% Mizar problem: e1_3_1,cat_3,75,6 
include('Axioms/SET010^0.ax').
thf(f1_s2_cat_3_type,type,( f1_s2_cat_3: $i )).
thf(f2_s2_cat_3_type,type,( f2_s2_cat_3: $i )).
thf(f3_s2_cat_3_type,type,( f3_s2_cat_3: $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(k7_partfun1_type,type,( k7_partfun1: $i > $i > $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $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(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
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_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(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_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(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
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_k7_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ( m1_subset_1 @ ( k7_partfun1 @ A @ B @ C ) @ A ) ) ),file(partfun1,k7_partfun1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_f1_s2_cat_3,axiom,( $true ),file(cat_3,f1_s2_cat_3)).
thf(dt_f2_s2_cat_3,axiom,( ~ ( v1_xboole_0 @ f2_s2_cat_3 ) ),file(cat_3,f2_s2_cat_3)).
thf(dt_f3_s2_cat_3,axiom,( ! [A: $i] : ( m1_subset_1 @ ( f3_s2_cat_3 @ A ) @ f2_s2_cat_3 ) ),file(cat_3,f3_s2_cat_3)).
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(s1_cat_3,axiom,( ! [A: $i] : ! [B: $i > $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ C ) & ! [D: $i] : ( m1_subset_1 @ ( B @ D ) @ C ) ) => ? [E: $i] : ( ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ A @ C ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ C ) ) ) & ! [F: $i] : ( ( r2_hidden @ F @ A ) => ( = @ ( k7_partfun1 @ C @ E @ F ) @ ( B @ F ) ) ) ) ) ),file(cat_3,s1_cat_3)).
thf(e1_3_1__cat_3,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ f1_s2_cat_3 @ f2_s2_cat_3 ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ f1_s2_cat_3 @ f2_s2_cat_3 ) ) ) & ! [B: $i] : ( ( r2_hidden @ B @ f1_s2_cat_3 ) => ( = @ ( k7_partfun1 @ f2_s2_cat_3 @ A @ B ) @ ( f3_s2_cat_3 @ B ) ) ) ) ),file(cat_3,e1_3_1__cat_3)).
