% Mizar problem: e12_19,scpqsort,2380,41 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(n2_type,type,( np__2: $i )).
thf(n3_type,type,( np__3: $i )).
thf(n4_type,type,( np__4: $i )).
thf(n5_type,type,( np__5: $i )).
thf(n6_type,type,( np__6: $i )).
thf(n7_type,type,( np__7: $i )).
thf(n8_type,type,( np__8: $i )).
thf(c4_19_type,type,( c4_19__scpqsort: $i )).
thf(c5_19_type,type,( c5_19__scpqsort: $i )).
thf(g1_extpro_1_type,type,( g1_extpro_1: $i > $i > $i > $i > $i > $i > $i > $i )).
thf(k10_scmpds_2_type,type,( k10_scmpds_2: $i > $i > $i > $i )).
thf(k11_scmpds_2_type,type,( k11_scmpds_2: $i > $i > $i > $i )).
thf(k13_scmpds_2_type,type,( k13_scmpds_2: $i > $i > $i > $i > $i )).
thf(k16_scmpds_2_type,type,( k16_scmpds_2: $i > $i > $i > $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_funct_2_type,type,( k1_funct_2: $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_ordinal4_type,type,( k1_ordinal4: $i > $i > $i )).
thf(k1_scmp_gcd_type,type,( k1_scmp_gcd: $i > $i )).
thf(k1_scmpds_2_type,type,( k1_scmpds_2: $i )).
thf(k1_scmpds_4_type,type,( k1_scmpds_4: $i > $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_memstr_0_type,type,( k2_memstr_0: $i > $i > $i )).
thf(k2_nat_1_type,type,( k2_nat_1: $i > $i > $i )).
thf(k2_scmp_gcd_type,type,( k2_scmp_gcd: $i )).
thf(k2_scmpds_8_type,type,( k2_scmpds_8: $i > $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_afinsq_1_type,type,( k3_afinsq_1: $i > $i )).
thf(k3_numbers_type,type,( k3_numbers: $i )).
thf(k3_relat_1_type,type,( k3_relat_1: $i > $i > $i )).
thf(k3_scmpds_4_type,type,( k3_scmpds_4: $i > $i > $i )).
thf(k3_scmpds_6_type,type,( k3_scmpds_6: $i > $i > $i > $i > $i )).
thf(k4_card_3_type,type,( k4_card_3: $i > $i )).
thf(k4_numbers_type,type,( k4_numbers: $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k4_scmpds_4_type,type,( k4_scmpds_4: $i > $i > $i )).
thf(k4_xcmplx_0_type,type,( k4_xcmplx_0: $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_numbers_type,type,( k6_numbers: $i )).
thf(k6_scmpds_4_type,type,( k6_scmpds_4: $i > $i > $i > $i )).
thf(k9_compos_1_type,type,( k9_compos_1: $i > $i > $i )).
thf(u1_compos_1_type,type,( u1_compos_1: $i > $i )).
thf(u1_extpro_1_type,type,( u1_extpro_1: $i > $i > $i )).
thf(u1_memstr_0_type,type,( u1_memstr_0: $i > $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(u2_memstr_0_type,type,( u2_memstr_0: $i > $i > $i )).
thf(u2_struct_0_type,type,( u2_struct_0: $i > $i )).
thf(l1_compos_1_type,type,( l1_compos_1: $i > $o )).
thf(l1_extpro_1_type,type,( l1_extpro_1: $i > $i > $o )).
thf(l1_memstr_0_type,type,( l1_memstr_0: $i > $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_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(v1_afinsq_1_type,type,( v1_afinsq_1: $i > $o )).
thf(v1_ami_2_type,type,( v1_ami_2: $i > $o )).
thf(v1_compos_0_type,type,( v1_compos_0: $i > $o )).
thf(v1_extpro_1_type,type,( v1_extpro_1: $i > $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_int_1_type,type,( v1_int_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_partfun1_type,type,( v1_partfun1: $i > $i > $o )).
thf(v1_pre_poly_type,type,( v1_pre_poly: $i > $o )).
thf(v1_rat_1_type,type,( v1_rat_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_scmpds_4_type,type,( v1_scmpds_4: $i > $o )).
thf(v1_scmpds_5_type,type,( v1_scmpds_5: $i > $o )).
thf(v1_setfam_1_type,type,( v1_setfam_1: $i > $o )).
thf(v1_valued_0_type,type,( v1_valued_0: $i > $o )).
thf(v1_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_compos_0_type,type,( v2_compos_0: $i > $o )).
thf(v2_compos_1_type,type,( v2_compos_1: $i > $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_memstr_0_type,type,( v2_memstr_0: $i > $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_pre_poly_type,type,( v2_pre_poly: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v2_scmpds_4_type,type,( v2_scmpds_4: $i > $o )).
thf(v2_setfam_1_type,type,( v2_setfam_1: $i > $o )).
thf(v2_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v2_valued_0_type,type,( v2_valued_0: $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $i > $o )).
thf(v3_amistd_5_type,type,( v3_amistd_5: $i > $i > $o )).
thf(v3_card_1_type,type,( v3_card_1: $i > $i > $o )).
thf(v3_compos_0_type,type,( v3_compos_0: $i > $o )).
thf(v3_extpro_1_type,type,( v3_extpro_1: $i > $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_1: $i > $o )).
thf(v3_memstr_0_type,type,( v3_memstr_0: $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_scmpds_4_type,type,( v3_scmpds_4: $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_amistd_5_type,type,( v4_amistd_5: $i > $i > $o )).
thf(v4_compos_1_type,type,( v4_compos_1: $i > $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_memstr_0_type,type,( v4_memstr_0: $i > $i > $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v4_scmpds_4_type,type,( v4_scmpds_4: $i > $o )).
thf(v4_valued_0_type,type,( v4_valued_0: $i > $o )).
thf(v5_compos_0_type,type,( v5_compos_0: $i > $o )).
thf(v5_funct_1_type,type,( v5_funct_1: $i > $i > $o )).
thf(v5_memstr_0_type,type,( v5_memstr_0: $i > $i > $i > $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v5_valued_0_type,type,( v5_valued_0: $i > $o )).
thf(v6_compos_0_type,type,( v6_compos_0: $i > $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v6_valued_0_type,type,( v6_valued_0: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(v7_valued_0_type,type,( v7_valued_0: $i > $o )).
thf(v8_valued_0_type,type,( v8_valued_0: $i > $o )).
thf(fc92_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v7_valued_0 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_valued_0 @ B ) & ( v7_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v7_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc92_valued_0)).
thf(fc94_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v8_valued_0 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_valued_0 @ B ) & ( v8_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v7_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc94_valued_0)).
thf(fc97_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v8_valued_0 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_valued_0 @ B ) & ( v7_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v8_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc97_valued_0)).
thf(fc98_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v8_valued_0 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_valued_0 @ B ) & ( v7_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ B @ A ) ) & ( v8_valued_0 @ ( k3_relat_1 @ B @ A ) ) ) ) ),file(valued_0,fc98_valued_0)).
thf(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(fc91_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v5_valued_0 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_valued_0 @ B ) & ( v5_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v5_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc91_valued_0)).
thf(fc93_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v6_valued_0 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_valued_0 @ B ) & ( v6_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v5_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc93_valued_0)).
thf(fc95_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v6_valued_0 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_valued_0 @ B ) & ( v5_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v6_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc95_valued_0)).
thf(fc96_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v6_valued_0 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_valued_0 @ B ) & ( v5_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ B @ A ) ) & ( v6_valued_0 @ ( k3_relat_1 @ B @ A ) ) ) ) ),file(valued_0,fc96_valued_0)).
thf(rc3_valued_0,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ k5_numbers ) ) ) & ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ( v1_partfun1 @ A @ k5_numbers ) & ( v1_funct_2 @ A @ k5_numbers @ k5_numbers ) & ( v1_valued_0 @ A ) & ( v2_valued_0 @ A ) & ( v3_valued_0 @ A ) & ( v4_valued_0 @ A ) & ( v5_valued_0 @ A ) ) ),file(valued_0,rc3_valued_0)).
thf(dt_k1_funct_2,axiom,( $true ),file(funct_2,k1_funct_2)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) ),file(relat_1,k3_relat_1)).
thf(dt_k4_card_3,axiom,( $true ),file(card_3,k4_card_3)).
thf(cc1_compos_1,axiom,( ! [A: $i] : ( ( l1_compos_1 @ A ) => ! [B: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( v1_zfmisc_1 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ ( u1_compos_1 @ A ) ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) ) => ( ~ ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ ( u1_compos_1 @ A ) ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v4_compos_1 @ B @ A ) ) ) ) ),file(compos_1,cc1_compos_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_scmpds_4,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ( v2_scmpds_4 @ A ) ) => ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ( v1_scmpds_4 @ A ) ) ) ),file(scmpds_4,cc1_scmpds_4)).
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(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
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(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_setfam_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ~ ( v2_setfam_1 @ A ) ) ),file(setfam_1,cc4_setfam_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(fc11_scmpds_6,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ( v2_scmpds_4 @ A ) & ( v3_scmpds_4 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v1_afinsq_1 @ B ) & ( v2_scmpds_4 @ B ) & ( v3_scmpds_4 @ B ) & ( v1_ami_2 @ C ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ D ) ) => ( ~ ( v1_xboole_0 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) & ( v1_relat_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) & ( v4_relat_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) @ k5_numbers ) & ( v5_relat_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) & ( v1_finset_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) & ( v1_afinsq_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) & ( v2_scmpds_4 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) & ( v3_scmpds_4 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) ) ) ),file(scmpds_6,fc11_scmpds_6)).
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_scmpds_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ( v3_scmpds_4 @ A ) & ( v4_scmpds_4 @ B ) & ( m1_subset_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) => ( ~ ( v1_xboole_0 @ ( k3_scmpds_4 @ A @ B ) ) & ( v1_relat_1 @ ( k3_scmpds_4 @ A @ B ) ) & ( v4_relat_1 @ ( k3_scmpds_4 @ A @ B ) @ k5_numbers ) & ( v5_relat_1 @ ( k3_scmpds_4 @ A @ B ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k3_scmpds_4 @ A @ B ) ) & ( v1_finset_1 @ ( k3_scmpds_4 @ A @ B ) ) & ( v1_afinsq_1 @ ( k3_scmpds_4 @ A @ B ) ) & ( v3_scmpds_4 @ ( k3_scmpds_4 @ A @ B ) ) ) ) ),file(scmpds_4,fc12_scmpds_4)).
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(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(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_scpqsort,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ( v3_scmpds_4 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v1_afinsq_1 @ B ) & ( v3_scmpds_4 @ B ) & ( v1_ami_2 @ C ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ D ) ) => ( ~ ( v1_xboole_0 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) & ( v1_relat_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) & ( v4_relat_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) @ k5_numbers ) & ( v5_relat_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) & ( v1_finset_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) & ( v1_afinsq_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) & ( v3_scmpds_4 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) ) ) ),file(scpqsort,fc1_scpqsort)).
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(fc29_scmpds_5,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ( v2_scmpds_4 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v1_afinsq_1 @ B ) & ( v2_scmpds_4 @ B ) & ( v3_scmpds_4 @ B ) ) => ( ~ ( v1_xboole_0 @ ( k1_ordinal4 @ A @ B ) ) & ( v1_relat_1 @ ( k1_ordinal4 @ A @ B ) ) & ( v4_relat_1 @ ( k1_ordinal4 @ A @ B ) @ k5_numbers ) & ( v5_relat_1 @ ( k1_ordinal4 @ A @ B ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k1_ordinal4 @ A @ B ) ) & ( v1_finset_1 @ ( k1_ordinal4 @ A @ B ) ) & ( v1_afinsq_1 @ ( k1_ordinal4 @ A @ B ) ) & ( v2_scmpds_4 @ ( k1_ordinal4 @ A @ B ) ) ) ) ),file(scmpds_5,fc29_scmpds_5)).
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(fc30_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_relat_1 @ C ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ B @ C ) ) & ( v4_relat_1 @ ( k3_relat_1 @ B @ C ) @ A ) ) ) ),file(relat_1,fc30_relat_1)).
thf(fc31_scmpds_5,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ( v2_scmpds_4 @ A ) & ( v4_scmpds_4 @ B ) & ( v1_scmpds_5 @ B ) & ( m1_subset_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) => ( ~ ( v1_xboole_0 @ ( k3_scmpds_4 @ A @ B ) ) & ( v1_relat_1 @ ( k3_scmpds_4 @ A @ B ) ) & ( v4_relat_1 @ ( k3_scmpds_4 @ A @ B ) @ k5_numbers ) & ( v5_relat_1 @ ( k3_scmpds_4 @ A @ B ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k3_scmpds_4 @ A @ B ) ) & ( v1_finset_1 @ ( k3_scmpds_4 @ A @ B ) ) & ( v1_afinsq_1 @ ( k3_scmpds_4 @ A @ B ) ) & ( v2_scmpds_4 @ ( k3_scmpds_4 @ A @ B ) ) ) ) ),file(scmpds_5,fc31_scmpds_5)).
thf(fc3_scmpds_8,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ( v3_scmpds_4 @ A ) & ( v1_ami_2 @ B ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ C ) ) => ( ~ ( v1_xboole_0 @ ( k2_scmpds_8 @ B @ C @ A ) ) & ( v1_relat_1 @ ( k2_scmpds_8 @ B @ C @ A ) ) & ( v4_relat_1 @ ( k2_scmpds_8 @ B @ C @ A ) @ k5_numbers ) & ( v5_relat_1 @ ( k2_scmpds_8 @ B @ C @ A ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k2_scmpds_8 @ B @ C @ A ) ) & ( v1_finset_1 @ ( k2_scmpds_8 @ B @ C @ A ) ) & ( v1_afinsq_1 @ ( k2_scmpds_8 @ B @ C @ A ) ) & ( v3_scmpds_4 @ ( k2_scmpds_8 @ B @ C @ A ) ) ) ) ),file(scmpds_8,fc3_scmpds_8)).
thf(fc55_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v1_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc55_valued_0)).
thf(fc56_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) & ( v2_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v2_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc56_valued_0)).
thf(fc57_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) & ( v3_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v3_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc57_valued_0)).
thf(fc58_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ k3_numbers ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v5_relat_1 @ ( k3_relat_1 @ A @ B ) @ k3_numbers ) ) ) ),file(valued_0,fc58_valued_0)).
thf(fc59_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ k4_numbers ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v5_relat_1 @ ( k3_relat_1 @ A @ B ) @ k4_numbers ) ) ) ),file(valued_0,fc59_valued_0)).
thf(fc60_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) & ( v4_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v4_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc60_valued_0)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_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(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(fc9_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ B @ A ) ) & ( v1_funcop_1 @ ( k3_relat_1 @ B @ A ) ) ) ) ),file(funcop_1,fc9_funcop_1)).
thf(fc9_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ k5_numbers @ k5_numbers ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ k5_numbers ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ k5_numbers @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ B ) ) ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ C ) ) & ( v1_partfun1 @ ( k3_relat_1 @ A @ C ) @ k5_numbers ) ) ) ),file(nat_1,fc9_nat_1)).
thf(fc9_scmpds_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ( v3_scmpds_4 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v1_afinsq_1 @ B ) & ( v3_scmpds_4 @ B ) ) => ( ~ ( v1_xboole_0 @ ( k1_ordinal4 @ A @ B ) ) & ( v1_relat_1 @ ( k1_ordinal4 @ A @ B ) ) & ( v4_relat_1 @ ( k1_ordinal4 @ A @ B ) @ k5_numbers ) & ( v5_relat_1 @ ( k1_ordinal4 @ A @ B ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k1_ordinal4 @ A @ B ) ) & ( v1_finset_1 @ ( k1_ordinal4 @ A @ B ) ) & ( v1_afinsq_1 @ ( k1_ordinal4 @ A @ B ) ) & ( v3_scmpds_4 @ ( k1_ordinal4 @ A @ B ) ) ) ) ),file(scmpds_4,fc9_scmpds_4)).
thf(rc13_pre_poly,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ k5_numbers ) ) ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v5_relat_1 @ B @ k5_numbers ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_funct_2 @ B @ A @ k5_numbers ) & ( v1_valued_0 @ B ) & ( v2_valued_0 @ B ) & ( v3_valued_0 @ B ) & ( v4_valued_0 @ B ) & ( v2_pre_poly @ B ) ) ),file(pre_poly,rc13_pre_poly)).
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(rc2_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) ) ),file(ordinal1,rc2_ordinal1)).
thf(rc2_scmpds_5,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ( v2_compos_1 @ A @ k1_scmpds_2 ) & ( v2_scmpds_4 @ A ) & ( v3_scmpds_4 @ A ) ) ),file(scmpds_5,rc2_scmpds_5)).
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(rc4_valued_0,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ A ) ) ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v3_funct_1 @ B ) & ( v1_funct_2 @ B @ k5_numbers @ A ) ) ),file(valued_0,rc4_valued_0)).
thf(rc5_valued_0,axiom,( ! [A: $i] : ( ~ ( v2_setfam_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ k5_numbers ) & ( v1_funct_2 @ B @ k5_numbers @ A ) ) ) ),file(valued_0,rc5_valued_0)).
thf(rc6_compos_0,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_compos_0 @ A ) & ( v2_compos_0 @ A ) & ( v3_compos_0 @ A ) & ( v5_compos_0 @ A ) ) ),file(compos_0,rc6_compos_0)).
thf(free_g1_extpro_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ! [G: $i] : ( ( ( m1_subset_1 @ C @ B ) & ( v1_compos_0 @ D ) & ( v2_compos_0 @ D ) & ( v3_compos_0 @ D ) & ( v5_compos_0 @ D ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ B @ A ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) & ( v1_relat_1 @ F ) & ( v4_relat_1 @ F @ A ) & ( v1_funct_1 @ F ) & ( v1_partfun1 @ F @ A ) & ( v1_funct_1 @ G ) & ( v1_funct_2 @ G @ D @ ( k1_funct_2 @ ( k4_card_3 @ ( k3_relat_1 @ E @ F ) ) @ ( k4_card_3 @ ( k3_relat_1 @ E @ F ) ) ) ) & ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ D @ ( k1_funct_2 @ ( k4_card_3 @ ( k3_relat_1 @ E @ F ) ) @ ( k4_card_3 @ ( k3_relat_1 @ E @ F ) ) ) ) ) ) ) => ! [H: $i] : ! [I: $i] : ! [J: $i] : ! [K: $i] : ! [L: $i] : ! [M: $i] : ! [N: $i] : ( ( = @ ( g1_extpro_1 @ A @ B @ C @ D @ E @ F @ G ) @ ( g1_extpro_1 @ H @ I @ J @ K @ L @ M @ N ) ) => ( ( = @ A @ H ) & ( = @ B @ I ) & ( = @ C @ J ) & ( = @ D @ K ) & ( = @ E @ L ) & ( = @ F @ M ) & ( = @ G @ N ) ) ) ) ),file(extpro_1,g1_extpro_1)).
thf(dt_g1_extpro_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ! [G: $i] : ( ( ( m1_subset_1 @ C @ B ) & ( v1_compos_0 @ D ) & ( v2_compos_0 @ D ) & ( v3_compos_0 @ D ) & ( v5_compos_0 @ D ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ B @ A ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) & ( v1_relat_1 @ F ) & ( v4_relat_1 @ F @ A ) & ( v1_funct_1 @ F ) & ( v1_partfun1 @ F @ A ) & ( v1_funct_1 @ G ) & ( v1_funct_2 @ G @ D @ ( k1_funct_2 @ ( k4_card_3 @ ( k3_relat_1 @ E @ F ) ) @ ( k4_card_3 @ ( k3_relat_1 @ E @ F ) ) ) ) & ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ D @ ( k1_funct_2 @ ( k4_card_3 @ ( k3_relat_1 @ E @ F ) ) @ ( k4_card_3 @ ( k3_relat_1 @ E @ F ) ) ) ) ) ) ) => ( ( v1_extpro_1 @ ( g1_extpro_1 @ A @ B @ C @ D @ E @ F @ G ) @ A ) & ( l1_extpro_1 @ ( g1_extpro_1 @ A @ B @ C @ D @ E @ F @ G ) @ A ) ) ) ),file(extpro_1,g1_extpro_1)).
thf(dt_k3_numbers,axiom,( $true ),file(numbers,k3_numbers)).
thf(dt_k4_numbers,axiom,( $true ),file(numbers,k4_numbers)).
thf(dt_l2_struct_0,axiom,( ! [A: $i] : ( ( l2_struct_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(struct_0,l2_struct_0)).
thf(dt_u1_extpro_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( l1_extpro_1 @ B @ A ) => ( ( v1_funct_1 @ ( u1_extpro_1 @ A @ B ) ) & ( v1_funct_2 @ ( u1_extpro_1 @ A @ B ) @ ( u1_compos_1 @ B ) @ ( k1_funct_2 @ ( k4_card_3 @ ( k3_relat_1 @ ( u1_memstr_0 @ A @ B ) @ ( u2_memstr_0 @ A @ B ) ) ) @ ( k4_card_3 @ ( k3_relat_1 @ ( u1_memstr_0 @ A @ B ) @ ( u2_memstr_0 @ A @ B ) ) ) ) ) & ( m1_subset_1 @ ( u1_extpro_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_compos_1 @ B ) @ ( k1_funct_2 @ ( k4_card_3 @ ( k3_relat_1 @ ( u1_memstr_0 @ A @ B ) @ ( u2_memstr_0 @ A @ B ) ) ) @ ( k4_card_3 @ ( k3_relat_1 @ ( u1_memstr_0 @ A @ B ) @ ( u2_memstr_0 @ A @ B ) ) ) ) ) ) ) ) ) ),file(extpro_1,u1_extpro_1)).
thf(dt_u1_memstr_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( l1_memstr_0 @ B @ A ) => ( ( v1_funct_1 @ ( u1_memstr_0 @ A @ B ) ) & ( v1_funct_2 @ ( u1_memstr_0 @ A @ B ) @ ( u1_struct_0 @ B ) @ A ) & ( m1_subset_1 @ ( u1_memstr_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ B ) @ A ) ) ) ) ) ),file(memstr_0,u1_memstr_0)).
thf(dt_u2_memstr_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( l1_memstr_0 @ B @ A ) => ( ( v1_relat_1 @ ( u2_memstr_0 @ A @ B ) ) & ( v4_relat_1 @ ( u2_memstr_0 @ A @ B ) @ A ) & ( v1_funct_1 @ ( u2_memstr_0 @ A @ B ) ) & ( v1_partfun1 @ ( u2_memstr_0 @ A @ B ) @ A ) ) ) ),file(memstr_0,u2_memstr_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(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_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(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(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_int_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_numbers ) => ( v1_int_1 @ A ) ) ),file(int_1,cc1_int_1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc1_pboole,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_relat_1 @ B ) & ~ ( v3_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ) ) ),file(pboole,cc1_pboole)).
thf(cc2_afinsq_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_ordinal1 @ B ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v3_card_1 @ B @ A ) ) => ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v5_ordinal1 @ B ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) ) ) ) ),file(afinsq_1,cc2_afinsq_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_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_setfam_1,axiom,( ! [A: $i] : ( ~ ( v2_setfam_1 @ A ) => ~ ( v1_xboole_0 @ A ) ) ),file(setfam_1,cc2_setfam_1)).
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(cc3_afinsq_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v5_ordinal1 @ B ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v3_card_1 @ B @ A ) ) => ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v5_ordinal1 @ B ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_finset_1 @ B ) & ( v3_card_1 @ B @ A ) ) ) ) ),file(afinsq_1,cc3_afinsq_1)).
thf(cc3_compos_1,axiom,( ! [A: $i] : ( ( l1_compos_1 @ A ) => ! [B: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ ( u1_compos_1 @ A ) ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v2_compos_1 @ B @ A ) ) => ( ~ ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ ( u1_compos_1 @ A ) ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v4_compos_1 @ B @ A ) ) ) ) ),file(compos_1,cc3_compos_1)).
thf(cc3_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc3_valued_0)).
thf(cc3_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xcmplx_0 @ A ) ) ),file(xreal_0,cc3_xreal_0)).
thf(cc4_afinsq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k1_numbers ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k1_numbers ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(afinsq_1,cc4_afinsq_1)).
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_pre_poly,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_pre_poly @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) ) ),file(pre_poly,cc4_pre_poly)).
thf(cc4_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc4_valued_0)).
thf(cc4_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_afinsq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k5_numbers ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k5_numbers ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v4_valued_0 @ A ) ) ) ),file(afinsq_1,cc5_afinsq_1)).
thf(cc5_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) => ( ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ) ),file(funct_1,cc5_funct_1)).
thf(cc5_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal1,cc5_ordinal1)).
thf(cc5_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(cc7_afinsq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) ) ) ),file(afinsq_1,cc7_afinsq_1)).
thf(cc8_afinsq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) ) ),file(afinsq_1,cc8_afinsq_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_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_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(fc10_scmpds_4,axiom,( ! [A: $i] : ( ( ( v4_scmpds_4 @ A ) & ( m1_subset_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) => ( ~ ( v1_xboole_0 @ ( k3_afinsq_1 @ A ) ) & ( v1_relat_1 @ ( k3_afinsq_1 @ A ) ) & ( v4_relat_1 @ ( k3_afinsq_1 @ A ) @ k5_numbers ) & ( v5_relat_1 @ ( k3_afinsq_1 @ A ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k3_afinsq_1 @ A ) ) & ( v1_finset_1 @ ( k3_afinsq_1 @ A ) ) & ( v1_afinsq_1 @ ( k3_afinsq_1 @ A ) ) & ( v3_scmpds_4 @ ( k3_afinsq_1 @ A ) ) ) ) ),file(scmpds_4,fc10_scmpds_4)).
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_scmpds_6,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ( v2_compos_1 @ A @ k1_scmpds_2 ) & ~ ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v1_afinsq_1 @ B ) & ( v2_compos_1 @ B @ k1_scmpds_2 ) & ( v1_ami_2 @ C ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ D ) ) => ( ~ ( v1_xboole_0 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) & ( v1_relat_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) & ( v4_relat_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) @ k5_numbers ) & ( v5_relat_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) & ( v1_finset_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) & ( v1_afinsq_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) ) & ( v2_compos_1 @ ( k3_scmpds_6 @ C @ D @ A @ B ) @ k1_scmpds_2 ) ) ) ),file(scmpds_6,fc12_scmpds_6)).
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_scmpds_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v4_scmpds_4 @ A ) & ( m1_subset_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v4_scmpds_4 @ B ) & ( m1_subset_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) => ( ~ ( v1_xboole_0 @ ( k4_scmpds_4 @ A @ B ) ) & ( v1_relat_1 @ ( k4_scmpds_4 @ A @ B ) ) & ( v4_relat_1 @ ( k4_scmpds_4 @ A @ B ) @ k5_numbers ) & ( v5_relat_1 @ ( k4_scmpds_4 @ A @ B ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k4_scmpds_4 @ A @ B ) ) & ( v1_finset_1 @ ( k4_scmpds_4 @ A @ B ) ) & ( v1_afinsq_1 @ ( k4_scmpds_4 @ A @ B ) ) & ( v3_scmpds_4 @ ( k4_scmpds_4 @ A @ B ) ) ) ) ),file(scmpds_4,fc13_scmpds_4)).
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(fc15_scmpds_5,axiom,( ! [A: $i] : ( ( ( v1_scmpds_5 @ A ) & ( m1_subset_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) => ( ~ ( v1_xboole_0 @ ( k3_afinsq_1 @ A ) ) & ( v1_relat_1 @ ( k3_afinsq_1 @ A ) ) & ( v4_relat_1 @ ( k3_afinsq_1 @ A ) @ k5_numbers ) & ( v5_relat_1 @ ( k3_afinsq_1 @ A ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k3_afinsq_1 @ A ) ) & ( v1_finset_1 @ ( k3_afinsq_1 @ A ) ) & ( v1_afinsq_1 @ ( k3_afinsq_1 @ A ) ) & ( v2_scmpds_4 @ ( k3_afinsq_1 @ A ) ) ) ) ),file(scmpds_5,fc15_scmpds_5)).
thf(fc15_xreal_0,axiom,( ! [A: $i] : ( ( ~ ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) => ( ( v1_xcmplx_0 @ ( k4_xcmplx_0 @ A ) ) & ~ ( v3_xxreal_0 @ ( k4_xcmplx_0 @ A ) ) ) ) ),file(xreal_0,fc15_xreal_0)).
thf(fc16_xreal_0,axiom,( ! [A: $i] : ( ( ~ ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) => ( ( v1_xcmplx_0 @ ( k4_xcmplx_0 @ A ) ) & ~ ( v2_xxreal_0 @ ( k4_xcmplx_0 @ A ) ) ) ) ),file(xreal_0,fc16_xreal_0)).
thf(fc17_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(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(fc24_scmpds_5,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ( v2_compos_1 @ A @ k1_scmpds_2 ) & ~ ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v1_afinsq_1 @ B ) & ( v2_compos_1 @ B @ k1_scmpds_2 ) ) => ( ( v5_ordinal1 @ ( k1_ordinal4 @ A @ B ) ) & ( v1_relat_1 @ ( k1_ordinal4 @ A @ B ) ) & ( v1_funct_1 @ ( k1_ordinal4 @ A @ B ) ) & ( v2_compos_1 @ ( k1_ordinal4 @ A @ B ) @ k1_scmpds_2 ) ) ) ),file(scmpds_5,fc24_scmpds_5)).
thf(fc25_scmpds_5,axiom,( ! [A: $i] : ( ( ( v6_compos_0 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( m1_subset_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) => ( v2_compos_1 @ ( k3_afinsq_1 @ A ) @ k1_scmpds_2 ) ) ),file(scmpds_5,fc25_scmpds_5)).
thf(fc27_scmpds_5,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ( v2_compos_1 @ A @ k1_scmpds_2 ) & ( v6_compos_0 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( m1_subset_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) => ( ~ ( v1_xboole_0 @ ( k3_scmpds_4 @ A @ B ) ) & ( v1_relat_1 @ ( k3_scmpds_4 @ A @ B ) ) & ( v4_relat_1 @ ( k3_scmpds_4 @ A @ B ) @ k5_numbers ) & ( v5_relat_1 @ ( k3_scmpds_4 @ A @ B ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k3_scmpds_4 @ A @ B ) ) & ( v1_finset_1 @ ( k3_scmpds_4 @ A @ B ) ) & ( v1_afinsq_1 @ ( k3_scmpds_4 @ A @ B ) ) & ( v2_compos_1 @ ( k3_scmpds_4 @ A @ B ) @ k1_scmpds_2 ) ) ) ),file(scmpds_5,fc27_scmpds_5)).
thf(fc28_scmpds_5,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v6_compos_0 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( m1_subset_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v6_compos_0 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( m1_subset_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) => ( ~ ( v1_xboole_0 @ ( k4_scmpds_4 @ A @ B ) ) & ( v1_relat_1 @ ( k4_scmpds_4 @ A @ B ) ) & ( v4_relat_1 @ ( k4_scmpds_4 @ A @ B ) @ k5_numbers ) & ( v5_relat_1 @ ( k4_scmpds_4 @ A @ B ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k4_scmpds_4 @ A @ B ) ) & ( v1_finset_1 @ ( k4_scmpds_4 @ A @ B ) ) & ( v1_afinsq_1 @ ( k4_scmpds_4 @ A @ B ) ) & ( v2_compos_1 @ ( k4_scmpds_4 @ A @ B ) @ k1_scmpds_2 ) ) ) ),file(scmpds_5,fc28_scmpds_5)).
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(fc32_scmpds_5,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_scmpds_5 @ A ) & ( m1_subset_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v4_scmpds_4 @ B ) & ( v1_scmpds_5 @ B ) & ( m1_subset_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) => ( ~ ( v1_xboole_0 @ ( k4_scmpds_4 @ A @ B ) ) & ( v1_relat_1 @ ( k4_scmpds_4 @ A @ B ) ) & ( v4_relat_1 @ ( k4_scmpds_4 @ A @ B ) @ k5_numbers ) & ( v5_relat_1 @ ( k4_scmpds_4 @ A @ B ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k4_scmpds_4 @ A @ B ) ) & ( v1_finset_1 @ ( k4_scmpds_4 @ A @ B ) ) & ( v1_afinsq_1 @ ( k4_scmpds_4 @ A @ B ) ) & ( v2_scmpds_4 @ ( k4_scmpds_4 @ A @ B ) ) ) ) ),file(scmpds_5,fc32_scmpds_5)).
thf(fc3_numbers,axiom,( ~ ( v1_xboole_0 @ k3_numbers ) ),file(numbers,fc3_numbers)).
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_numbers,axiom,( ~ ( v1_xboole_0 @ k4_numbers ) ),file(numbers,fc4_numbers)).
thf(fc4_scmpds_8,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ( v2_compos_1 @ A @ k1_scmpds_2 ) & ( v1_ami_2 @ B ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ C ) ) => ( ~ ( v1_xboole_0 @ ( k2_scmpds_8 @ B @ C @ A ) ) & ( v1_relat_1 @ ( k2_scmpds_8 @ B @ C @ A ) ) & ( v4_relat_1 @ ( k2_scmpds_8 @ B @ C @ A ) @ k5_numbers ) & ( v5_relat_1 @ ( k2_scmpds_8 @ B @ C @ A ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k2_scmpds_8 @ B @ C @ A ) ) & ( v1_finset_1 @ ( k2_scmpds_8 @ B @ C @ A ) ) & ( v1_afinsq_1 @ ( k2_scmpds_8 @ B @ C @ A ) ) & ( v2_compos_1 @ ( k2_scmpds_8 @ B @ C @ A ) @ k1_scmpds_2 ) ) ) ),file(scmpds_8,fc4_scmpds_8)).
thf(fc5_afinsq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_relat_1 @ B ) & ( v5_ordinal1 @ B ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) ) => ( ( v1_relat_1 @ ( k1_ordinal4 @ A @ B ) ) & ( v5_ordinal1 @ ( k1_ordinal4 @ A @ B ) ) & ( v1_funct_1 @ ( k1_ordinal4 @ A @ B ) ) & ( v1_finset_1 @ ( k1_ordinal4 @ A @ B ) ) ) ) ),file(afinsq_1,fc5_afinsq_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(fc61_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_valued_0 @ A ) ) => ( v1_xcmplx_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc61_valued_0)).
thf(fc62_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) ) => ( v1_xxreal_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc62_valued_0)).
thf(fc64_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) & ( v1_funct_1 @ A ) ) => ( v1_rat_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc64_valued_0)).
thf(fc65_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) & ( v1_funct_1 @ A ) ) => ( v1_int_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc65_valued_0)).
thf(fc6_afinsq_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v5_ordinal1 @ B ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v1_relat_1 @ C ) & ( v5_relat_1 @ C @ A ) & ( v5_ordinal1 @ C ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) ) => ( ( v1_relat_1 @ ( k1_ordinal4 @ B @ C ) ) & ( v5_relat_1 @ ( k1_ordinal4 @ B @ C ) @ A ) & ( v5_ordinal1 @ ( k1_ordinal4 @ B @ C ) ) & ( v1_funct_1 @ ( k1_ordinal4 @ B @ C ) ) ) ) ),file(afinsq_1,fc6_afinsq_1)).
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(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(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(rc12_pre_poly,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) & ( v4_valued_0 @ A ) & ( v2_pre_poly @ A ) ) ),file(pre_poly,rc12_pre_poly)).
thf(rc14_pre_poly,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v4_valued_0 @ B ) & ( v2_pre_poly @ B ) ) ),file(pre_poly,rc14_pre_poly)).
thf(rc1_afinsq_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v5_ordinal1 @ B ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) ) ),file(afinsq_1,rc1_afinsq_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_int_1,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) & ( v1_xxreal_0 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_int_1 @ A ) ) ),file(int_1,rc1_int_1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc1_scmpds_5,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v6_compos_0 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v4_scmpds_4 @ A ) & ( v1_scmpds_5 @ A ) ) ),file(scmpds_5,rc1_scmpds_5)).
thf(rc1_xreal_0,axiom,( ? [A: $i] : ( v1_xreal_0 @ A ) ),file(xreal_0,rc1_xreal_0)).
thf(rc2_afinsq_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v5_ordinal1 @ B ) & ( v1_funct_1 @ B ) & ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) ) ),file(afinsq_1,rc2_afinsq_1)).
thf(rc2_compos_1,axiom,( ! [A: $i] : ( ( l1_compos_1 @ A ) => ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ ( u1_compos_1 @ A ) ) & ( v1_funct_1 @ B ) & ( v3_card_1 @ B @ np__1 ) & ( v1_afinsq_1 @ B ) ) ) ),file(compos_1,rc2_compos_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_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_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_setfam_1,axiom,( ? [A: $i] : ~ ( v2_setfam_1 @ A ) ),file(setfam_1,rc2_setfam_1)).
thf(rc2_valued_0,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) & ( v5_relat_1 @ A @ k4_numbers ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) & ( v4_valued_0 @ A ) ) ),file(valued_0,rc2_valued_0)).
thf(rc2_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_afinsq_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v5_ordinal1 @ B ) & ( v1_funct_1 @ B ) & ~ ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(afinsq_1,rc3_afinsq_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_ordinal1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v5_ordinal1 @ B ) ) ),file(ordinal1,rc3_ordinal1)).
thf(rc3_pboole,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(pboole,rc3_pboole)).
thf(rc3_scmpds_4,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v4_scmpds_4 @ A ) ) ),file(scmpds_4,rc3_scmpds_4)).
thf(rc3_setfam_1,axiom,( ! [A: $i] : ( ~ ( v2_setfam_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ A ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(setfam_1,rc3_setfam_1)).
thf(rc3_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_afinsq_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v5_ordinal1 @ B ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v3_card_1 @ B @ A ) ) ) ),file(afinsq_1,rc4_afinsq_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_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_valued_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v3_card_1 @ A @ np__1 ) ) ),file(valued_1,rc4_valued_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(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_valued_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v5_relat_1 @ B @ k3_numbers ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_valued_0 @ B ) & ( v2_valued_0 @ B ) & ( v3_valued_0 @ B ) & ( v4_valued_0 @ B ) ) ),file(valued_1,rc5_valued_1)).
thf(rc6_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 ) ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v5_funct_1 @ C @ B ) & ( v1_partfun1 @ C @ A ) ) ) ),file(pboole,rc6_pboole)).
thf(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(rc7_pre_poly,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_pre_poly @ A ) ) ),file(pre_poly,rc7_pre_poly)).
thf(rc8_pre_poly,axiom,( ? [A: $i] : ( ( v4_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(pre_poly,rc8_pre_poly)).
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_afinsq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) => ( = @ ( k1_ordinal4 @ A @ k1_xboole_0 ) @ A ) ) ),file(afinsq_1,rd1_afinsq_1)).
thf(rd2_afinsq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) => ( = @ ( k1_ordinal4 @ k1_xboole_0 @ A ) @ A ) ) ),file(afinsq_1,rd2_afinsq_1)).
thf(abstractness_v1_extpro_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( l1_extpro_1 @ B @ A ) => ( ( v1_extpro_1 @ B @ A ) => ( = @ B @ ( g1_extpro_1 @ A @ ( u1_struct_0 @ B ) @ ( u2_struct_0 @ B ) @ ( u1_compos_1 @ B ) @ ( u1_memstr_0 @ A @ B ) @ ( u2_memstr_0 @ A @ B ) @ ( u1_extpro_1 @ A @ B ) ) ) ) ) ),file(extpro_1,v1_extpro_1)).
thf(dt_k1_ordinal4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v5_ordinal1 @ B ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ ( k1_ordinal4 @ A @ B ) ) & ( v5_ordinal1 @ ( k1_ordinal4 @ A @ B ) ) & ( v1_funct_1 @ ( k1_ordinal4 @ A @ B ) ) ) ) ),file(ordinal4,k1_ordinal4)).
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_k3_afinsq_1,axiom,( $true ),file(afinsq_1,k3_afinsq_1)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(dt_l1_compos_1,axiom,( $true ),file(compos_1,l1_compos_1)).
thf(dt_l1_extpro_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( l1_extpro_1 @ B @ A ) => ( ( l1_memstr_0 @ B @ A ) & ( l1_compos_1 @ B ) ) ) ),file(extpro_1,l1_extpro_1)).
thf(dt_l1_memstr_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( l1_memstr_0 @ B @ A ) => ( l2_struct_0 @ B ) ) ),file(memstr_0,l1_memstr_0)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(cc12_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v3_valued_0 @ B ) ) ) ),file(valued_0,cc12_valued_0)).
thf(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_afinsq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) ) ) ),file(afinsq_1,cc1_afinsq_1)).
thf(cc1_ami_3,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) => ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) & ~ ( v1_setfam_1 @ A ) ) ) ),file(ami_3,cc1_ami_3)).
thf(cc1_compos_0,axiom,( ! [A: $i] : ( ( v1_compos_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(compos_0,cc1_compos_0)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_1)).
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_memstr_0,axiom,( ! [A: $i] : ( ~ ( v1_setfam_1 @ A ) => ~ ( v1_xboole_0 @ A ) ) ),file(memstr_0,cc1_memstr_0)).
thf(cc1_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) ) ),file(nat_1,cc1_nat_1)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_1)).
thf(cc1_setfam_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_setfam_1 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ~ ( v1_xboole_0 @ B ) ) ) ),file(setfam_1,cc1_setfam_1)).
thf(cc1_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) ) ),file(valued_0,cc1_valued_0)).
thf(cc1_xreal_0,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc1_xreal_0)).
thf(cc2_compos_0,axiom,( ! [A: $i] : ( ( v5_compos_0 @ A ) => ~ ( v1_xboole_0 @ A ) ) ),file(compos_0,cc2_compos_0)).
thf(cc2_compos_1,axiom,( ! [A: $i] : ( ( l1_compos_1 @ A ) => ! [B: $i] : ( ( ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ ( u1_compos_1 @ A ) ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) ) => ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ ( u1_compos_1 @ A ) ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v2_compos_1 @ B @ A ) ) ) ) ),file(compos_1,cc2_compos_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_int_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_int_1 @ A ) ) ),file(int_1,cc2_int_1)).
thf(cc2_memstr_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_setfam_1 @ A ) & ( l1_memstr_0 @ B @ A ) ) => ! [C: $i] : ( ( ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ ( u1_struct_0 @ B ) ) & ( v1_funct_1 @ C ) & ( v5_funct_1 @ C @ ( k2_memstr_0 @ A @ B ) ) ) => ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ ( u1_struct_0 @ B ) ) & ( v1_funct_1 @ C ) & ( v5_funct_1 @ C @ ( k2_memstr_0 @ A @ B ) ) & ( v4_memstr_0 @ C @ A @ B ) ) ) ) ),file(memstr_0,cc2_memstr_0)).
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_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_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_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_int_1,axiom,( ! [A: $i] : ( ( v1_int_1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(int_1,cc3_int_1)).
thf(cc3_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v7_ordinal1 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(nat_1,cc3_nat_1)).
thf(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
thf(cc3_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) ) ) ),file(relat_1,cc3_relat_1)).
thf(cc3_setfam_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_setfam_1 @ A ) ) => ~ ( v2_setfam_1 @ A ) ) ),file(setfam_1,cc3_setfam_1)).
thf(cc3_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_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_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
thf(cc4_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ) ),file(relat_1,cc4_relat_1)).
thf(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_pre_poly,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_pre_poly @ A ) ) ) ),file(pre_poly,cc5_pre_poly)).
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_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_afinsq_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_afinsq_1 @ A ) ) ) ),file(afinsq_1,cc6_afinsq_1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(cc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) => ( v5_relat_1 @ C @ A ) ) ) ),file(relat_1,cc6_relat_1)).
thf(cc6_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_valued_0 @ A ) ) ) ),file(valued_0,cc6_valued_0)).
thf(cc6_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_pre_poly,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_pre_poly @ A ) ) ) ),file(pre_poly,cc7_pre_poly)).
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_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) ) ),file(valued_0,cc7_valued_0)).
thf(cc7_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) => ( ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc7_xxreal_0)).
thf(cc8_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
thf(cc8_pre_poly,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v2_pre_poly @ B ) ) ) ) ),file(pre_poly,cc8_pre_poly)).
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_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(cc9_afinsq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) ) ) ),file(afinsq_1,cc9_afinsq_1)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
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(fc10_scmpds_5,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_ami_2 @ B ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ C ) & ( v1_int_1 @ D ) ) => ( v6_compos_0 @ ( k13_scmpds_2 @ A @ B @ C @ D ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) ),file(scmpds_5,fc10_scmpds_5)).
thf(fc13_afinsq_1,axiom,( ! [A: $i] : ( v3_card_1 @ ( k3_afinsq_1 @ A ) @ np__1 ) ),file(afinsq_1,fc13_afinsq_1)).
thf(fc13_scmpds_5,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_ami_2 @ B ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ C ) & ( v1_int_1 @ D ) ) => ( v6_compos_0 @ ( k16_scmpds_2 @ A @ B @ C @ D ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) ),file(scmpds_5,fc13_scmpds_5)).
thf(fc17_afinsq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) ) => ( v5_relat_1 @ ( k3_afinsq_1 @ B ) @ A ) ) ),file(afinsq_1,fc17_afinsq_1)).
thf(fc17_scmpds_5,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ B ) & ( v1_int_1 @ C ) ) => ( v1_scmpds_5 @ ( k10_scmpds_2 @ A @ B @ C ) ) ) ),file(scmpds_5,fc17_scmpds_5)).
thf(fc18_scmpds_5,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ B ) & ( v1_int_1 @ C ) ) => ( v1_scmpds_5 @ ( k11_scmpds_2 @ A @ B @ C ) ) ) ),file(scmpds_5,fc18_scmpds_5)).
thf(fc1_int_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ( v1_int_1 @ B ) ) => ( v1_int_1 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(int_1,fc1_int_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_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc20_scmpds_5,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_ami_2 @ B ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ C ) & ( v1_int_1 @ D ) ) => ( v1_scmpds_5 @ ( k13_scmpds_2 @ A @ B @ C @ D ) ) ) ),file(scmpds_5,fc20_scmpds_5)).
thf(fc23_scmpds_5,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_ami_2 @ B ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ C ) & ( v1_int_1 @ D ) ) => ( v1_scmpds_5 @ ( k16_scmpds_2 @ A @ B @ C @ D ) ) ) ),file(scmpds_5,fc23_scmpds_5)).
thf(fc2_scmpds_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ B ) & ( v1_int_1 @ C ) ) => ( v4_scmpds_4 @ ( k10_scmpds_2 @ A @ B @ C ) ) ) ),file(scmpds_4,fc2_scmpds_4)).
thf(fc3_afinsq_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k3_afinsq_1 @ A ) ) ),file(afinsq_1,fc3_afinsq_1)).
thf(fc3_int_1,axiom,( ! [A: $i] : ( ( v1_int_1 @ A ) => ( ( v1_xcmplx_0 @ ( k4_xcmplx_0 @ A ) ) & ( v1_int_1 @ ( k4_xcmplx_0 @ A ) ) ) ) ),file(int_1,fc3_int_1)).
thf(fc3_memstr_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_setfam_1 @ A ) & ( v2_memstr_0 @ B @ A ) & ( l1_memstr_0 @ B @ A ) ) => ( ( v1_relat_1 @ ( k2_memstr_0 @ A @ B ) ) & ( v2_relat_1 @ ( k2_memstr_0 @ A @ B ) ) & ( v4_relat_1 @ ( k2_memstr_0 @ A @ B ) @ ( u1_struct_0 @ B ) ) & ( v1_funct_1 @ ( k2_memstr_0 @ A @ B ) ) & ( v1_partfun1 @ ( k2_memstr_0 @ A @ B ) @ ( u1_struct_0 @ B ) ) ) ) ),file(memstr_0,fc3_memstr_0)).
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_scmpds_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v5_funct_1 @ A @ ( k2_memstr_0 @ np__2 @ k1_scmpds_2 ) ) & ( v1_partfun1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_ami_2 @ B ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) ) => ( v1_int_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(scmpds_2,fc3_scmpds_2)).
thf(fc3_scmpds_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ B ) & ( v1_int_1 @ C ) ) => ( v4_scmpds_4 @ ( k11_scmpds_2 @ A @ B @ C ) ) ) ),file(scmpds_4,fc3_scmpds_4)).
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(fc5_scmpds_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_ami_2 @ B ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ C ) & ( v1_int_1 @ D ) ) => ( v4_scmpds_4 @ ( k13_scmpds_2 @ A @ B @ C @ D ) ) ) ),file(scmpds_4,fc5_scmpds_4)).
thf(fc63_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_valued_0 @ A ) ) => ( v1_xreal_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc63_valued_0)).
thf(fc66_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v4_valued_0 @ A ) ) => ( v7_ordinal1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc66_valued_0)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
thf(fc7_afinsq_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ ( k3_afinsq_1 @ A ) ) & ( v1_funct_1 @ ( k3_afinsq_1 @ A ) ) ) ),file(afinsq_1,fc7_afinsq_1)).
thf(fc7_scmpds_5,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ B ) & ( v1_int_1 @ C ) ) => ( v6_compos_0 @ ( k10_scmpds_2 @ A @ B @ C ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) ),file(scmpds_5,fc7_scmpds_5)).
thf(fc8_afinsq_1,axiom,( ! [A: $i] : ( ( v5_ordinal1 @ ( k3_afinsq_1 @ A ) ) & ( v1_finset_1 @ ( k3_afinsq_1 @ A ) ) ) ),file(afinsq_1,fc8_afinsq_1)).
thf(fc8_scmpds_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_ami_2 @ B ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ C ) & ( v1_int_1 @ D ) ) => ( v4_scmpds_4 @ ( k16_scmpds_2 @ A @ B @ C @ D ) ) ) ),file(scmpds_4,fc8_scmpds_4)).
thf(fc8_scmpds_5,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ B ) & ( v1_int_1 @ C ) ) => ( v6_compos_0 @ ( k11_scmpds_2 @ A @ B @ C ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) ),file(scmpds_5,fc8_scmpds_5)).
thf(rc10_extpro_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_setfam_1 @ A ) ) => ? [B: $i] : ( ( l1_extpro_1 @ B @ A ) & ~ ( v2_struct_0 @ B ) & ( v3_memstr_0 @ B @ A ) ) ) ),file(extpro_1,rc10_extpro_1)).
thf(rc1_compos_0,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_compos_0 @ A ) ) ),file(compos_0,rc1_compos_0)).
thf(rc1_extpro_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( l1_extpro_1 @ B @ A ) & ( v1_extpro_1 @ B @ A ) ) ),file(extpro_1,rc1_extpro_1)).
thf(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_1)).
thf(rc1_scmpds_2,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_ami_2 @ A ) ) ),file(scmpds_2,rc1_scmpds_2)).
thf(rc1_setfam_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_setfam_1 @ A ) ) ),file(setfam_1,rc1_setfam_1)).
thf(rc1_valued_0,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v4_valued_0 @ A ) ) ),file(valued_0,rc1_valued_0)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc1_xxreal_0,axiom,( ? [A: $i] : ( v1_xxreal_0 @ A ) ),file(xxreal_0,rc1_xxreal_0)).
thf(rc2_compos_0,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_compos_0 @ A ) & ( v2_compos_0 @ A ) & ( v3_compos_0 @ A ) ) ),file(compos_0,rc2_compos_0)).
thf(rc2_extpro_1,axiom,( ! [A: $i] : ( ~ ( v1_setfam_1 @ A ) => ? [B: $i] : ( ( l1_extpro_1 @ B @ A ) & ~ ( v2_struct_0 @ B ) ) ) ),file(extpro_1,rc2_extpro_1)).
thf(rc2_int_1,axiom,( ? [A: $i] : ( v1_int_1 @ A ) ),file(int_1,rc2_int_1)).
thf(rc2_valued_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) ) ),file(valued_1,rc2_valued_1)).
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_compos_0,axiom,( ? [A: $i] : ( ( v1_compos_0 @ A ) & ( v5_compos_0 @ A ) ) ),file(compos_0,rc3_compos_0)).
thf(rc3_memstr_0,axiom,( ! [A: $i] : ( ~ ( v1_setfam_1 @ A ) => ? [B: $i] : ( ( l1_memstr_0 @ B @ A ) & ( v2_memstr_0 @ B @ A ) ) ) ),file(memstr_0,rc3_memstr_0)).
thf(rc3_valued_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 ) ) ),file(valued_1,rc3_valued_1)).
thf(rc4_compos_0,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_compos_0 @ A ) & ( v2_compos_0 @ A ) & ( v3_compos_0 @ A ) & ( v5_compos_0 @ A ) ) ),file(compos_0,rc4_compos_0)).
thf(rc4_extpro_1,axiom,( ! [A: $i] : ( ~ ( v1_setfam_1 @ A ) => ? [B: $i] : ( ( l1_extpro_1 @ B @ A ) & ~ ( v2_struct_0 @ B ) & ( v2_memstr_0 @ B @ A ) & ( v3_extpro_1 @ B @ A ) ) ) ),file(extpro_1,rc4_extpro_1)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(rc4_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,rc4_xxreal_0)).
thf(rc5_memstr_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_setfam_1 @ A ) & ( l1_memstr_0 @ B @ A ) ) => ? [C: $i] : ( ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ ( u1_struct_0 @ B ) ) & ( v1_funct_1 @ C ) & ( v5_funct_1 @ C @ ( k2_memstr_0 @ A @ B ) ) ) ) ),file(memstr_0,rc5_memstr_0)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(rc6_memstr_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_setfam_1 @ A ) & ~ ( v2_struct_0 @ B ) & ( v2_memstr_0 @ B @ A ) & ( v3_memstr_0 @ B @ A ) & ( l1_memstr_0 @ B @ A ) & ( v7_ordinal1 @ C ) ) => ? [D: $i] : ( ~ ( v1_xboole_0 @ D ) & ( v1_relat_1 @ D ) & ( v4_relat_1 @ D @ ( u1_struct_0 @ B ) ) & ( v1_funct_1 @ D ) & ( v5_funct_1 @ D @ ( k2_memstr_0 @ A @ B ) ) & ( v1_partfun1 @ D @ ( u1_struct_0 @ B ) ) & ( v5_memstr_0 @ D @ A @ B @ C ) ) ) ),file(memstr_0,rc6_memstr_0)).
thf(rc6_valued_0,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v4_valued_0 @ B ) ) ),file(valued_0,rc6_valued_0)).
thf(rc7_memstr_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_setfam_1 @ A ) & ~ ( v2_struct_0 @ B ) & ( v2_memstr_0 @ B @ A ) & ( v3_memstr_0 @ B @ A ) & ( l1_memstr_0 @ B @ A ) ) => ? [C: $i] : ( ~ ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ ( u1_struct_0 @ B ) ) & ( v1_funct_1 @ C ) & ( v5_funct_1 @ C @ ( k2_memstr_0 @ A @ B ) ) ) ) ),file(memstr_0,rc7_memstr_0)).
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_extpro_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_setfam_1 @ A ) ) => ? [B: $i] : ( ( l1_extpro_1 @ B @ A ) & ~ ( v2_struct_0 @ B ) & ( v2_memstr_0 @ B @ A ) & ( v3_memstr_0 @ B @ A ) & ( v1_extpro_1 @ B @ A ) & ( v3_extpro_1 @ B @ A ) ) ) ),file(extpro_1,rc8_extpro_1)).
thf(rc8_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ? [C: $i] : ( ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v5_funct_1 @ C @ B ) ) ) ),file(funct_1,rc8_funct_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_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(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(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_k1_scmpds_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v1_afinsq_1 @ B ) ) => ( = @ ( k1_scmpds_4 @ A @ B ) @ ( k1_ordinal4 @ A @ B ) ) ) ),file(scmpds_4,k1_scmpds_4)).
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_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_k9_compos_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_compos_1 @ A ) & ( m1_subset_1 @ B @ ( u1_compos_1 @ A ) ) ) => ( = @ ( k9_compos_1 @ A @ B ) @ ( k3_afinsq_1 @ B ) ) ) ),file(compos_1,k9_compos_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_k10_scmpds_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ B ) & ( v1_int_1 @ C ) ) => ( m1_subset_1 @ ( k10_scmpds_2 @ A @ B @ C ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) ),file(scmpds_2,k10_scmpds_2)).
thf(dt_k11_scmpds_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ B ) & ( v1_int_1 @ C ) ) => ( m1_subset_1 @ ( k11_scmpds_2 @ A @ B @ C ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) ),file(scmpds_2,k11_scmpds_2)).
thf(dt_k13_scmpds_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_ami_2 @ B ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ C ) & ( v1_int_1 @ D ) ) => ( m1_subset_1 @ ( k13_scmpds_2 @ A @ B @ C @ D ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) ),file(scmpds_2,k13_scmpds_2)).
thf(dt_k16_scmpds_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_ami_2 @ B ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ C ) & ( v1_int_1 @ D ) ) => ( m1_subset_1 @ ( k16_scmpds_2 @ A @ B @ C @ D ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) ),file(scmpds_2,k16_scmpds_2)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k1_scmp_gcd,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v1_ami_2 @ ( k1_scmp_gcd @ A ) ) & ( m1_subset_1 @ ( k1_scmp_gcd @ A ) @ ( u1_struct_0 @ k1_scmpds_2 ) ) ) ) ),file(scmp_gcd,k1_scmp_gcd)).
thf(dt_k1_scmpds_2,axiom,( ( v1_extpro_1 @ k1_scmpds_2 @ np__2 ) & ( l1_extpro_1 @ k1_scmpds_2 @ np__2 ) ),file(scmpds_2,k1_scmpds_2)).
thf(dt_k1_scmpds_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v1_afinsq_1 @ B ) ) => ( ~ ( v1_xboole_0 @ ( k1_scmpds_4 @ A @ B ) ) & ( v1_relat_1 @ ( k1_scmpds_4 @ A @ B ) ) & ( v4_relat_1 @ ( k1_scmpds_4 @ A @ B ) @ k5_numbers ) & ( v5_relat_1 @ ( k1_scmpds_4 @ A @ B ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k1_scmpds_4 @ A @ B ) ) & ( v1_finset_1 @ ( k1_scmpds_4 @ A @ B ) ) & ( v1_afinsq_1 @ ( k1_scmpds_4 @ A @ B ) ) ) ) ),file(scmpds_4,k1_scmpds_4)).
thf(dt_k2_memstr_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_setfam_1 @ A ) & ( l1_memstr_0 @ B @ A ) ) => ( ( v1_relat_1 @ ( k2_memstr_0 @ A @ B ) ) & ( v4_relat_1 @ ( k2_memstr_0 @ A @ B ) @ ( u1_struct_0 @ B ) ) & ( v1_funct_1 @ ( k2_memstr_0 @ A @ B ) ) & ( v1_partfun1 @ ( k2_memstr_0 @ A @ B ) @ ( u1_struct_0 @ B ) ) ) ) ),file(memstr_0,k2_memstr_0)).
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_scmp_gcd,axiom,( ( v1_ami_2 @ k2_scmp_gcd ) & ( m1_subset_1 @ k2_scmp_gcd @ ( u1_struct_0 @ k1_scmpds_2 ) ) ),file(scmp_gcd,k2_scmp_gcd)).
thf(dt_k2_scmpds_8,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ B ) & ~ ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ k5_numbers ) & ( v5_relat_1 @ C @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) & ( v1_afinsq_1 @ C ) ) => ( ~ ( v1_xboole_0 @ ( k2_scmpds_8 @ A @ B @ C ) ) & ( v1_relat_1 @ ( k2_scmpds_8 @ A @ B @ C ) ) & ( v4_relat_1 @ ( k2_scmpds_8 @ A @ B @ C ) @ k5_numbers ) & ( v5_relat_1 @ ( k2_scmpds_8 @ A @ B @ C ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k2_scmpds_8 @ A @ B @ C ) ) & ( v1_finset_1 @ ( k2_scmpds_8 @ A @ B @ C ) ) & ( v1_afinsq_1 @ ( k2_scmpds_8 @ A @ B @ C ) ) ) ) ),file(scmpds_8,k2_scmpds_8)).
thf(dt_k2_xcmplx_0,axiom,( $true ),file(xcmplx_0,k2_xcmplx_0)).
thf(dt_k3_scmpds_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ( m1_subset_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) => ( ~ ( v1_xboole_0 @ ( k3_scmpds_4 @ A @ B ) ) & ( v1_relat_1 @ ( k3_scmpds_4 @ A @ B ) ) & ( v4_relat_1 @ ( k3_scmpds_4 @ A @ B ) @ k5_numbers ) & ( v5_relat_1 @ ( k3_scmpds_4 @ A @ B ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k3_scmpds_4 @ A @ B ) ) & ( v1_finset_1 @ ( k3_scmpds_4 @ A @ B ) ) & ( v1_afinsq_1 @ ( k3_scmpds_4 @ A @ B ) ) ) ) ),file(scmpds_4,k3_scmpds_4)).
thf(dt_k3_scmpds_6,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_int_1 @ B ) & ~ ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ k5_numbers ) & ( v5_relat_1 @ C @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) & ( v1_afinsq_1 @ C ) & ~ ( v1_xboole_0 @ D ) & ( v1_relat_1 @ D ) & ( v4_relat_1 @ D @ k5_numbers ) & ( v5_relat_1 @ D @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ D ) & ( v1_finset_1 @ D ) & ( v1_afinsq_1 @ D ) ) => ( ~ ( v1_xboole_0 @ ( k3_scmpds_6 @ A @ B @ C @ D ) ) & ( v1_relat_1 @ ( k3_scmpds_6 @ A @ B @ C @ D ) ) & ( v4_relat_1 @ ( k3_scmpds_6 @ A @ B @ C @ D ) @ k5_numbers ) & ( v5_relat_1 @ ( k3_scmpds_6 @ A @ B @ C @ D ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k3_scmpds_6 @ A @ B @ C @ D ) ) & ( v1_finset_1 @ ( k3_scmpds_6 @ A @ B @ C @ D ) ) & ( v1_afinsq_1 @ ( k3_scmpds_6 @ A @ B @ C @ D ) ) ) ) ),file(scmpds_6,k3_scmpds_6)).
thf(dt_k4_scmpds_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( m1_subset_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) => ( ~ ( v1_xboole_0 @ ( k4_scmpds_4 @ A @ B ) ) & ( v1_relat_1 @ ( k4_scmpds_4 @ A @ B ) ) & ( v4_relat_1 @ ( k4_scmpds_4 @ A @ B ) @ k5_numbers ) & ( v5_relat_1 @ ( k4_scmpds_4 @ A @ B ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k4_scmpds_4 @ A @ B ) ) & ( v1_finset_1 @ ( k4_scmpds_4 @ A @ B ) ) & ( v1_afinsq_1 @ ( k4_scmpds_4 @ A @ B ) ) ) ) ),file(scmpds_4,k4_scmpds_4)).
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_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_k6_scmpds_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_afinsq_1 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ B ) & ( v5_funct_1 @ B @ ( k2_memstr_0 @ np__2 @ k1_scmpds_2 ) ) & ( v1_partfun1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ k5_numbers ) & ( v5_relat_1 @ C @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ k5_numbers ) ) => ( ( v1_relat_1 @ ( k6_scmpds_4 @ A @ B @ C ) ) & ( v4_relat_1 @ ( k6_scmpds_4 @ A @ B @ C ) @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ ( k6_scmpds_4 @ A @ B @ C ) ) & ( v5_funct_1 @ ( k6_scmpds_4 @ A @ B @ C ) @ ( k2_memstr_0 @ np__2 @ k1_scmpds_2 ) ) & ( v1_partfun1 @ ( k6_scmpds_4 @ A @ B @ C ) @ ( u1_struct_0 @ k1_scmpds_2 ) ) ) ) ),file(scmpds_4,k6_scmpds_4)).
thf(dt_k9_compos_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_compos_1 @ A ) & ( m1_subset_1 @ B @ ( u1_compos_1 @ A ) ) ) => ( ( v1_relat_1 @ ( k9_compos_1 @ A @ B ) ) & ( v4_relat_1 @ ( k9_compos_1 @ A @ B ) @ k5_numbers ) & ( v5_relat_1 @ ( k9_compos_1 @ A @ B ) @ ( u1_compos_1 @ A ) ) & ( v1_funct_1 @ ( k9_compos_1 @ A @ B ) ) & ( v1_finset_1 @ ( k9_compos_1 @ A @ B ) ) ) ) ),file(compos_1,k9_compos_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_compos_1,axiom,( ! [A: $i] : ( ( l1_compos_1 @ A ) => ( ( v1_compos_0 @ ( u1_compos_1 @ A ) ) & ( v2_compos_0 @ ( u1_compos_1 @ A ) ) & ( v3_compos_0 @ ( u1_compos_1 @ A ) ) & ( v5_compos_0 @ ( u1_compos_1 @ A ) ) ) ) ),file(compos_1,u1_compos_1)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_c4_19__scpqsort,axiom,( m2_subset_1 @ c4_19__scpqsort @ k1_numbers @ k5_numbers ),file(scpqsort,c4_19__scpqsort)).
thf(dt_c5_19__scpqsort,axiom,( m2_subset_1 @ c5_19__scpqsort @ k1_numbers @ k5_numbers ),file(scpqsort,c5_19__scpqsort)).
thf(cc10_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( v5_funct_1 @ C @ B ) ) => ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) ) ) ) ),file(funct_1,cc10_funct_1)).
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(fc1_numbers,axiom,( ~ ( v1_xboole_0 @ k1_numbers ) ),file(numbers,fc1_numbers)).
thf(fc1_scmpds_2,axiom,( ~ ( v2_struct_0 @ k1_scmpds_2 ) & ( v1_extpro_1 @ k1_scmpds_2 @ np__2 ) ),file(scmpds_2,fc1_scmpds_2)).
thf(fc1_scmpds_3,axiom,( ( v1_extpro_1 @ k1_scmpds_2 @ np__2 ) & ( v3_amistd_5 @ k1_scmpds_2 @ np__2 ) ),file(scmpds_3,fc1_scmpds_3)).
thf(fc2_scmpds_2,axiom,( ( v2_memstr_0 @ k1_scmpds_2 @ np__2 ) & ( v3_memstr_0 @ k1_scmpds_2 @ np__2 ) & ( v1_extpro_1 @ k1_scmpds_2 @ np__2 ) ),file(scmpds_2,fc2_scmpds_2)).
thf(fc2_scmpds_3,axiom,( ( v1_extpro_1 @ k1_scmpds_2 @ np__2 ) & ( v4_amistd_5 @ k1_scmpds_2 @ np__2 ) ),file(scmpds_3,fc2_scmpds_3)).
thf(fc4_scmpds_2,axiom,( ( v1_extpro_1 @ k1_scmpds_2 @ np__2 ) & ( v3_extpro_1 @ k1_scmpds_2 @ np__2 ) ),file(scmpds_2,fc4_scmpds_2)).
thf(fc8_numbers,axiom,( ~ ( v1_finset_1 @ k1_numbers ) ),file(numbers,fc8_numbers)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
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(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(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(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_numerals,axiom,( ( v2_xxreal_0 @ np__2 ) & ( m2_subset_1 @ np__2 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__2 @ k5_numbers ) & ( m1_subset_1 @ np__2 @ k1_numbers ) ),file(numerals,spc2_numerals)).
thf(spc3_numerals,axiom,( ( v2_xxreal_0 @ np__3 ) & ( m2_subset_1 @ np__3 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__3 @ k5_numbers ) & ( m1_subset_1 @ np__3 @ k1_numbers ) ),file(numerals,spc3_numerals)).
thf(spc4_numerals,axiom,( ( v2_xxreal_0 @ np__4 ) & ( m2_subset_1 @ np__4 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__4 @ k5_numbers ) & ( m1_subset_1 @ np__4 @ k1_numbers ) ),file(numerals,spc4_numerals)).
thf(spc5_numerals,axiom,( ( v2_xxreal_0 @ np__5 ) & ( m2_subset_1 @ np__5 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__5 @ k5_numbers ) & ( m1_subset_1 @ np__5 @ k1_numbers ) ),file(numerals,spc5_numerals)).
thf(spc6_numerals,axiom,( ( v2_xxreal_0 @ np__6 ) & ( m2_subset_1 @ np__6 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__6 @ k5_numbers ) & ( m1_subset_1 @ np__6 @ k1_numbers ) ),file(numerals,spc6_numerals)).
thf(spc7_numerals,axiom,( ( v2_xxreal_0 @ np__7 ) & ( m2_subset_1 @ np__7 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__7 @ k5_numbers ) & ( m1_subset_1 @ np__7 @ k1_numbers ) ),file(numerals,spc7_numerals)).
thf(spc8_numerals,axiom,( ( v2_xxreal_0 @ np__8 ) & ( m2_subset_1 @ np__8 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__8 @ k5_numbers ) & ( m1_subset_1 @ np__8 @ k1_numbers ) ),file(numerals,spc8_numerals)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(spc2_boole,axiom,( ~ ( v1_xboole_0 @ np__2 ) ),file(boole,spc2_boole)).
thf(spc3_boole,axiom,( ~ ( v1_xboole_0 @ np__3 ) ),file(boole,spc3_boole)).
thf(spc4_boole,axiom,( ~ ( v1_xboole_0 @ np__4 ) ),file(boole,spc4_boole)).
thf(spc5_boole,axiom,( ~ ( v1_xboole_0 @ np__5 ) ),file(boole,spc5_boole)).
thf(spc6_boole,axiom,( ~ ( v1_xboole_0 @ np__6 ) ),file(boole,spc6_boole)).
thf(spc7_boole,axiom,( ~ ( v1_xboole_0 @ np__7 ) ),file(boole,spc7_boole)).
thf(spc8_boole,axiom,( ~ ( v1_xboole_0 @ np__8 ) ),file(boole,spc8_boole)).
thf(e11_19__scpqsort,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ A ) & ( v5_funct_1 @ A @ ( k2_memstr_0 @ np__2 @ k1_scmpds_2 ) ) & ( v1_partfun1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v5_memstr_0 @ A @ np__2 @ k1_scmpds_2 @ k6_numbers ) ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ k5_numbers ) ) => ( ( ( = @ ( k1_funct_1 @ A @ k2_scmp_gcd ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ A @ ( k1_scmp_gcd @ np__5 ) ) @ ( k2_nat_1 @ k6_numbers @ np__1 ) ) & ( = @ ( k1_funct_1 @ A @ ( k1_scmp_gcd @ np__4 ) ) @ ( k2_xcmplx_0 @ c4_19__scpqsort @ ( k1_funct_1 @ A @ ( k1_scmp_gcd @ np__5 ) ) ) ) & ( = @ ( k1_funct_1 @ A @ ( k1_scmp_gcd @ np__2 ) ) @ c5_19__scpqsort ) ) => ( ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ A @ B ) @ k2_scmp_gcd ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ A @ B ) @ ( k1_scmp_gcd @ np__1 ) ) @ ( k1_funct_1 @ A @ ( k1_scmp_gcd @ np__1 ) ) ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ A @ B ) @ ( k1_scmp_gcd @ np__5 ) ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ A @ B ) @ ( k1_scmp_gcd @ np__2 ) ) @ ( k1_funct_1 @ A @ ( k1_scmp_gcd @ np__2 ) ) ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ A @ B ) @ ( k1_scmp_gcd @ np__3 ) ) @ ( k1_funct_1 @ A @ ( k1_scmp_gcd @ np__3 ) ) ) & ! [C: $i] : ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers ) => ( ( r1_xxreal_0 @ np__8 @ C ) => ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ A @ B ) @ ( k1_scmp_gcd @ C ) ) @ ( k1_funct_1 @ A @ ( k1_scmp_gcd @ C ) ) ) ) ) & ? [C: $i] : ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers ) & ( = @ C @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ A @ B ) @ ( k1_scmp_gcd @ np__7 ) ) ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ A @ B ) @ ( k1_scmp_gcd @ np__4 ) ) @ ( k2_nat_1 @ c4_19__scpqsort @ C ) ) & ( r1_xxreal_0 @ C @ ( k1_funct_1 @ A @ ( k1_scmp_gcd @ np__5 ) ) ) & ! [D: $i] : ( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers ) => ~ ( ~ ( r1_xxreal_0 @ D @ ( k2_nat_1 @ c4_19__scpqsort @ C ) ) & ( r1_xxreal_0 @ D @ ( k1_funct_1 @ A @ ( k1_scmp_gcd @ np__4 ) ) ) & ( r1_xxreal_0 @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ A @ B ) @ ( k1_scmp_gcd @ D ) ) @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ A @ B ) @ ( k1_scmp_gcd @ c5_19__scpqsort ) ) ) ) ) & ( ( = @ C @ k6_numbers ) | ( r1_xxreal_0 @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ A @ B ) @ ( k1_scmp_gcd @ ( k2_nat_1 @ c4_19__scpqsort @ C ) ) ) @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ A @ B ) @ ( k1_scmp_gcd @ c5_19__scpqsort ) ) ) ) ) ) ) ) ) ),file(scpqsort,e11_19__scpqsort)).
thf(e10_19__scpqsort,axiom,( ! [A: $i] : ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers ) => ( ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ B ) & ( v5_funct_1 @ B @ ( k2_memstr_0 @ np__2 @ k1_scmpds_2 ) ) & ( v1_partfun1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v5_memstr_0 @ B @ np__2 @ k1_scmpds_2 @ k6_numbers ) ) => ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ k5_numbers ) & ( v5_relat_1 @ C @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ k5_numbers ) ) => ( ( ( = @ ( k1_funct_1 @ B @ k2_scmp_gcd ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__5 ) ) @ ( k2_nat_1 @ A @ np__1 ) ) & ( = @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__4 ) ) @ ( k2_xcmplx_0 @ c4_19__scpqsort @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__5 ) ) ) ) & ( = @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__2 ) ) @ c5_19__scpqsort ) ) => ( ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ k2_scmp_gcd ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__1 ) ) @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__1 ) ) ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__5 ) ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__2 ) ) @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__2 ) ) ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__3 ) ) @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__3 ) ) ) & ! [D: $i] : ( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers ) => ( ( r1_xxreal_0 @ np__8 @ D ) => ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ D ) ) @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ D ) ) ) ) ) & ? [D: $i] : ( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers ) & ( = @ D @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__7 ) ) ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__4 ) ) @ ( k2_nat_1 @ c4_19__scpqsort @ D ) ) & ( r1_xxreal_0 @ D @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__5 ) ) ) & ! [E: $i] : ( ( m2_subset_1 @ E @ k1_numbers @ k5_numbers ) => ~ ( ~ ( r1_xxreal_0 @ E @ ( k2_nat_1 @ c4_19__scpqsort @ D ) ) & ( r1_xxreal_0 @ E @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__4 ) ) ) & ( r1_xxreal_0 @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ E ) ) @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ c5_19__scpqsort ) ) ) ) ) & ( ( = @ D @ k6_numbers ) | ( r1_xxreal_0 @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ ( k2_nat_1 @ c4_19__scpqsort @ D ) ) ) @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ c5_19__scpqsort ) ) ) ) ) ) ) ) ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ B ) & ( v5_funct_1 @ B @ ( k2_memstr_0 @ np__2 @ k1_scmpds_2 ) ) & ( v1_partfun1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v5_memstr_0 @ B @ np__2 @ k1_scmpds_2 @ k6_numbers ) ) => ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ k5_numbers ) & ( v5_relat_1 @ C @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ k5_numbers ) ) => ( ( ( = @ ( k1_funct_1 @ B @ k2_scmp_gcd ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__5 ) ) @ ( k2_nat_1 @ ( k2_nat_1 @ A @ np__1 ) @ np__1 ) ) & ( = @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__4 ) ) @ ( k2_xcmplx_0 @ c4_19__scpqsort @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__5 ) ) ) ) & ( = @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__2 ) ) @ c5_19__scpqsort ) ) => ( ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ k2_scmp_gcd ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__1 ) ) @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__1 ) ) ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__5 ) ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__2 ) ) @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__2 ) ) ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__3 ) ) @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__3 ) ) ) & ! [D: $i] : ( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers ) => ( ( r1_xxreal_0 @ np__8 @ D ) => ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ D ) ) @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ D ) ) ) ) ) & ? [D: $i] : ( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers ) & ( = @ D @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__7 ) ) ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__4 ) ) @ ( k2_nat_1 @ c4_19__scpqsort @ D ) ) & ( r1_xxreal_0 @ D @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__5 ) ) ) & ! [E: $i] : ( ( m2_subset_1 @ E @ k1_numbers @ k5_numbers ) => ~ ( ~ ( r1_xxreal_0 @ E @ ( k2_nat_1 @ c4_19__scpqsort @ D ) ) & ( r1_xxreal_0 @ E @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__4 ) ) ) & ( r1_xxreal_0 @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ E ) ) @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ c5_19__scpqsort ) ) ) ) ) & ( ( = @ D @ k6_numbers ) | ( r1_xxreal_0 @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ ( k2_nat_1 @ c4_19__scpqsort @ D ) ) ) @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ c5_19__scpqsort ) ) ) ) ) ) ) ) ) ) ) ),file(scpqsort,e10_19__scpqsort)).
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(e12_19__scpqsort,conjecture,( ! [A: $i] : ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ B ) & ( v5_funct_1 @ B @ ( k2_memstr_0 @ np__2 @ k1_scmpds_2 ) ) & ( v1_partfun1 @ B @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v5_memstr_0 @ B @ np__2 @ k1_scmpds_2 @ k6_numbers ) ) => ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ k5_numbers ) & ( v5_relat_1 @ C @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ k5_numbers ) ) => ( ( ( = @ ( k1_funct_1 @ B @ k2_scmp_gcd ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__5 ) ) @ ( k2_nat_1 @ A @ np__1 ) ) & ( = @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__4 ) ) @ ( k2_xcmplx_0 @ c4_19__scpqsort @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__5 ) ) ) ) & ( = @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__2 ) ) @ c5_19__scpqsort ) ) => ( ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ k2_scmp_gcd ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__1 ) ) @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__1 ) ) ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__5 ) ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__2 ) ) @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__2 ) ) ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__3 ) ) @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__3 ) ) ) & ! [D: $i] : ( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers ) => ( ( r1_xxreal_0 @ np__8 @ D ) => ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ D ) ) @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ D ) ) ) ) ) & ? [D: $i] : ( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers ) & ( = @ D @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__7 ) ) ) & ( = @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ np__4 ) ) @ ( k2_nat_1 @ c4_19__scpqsort @ D ) ) & ( r1_xxreal_0 @ D @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__5 ) ) ) & ! [E: $i] : ( ( m2_subset_1 @ E @ k1_numbers @ k5_numbers ) => ~ ( ~ ( r1_xxreal_0 @ E @ ( k2_nat_1 @ c4_19__scpqsort @ D ) ) & ( r1_xxreal_0 @ E @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ np__4 ) ) ) & ( r1_xxreal_0 @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ E ) ) @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ c5_19__scpqsort ) ) ) ) ) & ( ( = @ D @ k6_numbers ) | ( r1_xxreal_0 @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ ( k2_nat_1 @ c4_19__scpqsort @ D ) ) ) @ ( k1_funct_1 @ ( k6_scmpds_4 @ ( k2_scmpds_8 @ k2_scmp_gcd @ np__5 @ ( k1_scmpds_4 @ ( k3_scmpds_4 @ ( k3_scmpds_4 @ ( k4_scmpds_4 @ ( k16_scmpds_2 @ k2_scmp_gcd @ k2_scmp_gcd @ np__7 @ np__5 ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__5 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k16_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__4 ) @ np__6 @ k6_numbers ) ) @ ( k13_scmpds_2 @ k2_scmp_gcd @ ( k1_scmp_gcd @ np__2 ) @ np__6 @ k6_numbers ) ) @ ( k3_scmpds_6 @ k2_scmp_gcd @ np__6 @ ( k4_scmpds_4 @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__4 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k11_scmpds_2 @ k2_scmp_gcd @ np__7 @ ( k4_xcmplx_0 @ np__1 ) ) ) @ ( k9_compos_1 @ k1_scmpds_2 @ ( k10_scmpds_2 @ k2_scmp_gcd @ np__5 @ k6_numbers ) ) ) ) ) @ B @ C ) @ ( k1_scmp_gcd @ c5_19__scpqsort ) ) ) ) ) ) ) ) ) ) ),file(scpqsort,e12_19__scpqsort)).
