% Mizar problem: e4_34_1_1,orders_3,690,8 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_34_type,type,( c1_34__orders_3: $i )).
thf(g1_cat_1_type,type,( g1_cat_1: $i > $i > $i > $i > $i > $i )).
thf(k1_cat_1_type,type,( k1_cat_1: $i > $i > $i > $i )).
thf(k1_domain_1_type,type,( k1_domain_1: $i > $i > $i > $i > $i )).
thf(k1_ens_1_type,type,( k1_ens_1: $i > $i )).
thf(k1_orders_3_type,type,( k1_orders_3: $i > $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_orders_3_type,type,( k2_orders_3: $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_relat_1_type,type,( k3_relat_1: $i > $i > $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(u1_cat_1_type,type,( u1_cat_1: $i > $i )).
thf(u1_graph_1_type,type,( u1_graph_1: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(u2_graph_1_type,type,( u2_graph_1: $i > $i )).
thf(u4_struct_0_type,type,( u4_struct_0: $i > $i )).
thf(l1_cat_1_type,type,( l1_cat_1: $i > $o )).
thf(l1_graph_1_type,type,( l1_graph_1: $i > $o )).
thf(l1_orders_2_type,type,( l1_orders_2: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l5_struct_0_type,type,( l5_struct_0: $i > $o )).
thf(m1_orders_3_type,type,( m1_orders_3: $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(v11_struct_0_type,type,( v11_struct_0: $i > $o )).
thf(v13_struct_0_type,type,( v13_struct_0: $i > $i > $o )).
thf(v14_struct_0_type,type,( v14_struct_0: $i > $o )).
thf(v15_struct_0_type,type,( v15_struct_0: $i > $o )).
thf(v1_cat_1_type,type,( v1_cat_1: $i > $o )).
thf(v1_cat_5_type,type,( v1_cat_5: $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_funct_2_type,type,( v1_funct_2: $i > $i > $i > $o )).
thf(v1_orders_3_type,type,( v1_orders_3: $i > $o )).
thf(v1_partfun1_type,type,( v1_partfun1: $i > $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_subset_1_type,type,( v1_subset_1: $i > $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_xtuple_0_type,type,( v1_xtuple_0: $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_cat_1_type,type,( v2_cat_1: $i > $o )).
thf(v2_funct_1_type,type,( v2_funct_1: $i > $o )).
thf(v2_orders_2_type,type,( v2_orders_2: $i > $o )).
thf(v2_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v3_cat_1_type,type,( v3_cat_1: $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_1: $i > $o )).
thf(v3_orders_2_type,type,( v3_orders_2: $i > $o )).
thf(v4_cat_1_type,type,( v4_cat_1: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_orders_2_type,type,( v4_orders_2: $i > $o )).
thf(v4_orders_3_type,type,( v4_orders_3: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_cat_1_type,type,( v5_cat_1: $i > $o )).
thf(v5_orders_2_type,type,( v5_orders_2: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v6_cat_1_type,type,( v6_cat_1: $i > $o )).
thf(v6_orders_2_type,type,( v6_orders_2: $i > $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(cc1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_partfun1 @ C @ A ) => ( v1_funct_2 @ C @ A @ B ) ) ) ),file(funct_2,cc1_funct_2)).
thf(cc2_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ~ ( v1_subset_1 @ B @ A ) => ~ ( v1_xboole_0 @ B ) ) ) ) ),file(subset_1,cc2_subset_1)).
thf(cc5_subset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,cc5_subset_1)).
thf(cc6_funct_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) ) ),file(funct_1,cc6_funct_1)).
thf(rc1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) ),file(funct_2,rc1_funct_2)).
thf(rc1_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) ) ),file(partfun1,rc1_partfun1)).
thf(rc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relset_1,rc1_relset_1)).
thf(rc21_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_zfmisc_1 @ B ) ) ) ),file(struct_0,rc21_struct_0)).
thf(rc22_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_zfmisc_1 @ B ) ) ) ),file(struct_0,rc22_struct_0)).
thf(rc3_orders_2,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v6_orders_2 @ B @ A ) ) ) ),file(orders_2,rc3_orders_2)).
thf(rc3_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ~ ( v1_xboole_0 @ C ) ) ) ),file(partfun1,rc3_partfun1)).
thf(rc3_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_subset_1 @ B @ A ) ) ),file(subset_1,rc3_subset_1)).
thf(rc4_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v1_subset_1 @ B @ A ) ) ) ),file(subset_1,rc4_subset_1)).
thf(rc5_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,rc5_subset_1)).
thf(rc6_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) ) ),file(funct_1,rc6_funct_1)).
thf(rc6_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,rc6_subset_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(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
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(cc14_struct_0,axiom,( ! [A: $i] : ( ( l5_struct_0 @ A ) => ( ( ( v2_struct_0 @ A ) & ( v14_struct_0 @ A ) ) => ( v11_struct_0 @ A ) ) ) ),file(struct_0,cc14_struct_0)).
thf(cc15_struct_0,axiom,( ! [A: $i] : ( ( l5_struct_0 @ A ) => ( ( ~ ( v11_struct_0 @ A ) & ( v14_struct_0 @ A ) ) => ~ ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc15_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_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_partfun1 @ C @ A ) ) ) ),file(partfun1,cc1_partfun1)).
thf(cc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_relat_1 @ C ) ) ),file(relset_1,cc1_relset_1)).
thf(cc1_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_xboole_0 @ B ) ) ) ),file(subset_1,cc1_subset_1)).
thf(cc2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_2 @ C @ A @ B ) => ( v1_partfun1 @ C @ A ) ) ) ) ),file(funct_2,cc2_funct_2)).
thf(cc2_orders_2,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_xboole_0 @ B ) => ( v6_orders_2 @ B @ A ) ) ) ) ),file(orders_2,cc2_orders_2)).
thf(cc2_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_xboole_0 @ B ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ~ ( v1_partfun1 @ C @ A ) ) ) ),file(partfun1,cc2_partfun1)).
thf(cc2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ) ),file(relset_1,cc2_relset_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(cc3_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_funct_1 @ B ) ) ) ),file(funct_1,cc3_funct_1)).
thf(cc3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_2 @ C @ A @ B ) => ( v1_partfun1 @ C @ A ) ) ) ) ),file(funct_2,cc3_funct_2)).
thf(cc3_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc3_relset_1)).
thf(cc3_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ( v1_xboole_0 @ B ) => ( v1_subset_1 @ B @ A ) ) ) ) ),file(subset_1,cc3_subset_1)).
thf(cc4_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) => ( ( v1_funct_2 @ B @ A @ A ) => ( v1_partfun1 @ B @ A ) ) ) ),file(funct_2,cc4_funct_2)).
thf(cc4_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc4_relset_1)).
thf(cc4_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ~ ( v1_subset_1 @ B @ A ) ) ) ),file(subset_1,cc4_subset_1)).
thf(cc5_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) => ( ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ) ),file(funct_1,cc5_funct_1)).
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_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(cc8_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) => ( ( v1_funct_1 @ C ) & ~ ( v1_xboole_0 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) ) ) ) ),file(funct_2,cc8_funct_2)).
thf(cc9_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_funct_1 @ B ) ) ) ),file(funct_1,cc9_funct_1)).
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_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc20_struct_0,axiom,( ! [A: $i] : ( ( ( v15_struct_0 @ A ) & ( l5_struct_0 @ A ) ) => ( v1_zfmisc_1 @ ( u4_struct_0 @ A ) ) ) ),file(struct_0,fc20_struct_0)).
thf(fc21_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v15_struct_0 @ A ) & ( l5_struct_0 @ A ) ) => ~ ( v1_zfmisc_1 @ ( u4_struct_0 @ A ) ) ) ),file(struct_0,fc21_struct_0)).
thf(fc4_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ A ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) ) => ( ( v1_funct_1 @ ( k3_relat_1 @ D @ C ) ) & ( v1_funct_2 @ ( k3_relat_1 @ D @ C ) @ A @ B ) ) ) ),file(funct_2,fc4_funct_2)).
thf(fc5_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ B @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ B ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( v1_funct_1 @ ( k3_relat_1 @ D @ C ) ) & ( v1_funct_2 @ ( k3_relat_1 @ D @ C ) @ A @ B ) ) ) ),file(funct_2,fc5_funct_2)).
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_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v2_funct_1 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v2_funct_1 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(funct_1,fc7_funct_1)).
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_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ B @ C ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) ) ) => ( ( v1_funct_1 @ ( k3_relat_1 @ D @ E ) ) & ( v1_funct_2 @ ( k3_relat_1 @ D @ E ) @ A @ C ) ) ) ),file(funct_2,fc8_funct_2)).
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_cat_5,axiom,( ? [A: $i] : ( ( l1_cat_1 @ A ) & ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( v14_struct_0 @ A ) & ( v1_cat_1 @ A ) & ( v2_cat_1 @ A ) & ( v3_cat_1 @ A ) & ( v4_cat_1 @ A ) & ( v5_cat_1 @ A ) & ( v6_cat_1 @ A ) & ( v1_cat_5 @ A ) ) ),file(cat_5,rc1_cat_5)).
thf(rc1_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(subset_1,rc1_subset_1)).
thf(rc25_struct_0,axiom,( ? [A: $i] : ( ( l5_struct_0 @ A ) & ~ ( v15_struct_0 @ A ) ) ),file(struct_0,rc25_struct_0)).
thf(rc2_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) ) ),file(funct_1,rc2_funct_1)).
thf(rc2_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v1_xboole_0 @ B ) ) ),file(subset_1,rc2_subset_1)).
thf(rc4_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(struct_0,rc4_struct_0)).
thf(rc5_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) ),file(funct_1,rc5_funct_1)).
thf(free_g1_cat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ B @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ B @ A ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) & ( v1_funct_1 @ E ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) ) => ! [F: $i] : ! [G: $i] : ! [H: $i] : ! [I: $i] : ! [J: $i] : ( ( = @ ( g1_cat_1 @ A @ B @ C @ D @ E ) @ ( g1_cat_1 @ F @ G @ H @ I @ J ) ) => ( ( = @ A @ F ) & ( = @ B @ G ) & ( = @ C @ H ) & ( = @ D @ I ) & ( = @ E @ J ) ) ) ) ),file(cat_1,g1_cat_1)).
thf(dt_g1_cat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ B @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ B @ A ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) & ( v1_funct_1 @ E ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) ) => ( ( v1_cat_1 @ ( g1_cat_1 @ A @ B @ C @ D @ E ) ) & ( l1_cat_1 @ ( g1_cat_1 @ A @ B @ C @ D @ E ) ) ) ) ),file(cat_1,g1_cat_1)).
thf(dt_l1_graph_1,axiom,( ! [A: $i] : ( ( l1_graph_1 @ A ) => ( l5_struct_0 @ A ) ) ),file(graph_1,l1_graph_1)).
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_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_l5_struct_0,axiom,( ! [A: $i] : ( ( l5_struct_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(struct_0,l5_struct_0)).
thf(dt_u1_cat_1,axiom,( ! [A: $i] : ( ( l1_cat_1 @ A ) => ( ( v1_funct_1 @ ( u1_cat_1 @ A ) ) & ( m1_subset_1 @ ( u1_cat_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u4_struct_0 @ A ) @ ( u4_struct_0 @ A ) ) @ ( u4_struct_0 @ A ) ) ) ) ) ) ),file(cat_1,u1_cat_1)).
thf(dt_u1_graph_1,axiom,( ! [A: $i] : ( ( l1_graph_1 @ A ) => ( ( v1_funct_1 @ ( u1_graph_1 @ A ) ) & ( v1_funct_2 @ ( u1_graph_1 @ A ) @ ( u4_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ ( u1_graph_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u4_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),file(graph_1,u1_graph_1)).
thf(dt_u2_graph_1,axiom,( ! [A: $i] : ( ( l1_graph_1 @ A ) => ( ( v1_funct_1 @ ( u2_graph_1 @ A ) ) & ( v1_funct_2 @ ( u2_graph_1 @ A ) @ ( u4_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ ( u2_graph_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u4_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),file(graph_1,u2_graph_1)).
thf(cc12_struct_0,axiom,( ! [A: $i] : ( ( l5_struct_0 @ A ) => ( ~ ( v2_struct_0 @ A ) => ( v14_struct_0 @ A ) ) ) ),file(struct_0,cc12_struct_0)).
thf(cc13_struct_0,axiom,( ! [A: $i] : ( ( l5_struct_0 @ A ) => ( ( v11_struct_0 @ A ) => ( v14_struct_0 @ A ) ) ) ),file(struct_0,cc13_struct_0)).
thf(cc16_struct_0,axiom,( ! [A: $i] : ( ( l5_struct_0 @ A ) => ( ( v11_struct_0 @ A ) => ( v15_struct_0 @ A ) ) ) ),file(struct_0,cc16_struct_0)).
thf(cc1_orders_2,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( v3_orders_2 @ A ) => ( v2_orders_2 @ A ) ) ) ),file(orders_2,cc1_orders_2)).
thf(cc1_orders_3,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( v2_struct_0 @ A ) => ( v1_orders_3 @ A ) ) ) ),file(orders_3,cc1_orders_3)).
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(cc2_funct_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) ) ) ),file(funct_1,cc2_funct_1)).
thf(cc4_funct_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) ) ),file(funct_1,cc4_funct_1)).
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_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) ) ) ),file(funct_1,cc8_funct_1)).
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(fc13_struct_0,axiom,( ! [A: $i] : ( ( ( v11_struct_0 @ A ) & ( l5_struct_0 @ A ) ) => ( v1_xboole_0 @ ( u4_struct_0 @ A ) ) ) ),file(struct_0,fc13_struct_0)).
thf(fc14_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v11_struct_0 @ A ) & ( l5_struct_0 @ A ) ) => ~ ( v1_xboole_0 @ ( u4_struct_0 @ A ) ) ) ),file(struct_0,fc14_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_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v1_funct_1 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(funct_1,fc2_funct_1)).
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(fc3_orders_3,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_orders_2 @ A ) ) => ~ ( v1_xboole_0 @ ( k1_orders_3 @ A @ A ) ) ) ),file(orders_3,fc3_orders_3)).
thf(fc5_orders_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( l1_orders_2 @ A ) & ~ ( v2_struct_0 @ B ) & ( v3_orders_2 @ B ) & ( v4_orders_2 @ B ) & ( v5_orders_2 @ B ) & ( l1_orders_2 @ B ) ) => ( v4_funct_1 @ ( k1_orders_3 @ A @ B ) ) ) ),file(orders_3,fc5_orders_3)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_0)).
thf(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(abstractness_v1_cat_1,axiom,( ! [A: $i] : ( ( l1_cat_1 @ A ) => ( ( v1_cat_1 @ A ) => ( = @ A @ ( g1_cat_1 @ ( u1_struct_0 @ A ) @ ( u4_struct_0 @ A ) @ ( u1_graph_1 @ A ) @ ( u2_graph_1 @ A ) @ ( u1_cat_1 @ A ) ) ) ) ) ),file(cat_1,v1_cat_1)).
thf(redefinition_k1_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ C @ A ) & ( m1_subset_1 @ D @ B ) ) => ( = @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k4_tarski @ C @ D ) ) ) ),file(domain_1,k1_domain_1)).
thf(redefinition_m1_orders_3,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v4_orders_3 @ A ) ) => ! [B: $i] : ( ( m1_orders_3 @ B @ A ) <=> ( m1_subset_1 @ B @ A ) ) ) ),file(orders_3,m1_orders_3)).
thf(dt_k1_cat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( l1_cat_1 @ A ) & ( m1_subset_1 @ B @ ( u4_struct_0 @ A ) ) & ( m1_subset_1 @ C @ ( u4_struct_0 @ A ) ) ) => ( m1_subset_1 @ ( k1_cat_1 @ A @ B @ C ) @ ( u4_struct_0 @ A ) ) ) ),file(cat_1,k1_cat_1)).
thf(dt_k1_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ C @ A ) & ( m1_subset_1 @ D @ B ) ) => ( m1_subset_1 @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(domain_1,k1_domain_1)).
thf(dt_k1_ens_1,axiom,( $true ),file(ens_1,k1_ens_1)).
thf(dt_k1_orders_3,axiom,( $true ),file(orders_3,k1_orders_3)).
thf(dt_k2_orders_3,axiom,( $true ),file(orders_3,k2_orders_3)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) ),file(relat_1,k3_relat_1)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_l1_cat_1,axiom,( ! [A: $i] : ( ( l1_cat_1 @ A ) => ( l1_graph_1 @ A ) ) ),file(cat_1,l1_cat_1)).
thf(dt_m1_orders_3,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v4_orders_3 @ A ) ) => ! [B: $i] : ( ( m1_orders_3 @ B @ A ) => ( ~ ( v2_struct_0 @ B ) & ( v3_orders_2 @ B ) & ( v4_orders_2 @ B ) & ( v5_orders_2 @ B ) & ( l1_orders_2 @ B ) ) ) ) ),file(orders_3,m1_orders_3)).
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_u4_struct_0,axiom,( $true ),file(struct_0,u4_struct_0)).
thf(dt_c1_34__orders_3,axiom,( ~ ( v1_xboole_0 @ c1_34__orders_3 ) & ( v4_orders_3 @ c1_34__orders_3 ) ),file(orders_3,c1_34__orders_3)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_1)).
thf(cc7_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v4_funct_1 @ A ) ) ),file(funct_1,cc7_funct_1)).
thf(fc10_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(subset_1,fc10_subset_1)).
thf(fc1_ens_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ( ( v4_funct_1 @ ( k1_ens_1 @ A ) ) & ~ ( v1_xboole_0 @ ( k1_ens_1 @ A ) ) ) ) ),file(ens_1,fc1_ens_1)).
thf(fc1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( v1_xtuple_0 @ ( k4_tarski @ A @ B ) ) ),file(xtuple_0,fc1_xtuple_0)).
thf(fc4_orders_3,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v4_orders_3 @ A ) ) => ~ ( v1_xboole_0 @ ( k2_orders_3 @ A ) ) ) ),file(orders_3,fc4_orders_3)).
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(rc4_orders_3,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_orders_3 @ A ) ) ),file(orders_3,rc4_orders_3)).
thf(e1_34_1_1__orders_3,axiom,( ! [A: $i] : ( ( m1_orders_3 @ A @ c1_34__orders_3 ) => ! [B: $i] : ( ( m1_orders_3 @ B @ c1_34__orders_3 ) => ! [C: $i] : ( ( m1_orders_3 @ C @ c1_34__orders_3 ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_ens_1 @ ( k2_orders_3 @ c1_34__orders_3 ) ) ) => ! [E: $i] : ( ( m1_subset_1 @ E @ ( k1_ens_1 @ ( k2_orders_3 @ c1_34__orders_3 ) ) ) => ( ( ( r2_hidden @ D @ ( k1_orders_3 @ A @ B ) ) & ( r2_hidden @ E @ ( k1_orders_3 @ B @ C ) ) ) => ( ( r2_hidden @ ( k3_relat_1 @ D @ E ) @ ( k1_ens_1 @ ( k2_orders_3 @ c1_34__orders_3 ) ) ) & ( r2_hidden @ ( k3_relat_1 @ D @ E ) @ ( k1_orders_3 @ A @ C ) ) ) ) ) ) ) ) ) ),file(orders_3,e1_34_1_1__orders_3)).
thf(e2_34_1_1__orders_3,axiom,( ! [A: $i] : ( ( m1_orders_3 @ A @ c1_34__orders_3 ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_ens_1 @ ( k2_orders_3 @ c1_34__orders_3 ) ) ) & ( r2_hidden @ B @ ( k1_orders_3 @ A @ A ) ) & ! [C: $i] : ( ( m1_orders_3 @ C @ c1_34__orders_3 ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_ens_1 @ ( k2_orders_3 @ c1_34__orders_3 ) ) ) => ( ( ( r2_hidden @ D @ ( k1_orders_3 @ A @ C ) ) => ( = @ ( k3_relat_1 @ B @ D ) @ D ) ) & ( ( r2_hidden @ D @ ( k1_orders_3 @ C @ A ) ) => ( = @ ( k3_relat_1 @ D @ B ) @ D ) ) ) ) ) ) ) ),file(orders_3,e2_34_1_1__orders_3)).
thf(e3_34_1_1__orders_3,axiom,( ! [A: $i] : ( ( m1_orders_3 @ A @ c1_34__orders_3 ) => ! [B: $i] : ( ( m1_orders_3 @ B @ c1_34__orders_3 ) => ! [C: $i] : ( ( m1_orders_3 @ C @ c1_34__orders_3 ) => ! [D: $i] : ( ( m1_orders_3 @ D @ c1_34__orders_3 ) => ! [E: $i] : ( ( m1_subset_1 @ E @ ( k1_ens_1 @ ( k2_orders_3 @ c1_34__orders_3 ) ) ) => ! [F: $i] : ( ( m1_subset_1 @ F @ ( k1_ens_1 @ ( k2_orders_3 @ c1_34__orders_3 ) ) ) => ! [G: $i] : ( ( m1_subset_1 @ G @ ( k1_ens_1 @ ( k2_orders_3 @ c1_34__orders_3 ) ) ) => ( ( ( r2_hidden @ E @ ( k1_orders_3 @ A @ B ) ) & ( r2_hidden @ F @ ( k1_orders_3 @ B @ C ) ) & ( r2_hidden @ G @ ( k1_orders_3 @ C @ D ) ) ) => ( = @ ( k3_relat_1 @ ( k3_relat_1 @ E @ F ) @ G ) @ ( k3_relat_1 @ E @ ( k3_relat_1 @ F @ G ) ) ) ) ) ) ) ) ) ) ) ),file(orders_3,e3_34_1_1__orders_3)).
thf(s1_cat_5,axiom,( ! [A: $i > $i > $i] : ! [B: $i > $i > $i > $o] : ! [C: $i] : ! [D: $i] : ( ( ! [E: $i] : ( ( m1_subset_1 @ E @ D ) => ! [F: $i] : ( ( m1_subset_1 @ F @ D ) => ! [G: $i] : ( ( m1_subset_1 @ G @ D ) => ! [H: $i] : ( ( m1_subset_1 @ H @ C ) => ! [I: $i] : ( ( m1_subset_1 @ I @ C ) => ( ( ( B @ E @ F @ H ) & ( B @ F @ G @ I ) ) => ( ( r2_hidden @ ( A @ I @ H ) @ C ) & ( B @ E @ G @ ( A @ I @ H ) ) ) ) ) ) ) ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ D ) => ? [F: $i] : ( ( m1_subset_1 @ F @ C ) & ( B @ E @ E @ F ) & ! [G: $i] : ( ( m1_subset_1 @ G @ D ) => ! [H: $i] : ( ( m1_subset_1 @ H @ C ) => ( ( ( B @ E @ G @ H ) => ( = @ ( A @ H @ F ) @ H ) ) & ( ( B @ G @ E @ H ) => ( = @ ( A @ F @ H ) @ H ) ) ) ) ) ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ D ) => ! [F: $i] : ( ( m1_subset_1 @ F @ D ) => ! [G: $i] : ( ( m1_subset_1 @ G @ D ) => ! [H: $i] : ( ( m1_subset_1 @ H @ D ) => ! [I: $i] : ( ( m1_subset_1 @ I @ C ) => ! [J: $i] : ( ( m1_subset_1 @ J @ C ) => ! [K: $i] : ( ( m1_subset_1 @ K @ C ) => ( ( ( B @ E @ F @ I ) & ( B @ F @ G @ J ) & ( B @ G @ H @ K ) ) => ( = @ ( A @ K @ ( A @ J @ I ) ) @ ( A @ ( A @ K @ J ) @ I ) ) ) ) ) ) ) ) ) ) ) => ? [E: $i] : ( ~ ( v2_struct_0 @ E ) & ~ ( v11_struct_0 @ E ) & ( v1_cat_1 @ E ) & ( v2_cat_1 @ E ) & ( v3_cat_1 @ E ) & ( v4_cat_1 @ E ) & ( v5_cat_1 @ E ) & ( v6_cat_1 @ E ) & ( v1_cat_5 @ E ) & ( l1_cat_1 @ E ) & ( = @ ( u1_struct_0 @ E ) @ D ) & ! [F: $i] : ( ( m1_subset_1 @ F @ D ) => ! [G: $i] : ( ( m1_subset_1 @ G @ D ) => ! [H: $i] : ( ( m1_subset_1 @ H @ C ) => ( ( B @ F @ G @ H ) => ( m1_subset_1 @ ( k1_domain_1 @ ( k2_zfmisc_1 @ D @ D ) @ C @ ( k1_domain_1 @ D @ D @ F @ G ) @ H ) @ ( u4_struct_0 @ E ) ) ) ) ) ) & ! [F: $i] : ( ( m1_subset_1 @ F @ ( u4_struct_0 @ E ) ) => ? [G: $i] : ( ( m1_subset_1 @ G @ D ) & ? [H: $i] : ( ( m1_subset_1 @ H @ D ) & ? [I: $i] : ( ( m1_subset_1 @ I @ C ) & ( = @ F @ ( k1_domain_1 @ ( k2_zfmisc_1 @ D @ D ) @ C @ ( k1_domain_1 @ D @ D @ G @ H ) @ I ) ) & ( B @ G @ H @ I ) ) ) ) ) & ! [F: $i] : ( ( m1_subset_1 @ F @ ( u4_struct_0 @ E ) ) => ! [G: $i] : ( ( m1_subset_1 @ G @ ( u4_struct_0 @ E ) ) => ! [H: $i] : ( ( m1_subset_1 @ H @ D ) => ! [I: $i] : ( ( m1_subset_1 @ I @ D ) => ! [J: $i] : ( ( m1_subset_1 @ J @ D ) => ! [K: $i] : ( ( m1_subset_1 @ K @ C ) => ! [L: $i] : ( ( m1_subset_1 @ L @ C ) => ( ( ( = @ F @ ( k1_domain_1 @ ( k2_zfmisc_1 @ D @ D ) @ C @ ( k1_domain_1 @ D @ D @ H @ I ) @ K ) ) & ( = @ G @ ( k1_domain_1 @ ( k2_zfmisc_1 @ D @ D ) @ C @ ( k1_domain_1 @ D @ D @ I @ J ) @ L ) ) ) => ( = @ ( k1_cat_1 @ E @ F @ G ) @ ( k4_tarski @ ( k1_domain_1 @ D @ D @ H @ J ) @ ( A @ L @ K ) ) ) ) ) ) ) ) ) ) ) ) ) ),file(cat_5,s1_cat_5)).
thf(e4_34_1_1__orders_3,conjecture,( ? [A: $i] : ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( v1_cat_1 @ A ) & ( v2_cat_1 @ A ) & ( v3_cat_1 @ A ) & ( v4_cat_1 @ A ) & ( v5_cat_1 @ A ) & ( v6_cat_1 @ A ) & ( v1_cat_5 @ A ) & ( l1_cat_1 @ A ) & ( = @ ( u1_struct_0 @ A ) @ c1_34__orders_3 ) & ! [B: $i] : ( ( m1_orders_3 @ B @ c1_34__orders_3 ) => ! [C: $i] : ( ( m1_orders_3 @ C @ c1_34__orders_3 ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_ens_1 @ ( k2_orders_3 @ c1_34__orders_3 ) ) ) => ( ( r2_hidden @ D @ ( k1_orders_3 @ B @ C ) ) => ( m1_subset_1 @ ( k1_domain_1 @ ( k2_zfmisc_1 @ c1_34__orders_3 @ c1_34__orders_3 ) @ ( k1_ens_1 @ ( k2_orders_3 @ c1_34__orders_3 ) ) @ ( k1_domain_1 @ c1_34__orders_3 @ c1_34__orders_3 @ B @ C ) @ D ) @ ( u4_struct_0 @ A ) ) ) ) ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ ( u4_struct_0 @ A ) ) => ? [C: $i] : ( ( m1_orders_3 @ C @ c1_34__orders_3 ) & ? [D: $i] : ( ( m1_orders_3 @ D @ c1_34__orders_3 ) & ? [E: $i] : ( ( m1_subset_1 @ E @ ( k1_ens_1 @ ( k2_orders_3 @ c1_34__orders_3 ) ) ) & ( = @ B @ ( k1_domain_1 @ ( k2_zfmisc_1 @ c1_34__orders_3 @ c1_34__orders_3 ) @ ( k1_ens_1 @ ( k2_orders_3 @ c1_34__orders_3 ) ) @ ( k1_domain_1 @ c1_34__orders_3 @ c1_34__orders_3 @ C @ D ) @ E ) ) & ( r2_hidden @ E @ ( k1_orders_3 @ C @ D ) ) ) ) ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ ( u4_struct_0 @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( u4_struct_0 @ A ) ) => ! [D: $i] : ( ( m1_orders_3 @ D @ c1_34__orders_3 ) => ! [E: $i] : ( ( m1_orders_3 @ E @ c1_34__orders_3 ) => ! [F: $i] : ( ( m1_orders_3 @ F @ c1_34__orders_3 ) => ! [G: $i] : ( ( m1_subset_1 @ G @ ( k1_ens_1 @ ( k2_orders_3 @ c1_34__orders_3 ) ) ) => ! [H: $i] : ( ( m1_subset_1 @ H @ ( k1_ens_1 @ ( k2_orders_3 @ c1_34__orders_3 ) ) ) => ( ( ( = @ B @ ( k1_domain_1 @ ( k2_zfmisc_1 @ c1_34__orders_3 @ c1_34__orders_3 ) @ ( k1_ens_1 @ ( k2_orders_3 @ c1_34__orders_3 ) ) @ ( k1_domain_1 @ c1_34__orders_3 @ c1_34__orders_3 @ D @ E ) @ G ) ) & ( = @ C @ ( k1_domain_1 @ ( k2_zfmisc_1 @ c1_34__orders_3 @ c1_34__orders_3 ) @ ( k1_ens_1 @ ( k2_orders_3 @ c1_34__orders_3 ) ) @ ( k1_domain_1 @ c1_34__orders_3 @ c1_34__orders_3 @ E @ F ) @ H ) ) ) => ( = @ ( k1_cat_1 @ A @ B @ C ) @ ( k4_tarski @ ( k1_domain_1 @ c1_34__orders_3 @ c1_34__orders_3 @ D @ F ) @ ( k3_relat_1 @ G @ H ) ) ) ) ) ) ) ) ) ) ) ) ),file(orders_3,e4_34_1_1__orders_3)).
