% Mizar problem: e4_25_1,domain_1,427,16 
include('Axioms/SET010^1.ax').
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(p1_s6_domain_1_type,type,( p1_s6_domain_1: $i > $o )).
thf(p2_s6_domain_1_type,type,( p2_s6_domain_1: $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $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(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(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(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_1)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
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(s5_domain_1,axiom,( ! [A: $i > $o] : ! [B: $i > $o] : ! [C: $i] : ( ~ ( v1_xboole_0 @ C ) => ( ! [D: $i] : ( ( m1_subset_1 @ D @ C ) => ( ( B @ D ) => ( A @ D ) ) ) => ( r1_tarski @ ( replSep1 @ ^ [D: $i] : ( m1_subset_1 @ D @ C ) @ ^ [D: $i] : D @ ^ [D: $i] : ( B @ D ) ) @ ( replSep1 @ ^ [D: $i] : ( m1_subset_1 @ D @ C ) @ ^ [D: $i] : D @ ^ [D: $i] : ( A @ D ) ) ) ) ) ),file(domain_1,s5_domain_1)).
thf(e4_25_1__domain_1,conjecture,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ( ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( ( p2_s6_domain_1 @ B ) => ( p1_s6_domain_1 @ B ) ) ) => ( r1_tarski @ ( replSep1 @ ^ [B: $i] : ( m1_subset_1 @ B @ A ) @ ^ [B: $i] : B @ ^ [B: $i] : ( p2_s6_domain_1 @ B ) ) @ ( replSep1 @ ^ [B: $i] : ( m1_subset_1 @ B @ A ) @ ^ [B: $i] : B @ ^ [B: $i] : ( p1_s6_domain_1 @ B ) ) ) ) ) ),file(domain_1,e4_25_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)).
