% Mizar problem: e5_24,cfuncdom,480,18 
include('Axioms/SET010^0.ax').
thf(c1_24_type,type,( c1_24__cfuncdom: $i )).
thf(c2_24_type,type,( c2_24__cfuncdom: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $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_numbers_type,type,( k2_numbers: $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k5_complex1_type,type,( k5_complex1: $i )).
thf(k6_complex1_type,type,( k6_complex1: $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $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_relat_1_type,type,( v1_relat_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(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_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_xcmplx_0,axiom,( ? [A: $i] : ( v1_xcmplx_0 @ A ) ),file(xcmplx_0,rc1_xcmplx_0)).
thf(rc2_xcmplx_0,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_xcmplx_0 @ A ) ) ),file(xcmplx_0,rc2_xcmplx_0)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k5_complex1,axiom,( = @ k5_complex1 @ k1_xboole_0 ),file(complex1,k5_complex1)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_numbers,axiom,( $true ),file(numbers,k2_numbers)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k5_complex1,axiom,( m1_subset_1 @ k5_complex1 @ k2_numbers ),file(complex1,k5_complex1)).
thf(dt_k6_complex1,axiom,( m1_subset_1 @ k6_complex1 @ k2_numbers ),file(complex1,k6_complex1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_c1_24__cfuncdom,axiom,( $true ),file(cfuncdom,c1_24__cfuncdom)).
thf(dt_c2_24__cfuncdom,axiom,( ~ ( v1_xboole_0 @ c2_24__cfuncdom ) ),file(cfuncdom,c2_24__cfuncdom)).
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_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(cc3_xcmplx_0,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k2_numbers ) => ( v1_xcmplx_0 @ A ) ) ),file(xcmplx_0,cc3_xcmplx_0)).
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(fc2_numbers,axiom,( ~ ( v1_xboole_0 @ k2_numbers ) ),file(numbers,fc2_numbers)).
thf(fc9_numbers,axiom,( ~ ( v1_finset_1 @ k2_numbers ) ),file(numbers,fc9_numbers)).
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(e4_24__cfuncdom,axiom,( ! [A: $i] : ( ( r2_hidden @ A @ c2_24__cfuncdom ) => ( ( ( = @ A @ c1_24__cfuncdom ) => ( r2_hidden @ k5_complex1 @ k2_numbers ) ) & ( ~ ( = @ A @ c1_24__cfuncdom ) => ( r2_hidden @ k6_complex1 @ k2_numbers ) ) ) ) ),file(cfuncdom,e4_24__cfuncdom)).
thf(s5_funct_2,axiom,( ! [A: $i > $i] : ! [B: $i] : ! [C: $i > $i] : ! [D: $i > $o] : ! [E: $i] : ( ! [F: $i] : ( ( r2_hidden @ F @ E ) => ( ( ( D @ F ) => ( r2_hidden @ ( C @ F ) @ B ) ) & ( ~ ( D @ F ) => ( r2_hidden @ ( A @ F ) @ B ) ) ) ) => ? [F: $i] : ( ( v1_funct_1 @ F ) & ( v1_funct_2 @ F @ E @ B ) & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ E @ B ) ) ) & ! [G: $i] : ( ( r2_hidden @ G @ E ) => ( ( ( D @ G ) => ( = @ ( k1_funct_1 @ F @ G ) @ ( C @ G ) ) ) & ( ~ ( D @ G ) => ( = @ ( k1_funct_1 @ F @ G ) @ ( A @ G ) ) ) ) ) ) ) ),file(funct_2,s5_funct_2)).
thf(e5_24__cfuncdom,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ c2_24__cfuncdom @ k2_numbers ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ c2_24__cfuncdom @ k2_numbers ) ) ) & ! [B: $i] : ( ( r2_hidden @ B @ c2_24__cfuncdom ) => ( ( ( = @ B @ c1_24__cfuncdom ) => ( = @ ( k1_funct_1 @ A @ B ) @ k5_complex1 ) ) & ( ~ ( = @ B @ c1_24__cfuncdom ) => ( = @ ( k1_funct_1 @ A @ B ) @ k6_complex1 ) ) ) ) ) ),file(cfuncdom,e5_24__cfuncdom)).
