% Mizar problem: e3_10_1_1,lmod_7,172,15 
include('Axioms/SET010^1.ax').
thf(f1_s10_lmod_7_type,type,( f1_s10_lmod_7: $i )).
thf(f3_s10_lmod_7_type,type,( f3_s10_lmod_7: $i )).
thf(f4_s10_lmod_7_type,type,( f4_s10_lmod_7: $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(p2_s10_lmod_7_type,type,( p2_s10_lmod_7: $i > $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
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_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_f1_s10_lmod_7,axiom,( ~ ( v1_xboole_0 @ f1_s10_lmod_7 ) ),file(lmod_7,f1_s10_lmod_7)).
thf(dt_f3_s10_lmod_7,axiom,( $true ),file(lmod_7,f3_s10_lmod_7)).
thf(dt_f4_s10_lmod_7,axiom,( m1_subset_1 @ f4_s10_lmod_7 @ f1_s10_lmod_7 ),file(lmod_7,f4_s10_lmod_7)).
thf(e2_10_1_1__lmod_7,axiom,( r2_hidden @ f4_s10_lmod_7 @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ f1_s10_lmod_7 ) @ ^ [A: $i] : A @ ^ [A: $i] : ( p2_s10_lmod_7 @ A @ f3_s10_lmod_7 ) ) ),file(lmod_7,e2_10_1_1__lmod_7)).
thf(s6_lmod_7,axiom,( ! [A: $i > $o] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ C ) & ( m1_subset_1 @ B @ C ) ) => ( ( r2_hidden @ B @ ( replSep1 @ ^ [D: $i] : ( m1_subset_1 @ D @ C ) @ ^ [D: $i] : D @ ^ [D: $i] : ( A @ D ) ) ) => ( A @ B ) ) ) ),file(lmod_7,s6_lmod_7)).
thf(e3_10_1_1__lmod_7,conjecture,( p2_s10_lmod_7 @ f4_s10_lmod_7 @ f3_s10_lmod_7 ),file(lmod_7,e3_10_1_1__lmod_7)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
