% Mizar problem: e3_35,binari_3,1529,48 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(n2_type,type,( np__2: $i )).
thf(k1_binari_2_type,type,( k1_binari_2: $i > $i )).
thf(k1_binari_3_type,type,( k1_binari_3: $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_zfmisc_1_type,type,( k1_zfmisc_1: $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_power_type,type,( k3_power: $i > $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k5_series_1_type,type,( k5_series_1: $i > $i > $i )).
thf(k6_margrel1_type,type,( k6_margrel1: $i )).
thf(k7_binarith_type,type,( k7_binarith: $i > $i > $i > $i )).
thf(m1_finseq_1_type,type,( m1_finseq_1: $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_xxreal_0_type,type,( r1_xxreal_0: $i > $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_int_1_type,type,( v1_int_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_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_xboolean_type,type,( v1_xboolean: $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_3_type,type,( v2_card_3: $i > $o )).
thf(v2_finseq_1_type,type,( v2_finseq_1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $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_ordinal1_type,type,( v3_ordinal1: $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_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(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(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_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relset_1,rc1_relset_1)).
thf(rc2_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(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(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(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(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(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_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
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_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_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_relat_1 @ C ) ) ),file(relset_1,cc1_relset_1)).
thf(cc1_xboolean,axiom,( ! [A: $i] : ( ( v1_xboolean @ A ) => ( v7_ordinal1 @ A ) ) ),file(xboolean,cc1_xboolean)).
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_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ) ),file(relset_1,cc2_relset_1)).
thf(cc3_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc3_relset_1)).
thf(cc4_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_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(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(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(cc8_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
thf(fc3_zfmisc_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ B ) => ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(zfmisc_1,fc3_zfmisc_1)).
thf(fc4_zfmisc_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(zfmisc_1,fc4_zfmisc_1)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
thf(rc1_xboolean,axiom,( ? [A: $i] : ( v1_xboolean @ A ) ),file(xboolean,rc1_xboolean)).
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_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) ) ),file(ordinal1,rc2_ordinal1)).
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(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
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_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k3_power,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xreal_0 @ A ) & ( v1_xreal_0 @ B ) ) => ( v1_xreal_0 @ ( k3_power @ A @ B ) ) ) ),file(power,k3_power)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_k6_margrel1,axiom,( $true ),file(margrel1,k6_margrel1)).
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(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(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(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
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_margrel1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k6_margrel1 ) => ( v1_xboolean @ A ) ) ),file(margrel1,cc2_margrel1)).
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_zfmisc_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ~ ( v1_xboole_0 @ A ) ) ),file(zfmisc_1,cc2_zfmisc_1)).
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_int_1,axiom,( ! [A: $i] : ( ( v1_int_1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(int_1,cc3_int_1)).
thf(cc3_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xcmplx_0 @ A ) ) ),file(xreal_0,cc3_xreal_0)).
thf(cc4_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xreal_0,cc4_xreal_0)).
thf(cc5_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal1,cc5_ordinal1)).
thf(cc9_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ( v4_funct_1 @ A ) ) ),file(finseq_1,cc9_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_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_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(fc1_int_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ( v1_int_1 @ B ) ) => ( v1_int_1 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(int_1,fc1_int_1)).
thf(fc2_margrel1,axiom,( ~ ( v1_xboole_0 @ k6_margrel1 ) ),file(margrel1,fc2_margrel1)).
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(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_int_1,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) & ( v1_xxreal_0 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_int_1 @ A ) ) ),file(int_1,rc1_int_1)).
thf(rc1_margrel1,axiom,( ? [A: $i] : ( ( v3_finseq_1 @ A ) & ( v2_card_3 @ A ) ) ),file(margrel1,rc1_margrel1)).
thf(rc1_nat_2,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) & ~ ( v1_zfmisc_1 @ A ) & ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_int_1 @ A ) ) ),file(nat_2,rc1_nat_2)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc1_xreal_0,axiom,( ? [A: $i] : ( v1_xreal_0 @ A ) ),file(xreal_0,rc1_xreal_0)).
thf(rc1_zfmisc_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_zfmisc_1 @ A ) ) ),file(zfmisc_1,rc1_zfmisc_1)).
thf(rc2_int_1,axiom,( ? [A: $i] : ( v1_int_1 @ A ) ),file(int_1,rc2_int_1)).
thf(rc2_xreal_0,axiom,( ? [A: $i] : ( ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc2_xreal_0)).
thf(rc2_zfmisc_1,axiom,( ? [A: $i] : ~ ( v1_zfmisc_1 @ A ) ),file(zfmisc_1,rc2_zfmisc_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_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(rc8_finseq_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v3_finseq_1 @ A ) ) ),file(finseq_1,rc8_finseq_1)).
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(commutativity_k2_xcmplx_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) ) => ( = @ ( k2_xcmplx_0 @ A @ B ) @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(xcmplx_0,k2_xcmplx_0)).
thf(reflexivity_r1_xxreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v1_xxreal_0 @ B ) ) => ( r1_xxreal_0 @ A @ A ) ) ),file(xxreal_0,r1_xxreal_0)).
thf(connectedness_r1_xxreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v1_xxreal_0 @ B ) ) => ( ( r1_xxreal_0 @ A @ B ) | ( r1_xxreal_0 @ B @ A ) ) ) ),file(xxreal_0,r1_xxreal_0)).
thf(redefinition_k1_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(redefinition_k5_series_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( v7_ordinal1 @ B ) ) => ( = @ ( k5_series_1 @ A @ B ) @ ( k3_power @ A @ B ) ) ) ),file(series_1,k5_series_1)).
thf(dt_k1_binari_2,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v3_card_1 @ ( k1_binari_2 @ A ) @ A ) & ( m2_finseq_1 @ ( k1_binari_2 @ A ) @ k6_margrel1 ) ) ) ),file(binari_2,k1_binari_2)).
thf(dt_k1_binari_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( v7_ordinal1 @ B ) ) => ( ( v3_card_1 @ ( k1_binari_3 @ A @ B ) @ A ) & ( m2_finseq_1 @ ( k1_binari_3 @ A @ B ) @ k6_margrel1 ) ) ) ),file(binari_3,k1_binari_3)).
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_k2_xcmplx_0,axiom,( $true ),file(xcmplx_0,k2_xcmplx_0)).
thf(dt_k5_series_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( v7_ordinal1 @ B ) ) => ( m2_subset_1 @ ( k5_series_1 @ A @ B ) @ k1_numbers @ k5_numbers ) ) ),file(series_1,k5_series_1)).
thf(dt_k7_binarith,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) & ( v3_card_1 @ B @ A ) & ( m1_finseq_1 @ B @ k6_margrel1 ) & ( v3_card_1 @ C @ A ) & ( m1_finseq_1 @ C @ k6_margrel1 ) ) => ( ( v3_card_1 @ ( k7_binarith @ A @ B @ C ) @ A ) & ( m2_finseq_1 @ ( k7_binarith @ A @ B @ C ) @ k6_margrel1 ) ) ) ),file(binarith,k7_binarith)).
thf(cc1_margrel1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v2_card_3 @ A ) ) ),file(margrel1,cc1_margrel1)).
thf(cc1_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) ) ),file(nat_1,cc1_nat_1)).
thf(cc1_zfmisc_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_zfmisc_1 @ A ) ) ),file(zfmisc_1,cc1_zfmisc_1)).
thf(cc2_int_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_int_1 @ A ) ) ),file(int_1,cc2_int_1)).
thf(cc2_xreal_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc2_xreal_0)).
thf(cc3_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v7_ordinal1 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(nat_1,cc3_nat_1)).
thf(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
thf(cc4_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(cc7_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
thf(cc8_finseq_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_finseq_1 @ A ) ) ),file(finseq_1,cc8_finseq_1)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
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(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(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
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(e2_35__binari_3,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ~ ( r1_xxreal_0 @ ( k5_series_1 @ np__2 @ np__1 ) @ ( k2_xcmplx_0 @ A @ np__1 ) ) => ( = @ ( k1_binari_3 @ np__1 @ ( k2_xcmplx_0 @ A @ np__1 ) ) @ ( k7_binarith @ np__1 @ ( k1_binari_3 @ np__1 @ A ) @ ( k1_binari_2 @ np__1 ) ) ) ) ) ),file(binari_3,e2_35__binari_3)).
thf(e1_35__binari_3,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) => ( ! [B: $i] : ( ( v7_ordinal1 @ B ) => ( ~ ( r1_xxreal_0 @ ( k5_series_1 @ np__2 @ A ) @ ( k2_xcmplx_0 @ B @ np__1 ) ) => ( = @ ( k1_binari_3 @ A @ ( k2_xcmplx_0 @ B @ np__1 ) ) @ ( k7_binarith @ A @ ( k1_binari_3 @ A @ B ) @ ( k1_binari_2 @ A ) ) ) ) ) => ! [B: $i] : ( ( v7_ordinal1 @ B ) => ( ~ ( r1_xxreal_0 @ ( k5_series_1 @ np__2 @ ( k2_xcmplx_0 @ A @ np__1 ) ) @ ( k2_xcmplx_0 @ B @ np__1 ) ) => ( = @ ( k1_binari_3 @ ( k2_xcmplx_0 @ A @ np__1 ) @ ( k2_xcmplx_0 @ B @ np__1 ) ) @ ( k7_binarith @ ( k2_xcmplx_0 @ A @ np__1 ) @ ( k1_binari_3 @ ( k2_xcmplx_0 @ A @ np__1 ) @ B ) @ ( k1_binari_2 @ ( k2_xcmplx_0 @ A @ np__1 ) ) ) ) ) ) ) ) ),file(binari_3,e1_35__binari_3)).
thf(s10_nat_1,axiom,( ! [A: $i > $o] : ( ( ( A @ np__1 ) & ! [B: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( v7_ordinal1 @ B ) ) => ( ( A @ B ) => ( A @ ( k1_nat_1 @ B @ np__1 ) ) ) ) ) => ! [B: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( v7_ordinal1 @ B ) ) => ( A @ B ) ) ) ),file(nat_1,s10_nat_1)).
thf(e3_35__binari_3,conjecture,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) => ! [B: $i] : ( ( v7_ordinal1 @ B ) => ( ~ ( r1_xxreal_0 @ ( k5_series_1 @ np__2 @ A ) @ ( k2_xcmplx_0 @ B @ np__1 ) ) => ( = @ ( k1_binari_3 @ A @ ( k2_xcmplx_0 @ B @ np__1 ) ) @ ( k7_binarith @ A @ ( k1_binari_3 @ A @ B ) @ ( k1_binari_2 @ A ) ) ) ) ) ) ),file(binari_3,e3_35__binari_3)).
