% Mizar problem: e7_1_1_1,jordan13,701,60 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(n2_type,type,( np__2: $i )).
thf(c1_1_type,type,( c1_1__jordan13: $i )).
thf(c2_1_type,type,( c2_1__jordan13: $i )).
thf(g1_rltopsp1_type,type,( g1_rltopsp1: $i > $i > $i > $i > $i > $i )).
thf(k10_finseq_1_type,type,( k10_finseq_1: $i > $i > $i )).
thf(k12_finseq_1_type,type,( k12_finseq_1: $i > $i > $i )).
thf(k13_finseq_1_type,type,( k13_finseq_1: $i > $i )).
thf(k15_euclid_type,type,( k15_euclid: $i > $i )).
thf(k1_card_1_type,type,( k1_card_1: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_jordan8_type,type,( k1_jordan8: $i > $i > $i )).
thf(k1_nat_1_type,type,( k1_nat_1: $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_xreal_0_type,type,( k1_xreal_0: $i > $i > $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_finseq_4_type,type,( k2_finseq_4: $i > $i > $i > $i )).
thf(k2_nat_1_type,type,( k2_nat_1: $i > $i > $i )).
thf(k2_xcmplx_0_type,type,( k2_xcmplx_0: $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_finseq_1_type,type,( k3_finseq_1: $i > $i )).
thf(k3_finseq_2_type,type,( k3_finseq_2: $i > $i )).
thf(k3_gobrd13_type,type,( k3_gobrd13: $i > $i > $i > $i )).
thf(k3_jordan11_type,type,( k3_jordan11: $i > $i > $i )).
thf(k3_jordan1h_type,type,( k3_jordan1h: $i > $i > $i )).
thf(k3_matrix_1_type,type,( k3_matrix_1: $i > $i > $i > $i > $i )).
thf(k4_gobrd13_type,type,( k4_gobrd13: $i > $i > $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k5_finseq_1_type,type,( k5_finseq_1: $i > $i )).
thf(k5_gobrd13_type,type,( k5_gobrd13: $i > $i > $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_numbers_type,type,( k6_numbers: $i )).
thf(k7_finseq_1_type,type,( k7_finseq_1: $i > $i > $i )).
thf(k7_nat_d_type,type,( k7_nat_d: $i > $i > $i )).
thf(k8_finseq_1_type,type,( k8_finseq_1: $i > $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(u1_algstr_0_type,type,( u1_algstr_0: $i > $i )).
thf(u1_pre_topc_type,type,( u1_pre_topc: $i > $i )).
thf(u1_rlvect_1_type,type,( u1_rlvect_1: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(u2_struct_0_type,type,( u2_struct_0: $i > $i )).
thf(l1_algstr_0_type,type,( l1_algstr_0: $i > $o )).
thf(l1_pre_topc_type,type,( l1_pre_topc: $i > $o )).
thf(l1_rltopsp1_type,type,( l1_rltopsp1: $i > $o )).
thf(l1_rlvect_1_type,type,( l1_rlvect_1: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l2_algstr_0_type,type,( l2_algstr_0: $i > $o )).
thf(l2_struct_0_type,type,( l2_struct_0: $i > $o )).
thf(m1_finseq_1_type,type,( m1_finseq_1: $i > $i > $o )).
thf(m1_finseq_2_type,type,( m1_finseq_2: $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_finseq_1_type,type,( m2_finseq_1: $i > $i > $o )).
thf(m2_subset_1_type,type,( m2_subset_1: $i > $i > $i > $o )).
thf(r1_goboard1_type,type,( r1_goboard1: $i > $i > $i > $o )).
thf(r1_gobrd13_type,type,( r1_gobrd13: $i > $i > $i > $i > $o )).
thf(r1_xboole_0_type,type,( r1_xboole_0: $i > $i > $o )).
thf(r1_xxreal_0_type,type,( r1_xxreal_0: $i > $i > $o )).
thf(r2_gobrd13_type,type,( r2_gobrd13: $i > $i > $i > $i > $o )).
thf(r3_gobrd13_type,type,( r3_gobrd13: $i > $i > $i > $i > $o )).
thf(v13_algstr_0_type,type,( v13_algstr_0: $i > $o )).
thf(v13_struct_0_type,type,( v13_struct_0: $i > $i > $o )).
thf(v1_card_1_type,type,( v1_card_1: $i > $o )).
thf(v1_finseq_1_type,type,( v1_finseq_1: $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_funct_2_type,type,( v1_funct_2: $i > $i > $i > $o )).
thf(v1_matrix_1_type,type,( v1_matrix_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_sppol_1_type,type,( v1_sppol_1: $i > $o )).
thf(v1_topreal1_type,type,( v1_topreal1: $i > $o )).
thf(v1_topreal2_type,type,( v1_topreal2: $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_compts_1_type,type,( v2_compts_1: $i > $i > $o )).
thf(v2_connsp_1_type,type,( v2_connsp_1: $i > $i > $o )).
thf(v2_finseq_1_type,type,( v2_finseq_1: $i > $o )).
thf(v2_finset_1_type,type,( v2_finset_1: $i > $o )).
thf(v2_funct_1_type,type,( v2_funct_1: $i > $o )).
thf(v2_goboard1_type,type,( v2_goboard1: $i > $o )).
thf(v2_monoid_0_type,type,( v2_monoid_0: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_pre_topc_type,type,( v2_pre_topc: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v2_rlvect_1_type,type,( v2_rlvect_1: $i > $o )).
thf(v2_sppol_1_type,type,( v2_sppol_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_card_1_type,type,( v3_card_1: $i > $i > $o )).
thf(v3_finseq_1_type,type,( v3_finseq_1: $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_1: $i > $o )).
thf(v3_goboard1_type,type,( v3_goboard1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(v3_rlvect_1_type,type,( v3_rlvect_1: $i > $o )).
thf(v3_valued_0_type,type,( v3_valued_0: $i > $o )).
thf(v3_xxreal_0_type,type,( v3_xxreal_0: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_goboard1_type,type,( v4_goboard1: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v4_rlvect_1_type,type,( v4_rlvect_1: $i > $o )).
thf(v5_finset_1_type,type,( v5_finset_1: $i > $o )).
thf(v5_goboard1_type,type,( v5_goboard1: $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_rltopsp1_type,type,( v5_rltopsp1: $i > $o )).
thf(v5_rlvect_1_type,type,( v5_rlvect_1: $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v6_rltopsp1_type,type,( v6_rltopsp1: $i > $o )).
thf(v6_rlvect_1_type,type,( v6_rlvect_1: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(v7_rltopsp1_type,type,( v7_rltopsp1: $i > $o )).
thf(v7_rlvect_1_type,type,( v7_rlvect_1: $i > $o )).
thf(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v8_rlvect_1_type,type,( v8_rlvect_1: $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_0: $i > $o )).
thf(v9_rltopsp1_type,type,( v9_rltopsp1: $i > $i > $o )).
thf(commutativity_k1_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ( = @ ( k1_nat_1 @ A @ B ) @ ( k1_nat_1 @ B @ A ) ) ) ),file(nat_1,k1_nat_1)).
thf(redefinition_k1_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ( = @ ( k1_nat_1 @ A @ B ) @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(nat_1,k1_nat_1)).
thf(dt_k1_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ( m2_subset_1 @ ( k1_nat_1 @ A @ B ) @ k1_numbers @ k5_numbers ) ) ),file(nat_1,k1_nat_1)).
thf(dt_l1_algstr_0,axiom,( ! [A: $i] : ( ( l1_algstr_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(algstr_0,l1_algstr_0)).
thf(dt_l2_algstr_0,axiom,( ! [A: $i] : ( ( l2_algstr_0 @ A ) => ( ( l2_struct_0 @ A ) & ( l1_algstr_0 @ A ) ) ) ),file(algstr_0,l2_algstr_0)).
thf(dt_l2_struct_0,axiom,( ! [A: $i] : ( ( l2_struct_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(struct_0,l2_struct_0)).
thf(cc10_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) => ( v13_struct_0 @ A @ np__1 ) ) ) ),file(struct_0,cc10_struct_0)).
thf(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(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(cc3_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_finset_1 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) => ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( v1_finset_1 @ C ) ) ) ) ) ),file(finset_1,cc3_finset_1)).
thf(cc5_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ( ~ ( v2_struct_0 @ A ) & ~ ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc5_struct_0)).
thf(cc6_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v7_struct_0 @ A ) => ( v8_struct_0 @ A ) ) ) ),file(struct_0,cc6_struct_0)).
thf(cc7_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ~ ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc7_struct_0)).
thf(cc9_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v13_struct_0 @ A @ k1_xboole_0 ) => ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc9_struct_0)).
thf(fc19_struct_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_card_1 @ A ) & ( v13_struct_0 @ B @ A ) & ( l1_struct_0 @ B ) ) => ( v3_card_1 @ ( u1_struct_0 @ B ) @ A ) ) ),file(struct_0,fc19_struct_0)).
thf(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(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(rc22_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_zfmisc_1 @ B ) ) ) ),file(struct_0,rc22_struct_0)).
thf(rc23_struct_0,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ? [B: $i] : ( ( l1_struct_0 @ B ) & ( v13_struct_0 @ B @ A ) ) ) ),file(struct_0,rc23_struct_0)).
thf(free_g1_rltopsp1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( m1_subset_1 @ B @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ k1_numbers @ A ) @ A ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ k1_numbers @ A ) @ A ) ) ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) => ! [F: $i] : ! [G: $i] : ! [H: $i] : ! [I: $i] : ! [J: $i] : ( ( = @ ( g1_rltopsp1 @ A @ B @ C @ D @ E ) @ ( g1_rltopsp1 @ F @ G @ H @ I @ J ) ) => ( ( = @ A @ F ) & ( = @ B @ G ) & ( = @ C @ H ) & ( = @ D @ I ) & ( = @ E @ J ) ) ) ) ),file(rltopsp1,g1_rltopsp1)).
thf(dt_g1_rltopsp1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( m1_subset_1 @ B @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ k1_numbers @ A ) @ A ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ k1_numbers @ A ) @ A ) ) ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) => ( ( v5_rltopsp1 @ ( g1_rltopsp1 @ A @ B @ C @ D @ E ) ) & ( l1_rltopsp1 @ ( g1_rltopsp1 @ A @ B @ C @ D @ E ) ) ) ) ),file(rltopsp1,g1_rltopsp1)).
thf(dt_k13_finseq_1,axiom,( $true ),file(finseq_1,k13_finseq_1)).
thf(dt_l1_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( l1_struct_0 @ A ) ) ),file(pre_topc,l1_pre_topc)).
thf(dt_l1_rlvect_1,axiom,( ! [A: $i] : ( ( l1_rlvect_1 @ A ) => ( l2_algstr_0 @ A ) ) ),file(rlvect_1,l1_rlvect_1)).
thf(dt_m1_finseq_2,axiom,( $true ),file(finseq_2,m1_finseq_2)).
thf(dt_u1_algstr_0,axiom,( ! [A: $i] : ( ( l1_algstr_0 @ A ) => ( ( v1_funct_1 @ ( u1_algstr_0 @ A ) ) & ( v1_funct_2 @ ( u1_algstr_0 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ ( u1_algstr_0 @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),file(algstr_0,u1_algstr_0)).
thf(dt_u1_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( m1_subset_1 @ ( u1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),file(pre_topc,u1_pre_topc)).
thf(dt_u1_rlvect_1,axiom,( ! [A: $i] : ( ( l1_rlvect_1 @ A ) => ( ( v1_funct_1 @ ( u1_rlvect_1 @ A ) ) & ( v1_funct_2 @ ( u1_rlvect_1 @ A ) @ ( k2_zfmisc_1 @ k1_numbers @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ ( u1_rlvect_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ k1_numbers @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),file(rlvect_1,u1_rlvect_1)).
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(cc1_sppol_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) => ( ( ~ ( v1_zfmisc_1 @ A ) & ( v1_sppol_1 @ A ) ) => ~ ( v2_sppol_1 @ A ) ) ) ),file(sppol_1,cc1_sppol_1)).
thf(cc1_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc1_struct_0)).
thf(cc1_topreal6,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_xboole_0 @ B ) => ( v2_connsp_1 @ B @ A ) ) ) ) ),file(topreal6,cc1_topreal6)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc2_sppol_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) => ( ( ~ ( v1_zfmisc_1 @ A ) & ( v2_sppol_1 @ A ) ) => ~ ( v1_sppol_1 @ A ) ) ) ),file(sppol_1,cc2_sppol_1)).
thf(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_1)).
thf(cc4_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc4_struct_0)).
thf(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(cc6_funct_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) ) ),file(funct_1,cc6_funct_1)).
thf(cc6_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(cc7_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ( v2_finseq_1 @ A ) ) ) ),file(finseq_1,cc7_finseq_1)).
thf(cc7_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(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_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(fc12_finseq_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k13_finseq_1 @ A ) ) ),file(finseq_1,fc12_finseq_1)).
thf(fc17_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v4_funct_1 @ A ) & ( v1_relat_1 @ C ) & ( v5_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) ) => ( ( v1_relat_1 @ ( k1_funct_1 @ C @ B ) ) & ( v1_funct_1 @ ( k1_funct_1 @ C @ B ) ) ) ) ),file(funct_1,fc17_funct_1)).
thf(fc18_funct_1,axiom,( ! [A: $i] : ( ( ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ~ ( v1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(funct_1,fc18_funct_1)).
thf(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(fc22_finseq_1,axiom,( ! [A: $i] : ( v4_funct_1 @ ( k13_finseq_1 @ A ) ) ),file(finseq_1,fc22_finseq_1)).
thf(fc24_relat_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) ) => ( v1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc24_relat_1)).
thf(fc27_finseq_1,axiom,( ! [A: $i] : ( v3_finseq_1 @ ( k13_finseq_1 @ A ) ) ),file(finseq_1,fc27_finseq_1)).
thf(fc28_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v7_ordinal1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) & ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( v3_card_1 @ C @ A ) & ( v1_finseq_1 @ C ) & ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( v3_card_1 @ D @ B ) & ( v1_finseq_1 @ D ) ) => ( ( v1_relat_1 @ ( k7_finseq_1 @ C @ D ) ) & ( v1_funct_1 @ ( k7_finseq_1 @ C @ D ) ) & ( v3_card_1 @ ( k7_finseq_1 @ C @ D ) @ ( k1_nat_1 @ A @ B ) ) & ( v1_finseq_1 @ ( k7_finseq_1 @ C @ D ) ) ) ) ),file(finseq_1,fc28_finseq_1)).
thf(fc29_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v3_finseq_1 @ A ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ( v1_finseq_1 @ ( k1_funct_1 @ B @ C ) ) ) ),file(finseq_1,fc29_finseq_1)).
thf(fc2_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc2_struct_0)).
thf(rc1_finseq_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ A ) ) ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_finseq_1 @ B ) ) ),file(finseq_1,rc1_finseq_1)).
thf(rc1_nat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) ),file(nat_1,rc1_nat_1)).
thf(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(rc2_finseq_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_finseq_1 @ B @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) & ( v1_finseq_1 @ B ) ) ),file(finseq_1,rc2_finseq_1)).
thf(rc2_goboard9,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_finseq_1 @ A ) & ( v2_finseq_1 @ A ) ) ),file(goboard9,rc2_goboard9)).
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_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_finseq_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finseq_1 @ A ) ) ),file(finseq_1,rc3_finseq_1)).
thf(rc3_nat_1,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) & ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) ),file(nat_1,rc3_nat_1)).
thf(rc3_ordinal1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v5_ordinal1 @ B ) ) ),file(ordinal1,rc3_ordinal1)).
thf(rc3_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relat_1,rc3_relat_1)).
thf(rc3_xreal_0,axiom,( ? [A: $i] : ( ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc3_xreal_0)).
thf(rc4_finseq_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v1_finseq_1 @ A ) & ( v2_finseq_1 @ A ) ) ),file(finseq_1,rc4_finseq_1)).
thf(rc4_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_finseq_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v1_finseq_1 @ A ) & ( v2_finseq_1 @ A ) ) ),file(finseq_1,rc5_finseq_1)).
thf(rc5_finset_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 ) & ( v1_finset_1 @ C ) ) ),file(finset_1,rc5_finset_1)).
thf(rc6_finseq_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_finseq_1 @ B @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ~ ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) & ( v1_finseq_1 @ B ) & ( v2_finseq_1 @ B ) ) ) ),file(finseq_1,rc6_finseq_1)).
thf(rc6_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ? [C: $i] : ( ~ ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) ) ) ),file(finset_1,rc6_finset_1)).
thf(rc6_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) ) ),file(funct_1,rc6_funct_1)).
thf(rc7_finseq_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v3_card_1 @ B @ A ) & ( v1_finseq_1 @ B ) & ( v2_finseq_1 @ B ) ) ) ),file(finseq_1,rc7_finseq_1)).
thf(rc7_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_zfmisc_1 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(finset_1,rc7_finset_1)).
thf(rc9_finseq_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v1_finseq_1 @ B ) & ( v2_finseq_1 @ B ) ) ),file(finseq_1,rc9_finseq_1)).
thf(rc9_funct_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) ),file(funct_1,rc9_funct_1)).
thf(projectivity_k1_card_1,axiom,( ! [A: $i] : ( = @ ( k1_card_1 @ ( k1_card_1 @ A ) ) @ ( k1_card_1 @ A ) ) ),file(card_1,k1_card_1)).
thf(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(abstractness_v5_rltopsp1,axiom,( ! [A: $i] : ( ( l1_rltopsp1 @ A ) => ( ( v5_rltopsp1 @ A ) => ( = @ A @ ( g1_rltopsp1 @ ( u1_struct_0 @ A ) @ ( u2_struct_0 @ A ) @ ( u1_algstr_0 @ A ) @ ( u1_rlvect_1 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ) ),file(rltopsp1,v5_rltopsp1)).
thf(redefinition_k3_finseq_2,axiom,( ! [A: $i] : ( = @ ( k3_finseq_2 @ A ) @ ( k13_finseq_1 @ A ) ) ),file(finseq_2,k3_finseq_2)).
thf(dt_k10_finseq_1,axiom,( $true ),file(finseq_1,k10_finseq_1)).
thf(dt_k1_card_1,axiom,( ! [A: $i] : ( v1_card_1 @ ( k1_card_1 @ A ) ) ),file(card_1,k1_card_1)).
thf(dt_k1_xreal_0,axiom,( $true ),file(xreal_0,k1_xreal_0)).
thf(dt_k2_xcmplx_0,axiom,( $true ),file(xcmplx_0,k2_xcmplx_0)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_finseq_2,axiom,( ! [A: $i] : ( m1_finseq_2 @ ( k3_finseq_2 @ A ) @ A ) ),file(finseq_2,k3_finseq_2)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(dt_k5_finseq_1,axiom,( $true ),file(finseq_1,k5_finseq_1)).
thf(dt_k7_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_finseq_1 @ B ) ) => ( ( v1_relat_1 @ ( k7_finseq_1 @ A @ B ) ) & ( v1_funct_1 @ ( k7_finseq_1 @ A @ B ) ) & ( v1_finseq_1 @ ( k7_finseq_1 @ A @ B ) ) ) ) ),file(finseq_1,k7_finseq_1)).
thf(dt_l1_rltopsp1,axiom,( ! [A: $i] : ( ( l1_rltopsp1 @ A ) => ( ( l1_rlvect_1 @ A ) & ( l1_pre_topc @ A ) ) ) ),file(rltopsp1,l1_rltopsp1)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_m1_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_finseq_1 @ B @ A ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_finseq_1 @ B ) ) ) ),file(finseq_1,m1_finseq_1)).
thf(cc10_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_finseq_1 @ B ) ) ) ),file(finseq_1,cc10_finseq_1)).
thf(cc10_ordinal1,axiom,( ! [A: $i] : ( ( v6_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v6_ordinal1 @ B ) ) ) ),file(ordinal1,cc10_ordinal1)).
thf(cc11_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v3_finseq_1 @ B ) ) ) ),file(finseq_1,cc11_finseq_1)).
thf(cc1_jordan2c,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ A ) ) ) ) => ( ( v2_compts_1 @ B @ ( k15_euclid @ A ) ) => ( v9_rltopsp1 @ B @ ( k15_euclid @ A ) ) ) ) ) ),file(jordan2c,cc1_jordan2c)).
thf(cc1_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) ) ),file(nat_1,cc1_nat_1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc2_euclid,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k15_euclid @ A ) ) ) => ( v1_finseq_1 @ B ) ) ) ),file(euclid,cc2_euclid)).
thf(cc2_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) ) ),file(finseq_1,cc2_finseq_1)).
thf(cc2_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_finset_1 @ B ) ) ) ),file(finset_1,cc2_finset_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_euclid,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k15_euclid @ A ) ) ) => ( v3_valued_0 @ B ) ) ) ),file(euclid,cc3_euclid)).
thf(cc3_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_finseq_1 @ B @ A ) => ( v5_relat_1 @ B @ A ) ) ),file(finseq_1,cc3_finseq_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_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xcmplx_0 @ A ) ) ),file(xreal_0,cc3_xreal_0)).
thf(cc3_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) ) => ( ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc3_xxreal_0)).
thf(cc4_euclid,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k15_euclid @ A ) ) ) => ( v3_card_1 @ B @ A ) ) ) ),file(euclid,cc4_euclid)).
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_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) ) ),file(finseq_1,cc5_finseq_1)).
thf(cc5_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_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(cc6_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finseq_1 @ A ) ) ) ),file(finseq_1,cc6_finseq_1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(cc6_xxreal_0,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) ) => ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc6_xxreal_0)).
thf(cc7_finset_1,axiom,( ! [A: $i] : ( ( v5_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_finset_1 @ B ) ) ) ),file(finset_1,cc7_finset_1)).
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_finset_1,axiom,( ! [A: $i] : ( ( v5_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_finset_1 @ B ) ) ) ),file(finset_1,cc8_finset_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_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
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_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ( v4_funct_1 @ A ) ) ),file(finseq_1,cc9_finseq_1)).
thf(cc9_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_funct_1 @ B ) ) ) ),file(funct_1,cc9_funct_1)).
thf(fc10_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_finseq_1 @ ( k10_finseq_1 @ A @ B ) ) ),file(finseq_1,fc10_finseq_1)).
thf(fc10_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v2_xxreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc10_xreal_0)).
thf(fc11_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( m1_subset_1 @ B @ ( k9_xtuple_0 @ A ) ) ) => ~ ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(funct_1,fc11_funct_1)).
thf(fc11_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v3_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v2_xxreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc11_xreal_0)).
thf(fc12_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v3_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v2_xxreal_0 @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc12_xreal_0)).
thf(fc13_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v3_xxreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc13_xreal_0)).
thf(fc14_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_finset_1 @ A ) & ( v1_finset_1 @ B ) ) => ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(finset_1,fc14_finset_1)).
thf(fc14_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v3_xxreal_0 @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc14_xreal_0)).
thf(fc16_finseq_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k5_finseq_1 @ A ) ) ),file(finseq_1,fc16_finseq_1)).
thf(fc17_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ~ ( v1_xboole_0 @ B ) & ( v1_finseq_1 @ B ) ) => ( ( v1_relat_1 @ ( k7_finseq_1 @ A @ B ) ) & ( v1_funct_1 @ ( k7_finseq_1 @ A @ B ) ) & ~ ( v1_xboole_0 @ ( k7_finseq_1 @ A @ B ) ) & ( v1_finseq_1 @ ( k7_finseq_1 @ A @ B ) ) ) ) ),file(finseq_1,fc17_finseq_1)).
thf(fc17_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc17_finset_1)).
thf(fc18_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ~ ( v1_xboole_0 @ B ) & ( v1_finseq_1 @ B ) ) => ( ( v1_relat_1 @ ( k7_finseq_1 @ B @ A ) ) & ( v1_funct_1 @ ( k7_finseq_1 @ B @ A ) ) & ~ ( v1_xboole_0 @ ( k7_finseq_1 @ B @ A ) ) & ( v1_finseq_1 @ ( k7_finseq_1 @ B @ A ) ) ) ) ),file(finseq_1,fc18_finseq_1)).
thf(fc19_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ~ ( v1_xboole_0 @ ( k10_finseq_1 @ A @ B ) ) ),file(finseq_1,fc19_finseq_1)).
thf(fc19_finset_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_finset_1 @ A ) ) => ( v1_finset_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(finset_1,fc19_finset_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(fc1_jordan2c,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v5_rltopsp1 @ ( k15_euclid @ A ) ) & ( v6_rltopsp1 @ ( k15_euclid @ A ) ) & ( v7_rltopsp1 @ ( k15_euclid @ A ) ) ) ) ),file(jordan2c,fc1_jordan2c)).
thf(fc1_jordan8,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) & ( v7_ordinal1 @ B ) ) => ( ~ ( v3_relat_1 @ ( k1_jordan8 @ A @ B ) ) & ( v1_matrix_1 @ ( k1_jordan8 @ A @ B ) ) & ( v2_goboard1 @ ( k1_jordan8 @ A @ B ) ) & ( v3_goboard1 @ ( k1_jordan8 @ A @ B ) ) ) ) ),file(jordan8,fc1_jordan8)).
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(fc24_finseq_1,axiom,( ! [A: $i] : ( v3_card_1 @ ( k5_finseq_1 @ A ) @ np__1 ) ),file(finseq_1,fc24_finseq_1)).
thf(fc25_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( v3_card_1 @ ( k10_finseq_1 @ A @ B ) @ np__2 ) ),file(finseq_1,fc25_finseq_1)).
thf(fc2_jordan8,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v2_compts_1 @ A @ ( k15_euclid @ np__2 ) ) & ~ ( v1_sppol_1 @ A ) & ~ ( v2_sppol_1 @ A ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) & ( v7_ordinal1 @ B ) ) => ( ( v1_matrix_1 @ ( k1_jordan8 @ A @ B ) ) & ( v4_goboard1 @ ( k1_jordan8 @ A @ B ) ) & ( v5_goboard1 @ ( k1_jordan8 @ A @ B ) ) ) ) ),file(jordan8,fc2_jordan8)).
thf(fc31_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v5_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc31_finset_1)).
thf(fc35_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finset_1 @ A ) ) => ( v1_finset_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(finset_1,fc35_finset_1)).
thf(fc37_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xreal_0 @ A ) & ( v1_xreal_0 @ B ) ) => ( v1_xreal_0 @ ( k1_xreal_0 @ A @ B ) ) ) ),file(xreal_0,fc37_xreal_0)).
thf(fc38_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xreal_0 @ A ) & ( v1_xreal_0 @ B ) ) => ( ~ ( v3_xxreal_0 @ ( k1_xreal_0 @ A @ B ) ) & ( v1_xreal_0 @ ( k1_xreal_0 @ A @ B ) ) ) ) ),file(xreal_0,fc38_xreal_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(fc4_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v7_ordinal1 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(nat_1,fc4_nat_1)).
thf(fc4_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v5_ordinal1 @ A ) ) => ( v3_ordinal1 @ ( k9_xtuple_0 @ A ) ) ) ),file(ordinal1,fc4_ordinal1)).
thf(fc5_euclid,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ~ ( v2_struct_0 @ ( k15_euclid @ A ) ) & ( v5_rltopsp1 @ ( k15_euclid @ A ) ) ) ) ),file(euclid,fc5_euclid)).
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_euclid,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v2_pre_topc @ ( k15_euclid @ A ) ) & ( v13_algstr_0 @ ( k15_euclid @ A ) ) & ( v2_rlvect_1 @ ( k15_euclid @ A ) ) & ( v3_rlvect_1 @ ( k15_euclid @ A ) ) & ( v4_rlvect_1 @ ( k15_euclid @ A ) ) & ( v5_rlvect_1 @ ( k15_euclid @ A ) ) & ( v6_rlvect_1 @ ( k15_euclid @ A ) ) & ( v7_rlvect_1 @ ( k15_euclid @ A ) ) & ( v8_rlvect_1 @ ( k15_euclid @ A ) ) & ( v5_rltopsp1 @ ( k15_euclid @ A ) ) ) ) ),file(euclid,fc6_euclid)).
thf(fc6_finseq_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ ( k5_finseq_1 @ A ) ) & ( v1_funct_1 @ ( k5_finseq_1 @ A ) ) ) ),file(finseq_1,fc6_finseq_1)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(fc7_euclid,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v2_monoid_0 @ ( k15_euclid @ A ) ) & ( v5_rltopsp1 @ ( k15_euclid @ A ) ) ) ) ),file(euclid,fc7_euclid)).
thf(fc7_finseq_1,axiom,( ! [A: $i] : ( v1_finseq_1 @ ( k5_finseq_1 @ A ) ) ),file(finseq_1,fc7_finseq_1)).
thf(fc8_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ ( k10_finseq_1 @ A @ B ) ) & ( v1_funct_1 @ ( k10_finseq_1 @ A @ B ) ) ) ),file(finseq_1,fc8_finseq_1)).
thf(fc8_sppol_2,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) => ( v1_topreal1 @ ( k5_finseq_1 @ A ) ) ) ),file(sppol_2,fc8_sppol_2)).
thf(fc9_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v3_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v3_xxreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc9_xreal_0)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_1)).
thf(rc1_jordan1a,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) & ~ ( v1_xboole_0 @ A ) & ( v1_topreal2 @ A ) & ( v2_compts_1 @ A @ ( k15_euclid @ np__2 ) ) & ~ ( v1_sppol_1 @ A ) & ~ ( v2_sppol_1 @ A ) ) ),file(jordan1a,rc1_jordan1a)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc1_sppol_1,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) & ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) & ( v2_compts_1 @ A @ ( k15_euclid @ np__2 ) ) & ( v1_sppol_1 @ A ) ) ),file(sppol_1,rc1_sppol_1)).
thf(rc1_topreal2,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) & ( v4_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_topreal2 @ A ) ) ),file(topreal2,rc1_topreal2)).
thf(rc1_xreal_0,axiom,( ? [A: $i] : ( v1_xreal_0 @ A ) ),file(xreal_0,rc1_xreal_0)).
thf(rc1_xxreal_0,axiom,( ? [A: $i] : ( v1_xxreal_0 @ A ) ),file(xxreal_0,rc1_xxreal_0)).
thf(rc2_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(finset_1,rc2_finset_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_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
thf(rc2_sppol_1,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) & ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) & ( v2_compts_1 @ A @ ( k15_euclid @ np__2 ) ) & ( v2_sppol_1 @ A ) ) ),file(sppol_1,rc2_sppol_1)).
thf(rc2_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) ) ),file(xxreal_0,rc2_xxreal_0)).
thf(rc3_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc3_finset_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_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) ),file(xxreal_0,rc3_xxreal_0)).
thf(rc4_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc4_funct_1)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(rc4_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,rc4_xxreal_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_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(rc8_finseq_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v3_finseq_1 @ A ) ) ),file(finseq_1,rc8_finseq_1)).
thf(rc8_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v5_finset_1 @ A ) ) ),file(finset_1,rc8_finset_1)).
thf(rc9_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finset_1 @ A ) ) ),file(finset_1,rc9_finset_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(projectivity_k3_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( = @ ( k3_finseq_1 @ ( k3_finseq_1 @ A ) ) @ ( k3_finseq_1 @ A ) ) ) ),file(finseq_1,k3_finseq_1)).
thf(symmetry_r1_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( r1_xboole_0 @ A @ B ) => ( r1_xboole_0 @ B @ A ) ) ),file(xboole_0,r1_xboole_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_k12_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) ) => ( = @ ( k12_finseq_1 @ A @ B ) @ ( k5_finseq_1 @ B ) ) ) ),file(finseq_1,k12_finseq_1)).
thf(redefinition_k2_finseq_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) & ( m1_subset_1 @ C @ A ) ) => ( = @ ( k2_finseq_4 @ A @ B @ C ) @ ( k10_finseq_1 @ B @ C ) ) ) ),file(finseq_4,k2_finseq_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_k3_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( = @ ( k3_finseq_1 @ A ) @ ( k1_card_1 @ A ) ) ) ),file(finseq_1,k3_finseq_1)).
thf(redefinition_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_k7_nat_d,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( v7_ordinal1 @ B ) ) => ( = @ ( k7_nat_d @ A @ B ) @ ( k1_xreal_0 @ A @ B ) ) ) ),file(nat_d,k7_nat_d)).
thf(redefinition_k8_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_finseq_1 @ B @ A ) & ( m1_finseq_1 @ C @ A ) ) => ( = @ ( k8_finseq_1 @ A @ B @ C ) @ ( k7_finseq_1 @ B @ C ) ) ) ),file(finseq_1,k8_finseq_1)).
thf(redefinition_m2_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m2_finseq_1 @ B @ A ) <=> ( m1_finseq_1 @ B @ A ) ) ),file(finseq_1,m2_finseq_1)).
thf(redefinition_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) <=> ( m1_subset_1 @ C @ B ) ) ) ),file(subset_1,m2_subset_1)).
thf(dt_k12_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) ) => ( m2_finseq_1 @ ( k12_finseq_1 @ A @ B ) @ A ) ) ),file(finseq_1,k12_finseq_1)).
thf(dt_k15_euclid,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v5_rltopsp1 @ ( k15_euclid @ A ) ) & ( l1_rltopsp1 @ ( k15_euclid @ A ) ) ) ) ),file(euclid,k15_euclid)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_jordan8,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) & ( v7_ordinal1 @ B ) ) => ( ( v1_matrix_1 @ ( k1_jordan8 @ A @ B ) ) & ( m2_finseq_1 @ ( k1_jordan8 @ A @ B ) @ ( k3_finseq_2 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) ) ) ),file(jordan8,k1_jordan8)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_finseq_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) & ( m1_subset_1 @ C @ A ) ) => ( m2_finseq_1 @ ( k2_finseq_4 @ A @ B @ C ) @ A ) ) ),file(finseq_4,k2_finseq_4)).
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_k3_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( m2_subset_1 @ ( k3_finseq_1 @ A ) @ k1_numbers @ k5_numbers ) ) ),file(finseq_1,k3_finseq_1)).
thf(dt_k3_gobrd13,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_finseq_1 @ A @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) & ~ ( v3_relat_1 @ B ) & ( v1_matrix_1 @ B ) & ( v2_goboard1 @ B ) & ( v3_goboard1 @ B ) & ( v4_goboard1 @ B ) & ( v5_goboard1 @ B ) & ( m1_finseq_1 @ B @ ( k3_finseq_2 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) & ( m1_subset_1 @ C @ k5_numbers ) ) => ( m1_subset_1 @ ( k3_gobrd13 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) ) ),file(gobrd13,k3_gobrd13)).
thf(dt_k3_jordan11,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_topreal2 @ A ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ( m2_subset_1 @ ( k3_jordan11 @ A @ B ) @ k1_numbers @ k5_numbers ) ) ),file(jordan11,k3_jordan11)).
thf(dt_k3_jordan1h,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_compts_1 @ A @ ( k15_euclid @ np__2 ) ) & ~ ( v1_sppol_1 @ A ) & ~ ( v2_sppol_1 @ A ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ( m2_subset_1 @ ( k3_jordan1h @ A @ B ) @ k1_numbers @ k5_numbers ) ) ),file(jordan1h,k3_jordan1h)).
thf(dt_k3_matrix_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_matrix_1 @ B ) & ( m1_finseq_1 @ B @ ( k3_finseq_2 @ A ) ) & ( v7_ordinal1 @ C ) & ( v7_ordinal1 @ D ) ) => ( m1_subset_1 @ ( k3_matrix_1 @ A @ B @ C @ D ) @ A ) ) ),file(matrix_1,k3_matrix_1)).
thf(dt_k4_gobrd13,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_finseq_1 @ A @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) & ~ ( v3_relat_1 @ B ) & ( v1_matrix_1 @ B ) & ( v2_goboard1 @ B ) & ( v3_goboard1 @ B ) & ( v4_goboard1 @ B ) & ( v5_goboard1 @ B ) & ( m1_finseq_1 @ B @ ( k3_finseq_2 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) & ( m1_subset_1 @ C @ k5_numbers ) ) => ( m1_subset_1 @ ( k4_gobrd13 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) ) ),file(gobrd13,k4_gobrd13)).
thf(dt_k5_gobrd13,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_finseq_1 @ A @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) & ~ ( v3_relat_1 @ B ) & ( v1_matrix_1 @ B ) & ( v2_goboard1 @ B ) & ( v3_goboard1 @ B ) & ( v4_goboard1 @ B ) & ( v5_goboard1 @ B ) & ( m1_finseq_1 @ B @ ( k3_finseq_2 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) & ( m1_subset_1 @ C @ k5_numbers ) ) => ( m1_subset_1 @ ( k5_gobrd13 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) ) ),file(gobrd13,k5_gobrd13)).
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_k7_nat_d,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( v7_ordinal1 @ B ) ) => ( m1_subset_1 @ ( k7_nat_d @ A @ B ) @ k5_numbers ) ) ),file(nat_d,k7_nat_d)).
thf(dt_k8_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_finseq_1 @ B @ A ) & ( m1_finseq_1 @ C @ A ) ) => ( m2_finseq_1 @ ( k8_finseq_1 @ A @ B @ C ) @ A ) ) ),file(finseq_1,k8_finseq_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_m2_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m2_finseq_1 @ B @ A ) => ( ( v1_funct_1 @ B ) & ( v1_finseq_1 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ A ) ) ) ) ) ),file(finseq_1,m2_finseq_1)).
thf(dt_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) => ( m1_subset_1 @ C @ A ) ) ) ),file(subset_1,m2_subset_1)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_c1_1__jordan13,axiom,( ~ ( v1_xboole_0 @ c1_1__jordan13 ) & ~ ( v1_sppol_1 @ c1_1__jordan13 ) & ~ ( v2_sppol_1 @ c1_1__jordan13 ) & ( v1_topreal2 @ c1_1__jordan13 ) & ( m1_subset_1 @ c1_1__jordan13 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) ),file(jordan13,c1_1__jordan13)).
thf(dt_c2_1__jordan13,axiom,( m1_subset_1 @ c2_1__jordan13 @ k5_numbers ),file(jordan13,c2_1__jordan13)).
thf(cc1_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_finseq_1 @ A ) ) ) ),file(finseq_1,cc1_finseq_1)).
thf(cc1_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc1_finset_1)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_1)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_1)).
thf(cc1_topreal2,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) => ( ( v1_topreal2 @ A ) => ( ~ ( v1_xboole_0 @ A ) & ( v2_compts_1 @ A @ ( k15_euclid @ np__2 ) ) ) ) ) ),file(topreal2,cc1_topreal2)).
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_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_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_topreal6,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) => ( ~ ( v1_sppol_1 @ A ) => ~ ( v1_xboole_0 @ A ) ) ) ),file(topreal6,cc2_topreal6)).
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_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_topreal6,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) => ( ~ ( v2_sppol_1 @ A ) => ~ ( v1_xboole_0 @ A ) ) ) ),file(topreal6,cc3_topreal6)).
thf(cc4_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_finseq_1 @ A ) ) ) ),file(finseq_1,cc4_finseq_1)).
thf(cc4_funct_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) ) ),file(funct_1,cc4_funct_1)).
thf(cc4_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(cc6_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_1)).
thf(cc6_topreal6,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) => ( ( v1_xboole_0 @ A ) => ( v1_sppol_1 @ A ) ) ) ),file(topreal6,cc6_topreal6)).
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_topreal6,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) => ( ( v1_xboole_0 @ A ) => ( v2_sppol_1 @ A ) ) ) ),file(topreal6,cc7_topreal6)).
thf(cc8_finseq_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_finseq_1 @ A ) ) ),file(finseq_1,cc8_finseq_1)).
thf(cc8_topreal6,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) ) => ( ( v1_topreal2 @ A ) => ( v2_connsp_1 @ A @ ( k15_euclid @ np__2 ) ) ) ) ),file(topreal6,cc8_topreal6)).
thf(cc9_finset_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_finset_1 @ A ) ) ) ),file(finset_1,cc9_finset_1)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(fc10_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc10_relat_1)).
thf(fc8_relat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ~ ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc8_relat_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_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(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(e6_1_1_1__jordan13,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ! [B: $i] : ? [C: $i] : ( ( ( = @ A @ k6_numbers ) => ( = @ C @ ( k12_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k3_jordan1h @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k3_jordan11 @ c1_1__jordan13 @ c2_1__jordan13 ) ) ) ) ) & ( ( = @ A @ np__1 ) => ( = @ C @ ( k2_finseq_4 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k3_jordan1h @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k3_jordan11 @ c1_1__jordan13 @ c2_1__jordan13 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_jordan1h @ c1_1__jordan13 @ c2_1__jordan13 ) @ np__1 ) @ ( k3_jordan11 @ c1_1__jordan13 @ c2_1__jordan13 ) ) ) ) ) & ( ( m2_finseq_1 @ B @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) => ( ( r1_xxreal_0 @ A @ np__1 ) | ! [D: $i] : ( ( m2_finseq_1 @ D @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) => ( ( = @ B @ D ) => ( ( ( = @ ( k3_finseq_1 @ D ) @ A ) => ( ( ( r1_goboard1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ D @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) ) => ( ( r1_xboole_0 @ ( k3_gobrd13 @ D @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ D ) @ np__1 ) ) @ c1_1__jordan13 ) | ( ~ ( ( r1_xboole_0 @ ( k4_gobrd13 @ D @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ D ) @ np__1 ) ) @ c1_1__jordan13 ) & ( r1_xboole_0 @ ( k5_gobrd13 @ D @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ D ) @ np__1 ) ) @ c1_1__jordan13 ) & ! [E: $i] : ( ( m1_subset_1 @ E @ k5_numbers ) => ! [F: $i] : ( ( m1_subset_1 @ F @ k5_numbers ) => ~ ( ( r2_gobrd13 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k8_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ D @ ( k12_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ E @ F ) ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ D ) @ np__1 ) ) & ( = @ C @ ( k8_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ D @ ( k12_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ E @ F ) ) ) ) ) ) ) ) & ~ ( ( r1_xboole_0 @ ( k4_gobrd13 @ D @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ D ) @ np__1 ) ) @ c1_1__jordan13 ) & ~ ( r1_xboole_0 @ ( k5_gobrd13 @ D @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ D ) @ np__1 ) ) @ c1_1__jordan13 ) & ! [E: $i] : ( ( m1_subset_1 @ E @ k5_numbers ) => ! [F: $i] : ( ( m1_subset_1 @ F @ k5_numbers ) => ~ ( ( r3_gobrd13 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k8_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ D @ ( k12_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ E @ F ) ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ D ) @ np__1 ) ) & ( = @ C @ ( k8_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ D @ ( k12_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ E @ F ) ) ) ) ) ) ) ) & ~ ( ~ ( r1_xboole_0 @ ( k4_gobrd13 @ D @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ D ) @ np__1 ) ) @ c1_1__jordan13 ) & ! [E: $i] : ( ( m1_subset_1 @ E @ k5_numbers ) => ! [F: $i] : ( ( m1_subset_1 @ F @ k5_numbers ) => ~ ( ( r1_gobrd13 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k8_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ D @ ( k12_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ E @ F ) ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ D ) @ np__1 ) ) & ( = @ C @ ( k8_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ D @ ( k12_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ E @ F ) ) ) ) ) ) ) ) ) ) ) & ( ~ ( ( r1_goboard1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ D @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) ) & ~ ( r1_xboole_0 @ ( k3_gobrd13 @ D @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ D ) @ np__1 ) ) @ c1_1__jordan13 ) ) => ( = @ C @ ( k8_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ D @ ( k12_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ np__1 @ np__1 ) ) ) ) ) ) ) & ( ~ ( = @ ( k3_finseq_1 @ D ) @ A ) => ( = @ C @ k1_xboole_0 ) ) ) ) ) ) ) & ~ ( ~ ( r1_xxreal_0 @ A @ np__1 ) & ~ ( m2_finseq_1 @ B @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) & ~ ( = @ C @ k1_xboole_0 ) ) ) ) ),file(jordan13,e6_1_1_1__jordan13)).
thf(s1_recdef_1,axiom,( ! [A: $i] : ! [B: $i > $i > $i > $o] : ( ! [C: $i] : ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers ) => ! [D: $i] : ? [E: $i] : ( B @ C @ D @ E ) ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ k5_numbers ) & ( = @ ( k1_funct_1 @ C @ k6_numbers ) @ A ) & ! [D: $i] : ( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers ) => ( B @ D @ ( k1_funct_1 @ C @ D ) @ ( k1_funct_1 @ C @ ( k2_nat_1 @ D @ np__1 ) ) ) ) ) ) ),file(recdef_1,s1_recdef_1)).
thf(e7_1_1_1__jordan13,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ k5_numbers ) & ( = @ ( k1_funct_1 @ A @ k6_numbers ) @ k1_xboole_0 ) & ! [B: $i] : ( ( m1_subset_1 @ B @ k5_numbers ) => ( ( ( = @ B @ k6_numbers ) => ( = @ ( k1_funct_1 @ A @ ( k2_nat_1 @ B @ np__1 ) ) @ ( k12_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k3_jordan1h @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k3_jordan11 @ c1_1__jordan13 @ c2_1__jordan13 ) ) ) ) ) & ( ( = @ B @ np__1 ) => ( = @ ( k1_funct_1 @ A @ ( k2_nat_1 @ B @ np__1 ) ) @ ( k2_finseq_4 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k3_jordan1h @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k3_jordan11 @ c1_1__jordan13 @ c2_1__jordan13 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_jordan1h @ c1_1__jordan13 @ c2_1__jordan13 ) @ np__1 ) @ ( k3_jordan11 @ c1_1__jordan13 @ c2_1__jordan13 ) ) ) ) ) & ( ( m2_finseq_1 @ ( k1_funct_1 @ A @ B ) @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) => ( ( r1_xxreal_0 @ B @ np__1 ) | ! [C: $i] : ( ( m2_finseq_1 @ C @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) => ( ( = @ ( k1_funct_1 @ A @ B ) @ C ) => ( ( ( = @ ( k3_finseq_1 @ C ) @ B ) => ( ( ( r1_goboard1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ C @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) ) => ( ( r1_xboole_0 @ ( k3_gobrd13 @ C @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ C ) @ np__1 ) ) @ c1_1__jordan13 ) | ( ~ ( ( r1_xboole_0 @ ( k4_gobrd13 @ C @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ C ) @ np__1 ) ) @ c1_1__jordan13 ) & ( r1_xboole_0 @ ( k5_gobrd13 @ C @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ C ) @ np__1 ) ) @ c1_1__jordan13 ) & ! [D: $i] : ( ( m1_subset_1 @ D @ k5_numbers ) => ! [E: $i] : ( ( m1_subset_1 @ E @ k5_numbers ) => ~ ( ( r2_gobrd13 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k8_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ C @ ( k12_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ D @ E ) ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ C ) @ np__1 ) ) & ( = @ ( k1_funct_1 @ A @ ( k2_nat_1 @ B @ np__1 ) ) @ ( k8_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ C @ ( k12_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ D @ E ) ) ) ) ) ) ) ) & ~ ( ( r1_xboole_0 @ ( k4_gobrd13 @ C @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ C ) @ np__1 ) ) @ c1_1__jordan13 ) & ~ ( r1_xboole_0 @ ( k5_gobrd13 @ C @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ C ) @ np__1 ) ) @ c1_1__jordan13 ) & ! [D: $i] : ( ( m1_subset_1 @ D @ k5_numbers ) => ! [E: $i] : ( ( m1_subset_1 @ E @ k5_numbers ) => ~ ( ( r3_gobrd13 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k8_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ C @ ( k12_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ D @ E ) ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ C ) @ np__1 ) ) & ( = @ ( k1_funct_1 @ A @ ( k2_nat_1 @ B @ np__1 ) ) @ ( k8_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ C @ ( k12_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ D @ E ) ) ) ) ) ) ) ) & ~ ( ~ ( r1_xboole_0 @ ( k4_gobrd13 @ C @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ C ) @ np__1 ) ) @ c1_1__jordan13 ) & ! [D: $i] : ( ( m1_subset_1 @ D @ k5_numbers ) => ! [E: $i] : ( ( m1_subset_1 @ E @ k5_numbers ) => ~ ( ( r1_gobrd13 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k8_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ C @ ( k12_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ D @ E ) ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ C ) @ np__1 ) ) & ( = @ ( k1_funct_1 @ A @ ( k2_nat_1 @ B @ np__1 ) ) @ ( k8_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ C @ ( k12_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ D @ E ) ) ) ) ) ) ) ) ) ) ) & ( ~ ( ( r1_goboard1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ C @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) ) & ~ ( r1_xboole_0 @ ( k3_gobrd13 @ C @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ ( k7_nat_d @ ( k3_finseq_1 @ C ) @ np__1 ) ) @ c1_1__jordan13 ) ) => ( = @ ( k1_funct_1 @ A @ ( k2_nat_1 @ B @ np__1 ) ) @ ( k8_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ C @ ( k12_finseq_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k3_matrix_1 @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) @ ( k1_jordan8 @ c1_1__jordan13 @ c2_1__jordan13 ) @ np__1 @ np__1 ) ) ) ) ) ) ) & ( ~ ( = @ ( k3_finseq_1 @ C ) @ B ) => ( = @ ( k1_funct_1 @ A @ ( k2_nat_1 @ B @ np__1 ) ) @ k1_xboole_0 ) ) ) ) ) ) ) & ~ ( ~ ( r1_xxreal_0 @ B @ np__1 ) & ~ ( m2_finseq_1 @ ( k1_funct_1 @ A @ B ) @ ( u1_struct_0 @ ( k15_euclid @ np__2 ) ) ) & ~ ( = @ ( k1_funct_1 @ A @ ( k2_nat_1 @ B @ np__1 ) ) @ k1_xboole_0 ) ) ) ) ) ),file(jordan13,e7_1_1_1__jordan13)).
