% Mizar problem: e3_23,rat_1,569,66 
include('Axioms/SET010^0.ax').
thf(c1_23_type,type,( c1_23__rat_1: $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_numbers_type,type,( k6_numbers: $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(r1_xxreal_0_type,type,( r1_xxreal_0: $i > $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_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_rat_1_type,type,( v1_rat_1: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_xcmplx_0_type,type,( v1_xcmplx_0: $i > $o )).
thf(v1_xreal_0_type,type,( v1_xreal_0: $i > $o )).
thf(v1_xxreal_0_type,type,( v1_xxreal_0: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_xxreal_0_type,type,( v3_xxreal_0: $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
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(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_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_nat_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ~ ( v3_xxreal_0 @ A ) ) ),file(nat_1,cc2_nat_1)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
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_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
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(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_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
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_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
thf(cc8_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) => ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc8_xxreal_0)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
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(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(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
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_rat_1,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) & ( v1_xxreal_0 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_rat_1 @ A ) ) ),file(rat_1,rc1_rat_1)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
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(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_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(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(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_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
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(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
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_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(fc1_numbers,axiom,( ~ ( v1_xboole_0 @ k1_numbers ) ),file(numbers,fc1_numbers)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_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(fc8_numbers,axiom,( ~ ( v1_finset_1 @ k1_numbers ) ),file(numbers,fc8_numbers)).
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_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_xxreal_0,axiom,( ? [A: $i] : ( v1_xxreal_0 @ A ) ),file(xxreal_0,rc1_xxreal_0)).
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(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_k6_numbers,axiom,( = @ k6_numbers @ k1_xboole_0 ),file(numbers,k6_numbers)).
thf(dt_k6_numbers,axiom,( m2_subset_1 @ k6_numbers @ k1_numbers @ k5_numbers ),file(numbers,k6_numbers)).
thf(dt_k7_xcmplx_0,axiom,( $true ),file(xcmplx_0,k7_xcmplx_0)).
thf(dt_c1_23__rat_1,axiom,( v1_rat_1 @ c1_23__rat_1 ),file(rat_1,c1_23__rat_1)).
thf(cc1_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) ) ),file(nat_1,cc1_nat_1)).
thf(cc1_rat_1,axiom,( ! [A: $i] : ( ( v1_rat_1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(rat_1,cc1_rat_1)).
thf(cc2_int_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_int_1 @ A ) ) ),file(int_1,cc2_int_1)).
thf(cc2_rat_1,axiom,( ! [A: $i] : ( ( v1_int_1 @ A ) => ( v1_rat_1 @ A ) ) ),file(rat_1,cc2_rat_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_int_1,axiom,( ! [A: $i] : ( ( v1_int_1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(int_1,cc3_int_1)).
thf(cc3_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v7_ordinal1 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(nat_1,cc3_nat_1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(fc4_rat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_rat_1 @ A ) & ( v1_rat_1 @ B ) ) => ( v1_rat_1 @ ( k7_xcmplx_0 @ A @ B ) ) ) ),file(rat_1,fc4_rat_1)).
thf(rc2_int_1,axiom,( ? [A: $i] : ( v1_int_1 @ A ) ),file(int_1,rc2_int_1)).
thf(rc2_rat_1,axiom,( ? [A: $i] : ( v1_rat_1 @ A ) ),file(rat_1,rc2_rat_1)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(e2_23__rat_1,axiom,( ? [A: $i] : ( ( v7_ordinal1 @ A ) & ~ ( = @ A @ k6_numbers ) & ? [B: $i] : ( ( v1_int_1 @ B ) & ( = @ c1_23__rat_1 @ ( k7_xcmplx_0 @ B @ A ) ) ) ) ),file(rat_1,e2_23__rat_1)).
thf(s5_nat_1,axiom,( ! [A: $i > $o] : ( ? [B: $i] : ( ( v7_ordinal1 @ B ) & ( A @ B ) ) => ? [B: $i] : ( ( v7_ordinal1 @ B ) & ( A @ B ) & ! [C: $i] : ( ( v7_ordinal1 @ C ) => ( ( A @ C ) => ( r1_xxreal_0 @ B @ C ) ) ) ) ) ),file(nat_1,s5_nat_1)).
thf(e3_23__rat_1,conjecture,( ? [A: $i] : ( ( v7_ordinal1 @ A ) & ~ ( = @ A @ k6_numbers ) & ? [B: $i] : ( ( v1_int_1 @ B ) & ( = @ c1_23__rat_1 @ ( k7_xcmplx_0 @ B @ A ) ) ) & ! [B: $i] : ( ( v7_ordinal1 @ B ) => ( ( ~ ( = @ B @ k6_numbers ) & ? [C: $i] : ( ( v1_int_1 @ C ) & ( = @ c1_23__rat_1 @ ( k7_xcmplx_0 @ C @ B ) ) ) ) => ( r1_xxreal_0 @ A @ B ) ) ) ) ),file(rat_1,e3_23__rat_1)).
