% Mizar problem: s8_lmod_7,lmod_7,140,10 
include('Axioms/SET010^1.ax').
thf(f1_s8_lmod_7_type,type,( f1_s8_lmod_7: $i )).
thf(f2_s8_lmod_7_type,type,( f2_s8_lmod_7: $i )).
thf(f3_s8_lmod_7_type,type,( f3_s8_lmod_7: $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_s8_lmod_7_type,type,( p1_s8_lmod_7: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(d2_xboole_0,axiom,( = @ k1_xboole_0 @ ( eps @ ^ [A: $i] : ( v1_xboole_0 @ A ) ) ),file(xboole_0,d2_xboole_0)).
thf(dt_f1_s8_lmod_7,axiom,( $true ),file(lmod_7,f1_s8_lmod_7)).
thf(dt_f2_s8_lmod_7,axiom,( ~ ( v1_xboole_0 @ f2_s8_lmod_7 ) ),file(lmod_7,f2_s8_lmod_7)).
thf(dt_f3_s8_lmod_7,axiom,( m1_subset_1 @ f3_s8_lmod_7 @ f2_s8_lmod_7 ),file(lmod_7,f3_s8_lmod_7)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(existence_m1_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( m1_subset_1 @ B @ A ) ),file(subset_1,m1_subset_1)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
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(t1_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ( m1_subset_1 @ A @ B ) ) ),file(subset,t1_subset)).
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(t7_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( r2_hidden @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t7_boole)).
thf(t8_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( v1_xboole_0 @ A ) & ~ ( = @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t8_boole)).
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(s8_lmod_7,conjecture,( ( ( r2_hidden @ f3_s8_lmod_7 @ f1_s8_lmod_7 ) & ( = @ f1_s8_lmod_7 @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ f2_s8_lmod_7 ) @ ^ [A: $i] : A @ ^ [A: $i] : ( p1_s8_lmod_7 @ A ) ) ) ) => ( p1_s8_lmod_7 @ f3_s8_lmod_7 ) ),file(lmod_7,s8_lmod_7)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
