% Mizar problem: e4_18_9_1,nfcont_2,926,45 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_18_type,type,( c1_18__nfcont_2: $i )).
thf(c1_18_9_type,type,( c1_18_9__nfcont_2: $i )).
thf(c4_18_type,type,( c4_18__nfcont_2: $i )).
thf(c7_18_type,type,( c7_18__nfcont_2: $i )).
thf(k1_normsp_0_type,type,( k1_normsp_0: $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_nat_1_type,type,( k2_nat_1: $i > $i > $i )).
thf(k2_xcmplx_0_type,type,( k2_xcmplx_0: $i > $i > $i )).
thf(k3_numbers_type,type,( k3_numbers: $i )).
thf(k3_power_type,type,( k3_power: $i > $i > $i )).
thf(k3_xcmplx_0_type,type,( k3_xcmplx_0: $i > $i > $i )).
thf(k4_numbers_type,type,( k4_numbers: $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k4_power_type,type,( k4_power: $i > $i > $i )).
thf(k5_algstr_0_type,type,( k5_algstr_0: $i > $i > $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_numbers_type,type,( k6_numbers: $i )).
thf(k8_real_1_type,type,( k8_real_1: $i > $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(l1_algstr_0_type,type,( l1_algstr_0: $i > $o )).
thf(l1_normsp_0_type,type,( l1_normsp_0: $i > $o )).
thf(l1_normsp_1_type,type,( l1_normsp_1: $i > $o )).
thf(l1_rlvect_1_type,type,( l1_rlvect_1: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l2_algstr_0_type,type,( l2_algstr_0: $i > $o )).
thf(l2_normsp_0_type,type,( l2_normsp_0: $i > $o )).
thf(l2_struct_0_type,type,( l2_struct_0: $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_subset_1_type,type,( m2_subset_1: $i > $i > $i > $o )).
thf(r1_xxreal_0_type,type,( r1_xxreal_0: $i > $i > $o )).
thf(v13_algstr_0_type,type,( v13_algstr_0: $i > $o )).
thf(v13_struct_0_type,type,( v13_struct_0: $i > $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_int_1_type,type,( v1_int_1: $i > $o )).
thf(v1_membered_type,type,( v1_membered: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_rat_1_type,type,( v1_rat_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_valued_0_type,type,( v1_valued_0: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_xcmplx_0_type,type,( v1_xcmplx_0: $i > $o )).
thf(v1_xreal_0_type,type,( v1_xreal_0: $i > $o )).
thf(v1_xxreal_0_type,type,( v1_xxreal_0: $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_funct_1_type,type,( v2_funct_1: $i > $o )).
thf(v2_membered_type,type,( v2_membered: $i > $o )).
thf(v2_normsp_1_type,type,( v2_normsp_1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_rlvect_1_type,type,( v2_rlvect_1: $i > $o )).
thf(v2_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v2_valued_0_type,type,( v2_valued_0: $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_1: $i > $o )).
thf(v3_lopban_1_type,type,( v3_lopban_1: $i > $o )).
thf(v3_membered_type,type,( v3_membered: $i > $o )).
thf(v3_normsp_0_type,type,( v3_normsp_0: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_rlvect_1_type,type,( v3_rlvect_1: $i > $o )).
thf(v3_valued_0_type,type,( v3_valued_0: $i > $o )).
thf(v3_xxreal_0_type,type,( v3_xxreal_0: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_membered_type,type,( v4_membered: $i > $o )).
thf(v4_normsp_0_type,type,( v4_normsp_0: $i > $o )).
thf(v4_rlvect_1_type,type,( v4_rlvect_1: $i > $o )).
thf(v4_valued_0_type,type,( v4_valued_0: $i > $o )).
thf(v5_membered_type,type,( v5_membered: $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v5_rlvect_1_type,type,( v5_rlvect_1: $i > $o )).
thf(v5_valued_0_type,type,( v5_valued_0: $i > $o )).
thf(v6_membered_type,type,( v6_membered: $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v6_rlvect_1_type,type,( v6_rlvect_1: $i > $o )).
thf(v6_valued_0_type,type,( v6_valued_0: $i > $o )).
thf(v7_membered_type,type,( v7_membered: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(v7_rlvect_1_type,type,( v7_rlvect_1: $i > $o )).
thf(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v7_valued_0_type,type,( v7_valued_0: $i > $o )).
thf(v8_rlvect_1_type,type,( v8_rlvect_1: $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_0: $i > $o )).
thf(v8_valued_0_type,type,( v8_valued_0: $i > $o )).
thf(cc23_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v5_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v7_valued_0 @ A ) ) ) ),file(valued_0,cc23_valued_0)).
thf(cc24_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v6_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v8_valued_0 @ A ) ) ) ),file(valued_0,cc24_valued_0)).
thf(cc10_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_valued_0 @ B ) ) ) ),file(valued_0,cc10_valued_0)).
thf(cc11_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v2_valued_0 @ B ) ) ) ),file(valued_0,cc11_valued_0)).
thf(cc22_valued_0,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v5_valued_0 @ A ) & ( v6_valued_0 @ A ) ) ) ),file(valued_0,cc22_valued_0)).
thf(dt_k3_numbers,axiom,( $true ),file(numbers,k3_numbers)).
thf(dt_k4_numbers,axiom,( $true ),file(numbers,k4_numbers)).
thf(cc10_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k4_numbers ) ) => ( v5_membered @ A ) ) ),file(membered,cc10_membered)).
thf(cc12_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v3_valued_0 @ B ) ) ) ),file(valued_0,cc12_valued_0)).
thf(cc13_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_relat_1 @ B @ k3_numbers ) ) ) ),file(valued_0,cc13_valued_0)).
thf(cc14_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_relat_1 @ B @ k4_numbers ) ) ) ),file(valued_0,cc14_valued_0)).
thf(cc2_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) ) ),file(valued_0,cc2_valued_0)).
thf(cc30_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k1_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc30_valued_0)).
thf(cc31_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k5_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) ) ),file(valued_0,cc31_valued_0)).
thf(cc3_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc3_valued_0)).
thf(cc4_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc4_valued_0)).
thf(cc5_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_valued_0 @ A ) ) ) ),file(valued_0,cc5_valued_0)).
thf(cc6_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_valued_0 @ A ) ) ) ),file(valued_0,cc6_valued_0)).
thf(cc9_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k3_numbers ) ) => ( v4_membered @ A ) ) ),file(membered,cc9_membered)).
thf(fc3_numbers,axiom,( ~ ( v1_xboole_0 @ k3_numbers ) ),file(numbers,fc3_numbers)).
thf(fc4_membered,axiom,( v4_membered @ k3_numbers ),file(membered,fc4_membered)).
thf(fc4_numbers,axiom,( ~ ( v1_xboole_0 @ k4_numbers ) ),file(numbers,fc4_numbers)).
thf(fc57_membered,axiom,( v7_membered @ k3_numbers ),file(membered,fc57_membered)).
thf(fc58_membered,axiom,( v7_membered @ k4_numbers ),file(membered,fc58_membered)).
thf(fc5_membered,axiom,( v5_membered @ k4_numbers ),file(membered,fc5_membered)).
thf(fc6_numbers,axiom,( ~ ( v1_finset_1 @ k4_numbers ) ),file(numbers,fc6_numbers)).
thf(fc7_numbers,axiom,( ~ ( v1_finset_1 @ k3_numbers ) ),file(numbers,fc7_numbers)).
thf(rc2_valued_0,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) & ( v5_relat_1 @ A @ k4_numbers ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) & ( v4_valued_0 @ A ) ) ),file(valued_0,rc2_valued_0)).
thf(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(cc15_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_valued_0 @ B ) ) ) ),file(valued_0,cc15_valued_0)).
thf(cc1_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) ) ),file(valued_0,cc1_valued_0)).
thf(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(cc7_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) ) ),file(valued_0,cc7_valued_0)).
thf(cc8_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc8_valued_0)).
thf(rc1_valued_0,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v4_valued_0 @ A ) ) ),file(valued_0,rc1_valued_0)).
thf(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(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(cc15_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_rat_1 @ B ) ) ) ),file(membered,cc15_membered)).
thf(cc22_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_membered @ B ) ) ) ),file(membered,cc22_membered)).
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_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
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_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ( v3_membered @ A ) ) ),file(membered,cc3_membered)).
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(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(cc9_valued_0,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) ) ),file(valued_0,cc9_valued_0)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
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(rc2_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) ) ),file(ordinal1,rc2_ordinal1)).
thf(dt_l1_algstr_0,axiom,( ! [A: $i] : ( ( l1_algstr_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(algstr_0,l1_algstr_0)).
thf(dt_l2_struct_0,axiom,( ! [A: $i] : ( ( l2_struct_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(struct_0,l2_struct_0)).
thf(cc10_ordinal1,axiom,( ! [A: $i] : ( ( v6_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v6_ordinal1 @ B ) ) ) ),file(ordinal1,cc10_ordinal1)).
thf(cc10_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) => ( v13_struct_0 @ A @ np__1 ) ) ) ),file(struct_0,cc10_struct_0)).
thf(cc11_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_membered,axiom,( ! [A: $i] : ( ( v1_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xcmplx_0 @ B ) ) ) ),file(membered,cc12_membered)).
thf(cc13_membered,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xxreal_0 @ B ) ) ) ),file(membered,cc13_membered)).
thf(cc16_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_int_1 @ B ) ) ) ),file(membered,cc16_membered)).
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(cc19_membered,axiom,( ! [A: $i] : ( ( v1_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_membered @ B ) ) ) ),file(membered,cc19_membered)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc20_membered,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v2_membered @ B ) ) ) ),file(membered,cc20_membered)).
thf(cc23_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_membered @ B ) ) ) ),file(membered,cc23_membered)).
thf(cc2_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ( v4_membered @ A ) ) ),file(membered,cc2_membered)).
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(cc5_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal1,cc5_ordinal1)).
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(cc6_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v7_struct_0 @ A ) => ( v8_struct_0 @ A ) ) ) ),file(struct_0,cc6_struct_0)).
thf(cc7_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ~ ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc7_struct_0)).
thf(cc8_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(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_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(fc6_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc6_struct_0)).
thf(fc7_struct_0,axiom,( ! [A: $i] : ( ( ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc7_struct_0)).
thf(fc8_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_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(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc20_struct_0,axiom,( ? [A: $i] : ( ( l2_struct_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) ),file(struct_0,rc20_struct_0)).
thf(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(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(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(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
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(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_xcmplx_0,axiom,( $true ),file(xcmplx_0,k2_xcmplx_0)).
thf(dt_k3_power,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xreal_0 @ A ) & ( v1_xreal_0 @ B ) ) => ( v1_xreal_0 @ ( k3_power @ A @ B ) ) ) ),file(power,k3_power)).
thf(dt_k3_xcmplx_0,axiom,( $true ),file(xcmplx_0,k3_xcmplx_0)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(dt_l1_normsp_0,axiom,( ! [A: $i] : ( ( l1_normsp_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(normsp_0,l1_normsp_0)).
thf(dt_l1_rlvect_1,axiom,( ! [A: $i] : ( ( l1_rlvect_1 @ A ) => ( l2_algstr_0 @ A ) ) ),file(rlvect_1,l1_rlvect_1)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_l2_algstr_0,axiom,( ! [A: $i] : ( ( l2_algstr_0 @ A ) => ( ( l2_struct_0 @ A ) & ( l1_algstr_0 @ A ) ) ) ),file(algstr_0,l2_algstr_0)).
thf(dt_l2_normsp_0,axiom,( ! [A: $i] : ( ( l2_normsp_0 @ A ) => ( ( l1_normsp_0 @ A ) & ( l2_struct_0 @ A ) ) ) ),file(normsp_0,l2_normsp_0)).
thf(cc11_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k5_numbers ) ) => ( v6_membered @ A ) ) ),file(membered,cc11_membered)).
thf(cc14_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xreal_0 @ B ) ) ) ),file(membered,cc14_membered)).
thf(cc17_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v7_ordinal1 @ B ) ) ) ),file(membered,cc17_membered)).
thf(cc18_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_membered @ A ) ) ),file(membered,cc18_membered)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_1)).
thf(cc1_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ( v5_membered @ A ) ) ),file(membered,cc1_membered)).
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(cc21_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v3_membered @ B ) ) ) ),file(membered,cc21_membered)).
thf(cc24_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v6_membered @ B ) ) ) ),file(membered,cc24_membered)).
thf(cc26_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_membered @ A ) ) ),file(membered,cc26_membered)).
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_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
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_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v2_membered @ A ) ) ),file(membered,cc4_membered)).
thf(cc4_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
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_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v1_membered @ A ) ) ),file(membered,cc5_membered)).
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_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
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_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v4_funct_1 @ A ) ) ),file(funct_1,cc7_funct_1)).
thf(cc7_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
thf(cc7_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_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) ) => ( v3_membered @ A ) ) ),file(membered,cc8_membered)).
thf(cc8_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
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_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
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_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_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_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_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(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(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_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_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_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(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(fc59_membered,axiom,( v7_membered @ k4_ordinal1 ),file(membered,fc59_membered)).
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(fc6_membered,axiom,( v6_membered @ k4_ordinal1 ),file(membered,fc6_membered)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
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(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(rc1_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc1_membered)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc1_xreal_0,axiom,( ? [A: $i] : ( v1_xreal_0 @ A ) ),file(xreal_0,rc1_xreal_0)).
thf(rc1_xxreal_0,axiom,( ? [A: $i] : ( v1_xxreal_0 @ A ) ),file(xxreal_0,rc1_xxreal_0)).
thf(rc2_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc2_membered)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc2_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) ) ),file(xxreal_0,rc2_xxreal_0)).
thf(rc3_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) & ( v7_membered @ A ) ) ),file(membered,rc3_membered)).
thf(rc3_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) ),file(xxreal_0,rc3_xxreal_0)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(rc4_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(struct_0,rc4_struct_0)).
thf(rc4_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,rc4_xxreal_0)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
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_k8_real_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k1_numbers ) & ( v1_xreal_0 @ B ) ) => ( = @ ( k8_real_1 @ A @ B ) @ ( k8_real_1 @ B @ A ) ) ) ),file(real_1,k8_real_1)).
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(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(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_k4_power,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k1_numbers ) & ( m1_subset_1 @ B @ k1_numbers ) ) => ( = @ ( k4_power @ A @ B ) @ ( k3_power @ A @ B ) ) ) ),file(power,k4_power)).
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_k8_real_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k1_numbers ) & ( v1_xreal_0 @ B ) ) => ( = @ ( k8_real_1 @ A @ B ) @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(real_1,k8_real_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(dt_k1_normsp_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_normsp_0 @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) ) => ( m1_subset_1 @ ( k1_normsp_0 @ A @ B ) @ k1_numbers ) ) ),file(normsp_0,k1_normsp_0)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
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_k4_power,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k1_numbers ) & ( m1_subset_1 @ B @ k1_numbers ) ) => ( m1_subset_1 @ ( k4_power @ A @ B ) @ k1_numbers ) ) ),file(power,k4_power)).
thf(dt_k5_algstr_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( l2_algstr_0 @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) => ( m1_subset_1 @ ( k5_algstr_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ) ),file(algstr_0,k5_algstr_0)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_k6_numbers,axiom,( m2_subset_1 @ k6_numbers @ k1_numbers @ k5_numbers ),file(numbers,k6_numbers)).
thf(dt_k8_real_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k1_numbers ) & ( v1_xreal_0 @ B ) ) => ( m1_subset_1 @ ( k8_real_1 @ A @ B ) @ k1_numbers ) ) ),file(real_1,k8_real_1)).
thf(dt_l1_normsp_1,axiom,( ! [A: $i] : ( ( l1_normsp_1 @ A ) => ( ( l1_rlvect_1 @ A ) & ( l2_normsp_0 @ A ) ) ) ),file(normsp_1,l1_normsp_1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
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_c1_18__nfcont_2,axiom,( ~ ( v2_struct_0 @ c1_18__nfcont_2 ) & ( v13_algstr_0 @ c1_18__nfcont_2 ) & ( v2_rlvect_1 @ c1_18__nfcont_2 ) & ( v3_rlvect_1 @ c1_18__nfcont_2 ) & ( v4_rlvect_1 @ c1_18__nfcont_2 ) & ( v5_rlvect_1 @ c1_18__nfcont_2 ) & ( v6_rlvect_1 @ c1_18__nfcont_2 ) & ( v7_rlvect_1 @ c1_18__nfcont_2 ) & ( v8_rlvect_1 @ c1_18__nfcont_2 ) & ( v3_normsp_0 @ c1_18__nfcont_2 ) & ( v4_normsp_0 @ c1_18__nfcont_2 ) & ( v2_normsp_1 @ c1_18__nfcont_2 ) & ( v3_lopban_1 @ c1_18__nfcont_2 ) & ( l1_normsp_1 @ c1_18__nfcont_2 ) ),file(nfcont_2,c1_18__nfcont_2)).
thf(dt_c1_18_9__nfcont_2,axiom,( m1_subset_1 @ c1_18_9__nfcont_2 @ ( u1_struct_0 @ c1_18__nfcont_2 ) ),file(nfcont_2,c1_18_9__nfcont_2)).
thf(dt_c4_18__nfcont_2,axiom,( m1_subset_1 @ c4_18__nfcont_2 @ k1_numbers ),file(nfcont_2,c4_18__nfcont_2)).
thf(dt_c7_18__nfcont_2,axiom,( m1_subset_1 @ c7_18__nfcont_2 @ ( u1_struct_0 @ c1_18__nfcont_2 ) ),file(nfcont_2,c7_18__nfcont_2)).
thf(cc1_xreal_0,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc1_xreal_0)).
thf(cc25_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ( v6_membered @ A ) ) ),file(membered,cc25_membered)).
thf(fc1_normsp_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v5_rlvect_1 @ A ) & ( v6_rlvect_1 @ A ) & ( v7_rlvect_1 @ A ) & ( v8_rlvect_1 @ A ) & ( v3_normsp_0 @ A ) & ( v4_normsp_0 @ A ) & ( v2_normsp_1 @ A ) & ( l1_normsp_1 @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) ) => ~ ( v3_xxreal_0 @ ( k1_normsp_0 @ A @ B ) ) ) ),file(normsp_1,fc1_normsp_1)).
thf(fc1_numbers,axiom,( ~ ( v1_xboole_0 @ k1_numbers ) ),file(numbers,fc1_numbers)).
thf(fc3_membered,axiom,( v3_membered @ k1_numbers ),file(membered,fc3_membered)).
thf(fc56_membered,axiom,( v7_membered @ k1_numbers ),file(membered,fc56_membered)).
thf(fc8_numbers,axiom,( ~ ( v1_finset_1 @ k1_numbers ) ),file(numbers,fc8_numbers)).
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(e3_18_9_1__nfcont_2,axiom,( r1_xxreal_0 @ ( k1_normsp_0 @ c1_18__nfcont_2 @ ( k5_algstr_0 @ c1_18__nfcont_2 @ c1_18_9__nfcont_2 @ c7_18__nfcont_2 ) ) @ ( k8_real_1 @ ( k1_normsp_0 @ c1_18__nfcont_2 @ ( k5_algstr_0 @ c1_18__nfcont_2 @ c1_18_9__nfcont_2 @ c7_18__nfcont_2 ) ) @ ( k4_power @ c4_18__nfcont_2 @ k6_numbers ) ) ),file(nfcont_2,e3_18_9_1__nfcont_2)).
thf(e1_18_9_1__nfcont_2,axiom,( ! [A: $i] : ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers ) => ( ( r1_xxreal_0 @ ( k1_normsp_0 @ c1_18__nfcont_2 @ ( k5_algstr_0 @ c1_18__nfcont_2 @ c1_18_9__nfcont_2 @ c7_18__nfcont_2 ) ) @ ( k8_real_1 @ ( k1_normsp_0 @ c1_18__nfcont_2 @ ( k5_algstr_0 @ c1_18__nfcont_2 @ c1_18_9__nfcont_2 @ c7_18__nfcont_2 ) ) @ ( k4_power @ c4_18__nfcont_2 @ A ) ) ) => ( r1_xxreal_0 @ ( k1_normsp_0 @ c1_18__nfcont_2 @ ( k5_algstr_0 @ c1_18__nfcont_2 @ c1_18_9__nfcont_2 @ c7_18__nfcont_2 ) ) @ ( k8_real_1 @ ( k1_normsp_0 @ c1_18__nfcont_2 @ ( k5_algstr_0 @ c1_18__nfcont_2 @ c1_18_9__nfcont_2 @ c7_18__nfcont_2 ) ) @ ( k4_power @ c4_18__nfcont_2 @ ( k2_nat_1 @ A @ np__1 ) ) ) ) ) ) ),file(nfcont_2,e1_18_9_1__nfcont_2)).
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(e4_18_9_1__nfcont_2,conjecture,( ! [A: $i] : ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers ) => ( r1_xxreal_0 @ ( k1_normsp_0 @ c1_18__nfcont_2 @ ( k5_algstr_0 @ c1_18__nfcont_2 @ c1_18_9__nfcont_2 @ c7_18__nfcont_2 ) ) @ ( k8_real_1 @ ( k1_normsp_0 @ c1_18__nfcont_2 @ ( k5_algstr_0 @ c1_18__nfcont_2 @ c1_18_9__nfcont_2 @ c7_18__nfcont_2 ) ) @ ( k4_power @ c4_18__nfcont_2 @ A ) ) ) ) ),file(nfcont_2,e4_18_9_1__nfcont_2)).
