% Mizar problem: e10_8_1,scheme1,602,30 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(n2_type,type,( np__2: $i )).
thf(n3_type,type,( np__3: $i )).
thf(n4_type,type,( np__4: $i )).
thf(c1_8_1_type,type,( c1_8_1__scheme1: $i )).
thf(c2_8_1_type,type,( c2_8_1__scheme1: $i )).
thf(c3_8_1_type,type,( c3_8_1__scheme1: $i )).
thf(c4_8_1_type,type,( c4_8_1__scheme1: $i )).
thf(f1_s4_scheme1_type,type,( f1_s4_scheme1: $i > $i )).
thf(f2_s4_scheme1_type,type,( f2_s4_scheme1: $i > $i )).
thf(f3_s4_scheme1_type,type,( f3_s4_scheme1: $i > $i )).
thf(f4_s4_scheme1_type,type,( f4_s4_scheme1: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_seq_1_type,type,( k1_seq_1: $i > $i > $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(k4_numbers_type,type,( k4_numbers: $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_xcmplx_0_type,type,( k6_xcmplx_0: $i > $i > $i )).
thf(k7_xcmplx_0_type,type,( k7_xcmplx_0: $i > $i > $i )).
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(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_funct_2_type,type,( v1_funct_2: $i > $i > $i > $o )).
thf(v1_int_1_type,type,( v1_int_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_rat_1_type,type,( v1_rat_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_valued_0_type,type,( v1_valued_0: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_xcmplx_0_type,type,( v1_xcmplx_0: $i > $o )).
thf(v1_xreal_0_type,type,( v1_xreal_0: $i > $o )).
thf(v1_xxreal_0_type,type,( v1_xxreal_0: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $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_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_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v4_valued_0_type,type,( v4_valued_0: $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(dt_k3_numbers,axiom,( $true ),file(numbers,k3_numbers)).
thf(dt_k4_numbers,axiom,( $true ),file(numbers,k4_numbers)).
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(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc2_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) ) ),file(valued_0,cc2_valued_0)).
thf(cc3_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(fc3_numbers,axiom,( ~ ( v1_xboole_0 @ k3_numbers ) ),file(numbers,fc3_numbers)).
thf(fc4_numbers,axiom,( ~ ( v1_xboole_0 @ k4_numbers ) ),file(numbers,fc4_numbers)).
thf(fc64_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) & ( v1_funct_1 @ A ) ) => ( v1_rat_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc64_valued_0)).
thf(fc65_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) & ( v1_funct_1 @ A ) ) => ( v1_int_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc65_valued_0)).
thf(fc6_numbers,axiom,( ~ ( v1_finset_1 @ k4_numbers ) ),file(numbers,fc6_numbers)).
thf(fc7_numbers,axiom,( ~ ( v1_finset_1 @ k3_numbers ) ),file(numbers,fc7_numbers)).
thf(rc2_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) ) ),file(ordinal1,rc2_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(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(cc15_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_valued_0 @ B ) ) ) ),file(valued_0,cc15_valued_0)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
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_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_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_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_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_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_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) ) ),file(valued_0,cc7_valued_0)).
thf(cc7_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) => ( ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc7_xxreal_0)).
thf(cc8_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(fc17_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 @ ( k6_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc17_xreal_0)).
thf(fc18_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v2_xxreal_0 @ ( k6_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc18_xreal_0)).
thf(fc21_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 @ ( k6_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc21_xreal_0)).
thf(fc22_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v3_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v2_xxreal_0 @ ( k6_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc22_xreal_0)).
thf(fc31_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v2_xxreal_0 @ ( k7_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc31_xreal_0)).
thf(fc32_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v2_xxreal_0 @ ( k7_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc32_xreal_0)).
thf(fc33_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 @ ( k7_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc33_xreal_0)).
thf(fc61_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_valued_0 @ A ) ) => ( v1_xcmplx_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc61_valued_0)).
thf(fc62_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) ) => ( v1_xxreal_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc62_valued_0)).
thf(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(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc1_valued_0,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v4_valued_0 @ A ) ) ),file(valued_0,rc1_valued_0)).
thf(rc1_xxreal_0,axiom,( ? [A: $i] : ( v1_xxreal_0 @ A ) ),file(xxreal_0,rc1_xxreal_0)).
thf(rc2_xreal_0,axiom,( ? [A: $i] : ( ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc2_xreal_0)).
thf(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_xreal_0,axiom,( ? [A: $i] : ( ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc3_xreal_0)).
thf(rc3_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) ),file(xxreal_0,rc3_xxreal_0)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
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(rc4_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,rc4_xxreal_0)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
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(cc30_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k1_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc30_valued_0)).
thf(cc31_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k5_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) ) ),file(valued_0,cc31_valued_0)).
thf(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_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xcmplx_0 @ A ) ) ),file(xreal_0,cc3_xreal_0)).
thf(cc4_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
thf(cc4_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_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xreal_0,cc4_xreal_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_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
thf(cc8_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
thf(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(fc19_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 @ ( k6_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc19_xreal_0)).
thf(fc20_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v3_xxreal_0 @ ( k6_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc20_xreal_0)).
thf(fc34_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v3_xxreal_0 @ ( k7_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc34_xreal_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(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
thf(fc7_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xreal_0 @ A ) & ( v1_xreal_0 @ B ) ) => ( v1_xreal_0 @ ( k6_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc7_xreal_0)).
thf(fc8_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xreal_0 @ A ) & ( v1_xreal_0 @ B ) ) => ( v1_xreal_0 @ ( k7_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc8_xreal_0)).
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_xreal_0,axiom,( ? [A: $i] : ( v1_xreal_0 @ A ) ),file(xreal_0,rc1_xreal_0)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k1_seq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_valued_0 @ A ) ) => ( = @ ( k1_seq_1 @ A @ B ) @ ( k1_funct_1 @ A @ B ) ) ) ),file(seq_1,k1_seq_1)).
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_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
thf(redefinition_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) <=> ( m1_subset_1 @ C @ B ) ) ) ),file(subset_1,m2_subset_1)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k1_seq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_valued_0 @ A ) ) => ( m1_subset_1 @ ( k1_seq_1 @ A @ B ) @ k1_numbers ) ) ),file(seq_1,k1_seq_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_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_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_k6_xcmplx_0,axiom,( $true ),file(xcmplx_0,k6_xcmplx_0)).
thf(dt_k7_xcmplx_0,axiom,( $true ),file(xcmplx_0,k7_xcmplx_0)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) => ( m1_subset_1 @ C @ A ) ) ) ),file(subset_1,m2_subset_1)).
thf(dt_c1_8_1__scheme1,axiom,( m1_subset_1 @ c1_8_1__scheme1 @ ( k1_zfmisc_1 @ k5_numbers ) ),file(scheme1,c1_8_1__scheme1)).
thf(dt_c2_8_1__scheme1,axiom,( m1_subset_1 @ c2_8_1__scheme1 @ ( k1_zfmisc_1 @ k5_numbers ) ),file(scheme1,c2_8_1__scheme1)).
thf(dt_c3_8_1__scheme1,axiom,( m1_subset_1 @ c3_8_1__scheme1 @ ( k1_zfmisc_1 @ k5_numbers ) ),file(scheme1,c3_8_1__scheme1)).
thf(dt_c4_8_1__scheme1,axiom,( m1_subset_1 @ c4_8_1__scheme1 @ ( k1_zfmisc_1 @ k5_numbers ) ),file(scheme1,c4_8_1__scheme1)).
thf(dt_f1_s4_scheme1,axiom,( ! [A: $i] : ( m1_subset_1 @ ( f1_s4_scheme1 @ A ) @ k1_numbers ) ),file(scheme1,f1_s4_scheme1)).
thf(dt_f2_s4_scheme1,axiom,( ! [A: $i] : ( m1_subset_1 @ ( f2_s4_scheme1 @ A ) @ k1_numbers ) ),file(scheme1,f2_s4_scheme1)).
thf(dt_f3_s4_scheme1,axiom,( ! [A: $i] : ( m1_subset_1 @ ( f3_s4_scheme1 @ A ) @ k1_numbers ) ),file(scheme1,f3_s4_scheme1)).
thf(dt_f4_s4_scheme1,axiom,( ! [A: $i] : ( m1_subset_1 @ ( f4_s4_scheme1 @ A ) @ k1_numbers ) ),file(scheme1,f4_s4_scheme1)).
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_xreal_0,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc1_xreal_0)).
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(fc1_numbers,axiom,( ~ ( v1_xboole_0 @ k1_numbers ) ),file(numbers,fc1_numbers)).
thf(fc8_numbers,axiom,( ~ ( v1_finset_1 @ k1_numbers ) ),file(numbers,fc8_numbers)).
thf(spc1_numerals,axiom,( ( v2_xxreal_0 @ np__1 ) & ( m2_subset_1 @ np__1 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__1 @ k5_numbers ) & ( m1_subset_1 @ np__1 @ k1_numbers ) ),file(numerals,spc1_numerals)).
thf(spc2_numerals,axiom,( ( v2_xxreal_0 @ np__2 ) & ( m2_subset_1 @ np__2 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__2 @ k5_numbers ) & ( m1_subset_1 @ np__2 @ k1_numbers ) ),file(numerals,spc2_numerals)).
thf(spc3_numerals,axiom,( ( v2_xxreal_0 @ np__3 ) & ( m2_subset_1 @ np__3 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__3 @ k5_numbers ) & ( m1_subset_1 @ np__3 @ k1_numbers ) ),file(numerals,spc3_numerals)).
thf(spc4_numerals,axiom,( ( v2_xxreal_0 @ np__4 ) & ( m2_subset_1 @ np__4 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__4 @ k5_numbers ) & ( m1_subset_1 @ np__4 @ k1_numbers ) ),file(numerals,spc4_numerals)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(spc2_boole,axiom,( ~ ( v1_xboole_0 @ np__2 ) ),file(boole,spc2_boole)).
thf(spc3_boole,axiom,( ~ ( v1_xboole_0 @ np__3 ) ),file(boole,spc3_boole)).
thf(spc4_boole,axiom,( ~ ( v1_xboole_0 @ np__4 ) ),file(boole,spc4_boole)).
thf(e9_8_1__scheme1,axiom,( ! [A: $i] : ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers ) => ? [B: $i] : ( ( m1_subset_1 @ B @ k1_numbers ) & ( ( r2_hidden @ A @ c1_8_1__scheme1 ) => ( = @ B @ ( f1_s4_scheme1 @ ( k7_xcmplx_0 @ A @ np__4 ) ) ) ) & ( ( r2_hidden @ A @ c2_8_1__scheme1 ) => ( = @ B @ ( f2_s4_scheme1 @ ( k7_xcmplx_0 @ ( k6_xcmplx_0 @ A @ np__1 ) @ np__4 ) ) ) ) & ( ( r2_hidden @ A @ c3_8_1__scheme1 ) => ( = @ B @ ( f3_s4_scheme1 @ ( k7_xcmplx_0 @ ( k6_xcmplx_0 @ A @ np__2 ) @ np__4 ) ) ) ) & ( ( r2_hidden @ A @ c4_8_1__scheme1 ) => ( = @ B @ ( f4_s4_scheme1 @ ( k7_xcmplx_0 @ ( k6_xcmplx_0 @ A @ np__3 ) @ np__4 ) ) ) ) ) ) ),file(scheme1,e9_8_1__scheme1)).
thf(s3_funct_2,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ! [C: $i] : ( ! [D: $i] : ( ( m1_subset_1 @ D @ C ) => ? [E: $i] : ( ( m1_subset_1 @ E @ B ) & ( A @ D @ E ) ) ) => ? [D: $i] : ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ C @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ C @ B ) ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ C ) => ( A @ E @ ( k3_funct_2 @ C @ B @ D @ E ) ) ) ) ) ),file(funct_2,s3_funct_2)).
thf(e10_8_1__scheme1,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ k5_numbers @ k1_numbers ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ k1_numbers ) ) ) & ! [B: $i] : ( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers ) => ( ( ( r2_hidden @ B @ c1_8_1__scheme1 ) => ( = @ ( k1_seq_1 @ A @ B ) @ ( f1_s4_scheme1 @ ( k7_xcmplx_0 @ B @ np__4 ) ) ) ) & ( ( r2_hidden @ B @ c2_8_1__scheme1 ) => ( = @ ( k1_seq_1 @ A @ B ) @ ( f2_s4_scheme1 @ ( k7_xcmplx_0 @ ( k6_xcmplx_0 @ B @ np__1 ) @ np__4 ) ) ) ) & ( ( r2_hidden @ B @ c3_8_1__scheme1 ) => ( = @ ( k1_seq_1 @ A @ B ) @ ( f3_s4_scheme1 @ ( k7_xcmplx_0 @ ( k6_xcmplx_0 @ B @ np__2 ) @ np__4 ) ) ) ) & ( ( r2_hidden @ B @ c4_8_1__scheme1 ) => ( = @ ( k1_seq_1 @ A @ B ) @ ( f4_s4_scheme1 @ ( k7_xcmplx_0 @ ( k6_xcmplx_0 @ B @ np__3 ) @ np__4 ) ) ) ) ) ) ) ),file(scheme1,e10_8_1__scheme1)).
