% Mizar problem: e3_112_1_1,hermitan,2252,8 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_112_type,type,( c1_112__hermitan: $i )).
thf(c2_112_type,type,( c2_112__hermitan: $i )).
thf(c3_112_type,type,( c3_112__hermitan: $i )).
thf(g1_vectsp_1_type,type,( g1_vectsp_1: $i > $i > $i > $i > $i > $i )).
thf(g6_algstr_0_type,type,( g6_algstr_0: $i > $i > $i > $i > $i > $i )).
thf(k13_bilinear_type,type,( k13_bilinear: $i > $i > $i > $i > $i )).
thf(k14_bilinear_type,type,( k14_bilinear: $i > $i > $i > $i > $i )).
thf(k1_binop_1_type,type,( k1_binop_1: $i > $i > $i > $i )).
thf(k1_complfld_type,type,( k1_complfld: $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_binop_1_type,type,( k2_binop_1: $i > $i > $i > $i > $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_hermitan_type,type,( k3_hermitan: $i > $i > $i > $i )).
thf(k3_vectsp_4_type,type,( k3_vectsp_4: $i > $i > $i > $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_vectsp10_type,type,( k6_vectsp10: $i > $i > $i > $i )).
thf(u1_algstr_0_type,type,( u1_algstr_0: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(u1_vectsp_1_type,type,( u1_vectsp_1: $i > $i > $i )).
thf(u2_algstr_0_type,type,( u2_algstr_0: $i > $i )).
thf(u2_struct_0_type,type,( u2_struct_0: $i > $i )).
thf(u3_struct_0_type,type,( u3_struct_0: $i > $i )).
thf(l1_algstr_0_type,type,( l1_algstr_0: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l1_vectsp_1_type,type,( l1_vectsp_1: $i > $i > $o )).
thf(l2_algstr_0_type,type,( l2_algstr_0: $i > $o )).
thf(l2_struct_0_type,type,( l2_struct_0: $i > $o )).
thf(l3_algstr_0_type,type,( l3_algstr_0: $i > $o )).
thf(l3_struct_0_type,type,( l3_struct_0: $i > $o )).
thf(l4_algstr_0_type,type,( l4_algstr_0: $i > $o )).
thf(l4_struct_0_type,type,( l4_struct_0: $i > $o )).
thf(l5_algstr_0_type,type,( l5_algstr_0: $i > $o )).
thf(l6_algstr_0_type,type,( l6_algstr_0: $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m1_vectsp_4_type,type,( m1_vectsp_4: $i > $i > $i > $o )).
thf(m2_subset_1_type,type,( m2_subset_1: $i > $i > $i > $o )).
thf(v10_vectsp_1_type,type,( v10_vectsp_1: $i > $i > $o )).
thf(v11_vectsp_1_type,type,( v11_vectsp_1: $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_bilinear_type,type,( v1_bilinear: $i > $i > $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_funct_2_type,type,( v1_funct_2: $i > $i > $i > $o )).
thf(v1_group_1_type,type,( v1_group_1: $i > $o )).
thf(v1_int_1_type,type,( v1_int_1: $i > $o )).
thf(v1_membered_type,type,( v1_membered: $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_vectsp_1_type,type,( v1_vectsp_1: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_xcmplx_0_type,type,( v1_xcmplx_0: $i > $o )).
thf(v1_xreal_0_type,type,( v1_xreal_0: $i > $o )).
thf(v1_xxreal_0_type,type,( v1_xxreal_0: $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_bilinear_type,type,( v2_bilinear: $i > $i > $i > $i > $o )).
thf(v2_hermitan_type,type,( v2_hermitan: $i > $i > $i > $o )).
thf(v2_membered_type,type,( v2_membered: $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_vectsp_1_type,type,( v2_vectsp_1: $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $i > $o )).
thf(v33_algstr_0_type,type,( v33_algstr_0: $i > $o )).
thf(v36_algstr_0_type,type,( v36_algstr_0: $i > $o )).
thf(v3_bilinear_type,type,( v3_bilinear: $i > $i > $i > $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_1: $i > $o )).
thf(v3_group_1_type,type,( v3_group_1: $i > $o )).
thf(v3_membered_type,type,( v3_membered: $i > $o )).
thf(v3_rlvect_1_type,type,( v3_rlvect_1: $i > $o )).
thf(v3_vectsp_1_type,type,( v3_vectsp_1: $i > $o )).
thf(v3_xxreal_0_type,type,( v3_xxreal_0: $i > $o )).
thf(v4_bilinear_type,type,( v4_bilinear: $i > $i > $i > $i > $o )).
thf(v4_membered_type,type,( v4_membered: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v4_rlvect_1_type,type,( v4_rlvect_1: $i > $o )).
thf(v4_vectsp_1_type,type,( v4_vectsp_1: $i > $o )).
thf(v5_group_1_type,type,( v5_group_1: $i > $o )).
thf(v5_membered_type,type,( v5_membered: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v5_vectsp_1_type,type,( v5_vectsp_1: $i > $o )).
thf(v6_membered_type,type,( v6_membered: $i > $o )).
thf(v6_struct_0_type,type,( v6_struct_0: $i > $o )).
thf(v6_vectsp_1_type,type,( v6_vectsp_1: $i > $o )).
thf(v7_membered_type,type,( v7_membered: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v7_vectsp_1_type,type,( v7_vectsp_1: $i > $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_0: $i > $o )).
thf(v8_vectsp_1_type,type,( v8_vectsp_1: $i > $i > $o )).
thf(v9_vectsp_1_type,type,( v9_vectsp_1: $i > $i > $o )).
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(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(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(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
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(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(cc4_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v2_membered @ A ) ) ),file(membered,cc4_membered)).
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(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(fc59_membered,axiom,( v7_membered @ k4_ordinal1 ),file(membered,fc59_membered)).
thf(fc6_membered,axiom,( v6_membered @ k4_ordinal1 ),file(membered,fc6_membered)).
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(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
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_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
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(cc11_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k5_numbers ) ) => ( v6_membered @ A ) ) ),file(membered,cc11_membered)).
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(cc1_xcmplx_0,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) => ( v1_xcmplx_0 @ A ) ) ),file(xcmplx_0,cc1_xcmplx_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(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(cc25_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ( v6_membered @ A ) ) ),file(membered,cc25_membered)).
thf(cc3_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ( v3_membered @ A ) ) ),file(membered,cc3_membered)).
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_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xreal_0,cc4_xreal_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_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(fc1_numbers,axiom,( ~ ( v1_xboole_0 @ k1_numbers ) ),file(numbers,fc1_numbers)).
thf(fc25_hermitan,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v7_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v8_vectsp_1 @ A @ k1_complfld ) & ( v9_vectsp_1 @ A @ k1_complfld ) & ( v10_vectsp_1 @ A @ k1_complfld ) & ( v11_vectsp_1 @ A @ k1_complfld ) & ( l1_vectsp_1 @ A @ k1_complfld ) & ~ ( v2_struct_0 @ B ) & ~ ( v7_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v2_rlvect_1 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( v8_vectsp_1 @ B @ k1_complfld ) & ( v9_vectsp_1 @ B @ k1_complfld ) & ( v10_vectsp_1 @ B @ k1_complfld ) & ( v11_vectsp_1 @ B @ k1_complfld ) & ( l1_vectsp_1 @ B @ k1_complfld ) & ( v1_funct_1 @ C ) & ~ ( v3_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) ) ) ) => ( ( v1_funct_1 @ ( k3_hermitan @ A @ B @ C ) ) & ~ ( v3_funct_1 @ ( k3_hermitan @ A @ B @ C ) ) & ( v1_funct_2 @ ( k3_hermitan @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) ) ) ),file(hermitan,fc25_hermitan)).
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(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_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(rc4_vectsp_1,axiom,( ? [A: $i] : ( ( l4_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v1_group_1 @ A ) & ( v3_group_1 @ A ) & ( v5_group_1 @ A ) ) ),file(vectsp_1,rc4_vectsp_1)).
thf(rc4_xreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc4_xreal_0)).
thf(rc4_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,rc4_xxreal_0)).
thf(rc5_hermitan,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v7_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v8_vectsp_1 @ A @ k1_complfld ) & ( v9_vectsp_1 @ A @ k1_complfld ) & ( v10_vectsp_1 @ A @ k1_complfld ) & ( v11_vectsp_1 @ A @ k1_complfld ) & ( l1_vectsp_1 @ A @ k1_complfld ) & ~ ( v2_struct_0 @ B ) & ~ ( v7_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v2_rlvect_1 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( v8_vectsp_1 @ B @ k1_complfld ) & ( v9_vectsp_1 @ B @ k1_complfld ) & ( v10_vectsp_1 @ B @ k1_complfld ) & ( v11_vectsp_1 @ B @ k1_complfld ) & ( l1_vectsp_1 @ B @ k1_complfld ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) ) ) & ~ ( v1_zfmisc_1 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) & ( v5_relat_1 @ C @ ( u1_struct_0 @ k1_complfld ) ) & ( v1_funct_1 @ C ) & ~ ( v3_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) & ( v1_bilinear @ C @ k1_complfld @ A @ B ) & ( v2_bilinear @ C @ k1_complfld @ A @ B ) & ( v4_bilinear @ C @ k1_complfld @ A @ B ) & ( v2_hermitan @ C @ A @ B ) ) ) ),file(hermitan,rc5_hermitan)).
thf(dt_l3_algstr_0,axiom,( ! [A: $i] : ( ( l3_algstr_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(algstr_0,l3_algstr_0)).
thf(dt_l3_struct_0,axiom,( ! [A: $i] : ( ( l3_struct_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(struct_0,l3_struct_0)).
thf(dt_l4_algstr_0,axiom,( ! [A: $i] : ( ( l4_algstr_0 @ A ) => ( ( l3_struct_0 @ A ) & ( l3_algstr_0 @ A ) ) ) ),file(algstr_0,l4_algstr_0)).
thf(dt_l4_struct_0,axiom,( ! [A: $i] : ( ( l4_struct_0 @ A ) => ( ( l2_struct_0 @ A ) & ( l3_struct_0 @ A ) ) ) ),file(struct_0,l4_struct_0)).
thf(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(cc16_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_int_1 @ B ) ) ) ),file(membered,cc16_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_xcmplx_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xcmplx_0 @ A ) ) ),file(xcmplx_0,cc2_xcmplx_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_struct_0,axiom,( ! [A: $i] : ( ( l4_struct_0 @ A ) => ( ~ ( v6_struct_0 @ A ) => ~ ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc3_struct_0)).
thf(cc3_vectsp10,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v6_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v33_algstr_0 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v3_group_1 @ A ) & ( v5_group_1 @ A ) & ( v4_vectsp_1 @ A ) & ( v5_vectsp_1 @ A ) & ( l6_algstr_0 @ A ) & ~ ( v2_struct_0 @ B ) & ~ ( v7_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v2_rlvect_1 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( v8_vectsp_1 @ B @ A ) & ( v9_vectsp_1 @ B @ A ) & ( v10_vectsp_1 @ B @ A ) & ( v11_vectsp_1 @ B @ A ) & ( l1_vectsp_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) ) ) => ( ( ( v1_funct_1 @ C ) & ( v1_zfmisc_1 @ C ) & ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) ) => ( ( v1_funct_1 @ C ) & ( v3_funct_1 @ C ) & ( v1_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),file(vectsp10,cc3_vectsp10)).
thf(cc3_vectsp_1,axiom,( ! [A: $i] : ( ( l4_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v4_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v3_vectsp_1 @ A ) & ( v6_vectsp_1 @ A ) ) ) ) ),file(vectsp_1,cc3_vectsp_1)).
thf(cc4_vectsp_1,axiom,( ! [A: $i] : ( ( l4_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v3_vectsp_1 @ A ) & ( v6_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v1_group_1 @ A ) ) ) ) ),file(vectsp_1,cc4_vectsp_1)).
thf(cc5_vectsp_1,axiom,( ! [A: $i] : ( ( l4_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v4_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v1_group_1 @ A ) ) ) ) ),file(vectsp_1,cc5_vectsp_1)).
thf(cc6_vectsp_1,axiom,( ! [A: $i] : ( ( l4_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v5_group_1 @ A ) & ( v6_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v3_vectsp_1 @ A ) ) ) ) ),file(vectsp_1,cc6_vectsp_1)).
thf(rc11_vectsp_1,axiom,( ? [A: $i] : ( ( l4_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v4_vectsp_1 @ A ) ) ),file(vectsp_1,rc11_vectsp_1)).
thf(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(rc3_vectsp_1,axiom,( ? [A: $i] : ( ( l3_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v3_group_1 @ A ) & ( v5_group_1 @ A ) ) ),file(vectsp_1,rc3_vectsp_1)).
thf(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(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(free_g1_vectsp_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( l1_struct_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) & ( m1_subset_1 @ D @ B ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ B ) @ B ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ B ) @ B ) ) ) ) => ! [F: $i] : ! [G: $i] : ! [H: $i] : ! [I: $i] : ! [J: $i] : ( ( = @ ( g1_vectsp_1 @ A @ B @ C @ D @ E ) @ ( g1_vectsp_1 @ F @ G @ H @ I @ J ) ) => ( ( = @ A @ F ) & ( = @ B @ G ) & ( = @ C @ H ) & ( = @ D @ I ) & ( = @ E @ J ) ) ) ) ),file(vectsp_1,g1_vectsp_1)).
thf(free_g6_algstr_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) & ( m1_subset_1 @ D @ A ) & ( m1_subset_1 @ E @ A ) ) => ! [F: $i] : ! [G: $i] : ! [H: $i] : ! [I: $i] : ! [J: $i] : ( ( = @ ( g6_algstr_0 @ A @ B @ C @ D @ E ) @ ( g6_algstr_0 @ F @ G @ H @ I @ J ) ) => ( ( = @ A @ F ) & ( = @ B @ G ) & ( = @ C @ H ) & ( = @ D @ I ) & ( = @ E @ J ) ) ) ) ),file(algstr_0,g6_algstr_0)).
thf(dt_g1_vectsp_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( l1_struct_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) & ( m1_subset_1 @ D @ B ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ B ) @ B ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ B ) @ B ) ) ) ) => ( ( v7_vectsp_1 @ ( g1_vectsp_1 @ A @ B @ C @ D @ E ) @ A ) & ( l1_vectsp_1 @ ( g1_vectsp_1 @ A @ B @ C @ D @ E ) @ A ) ) ) ),file(vectsp_1,g1_vectsp_1)).
thf(dt_g6_algstr_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) & ( m1_subset_1 @ D @ A ) & ( m1_subset_1 @ E @ A ) ) => ( ( v36_algstr_0 @ ( g6_algstr_0 @ A @ B @ C @ D @ E ) ) & ( l6_algstr_0 @ ( g6_algstr_0 @ A @ B @ C @ D @ E ) ) ) ) ),file(algstr_0,g6_algstr_0)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_l1_algstr_0,axiom,( ! [A: $i] : ( ( l1_algstr_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(algstr_0,l1_algstr_0)).
thf(dt_l2_struct_0,axiom,( ! [A: $i] : ( ( l2_struct_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(struct_0,l2_struct_0)).
thf(dt_l5_algstr_0,axiom,( ! [A: $i] : ( ( l5_algstr_0 @ A ) => ( ( l4_algstr_0 @ A ) & ( l4_struct_0 @ A ) ) ) ),file(algstr_0,l5_algstr_0)).
thf(dt_u1_algstr_0,axiom,( ! [A: $i] : ( ( l1_algstr_0 @ A ) => ( ( v1_funct_1 @ ( u1_algstr_0 @ A ) ) & ( v1_funct_2 @ ( u1_algstr_0 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ ( u1_algstr_0 @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),file(algstr_0,u1_algstr_0)).
thf(dt_u1_vectsp_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_struct_0 @ A ) & ( l1_vectsp_1 @ B @ A ) ) => ( ( v1_funct_1 @ ( u1_vectsp_1 @ A @ B ) ) & ( v1_funct_2 @ ( u1_vectsp_1 @ A @ B ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ B ) ) & ( m1_subset_1 @ ( u1_vectsp_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ B ) ) ) ) ) ) ),file(vectsp_1,u1_vectsp_1)).
thf(dt_u2_algstr_0,axiom,( ! [A: $i] : ( ( l3_algstr_0 @ A ) => ( ( v1_funct_1 @ ( u2_algstr_0 @ A ) ) & ( v1_funct_2 @ ( u2_algstr_0 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ ( u2_algstr_0 @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),file(algstr_0,u2_algstr_0)).
thf(dt_u2_struct_0,axiom,( ! [A: $i] : ( ( l2_struct_0 @ A ) => ( m1_subset_1 @ ( u2_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,u2_struct_0)).
thf(dt_u3_struct_0,axiom,( ! [A: $i] : ( ( l3_struct_0 @ A ) => ( m1_subset_1 @ ( u3_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,u3_struct_0)).
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(cc17_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v7_ordinal1 @ B ) ) ) ),file(membered,cc17_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(cc1_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ( v5_membered @ A ) ) ),file(membered,cc1_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(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_vectsp_1,axiom,( ! [A: $i] : ( ( l6_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v1_vectsp_1 @ A ) & ( v2_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v5_vectsp_1 @ A ) ) ) ) ),file(vectsp_1,cc2_vectsp_1)).
thf(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(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(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_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(fc9_vectsp_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( l1_struct_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) & ( m1_subset_1 @ D @ B ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ B ) @ B ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ B ) @ B ) ) ) ) => ( ~ ( v2_struct_0 @ ( g1_vectsp_1 @ A @ B @ C @ D @ E ) ) & ( v7_vectsp_1 @ ( g1_vectsp_1 @ A @ B @ C @ D @ E ) @ A ) ) ) ),file(vectsp_1,fc9_vectsp_1)).
thf(rc1_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc1_membered)).
thf(rc1_vectsp10,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v6_struct_0 @ A ) & ( l6_algstr_0 @ A ) ) => ? [B: $i] : ( ( l1_vectsp_1 @ B @ A ) & ~ ( v7_struct_0 @ B ) ) ) ),file(vectsp10,rc1_vectsp10)).
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_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc2_membered)).
thf(rc2_vectsp_1,axiom,( ? [A: $i] : ( ( l5_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v4_vectsp_1 @ A ) ) ),file(vectsp_1,rc2_vectsp_1)).
thf(rc3_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) & ( v7_membered @ A ) ) ),file(membered,rc3_membered)).
thf(rc4_vectsp10,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v6_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v3_group_1 @ A ) & ( v5_vectsp_1 @ A ) & ( v6_vectsp_1 @ A ) & ( l6_algstr_0 @ A ) ) => ? [B: $i] : ( ( l1_vectsp_1 @ B @ A ) & ~ ( v2_struct_0 @ B ) & ~ ( v7_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v2_rlvect_1 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( v7_vectsp_1 @ B @ A ) & ( v8_vectsp_1 @ B @ A ) & ( v9_vectsp_1 @ B @ A ) & ( v10_vectsp_1 @ B @ A ) & ( v11_vectsp_1 @ B @ A ) ) ) ),file(vectsp10,rc4_vectsp10)).
thf(abstractness_v36_algstr_0,axiom,( ! [A: $i] : ( ( l6_algstr_0 @ A ) => ( ( v36_algstr_0 @ A ) => ( = @ A @ ( g6_algstr_0 @ ( u1_struct_0 @ A ) @ ( u1_algstr_0 @ A ) @ ( u2_algstr_0 @ A ) @ ( u3_struct_0 @ A ) @ ( u2_struct_0 @ A ) ) ) ) ) ),file(algstr_0,v36_algstr_0)).
thf(abstractness_v7_vectsp_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_struct_0 @ A ) & ( l1_vectsp_1 @ B @ A ) ) => ( ( v7_vectsp_1 @ B @ A ) => ( = @ B @ ( g1_vectsp_1 @ A @ ( u1_struct_0 @ B ) @ ( u1_algstr_0 @ B ) @ ( u2_struct_0 @ B ) @ ( u1_vectsp_1 @ A @ B ) ) ) ) ) ),file(vectsp_1,v7_vectsp_1)).
thf(dt_k1_binop_1,axiom,( $true ),file(binop_1,k1_binop_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_l6_algstr_0,axiom,( ! [A: $i] : ( ( l6_algstr_0 @ A ) => ( ( l2_algstr_0 @ A ) & ( l5_algstr_0 @ A ) ) ) ),file(algstr_0,l6_algstr_0)).
thf(dt_m1_vectsp_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v3_group_1 @ A ) & ( v4_vectsp_1 @ A ) & ( v5_vectsp_1 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( l6_algstr_0 @ A ) & ~ ( v2_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v8_vectsp_1 @ B @ A ) & ( v9_vectsp_1 @ B @ A ) & ( v10_vectsp_1 @ B @ A ) & ( v11_vectsp_1 @ B @ A ) & ( v2_rlvect_1 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( l1_vectsp_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_vectsp_4 @ C @ A @ B ) => ( ~ ( v2_struct_0 @ C ) & ( v13_algstr_0 @ C ) & ( v8_vectsp_1 @ C @ A ) & ( v9_vectsp_1 @ C @ A ) & ( v10_vectsp_1 @ C @ A ) & ( v11_vectsp_1 @ C @ A ) & ( v2_rlvect_1 @ C ) & ( v3_rlvect_1 @ C ) & ( v4_rlvect_1 @ C ) & ( l1_vectsp_1 @ C @ A ) ) ) ) ),file(vectsp_4,m1_vectsp_4)).
thf(cc18_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_membered @ A ) ) ),file(membered,cc18_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(cc1_vectsp_1,axiom,( ! [A: $i] : ( ( l6_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v5_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v1_vectsp_1 @ A ) & ( v2_vectsp_1 @ A ) ) ) ) ),file(vectsp_1,cc1_vectsp_1)).
thf(cc26_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_membered @ A ) ) ),file(membered,cc26_membered)).
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(cc4_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc4_relset_1)).
thf(cc4_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc4_struct_0)).
thf(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(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(fc23_hermitan,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_vectsp_1 @ A @ k1_complfld ) & ~ ( v2_struct_0 @ B ) & ( l1_vectsp_1 @ B @ k1_complfld ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) & ( v3_bilinear @ C @ k1_complfld @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) ) ) ) => ( ( v1_funct_1 @ ( k3_hermitan @ A @ B @ C ) ) & ( v1_funct_2 @ ( k3_hermitan @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) & ( v2_hermitan @ ( k3_hermitan @ A @ B @ C ) @ A @ B ) ) ) ),file(hermitan,fc23_hermitan)).
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(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_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc1_xcmplx_0,axiom,( ? [A: $i] : ( v1_xcmplx_0 @ A ) ),file(xcmplx_0,rc1_xcmplx_0)).
thf(rc2_vectsp10,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( l6_algstr_0 @ A ) ) => ? [B: $i] : ( ( l1_vectsp_1 @ B @ A ) & ~ ( v2_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( v7_vectsp_1 @ B @ A ) ) ) ),file(vectsp10,rc2_vectsp10)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc2_xcmplx_0,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_xcmplx_0 @ A ) ) ),file(xcmplx_0,rc2_xcmplx_0)).
thf(rc3_vectsp10,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v3_group_1 @ A ) & ( v5_vectsp_1 @ A ) & ( v6_vectsp_1 @ A ) & ( l6_algstr_0 @ A ) ) => ? [B: $i] : ( ( l1_vectsp_1 @ B @ A ) & ~ ( v2_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( v7_vectsp_1 @ B @ A ) & ( v8_vectsp_1 @ B @ A ) & ( v9_vectsp_1 @ B @ A ) & ( v10_vectsp_1 @ B @ A ) & ( v11_vectsp_1 @ B @ A ) ) ) ),file(vectsp10,rc3_vectsp10)).
thf(rc4_hermitan,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_vectsp_1 @ A @ k1_complfld ) & ~ ( v2_struct_0 @ B ) & ( l1_vectsp_1 @ B @ k1_complfld ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) & ( v5_relat_1 @ C @ ( u1_struct_0 @ k1_complfld ) ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) & ( v1_bilinear @ C @ k1_complfld @ A @ B ) & ( v2_bilinear @ C @ k1_complfld @ A @ B ) & ( v4_bilinear @ C @ k1_complfld @ A @ B ) & ( v2_hermitan @ C @ A @ B ) ) ) ),file(hermitan,rc4_hermitan)).
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(rc5_vectsp_1,axiom,( ? [A: $i] : ( ( l6_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ~ ( v6_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v33_algstr_0 @ A ) & ( v36_algstr_0 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v3_group_1 @ A ) & ( v5_group_1 @ A ) & ( v3_vectsp_1 @ A ) & ( v4_vectsp_1 @ A ) & ( v5_vectsp_1 @ A ) & ( v6_vectsp_1 @ A ) ) ),file(vectsp_1,rc5_vectsp_1)).
thf(rc6_vectsp_1,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ? [B: $i] : ( ( l1_vectsp_1 @ B @ A ) & ( v7_vectsp_1 @ B @ A ) ) ) ),file(vectsp_1,rc6_vectsp_1)).
thf(rc7_vectsp_1,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ? [B: $i] : ( ( l1_vectsp_1 @ B @ A ) & ~ ( v2_struct_0 @ B ) & ( v7_vectsp_1 @ B @ A ) ) ) ),file(vectsp_1,rc7_vectsp_1)).
thf(rc8_vectsp_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v3_group_1 @ A ) & ( v4_vectsp_1 @ A ) & ( v5_vectsp_1 @ A ) & ( l6_algstr_0 @ A ) ) => ? [B: $i] : ( ( l1_vectsp_1 @ B @ A ) & ~ ( v2_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v2_rlvect_1 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( v7_vectsp_1 @ B @ A ) & ( v8_vectsp_1 @ B @ A ) & ( v9_vectsp_1 @ B @ A ) & ( v10_vectsp_1 @ B @ A ) & ( v11_vectsp_1 @ B @ A ) ) ) ),file(vectsp_1,rc8_vectsp_1)).
thf(redefinition_k2_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) & ( m1_subset_1 @ E @ A ) & ( m1_subset_1 @ F @ B ) ) => ( = @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_binop_1 @ D @ E @ F ) ) ) ),file(binop_1,k2_binop_1)).
thf(dt_k13_bilinear,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v3_group_1 @ A ) & ( v4_vectsp_1 @ A ) & ( v5_vectsp_1 @ A ) & ( l6_algstr_0 @ A ) & ~ ( v2_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v2_rlvect_1 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( v8_vectsp_1 @ B @ A ) & ( v9_vectsp_1 @ B @ A ) & ( v10_vectsp_1 @ B @ A ) & ( v11_vectsp_1 @ B @ A ) & ( l1_vectsp_1 @ B @ A ) & ~ ( v2_struct_0 @ C ) & ( l1_vectsp_1 @ C @ A ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) @ ( u1_struct_0 @ A ) ) & ( v2_bilinear @ D @ A @ B @ C ) & ( v4_bilinear @ D @ A @ B @ C ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) @ ( u1_struct_0 @ A ) ) ) ) ) => ( ~ ( v2_struct_0 @ ( k13_bilinear @ A @ B @ C @ D ) ) & ( v7_vectsp_1 @ ( k13_bilinear @ A @ B @ C @ D ) @ A ) & ( m1_vectsp_4 @ ( k13_bilinear @ A @ B @ C @ D ) @ A @ B ) ) ) ),file(bilinear,k13_bilinear)).
thf(dt_k14_bilinear,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v3_group_1 @ A ) & ( v4_vectsp_1 @ A ) & ( v5_vectsp_1 @ A ) & ( l6_algstr_0 @ A ) & ~ ( v2_struct_0 @ B ) & ( l1_vectsp_1 @ B @ A ) & ~ ( v2_struct_0 @ C ) & ( v13_algstr_0 @ C ) & ( v2_rlvect_1 @ C ) & ( v3_rlvect_1 @ C ) & ( v4_rlvect_1 @ C ) & ( v8_vectsp_1 @ C @ A ) & ( v9_vectsp_1 @ C @ A ) & ( v10_vectsp_1 @ C @ A ) & ( v11_vectsp_1 @ C @ A ) & ( l1_vectsp_1 @ C @ A ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) @ ( u1_struct_0 @ A ) ) & ( v1_bilinear @ D @ A @ B @ C ) & ( v3_bilinear @ D @ A @ B @ C ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) ) @ ( u1_struct_0 @ A ) ) ) ) ) => ( ~ ( v2_struct_0 @ ( k14_bilinear @ A @ B @ C @ D ) ) & ( v7_vectsp_1 @ ( k14_bilinear @ A @ B @ C @ D ) @ A ) & ( m1_vectsp_4 @ ( k14_bilinear @ A @ B @ C @ D ) @ A @ C ) ) ) ),file(bilinear,k14_bilinear)).
thf(dt_k1_complfld,axiom,( ( v36_algstr_0 @ k1_complfld ) & ( l6_algstr_0 @ k1_complfld ) ),file(complfld,k1_complfld)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) & ( m1_subset_1 @ E @ A ) & ( m1_subset_1 @ F @ B ) ) => ( m1_subset_1 @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ C ) ) ),file(binop_1,k2_binop_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_hermitan,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_vectsp_1 @ A @ k1_complfld ) & ~ ( v2_struct_0 @ B ) & ( l1_vectsp_1 @ B @ k1_complfld ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) ) ) ) => ( ( v1_funct_1 @ ( k3_hermitan @ A @ B @ C ) ) & ( v1_funct_2 @ ( k3_hermitan @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) & ( m1_subset_1 @ ( k3_hermitan @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) ) ) ) ) ),file(hermitan,k3_hermitan)).
thf(dt_k3_vectsp_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v3_group_1 @ A ) & ( v4_vectsp_1 @ A ) & ( v5_vectsp_1 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( l6_algstr_0 @ A ) & ~ ( v2_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v8_vectsp_1 @ B @ A ) & ( v9_vectsp_1 @ B @ A ) & ( v10_vectsp_1 @ B @ A ) & ( v11_vectsp_1 @ B @ A ) & ( v2_rlvect_1 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( l1_vectsp_1 @ B @ A ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) & ( m1_vectsp_4 @ D @ A @ B ) ) => ( m1_subset_1 @ ( k3_vectsp_4 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) ) ),file(vectsp_4,k3_vectsp_4)).
thf(dt_k6_vectsp10,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v3_group_1 @ A ) & ( v4_vectsp_1 @ A ) & ( v5_vectsp_1 @ A ) & ( l6_algstr_0 @ A ) & ~ ( v2_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v2_rlvect_1 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( v8_vectsp_1 @ B @ A ) & ( v9_vectsp_1 @ B @ A ) & ( v10_vectsp_1 @ B @ A ) & ( v11_vectsp_1 @ B @ A ) & ( l1_vectsp_1 @ B @ A ) & ( m1_vectsp_4 @ C @ A @ B ) ) => ( ~ ( v2_struct_0 @ ( k6_vectsp10 @ A @ B @ C ) ) & ( v13_algstr_0 @ ( k6_vectsp10 @ A @ B @ C ) ) & ( v2_rlvect_1 @ ( k6_vectsp10 @ A @ B @ C ) ) & ( v3_rlvect_1 @ ( k6_vectsp10 @ A @ B @ C ) ) & ( v4_rlvect_1 @ ( k6_vectsp10 @ A @ B @ C ) ) & ( v7_vectsp_1 @ ( k6_vectsp10 @ A @ B @ C ) @ A ) & ( v8_vectsp_1 @ ( k6_vectsp10 @ A @ B @ C ) @ A ) & ( v9_vectsp_1 @ ( k6_vectsp10 @ A @ B @ C ) @ A ) & ( v10_vectsp_1 @ ( k6_vectsp10 @ A @ B @ C ) @ A ) & ( v11_vectsp_1 @ ( k6_vectsp10 @ A @ B @ C ) @ A ) & ( l1_vectsp_1 @ ( k6_vectsp10 @ A @ B @ C ) @ A ) ) ) ),file(vectsp10,k6_vectsp10)).
thf(dt_l1_vectsp_1,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ! [B: $i] : ( ( l1_vectsp_1 @ B @ A ) => ( l2_algstr_0 @ B ) ) ) ),file(vectsp_1,l1_vectsp_1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_c1_112__hermitan,axiom,( ~ ( v2_struct_0 @ c1_112__hermitan ) & ( v13_algstr_0 @ c1_112__hermitan ) & ( v2_rlvect_1 @ c1_112__hermitan ) & ( v3_rlvect_1 @ c1_112__hermitan ) & ( v4_rlvect_1 @ c1_112__hermitan ) & ( v8_vectsp_1 @ c1_112__hermitan @ k1_complfld ) & ( v9_vectsp_1 @ c1_112__hermitan @ k1_complfld ) & ( v10_vectsp_1 @ c1_112__hermitan @ k1_complfld ) & ( v11_vectsp_1 @ c1_112__hermitan @ k1_complfld ) & ( l1_vectsp_1 @ c1_112__hermitan @ k1_complfld ) ),file(hermitan,c1_112__hermitan)).
thf(dt_c2_112__hermitan,axiom,( ~ ( v2_struct_0 @ c2_112__hermitan ) & ( v13_algstr_0 @ c2_112__hermitan ) & ( v2_rlvect_1 @ c2_112__hermitan ) & ( v3_rlvect_1 @ c2_112__hermitan ) & ( v4_rlvect_1 @ c2_112__hermitan ) & ( v8_vectsp_1 @ c2_112__hermitan @ k1_complfld ) & ( v9_vectsp_1 @ c2_112__hermitan @ k1_complfld ) & ( v10_vectsp_1 @ c2_112__hermitan @ k1_complfld ) & ( v11_vectsp_1 @ c2_112__hermitan @ k1_complfld ) & ( l1_vectsp_1 @ c2_112__hermitan @ k1_complfld ) ),file(hermitan,c2_112__hermitan)).
thf(dt_c3_112__hermitan,axiom,( ( v1_funct_1 @ c3_112__hermitan ) & ( v1_funct_2 @ c3_112__hermitan @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_112__hermitan ) @ ( u1_struct_0 @ c2_112__hermitan ) ) @ ( u1_struct_0 @ k1_complfld ) ) & ( v1_bilinear @ c3_112__hermitan @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan ) & ( v2_bilinear @ c3_112__hermitan @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan ) & ( v4_bilinear @ c3_112__hermitan @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan ) & ( v2_hermitan @ c3_112__hermitan @ c1_112__hermitan @ c2_112__hermitan ) & ( m1_subset_1 @ c3_112__hermitan @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_112__hermitan ) @ ( u1_struct_0 @ c2_112__hermitan ) ) @ ( u1_struct_0 @ k1_complfld ) ) ) ) ),file(hermitan,c3_112__hermitan)).
thf(cc1_complfld,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_complfld ) ) => ( v1_xcmplx_0 @ A ) ) ),file(complfld,cc1_complfld)).
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(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(fc1_complfld,axiom,( ~ ( v2_struct_0 @ k1_complfld ) & ( v36_algstr_0 @ k1_complfld ) ),file(complfld,fc1_complfld)).
thf(fc21_hermitan,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_vectsp_1 @ A @ k1_complfld ) & ~ ( v2_struct_0 @ B ) & ( l1_vectsp_1 @ B @ k1_complfld ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) & ( v1_bilinear @ C @ k1_complfld @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) ) ) ) => ( ( v1_funct_1 @ ( k3_hermitan @ A @ B @ C ) ) & ( v1_funct_2 @ ( k3_hermitan @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) & ( v1_bilinear @ ( k3_hermitan @ A @ B @ C ) @ k1_complfld @ A @ B ) ) ) ),file(hermitan,fc21_hermitan)).
thf(fc22_hermitan,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_vectsp_1 @ A @ k1_complfld ) & ~ ( v2_struct_0 @ B ) & ( l1_vectsp_1 @ B @ k1_complfld ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) & ( v2_bilinear @ C @ k1_complfld @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) ) ) ) => ( ( v1_funct_1 @ ( k3_hermitan @ A @ B @ C ) ) & ( v1_funct_2 @ ( k3_hermitan @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) & ( v2_bilinear @ ( k3_hermitan @ A @ B @ C ) @ k1_complfld @ A @ B ) ) ) ),file(hermitan,fc22_hermitan)).
thf(fc24_hermitan,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_vectsp_1 @ A @ k1_complfld ) & ~ ( v2_struct_0 @ B ) & ( l1_vectsp_1 @ B @ k1_complfld ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) & ( v2_hermitan @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) ) ) ) => ( ( v1_funct_1 @ ( k3_hermitan @ A @ B @ C ) ) & ( v1_funct_2 @ ( k3_hermitan @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u1_struct_0 @ k1_complfld ) ) & ( v3_bilinear @ ( k3_hermitan @ A @ B @ C ) @ k1_complfld @ A @ B ) ) ) ),file(hermitan,fc24_hermitan)).
thf(fc2_complfld,axiom,( ( v36_algstr_0 @ k1_complfld ) & ( v4_vectsp_1 @ k1_complfld ) ),file(complfld,fc2_complfld)).
thf(fc3_complfld,axiom,( ~ ( v6_struct_0 @ k1_complfld ) & ( v13_algstr_0 @ k1_complfld ) & ( v33_algstr_0 @ k1_complfld ) & ( v36_algstr_0 @ k1_complfld ) & ( v3_group_1 @ k1_complfld ) & ( v5_group_1 @ k1_complfld ) & ( v3_vectsp_1 @ k1_complfld ) & ( v5_vectsp_1 @ k1_complfld ) & ( v6_vectsp_1 @ k1_complfld ) & ( v2_rlvect_1 @ k1_complfld ) & ( v3_rlvect_1 @ k1_complfld ) & ( v4_rlvect_1 @ k1_complfld ) ),file(complfld,fc3_complfld)).
thf(e2_112_1_1__hermitan,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( u1_struct_0 @ ( k6_vectsp10 @ k1_complfld @ c1_112__hermitan @ ( k13_bilinear @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan @ c3_112__hermitan ) ) ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k6_vectsp10 @ k1_complfld @ c2_112__hermitan @ ( k14_bilinear @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan @ ( k3_hermitan @ c1_112__hermitan @ c2_112__hermitan @ c3_112__hermitan ) ) ) ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ k1_complfld ) ) & ! [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ c1_112__hermitan ) ) => ! [E: $i] : ( ( m1_subset_1 @ E @ ( u1_struct_0 @ c2_112__hermitan ) ) => ( ( ( = @ A @ ( k3_vectsp_4 @ k1_complfld @ c1_112__hermitan @ D @ ( k13_bilinear @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan @ c3_112__hermitan ) ) ) & ( = @ B @ ( k3_vectsp_4 @ k1_complfld @ c2_112__hermitan @ E @ ( k14_bilinear @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan @ ( k3_hermitan @ c1_112__hermitan @ c2_112__hermitan @ c3_112__hermitan ) ) ) ) ) => ( = @ C @ ( k2_binop_1 @ ( u1_struct_0 @ c1_112__hermitan ) @ ( u1_struct_0 @ c2_112__hermitan ) @ ( u1_struct_0 @ k1_complfld ) @ c3_112__hermitan @ D @ E ) ) ) ) ) ) ) ) ),file(hermitan,e2_112_1_1__hermitan)).
thf(s3_binop_1,axiom,( ! [A: $i > $i > $i > $o] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ! [E: $i] : ( ( m1_subset_1 @ E @ D ) => ! [F: $i] : ( ( m1_subset_1 @ F @ C ) => ? [G: $i] : ( ( m1_subset_1 @ G @ B ) & ( A @ E @ F @ G ) ) ) ) => ? [E: $i] : ( ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ D @ C ) @ B ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ D @ C ) @ B ) ) ) & ! [F: $i] : ( ( m1_subset_1 @ F @ D ) => ! [G: $i] : ( ( m1_subset_1 @ G @ C ) => ( A @ F @ G @ ( k2_binop_1 @ D @ C @ B @ E @ F @ G ) ) ) ) ) ) ),file(binop_1,s3_binop_1)).
thf(e3_112_1_1__hermitan,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ ( u1_struct_0 @ ( k6_vectsp10 @ k1_complfld @ c1_112__hermitan @ ( k13_bilinear @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan @ c3_112__hermitan ) ) ) @ ( u1_struct_0 @ ( k6_vectsp10 @ k1_complfld @ c2_112__hermitan @ ( k14_bilinear @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan @ ( k3_hermitan @ c1_112__hermitan @ c2_112__hermitan @ c3_112__hermitan ) ) ) ) ) @ ( u1_struct_0 @ k1_complfld ) ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ ( k6_vectsp10 @ k1_complfld @ c1_112__hermitan @ ( k13_bilinear @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan @ c3_112__hermitan ) ) ) @ ( u1_struct_0 @ ( k6_vectsp10 @ k1_complfld @ c2_112__hermitan @ ( k14_bilinear @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan @ ( k3_hermitan @ c1_112__hermitan @ c2_112__hermitan @ c3_112__hermitan ) ) ) ) ) @ ( u1_struct_0 @ k1_complfld ) ) ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k6_vectsp10 @ k1_complfld @ c1_112__hermitan @ ( k13_bilinear @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan @ c3_112__hermitan ) ) ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_vectsp10 @ k1_complfld @ c2_112__hermitan @ ( k14_bilinear @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan @ ( k3_hermitan @ c1_112__hermitan @ c2_112__hermitan @ c3_112__hermitan ) ) ) ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ c1_112__hermitan ) ) => ! [E: $i] : ( ( m1_subset_1 @ E @ ( u1_struct_0 @ c2_112__hermitan ) ) => ( ( ( = @ B @ ( k3_vectsp_4 @ k1_complfld @ c1_112__hermitan @ D @ ( k13_bilinear @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan @ c3_112__hermitan ) ) ) & ( = @ C @ ( k3_vectsp_4 @ k1_complfld @ c2_112__hermitan @ E @ ( k14_bilinear @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan @ ( k3_hermitan @ c1_112__hermitan @ c2_112__hermitan @ c3_112__hermitan ) ) ) ) ) => ( = @ ( k2_binop_1 @ ( u1_struct_0 @ ( k6_vectsp10 @ k1_complfld @ c1_112__hermitan @ ( k13_bilinear @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan @ c3_112__hermitan ) ) ) @ ( u1_struct_0 @ ( k6_vectsp10 @ k1_complfld @ c2_112__hermitan @ ( k14_bilinear @ k1_complfld @ c1_112__hermitan @ c2_112__hermitan @ ( k3_hermitan @ c1_112__hermitan @ c2_112__hermitan @ c3_112__hermitan ) ) ) ) @ ( u1_struct_0 @ k1_complfld ) @ A @ B @ C ) @ ( k2_binop_1 @ ( u1_struct_0 @ c1_112__hermitan ) @ ( u1_struct_0 @ c2_112__hermitan ) @ ( u1_struct_0 @ k1_complfld ) @ c3_112__hermitan @ D @ E ) ) ) ) ) ) ) ) ),file(hermitan,e3_112_1_1__hermitan)).
