% Mizar problem: e1_1_1_1,cfuncdom,52,8 
include('Axioms/SET010^0.ax').
thf(c1_1_type,type,( c1_1__cfuncdom: $i )).
thf(k1_binop_1_type,type,( k1_binop_1: $i > $i > $i > $i )).
thf(k1_funcsdom_type,type,( k1_funcsdom: $i > $i > $i > $i > $i > $i )).
thf(k1_funct_2_type,type,( k1_funct_2: $i > $i > $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k27_binop_2_type,type,( k27_binop_2: $i )).
thf(k2_binop_1_type,type,( k2_binop_1: $i > $i > $i > $i > $i > $i > $i )).
thf(k2_numbers_type,type,( k2_numbers: $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_funcop_1_type,type,( k3_funcop_1: $i > $i > $i > $i )).
thf(k3_funcsdom_type,type,( k3_funcsdom: $i > $i > $i > $i > $i > $i )).
thf(k9_funct_2_type,type,( k9_funct_2: $i > $i > $i )).
thf(m1_funct_2_type,type,( m1_funct_2: $i > $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_funct_2_type,type,( m2_funct_2: $i > $i > $i > $i > $o )).
thf(r2_funct_2_type,type,( r2_funct_2: $i > $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_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_binop_1,axiom,( $true ),file(binop_1,k1_binop_1)).
thf(dt_k1_funct_2,axiom,( $true ),file(funct_2,k1_funct_2)).
thf(dt_k3_funcop_1,axiom,( $true ),file(funcop_1,k3_funcop_1)).
thf(dt_m1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_funct_2 @ C @ A @ B ) => ~ ( v1_xboole_0 @ C ) ) ),file(funct_2,m1_funct_2)).
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(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_funcsdom,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ ( k9_funct_2 @ A @ B ) @ ( k9_funct_2 @ A @ B ) ) @ ( k9_funct_2 @ A @ B ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( k9_funct_2 @ A @ B ) @ ( k9_funct_2 @ A @ B ) ) @ ( k9_funct_2 @ A @ B ) ) ) ) & ( m1_subset_1 @ D @ ( k9_funct_2 @ A @ B ) ) & ( m1_subset_1 @ E @ ( k9_funct_2 @ A @ B ) ) ) => ( = @ ( k1_funcsdom @ A @ B @ C @ D @ E ) @ ( k1_binop_1 @ C @ D @ E ) ) ) ),file(funcsdom,k1_funcsdom)).
thf(redefinition_k2_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) & ( m1_subset_1 @ E @ A ) & ( m1_subset_1 @ F @ B ) ) => ( = @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_binop_1 @ D @ E @ F ) ) ) ),file(binop_1,k2_binop_1)).
thf(redefinition_k3_funcsdom,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ B @ A ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ B @ A ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) ) => ( = @ ( k3_funcsdom @ A @ B @ C @ D @ E ) @ ( k3_funcop_1 @ C @ D @ E ) ) ) ),file(funcsdom,k3_funcsdom)).
thf(redefinition_k9_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ( = @ ( k9_funct_2 @ A @ B ) @ ( k1_funct_2 @ A @ B ) ) ) ),file(funct_2,k9_funct_2)).
thf(redefinition_m2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( m1_funct_2 @ C @ A @ B ) ) => ! [D: $i] : ( ( m2_funct_2 @ D @ A @ B @ C ) <=> ( m1_subset_1 @ D @ C ) ) ) ),file(funct_2,m2_funct_2)).
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_k1_funcsdom,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ ( k9_funct_2 @ A @ B ) @ ( k9_funct_2 @ A @ B ) ) @ ( k9_funct_2 @ A @ B ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( k9_funct_2 @ A @ B ) @ ( k9_funct_2 @ A @ B ) ) @ ( k9_funct_2 @ A @ B ) ) ) ) & ( m1_subset_1 @ D @ ( k9_funct_2 @ A @ B ) ) & ( m1_subset_1 @ E @ ( k9_funct_2 @ A @ B ) ) ) => ( m2_funct_2 @ ( k1_funcsdom @ A @ B @ C @ D @ E ) @ A @ B @ ( k9_funct_2 @ A @ B ) ) ) ),file(funcsdom,k1_funcsdom)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k27_binop_2,axiom,( ( v1_funct_1 @ k27_binop_2 ) & ( v1_funct_2 @ k27_binop_2 @ ( k2_zfmisc_1 @ k2_numbers @ k2_numbers ) @ k2_numbers ) & ( m1_subset_1 @ k27_binop_2 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ k2_numbers @ k2_numbers ) @ k2_numbers ) ) ) ),file(binop_2,k27_binop_2)).
thf(dt_k2_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) & ( m1_subset_1 @ E @ A ) & ( m1_subset_1 @ F @ B ) ) => ( m1_subset_1 @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ C ) ) ),file(binop_1,k2_binop_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_k3_funcsdom,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ B @ A ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ B @ A ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) ) => ( m2_funct_2 @ ( k3_funcsdom @ A @ B @ C @ D @ E ) @ B @ A @ ( k9_funct_2 @ B @ A ) ) ) ),file(funcsdom,k3_funcsdom)).
thf(dt_k9_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ( m1_funct_2 @ ( k9_funct_2 @ A @ B ) @ A @ B ) ) ),file(funct_2,k9_funct_2)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_m2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( m1_funct_2 @ C @ A @ B ) ) => ! [D: $i] : ( ( m2_funct_2 @ D @ A @ B @ C ) => ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),file(funct_2,m2_funct_2)).
thf(dt_c1_1__cfuncdom,axiom,( ~ ( v1_xboole_0 @ c1_1__cfuncdom ) ),file(cfuncdom,c1_1__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(s4_binop_1,axiom,( ! [A: $i > $i > $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ? [E: $i] : ( ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ D @ C ) @ B ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ D @ C ) @ B ) ) ) & ! [F: $i] : ( ( m1_subset_1 @ F @ D ) => ! [G: $i] : ( ( m1_subset_1 @ G @ C ) => ( = @ ( k2_binop_1 @ D @ C @ B @ E @ F @ G ) @ ( A @ F @ G ) ) ) ) ) ),file(binop_1,s4_binop_1)).
thf(e1_1_1_1__cfuncdom,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ ( k9_funct_2 @ c1_1__cfuncdom @ k2_numbers ) @ ( k9_funct_2 @ c1_1__cfuncdom @ k2_numbers ) ) @ ( k9_funct_2 @ c1_1__cfuncdom @ k2_numbers ) ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( k9_funct_2 @ c1_1__cfuncdom @ k2_numbers ) @ ( k9_funct_2 @ c1_1__cfuncdom @ k2_numbers ) ) @ ( k9_funct_2 @ c1_1__cfuncdom @ k2_numbers ) ) ) ) & ! [B: $i] : ( ( m2_funct_2 @ B @ c1_1__cfuncdom @ k2_numbers @ ( k9_funct_2 @ c1_1__cfuncdom @ k2_numbers ) ) => ! [C: $i] : ( ( m2_funct_2 @ C @ c1_1__cfuncdom @ k2_numbers @ ( k9_funct_2 @ c1_1__cfuncdom @ k2_numbers ) ) => ( r2_funct_2 @ c1_1__cfuncdom @ k2_numbers @ ( k1_funcsdom @ c1_1__cfuncdom @ k2_numbers @ A @ B @ C ) @ ( k3_funcsdom @ k2_numbers @ c1_1__cfuncdom @ k27_binop_2 @ B @ C ) ) ) ) ) ),file(cfuncdom,e1_1_1_1__cfuncdom)).
