% Mizar problem: e2_20_1_1,domain_1,355,32 
include('Axioms/SET010^1.ax').
thf(c1_20_1_type,type,( c1_20_1__domain_1: $i )).
thf(c1_20_1_1_type,type,( c1_20_1_1__domain_1: $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(p1_s1_domain_1_type,type,( p1_s1_domain_1: $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(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(rc2_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(cc3_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) ) ) ),file(relat_1,cc3_relat_1)).
thf(cc4_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ) ),file(relat_1,cc4_relat_1)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_1)).
thf(d2_xboole_0,axiom,( = @ k1_xboole_0 @ ( eps @ ^ [A: $i] : ( v1_xboole_0 @ A ) ) ),file(xboole_0,d2_xboole_0)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_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(t2_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ A @ B ) => ( ( v1_xboole_0 @ B ) | ( r2_hidden @ A @ B ) ) ) ),file(subset,t2_subset)).
thf(t6_boole,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( = @ A @ k1_xboole_0 ) ) ),file(boole,t6_boole)).
thf(t8_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( v1_xboole_0 @ A ) & ~ ( = @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t8_boole)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(existence_m1_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( m1_subset_1 @ B @ A ) ),file(subset_1,m1_subset_1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_c1_20_1__domain_1,axiom,( ~ ( v1_xboole_0 @ c1_20_1__domain_1 ) ),file(domain_1,c1_20_1__domain_1)).
thf(dt_c1_20_1_1__domain_1,axiom,( $true ),file(domain_1,c1_20_1_1__domain_1)).
thf(t1_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ( m1_subset_1 @ A @ B ) ) ),file(subset,t1_subset)).
thf(t7_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( r2_hidden @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t7_boole)).
thf(e1_20_1_1__domain_1,axiom,( r2_hidden @ c1_20_1_1__domain_1 @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ c1_20_1__domain_1 ) @ ^ [A: $i] : A @ ^ [A: $i] : ( p1_s1_domain_1 @ A ) ) ),file(domain_1,e1_20_1_1__domain_1)).
thf(e2_20_1_1__domain_1,conjecture,( ? [A: $i] : ( ( m1_subset_1 @ A @ c1_20_1__domain_1 ) & ( = @ c1_20_1_1__domain_1 @ A ) & ( p1_s1_domain_1 @ A ) ) ),file(domain_1,e2_20_1_1__domain_1)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
