% Mizar problem: e2_7_1_1,commacat,243,51 
include('Axioms/SET010^2.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_7_type,type,( c1_7__commacat: $i )).
thf(c2_7_type,type,( c2_7__commacat: $i )).
thf(c3_7_type,type,( c3_7__commacat: $i )).
thf(c4_7_type,type,( c4_7__commacat: $i )).
thf(c5_7_type,type,( c5_7__commacat: $i )).
thf(k13_mcart_1_type,type,( k13_mcart_1: $i > $i )).
thf(k14_mcart_1_type,type,( k14_mcart_1: $i > $i )).
thf(k1_commacat_type,type,( k1_commacat: $i > $i > $i > $i > $i > $i )).
thf(k1_domain_1_type,type,( k1_domain_1: $i > $i > $i > $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_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_commacat_type,type,( k2_commacat: $i > $i > $i > $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_commacat_type,type,( k3_commacat: $i > $i > $i > $i > $i > $i > $i )).
thf(k4_commacat_type,type,( k4_commacat: $i > $i > $i > $i > $i > $i > $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(k5_commacat_type,type,( k5_commacat: $i > $i > $i > $i > $i > $i > $i > $i )).
thf(k8_mcart_1_type,type,( k8_mcart_1: $i > $i > $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $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_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_cat_1_type,type,( m2_cat_1: $i > $i > $i > $o )).
thf(m2_subset_1_type,type,( m2_subset_1: $i > $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_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_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v3_cat_1_type,type,( v3_cat_1: $i > $o )).
thf(v4_cat_1_type,type,( v4_cat_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(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(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(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(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_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(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_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(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_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(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(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(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(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_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_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_0)).
thf(rc25_struct_0,axiom,( ? [A: $i] : ( ( l5_struct_0 @ A ) & ~ ( v15_struct_0 @ A ) ) ),file(struct_0,rc25_struct_0)).
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(dt_k13_mcart_1,axiom,( $true ),file(mcart_1,k13_mcart_1)).
thf(dt_k14_mcart_1,axiom,( $true ),file(mcart_1,k14_mcart_1)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
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_subset_1,axiom,( $true ),file(subset_1,m1_subset_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_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_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(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_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(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(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(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(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( v1_xtuple_0 @ ( k4_tarski @ A @ B ) ) ),file(xtuple_0,fc1_xtuple_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(fc4_xtuple_0,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(xtuple_0,fc4_xtuple_0)).
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(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(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(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(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
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_k3_commacat,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $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 ) & ~ ( v2_struct_0 @ C ) & ~ ( v11_struct_0 @ C ) & ( v2_cat_1 @ C ) & ( v3_cat_1 @ C ) & ( v4_cat_1 @ C ) & ( v5_cat_1 @ C ) & ( v6_cat_1 @ C ) & ( l1_cat_1 @ C ) & ( m2_cat_1 @ D @ A @ C ) & ( m2_cat_1 @ E @ B @ C ) & ( m1_subset_1 @ F @ ( k2_commacat @ A @ B @ C @ D @ E ) ) ) => ( = @ ( k3_commacat @ A @ B @ C @ D @ E @ F ) @ ( k13_mcart_1 @ F ) ) ) ),file(commacat,k3_commacat)).
thf(redefinition_k4_commacat,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $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 ) & ~ ( v2_struct_0 @ C ) & ~ ( v11_struct_0 @ C ) & ( v2_cat_1 @ C ) & ( v3_cat_1 @ C ) & ( v4_cat_1 @ C ) & ( v5_cat_1 @ C ) & ( v6_cat_1 @ C ) & ( l1_cat_1 @ C ) & ( m2_cat_1 @ D @ A @ C ) & ( m2_cat_1 @ E @ B @ C ) & ( m1_subset_1 @ F @ ( k2_commacat @ A @ B @ C @ D @ E ) ) ) => ( = @ ( k4_commacat @ A @ B @ C @ D @ E @ F ) @ ( k14_mcart_1 @ F ) ) ) ),file(commacat,k4_commacat)).
thf(redefinition_k8_mcart_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) ) => ( = @ ( k8_mcart_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ C @ D ) ) ) ),file(mcart_1,k8_mcart_1)).
thf(redefinition_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) <=> ( m1_subset_1 @ C @ B ) ) ) ),file(subset_1,m2_subset_1)).
thf(dt_k1_commacat,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $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 ) & ~ ( v2_struct_0 @ C ) & ~ ( v11_struct_0 @ C ) & ( v2_cat_1 @ C ) & ( v3_cat_1 @ C ) & ( v4_cat_1 @ C ) & ( v5_cat_1 @ C ) & ( v6_cat_1 @ C ) & ( l1_cat_1 @ C ) & ( m2_cat_1 @ D @ A @ C ) & ( m2_cat_1 @ E @ B @ C ) ) => ( ~ ( v1_xboole_0 @ ( k1_commacat @ A @ B @ C @ D @ E ) ) & ( m1_subset_1 @ ( k1_commacat @ A @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u4_struct_0 @ C ) ) ) ) ) ) ),file(commacat,k1_commacat)).
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_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k2_commacat,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $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 ) & ~ ( v2_struct_0 @ C ) & ~ ( v11_struct_0 @ C ) & ( v2_cat_1 @ C ) & ( v3_cat_1 @ C ) & ( v4_cat_1 @ C ) & ( v5_cat_1 @ C ) & ( v6_cat_1 @ C ) & ( l1_cat_1 @ C ) & ( m2_cat_1 @ D @ A @ C ) & ( m2_cat_1 @ E @ B @ C ) ) => ( ~ ( v1_xboole_0 @ ( k2_commacat @ A @ B @ C @ D @ E ) ) & ( m1_subset_1 @ ( k2_commacat @ A @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k8_mcart_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u4_struct_0 @ C ) ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u4_struct_0 @ C ) ) @ ( k1_commacat @ A @ B @ C @ D @ E ) @ ( k1_commacat @ A @ B @ C @ D @ E ) ) @ ( k2_zfmisc_1 @ ( u4_struct_0 @ A ) @ ( u4_struct_0 @ B ) ) ) ) ) ) ) ),file(commacat,k2_commacat)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_commacat,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $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 ) & ~ ( v2_struct_0 @ C ) & ~ ( v11_struct_0 @ C ) & ( v2_cat_1 @ C ) & ( v3_cat_1 @ C ) & ( v4_cat_1 @ C ) & ( v5_cat_1 @ C ) & ( v6_cat_1 @ C ) & ( l1_cat_1 @ C ) & ( m2_cat_1 @ D @ A @ C ) & ( m2_cat_1 @ E @ B @ C ) & ( m1_subset_1 @ F @ ( k2_commacat @ A @ B @ C @ D @ E ) ) ) => ( m2_subset_1 @ ( k3_commacat @ A @ B @ C @ D @ E @ F ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u4_struct_0 @ C ) ) @ ( k1_commacat @ A @ B @ C @ D @ E ) ) ) ),file(commacat,k3_commacat)).
thf(dt_k4_commacat,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $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 ) & ~ ( v2_struct_0 @ C ) & ~ ( v11_struct_0 @ C ) & ( v2_cat_1 @ C ) & ( v3_cat_1 @ C ) & ( v4_cat_1 @ C ) & ( v5_cat_1 @ C ) & ( v6_cat_1 @ C ) & ( l1_cat_1 @ C ) & ( m2_cat_1 @ D @ A @ C ) & ( m2_cat_1 @ E @ B @ C ) & ( m1_subset_1 @ F @ ( k2_commacat @ A @ B @ C @ D @ E ) ) ) => ( m2_subset_1 @ ( k4_commacat @ A @ B @ C @ D @ E @ F ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u4_struct_0 @ C ) ) @ ( k1_commacat @ A @ B @ C @ D @ E ) ) ) ),file(commacat,k4_commacat)).
thf(dt_k5_commacat,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ! [G: $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 ) & ~ ( v2_struct_0 @ C ) & ~ ( v11_struct_0 @ C ) & ( v2_cat_1 @ C ) & ( v3_cat_1 @ C ) & ( v4_cat_1 @ C ) & ( v5_cat_1 @ C ) & ( v6_cat_1 @ C ) & ( l1_cat_1 @ C ) & ( m2_cat_1 @ D @ A @ C ) & ( m2_cat_1 @ E @ B @ C ) & ( m1_subset_1 @ F @ ( k2_commacat @ A @ B @ C @ D @ E ) ) & ( m1_subset_1 @ G @ ( k2_commacat @ A @ B @ C @ D @ E ) ) ) => ( m2_subset_1 @ ( k5_commacat @ A @ B @ C @ D @ E @ F @ G ) @ ( k2_zfmisc_1 @ ( k8_mcart_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u4_struct_0 @ C ) ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( u4_struct_0 @ C ) ) @ ( k1_commacat @ A @ B @ C @ D @ E ) @ ( k1_commacat @ A @ B @ C @ D @ E ) ) @ ( k2_zfmisc_1 @ ( u4_struct_0 @ A ) @ ( u4_struct_0 @ B ) ) ) @ ( k2_commacat @ A @ B @ C @ D @ E ) ) ) ),file(commacat,k5_commacat)).
thf(dt_k8_mcart_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) ) => ( m1_subset_1 @ ( k8_mcart_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ),file(mcart_1,k8_mcart_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_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_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) => ( m1_subset_1 @ C @ A ) ) ) ),file(subset_1,m2_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_7__commacat,axiom,( ~ ( v2_struct_0 @ c1_7__commacat ) & ~ ( v11_struct_0 @ c1_7__commacat ) & ( v2_cat_1 @ c1_7__commacat ) & ( v3_cat_1 @ c1_7__commacat ) & ( v4_cat_1 @ c1_7__commacat ) & ( v5_cat_1 @ c1_7__commacat ) & ( v6_cat_1 @ c1_7__commacat ) & ( l1_cat_1 @ c1_7__commacat ) ),file(commacat,c1_7__commacat)).
thf(dt_c2_7__commacat,axiom,( ~ ( v2_struct_0 @ c2_7__commacat ) & ~ ( v11_struct_0 @ c2_7__commacat ) & ( v2_cat_1 @ c2_7__commacat ) & ( v3_cat_1 @ c2_7__commacat ) & ( v4_cat_1 @ c2_7__commacat ) & ( v5_cat_1 @ c2_7__commacat ) & ( v6_cat_1 @ c2_7__commacat ) & ( l1_cat_1 @ c2_7__commacat ) ),file(commacat,c2_7__commacat)).
thf(dt_c3_7__commacat,axiom,( ~ ( v2_struct_0 @ c3_7__commacat ) & ~ ( v11_struct_0 @ c3_7__commacat ) & ( v2_cat_1 @ c3_7__commacat ) & ( v3_cat_1 @ c3_7__commacat ) & ( v4_cat_1 @ c3_7__commacat ) & ( v5_cat_1 @ c3_7__commacat ) & ( v6_cat_1 @ c3_7__commacat ) & ( l1_cat_1 @ c3_7__commacat ) ),file(commacat,c3_7__commacat)).
thf(dt_c4_7__commacat,axiom,( m2_cat_1 @ c4_7__commacat @ c1_7__commacat @ c3_7__commacat ),file(commacat,c4_7__commacat)).
thf(dt_c5_7__commacat,axiom,( m2_cat_1 @ c5_7__commacat @ c2_7__commacat @ c3_7__commacat ),file(commacat,c5_7__commacat)).
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(e1_7_1_1__commacat,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ ( replSep2 @ ^ [B: $i] : ( m2_subset_1 @ B @ ( k2_zfmisc_1 @ ( k8_mcart_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) @ ( k2_zfmisc_1 @ ( u4_struct_0 @ c1_7__commacat ) @ ( u4_struct_0 @ c2_7__commacat ) ) ) @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) @ ^ [B: $i] : ^ [C: $i] : ( m2_subset_1 @ C @ ( k2_zfmisc_1 @ ( k8_mcart_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) @ ( k2_zfmisc_1 @ ( u4_struct_0 @ c1_7__commacat ) @ ( u4_struct_0 @ c2_7__commacat ) ) ) @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) @ ^ [B: $i] : ^ [C: $i] : ( k1_domain_1 @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ B @ C ) @ ^ [B: $i] : ^ [C: $i] : ( = @ ( k3_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat @ B ) @ ( k4_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat @ C ) ) ) ) & ! [B: $i] : ~ ( ? [C: $i] : ( ( m2_subset_1 @ C @ ( k2_zfmisc_1 @ ( k8_mcart_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) @ ( k2_zfmisc_1 @ ( u4_struct_0 @ c1_7__commacat ) @ ( u4_struct_0 @ c2_7__commacat ) ) ) @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) & ? [D: $i] : ( ( m2_subset_1 @ D @ ( k2_zfmisc_1 @ ( k8_mcart_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) @ ( k2_zfmisc_1 @ ( u4_struct_0 @ c1_7__commacat ) @ ( u4_struct_0 @ c2_7__commacat ) ) ) @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) & ( = @ A @ ( k1_domain_1 @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ C @ D ) ) & ( = @ B @ ( k5_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat @ D @ C ) ) ) ) ) ) ),file(commacat,e1_7_1_1__commacat)).
thf(s1_classes1,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ( ! [C: $i] : ~ ( ( r2_hidden @ C @ B ) & ! [D: $i] : ~ ( A @ C @ D ) ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( A @ D @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),file(classes1,s1_classes1)).
thf(e2_7_1_1__commacat,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( replSep2 @ ^ [B: $i] : ( m2_subset_1 @ B @ ( k2_zfmisc_1 @ ( k8_mcart_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) @ ( k2_zfmisc_1 @ ( u4_struct_0 @ c1_7__commacat ) @ ( u4_struct_0 @ c2_7__commacat ) ) ) @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) @ ^ [B: $i] : ^ [C: $i] : ( m2_subset_1 @ C @ ( k2_zfmisc_1 @ ( k8_mcart_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) @ ( k2_zfmisc_1 @ ( u4_struct_0 @ c1_7__commacat ) @ ( u4_struct_0 @ c2_7__commacat ) ) ) @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) @ ^ [B: $i] : ^ [C: $i] : ( k1_domain_1 @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ B @ C ) @ ^ [B: $i] : ^ [C: $i] : ( = @ ( k3_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat @ B ) @ ( k4_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat @ C ) ) ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( replSep2 @ ^ [C: $i] : ( m2_subset_1 @ C @ ( k2_zfmisc_1 @ ( k8_mcart_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) @ ( k2_zfmisc_1 @ ( u4_struct_0 @ c1_7__commacat ) @ ( u4_struct_0 @ c2_7__commacat ) ) ) @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) @ ^ [C: $i] : ^ [D: $i] : ( m2_subset_1 @ D @ ( k2_zfmisc_1 @ ( k8_mcart_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) @ ( k2_zfmisc_1 @ ( u4_struct_0 @ c1_7__commacat ) @ ( u4_struct_0 @ c2_7__commacat ) ) ) @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) @ ^ [C: $i] : ^ [D: $i] : ( k1_domain_1 @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ C @ D ) @ ^ [C: $i] : ^ [D: $i] : ( = @ ( k3_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat @ C ) @ ( k4_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat @ D ) ) ) ) => ? [C: $i] : ( ( m2_subset_1 @ C @ ( k2_zfmisc_1 @ ( k8_mcart_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) @ ( k2_zfmisc_1 @ ( u4_struct_0 @ c1_7__commacat ) @ ( u4_struct_0 @ c2_7__commacat ) ) ) @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) & ? [D: $i] : ( ( m2_subset_1 @ D @ ( k2_zfmisc_1 @ ( k8_mcart_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_7__commacat ) @ ( u1_struct_0 @ c2_7__commacat ) ) @ ( u4_struct_0 @ c3_7__commacat ) ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ ( k1_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) @ ( k2_zfmisc_1 @ ( u4_struct_0 @ c1_7__commacat ) @ ( u4_struct_0 @ c2_7__commacat ) ) ) @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) ) & ( = @ B @ ( k1_domain_1 @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ ( k2_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat ) @ C @ D ) ) & ( = @ ( k1_funct_1 @ A @ B ) @ ( k5_commacat @ c1_7__commacat @ c2_7__commacat @ c3_7__commacat @ c4_7__commacat @ c5_7__commacat @ D @ C ) ) ) ) ) ) ),file(commacat,e2_7_1_1__commacat)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
