% Mizar problem: e3_23,scmp_gcd,2126,27 
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(n5_type,type,( np__5: $i )).
thf(c1_23_type,type,( c1_23__scmp_gcd: $i )).
thf(c2_23_type,type,( c2_23__scmp_gcd: $i )).
thf(g1_extpro_1_type,type,( g1_extpro_1: $i > $i > $i > $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_scmp_gcd_type,type,( k1_scmp_gcd: $i > $i )).
thf(k1_scmpds_2_type,type,( k1_scmpds_2: $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_2_type,type,( k2_scmpds_2: $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_extpro_1_type,type,( k3_extpro_1: $i > $i > $i > $i > $i )).
thf(k3_relat_1_type,type,( k3_relat_1: $i > $i > $i )).
thf(k3_scmp_gcd_type,type,( k3_scmp_gcd: $i )).
thf(k4_card_3_type,type,( k4_card_3: $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k4_scmp_gcd_type,type,( k4_scmp_gcd: $i )).
thf(k4_scmpds_2_type,type,( k4_scmpds_2: $i > $i )).
thf(k5_extpro_1_type,type,( k5_extpro_1: $i > $i > $i > $i > $i > $i )).
thf(k5_memstr_0_type,type,( k5_memstr_0: $i > $i > $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_numbers_type,type,( k6_numbers: $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_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(r1_xxreal_0_type,type,( r1_xxreal_0: $i > $i > $o )).
thf(v13_struct_0_type,type,( v13_struct_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_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_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_setfam_1_type,type,( v1_setfam_1: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_xcmplx_0_type,type,( v1_xcmplx_0: $i > $o )).
thf(v1_xreal_0_type,type,( v1_xreal_0: $i > $o )).
thf(v1_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_memstr_0_type,type,( v2_memstr_0: $i > $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v2_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $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_memstr_0_type,type,( v3_memstr_0: $i > $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_valued_0_type,type,( v3_valued_0: $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_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_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_0: $i > $o )).
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(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(rc21_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_zfmisc_1 @ B ) ) ) ),file(struct_0,rc21_struct_0)).
thf(rc22_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_zfmisc_1 @ B ) ) ) ),file(struct_0,rc22_struct_0)).
thf(rc2_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) ) ),file(ordinal1,rc2_ordinal1)).
thf(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_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_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) => ( v13_struct_0 @ A @ np__1 ) ) ) ),file(struct_0,cc10_struct_0)).
thf(cc11_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v13_struct_0 @ A @ np__1 ) => ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) ) ) ),file(struct_0,cc11_struct_0)).
thf(cc17_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v7_struct_0 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc17_struct_0)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc2_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v7_struct_0 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc2_struct_0)).
thf(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(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_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal1,cc5_ordinal1)).
thf(cc5_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ( ~ ( v2_struct_0 @ A ) & ~ ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc5_struct_0)).
thf(cc6_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v7_struct_0 @ A ) => ( v8_struct_0 @ A ) ) ) ),file(struct_0,cc6_struct_0)).
thf(cc7_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(cc7_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ~ ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc7_struct_0)).
thf(cc8_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(cc9_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v13_struct_0 @ A @ k1_xboole_0 ) => ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc9_struct_0)).
thf(fc6_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc6_struct_0)).
thf(fc7_struct_0,axiom,( ! [A: $i] : ( ( ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc7_struct_0)).
thf(fc8_struct_0,axiom,( ! [A: $i] : ( ( ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc8_struct_0)).
thf(fc9_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc9_struct_0)).
thf(rc1_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_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc20_struct_0,axiom,( ? [A: $i] : ( ( l2_struct_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) ),file(struct_0,rc20_struct_0)).
thf(rc2_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_memstr_0,axiom,( ! [A: $i] : ( ~ ( v1_setfam_1 @ A ) => ? [B: $i] : ( ( l1_memstr_0 @ B @ A ) & ( v13_struct_0 @ B @ np__1 ) ) ) ),file(memstr_0,rc2_memstr_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_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(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_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_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(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_memstr_0,axiom,( ! [A: $i] : ( ~ ( v1_setfam_1 @ A ) => ~ ( v1_xboole_0 @ A ) ) ),file(memstr_0,cc1_memstr_0)).
thf(cc1_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc1_struct_0)).
thf(cc2_compos_0,axiom,( ! [A: $i] : ( ( v5_compos_0 @ A ) => ~ ( v1_xboole_0 @ A ) ) ),file(compos_0,cc2_compos_0)).
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_xreal_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc2_xreal_0)).
thf(cc3_int_1,axiom,( ! [A: $i] : ( ( v1_int_1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(int_1,cc3_int_1)).
thf(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
thf(cc3_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xcmplx_0 @ A ) ) ),file(xreal_0,cc3_xreal_0)).
thf(cc4_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
thf(cc4_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc4_struct_0)).
thf(cc4_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xreal_0,cc4_xreal_0)).
thf(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(cc7_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
thf(cc8_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
thf(cc8_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v13_struct_0 @ A @ k1_xboole_0 ) ) ) ),file(struct_0,cc8_struct_0)).
thf(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(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(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_struct_0,axiom,( ! [A: $i] : ( ( ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc1_struct_0)).
thf(fc2_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc2_struct_0)).
thf(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(fc5_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xreal_0 @ A ) & ( v1_xreal_0 @ B ) ) => ( v1_xreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc5_xreal_0)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
thf(rc1_compos_0,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_compos_0 @ A ) ) ),file(compos_0,rc1_compos_0)).
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_xreal_0,axiom,( ? [A: $i] : ( v1_xreal_0 @ A ) ),file(xreal_0,rc1_xreal_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_int_1,axiom,( ? [A: $i] : ( v1_int_1 @ A ) ),file(int_1,rc2_int_1)).
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_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(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_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(rc4_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(struct_0,rc4_struct_0)).
thf(rc4_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_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(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(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(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(reflexivity_r1_xxreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v1_xxreal_0 @ B ) ) => ( r1_xxreal_0 @ A @ A ) ) ),file(xxreal_0,r1_xxreal_0)).
thf(connectedness_r1_xxreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v1_xxreal_0 @ B ) ) => ( ( r1_xxreal_0 @ A @ B ) | ( r1_xxreal_0 @ B @ A ) ) ) ),file(xxreal_0,r1_xxreal_0)).
thf(redefinition_k2_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( v7_ordinal1 @ B ) ) => ( = @ ( k2_nat_1 @ A @ B ) @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(nat_1,k2_nat_1)).
thf(redefinition_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_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) <=> ( m1_subset_1 @ C @ B ) ) ) ),file(subset_1,m2_subset_1)).
thf(dt_k1_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_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_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ( v1_int_1 @ B ) ) => ( ( v1_ami_2 @ ( k2_scmpds_2 @ A @ B ) ) & ( m1_subset_1 @ ( k2_scmpds_2 @ A @ B ) @ ( u1_struct_0 @ k1_scmpds_2 ) ) ) ) ),file(scmpds_2,k2_scmpds_2)).
thf(dt_k2_xcmplx_0,axiom,( $true ),file(xcmplx_0,k2_xcmplx_0)).
thf(dt_k3_extpro_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_setfam_1 @ A ) & ~ ( v2_struct_0 @ B ) & ( v2_memstr_0 @ B @ A ) & ( v3_memstr_0 @ B @ A ) & ( l1_extpro_1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v5_relat_1 @ C @ ( u1_compos_1 @ B ) ) & ( v1_funct_1 @ C ) & ( 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 ) ) ) => ( m1_subset_1 @ ( k3_extpro_1 @ A @ B @ C @ D ) @ ( u1_compos_1 @ B ) ) ) ),file(extpro_1,k3_extpro_1)).
thf(dt_k3_scmp_gcd,axiom,( ( v1_ami_2 @ k3_scmp_gcd ) & ( m1_subset_1 @ k3_scmp_gcd @ ( u1_struct_0 @ k1_scmpds_2 ) ) ),file(scmp_gcd,k3_scmp_gcd)).
thf(dt_k4_scmp_gcd,axiom,( ~ ( v1_xboole_0 @ k4_scmp_gcd ) & ( v1_relat_1 @ k4_scmp_gcd ) & ( v4_relat_1 @ k4_scmp_gcd @ k5_numbers ) & ( v5_relat_1 @ k4_scmp_gcd @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ k4_scmp_gcd ) & ( v1_finset_1 @ k4_scmp_gcd ) & ( v1_afinsq_1 @ k4_scmp_gcd ) ),file(scmp_gcd,k4_scmp_gcd)).
thf(dt_k4_scmpds_2,axiom,( ! [A: $i] : ( ( ( v1_ami_2 @ A ) & ( m1_subset_1 @ A @ ( u1_struct_0 @ k1_scmpds_2 ) ) ) => ( m1_subset_1 @ ( k4_scmpds_2 @ A ) @ ( u1_compos_1 @ k1_scmpds_2 ) ) ) ),file(scmpds_2,k4_scmpds_2)).
thf(dt_k5_extpro_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ~ ( v1_setfam_1 @ A ) & ~ ( v2_struct_0 @ B ) & ( v2_memstr_0 @ B @ A ) & ( v3_memstr_0 @ B @ A ) & ( l1_extpro_1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ k5_numbers ) & ( v5_relat_1 @ C @ ( u1_compos_1 @ B ) ) & ( v1_funct_1 @ C ) & ( 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 ) ) & ( v7_ordinal1 @ E ) ) => ( ( v1_relat_1 @ ( k5_extpro_1 @ A @ B @ C @ D @ E ) ) & ( v4_relat_1 @ ( k5_extpro_1 @ A @ B @ C @ D @ E ) @ ( u1_struct_0 @ B ) ) & ( v1_funct_1 @ ( k5_extpro_1 @ A @ B @ C @ D @ E ) ) & ( v5_funct_1 @ ( k5_extpro_1 @ A @ B @ C @ D @ E ) @ ( k2_memstr_0 @ A @ B ) ) & ( v1_partfun1 @ ( k5_extpro_1 @ A @ B @ C @ D @ E ) @ ( u1_struct_0 @ B ) ) ) ) ),file(extpro_1,k5_extpro_1)).
thf(dt_k5_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 ) & ( 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 ) ) ) => ( m2_subset_1 @ ( k5_memstr_0 @ A @ B @ C ) @ k1_numbers @ k5_numbers ) ) ),file(memstr_0,k5_memstr_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_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) => ( m1_subset_1 @ C @ A ) ) ) ),file(subset_1,m2_subset_1)).
thf(dt_u1_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_c1_23__scmp_gcd,axiom,( ( v1_relat_1 @ c1_23__scmp_gcd ) & ( v4_relat_1 @ c1_23__scmp_gcd @ k5_numbers ) & ( v5_relat_1 @ c1_23__scmp_gcd @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ c1_23__scmp_gcd ) & ( v1_partfun1 @ c1_23__scmp_gcd @ k5_numbers ) ),file(scmp_gcd,c1_23__scmp_gcd)).
thf(dt_c2_23__scmp_gcd,axiom,( ( v1_relat_1 @ c2_23__scmp_gcd ) & ( v4_relat_1 @ c2_23__scmp_gcd @ k5_numbers ) & ( v5_relat_1 @ c2_23__scmp_gcd @ ( u1_compos_1 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ c2_23__scmp_gcd ) & ( v1_partfun1 @ c2_23__scmp_gcd @ k5_numbers ) ),file(scmp_gcd,c2_23__scmp_gcd)).
thf(cc1_xreal_0,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc1_xreal_0)).
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(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(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(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(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(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(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(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(spc5_boole,axiom,( ~ ( v1_xboole_0 @ np__5 ) ),file(boole,spc5_boole)).
thf(e1_23__scmp_gcd,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 ) ) ) => ! [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 ) ) ) => ~ ( ( r1_tarski @ k4_scmp_gcd @ c1_23__scmp_gcd ) & ( r1_tarski @ k4_scmp_gcd @ c2_23__scmp_gcd ) & ( = @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ A ) @ np__5 ) & ~ ( r1_xxreal_0 @ ( k1_funct_1 @ A @ k3_scmp_gcd ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ A @ k2_scmp_gcd ) @ k6_numbers ) & ( r1_xxreal_0 @ ( k1_funct_1 @ A @ ( k2_scmpds_2 @ ( k1_funct_1 @ A @ k3_scmp_gcd ) @ np__3 ) ) @ k6_numbers ) & ( r1_xxreal_0 @ k6_numbers @ ( k1_funct_1 @ A @ ( k2_scmpds_2 @ ( k1_funct_1 @ A @ k3_scmp_gcd ) @ np__3 ) ) ) & ( r1_xxreal_0 @ ( k1_funct_1 @ A @ ( k2_scmpds_2 @ ( k1_funct_1 @ A @ k3_scmp_gcd ) @ np__3 ) ) @ ( k1_funct_1 @ A @ ( k2_scmpds_2 @ ( k1_funct_1 @ A @ k3_scmp_gcd ) @ np__2 ) ) ) & ( = @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ B ) @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ A ) ) & ( = @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ ( k1_funct_1 @ A @ k3_scmp_gcd ) ) & ( = @ ( k1_funct_1 @ B @ k2_scmp_gcd ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ A @ k3_scmp_gcd ) @ np__2 ) ) @ ( k1_funct_1 @ A @ ( k2_scmpds_2 @ ( k1_funct_1 @ A @ k3_scmp_gcd ) @ np__2 ) ) ) & ( = @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ A @ k3_scmp_gcd ) @ np__3 ) ) @ ( k1_funct_1 @ A @ ( k2_scmpds_2 @ ( k1_funct_1 @ A @ k3_scmp_gcd ) @ np__3 ) ) ) & ! [C: $i] : ( ( m1_subset_1 @ C @ k5_numbers ) => ~ ( ( = @ ( k3_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ A @ C ) ) @ ( k4_scmpds_2 @ k3_scmp_gcd ) ) & ( = @ ( k1_funct_1 @ A @ k3_scmp_gcd ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ A @ C ) @ k3_scmp_gcd ) ) & ( = @ ( k3_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ B @ C ) ) @ ( k4_scmpds_2 @ k3_scmp_gcd ) ) & ( = @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ B @ C ) @ k3_scmp_gcd ) ) & ! [D: $i] : ( ( m1_subset_1 @ D @ k5_numbers ) => ( ( r1_xxreal_0 @ D @ ( k2_xcmplx_0 @ ( k1_funct_1 @ A @ k3_scmp_gcd ) @ np__1 ) ) => ( ( r1_xxreal_0 @ D @ np__1 ) | ( ( = @ ( k1_funct_1 @ A @ ( k1_scmp_gcd @ D ) ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ A @ C ) @ ( k1_scmp_gcd @ D ) ) ) & ( = @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ D ) ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ B @ C ) @ ( k1_scmp_gcd @ D ) ) ) ) ) ) ) & ! [D: $i] : ( ( m1_subset_1 @ D @ k5_numbers ) => ! [E: $i] : ( ( ( v1_ami_2 @ E ) & ( m1_subset_1 @ E @ ( u1_struct_0 @ k1_scmpds_2 ) ) ) => ( ( ( r1_xxreal_0 @ D @ C ) & ( = @ ( k1_funct_1 @ A @ E ) @ ( k1_funct_1 @ B @ E ) ) ) => ( ( = @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ A @ D ) ) @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ B @ D ) ) ) & ( = @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ A @ D ) @ E ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ B @ D ) @ E ) ) ) ) ) ) ) ) ) ) ) ),file(scmp_gcd,e1_23__scmp_gcd)).
thf(e2_23__scmp_gcd,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ 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 ) ) ) => ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ C ) & ( v5_funct_1 @ C @ ( k2_memstr_0 @ np__2 @ k1_scmpds_2 ) ) & ( v1_partfun1 @ C @ ( u1_struct_0 @ k1_scmpds_2 ) ) ) => ~ ( ( r1_tarski @ k4_scmp_gcd @ c1_23__scmp_gcd ) & ( r1_tarski @ k4_scmp_gcd @ c2_23__scmp_gcd ) & ( = @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ B ) @ np__5 ) & ~ ( r1_xxreal_0 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ B @ k2_scmp_gcd ) @ k6_numbers ) & ( r1_xxreal_0 @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__3 ) ) @ A ) & ( r1_xxreal_0 @ k6_numbers @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__3 ) ) ) & ( r1_xxreal_0 @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__3 ) ) @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__2 ) ) ) & ( = @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ C ) @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ B ) ) & ( = @ ( k1_funct_1 @ C @ k3_scmp_gcd ) @ ( k1_funct_1 @ B @ k3_scmp_gcd ) ) & ( = @ ( k1_funct_1 @ C @ k2_scmp_gcd ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ C @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__2 ) ) @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__2 ) ) ) & ( = @ ( k1_funct_1 @ C @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__3 ) ) @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__3 ) ) ) & ! [D: $i] : ( ( m1_subset_1 @ D @ k5_numbers ) => ~ ( ( = @ ( k3_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ B @ D ) ) @ ( k4_scmpds_2 @ k3_scmp_gcd ) ) & ( = @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ B @ D ) @ k3_scmp_gcd ) ) & ( = @ ( k3_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ C @ D ) ) @ ( k4_scmpds_2 @ k3_scmp_gcd ) ) & ( = @ ( k1_funct_1 @ C @ k3_scmp_gcd ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ C @ D ) @ k3_scmp_gcd ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ k5_numbers ) => ( ( r1_xxreal_0 @ E @ ( k2_xcmplx_0 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__1 ) ) => ( ( r1_xxreal_0 @ E @ np__1 ) | ( ( = @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ E ) ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ B @ D ) @ ( k1_scmp_gcd @ E ) ) ) & ( = @ ( k1_funct_1 @ C @ ( k1_scmp_gcd @ E ) ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ C @ D ) @ ( k1_scmp_gcd @ E ) ) ) ) ) ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ k5_numbers ) => ! [F: $i] : ( ( ( v1_ami_2 @ F ) & ( m1_subset_1 @ F @ ( u1_struct_0 @ k1_scmpds_2 ) ) ) => ( ( ( r1_xxreal_0 @ E @ D ) & ( = @ ( k1_funct_1 @ B @ F ) @ ( k1_funct_1 @ C @ F ) ) ) => ( ( = @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ B @ E ) ) @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ C @ E ) ) ) & ( = @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ B @ E ) @ F ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ C @ E ) @ F ) ) ) ) ) ) ) ) ) ) ) => ! [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 ) ) ) => ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ C ) & ( v5_funct_1 @ C @ ( k2_memstr_0 @ np__2 @ k1_scmpds_2 ) ) & ( v1_partfun1 @ C @ ( u1_struct_0 @ k1_scmpds_2 ) ) ) => ~ ( ( r1_tarski @ k4_scmp_gcd @ c1_23__scmp_gcd ) & ( r1_tarski @ k4_scmp_gcd @ c2_23__scmp_gcd ) & ( = @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ B ) @ np__5 ) & ~ ( r1_xxreal_0 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ B @ k2_scmp_gcd ) @ k6_numbers ) & ( r1_xxreal_0 @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__3 ) ) @ ( k2_nat_1 @ A @ np__1 ) ) & ( r1_xxreal_0 @ k6_numbers @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__3 ) ) ) & ( r1_xxreal_0 @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__3 ) ) @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__2 ) ) ) & ( = @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ C ) @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ B ) ) & ( = @ ( k1_funct_1 @ C @ k3_scmp_gcd ) @ ( k1_funct_1 @ B @ k3_scmp_gcd ) ) & ( = @ ( k1_funct_1 @ C @ k2_scmp_gcd ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ C @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__2 ) ) @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__2 ) ) ) & ( = @ ( k1_funct_1 @ C @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__3 ) ) @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__3 ) ) ) & ! [D: $i] : ( ( m1_subset_1 @ D @ k5_numbers ) => ~ ( ( = @ ( k3_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ B @ D ) ) @ ( k4_scmpds_2 @ k3_scmp_gcd ) ) & ( = @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ B @ D ) @ k3_scmp_gcd ) ) & ( = @ ( k3_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ C @ D ) ) @ ( k4_scmpds_2 @ k3_scmp_gcd ) ) & ( = @ ( k1_funct_1 @ C @ k3_scmp_gcd ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ C @ D ) @ k3_scmp_gcd ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ k5_numbers ) => ( ( r1_xxreal_0 @ E @ ( k2_xcmplx_0 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__1 ) ) => ( ( r1_xxreal_0 @ E @ np__1 ) | ( ( = @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ E ) ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ B @ D ) @ ( k1_scmp_gcd @ E ) ) ) & ( = @ ( k1_funct_1 @ C @ ( k1_scmp_gcd @ E ) ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ C @ D ) @ ( k1_scmp_gcd @ E ) ) ) ) ) ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ k5_numbers ) => ! [F: $i] : ( ( ( v1_ami_2 @ F ) & ( m1_subset_1 @ F @ ( u1_struct_0 @ k1_scmpds_2 ) ) ) => ( ( ( r1_xxreal_0 @ E @ D ) & ( = @ ( k1_funct_1 @ B @ F ) @ ( k1_funct_1 @ C @ F ) ) ) => ( ( = @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ B @ E ) ) @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ C @ E ) ) ) & ( = @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ B @ E ) @ F ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ C @ E ) @ F ) ) ) ) ) ) ) ) ) ) ) ) ) ),file(scmp_gcd,e2_23__scmp_gcd)).
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(e3_23__scmp_gcd,conjecture,( ! [A: $i] : ( ( m1_subset_1 @ A @ 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 ) ) ) => ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ ( u1_struct_0 @ k1_scmpds_2 ) ) & ( v1_funct_1 @ C ) & ( v5_funct_1 @ C @ ( k2_memstr_0 @ np__2 @ k1_scmpds_2 ) ) & ( v1_partfun1 @ C @ ( u1_struct_0 @ k1_scmpds_2 ) ) ) => ~ ( ( r1_tarski @ k4_scmp_gcd @ c1_23__scmp_gcd ) & ( r1_tarski @ k4_scmp_gcd @ c2_23__scmp_gcd ) & ( = @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ B ) @ np__5 ) & ~ ( r1_xxreal_0 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ B @ k2_scmp_gcd ) @ k6_numbers ) & ( r1_xxreal_0 @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__3 ) ) @ A ) & ( r1_xxreal_0 @ k6_numbers @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__3 ) ) ) & ( r1_xxreal_0 @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__3 ) ) @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__2 ) ) ) & ( = @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ C ) @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ B ) ) & ( = @ ( k1_funct_1 @ C @ k3_scmp_gcd ) @ ( k1_funct_1 @ B @ k3_scmp_gcd ) ) & ( = @ ( k1_funct_1 @ C @ k2_scmp_gcd ) @ k6_numbers ) & ( = @ ( k1_funct_1 @ C @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__2 ) ) @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__2 ) ) ) & ( = @ ( k1_funct_1 @ C @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__3 ) ) @ ( k1_funct_1 @ B @ ( k2_scmpds_2 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__3 ) ) ) & ! [D: $i] : ( ( m1_subset_1 @ D @ k5_numbers ) => ~ ( ( = @ ( k3_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ B @ D ) ) @ ( k4_scmpds_2 @ k3_scmp_gcd ) ) & ( = @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ B @ D ) @ k3_scmp_gcd ) ) & ( = @ ( k3_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ C @ D ) ) @ ( k4_scmpds_2 @ k3_scmp_gcd ) ) & ( = @ ( k1_funct_1 @ C @ k3_scmp_gcd ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ C @ D ) @ k3_scmp_gcd ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ k5_numbers ) => ( ( r1_xxreal_0 @ E @ ( k2_xcmplx_0 @ ( k1_funct_1 @ B @ k3_scmp_gcd ) @ np__1 ) ) => ( ( r1_xxreal_0 @ E @ np__1 ) | ( ( = @ ( k1_funct_1 @ B @ ( k1_scmp_gcd @ E ) ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ B @ D ) @ ( k1_scmp_gcd @ E ) ) ) & ( = @ ( k1_funct_1 @ C @ ( k1_scmp_gcd @ E ) ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ C @ D ) @ ( k1_scmp_gcd @ E ) ) ) ) ) ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ k5_numbers ) => ! [F: $i] : ( ( ( v1_ami_2 @ F ) & ( m1_subset_1 @ F @ ( u1_struct_0 @ k1_scmpds_2 ) ) ) => ( ( ( r1_xxreal_0 @ E @ D ) & ( = @ ( k1_funct_1 @ B @ F ) @ ( k1_funct_1 @ C @ F ) ) ) => ( ( = @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ B @ E ) ) @ ( k5_memstr_0 @ np__2 @ k1_scmpds_2 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ C @ E ) ) ) & ( = @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c1_23__scmp_gcd @ B @ E ) @ F ) @ ( k1_funct_1 @ ( k5_extpro_1 @ np__2 @ k1_scmpds_2 @ c2_23__scmp_gcd @ C @ E ) @ F ) ) ) ) ) ) ) ) ) ) ) ) ),file(scmp_gcd,e3_23__scmp_gcd)).
