% Mizar problem: e3_53_1_1,group_10,3384,17 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_53_type,type,( c1_53__group_10: $i )).
thf(c2_53_type,type,( c2_53__group_10: $i )).
thf(c3_53_type,type,( c3_53__group_10: $i )).
thf(k15_group_10_type,type,( k15_group_10: $i > $i > $i )).
thf(k16_group_10_type,type,( k16_group_10: $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_group_1_type,type,( k1_group_1: $i > $i )).
thf(k1_group_3_type,type,( k1_group_3: $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_partfun1_type,type,( k1_partfun1: $i > $i > $i > $i > $i > $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_funct_2_type,type,( k3_funct_2: $i > $i > $i > $i > $i )).
thf(k3_numbers_type,type,( k3_numbers: $i )).
thf(k3_relat_1_type,type,( k3_relat_1: $i > $i > $i )).
thf(k4_numbers_type,type,( k4_numbers: $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k4_relat_1_type,type,( k4_relat_1: $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_algstr_0_type,type,( k6_algstr_0: $i > $i > $i > $i )).
thf(k6_partfun1_type,type,( k6_partfun1: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l3_algstr_0_type,type,( l3_algstr_0: $i > $o )).
thf(m1_group_2_type,type,( m1_group_2: $i > $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(r2_funct_2_type,type,( r2_funct_2: $i > $i > $i > $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_group_1_type,type,( v1_group_1: $i > $o )).
thf(v1_group_10_type,type,( v1_group_10: $i > $i > $i > $o )).
thf(v1_int_1_type,type,( v1_int_1: $i > $o )).
thf(v1_int_2_type,type,( v1_int_2: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_partfun1_type,type,( v1_partfun1: $i > $i > $o )).
thf(v1_rat_1_type,type,( v1_rat_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_subset_1_type,type,( v1_subset_1: $i > $i > $o )).
thf(v1_valued_0_type,type,( v1_valued_0: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_xcmplx_0_type,type,( v1_xcmplx_0: $i > $o )).
thf(v1_xreal_0_type,type,( v1_xreal_0: $i > $o )).
thf(v1_xxreal_0_type,type,( v1_xxreal_0: $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_card_1_type,type,( v2_card_1: $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_group_1_type,type,( v2_group_1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v2_valued_0_type,type,( v2_valued_0: $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $i > $o )).
thf(v3_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_group_1_type,type,( v3_group_1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $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_group_1_type,type,( v4_group_1: $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_finset_1_type,type,( v5_finset_1: $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v5_valued_0_type,type,( v5_valued_0: $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v6_valued_0_type,type,( v6_valued_0: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v7_valued_0_type,type,( v7_valued_0: $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_0: $i > $o )).
thf(v8_valued_0_type,type,( v8_valued_0: $i > $o )).
thf(fc92_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v7_valued_0 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_valued_0 @ B ) & ( v7_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v7_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc92_valued_0)).
thf(fc94_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v8_valued_0 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_valued_0 @ B ) & ( v8_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v7_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc94_valued_0)).
thf(fc97_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v8_valued_0 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_valued_0 @ B ) & ( v7_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v8_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc97_valued_0)).
thf(fc98_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v8_valued_0 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_valued_0 @ B ) & ( v7_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ B @ A ) ) & ( v8_valued_0 @ ( k3_relat_1 @ B @ A ) ) ) ) ),file(valued_0,fc98_valued_0)).
thf(cc12_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_valued_0 @ A ) & ( v5_valued_0 @ A ) & ( v1_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) & ( v3_valued_0 @ A ) & ( v1_finseq_1 @ A ) ) ) ),file(finseq_1,cc12_finseq_1)).
thf(cc23_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v5_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v7_valued_0 @ A ) ) ) ),file(valued_0,cc23_valued_0)).
thf(cc24_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v6_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v8_valued_0 @ A ) ) ) ),file(valued_0,cc24_valued_0)).
thf(fc91_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v5_valued_0 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_valued_0 @ B ) & ( v5_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v5_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc91_valued_0)).
thf(fc93_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v6_valued_0 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_valued_0 @ B ) & ( v6_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v5_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc93_valued_0)).
thf(fc95_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v6_valued_0 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_valued_0 @ B ) & ( v5_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v6_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc95_valued_0)).
thf(fc96_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v6_valued_0 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_valued_0 @ B ) & ( v5_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ B @ A ) ) & ( v6_valued_0 @ ( k3_relat_1 @ B @ A ) ) ) ) ),file(valued_0,fc96_valued_0)).
thf(rc3_valued_0,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ k5_numbers ) ) ) & ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ( v1_partfun1 @ A @ k5_numbers ) & ( v1_funct_2 @ A @ k5_numbers @ k5_numbers ) & ( v1_valued_0 @ A ) & ( v2_valued_0 @ A ) & ( v3_valued_0 @ A ) & ( v4_valued_0 @ A ) & ( v5_valued_0 @ A ) ) ),file(valued_0,rc3_valued_0)).
thf(redefinition_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) <=> ( m1_subset_1 @ C @ B ) ) ) ),file(subset_1,m2_subset_1)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
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(cc10_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_valued_0 @ B ) ) ) ),file(valued_0,cc10_valued_0)).
thf(cc11_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v2_valued_0 @ B ) ) ) ),file(valued_0,cc11_valued_0)).
thf(cc1_xreal_0,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc1_xreal_0)).
thf(cc22_valued_0,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v5_valued_0 @ A ) & ( v6_valued_0 @ A ) ) ) ),file(valued_0,cc22_valued_0)).
thf(cc30_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k1_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc30_valued_0)).
thf(cc4_card_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc4_card_1)).
thf(cc8_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
thf(fc4_card_1,axiom,( v1_card_1 @ k4_ordinal1 ),file(card_1,fc4_card_1)).
thf(fc55_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v1_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc55_valued_0)).
thf(fc56_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) & ( v2_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v2_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc56_valued_0)).
thf(fc5_card_1,axiom,( v2_card_1 @ k4_ordinal1 ),file(card_1,fc5_card_1)).
thf(fc61_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_valued_0 @ A ) ) => ( v1_xcmplx_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc61_valued_0)).
thf(fc62_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) ) => ( v1_xxreal_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc62_valued_0)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
thf(fc7_card_1,axiom,( ~ ( v1_finset_1 @ k4_ordinal1 ) ),file(card_1,fc7_card_1)).
thf(rc1_int_1,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) & ( v1_xxreal_0 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_int_1 @ A ) ) ),file(int_1,rc1_int_1)).
thf(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(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
thf(dt_k3_numbers,axiom,( $true ),file(numbers,k3_numbers)).
thf(dt_k4_numbers,axiom,( $true ),file(numbers,k4_numbers)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(cc11_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v13_struct_0 @ A @ np__1 ) => ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) ) ) ),file(struct_0,cc11_struct_0)).
thf(cc12_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v3_valued_0 @ B ) ) ) ),file(valued_0,cc12_valued_0)).
thf(cc13_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_relat_1 @ B @ k3_numbers ) ) ) ),file(valued_0,cc13_valued_0)).
thf(cc14_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_relat_1 @ B @ k4_numbers ) ) ) ),file(valued_0,cc14_valued_0)).
thf(cc1_int_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_numbers ) => ( v1_int_1 @ A ) ) ),file(int_1,cc1_int_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_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) ) ),file(valued_0,cc2_valued_0)).
thf(cc31_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k5_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) ) ),file(valued_0,cc31_valued_0)).
thf(cc3_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc3_valued_0)).
thf(cc4_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc4_valued_0)).
thf(cc5_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_valued_0 @ A ) ) ) ),file(valued_0,cc5_valued_0)).
thf(cc6_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_valued_0 @ A ) ) ) ),file(valued_0,cc6_valued_0)).
thf(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(cc9_card_1,axiom,( ! [A: $i] : ( ( v3_card_1 @ A @ np__1 ) => ( ~ ( v1_xboole_0 @ A ) & ( v1_zfmisc_1 @ A ) ) ) ),file(card_1,cc9_card_1)).
thf(fc57_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) & ( v3_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v3_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc57_valued_0)).
thf(fc58_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ k3_numbers ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v5_relat_1 @ ( k3_relat_1 @ A @ B ) @ k3_numbers ) ) ) ),file(valued_0,fc58_valued_0)).
thf(fc59_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ k4_numbers ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v5_relat_1 @ ( k3_relat_1 @ A @ B ) @ k4_numbers ) ) ) ),file(valued_0,fc59_valued_0)).
thf(fc63_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_valued_0 @ A ) ) => ( v1_xreal_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc63_valued_0)).
thf(fc64_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) & ( v1_funct_1 @ A ) ) => ( v1_rat_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc64_valued_0)).
thf(fc65_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) & ( v1_funct_1 @ A ) ) => ( v1_int_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc65_valued_0)).
thf(fc8_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ k5_numbers @ k5_numbers ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ k5_numbers ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ k5_numbers @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ B ) ) ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ C ) ) & ( v4_relat_1 @ ( k3_relat_1 @ A @ C ) @ k5_numbers ) & ( v5_relat_1 @ ( k3_relat_1 @ A @ C ) @ B ) & ( v1_funct_1 @ ( k3_relat_1 @ A @ C ) ) ) ) ),file(nat_1,fc8_nat_1)).
thf(fc9_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ k5_numbers @ k5_numbers ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ k5_numbers ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ k5_numbers @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ B ) ) ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ C ) ) & ( v1_partfun1 @ ( k3_relat_1 @ A @ C ) @ k5_numbers ) ) ) ),file(nat_1,fc9_nat_1)).
thf(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(rc2_valued_0,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) & ( v5_relat_1 @ A @ k4_numbers ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) & ( v4_valued_0 @ A ) ) ),file(valued_0,rc2_valued_0)).
thf(rc3_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(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_valued_0,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ A ) ) ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v3_funct_1 @ B ) & ( v1_funct_2 @ B @ k5_numbers @ A ) ) ),file(valued_0,rc4_valued_0)).
thf(rc7_card_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v3_card_1 @ B @ np__1 ) ) ) ),file(card_1,rc7_card_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(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(spc1_numerals,axiom,( ( v2_xxreal_0 @ np__1 ) & ( m2_subset_1 @ np__1 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__1 @ k5_numbers ) & ( m1_subset_1 @ np__1 @ k1_numbers ) ),file(numerals,spc1_numerals)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(cc10_card_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_zfmisc_1 @ A ) ) => ( v3_card_1 @ A @ np__1 ) ) ),file(card_1,cc10_card_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(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_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(cc15_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_valued_0 @ B ) ) ) ),file(valued_0,cc15_valued_0)).
thf(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_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) ) ),file(valued_0,cc1_valued_0)).
thf(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_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_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(cc2_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ~ ( v1_subset_1 @ B @ A ) => ~ ( v1_xboole_0 @ B ) ) ) ) ),file(subset_1,cc2_subset_1)).
thf(cc3_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) ) => ( ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc3_xxreal_0)).
thf(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_1)).
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_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_subset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,cc5_subset_1)).
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_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_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v7_struct_0 @ A ) => ( v8_struct_0 @ A ) ) ) ),file(struct_0,cc6_struct_0)).
thf(cc6_xxreal_0,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) ) => ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc6_xxreal_0)).
thf(cc7_card_1,axiom,( ! [A: $i] : ( ( v3_card_1 @ A @ k1_xboole_0 ) => ( v1_xboole_0 @ A ) ) ),file(card_1,cc7_card_1)).
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_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) ) ),file(valued_0,cc7_valued_0)).
thf(cc8_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_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc8_valued_0)).
thf(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_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(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
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(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(fc60_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) & ( v4_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v4_valued_0 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc60_valued_0)).
thf(fc66_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v4_valued_0 @ A ) ) => ( v7_ordinal1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc66_valued_0)).
thf(fc6_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_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_funct_1 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v2_funct_1 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(funct_1,fc7_funct_1)).
thf(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(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(rc1_valued_0,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v4_valued_0 @ A ) ) ),file(valued_0,rc1_valued_0)).
thf(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(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(rc2_card_1,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) ),file(card_1,rc2_card_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_newton,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) & ( v1_int_1 @ A ) & ( v1_int_2 @ A ) & ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) ),file(newton,rc2_newton)).
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(rc2_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) ) ),file(xxreal_0,rc2_xxreal_0)).
thf(rc3_ordinal1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v5_ordinal1 @ B ) ) ),file(ordinal1,rc3_ordinal1)).
thf(rc3_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_subset_1 @ B @ A ) ) ),file(subset_1,rc3_subset_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_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v1_subset_1 @ B @ A ) ) ) ),file(subset_1,rc4_subset_1)).
thf(rc4_xreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc4_xreal_0)).
thf(rc5_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ? [B: $i] : ( v3_card_1 @ B @ A ) ) ),file(card_1,rc5_card_1)).
thf(rc5_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) ),file(funct_1,rc5_funct_1)).
thf(rc5_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,rc5_subset_1)).
thf(rc6_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v3_card_1 @ B @ A ) ) ) ),file(card_1,rc6_card_1)).
thf(rc6_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,rc6_subset_1)).
thf(rc6_valued_0,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v4_valued_0 @ B ) ) ),file(valued_0,rc6_valued_0)).
thf(rc7_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(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(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_group_3,axiom,( $true ),file(group_3,k1_group_3)).
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_relat_1,axiom,( ! [A: $i] : ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ),file(relat_1,k4_relat_1)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(cc1_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(card_1,cc1_card_1)).
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_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_partfun1 @ C @ A ) => ( v1_funct_2 @ C @ A @ B ) ) ) ),file(funct_2,cc1_funct_2)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
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_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_xboole_0 @ B ) ) ) ),file(subset_1,cc1_subset_1)).
thf(cc2_card_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc2_card_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_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_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_2 @ C @ A @ B ) => ( v1_partfun1 @ C @ A ) ) ) ) ),file(funct_2,cc2_funct_2)).
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(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_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_2 @ C @ A @ B ) => ( v1_partfun1 @ C @ A ) ) ) ) ),file(funct_2,cc3_funct_2)).
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_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc3_relset_1)).
thf(cc3_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ( v1_xboole_0 @ B ) => ( v1_subset_1 @ B @ A ) ) ) ) ),file(subset_1,cc3_subset_1)).
thf(cc3_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xcmplx_0 @ A ) ) ),file(xreal_0,cc3_xreal_0)).
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_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc4_relset_1)).
thf(cc4_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc4_struct_0)).
thf(cc4_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ~ ( v1_subset_1 @ B @ A ) ) ) ),file(subset_1,cc4_subset_1)).
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_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_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(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_card_1,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v1_finset_1 @ A ) ) => ( v7_ordinal1 @ A ) ) ),file(card_1,cc6_card_1)).
thf(cc6_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_1)).
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_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ~ ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc7_struct_0)).
thf(cc7_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) => ( ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc7_xxreal_0)).
thf(cc8_card_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_card_1 @ A @ k1_xboole_0 ) ) ),file(card_1,cc8_card_1)).
thf(cc8_finseq_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_finseq_1 @ A ) ) ),file(finseq_1,cc8_finseq_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_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ! [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_xboole_0 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) ) ) ) ),file(funct_2,cc8_funct_2)).
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_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_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_funct_1 @ B ) ) ) ),file(funct_1,cc9_funct_1)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(cc9_valued_0,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) ) ),file(valued_0,cc9_valued_0)).
thf(fc10_card_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_finset_1 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(card_1,fc10_card_1)).
thf(fc10_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(subset_1,fc10_subset_1)).
thf(fc11_card_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_finset_1 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_finset_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) ),file(card_1,fc11_card_1)).
thf(fc11_funct_2,axiom,( ! [A: $i] : ( ( v1_relat_1 @ ( k4_relat_1 @ A ) ) & ( v4_relat_1 @ ( k4_relat_1 @ A ) @ A ) & ( v1_funct_1 @ ( k4_relat_1 @ A ) ) & ( v1_partfun1 @ ( k4_relat_1 @ A ) @ A ) ) ),file(funct_2,fc11_funct_2)).
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(fc17_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc17_finset_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(fc1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ) ),file(funct_2,fc1_funct_2)).
thf(fc1_group_10,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v2_struct_0 @ B ) & ( v2_group_1 @ B ) & ( l3_algstr_0 @ B ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( u1_struct_0 @ B ) @ ( k1_funct_2 @ A @ A ) ) & ( v1_group_10 @ D @ B @ A ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ B ) @ ( k1_funct_2 @ A @ A ) ) ) ) ) => ( ( v1_funct_1 @ ( k1_funct_1 @ D @ C ) ) & ( v2_funct_1 @ ( k1_funct_1 @ D @ C ) ) & ( v1_funct_2 @ ( k1_funct_1 @ D @ C ) @ A @ A ) ) ) ),file(group_10,fc1_group_10)).
thf(fc1_group_3,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_group_1 @ A ) & ( v3_group_1 @ A ) & ( l3_algstr_0 @ A ) ) => ~ ( v1_xboole_0 @ ( k1_group_3 @ A ) ) ) ),file(group_3,fc1_group_3)).
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(fc20_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ B @ A ) ) & ( v1_finset_1 @ ( k3_relat_1 @ B @ A ) ) ) ) ),file(finset_1,fc20_finset_1)).
thf(fc2_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v1_funct_1 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(funct_1,fc2_funct_1)).
thf(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(fc31_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v5_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc31_finset_1)).
thf(fc3_funct_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ ( k4_relat_1 @ A ) ) & ( v1_funct_1 @ ( k4_relat_1 @ A ) ) ) ),file(funct_1,fc3_funct_1)).
thf(fc3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_xboole_0 @ B ) ) => ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ) ),file(funct_2,fc3_funct_2)).
thf(fc4_funct_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ ( k4_relat_1 @ A ) ) & ( v2_funct_1 @ ( k4_relat_1 @ A ) ) ) ),file(funct_1,fc4_funct_1)).
thf(fc4_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ A ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) ) => ( ( v1_funct_1 @ ( k3_relat_1 @ D @ C ) ) & ( v1_funct_2 @ ( k3_relat_1 @ D @ C ) @ A @ B ) ) ) ),file(funct_2,fc4_funct_2)).
thf(fc5_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ B @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ B ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( v1_funct_1 @ ( k3_relat_1 @ D @ C ) ) & ( v1_funct_2 @ ( k3_relat_1 @ D @ C ) @ A @ B ) ) ) ),file(funct_2,fc5_funct_2)).
thf(fc7_relset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ( ~ ( v1_xboole_0 @ ( k4_relat_1 @ A ) ) & ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ) ) ),file(relset_1,fc7_relset_1)).
thf(fc8_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ B @ C ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) ) ) => ( ( v1_funct_1 @ ( k3_relat_1 @ D @ E ) ) & ( v1_funct_2 @ ( k3_relat_1 @ D @ E ) @ A @ C ) ) ) ),file(funct_2,fc8_funct_2)).
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_card_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(card_1,fc9_card_1)).
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_card_1,axiom,( ? [A: $i] : ( v1_card_1 @ A ) ),file(card_1,rc1_card_1)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) ),file(funct_2,rc1_funct_2)).
thf(rc1_group_10,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v1_group_1 @ A ) & ( l3_algstr_0 @ A ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( k1_funct_2 @ B @ B ) ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ ( u1_struct_0 @ A ) ) & ( v5_relat_1 @ C @ ( k1_funct_2 @ B @ B ) ) & ~ ( v1_xboole_0 @ C ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) ) & ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( k1_funct_2 @ B @ B ) ) & ( v1_group_10 @ C @ A @ B ) ) ) ),file(group_10,rc1_group_10)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relset_1,rc1_relset_1)).
thf(rc1_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(subset_1,rc1_subset_1)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc1_xreal_0,axiom,( ? [A: $i] : ( v1_xreal_0 @ A ) ),file(xreal_0,rc1_xreal_0)).
thf(rc1_xxreal_0,axiom,( ? [A: $i] : ( v1_xxreal_0 @ A ) ),file(xxreal_0,rc1_xxreal_0)).
thf(rc2_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_int_1,axiom,( ? [A: $i] : ( v1_int_1 @ A ) ),file(int_1,rc2_int_1)).
thf(rc2_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v1_xboole_0 @ B ) ) ),file(subset_1,rc2_subset_1)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc3_card_1,axiom,( ? [A: $i] : ~ ( v1_finset_1 @ A ) ),file(card_1,rc3_card_1)).
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_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) ),file(xxreal_0,rc3_xxreal_0)).
thf(rc4_card_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_finset_1 @ B ) ) ) ),file(card_1,rc4_card_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_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,rc4_xxreal_0)).
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(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
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_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(symmetry_r2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( r2_funct_2 @ A @ B @ C @ D ) => ( r2_funct_2 @ A @ B @ D @ C ) ) ) ),file(funct_2,r2_funct_2)).
thf(reflexivity_r2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( r2_funct_2 @ A @ B @ C @ C ) ) ),file(funct_2,r2_funct_2)).
thf(redefinition_k1_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ( v1_funct_1 @ E ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_funct_1 @ F ) & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ C @ D ) ) ) ) => ( = @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) @ ( k3_relat_1 @ E @ F ) ) ) ),file(partfun1,k1_partfun1)).
thf(redefinition_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ),file(funct_2,k3_funct_2)).
thf(redefinition_k6_partfun1,axiom,( ! [A: $i] : ( = @ ( k6_partfun1 @ A ) @ ( k4_relat_1 @ A ) ) ),file(partfun1,k6_partfun1)).
thf(redefinition_r2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( r2_funct_2 @ A @ B @ C @ D ) <=> ( = @ C @ D ) ) ) ),file(funct_2,r2_funct_2)).
thf(dt_k15_group_10,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_group_1 @ A ) & ( v3_group_1 @ A ) & ( l3_algstr_0 @ A ) & ( v7_ordinal1 @ B ) ) => ( m1_subset_1 @ ( k15_group_10 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_group_3 @ A ) ) ) ) ),file(group_10,k15_group_10)).
thf(dt_k16_group_10,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) & ( v2_group_1 @ A ) & ( v3_group_1 @ A ) & ( l3_algstr_0 @ A ) & ( v7_ordinal1 @ B ) & ( v1_int_2 @ B ) & ( m1_group_2 @ C @ A ) & ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) ) ) => ( ( v1_funct_1 @ ( k16_group_10 @ A @ B @ C @ D ) ) & ( v1_funct_2 @ ( k16_group_10 @ A @ B @ C @ D ) @ ( k15_group_10 @ A @ B ) @ ( k15_group_10 @ A @ B ) ) & ( m1_subset_1 @ ( k16_group_10 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k15_group_10 @ A @ B ) @ ( k15_group_10 @ A @ B ) ) ) ) ) ) ),file(group_10,k16_group_10)).
thf(dt_k1_funct_2,axiom,( $true ),file(funct_2,k1_funct_2)).
thf(dt_k1_group_1,axiom,( ! [A: $i] : ( ( l3_algstr_0 @ A ) => ( m1_subset_1 @ ( k1_group_1 @ A ) @ ( u1_struct_0 @ A ) ) ) ),file(group_1,k1_group_1)).
thf(dt_k1_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ( v1_funct_1 @ E ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_funct_1 @ F ) & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ C @ D ) ) ) ) => ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) ) & ( m1_subset_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ D ) ) ) ) ) ),file(partfun1,k1_partfun1)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ B ) ) ),file(funct_2,k3_funct_2)).
thf(dt_k6_algstr_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( l3_algstr_0 @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) => ( m1_subset_1 @ ( k6_algstr_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ) ),file(algstr_0,k6_algstr_0)).
thf(dt_k6_partfun1,axiom,( ! [A: $i] : ( ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A ) & ( m1_subset_1 @ ( k6_partfun1 @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) ) ),file(partfun1,k6_partfun1)).
thf(dt_l3_algstr_0,axiom,( ! [A: $i] : ( ( l3_algstr_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(algstr_0,l3_algstr_0)).
thf(dt_m1_group_2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_group_1 @ A ) & ( l3_algstr_0 @ A ) ) => ! [B: $i] : ( ( m1_group_2 @ B @ A ) => ( ~ ( v2_struct_0 @ B ) & ( v2_group_1 @ B ) & ( l3_algstr_0 @ B ) ) ) ) ),file(group_2,m1_group_2)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_c1_53__group_10,axiom,( ~ ( v2_struct_0 @ c1_53__group_10 ) & ( v8_struct_0 @ c1_53__group_10 ) & ( v2_group_1 @ c1_53__group_10 ) & ( v3_group_1 @ c1_53__group_10 ) & ( l3_algstr_0 @ c1_53__group_10 ) ),file(group_10,c1_53__group_10)).
thf(dt_c2_53__group_10,axiom,( ( v7_ordinal1 @ c2_53__group_10 ) & ( v1_int_2 @ c2_53__group_10 ) ),file(group_10,c2_53__group_10)).
thf(dt_c3_53__group_10,axiom,( m1_group_2 @ c3_53__group_10 @ c1_53__group_10 ),file(group_10,c3_53__group_10)).
thf(cc1_group_1,axiom,( ! [A: $i] : ( ( l3_algstr_0 @ A ) => ( ( v2_group_1 @ A ) => ( v1_group_1 @ A ) ) ) ),file(group_1,cc1_group_1)).
thf(cc1_group_2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_group_1 @ A ) & ( v3_group_1 @ A ) & ( l3_algstr_0 @ A ) ) => ! [B: $i] : ( ( m1_group_2 @ B @ A ) => ( v3_group_1 @ B ) ) ) ),file(group_2,cc1_group_2)).
thf(cc1_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) ) ),file(nat_1,cc1_nat_1)).
thf(cc1_nat_3,axiom,( ! [A: $i] : ( ( ( v7_ordinal1 @ A ) & ( v1_int_2 @ A ) ) => ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) & ( v1_int_2 @ A ) ) ) ),file(nat_3,cc1_nat_3)).
thf(cc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_relat_1 @ C ) ) ),file(relset_1,cc1_relset_1)).
thf(cc2_int_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_int_1 @ A ) ) ),file(int_1,cc2_int_1)).
thf(cc2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ) ),file(relset_1,cc2_relset_1)).
thf(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_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc3_card_1)).
thf(cc3_group_2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) & ( v2_group_1 @ A ) & ( v3_group_1 @ A ) & ( l3_algstr_0 @ A ) ) => ! [B: $i] : ( ( m1_group_2 @ B @ A ) => ( v8_struct_0 @ B ) ) ) ),file(group_2,cc3_group_2)).
thf(cc3_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v7_ordinal1 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(nat_1,cc3_nat_1)).
thf(cc4_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) => ( ( v1_funct_2 @ B @ A @ A ) => ( v1_partfun1 @ B @ A ) ) ) ),file(funct_2,cc4_funct_2)).
thf(cc5_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc5_card_1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(fc10_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( v4_funct_1 @ ( k1_funct_2 @ A @ B ) ) ),file(funct_2,fc10_funct_2)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc2_funct_2,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ) ),file(funct_2,fc2_funct_2)).
thf(fc4_group_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_group_1 @ A ) & ( v3_group_1 @ A ) & ( l3_algstr_0 @ A ) ) => ~ ( v4_group_1 @ ( k1_group_1 @ A ) @ A ) ) ),file(group_1,fc4_group_1)).
thf(fc5_group_10,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) & ( v2_group_1 @ A ) & ( v3_group_1 @ A ) & ( l3_algstr_0 @ A ) & ( v7_ordinal1 @ B ) & ( v1_int_2 @ B ) ) => ( ~ ( v1_xboole_0 @ ( k15_group_10 @ A @ B ) ) & ( v1_finset_1 @ ( k15_group_10 @ A @ B ) ) ) ) ),file(group_10,fc5_group_10)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(e2_53_1_1__group_10,axiom,( r2_funct_2 @ ( k15_group_10 @ c1_53__group_10 @ c2_53__group_10 ) @ ( k15_group_10 @ c1_53__group_10 @ c2_53__group_10 ) @ ( k16_group_10 @ c1_53__group_10 @ c2_53__group_10 @ c3_53__group_10 @ ( k1_group_1 @ c3_53__group_10 ) ) @ ( k6_partfun1 @ ( k15_group_10 @ c1_53__group_10 @ c2_53__group_10 ) ) ),file(group_10,e2_53_1_1__group_10)).
thf(e1_53_1_1__group_10,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( u1_struct_0 @ c3_53__group_10 ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ c3_53__group_10 ) ) => ( r2_funct_2 @ ( k15_group_10 @ c1_53__group_10 @ c2_53__group_10 ) @ ( k15_group_10 @ c1_53__group_10 @ c2_53__group_10 ) @ ( k16_group_10 @ c1_53__group_10 @ c2_53__group_10 @ c3_53__group_10 @ ( k6_algstr_0 @ c3_53__group_10 @ A @ B ) ) @ ( k1_partfun1 @ ( k15_group_10 @ c1_53__group_10 @ c2_53__group_10 ) @ ( k15_group_10 @ c1_53__group_10 @ c2_53__group_10 ) @ ( k15_group_10 @ c1_53__group_10 @ c2_53__group_10 ) @ ( k15_group_10 @ c1_53__group_10 @ c2_53__group_10 ) @ ( k16_group_10 @ c1_53__group_10 @ c2_53__group_10 @ c3_53__group_10 @ B ) @ ( k16_group_10 @ c1_53__group_10 @ c2_53__group_10 @ c3_53__group_10 @ A ) ) ) ) ) ),file(group_10,e1_53_1_1__group_10)).
thf(s1_group_10,axiom,( ! [A: $i] : ! [B: $i > $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ C ) & ( v2_group_1 @ C ) & ( l3_algstr_0 @ C ) & ! [D: $i] : ( ( v1_funct_1 @ ( B @ D ) ) & ( v1_funct_2 @ ( B @ D ) @ A @ A ) & ( m1_subset_1 @ ( B @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) ) ) => ( ( ( r2_funct_2 @ A @ A @ ( B @ ( k1_group_1 @ C ) ) @ ( k6_partfun1 @ A ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) ) => ! [F: $i] : ( ( m1_subset_1 @ F @ ( u1_struct_0 @ C ) ) => ( r2_funct_2 @ A @ A @ ( B @ ( k6_algstr_0 @ C @ E @ F ) ) @ ( k1_partfun1 @ A @ A @ A @ A @ ( B @ F ) @ ( B @ E ) ) ) ) ) ) => ? [E: $i] : ( ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( u1_struct_0 @ C ) @ ( k1_funct_2 @ A @ A ) ) & ( v1_group_10 @ E @ C @ A ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ C ) @ ( k1_funct_2 @ A @ A ) ) ) ) & ! [F: $i] : ( ( m1_subset_1 @ F @ ( u1_struct_0 @ C ) ) => ( = @ ( k3_funct_2 @ ( u1_struct_0 @ C ) @ ( k1_funct_2 @ A @ A ) @ E @ F ) @ ( B @ F ) ) ) ) ) ) ),file(group_10,s1_group_10)).
thf(e3_53_1_1__group_10,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ ( u1_struct_0 @ c3_53__group_10 ) @ ( k1_funct_2 @ ( k15_group_10 @ c1_53__group_10 @ c2_53__group_10 ) @ ( k15_group_10 @ c1_53__group_10 @ c2_53__group_10 ) ) ) & ( v1_group_10 @ A @ c3_53__group_10 @ ( k15_group_10 @ c1_53__group_10 @ c2_53__group_10 ) ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c3_53__group_10 ) @ ( k1_funct_2 @ ( k15_group_10 @ c1_53__group_10 @ c2_53__group_10 ) @ ( k15_group_10 @ c1_53__group_10 @ c2_53__group_10 ) ) ) ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ c3_53__group_10 ) ) => ( = @ ( k3_funct_2 @ ( u1_struct_0 @ c3_53__group_10 ) @ ( k1_funct_2 @ ( k15_group_10 @ c1_53__group_10 @ c2_53__group_10 ) @ ( k15_group_10 @ c1_53__group_10 @ c2_53__group_10 ) ) @ A @ B ) @ ( k16_group_10 @ c1_53__group_10 @ c2_53__group_10 @ c3_53__group_10 @ B ) ) ) ) ),file(group_10,e3_53_1_1__group_10)).
