% Mizar problem: e1_35_1,waybel_0,714,8 
include('Axioms/SET010^1.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_35_type,type,( c1_35__waybel_0: $i )).
thf(c1_35_1_type,type,( c1_35_1__waybel_0: $i )).
thf(c2_35_type,type,( c2_35__waybel_0: $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k2_waybel_0_type,type,( k2_waybel_0: $i > $i > $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(l1_orders_2_type,type,( l1_orders_2: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l1_waybel_0_type,type,( l1_waybel_0: $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(r1_orders_2_type,type,( r1_orders_2: $i > $i > $i > $o )).
thf(r1_waybel_0_type,type,( r1_waybel_0: $i > $i > $i > $o )).
thf(v13_struct_0_type,type,( v13_struct_0: $i > $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v5_finset_1_type,type,( v5_finset_1: $i > $o )).
thf(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_0: $i > $o )).
thf(cc11_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v13_struct_0 @ A @ np__1 ) => ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) ) ) ),file(struct_0,cc11_struct_0)).
thf(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_1)).
thf(cc5_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_1)).
thf(cc7_finset_1,axiom,( ! [A: $i] : ( ( v5_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_finset_1 @ B ) ) ) ),file(finset_1,cc7_finset_1)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_1)).
thf(rc8_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v5_finset_1 @ A ) ) ),file(finset_1,rc8_finset_1)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(cc10_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) => ( v13_struct_0 @ A @ np__1 ) ) ) ),file(struct_0,cc10_struct_0)).
thf(cc17_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v7_struct_0 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc17_struct_0)).
thf(cc1_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc1_finset_1)).
thf(cc2_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v7_struct_0 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc2_struct_0)).
thf(cc5_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ( ~ ( v2_struct_0 @ A ) & ~ ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc5_struct_0)).
thf(cc6_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_1)).
thf(cc6_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v7_struct_0 @ A ) => ( v8_struct_0 @ A ) ) ) ),file(struct_0,cc6_struct_0)).
thf(cc7_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ~ ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc7_struct_0)).
thf(cc9_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v13_struct_0 @ A @ k1_xboole_0 ) => ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc9_struct_0)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc6_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc6_struct_0)).
thf(fc7_struct_0,axiom,( ! [A: $i] : ( ( ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc7_struct_0)).
thf(fc8_struct_0,axiom,( ! [A: $i] : ( ( ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc8_struct_0)).
thf(fc9_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc9_struct_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(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(cc1_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc1_struct_0)).
thf(cc4_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc4_struct_0)).
thf(cc8_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v13_struct_0 @ A @ k1_xboole_0 ) ) ) ),file(struct_0,cc8_struct_0)).
thf(fc1_struct_0,axiom,( ! [A: $i] : ( ( ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc1_struct_0)).
thf(fc2_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc2_struct_0)).
thf(dt_k2_waybel_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) & ~ ( v2_struct_0 @ B ) & ( l1_waybel_0 @ B @ A ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) ) => ( m1_subset_1 @ ( k2_waybel_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ) ),file(waybel_0,k2_waybel_0)).
thf(dt_l1_orders_2,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( l1_struct_0 @ A ) ) ),file(orders_2,l1_orders_2)).
thf(dt_l1_waybel_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ! [B: $i] : ( ( l1_waybel_0 @ B @ A ) => ( l1_orders_2 @ B ) ) ) ),file(waybel_0,l1_waybel_0)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_c1_35__waybel_0,axiom,( ~ ( v2_struct_0 @ c1_35__waybel_0 ) & ( l1_orders_2 @ c1_35__waybel_0 ) ),file(waybel_0,c1_35__waybel_0)).
thf(dt_c1_35_1__waybel_0,axiom,( m1_subset_1 @ c1_35_1__waybel_0 @ ( u1_struct_0 @ c2_35__waybel_0 ) ),file(waybel_0,c1_35_1__waybel_0)).
thf(dt_c2_35__waybel_0,axiom,( ~ ( v2_struct_0 @ c2_35__waybel_0 ) & ( l1_waybel_0 @ c2_35__waybel_0 @ c1_35__waybel_0 ) ),file(waybel_0,c2_35__waybel_0)).
thf(s1_waybel_0,axiom,( ! [A: $i > $o] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ C ) & ( l1_orders_2 @ C ) & ~ ( v2_struct_0 @ B ) & ( l1_waybel_0 @ B @ C ) ) => ( ( r1_waybel_0 @ C @ B @ ( replSep1 @ ^ [D: $i] : ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) @ ^ [D: $i] : ( k2_waybel_0 @ C @ B @ D ) @ ^ [D: $i] : ( A @ ( k2_waybel_0 @ C @ B @ D ) ) ) ) <=> ? [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) ) => ( ( r1_orders_2 @ B @ D @ E ) => ( A @ ( k2_waybel_0 @ C @ B @ E ) ) ) ) ) ) ) ),file(waybel_0,s1_waybel_0)).
thf(e1_35_1__waybel_0,conjecture,( ( r1_waybel_0 @ c1_35__waybel_0 @ c2_35__waybel_0 @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ ( u1_struct_0 @ c2_35__waybel_0 ) ) @ ^ [A: $i] : ( k2_waybel_0 @ c1_35__waybel_0 @ c2_35__waybel_0 @ A ) @ ^ [A: $i] : ( r1_orders_2 @ c1_35__waybel_0 @ ( k2_waybel_0 @ c1_35__waybel_0 @ c2_35__waybel_0 @ A ) @ ( k2_waybel_0 @ c1_35__waybel_0 @ c2_35__waybel_0 @ c1_35_1__waybel_0 ) ) ) ) <=> ? [A: $i] : ( ( m1_subset_1 @ A @ ( u1_struct_0 @ c2_35__waybel_0 ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ c2_35__waybel_0 ) ) => ( ( r1_orders_2 @ c2_35__waybel_0 @ A @ B ) => ( r1_orders_2 @ c1_35__waybel_0 @ ( k2_waybel_0 @ c1_35__waybel_0 @ c2_35__waybel_0 @ B ) @ ( k2_waybel_0 @ c1_35__waybel_0 @ c2_35__waybel_0 @ c1_35_1__waybel_0 ) ) ) ) ) ),file(waybel_0,e1_35_1__waybel_0)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
