, v1_partfun1: $i > $i > $o).
thf(v1_relat_1_type, type, v1_relat_1: $i > $o).
thf(v1_relat_2_type, type, v1_relat_2: $i > $o).
thf(v1_rewrite1_type, type, v1_rewrite1: $i > $o).
thf(v1_setfam_1_type, type, v1_setfam_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_xtuple_0_type, type, v1_xtuple_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_card_1_type, type, v2_card_1: $i > $o).
thf(v2_finseq_1_type, type, v2_finseq_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_funct_2_type, type, v2_funct_2: $i > $i > $o).
thf(v2_ordinal1_type, type, v2_ordinal1: $i > $o).
thf(v2_relat_1_type, type, v2_relat_1: $i > $o).
thf(v2_relat_2_type, type, v2_relat_2: $i > $o).
thf(v2_rewrite1_type, type, v2_rewrite1: $i > $o).
thf(v2_struct_0_type, type, v2_struct_0: $i > $o).
thf(v2_xxreal_0_type, type, v2_xxreal_0: $i > $o).
thf(v3_card_1_type, type, v3_card_1: $i > $i > $o).
thf(v3_finseq_1_type, type, v3_finseq_1: $i > $o).
thf(v3_funct_1_type, type, v3_funct_1: $i > $o).
thf(v3_funct_2_type, type, v3_funct_2: $i > $i > $i > $o).
thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o).
thf(v3_relat_1_type, type, v3_relat_1: $i > $o).
thf(v3_relat_2_type, type, v3_relat_2: $i > $o).
thf(v3_rewrite1_type, type, v3_rewrite1: $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_msualg_1_type, type, v4_msualg_1: $i > $i > $o).
thf(v4_relat_1_type, type, v4_relat_1: $i > $i > $o).
thf(v4_relat_2_type, type, v4_relat_2: $i > $o).
thf(v4_rewrite1_type, type, v4_rewrite1: $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_rewrite1_type, type, v5_rewrite1: $i > $o).
thf(v6_ordinal1_type, type, v6_ordinal1: $i > $o).
thf(v6_rewrite1_type, type, v6_rewrite1: $i > $o).
thf(v7_ordinal1_type, type, v7_ordinal1: $i > $o).
thf(v7_rewrite1_type, type, v7_rewrite1: $i > $o).
thf(v7_struct_0_type, type, v7_struct_0: $i > $o).
thf(v8_relat_2_type, type, v8_relat_2: $i > $o).
thf(v8_rewrite1_type, type, v8_rewrite1: $i > $o).
thf(v8_struct_0_type, type, v8_struct_0: $i > $o).
thf(v9_rewrite1_type, type, v9_rewrite1: $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_rewrite1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v5_rewrite1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v4_rewrite1 @ A) ) ) ) , file(rewrite1, cc10_rewrite1)).
thf(cc10_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ( ~ ( (v2_struct_0 @ A) )  &  (v7_struct_0 @ A) )  =>  ( (v13_struct_0 @ A)  @ np__1) ) ) ) , file(struct_0, cc10_struct_0)).
thf(cc11_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_finseq_1 @ B) ) ) ) ) , file(finseq_1, cc11_finseq_1)).
thf(cc11_rewrite1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v2_rewrite1 @ A)  &  (v4_rewrite1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  (v8_rewrite1 @ A) ) ) ) , file(rewrite1, cc11_rewrite1)).
thf(cc11_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ( (v13_struct_0 @ A)  @ np__1)  =>  ( ~ ( (v2_struct_0 @ A) )  &  (v7_struct_0 @ A) ) ) ) ) , file(struct_0, cc11_struct_0)).
thf(cc12_rewrite1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v6_rewrite1 @ A) ) ) ) , file(rewrite1, cc12_rewrite1)).
thf(cc12_struct_0, axiom,  (! [A: $i] :  ( (l5_struct_0 @ A)  =>  ( ~ ( (v2_struct_0 @ A) )  =>  (v14_struct_0 @ A) ) ) ) , file(struct_0, cc12_struct_0)).
thf(cc13_rewrite1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v3_rewrite1 @ A)  &  (v9_rewrite1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  (v7_rewrite1 @ A) ) ) ) , file(rewrite1, cc13_rewrite1)).
thf(cc13_struct_0, axiom,  (! [A: $i] :  ( (l5_struct_0 @ A)  =>  ( (v11_struct_0 @ A)  =>  (v14_struct_0 @ A) ) ) ) , file(struct_0, cc13_struct_0)).
thf(cc14_rewrite1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v10_rewrite1 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v3_rewrite1 @ A)  &  (v7_rewrite1 @ A) ) ) ) ) , file(rewrite1, cc14_rewrite1)).
thf(cc14_struct_0, axiom,  (! [A: $i] :  ( (l5_struct_0 @ A)  =>  ( ( (v2_struct_0 @ A)  &  (v14_struct_0 @ A) )  =>  (v11_struct_0 @ A) ) ) ) , file(struct_0, cc14_struct_0)).
thf(cc15_rewrite1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v3_rewrite1 @ A)  &  (v7_rewrite1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  (v10_rewrite1 @ A) ) ) ) , file(rewrite1, cc15_rewrite1)).
thf(cc15_struct_0, axiom,  (! [A: $i] :  ( (l5_struct_0 @ A)  =>  ( ( ~ ( (v11_struct_0 @ A) )  &  (v14_struct_0 @ A) )  =>  ~ ( (v2_struct_0 @ A) ) ) ) ) , file(struct_0, cc15_struct_0)).
thf(cc16_struct_0, axiom,  (! [A: $i] :  ( (l5_struct_0 @ A)  =>  ( (v11_struct_0 @ A)  =>  (v15_struct_0 @ A) ) ) ) , file(struct_0, cc16_struct_0)).
thf(cc17_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v7_struct_0 @ A) )  =>  ~ ( (v2_struct_0 @ A) ) ) ) ) , file(struct_0, cc17_struct_0)).
thf(cc1_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_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_funct_7, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_funcop_1 @ A) ) ) ) ) , file(funct_7, cc1_funct_7)).
thf(cc1_msualg_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_msualg_1 @ A) )  &  ( ( (v4_msualg_1 @ B)  @ A)  &  ( (l3_msualg_1 @ B)  @ A) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k10_xtuple_0 @  ( (u3_msualg_1 @ A)  @ B) ) )  =>  ~ ( (v1_xboole_0 @ C) ) ) ) ) ) , file(msualg_1, cc1_msualg_1)).
thf(cc1_msualg_6, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  =>  (! [B: $i] :  ( ( (l3_msualg_1 @ B)  @ A)  =>  ( ( (v4_msualg_1 @ B)  @ A)  =>  ( (v1_msualg_6 @ B)  @ A) ) ) ) ) ) , file(msualg_6, cc1_msualg_6)).
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_partfun1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v1_partfun1 @ C)  @ A) ) ) ) ) , file(partfun1, cc1_partfun1)).
thf(cc1_pboole, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  =>  ( (v1_relat_1 @ B)  &  ( ~ ( (v3_relat_1 @ B) )  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) ) ) , file(pboole, cc1_pboole)).
thf(cc1_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_relat_1 @ A) ) ) , file(relat_1, cc1_relat_1)).
thf(cc1_relset_1, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_relat_1 @ C) ) ) ) , file(relset_1, cc1_relset_1)).
thf(cc1_rewrite1, axiom,  (! [A: $i] :  ( (v1_relat_1 @ A)  =>  (! [B: $i] :  ( ( (m1_rewrite1 @ B)  @ A)  =>  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(rewrite1, cc1_rewrite1)).
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_xreal_0, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc1_xreal_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_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_funct_7, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v1_funct_7 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_funcop_1 @ A)  &  (v1_finseq_1 @ A) ) ) ) ) ) , file(funct_7, cc2_funct_7)).
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_partfun1, 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_partfun1 @ C)  @ A) ) ) ) ) ) , file(partfun1, cc2_partfun1)).
thf(cc2_pboole, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v3_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  =>  ( (v1_relat_1 @ B)  &  ( ~ ( (v2_relat_1 @ B) )  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) ) ) , file(pboole, cc2_pboole)).
thf(cc2_relat_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_relat_1 @ B) ) ) ) ) , file(relat_1, cc2_relat_1)).
thf(cc2_relset_1, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v5_relat_1 @ C)  @ B) ) ) ) ) , file(relset_1, cc2_relset_1)).
thf(cc2_rewrite1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_rewrite1 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v2_relat_2 @ A)  &  (v1_rewrite1 @ A) ) ) ) ) , file(rewrite1, cc2_rewrite1)).
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_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(cc3_card_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_card_1 @ A) ) ) , file(card_1, cc3_card_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_funct_7, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v1_funct_7 @ A) ) ) ) ) ) , file(funct_7, cc3_funct_7)).
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_partfun1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v3_relat_2 @ A)  &  (v8_relat_2 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  (v1_relat_2 @ A) ) ) ) , file(partfun1, cc3_partfun1)).
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_rewrite1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v2_relat_2 @ A)  &  (v1_rewrite1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  (v3_rewrite1 @ A) ) ) ) , file(rewrite1, cc3_rewrite1)).
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_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_pboole, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  =>  ( (v1_relat_1 @ B)  &  ( ~ ( (v3_relat_1 @ B) )  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) ) ) , file(pboole, cc4_pboole)).
thf(cc4_relat_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v2_relat_1 @ A) ) ) ) , file(relat_1, cc4_relat_1)).
thf(cc4_relset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) )  =>  (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc4_relset_1)).
thf(cc4_rewrite1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v2_rewrite1 @ A)  &  (v3_rewrite1 @ A) ) ) ) ) , file(rewrite1, cc4_rewrite1)).
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_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_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_funct_2, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_funct_1 @ C)  &  ( ( (v3_funct_2 @ C)  @ A)  @ B) )  =>  ( (v1_funct_1 @ C)  &  ( (v2_funct_1 @ C)  &  ( (v2_funct_2 @ C)  @ B) ) ) ) ) ) ) , file(funct_2, cc5_funct_2)).
thf(cc5_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v3_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc5_ordinal1)).
thf(cc5_pboole, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) )  =>  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) ) ) , file(pboole, cc5_pboole)).
thf(cc5_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ B) )  =>  ( (v4_relat_1 @ C)  @ A) ) ) ) ) , file(relat_1, cc5_relat_1)).
thf(cc5_rewrite1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_rewrite1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v2_rewrite1 @ A) ) ) ) , file(rewrite1, cc5_rewrite1)).
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_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_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_funct_2, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_funct_1 @ C)  &  ( (v2_funct_1 @ C)  &  ( (v2_funct_2 @ C)  @ B) ) )  =>  ( (v1_funct_1 @ C)  &  ( ( (v3_funct_2 @ C)  @ A)  @ B) ) ) ) ) ) , file(funct_2, cc6_funct_2)).
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_rewrite1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v8_rewrite1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v7_rewrite1 @ A) ) ) ) , file(rewrite1, cc6_rewrite1)).
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_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_funct_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v4_funct_1 @ A) ) ) , file(funct_1, cc7_funct_1)).
thf(cc7_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) )  =>  ( ( (v1_relat_2 @ B)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  ( ( (v1_funct_2 @ B)  @ A)  @ A) ) ) )  =>  ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ A)  @ A)  &  ( ( (v3_funct_2 @ B)  @ A)  @ A) ) ) ) ) ) ) , file(funct_2, cc7_funct_2)).
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_rewrite1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v7_rewrite1 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v8_rewrite1 @ A)  &  (v9_rewrite1 @ A) ) ) ) ) , file(rewrite1, cc7_rewrite1)).
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_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_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_rewrite1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v6_rewrite1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v7_rewrite1 @ A) ) ) ) , file(rewrite1, cc8_rewrite1)).
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_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_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_rewrite1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v8_rewrite1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v5_rewrite1 @ A) ) ) ) , file(rewrite1, cc9_rewrite1)).
thf(cc9_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ( (v13_struct_0 @ A)  @ k1_xboole_0)  =>  (v2_struct_0 @ A) ) ) ) , file(struct_0, cc9_struct_0)).
thf(commutativity_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_xcmplx_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k3_xcmplx_0 @ A)  @ B) )  @  ( (k3_xcmplx_0 @ B)  @ A) ) ) ) , file(xcmplx_0, k3_xcmplx_0)).
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(d1_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( ~ ( ( (= @ B)  @ k1_xboole_0) )  =>  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  <=>  ( (= @ A)  @  ( (k1_relset_1 @ A)  @ C) ) ) )  &  ( ( (= @ B)  @ k1_xboole_0)  =>  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  <=>  ( (= @ C)  @ k1_xboole_0) ) ) ) ) ) ) ) , file(funct_2, d1_funct_2)).
thf(d1_tarski, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (= @ B)  @  (k1_tarski @ A) )  <=>  (! [C: $i] :  ( ( (r2_hidden @ C)  @ B)  <=>  ( (= @ C)  @ A) ) ) ) ) ) , file(tarski, d1_tarski)).
thf(d2_rewrite1, axiom,  (! [A: $i] :  ( (v1_relat_1 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) )  =>  ( ( (m1_rewrite1 @ B)  @ A)  <=>  ( ~ ( ( (r1_xxreal_0 @  (k3_finseq_1 @ B) )  @ k6_numbers) )  &  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ k5_numbers)  =>  ( ( ( (r2_hidden @ C)  @  (k4_finseq_1 @ B) )  &  ( (r2_hidden @  ( (k2_nat_1 @ C)  @ np__1) )  @  (k4_finseq_1 @ B) ) )  =>  ( (r2_hidden @  ( (k4_tarski @  ( (k1_funct_1 @ B)  @ C) )  @  ( (k1_funct_1 @ B)  @  ( (k2_nat_1 @ C)  @ np__1) ) ) )  @ A) ) ) ) ) ) ) ) ) ) , file(rewrite1, d2_rewrite1)).
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(d5_tarski, axiom,  (! [A: $i] :  (! [B: $i] :  ( (= @  ( (k4_tarski @ A)  @ B) )  @  ( (k2_tarski @  ( (k2_tarski @ A)  @ B) )  @  (k1_tarski @ A) ) ) ) ) , file(tarski, d5_tarski)).
thf(d6_msualg_6, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  =>  (! [B: $i] :  ( ( ( (v4_msualg_1 @ B)  @ A)  &  ( (l3_msualg_1 @ B)  @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @  (u1_struct_0 @ A) )  =>  ( ( ( (r1_rewrite1 @  (k3_msualg_6 @ A) )  @ C)  @ D)  =>  (! [E: $i] :  ( ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @  ( (k1_funct_1 @  ( (u3_msualg_1 @ A)  @ B) )  @ C) )  @  ( (k1_funct_1 @  ( (u3_msualg_1 @ A)  @ B) )  @ D) )  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k1_funct_1 @  ( (u3_msualg_1 @ A)  @ B) )  @ C) )  @  ( (k1_funct_1 @  ( (u3_msualg_1 @ A)  @ B) )  @ D) ) ) ) ) )  =>  ( ( ( ( ( (m2_msualg_6 @ E)  @ A)  @ B)  @ C)  @ D)  <=>  (? [F: $i] :  ( ( (m1_rewrite1 @ F)  @  (k3_msualg_6 @ A) )  &  (? [G: $i] :  ( ( (v1_relat_1 @ G)  &  ( (v1_funct_1 @ G)  &  ( (v1_finseq_1 @ G)  &  (v1_funcop_1 @ G) ) ) )  &  ( ( (= @ E)  @  ( (k4_funct_7 @  ( (k1_funct_1 @  ( (u3_msualg_1 @ A)  @ B) )  @ C) )  @ G) )  &  ( ( (= @  (k3_finseq_1 @ F) )  @  ( (k2_nat_1 @  (k3_finseq_1 @ G) )  @ np__1) )  &  ( ( (= @ C)  @  ( (k1_funct_1 @ F)  @ np__1) )  &  ( ( (= @ D)  @  ( (k1_funct_1 @ F)  @  (k3_finseq_1 @ F) ) )  &  (! [H: $i] :  ( ( (m1_subset_1 @ H)  @ k5_numbers)  =>  (! [I: $i] :  ( ( (v1_relat_1 @ I)  &  (v1_funct_1 @ I) )  =>  (! [J: $i] :  ( ( (m1_subset_1 @ J)  @  (u1_struct_0 @ A) )  =>  (! [K: $i] :  ( ( (m1_subset_1 @ K)  @  (u1_struct_0 @ A) )  =>  ( ( ( (r2_hidden @ H)  @  (k4_finseq_1 @ G) )  &  ( ( (= @ I)  @  ( (k1_funct_1 @ G)  @ H) )  &  ( ( (= @ J)  @  ( (k1_funct_1 @ F)  @ H) )  &  ( (= @ K)  @  ( (k1_funct_1 @ F)  @  ( (k2_nat_1 @ H)  @ np__1) ) ) ) ) )  =>  ( ( ( ( (r1_msualg_6 @ A)  @ J)  @ K)  @ B)  @ I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(msualg_6, d6_msualg_6)).
thf(d7_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( (v1_funct_1 @ C)  &  (v1_finseq_1 @ C) ) )  =>  ( ( (= @ C)  @  ( (k7_finseq_1 @ A)  @ B) )  <=>  ( ( (= @  (k4_finseq_1 @ C) )  @  (k2_finseq_1 @  ( (k2_nat_1 @  (k3_finseq_1 @ A) )  @  (k3_finseq_1 @ B) ) ) )  &  ( (! [D: $i] :  ( (v7_ordinal1 @ D)  =>  ( ( (r2_hidden @ D)  @  (k4_finseq_1 @ A) )  =>  ( (= @  ( (k1_funct_1 @ C)  @ D) )  @  ( (k1_funct_1 @ A)  @ D) ) ) ) )  &  (! [D: $i] :  ( (v7_ordinal1 @ D)  =>  ( ( (r2_hidden @ D)  @  (k4_finseq_1 @ B) )  =>  ( (= @  ( (k1_funct_1 @ C)  @  ( (k2_nat_1 @  (k3_finseq_1 @ A) )  @ D) ) )  @  ( (k1_funct_1 @ B)  @ D) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(finseq_1, d7_finseq_1)).
thf(dt_f1_s1_msualg_6, axiom,  ( ~ ( (v2_struct_0 @ f1_s1_msualg_6) )  &  ( ~ ( (v11_struct_0 @ f1_s1_msualg_6) )  &  (l1_msualg_1 @ f1_s1_msualg_6) ) ) , file(msualg_6, f1_s1_msualg_6)).
thf(dt_f2_s1_msualg_6, axiom,  ( ( (v4_msualg_1 @ f2_s1_msualg_6)  @ f1_s1_msualg_6)  &  ( (l3_msualg_1 @ f2_s1_msualg_6)  @ f1_s1_msualg_6) ) , file(msualg_6, f2_s1_msualg_6)).
thf(dt_k10_xtuple_0, axiom, $true, file(xtuple_0, k10_xtuple_0)).
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_funct_1, axiom, $true, file(funct_1, k1_funct_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_partfun1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( ( (v1_funct_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  &  ( (v1_funct_1 @ F)  &  ( (m1_subset_1 @ F)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ C)  @ D) ) ) ) )  =>  ( (v1_funct_1 @  ( ( ( ( ( (k1_partfun1 @ A)  @ B)  @ C)  @ D)  @ E)  @ F) )  &  ( (m1_subset_1 @  ( ( ( ( ( (k1_partfun1 @ A)  @ B)  @ C)  @ D)  @ E)  @ F) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ D) ) ) ) ) ) , file(partfun1, k1_partfun1)).
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_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_msualg_6, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  =>  ( (m1_subset_1 @  (k3_msualg_6 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) ) ) ) ) , file(msualg_6, k3_msualg_6)).
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_xcmplx_0, axiom, $true, file(xcmplx_0, k3_xcmplx_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_funct_7, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v1_funcop_1 @ B)  &  (v1_finseq_1 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k4_funct_7 @ A)  @ B) )  &  (v1_funct_1 @  ( (k4_funct_7 @ A)  @ B) ) ) ) ) , file(funct_7, k4_funct_7)).
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_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (m1_subset_1 @ F)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ C)  @ D) ) ) )  =>  ( (m1_subset_1 @  ( ( ( ( ( (k4_relset_1 @ A)  @ B)  @ C)  @ D)  @ E)  @ F) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ D) ) ) ) ) , file(relset_1, k4_relset_1)).
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_finseq_1, axiom, $true, file(finseq_1, k5_finseq_1)).
thf(dt_k5_numbers, axiom,  ( (m1_subset_1 @ k5_numbers)  @  (k1_zfmisc_1 @ k1_numbers) ) , file(numbers, k5_numbers)).
thf(dt_k5_relat_1, axiom,  (! [A: $i, B: $i] :  ( (v1_relat_1 @ A)  =>  (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) , file(relat_1, k5_relat_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_finseq_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k7_finseq_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k7_finseq_1 @ A)  @ B) )  &  (v1_finseq_1 @  ( (k7_finseq_1 @ A)  @ B) ) ) ) ) ) , file(finseq_1, k7_finseq_1)).
thf(dt_k9_finseq_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @  (k9_finseq_1 @ A) )  &  (v1_funct_1 @  (k9_finseq_1 @ A) ) ) ) , file(finseq_1, k9_finseq_1)).
thf(dt_k9_xtuple_0, axiom, $true, file(xtuple_0, k9_xtuple_0)).
thf(dt_l1_msualg_1, axiom,  (! [A: $i] :  ( (l1_msualg_1 @ A)  =>  (l5_struct_0 @ A) ) ) , file(msualg_1, l1_msualg_1)).
thf(dt_l1_struct_0, axiom, $true, file(struct_0, l1_struct_0)).
thf(dt_l2_msualg_1, axiom, $true, file(msualg_1, l2_msualg_1)).
thf(dt_l3_msualg_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_msualg_1 @ A) )  =>  (! [B: $i] :  ( ( (l3_msualg_1 @ B)  @ A)  =>  ( (l2_msualg_1 @ B)  @ A) ) ) ) ) , file(msualg_1, l3_msualg_1)).
thf(dt_l5_struct_0, axiom,  (! [A: $i] :  ( (l5_struct_0 @ A)  =>  (l1_struct_0 @ A) ) ) , file(struct_0, l5_struct_0)).
thf(dt_m1_rewrite1, axiom,  (! [A: $i] :  ( (v1_relat_1 @ A)  =>  (! [B: $i] :  ( ( (m1_rewrite1 @ B)  @ A)  =>  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) ) ) ) ) ) , file(rewrite1, m1_rewrite1)).
thf(dt_m1_subset_1, axiom, $true, file(subset_1, m1_subset_1)).
thf(dt_m2_msualg_6, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  &  ( ( ( (v4_msualg_1 @ B)  @ A)  &  ( (l3_msualg_1 @ B)  @ A) )  &  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ D)  @  (u1_struct_0 @ A) ) ) ) )  =>  (! [E: $i] :  ( ( ( ( ( (m2_msualg_6 @ E)  @ A)  @ B)  @ C)  @ D)  =>  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @  ( (k1_funct_1 @  ( (u3_msualg_1 @ A)  @ B) )  @ C) )  @  ( (k1_funct_1 @  ( (u3_msualg_1 @ A)  @ B) )  @ D) )  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k1_funct_1 @  ( (u3_msualg_1 @ A)  @ B) )  @ C) )  @  ( (k1_funct_1 @  ( (u3_msualg_1 @ A)  @ B) )  @ D) ) ) ) ) ) ) ) ) ) , file(msualg_6, m2_msualg_6)).
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_struct_0, axiom, $true, file(struct_0, u1_struct_0)).
thf(dt_u3_msualg_1, axiom,  (! [A: $i, B: $i] :  ( ( (l1_struct_0 @ A)  &  ( (l2_msualg_1 @ B)  @ A) )  =>  ( (v1_relat_1 @  ( (u3_msualg_1 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (u3_msualg_1 @ A)  @ B) )  @  (u1_struct_0 @ A) )  &  ( (v1_funct_1 @  ( (u3_msualg_1 @ A)  @ B) )  &  ( (v1_partfun1 @  ( (u3_msualg_1 @ A)  @ B) )  @  (u1_struct_0 @ A) ) ) ) ) ) ) , file(msualg_1, u3_msualg_1)).
thf(existence_l1_msualg_1, axiom,  (? [A: $i] :  (l1_msualg_1 @ A) ) , file(msualg_1, l1_msualg_1)).
thf(existence_l1_struct_0, axiom,  (? [A: $i] :  (l1_struct_0 @ A) ) , file(struct_0, l1_struct_0)).
thf(existence_l2_msualg_1, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  (? [B: $i] :  ( (l2_msualg_1 @ B)  @ A) ) ) ) , file(msualg_1, l2_msualg_1)).
thf(existence_l3_msualg_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_msualg_1 @ A) )  =>  (? [B: $i] :  ( (l3_msualg_1 @ B)  @ A) ) ) ) , file(msualg_1, l3_msualg_1)).
thf(existence_l5_struct_0, axiom,  (? [A: $i] :  (l5_struct_0 @ A) ) , file(struct_0, l5_struct_0)).
thf(existence_m1_rewrite1, axiom,  (! [A: $i] :  ( (v1_relat_1 @ A)  =>  (? [B: $i] :  ( (m1_rewrite1 @ B)  @ A) ) ) ) , file(rewrite1, m1_rewrite1)).
thf(existence_m1_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_subset_1 @ B)  @ A) ) ) , file(subset_1, m1_subset_1)).
thf(existence_m2_msualg_6, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  &  ( ( ( (v4_msualg_1 @ B)  @ A)  &  ( (l3_msualg_1 @ B)  @ A) )  &  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ D)  @  (u1_struct_0 @ A) ) ) ) )  =>  (? [E: $i] :  ( ( ( ( (m2_msualg_6 @ E)  @ A)  @ B)  @ C)  @ D) ) ) ) , file(msualg_6, m2_msualg_6)).
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_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  (v1_setfam_1 @  (k10_xtuple_0 @ A) ) ) ) , file(funct_1, fc10_funct_1)).
thf(fc10_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_xboole_0 @  (k9_xtuple_0 @ A) ) ) ) , file(relat_1, fc10_relat_1)).
thf(fc10_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_relat_1 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k9_xtuple_0 @ A) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @  ( (k5_relat_1 @ A)  @ B) ) )  &  (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(relset_1, fc10_relset_1)).
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_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_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_finseq_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v2_finseq_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(finseq_1, fc13_finseq_1)).
thf(fc13_funcop_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_funcop_1 @ A) ) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v1_funcop_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(funcop_1, fc13_funcop_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_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_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_finseq_1, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k5_finseq_1 @ A) ) ) ) , file(finseq_1, fc16_finseq_1)).
thf(fc16_funcop_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_funct_1 @ A) ) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v3_funct_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(funcop_1, fc16_funcop_1)).
thf(fc16_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ B) )  =>  ( (v1_xboole_0 @  ( (k5_relat_1 @ A)  @ B) )  &  (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(relat_1, fc16_relat_1)).
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_finseq_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_finseq_1 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k7_finseq_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k7_finseq_1 @ A)  @ B) )  &  ( ~ ( (v1_xboole_0 @  ( (k7_finseq_1 @ A)  @ B) ) )  &  (v1_finseq_1 @  ( (k7_finseq_1 @ A)  @ B) ) ) ) ) ) ) , file(finseq_1, fc17_finseq_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_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_xboole_0 @  ( (k5_relat_1 @ A)  @ B) )  &  (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(relat_1, fc17_relat_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_finseq_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_finseq_1 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k7_finseq_1 @ B)  @ A) )  &  ( (v1_funct_1 @  ( (k7_finseq_1 @ B)  @ A) )  &  ( ~ ( (v1_xboole_0 @  ( (k7_finseq_1 @ B)  @ A) ) )  &  (v1_finseq_1 @  ( (k7_finseq_1 @ B)  @ A) ) ) ) ) ) ) , file(finseq_1, fc18_finseq_1)).
thf(fc18_funct_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_zfmisc_1 @ A) )  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ~ ( (v1_zfmisc_1 @  (k9_xtuple_0 @ A) ) ) ) ) , file(funct_1, fc18_funct_1)).
thf(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_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_funct_1, axiom,  (! [A: $i, B: $i] :  (v1_funct_1 @  (k1_tarski @  ( (k4_tarski @ A)  @ B) ) ) ) , file(funct_1, fc1_funct_1)).
thf(fc1_msualg_1, axiom,  (! [A: $i, B: $i] :  ( ( (l1_struct_0 @ A)  &  ( ( (v4_msualg_1 @ B)  @ A)  &  ( (l2_msualg_1 @ B)  @ A) ) )  =>  ( (v1_relat_1 @  ( (u3_msualg_1 @ A)  @ B) )  &  ( (v2_relat_1 @  ( (u3_msualg_1 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (u3_msualg_1 @ A)  @ B) )  @  (u1_struct_0 @ A) )  &  ( (v1_funct_1 @  ( (u3_msualg_1 @ A)  @ B) )  &  ( (v1_partfun1 @  ( (u3_msualg_1 @ A)  @ B) )  @  (u1_struct_0 @ A) ) ) ) ) ) ) ) , file(msualg_1, fc1_msualg_1)).
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_pboole, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @ B)  &  ( (v1_funct_1 @ D)  &  ( (v1_partfun1 @ D)  @ B) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ C)  @ D) )  &  ( ( (v4_relat_1 @  ( (k3_relat_1 @ C)  @ D) )  @ A)  &  ( (v1_funct_1 @  ( (k3_relat_1 @ C)  @ D) )  &  ( (v1_partfun1 @  ( (k3_relat_1 @ C)  @ D) )  @ A) ) ) ) ) ) , file(pboole, fc1_pboole)).
thf(fc1_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_xboole_0, axiom,  (v1_xboole_0 @ k1_xboole_0) , file(xboole_0, fc1_xboole_0)).
thf(fc1_xtuple_0, axiom,  (! [A: $i, B: $i] :  (v1_xtuple_0 @  ( (k4_tarski @ A)  @ B) ) ) , file(xtuple_0, fc1_xtuple_0)).
thf(fc20_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_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(fc23_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_relat_1 @ A) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v3_relat_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(relat_1, fc23_relat_1)).
thf(fc23_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 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc23_xreal_0)).
thf(fc24_finseq_1, axiom,  (! [A: $i] :  ( (v3_card_1 @  (k5_finseq_1 @ A) )  @ np__1) ) , file(finseq_1, fc24_finseq_1)).
thf(fc24_relat_1, axiom,  (! [A: $i] :  ( ( (v1_zfmisc_1 @ A)  &  (v1_relat_1 @ A) )  =>  (v1_zfmisc_1 @  (k9_xtuple_0 @ A) ) ) ) , file(relat_1, fc24_relat_1)).
thf(fc24_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 @  ( (k3_xcmplx_0 @ B)  @ A) ) ) ) ) , file(xreal_0, fc24_xreal_0)).
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(fc25_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 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc25_xreal_0)).
thf(fc26_relat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_relat_1 @ C)  &  ( (v5_relat_1 @ C)  @ B) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ C)  @ A) )  &  ( (v5_relat_1 @  ( (k5_relat_1 @ C)  @ A) )  @ B) ) ) ) , file(relat_1, fc26_relat_1)).
thf(fc26_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 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc26_xreal_0)).
thf(fc27_relat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_relat_1 @ C)  &  ( (v4_relat_1 @ C)  @ B) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ C)  @ A) )  &  ( ( (v4_relat_1 @  ( (k5_relat_1 @ C)  @ A) )  @ A)  &  ( (v4_relat_1 @  ( (k5_relat_1 @ C)  @ A) )  @ B) ) ) ) ) , file(relat_1, fc27_relat_1)).
thf(fc28_finseq_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ( (m1_subset_1 @ B)  @ k5_numbers)  &  ( ( (v1_relat_1 @ C)  &  ( (v1_funct_1 @ C)  &  ( ( (v3_card_1 @ C)  @ A)  &  (v1_finseq_1 @ C) ) ) )  &  ( (v1_relat_1 @ D)  &  ( (v1_funct_1 @ D)  &  ( ( (v3_card_1 @ D)  @ B)  &  (v1_finseq_1 @ D) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k7_finseq_1 @ C)  @ D) )  &  ( (v1_funct_1 @  ( (k7_finseq_1 @ C)  @ D) )  &  ( ( (v3_card_1 @  ( (k7_finseq_1 @ C)  @ D) )  @  ( (k1_nat_1 @ A)  @ B) )  &  (v1_finseq_1 @  ( (k7_finseq_1 @ C)  @ D) ) ) ) ) ) ) , file(finseq_1, fc28_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_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_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  (v7_ordinal1 @ B) )  =>  (v7_ordinal1 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) , file(nat_1, fc2_nat_1)).
thf(fc2_pboole, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ~ ( (v1_xboole_0 @  ( (k1_funct_1 @ B)  @ C) ) ) ) ) , file(pboole, fc2_pboole)).
thf(fc2_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  ~ ( (v1_xboole_0 @  (u1_struct_0 @ A) ) ) ) ) , file(struct_0, fc2_struct_0)).
thf(fc2_xboole_0, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k1_tarski @ A) ) ) ) , file(xboole_0, fc2_xboole_0)).
thf(fc30_relat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  &  (v1_relat_1 @ C) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ B)  @ C) )  &  ( (v4_relat_1 @  ( (k3_relat_1 @ B)  @ C) )  @ A) ) ) ) , file(relat_1, fc30_relat_1)).
thf(fc3_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_finset_1 @  (k1_finseq_1 @ A) ) ) ) , file(finseq_1, fc3_finseq_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_funct_7, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (v1_funcop_1 @  (k5_finseq_1 @ A) ) ) ) , file(funct_7, fc3_funct_7)).
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_partfun1, axiom,  (! [A: $i] :  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  ( (v3_relat_2 @  (k4_relat_1 @ A) )  &  ( (v4_relat_2 @  (k4_relat_1 @ A) )  &  (v8_relat_2 @  (k4_relat_1 @ A) ) ) ) ) ) , file(partfun1, fc3_partfun1)).
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(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_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_xtuple_0, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_xboole_0 @  (k9_xtuple_0 @ A) ) ) ) , file(xtuple_0, fc4_xtuple_0)).
thf(fc5_card_1, axiom,  (v2_card_1 @ k4_ordinal1) , file(card_1, fc5_card_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_ordinal1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v5_ordinal1 @ A) ) )  &  (v3_ordinal1 @ B) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  ( ( (v5_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  @  (k10_xtuple_0 @ A) )  &  (v5_ordinal1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) ) , file(ordinal1, fc5_ordinal1)).
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_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(fc5_xtuple_0, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_xboole_0 @  (k10_xtuple_0 @ A) ) ) ) , file(xtuple_0, fc5_xtuple_0)).
thf(fc6_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_finseq_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @  (k5_finseq_1 @ A) )  &  (v1_funct_1 @  (k5_finseq_1 @ A) ) ) ) , file(finseq_1, fc6_finseq_1)).
thf(fc6_funct_2, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_funct_1 @ B)  &  ( ( (v2_funct_2 @ B)  @ A)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) )  &  ( (v1_funct_1 @ C)  &  ( ( (v2_funct_2 @ C)  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ C)  @ B) )  &  ( (v2_funct_2 @  ( (k3_relat_1 @ C)  @ B) )  @ A) ) ) ) , file(funct_2, fc6_funct_2)).
thf(fc6_ordinal1, axiom,  ( ~ ( (v1_xboole_0 @ k4_ordinal1) )  &  (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1)).
thf(fc6_relat_1, axiom,  (! [A: $i, B: $i] :  (v1_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) , file(relat_1, fc6_relat_1)).
thf(fc6_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v7_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  ~ ( (v1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) ) , file(struct_0, fc6_struct_0)).
thf(fc6_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  (v1_xreal_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc6_xreal_0)).
thf(fc7_card_1, axiom,  ~ ( (v1_finset_1 @ k4_ordinal1) ) , file(card_1, fc7_card_1)).
thf(fc7_finseq_1, axiom,  (! [A: $i] :  (v1_finseq_1 @  (k5_finseq_1 @ A) ) ) , file(finseq_1, fc7_finseq_1)).
thf(fc7_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_funct_1 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v2_funct_1 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v2_funct_1 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(funct_1, fc7_funct_1)).
thf(fc7_funct_2, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ A)  @ A)  &  ( ( ( (v3_funct_2 @ B)  @ A)  @ A)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ A)  &  ( ( ( (v3_funct_2 @ C)  @ A)  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ B)  @ C) )  &  ( ( ( (v1_funct_2 @  ( (k3_relat_1 @ B)  @ C) )  @ A)  @ A)  &  ( ( (v3_funct_2 @  ( (k3_relat_1 @ B)  @ C) )  @ A)  @ A) ) ) ) ) , file(funct_2, fc7_funct_2)).
thf(fc7_funct_7, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_funcop_1 @ A)  &  (v1_finseq_1 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v1_funcop_1 @ B)  &  (v1_finseq_1 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k7_finseq_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k7_finseq_1 @ A)  @ B) )  &  ( (v1_funcop_1 @  ( (k7_finseq_1 @ A)  @ B) )  &  (v1_finseq_1 @  ( (k7_finseq_1 @ A)  @ B) ) ) ) ) ) ) , file(funct_7, fc7_funct_7)).
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(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_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(funct_1, fc8_funct_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(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_funct_7, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (v1_funct_7 @  (k5_finseq_1 @ A) ) ) ) , file(funct_7, fc9_funct_7)).
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(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(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_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_funct_7, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( (v1_funcop_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) ) ) ) ) , file(funct_7, rc1_funct_7)).
thf(rc1_msualg_4, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v2_funcop_1 @ B) ) ) ) ) ) ) , file(msualg_4, rc1_msualg_4)).
thf(rc1_msualg_6, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  =>  (? [B: $i] :  ( ( (l3_msualg_1 @ B)  @ A)  &  ( (v4_msualg_1 @ B)  @ A) ) ) ) ) , file(msualg_6, rc1_msualg_6)).
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_partfun1, 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) ) ) ) ) ) ) , file(partfun1, rc1_partfun1)).
thf(rc1_pboole, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) , file(pboole, rc1_pboole)).
thf(rc1_relat_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_relat_1 @ A) ) ) , file(relat_1, rc1_relat_1)).
thf(rc1_relset_1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (v1_xboole_0 @ C)  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v5_relat_1 @ C)  @ B) ) ) ) ) ) ) , file(relset_1, rc1_relset_1)).
thf(rc1_rewrite1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  (v10_rewrite1 @ A) ) ) ) , file(rewrite1, rc1_rewrite1)).
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_xtuple_0, axiom,  (? [A: $i] :  (v1_xtuple_0 @ A) ) , file(xtuple_0, rc1_xtuple_0)).
thf(rc1_xxreal_0, axiom,  (? [A: $i] :  (v1_xxreal_0 @ A) ) , file(xxreal_0, rc1_xxreal_0)).
thf(rc21_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_zfmisc_1 @ B) ) ) ) ) ) , file(struct_0, rc21_struct_0)).
thf(rc22_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v7_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ~ ( (v1_zfmisc_1 @ B) ) ) ) ) ) , file(struct_0, rc22_struct_0)).
thf(rc23_struct_0, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (? [B: $i] :  ( (l1_struct_0 @ B)  &  ( (v13_struct_0 @ B)  @ A) ) ) ) ) , file(struct_0, rc23_struct_0)).
thf(rc25_struct_0, axiom,  (? [A: $i] :  ( (l5_struct_0 @ A)  &  ~ ( (v15_struct_0 @ A) ) ) ) , file(struct_0, rc25_struct_0)).
thf(rc2_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_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_funct_2, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  ( ( ( (v1_funct_2 @ B)  @ A)  @ A)  &  ( ( (v3_funct_2 @ B)  @ A)  @ A) ) ) ) ) ) ) ) ) ) , file(funct_2, rc2_funct_2)).
thf(rc2_funct_7, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_finseq_1 @ A)  &  ( (v2_finseq_1 @ A)  &  (v1_funct_7 @ A) ) ) ) ) ) ) ) ) ) , file(funct_7, rc2_funct_7)).
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_partfun1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_relat_2 @ B)  &  ( (v3_relat_2 @ B)  &  ( (v4_relat_2 @ B)  &  ( (v8_relat_2 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) ) ) ) ) , file(partfun1, rc2_partfun1)).
thf(rc2_pboole, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v3_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) , file(pboole, rc2_pboole)).
thf(rc2_relat_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  (v2_relat_1 @ A) ) ) , file(relat_1, rc2_relat_1)).
thf(rc2_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_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_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_partfun1, 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_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( ( (v5_relat_1 @ C)  @ B)  &  ( (v1_funct_1 @ C)  &  ~ ( (v1_xboole_0 @ C) ) ) ) ) ) ) ) ) ) , file(partfun1, rc3_partfun1)).
thf(rc3_pboole, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) , file(pboole, rc3_pboole)).
thf(rc3_relat_1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v5_relat_1 @ C)  @ B) ) ) ) ) , file(relat_1, rc3_relat_1)).
thf(rc3_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_pboole, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v1_funcop_1 @ B) ) ) ) ) ) ) , file(pboole, rc4_pboole)).
thf(rc4_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(struct_0, rc4_struct_0)).
thf(rc4_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_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(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_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(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_funct_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v4_funct_1 @ A) ) ) , file(funct_1, rc7_funct_1)).
thf(rc7_pboole, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [C: $i] :  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ B)  &  ( ( (v5_relat_1 @ C)  @ A)  &  ( (v1_funct_1 @ C)  &  ( (v1_partfun1 @ C)  @ B) ) ) ) ) ) ) ) , file(pboole, rc7_pboole)).
thf(rc8_finseq_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_finseq_1 @ A) ) ) , file(finseq_1, rc8_finseq_1)).
thf(rc9_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v1_finseq_1 @ B)  &  (v2_finseq_1 @ B) ) ) ) ) ) ) ) ) , file(finseq_1, rc9_finseq_1)).
thf(rc9_funct_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) ) ) ) ) , file(funct_1, rc9_funct_1)).
thf(rd1_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(rd4_relat_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @ A)  =>  ( (= @  ( (k5_relat_1 @ A)  @  (k9_xtuple_0 @ A) ) )  @ A) ) ) , file(relat_1, rd4_relat_1)).
thf(rd5_relat_1, axiom,  (! [A: $i, B: $i] :  ( (v1_relat_1 @ A)  =>  ( (= @  ( (k5_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  @ B) )  @  ( (k5_relat_1 @ A)  @ B) ) ) ) , file(relat_1, rd5_relat_1)).
thf(rd8_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( (= @  ( (k5_relat_1 @ B)  @ A) )  @ B) ) ) , file(relat_1, rd8_relat_1)).
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_partfun1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( ( (v1_funct_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  &  ( (v1_funct_1 @ F)  &  ( (m1_subset_1 @ F)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ C)  @ D) ) ) ) )  =>  ( (= @  ( ( ( ( ( (k1_partfun1 @ A)  @ B)  @ C)  @ D)  @ E)  @ F) )  @  ( (k3_relat_1 @ E)  @ F) ) ) ) , file(partfun1, k1_partfun1)).
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_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_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (m1_subset_1 @ F)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ C)  @ D) ) ) )  =>  ( (= @  ( ( ( ( ( (k4_relset_1 @ A)  @ B)  @ C)  @ D)  @ E)  @ F) )  @  ( (k3_relat_1 @ E)  @ F) ) ) ) , file(relset_1, k4_relset_1)).
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_k9_finseq_1, axiom,  (! [A: $i] :  ( (= @  (k9_finseq_1 @ A) )  @  (k5_finseq_1 @ A) ) ) , file(finseq_1, k9_finseq_1)).
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(redefinition_r1_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ~ ( (v1_xboole_0 @ D) )  &  ( ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ B)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ F)  &  ( ( ( (v1_funct_2 @ F)  @ C)  @ D)  &  ( (m1_subset_1 @ F)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ C)  @ D) ) ) ) ) ) ) )  =>  ( ( ( ( ( ( (r1_funct_2 @ A)  @ B)  @ C)  @ D)  @ E)  @ F)  <=>  ( (= @ E)  @ F) ) ) ) , file(funct_2, r1_funct_2)).
thf(redefinition_r2_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)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( ( ( ( (r2_funct_2 @ A)  @ B)  @ C)  @ D)  <=>  ( (= @ C)  @ D) ) ) ) , file(funct_2, r2_funct_2)).
thf(redefinition_r2_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  =>  ( ( ( ( (r2_relset_1 @ A)  @ B)  @ C)  @ D)  <=>  ( (= @ C)  @ D) ) ) ) , file(relset_1, r2_relset_1)).
thf(reflexivity_r1_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ~ ( (v1_xboole_0 @ D) )  &  ( ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ B)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ F)  &  ( ( ( (v1_funct_2 @ F)  @ C)  @ D)  &  ( (m1_subset_1 @ F)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ C)  @ D) ) ) ) ) ) ) )  =>  ( ( ( ( ( (r1_funct_2 @ A)  @ B)  @ C)  @ D)  @ E)  @ E) ) ) , file(funct_2, r1_funct_2)).
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(reflexivity_r2_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)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( ( ( (r2_funct_2 @ A)  @ B)  @ C)  @ C) ) ) , file(funct_2, r2_funct_2)).
thf(reflexivity_r2_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  =>  ( ( ( (r2_relset_1 @ A)  @ B)  @ C)  @ C) ) ) , file(relset_1, r2_relset_1)).
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_r2, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r2)).
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__r0_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_rm2)).
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_r2, axiom,  ( (r1_xxreal_0 @ np__1)  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r2)).
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__r1_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r0, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @ np__0) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r1, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r2, axiom,  ( (r1_xxreal_0 @ np__2)  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r2_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r2_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_rm2)).
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_r2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r2)).
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(rqLessOrEqual__r1_xxreal_0__rm1_rm2, axiom,  ~ ( ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r0, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r0)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r1)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r2)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_rm1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_rm2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_rm2)).
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_r2_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @ np__2) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r2_r2)).
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__r0_rm2_rm2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2)).
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_r1_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @ np__1) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r1_r2)).
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__r1_rm2_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r2_r0_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @ np__0) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_r0_r2)).
thf(rqRealAdd__k2_xcmplx_0__r2_rm1_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm1_r1)).
thf(rqRealAdd__k2_xcmplx_0__r2_rm2_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm2_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(rqRealAdd__k2_xcmplx_0__rm1_r2_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r2_r1)).
thf(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2)).
thf(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1)).
thf(rqRealAdd__k2_xcmplx_0__rm2_r2_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__2) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r2_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_r2_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r2_rm2)).
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__r0_rm2_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm2_r2)).
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__r1_r2_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r2_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r1_rm1_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rm1_r2)).
thf(rqRealDiff__k6_xcmplx_0__r2_r0_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @ np__0) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r0_r2)).
thf(rqRealDiff__k6_xcmplx_0__r2_r1_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @ np__1) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r1_r1)).
thf(rqRealDiff__k6_xcmplx_0__r2_r2_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @ np__2) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r2_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_r1_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2)).
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(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1)).
thf(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__0) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2)).
thf(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_r0_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__0)  @ np__0) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_r1_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__0)  @ np__1) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r1_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_r2_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__0)  @ np__2) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r2_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_rm2_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rm2_r0)).
thf(rqRealMult__k3_xcmplx_0__r1_r0_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__1)  @ np__0) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__r1_r1_r1, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__1)  @ np__1) )  @ np__1) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r1_r1)).
thf(rqRealMult__k3_xcmplx_0__r1_r2_r2, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__1)  @ np__2) )  @ np__2) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r2_r2)).
thf(rqRealMult__k3_xcmplx_0__r1_rm2_rm2, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rm2_rm2)).
thf(rqRealMult__k3_xcmplx_0__r2_r0_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__2)  @ np__0) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r2_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__r2_r1_r2, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__2)  @ np__1) )  @ np__2) , file(arithm, rqRealMult__k3_xcmplx_0__r2_r1_r2)).
thf(rqRealMult__k3_xcmplx_0__rm2_r0_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__0) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__rm2_r1_rm2, axiom,  ( (= @  ( (k3_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_r1_rm2)).
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__r2_rm2, axiom,  ( (= @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r2_rm2)).
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(rqRealNeg__k4_xcmplx_0__rm2_r2, axiom,  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__2) ) )  @ np__2) , file(arithm, rqRealNeg__k4_xcmplx_0__rm2_r2)).
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(spc2_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k3_xcmplx_0 @ A)  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ A) ) ) ) , file(arithm, spc2_arithm)).
thf(spc2_boole, axiom,  ~ ( (v1_xboole_0 @ np__2) ) , file(boole, spc2_boole)).
thf(spc2_numerals, axiom,  ( ( (v2_xxreal_0 @ np__2)  &  ( ( (m2_subset_1 @ np__2)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__2)  @ k5_numbers)  &  ( (m1_subset_1 @ np__2)  @ k1_numbers) ) ) , file(numerals, spc2_numerals)).
thf(spc5_arithm, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_xcmplx_0 @ A)  &  ( (v1_xcmplx_0 @ B)  &  (v1_xcmplx_0 @ C) ) )  =>  ( (= @  ( (k3_xcmplx_0 @  ( (k2_xcmplx_0 @ A)  @ B) )  @ C) )  @  ( (k2_xcmplx_0 @  ( (k3_xcmplx_0 @ A)  @ C) )  @  ( (k3_xcmplx_0 @ B)  @ C) ) ) ) ) , file(arithm, spc5_arithm)).
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(spc7_arithm, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_xcmplx_0 @ A)  &  ( (v1_xcmplx_0 @ B)  &  (v1_xcmplx_0 @ C) ) )  =>  ( (= @  ( (k3_xcmplx_0 @  ( (k3_xcmplx_0 @ A)  @ B) )  @ C) )  @  ( (k3_xcmplx_0 @ A)  @  ( (k3_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(symmetry_r1_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ~ ( (v1_xboole_0 @ D) )  &  ( ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ B)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ F)  &  ( ( ( (v1_funct_2 @ F)  @ C)  @ D)  &  ( (m1_subset_1 @ F)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ C)  @ D) ) ) ) ) ) ) )  =>  ( ( ( ( ( ( (r1_funct_2 @ A)  @ B)  @ C)  @ D)  @ E)  @ F)  =>  ( ( ( ( ( (r1_funct_2 @ A)  @ B)  @ C)  @ D)  @ F)  @ E) ) ) ) , file(funct_2, r1_funct_2)).
thf(symmetry_r2_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)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( ( ( ( (r2_funct_2 @ A)  @ B)  @ C)  @ D)  =>  ( ( ( (r2_funct_2 @ A)  @ B)  @ D)  @ C) ) ) ) , file(funct_2, r2_funct_2)).
thf(symmetry_r2_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  =>  ( ( ( ( (r2_relset_1 @ A)  @ B)  @ C)  @ D)  =>  ( ( ( (r2_relset_1 @ A)  @ B)  @ D)  @ C) ) ) ) , file(relset_1, r2_relset_1)).
thf(t12_rewrite1, axiom,  (! [A: $i] :  ( (v1_relat_1 @ A)  =>  (! [B: $i] :  ( ( (r1_rewrite1 @ A)  @ B)  @ B) ) ) ) , file(rewrite1, t12_rewrite1)).
thf(t13_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) )  =>  ( ( ( (= @  (k4_finseq_1 @ A) )  @  (k4_finseq_1 @ B) )  &  (! [C: $i] :  ( (v7_ordinal1 @ C)  =>  ( ( (r2_hidden @ C)  @  (k4_finseq_1 @ A) )  =>  ( (= @  ( (k1_funct_1 @ A)  @ C) )  @  ( (k1_funct_1 @ B)  @ C) ) ) ) ) )  =>  ( (= @ A)  @ B) ) ) ) ) ) , file(finseq_1, t13_finseq_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(t15_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ B)  @  (k2_finseq_1 @ A) ) )  &  ( (v1_funct_1 @  ( (k5_relat_1 @ B)  @  (k2_finseq_1 @ A) ) )  &  (v1_finseq_1 @  ( (k5_relat_1 @ B)  @  (k2_finseq_1 @ A) ) ) ) ) ) ) ) ) , file(finseq_1, t15_finseq_1)).
thf(t16_msualg_6, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  =>  (! [B: $i] :  ( ( ( (v4_msualg_1 @ B)  @ A)  &  ( (l3_msualg_1 @ B)  @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  =>  ( ( ( ( (m2_msualg_6 @  (k6_partfun1 @  ( (k1_funct_1 @  ( (u3_msualg_1 @ A)  @ B) )  @ C) ) )  @ A)  @ B)  @ C)  @ C) ) ) ) ) ) ) , file(msualg_6, t16_msualg_6)).
thf(t16_rewrite1, axiom,  (! [A: $i] :  ( (v1_relat_1 @ A)  =>  (! [B: $i] :  (! [C: $i] :  (! [D: $i] :  ( ( ( ( (r1_rewrite1 @ A)  @ B)  @ C)  &  ( ( (r1_rewrite1 @ A)  @ C)  @ D) )  =>  ( ( (r1_rewrite1 @ A)  @ B)  @ D) ) ) ) ) ) ) , file(rewrite1, t16_rewrite1)).
thf(t17_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( (v1_funct_1 @ C)  &  (v1_finseq_1 @ C) ) )  =>  ( ( ( (r1_xxreal_0 @ A)  @  (k3_finseq_1 @ B) )  &  ( (= @ C)  @  ( (k5_relat_1 @ B)  @  (k2_finseq_1 @ A) ) ) )  =>  ( ( (= @  (k3_finseq_1 @ C) )  @ A)  &  ( (= @  (k4_finseq_1 @ C) )  @  (k2_finseq_1 @ A) ) ) ) ) ) ) ) ) ) , file(finseq_1, t17_finseq_1)).
thf(t17_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( ( ( (r2_relset_1 @ A)  @ B)  @  ( ( ( ( ( (k4_relset_1 @ A)  @ A)  @ A)  @ B)  @  (k6_partfun1 @ A) )  @ C) )  @ C)  &  ( ( ( (r2_relset_1 @ A)  @ B)  @  ( ( ( ( ( (k4_relset_1 @ A)  @ B)  @ B)  @ B)  @ C)  @  (k6_partfun1 @ B) ) )  @ C) ) ) ) ) ) , file(funct_2, t17_funct_2)).
thf(t17_msualg_6, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  =>  (! [B: $i] :  ( ( ( (v4_msualg_1 @ B)  @ A)  &  ( (l3_msualg_1 @ B)  @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @  (u1_struct_0 @ A) )  =>  (! [E: $i] :  ( ( (v1_relat_1 @ E)  &  (v1_funct_1 @ E) )  =>  ( ( ( ( ( (r1_msualg_6 @ A)  @ C)  @ D)  @ B)  @ E)  =>  ( ( ( (r1_rewrite1 @  (k3_msualg_6 @ A) )  @ C)  @ D)  &  ( ( ( ( (m2_msualg_6 @ E)  @ A)  @ B)  @ C)  @ D) ) ) ) ) ) ) ) ) ) ) ) ) , file(msualg_6, t17_msualg_6)).
thf(t19_msualg_6, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v11_struct_0 @ A) )  &  (l1_msualg_1 @ A) ) )  =>  (! [B: $i] :  ( ( ( (v4_msualg_1 @ B)  @ A)  &  ( (l3_msualg_1 @ B)  @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @  (u1_struct_0 @ A) )  =>  (! [E: $i] :  ( ( (m1_subset_1 @ E)  @  (u1_struct_0 @ A) )  =>  ( ( ( (r1_rewrite1 @  (k3_msualg_6 @ A) )  @ C)  @ D)  =>  (! [F: $i] :  ( ( ( ( ( (m2_msualg_6 @ F)  @ A)  @ B)  @ C)  @ D)  =>  (! [G: $i] :  ( ( (v1_relat_1 @ G)  &  (v1_funct_1 @ G) )  =>  ( ( ( ( ( (r1_msualg_6 @ A)  @ D)  @ E)  @ B)  @ G)  =>  ( ( ( ( (m2_msualg_6 @  ( (k3_relat_1 @ F)  @ G) )  @ A)  @ B)  @ C)  @ E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(msualg_6, t19_msualg_6)).
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(t22_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) )  =>  ( (= @  (k3_finseq_1 @  ( (k7_finseq_1 @ A)  @ B) ) )  @  ( (k2_nat_1 @  (k3_finseq_1 @ A) )  @  (k3_finseq_1 @ B) ) ) ) ) ) ) , file(finseq_1, t22_finseq_1)).
thf(t22_funct_7, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) )  =>  ( ( (= @  (k3_finseq_1 @ A) )  @  ( (k2_nat_1 @  (k3_finseq_1 @ B) )  @ np__1) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ k5_numbers)  =>  ( ( (r2_hidden @ C)  @  (k4_finseq_1 @ B) )  <=>  ( ( (r2_hidden @ C)  @  (k4_finseq_1 @ A) )  &  ( (r2_hidden @  ( (k2_nat_1 @ C)  @ np__1) )  @  (k4_finseq_1 @ A) ) ) ) ) ) ) ) ) ) ) , file(funct_7, t22_funct_7)).
thf(t25_finseq_3, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ( ( (r2_hidden @ B)  @  ( (k1_relset_1 @ k5_numbers)  @ A) )  <=>  ( ( (r1_xxreal_0 @ np__1)  @ B)  &  ( (r1_xxreal_0 @ B)  @  (k3_finseq_1 @ A) ) ) ) ) ) ) ) , file(finseq_3, t25_finseq_3)).
thf(t2_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k3_xcmplx_0 @ A)  @ k6_numbers) )  @ k6_numbers) ) ) , file(arithm, t2_arithm)).
thf(t2_finseq_1, axiom,  ( ( (= @  (k2_finseq_1 @ np__1) )  @  (k1_tarski @ np__1) )  &  ( (= @  (k2_finseq_1 @ np__2) )  @  ( (k2_tarski @ np__1)  @ np__2) ) ) , file(finseq_1, t2_finseq_1)).
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(t39_funct_7, axiom,  (! [A: $i] :  ( (= @  ( (k4_funct_7 @ A)  @ k1_xboole_0) )  @  (k6_partfun1 @ A) ) ) , file(funct_7, t39_funct_7)).
thf(t3_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k3_xcmplx_0 @ np__1)  @ A) )  @ A) ) ) , file(arithm, t3_arithm)).
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_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) )  =>  ( ( (= @ B)  @  (k9_finseq_1 @ A) )  <=>  ( ( (= @  (k3_finseq_1 @ B) )  @ np__1)  &  ( (= @  ( (k1_funct_1 @ B)  @ np__1) )  @ A) ) ) ) ) ) , file(finseq_1, t40_finseq_1)).
thf(t41_funct_7, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v1_funcop_1 @ B)  &  (v1_finseq_1 @ B) ) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  (v1_funct_1 @ C) )  =>  ( (= @  ( (k4_funct_7 @ A)  @  ( (k7_finseq_1 @ B)  @  (k9_finseq_1 @ C) ) ) )  @  ( (k3_relat_1 @  ( (k4_funct_7 @ A)  @ B) )  @ C) ) ) ) ) ) ) , file(funct_7, t41_funct_7)).
thf(t42_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) )  =>  ( (= @  ( (k1_funct_1 @  ( (k7_finseq_1 @ B)  @  (k9_finseq_1 @ A) ) )  @  ( (k2_nat_1 @  (k3_finseq_1 @ B) )  @ np__1) ) )  @ A) ) ) ) , file(finseq_1, t42_finseq_1)).
thf(t46_funct_7, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) )  =>  ( ( (r1_tarski @  (k9_xtuple_0 @ B) )  @ A)  =>  ( (= @  ( (k4_funct_7 @ A)  @  (k9_finseq_1 @ B) ) )  @ B) ) ) ) ) , file(funct_7, t46_funct_7)).
thf(t47_funct_1, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  (v1_funct_1 @ C) )  =>  ( ( (r2_hidden @ A)  @  (k9_xtuple_0 @  ( (k5_relat_1 @ C)  @ B) ) )  =>  ( (= @  ( (k1_funct_1 @  ( (k5_relat_1 @ C)  @ B) )  @ A) )  @  ( (k1_funct_1 @ C)  @ A) ) ) ) ) ) ) , file(funct_1, t47_funct_1)).
thf(t49_funct_1, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  (v1_funct_1 @ C) )  =>  ( ( (r2_hidden @ A)  @ B)  =>  ( (= @  ( (k1_funct_1 @  ( (k5_relat_1 @ C)  @ B) )  @ A) )  @  ( (k1_funct_1 @ C)  @ A) ) ) ) ) ) ) , file(funct_1, t49_funct_1)).
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(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(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(s1_nat_1, axiom,  (! [A: $i > $o] :  ( ( (A @ k6_numbers)  &  (! [B: $i] :  ( ( ( (m2_subset_1 @ B)  @ k1_numbers)  @ k5_numbers)  =>  ( (A @ B)  =>  (A @  ( (k2_nat_1 @ B)  @ np__1) ) ) ) ) )  =>  (! [B: $i] :  ( ( ( (m2_subset_1 @ B)  @ k1_numbers)  @ k5_numbers)  =>  (A @ B) ) ) ) ) , file(nat_1, s1_nat_1)).
thf(s1_msualg_6, conjecture,  ( ( (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (u1_struct_0 @ f1_s1_msualg_6) )  =>  ( ( (p1_s1_msualg_6 @  (k6_partfun1 @  ( (k1_funct_1 @  ( (u3_msualg_1 @ f1_s1_msualg_6)  @ f2_s1_msualg_6) )  @ A) ) )  @ A)  @ A) ) )  &  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (u1_struct_0 @ f1_s1_msualg_6) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ f1_s1_msualg_6) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ f1_s1_msualg_6) )  =>  ( ( ( (r1_rewrite1 @  (k3_msualg_6 @ f1_s1_msualg_6) )  @ A)  @ B)  =>  (! [D: $i] :  ( ( ( ( ( (m2_msualg_6 @ D)  @ f1_s1_msualg_6)  @ f2_s1_msualg_6)  @ A)  @ B)  =>  ( ( ( (p1_s1_msualg_6 @ D)  @ A)  @ B)  =>  (! [E: $i] :  ( ( (v1_relat_1 @ E)  &  (v1_funct_1 @ E) )  =>  ( ( ( ( ( (r1_msualg_6 @ f1_s1_msualg_6)  @ B)  @ C)  @ f2_s1_msualg_6)  @ E)  =>  ( ( (p1_s1_msualg_6 @  ( (k3_relat_1 @ D)  @ E) )  @ A)  @ C) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (u1_struct_0 @ f1_s1_msualg_6) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ f1_s1_msualg_6) )  =>  ( ( ( (r1_rewrite1 @  (k3_msualg_6 @ f1_s1_msualg_6) )  @ A)  @ B)  =>  (! [C: $i] :  ( ( ( ( ( (m2_msualg_6 @ C)  @ f1_s1_msualg_6)  @ f2_s1_msualg_6)  @ A)  @ B)  =>  ( ( (p1_s1_msualg_6 @ C)  @ A)  @ B) ) ) ) ) ) ) ) ) , file(msualg_6, s1_msualg_6)).
