% Mizar problem: s3_cat_5,cat_5,725,16 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(f1_s3_cat_5_type,type,( f1_s3_cat_5: $i )).
thf(f2_s3_cat_5_type,type,( f2_s3_cat_5: $i )).
thf(f3_s3_cat_5_type,type,( f3_s3_cat_5: $i > $i )).
thf(f4_s3_cat_5_type,type,( f4_s3_cat_5: $i > $i )).
thf(k10_xtuple_0_type,type,( k10_xtuple_0: $i > $i )).
thf(k1_cat_1_type,type,( k1_cat_1: $i > $i > $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_graph_1_type,type,( k1_graph_1: $i > $i > $i )).
thf(k1_relset_1_type,type,( k1_relset_1: $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_graph_1_type,type,( k2_graph_1: $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_funct_2_type,type,( k3_funct_2: $i > $i > $i > $i > $i )).
thf(k3_graph_1_type,type,( k3_graph_1: $i > $i > $i )).
thf(k4_cat_1_type,type,( k4_cat_1: $i > $i > $i )).
thf(k4_graph_1_type,type,( k4_graph_1: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $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_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l5_struct_0_type,type,( l5_struct_0: $i > $o )).
thf(m1_cat_1_type,type,( m1_cat_1: $i > $i > $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_cat_1_type,type,( m2_cat_1: $i > $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $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_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_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_setfam_1_type,type,( v1_setfam_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_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_relat_1_type,type,( v2_relat_1: $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_relat_1_type,type,( v3_relat_1: $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_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_cat_1_type,type,( v5_cat_1: $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(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_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(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(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(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(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(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(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_cat_1,axiom,( ! [A: $i] : ( ( l1_cat_1 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( v3_cat_1 @ A ) & ( v5_cat_1 @ A ) ) ) ) ),file(cat_1,cc1_cat_1)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_1)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_1)).
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_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc1_struct_0)).
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_cat_1,axiom,( ! [A: $i] : ( ( l1_cat_1 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( v15_struct_0 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( v4_cat_1 @ A ) & ( v6_cat_1 @ A ) ) ) ) ),file(cat_1,cc2_cat_1)).
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(cc2_relat_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_relat_1 @ B ) ) ) ),file(relat_1,cc2_relat_1)).
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(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(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_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(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_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_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(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_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(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_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) => ( v4_relat_1 @ C @ A ) ) ) ),file(relat_1,cc5_relat_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(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(cc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) => ( v5_relat_1 @ C @ A ) ) ) ),file(relat_1,cc6_relat_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_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v4_funct_1 @ A ) ) ),file(funct_1,cc7_funct_1)).
thf(cc7_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) ) ) ),file(relat_1,cc7_relat_1)).
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_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_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) => ( ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) ) ) ),file(relat_1,cc8_relat_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(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(d1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ~ ( = @ B @ k1_xboole_0 ) => ( ( v1_funct_2 @ C @ A @ B ) <=> ( = @ A @ ( k1_relset_1 @ A @ C ) ) ) ) & ( ( = @ B @ k1_xboole_0 ) => ( ( v1_funct_2 @ C @ A @ B ) <=> ( = @ C @ k1_xboole_0 ) ) ) ) ) ),file(funct_2,d1_funct_2)).
thf(d2_xboole_0,axiom,( = @ k1_xboole_0 @ ( eps @ ^ [A: $i] : ( v1_xboole_0 @ A ) ) ),file(xboole_0,d2_xboole_0)).
thf(d3_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ! [B: $i] : ( ( = @ B @ ( k10_xtuple_0 @ A ) ) <=> ! [C: $i] : ( ( r2_hidden @ C @ B ) <=> ? [D: $i] : ( ( r2_hidden @ D @ ( k9_xtuple_0 @ A ) ) & ( = @ C @ ( k1_funct_1 @ A @ D ) ) ) ) ) ) ),file(funct_1,d3_funct_1)).
thf(d3_graph_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_graph_1 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( u4_struct_0 @ A ) ) => ( = @ ( k3_graph_1 @ A @ B ) @ ( k3_funct_2 @ ( u4_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_graph_1 @ A ) @ B ) ) ) ) ),file(graph_1,d3_graph_1)).
thf(d3_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( ( r1_tarski @ A @ B ) <=> ! [C: $i] : ( ( r2_hidden @ C @ A ) => ( r2_hidden @ C @ B ) ) ) ),file(tarski,d3_tarski)).
thf(d4_graph_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_graph_1 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( u4_struct_0 @ A ) ) => ( = @ ( k4_graph_1 @ A @ B ) @ ( k3_funct_2 @ ( u4_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u2_graph_1 @ A ) @ B ) ) ) ) ),file(graph_1,d4_graph_1)).
thf(dt_f1_s3_cat_5,axiom,( ~ ( v2_struct_0 @ f1_s3_cat_5 ) & ~ ( v11_struct_0 @ f1_s3_cat_5 ) & ( v2_cat_1 @ f1_s3_cat_5 ) & ( v3_cat_1 @ f1_s3_cat_5 ) & ( v4_cat_1 @ f1_s3_cat_5 ) & ( v5_cat_1 @ f1_s3_cat_5 ) & ( v6_cat_1 @ f1_s3_cat_5 ) & ( l1_cat_1 @ f1_s3_cat_5 ) ),file(cat_5,f1_s3_cat_5)).
thf(dt_f2_s3_cat_5,axiom,( ~ ( v2_struct_0 @ f2_s3_cat_5 ) & ~ ( v11_struct_0 @ f2_s3_cat_5 ) & ( v2_cat_1 @ f2_s3_cat_5 ) & ( v3_cat_1 @ f2_s3_cat_5 ) & ( v4_cat_1 @ f2_s3_cat_5 ) & ( v5_cat_1 @ f2_s3_cat_5 ) & ( v6_cat_1 @ f2_s3_cat_5 ) & ( l1_cat_1 @ f2_s3_cat_5 ) ),file(cat_5,f2_s3_cat_5)).
thf(dt_f3_s3_cat_5,axiom,( ! [A: $i] : ( m1_subset_1 @ ( f3_s3_cat_5 @ A ) @ ( u1_struct_0 @ f2_s3_cat_5 ) ) ),file(cat_5,f3_s3_cat_5)).
thf(dt_f4_s3_cat_5,axiom,( $true ),file(cat_5,f4_s3_cat_5)).
thf(dt_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
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_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_graph_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_graph_1 @ A ) & ( m1_subset_1 @ B @ ( u4_struct_0 @ A ) ) ) => ( m1_subset_1 @ ( k1_graph_1 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ),file(graph_1,k1_graph_1)).
thf(dt_k1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( m1_subset_1 @ ( k1_relset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(relset_1,k1_relset_1)).
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(dt_k2_graph_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_graph_1 @ A ) & ( m1_subset_1 @ B @ ( u4_struct_0 @ A ) ) ) => ( m1_subset_1 @ ( k2_graph_1 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ),file(graph_1,k2_graph_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ B ) ) ),file(funct_2,k3_funct_2)).
thf(dt_k3_graph_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_graph_1 @ A ) & ( m1_subset_1 @ B @ ( u4_struct_0 @ A ) ) ) => ( m1_subset_1 @ ( k3_graph_1 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ),file(graph_1,k3_graph_1)).
thf(dt_k4_cat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( v5_cat_1 @ A ) & ( v6_cat_1 @ A ) & ( l1_cat_1 @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) ) => ( m1_cat_1 @ ( k4_cat_1 @ A @ B ) @ A @ B @ B ) ) ),file(cat_1,k4_cat_1)).
thf(dt_k4_graph_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_graph_1 @ A ) & ( m1_subset_1 @ B @ ( u4_struct_0 @ A ) ) ) => ( m1_subset_1 @ ( k4_graph_1 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ),file(graph_1,k4_graph_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_l1_cat_1,axiom,( ! [A: $i] : ( ( l1_cat_1 @ A ) => ( l1_graph_1 @ A ) ) ),file(cat_1,l1_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_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_m1_cat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_cat_1 @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) => ! [D: $i] : ( ( m1_cat_1 @ D @ A @ B @ C ) => ( m1_subset_1 @ D @ ( u4_struct_0 @ A ) ) ) ) ),file(cat_1,m1_cat_1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_m2_cat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( v2_cat_1 @ A ) & ( v3_cat_1 @ A ) & ( v4_cat_1 @ A ) & ( v5_cat_1 @ A ) & ( v6_cat_1 @ A ) & ( l1_cat_1 @ A ) & ~ ( v2_struct_0 @ B ) & ~ ( v11_struct_0 @ B ) & ( v2_cat_1 @ B ) & ( v3_cat_1 @ B ) & ( v4_cat_1 @ B ) & ( v5_cat_1 @ B ) & ( v6_cat_1 @ B ) & ( l1_cat_1 @ B ) ) => ! [C: $i] : ( ( m2_cat_1 @ C @ A @ B ) => ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( u4_struct_0 @ A ) @ ( u4_struct_0 @ B ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u4_struct_0 @ A ) @ ( u4_struct_0 @ B ) ) ) ) ) ) ) ),file(cat_1,m2_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_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
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(dt_u4_struct_0,axiom,( $true ),file(struct_0,u4_struct_0)).
thf(existence_l1_cat_1,axiom,( ? [A: $i] : ( l1_cat_1 @ A ) ),file(cat_1,l1_cat_1)).
thf(existence_l1_graph_1,axiom,( ? [A: $i] : ( l1_graph_1 @ A ) ),file(graph_1,l1_graph_1)).
thf(existence_l1_struct_0,axiom,( ? [A: $i] : ( l1_struct_0 @ A ) ),file(struct_0,l1_struct_0)).
thf(existence_l5_struct_0,axiom,( ? [A: $i] : ( l5_struct_0 @ A ) ),file(struct_0,l5_struct_0)).
thf(existence_m1_cat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_cat_1 @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) => ? [D: $i] : ( m1_cat_1 @ D @ A @ B @ C ) ) ),file(cat_1,m1_cat_1)).
thf(existence_m1_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( m1_subset_1 @ B @ A ) ),file(subset_1,m1_subset_1)).
thf(existence_m2_cat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( v2_cat_1 @ A ) & ( v3_cat_1 @ A ) & ( v4_cat_1 @ A ) & ( v5_cat_1 @ A ) & ( v6_cat_1 @ A ) & ( l1_cat_1 @ A ) & ~ ( v2_struct_0 @ B ) & ~ ( v11_struct_0 @ B ) & ( v2_cat_1 @ B ) & ( v3_cat_1 @ B ) & ( v4_cat_1 @ B ) & ( v5_cat_1 @ B ) & ( v6_cat_1 @ B ) & ( l1_cat_1 @ B ) ) => ? [C: $i] : ( m2_cat_1 @ C @ A @ B ) ) ),file(cat_1,m2_cat_1)).
thf(fc10_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( v1_setfam_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(funct_1,fc10_funct_1)).
thf(fc10_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc10_relat_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(fc11_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( m1_subset_1 @ B @ ( k9_xtuple_0 @ A ) ) ) => ~ ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(funct_1,fc11_funct_1)).
thf(fc11_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k10_xtuple_0 @ A ) ) ) ),file(relat_1,fc11_relat_1)).
thf(fc12_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) => ( v1_zfmisc_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(funct_1,fc12_funct_1)).
thf(fc13_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) => ~ ( v1_zfmisc_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(funct_1,fc13_funct_1)).
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(fc17_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v4_funct_1 @ A ) & ( v1_relat_1 @ C ) & ( v5_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) ) => ( ( v1_relat_1 @ ( k1_funct_1 @ C @ B ) ) & ( v1_funct_1 @ ( k1_funct_1 @ C @ B ) ) ) ) ),file(funct_1,fc17_funct_1)).
thf(fc18_funct_1,axiom,( ! [A: $i] : ( ( ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ~ ( v1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(funct_1,fc18_funct_1)).
thf(fc19_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(funct_1,fc19_funct_1)).
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(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(fc24_relat_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) ) => ( v1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc24_relat_1)).
thf(fc25_relat_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) ) => ( v1_zfmisc_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(relat_1,fc25_relat_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(fc4_xtuple_0,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(xtuple_0,fc4_xtuple_0)).
thf(fc5_xtuple_0,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k10_xtuple_0 @ A ) ) ) ),file(xtuple_0,fc5_xtuple_0)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
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_relat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ~ ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc8_relat_1)).
thf(fc8_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) => ( v1_relat_1 @ ( k9_xtuple_0 @ D ) ) ) ),file(relset_1,fc8_relset_1)).
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_relat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ~ ( v1_xboole_0 @ ( k10_xtuple_0 @ A ) ) ) ),file(relat_1,fc9_relat_1)).
thf(fc9_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) ) => ( v1_relat_1 @ ( k10_xtuple_0 @ D ) ) ) ),file(relset_1,fc9_relset_1)).
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_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_1)).
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(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(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
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(rc25_struct_0,axiom,( ? [A: $i] : ( ( l5_struct_0 @ A ) & ~ ( v15_struct_0 @ A ) ) ),file(struct_0,rc25_struct_0)).
thf(rc2_cat_1,axiom,( ? [A: $i] : ( ( l1_cat_1 @ A ) & ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) ) ),file(cat_1,rc2_cat_1)).
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_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_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(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc3_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc3_funct_1)).
thf(rc3_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relat_1,rc3_relat_1)).
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_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc4_funct_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(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_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) ),file(funct_1,rc5_funct_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(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(rc9_funct_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) ),file(funct_1,rc9_funct_1)).
thf(rd3_cat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( v2_cat_1 @ A ) & ( v3_cat_1 @ A ) & ( v4_cat_1 @ A ) & ( v5_cat_1 @ A ) & ( v6_cat_1 @ A ) & ( l1_cat_1 @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) ) => ( = @ ( k3_graph_1 @ A @ ( k4_cat_1 @ A @ B ) ) @ B ) ) ),file(cat_1,rd3_cat_1)).
thf(rd4_cat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( v2_cat_1 @ A ) & ( v3_cat_1 @ A ) & ( v4_cat_1 @ A ) & ( v5_cat_1 @ A ) & ( v6_cat_1 @ A ) & ( l1_cat_1 @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) ) => ( = @ ( k4_graph_1 @ A @ ( k4_cat_1 @ A @ B ) ) @ B ) ) ),file(cat_1,rd4_cat_1)).
thf(redefinition_k1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( = @ ( k1_relset_1 @ A @ B ) @ ( k9_xtuple_0 @ B ) ) ) ),file(relset_1,k1_relset_1)).
thf(redefinition_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ),file(funct_2,k3_funct_2)).
thf(redefinition_k3_graph_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_graph_1 @ A ) & ( m1_subset_1 @ B @ ( u4_struct_0 @ A ) ) ) => ( = @ ( k3_graph_1 @ A @ B ) @ ( k1_graph_1 @ A @ B ) ) ) ),file(graph_1,k3_graph_1)).
thf(redefinition_k4_graph_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_graph_1 @ A ) & ( m1_subset_1 @ B @ ( u4_struct_0 @ A ) ) ) => ( = @ ( k4_graph_1 @ A @ B ) @ ( k2_graph_1 @ A @ B ) ) ) ),file(graph_1,k4_graph_1)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
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(t3_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) <=> ( r1_tarski @ A @ B ) ) ),file(subset,t3_subset)).
thf(t4_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( v1_relat_1 @ C ) => ( ( ( r1_tarski @ ( k9_xtuple_0 @ C ) @ A ) & ( r1_tarski @ ( k10_xtuple_0 @ C ) @ B ) ) => ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ),file(relset_1,t4_relset_1)).
thf(t4_subset,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ A @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) ) => ( m1_subset_1 @ A @ C ) ) ),file(subset,t4_subset)).
thf(t5_subset,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ~ ( ( r2_hidden @ A @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) & ( v1_xboole_0 @ C ) ) ),file(subset,t5_subset)).
thf(t61_cat_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( v2_cat_1 @ A ) & ( v3_cat_1 @ A ) & ( v4_cat_1 @ A ) & ( v5_cat_1 @ A ) & ( v6_cat_1 @ A ) & ( l1_cat_1 @ A ) ) => ! [B: $i] : ( ( ~ ( v2_struct_0 @ B ) & ~ ( v11_struct_0 @ B ) & ( v2_cat_1 @ B ) & ( v3_cat_1 @ B ) & ( v4_cat_1 @ B ) & ( v5_cat_1 @ B ) & ( v6_cat_1 @ B ) & ( l1_cat_1 @ B ) ) => ! [C: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( u4_struct_0 @ A ) @ ( u4_struct_0 @ B ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u4_struct_0 @ A ) @ ( u4_struct_0 @ B ) ) ) ) ) => ( ( ! [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) ) => ? [E: $i] : ( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) ) & ( = @ ( k3_funct_2 @ ( u4_struct_0 @ A ) @ ( u4_struct_0 @ B ) @ C @ ( k4_cat_1 @ A @ D ) ) @ ( k4_cat_1 @ B @ E ) ) ) ) & ! [D: $i] : ( ( m1_subset_1 @ D @ ( u4_struct_0 @ A ) ) => ( ( = @ ( k3_funct_2 @ ( u4_struct_0 @ A ) @ ( u4_struct_0 @ B ) @ C @ ( k4_cat_1 @ A @ ( k3_graph_1 @ A @ D ) ) ) @ ( k4_cat_1 @ B @ ( k3_graph_1 @ B @ ( k3_funct_2 @ ( u4_struct_0 @ A ) @ ( u4_struct_0 @ B ) @ C @ D ) ) ) ) & ( = @ ( k3_funct_2 @ ( u4_struct_0 @ A ) @ ( u4_struct_0 @ B ) @ C @ ( k4_cat_1 @ A @ ( k4_graph_1 @ A @ D ) ) ) @ ( k4_cat_1 @ B @ ( k4_graph_1 @ B @ ( k3_funct_2 @ ( u4_struct_0 @ A ) @ ( u4_struct_0 @ B ) @ C @ D ) ) ) ) ) ) & ! [D: $i] : ( ( m1_subset_1 @ D @ ( u4_struct_0 @ A ) ) => ! [E: $i] : ( ( m1_subset_1 @ E @ ( u4_struct_0 @ A ) ) => ( ( = @ ( k3_graph_1 @ A @ E ) @ ( k4_graph_1 @ A @ D ) ) => ( = @ ( k3_funct_2 @ ( u4_struct_0 @ A ) @ ( u4_struct_0 @ B ) @ C @ ( k1_cat_1 @ A @ D @ E ) ) @ ( k1_cat_1 @ B @ ( k3_funct_2 @ ( u4_struct_0 @ A ) @ ( u4_struct_0 @ B ) @ C @ D ) @ ( k3_funct_2 @ ( u4_struct_0 @ A ) @ ( u4_struct_0 @ B ) @ C @ E ) ) ) ) ) ) ) => ( m2_cat_1 @ C @ A @ B ) ) ) ) ) ),file(cat_1,t61_cat_1)).
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(s3_funct_1,axiom,( ! [A: $i > $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( = @ ( k1_funct_1 @ C @ D ) @ ( A @ D ) ) ) ) ),file(funct_1,s3_funct_1)).
thf(s3_cat_5,conjecture,( ( ! [A: $i] : ( ( m1_subset_1 @ A @ ( u4_struct_0 @ f1_s3_cat_5 ) ) => ( ( m1_subset_1 @ ( f4_s3_cat_5 @ A ) @ ( u4_struct_0 @ f2_s3_cat_5 ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ ( u4_struct_0 @ f2_s3_cat_5 ) ) => ( ( = @ B @ ( f4_s3_cat_5 @ A ) ) => ( ( = @ ( k3_graph_1 @ f2_s3_cat_5 @ B ) @ ( f3_s3_cat_5 @ ( k3_graph_1 @ f1_s3_cat_5 @ A ) ) ) & ( = @ ( k4_graph_1 @ f2_s3_cat_5 @ B ) @ ( f3_s3_cat_5 @ ( k4_graph_1 @ f1_s3_cat_5 @ A ) ) ) ) ) ) ) ) & ! [A: $i] : ( ( m1_subset_1 @ A @ ( u1_struct_0 @ f1_s3_cat_5 ) ) => ( = @ ( f4_s3_cat_5 @ ( k4_cat_1 @ f1_s3_cat_5 @ A ) ) @ ( k4_cat_1 @ f2_s3_cat_5 @ ( f3_s3_cat_5 @ A ) ) ) ) & ! [A: $i] : ( ( m1_subset_1 @ A @ ( u4_struct_0 @ f1_s3_cat_5 ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( u4_struct_0 @ f1_s3_cat_5 ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( u4_struct_0 @ f2_s3_cat_5 ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( u4_struct_0 @ f2_s3_cat_5 ) ) => ( ( ( = @ C @ ( f4_s3_cat_5 @ A ) ) & ( = @ D @ ( f4_s3_cat_5 @ B ) ) & ( = @ ( k3_graph_1 @ f1_s3_cat_5 @ B ) @ ( k4_graph_1 @ f1_s3_cat_5 @ A ) ) ) => ( = @ ( f4_s3_cat_5 @ ( k1_cat_1 @ f1_s3_cat_5 @ A @ B ) ) @ ( k1_cat_1 @ f2_s3_cat_5 @ C @ D ) ) ) ) ) ) ) ) => ? [A: $i] : ( ( m2_cat_1 @ A @ f1_s3_cat_5 @ f2_s3_cat_5 ) & ! [B: $i] : ( ( m1_subset_1 @ B @ ( u4_struct_0 @ f1_s3_cat_5 ) ) => ( = @ ( k3_funct_2 @ ( u4_struct_0 @ f1_s3_cat_5 ) @ ( u4_struct_0 @ f2_s3_cat_5 ) @ A @ B ) @ ( f4_s3_cat_5 @ B ) ) ) ) ),file(cat_5,s3_cat_5)).
