% Mizar problem: s1_birkhoff,birkhoff,106,12 
include('Axioms/SET010^1.ax').
thf(n1_type,type,( np__1: $i )).
thf(f1_s1_birkhoff_type,type,( f1_s1_birkhoff: $i )).
thf(f2_s1_birkhoff_type,type,( f2_s1_birkhoff: $i )).
thf(g3_lattices_type,type,( g3_lattices: $i > $i > $i > $i )).
thf(g3_msualg_1_type,type,( g3_msualg_1: $i > $i > $i > $i )).
thf(k10_pralg_2_type,type,( k10_pralg_2: $i > $i > $i > $i )).
thf(k12_card_3_type,type,( k12_card_3: $i > $i > $i )).
thf(k12_msualg_4_type,type,( k12_msualg_4: $i > $i > $i > $i )).
thf(k13_finseq_1_type,type,( k13_finseq_1: $i > $i )).
thf(k13_msualg_4_type,type,( k13_msualg_4: $i > $i > $i > $i )).
thf(k13_pralg_2_type,type,( k13_pralg_2: $i > $i > $i > $i )).
thf(k14_pralg_2_type,type,( k14_pralg_2: $i > $i > $i > $i )).
thf(k15_msualg_4_type,type,( k15_msualg_4: $i > $i > $i > $i )).
thf(k16_msualg_4_type,type,( k16_msualg_4: $i > $i > $i > $i > $i > $i )).
thf(k17_msualg_4_type,type,( k17_msualg_4: $i > $i > $i > $i > $i )).
thf(k19_msualg_4_type,type,( k19_msualg_4: $i > $i > $i > $i > $i )).
thf(k1_binop_1_type,type,( k1_binop_1: $i > $i > $i > $i )).
thf(k1_closure2_type,type,( k1_closure2: $i > $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_mboolean_type,type,( k1_mboolean: $i > $i > $i )).
thf(k1_msualg_3_type,type,( k1_msualg_3: $i > $i > $i > $i > $i > $i )).
thf(k1_partfun1_type,type,( k1_partfun1: $i > $i > $i > $i > $i > $i > $i )).
thf(k1_pzfmisc1_type,type,( k1_pzfmisc1: $i > $i > $i )).
thf(k1_relset_1_type,type,( k1_relset_1: $i > $i > $i )).
thf(k1_tarski_type,type,( k1_tarski: $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_closure2_type,type,( k2_closure2: $i > $i > $i )).
thf(k2_funcop_1_type,type,( k2_funcop_1: $i > $i > $i )).
thf(k2_mssubfam_type,type,( k2_mssubfam: $i > $i > $i > $i > $i )).
thf(k2_msualg_4_type,type,( k2_msualg_4: $i > $i > $i > $i > $i )).
thf(k2_pralg_3_type,type,( k2_pralg_3: $i > $i > $i > $i > $i )).
thf(k2_tarski_type,type,( k2_tarski: $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_finseq_2_type,type,( k3_finseq_2: $i > $i )).
thf(k3_funct_2_type,type,( k3_funct_2: $i > $i > $i > $i > $i )).
thf(k3_mssubfam_type,type,( k3_mssubfam: $i > $i > $i > $i )).
thf(k3_msualg_3_type,type,( k3_msualg_3: $i > $i > $i > $i > $i > $i > $i )).
thf(k3_pboole_type,type,( k3_pboole: $i > $i > $i > $i )).
thf(k3_relat_1_type,type,( k3_relat_1: $i > $i > $i )).
thf(k4_card_3_type,type,( k4_card_3: $i > $i )).
thf(k4_closure2_type,type,( k4_closure2: $i > $i > $i > $i )).
thf(k4_mssubfam_type,type,( k4_mssubfam: $i > $i > $i > $i )).
thf(k4_msualg_4_type,type,( k4_msualg_4: $i > $i > $i > $i )).
thf(k4_msualg_5_type,type,( k4_msualg_5: $i > $i > $i > $i > $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(k5_closure2_type,type,( k5_closure2: $i > $i > $i > $i )).
thf(k5_msualg_5_type,type,( k5_msualg_5: $i > $i > $i )).
thf(k5_pralg_2_type,type,( k5_pralg_2: $i > $i > $i > $i > $i )).
thf(k6_closure2_type,type,( k6_closure2: $i > $i > $i )).
thf(k6_finseq_2_type,type,( k6_finseq_2: $i > $i > $i )).
thf(k6_msualg_3_type,type,( k6_msualg_3: $i > $i > $i > $i > $i )).
thf(k6_msualg_5_type,type,( k6_msualg_5: $i > $i > $i )).
thf(k6_pboole_type,type,( k6_pboole: $i > $i > $i > $i )).
thf(k7_funcop_1_type,type,( k7_funcop_1: $i > $i > $i )).
thf(k7_msafree2_type,type,( k7_msafree2: $i > $i )).
thf(k8_pboole_type,type,( k8_pboole: $i > $i > $i )).
thf(k8_setfam_1_type,type,( k8_setfam_1: $i > $i > $i )).
thf(k9_pralg_2_type,type,( k9_pralg_2: $i > $i > $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(u1_lattices_type,type,( u1_lattices: $i > $i )).
thf(u1_msualg_1_type,type,( u1_msualg_1: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(u2_lattices_type,type,( u2_lattices: $i > $i )).
thf(u2_msualg_1_type,type,( u2_msualg_1: $i > $i )).
thf(u3_msualg_1_type,type,( u3_msualg_1: $i > $i > $i )).
thf(u4_msualg_1_type,type,( u4_msualg_1: $i > $i > $i )).
thf(u4_struct_0_type,type,( u4_struct_0: $i > $i )).
thf(l1_lattices_type,type,( l1_lattices: $i > $o )).
thf(l1_msualg_1_type,type,( l1_msualg_1: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l2_lattices_type,type,( l2_lattices: $i > $o )).
thf(l2_msualg_1_type,type,( l2_msualg_1: $i > $i > $o )).
thf(l3_lattices_type,type,( l3_lattices: $i > $o )).
thf(l3_msualg_1_type,type,( l3_msualg_1: $i > $i > $o )).
thf(l5_struct_0_type,type,( l5_struct_0: $i > $o )).
thf(m1_closure2_type,type,( m1_closure2: $i > $i > $i > $i > $o )).
thf(m1_finseq_2_type,type,( m1_finseq_2: $i > $i > $o )).
thf(m1_msualg_2_type,type,( m1_msualg_2: $i > $i > $i > $o )).
thf(m1_msualg_4_type,type,( m1_msualg_4: $i > $i > $i > $i > $o )).
thf(m1_pralg_2_type,type,( m1_pralg_2: $i > $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_nat_lat_type,type,( m2_nat_lat: $i > $i > $o )).
thf(m2_pboole_type,type,( m2_pboole: $i > $i > $i > $i > $o )).
thf(m3_pboole_type,type,( m3_pboole: $i > $i > $i > $o )).
thf(p1_s1_birkhoff_type,type,( p1_s1_birkhoff: $i > $o )).
thf(r1_msualg_3_type,type,( r1_msualg_3: $i > $i > $i > $i > $o )).
thf(r1_pboole_type,type,( r1_pboole: $i > $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(r2_msualg_3_type,type,( r2_msualg_3: $i > $i > $i > $i > $o )).
thf(r2_pboole_type,type,( r2_pboole: $i > $i > $i > $o )).
thf(r2_relset_1_type,type,( r2_relset_1: $i > $i > $i > $i > $o )).
thf(r3_msualg_3_type,type,( r3_msualg_3: $i > $i > $i > $i > $o )).
thf(r5_msualg_3_type,type,( r5_msualg_3: $i > $i > $i > $o )).
thf(r6_msualg_3_type,type,( r6_msualg_3: $i > $i > $i > $o )).
thf(r6_pboole_type,type,( r6_pboole: $i > $i > $i > $o )).
thf(r8_pboole_type,type,( r8_pboole: $i > $i > $i > $o )).
thf(v10_lattices_type,type,( v10_lattices: $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_lattices_type,type,( v15_lattices: $i > $o )).
thf(v15_struct_0_type,type,( v15_struct_0: $i > $o )).
thf(v1_closure2_type,type,( v1_closure2: $i > $i > $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_funcop_1_type,type,( v1_funcop_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_msualg_4_type,type,( v1_msualg_4: $i > $i > $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_partfun1_type,type,( v1_partfun1: $i > $i > $o )).
thf(v1_prob_2_type,type,( v1_prob_2: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $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_card_3_type,type,( v2_card_3: $i > $o )).
thf(v2_closure2_type,type,( v2_closure2: $i > $i > $i > $o )).
thf(v2_finset_1_type,type,( v2_finset_1: $i > $o )).
thf(v2_funcop_1_type,type,( v2_funcop_1: $i > $o )).
thf(v2_msafree2_type,type,( v2_msafree2: $i > $o )).
thf(v2_msualg_3_type,type,( v2_msualg_3: $i > $i > $i > $i > $o )).
thf(v2_msualg_4_type,type,( v2_msualg_4: $i > $i > $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $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_closure2_type,type,( v3_closure2: $i > $i > $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_1: $i > $o )).
thf(v3_lattices_type,type,( v3_lattices: $i > $o )).
thf(v3_msafree2_type,type,( v3_msafree2: $i > $i > $o )).
thf(v3_msualg_1_type,type,( v3_msualg_1: $i > $i > $o )).
thf(v3_msualg_4_type,type,( v3_msualg_4: $i > $i > $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(v3_relat_2_type,type,( v3_relat_2: $i > $o )).
thf(v4_closure2_type,type,( v4_closure2: $i > $i > $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_msafree2_type,type,( v4_msafree2: $i > $i > $o )).
thf(v4_msualg_1_type,type,( v4_msualg_1: $i > $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_closure2_type,type,( v5_closure2: $i > $i > $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v6_closure2_type,type,( v6_closure2: $i > $i > $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v8_relat_2_type,type,( v8_relat_2: $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_0: $i > $o )).
thf(abstractness_v3_lattices,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( v3_lattices @ A ) => ( = @ A @ ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ) ) ),file(lattices,v3_lattices)).
thf(abstractness_v3_msualg_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( l3_msualg_1 @ B @ A ) ) => ( ( v3_msualg_1 @ B @ A ) => ( = @ B @ ( g3_msualg_1 @ A @ ( u3_msualg_1 @ A @ B ) @ ( u4_msualg_1 @ A @ B ) ) ) ) ) ),file(msualg_1,v3_msualg_1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(cc10_ordinal1,axiom,( ! [A: $i] : ( ( v6_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v6_ordinal1 @ B ) ) ) ),file(ordinal1,cc10_ordinal1)).
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_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) => ( ( v2_closure2 @ C @ A @ B ) => ( v1_closure2 @ C @ A @ B ) ) ) ) ),file(closure2,cc1_closure2)).
thf(cc1_funcop_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_funcop_1 @ B ) ) ) ) ),file(funcop_1,cc1_funcop_1)).
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(cc1_msafree1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v3_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_prob_2 @ B ) ) ) ),file(msafree1,cc1_msafree1)).
thf(cc1_msafree2,axiom,( ! [A: $i] : ( ( l1_msualg_1 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v11_struct_0 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_msafree2 @ A ) ) ) ) ),file(msafree2,cc1_msafree2)).
thf(cc1_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v3_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v2_finset_1 @ B ) ) ) ),file(mssubfam,cc1_mssubfam)).
thf(cc1_msualg_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ! [D: $i] : ( ( m1_msualg_4 @ D @ A @ B @ C ) => ( v2_funcop_1 @ D ) ) ) ),file(msualg_4,cc1_msualg_4)).
thf(cc1_msualg_5,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( l3_msualg_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) => ( ( v2_msualg_4 @ C @ A @ B ) => ( v1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) ) ) ) ) ),file(msualg_5,cc1_msualg_5)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc1_pboole,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_relat_1 @ B ) & ~ ( v3_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ) ) ),file(pboole,cc1_pboole)).
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(cc2_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) => ( ( v4_closure2 @ C @ A @ B ) => ( v3_closure2 @ C @ A @ B ) ) ) ) ),file(closure2,cc2_closure2)).
thf(cc2_funcop_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funcop_1 @ A ) ) ) ),file(funcop_1,cc2_funcop_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_msafree2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( l3_msualg_1 @ B @ A ) => ( ( ( v4_msualg_1 @ B @ A ) & ( v4_msafree2 @ B @ A ) ) => ( ( v4_msualg_1 @ B @ A ) & ( v3_msafree2 @ B @ A ) ) ) ) ) ),file(msafree2,cc2_msafree2)).
thf(cc2_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v2_finset_1 @ B ) ) => ! [C: $i] : ( ( m3_pboole @ C @ A @ B ) => ( v2_finset_1 @ C ) ) ) ),file(mssubfam,cc2_mssubfam)).
thf(cc2_msualg_9,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) & ( m1_pralg_2 @ D @ B @ A ) ) => ! [E: $i] : ( ( m1_subset_1 @ E @ ( k1_funct_1 @ ( k10_pralg_2 @ B @ A @ D ) @ C ) ) => ( ( v1_relat_1 @ E ) & ( v1_funct_1 @ E ) ) ) ) ),file(msualg_9,cc2_msualg_9)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc2_pboole,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v3_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_relat_1 @ B ) & ~ ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ) ) ),file(pboole,cc2_pboole)).
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_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) => ( ( v4_closure2 @ C @ A @ B ) => ( v5_closure2 @ C @ A @ B ) ) ) ) ),file(closure2,cc3_closure2)).
thf(cc3_funcop_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) ) ),file(funcop_1,cc3_funcop_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_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
thf(cc3_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ! [D: $i] : ( ( m2_pboole @ D @ A @ B @ C ) => ( v1_funcop_1 @ D ) ) ) ),file(pboole,cc3_pboole)).
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(cc4_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) => ( ( v5_closure2 @ C @ A @ B ) => ~ ( v1_xboole_0 @ C ) ) ) ) ),file(closure2,cc4_closure2)).
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_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
thf(cc4_pboole,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_relat_1 @ B ) & ~ ( v3_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ) ) ),file(pboole,cc4_pboole)).
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(cc5_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) => ( ( v2_closure2 @ C @ A @ B ) => ( v6_closure2 @ C @ A @ B ) ) ) ) ),file(closure2,cc5_closure2)).
thf(cc5_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal1,cc5_ordinal1)).
thf(cc5_pboole,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ~ ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ) ) ),file(pboole,cc5_pboole)).
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_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) => ( ( v6_closure2 @ C @ A @ B ) => ~ ( v1_xboole_0 @ C ) ) ) ) ),file(closure2,cc6_closure2)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
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_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
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(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_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
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(commutativity_k2_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ B @ A ) ) ),file(tarski,k2_tarski)).
thf(commutativity_k3_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ( = @ ( k3_pboole @ A @ B @ C ) @ ( k3_pboole @ A @ C @ B ) ) ) ),file(pboole,k3_pboole)).
thf(commutativity_k4_msualg_5,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_msualg_4 @ C @ A @ B ) & ( m1_msualg_4 @ C @ A @ B @ B ) & ( v1_msualg_4 @ D @ A @ B ) & ( m1_msualg_4 @ D @ A @ B @ B ) ) => ( = @ ( k4_msualg_5 @ A @ B @ C @ D ) @ ( k4_msualg_5 @ A @ B @ D @ C ) ) ) ),file(msualg_5,k4_msualg_5)).
thf(d10_pralg_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ B ) & ( l1_msualg_1 @ B ) ) => ! [C: $i] : ( ( m1_pralg_2 @ C @ A @ B ) => ! [D: $i] : ( ( ( v1_relat_1 @ D ) & ( v4_relat_1 @ D @ ( u1_struct_0 @ B ) ) & ( v1_funct_1 @ D ) & ( v1_partfun1 @ D @ ( u1_struct_0 @ B ) ) ) => ( ( = @ D @ ( k10_pralg_2 @ A @ B @ C ) ) <=> ! [E: $i] : ( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) ) => ( = @ ( k1_funct_1 @ D @ E ) @ ( k4_card_3 @ ( k9_pralg_2 @ A @ B @ E @ C ) ) ) ) ) ) ) ) ),file(pralg_2,d10_pralg_2)).
thf(d14_msualg_4,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ! [C: $i] : ( ( ( v2_msualg_4 @ C @ A @ B ) & ( v3_msualg_4 @ C @ A @ B ) & ( m1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) => ( = @ ( k13_msualg_4 @ A @ B @ C ) @ ( g3_msualg_1 @ A @ ( k4_msualg_4 @ A @ B @ C ) @ ( k12_msualg_4 @ A @ B @ C ) ) ) ) ) ) ),file(msualg_4,d14_msualg_4)).
thf(d14_pralg_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ B ) & ~ ( v11_struct_0 @ B ) & ( l1_msualg_1 @ B ) ) => ! [C: $i] : ( ( m1_pralg_2 @ C @ A @ B ) => ( = @ ( k14_pralg_2 @ A @ B @ C ) @ ( g3_msualg_1 @ B @ ( k10_pralg_2 @ A @ B @ C ) @ ( k13_pralg_2 @ A @ B @ C ) ) ) ) ) ),file(pralg_2,d14_pralg_2)).
thf(d16_pboole,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ! [D: $i] : ( ( ( v1_relat_1 @ D ) & ( v4_relat_1 @ D @ A ) & ( v1_funct_1 @ D ) & ( v1_partfun1 @ D @ A ) ) => ( ( = @ D @ ( k6_pboole @ A @ B @ C ) ) <=> ! [E: $i] : ( ( r2_hidden @ E @ A ) => ( = @ ( k1_funct_1 @ D @ E ) @ ( k2_zfmisc_1 @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) ) ) ) ) ) ) ) ),file(pboole,d16_pboole)).
thf(d17_msualg_4,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ! [C: $i] : ( ( ( v4_msualg_1 @ C @ A ) & ( l3_msualg_1 @ C @ A ) ) => ! [D: $i] : ( ( m2_pboole @ D @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ C ) ) => ! [E: $i] : ( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) ) => ! [F: $i] : ( ( ( v3_relat_2 @ F ) & ( v8_relat_2 @ F ) & ( v1_partfun1 @ F @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ E ) ) & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ E ) @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ E ) ) ) ) ) => ( ( = @ F @ ( k16_msualg_4 @ A @ B @ C @ D @ E ) ) <=> ! [G: $i] : ( ( m1_subset_1 @ G @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ E ) ) => ! [H: $i] : ( ( m1_subset_1 @ H @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ E ) ) => ( ( r2_hidden @ ( k4_tarski @ G @ H ) @ F ) <=> ( = @ ( k3_funct_2 @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ E ) @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ C ) @ E ) @ ( k1_msualg_3 @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ C ) @ D @ E ) @ G ) @ ( k3_funct_2 @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ E ) @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ C ) @ E ) @ ( k1_msualg_3 @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ C ) @ D @ E ) @ H ) ) ) ) ) ) ) ) ) ) ) ) ),file(msualg_4,d17_msualg_4)).
thf(d18_msualg_4,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ! [C: $i] : ( ( ( v4_msualg_1 @ C @ A ) & ( l3_msualg_1 @ C @ A ) ) => ! [D: $i] : ( ( m2_pboole @ D @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ C ) ) => ( ( r1_msualg_3 @ A @ B @ C @ D ) => ! [E: $i] : ( ( ( v2_msualg_4 @ E @ A @ B ) & ( v3_msualg_4 @ E @ A @ B ) & ( m1_msualg_4 @ E @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) => ( ( = @ E @ ( k17_msualg_4 @ A @ B @ C @ D ) ) <=> ! [F: $i] : ( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) ) => ( r2_relset_1 @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ F ) @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ F ) @ ( k2_msualg_4 @ A @ B @ E @ F ) @ ( k16_msualg_4 @ A @ B @ C @ D @ F ) ) ) ) ) ) ) ) ) ) ),file(msualg_4,d18_msualg_4)).
thf(d1_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( = @ C @ ( k1_closure2 @ A @ B ) ) <=> ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( m3_pboole @ D @ A @ B ) ) ) ) ),file(closure2,d1_closure2)).
thf(d1_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( m3_pboole @ C @ A @ ( k1_mboolean @ A @ B ) ) => ! [D: $i] : ( ( ( v1_relat_1 @ D ) & ( v4_relat_1 @ D @ A ) & ( v1_funct_1 @ D ) & ( v1_partfun1 @ D @ A ) ) => ( ( = @ D @ ( k3_mssubfam @ A @ B @ C ) ) <=> ! [E: $i] : ~ ( ( r2_hidden @ E @ A ) & ! [F: $i] : ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k1_funct_1 @ B @ E ) ) ) ) => ~ ( ( = @ F @ ( k1_funct_1 @ C @ E ) ) & ( = @ ( k1_funct_1 @ D @ E ) @ ( k8_setfam_1 @ ( k1_funct_1 @ B @ E ) @ F ) ) ) ) ) ) ) ) ) ),file(mssubfam,d1_mssubfam)).
thf(d2_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_funcop_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) ) ) ),file(funcop_1,d2_funcop_1)).
thf(d2_msualg_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( m1_msualg_4 @ C @ A @ B @ B ) => ( ( v1_msualg_4 @ C @ A @ B ) <=> ! [D: $i] : ! [E: $i] : ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ B @ D ) ) ) ) => ( ( ( r2_hidden @ D @ A ) & ( = @ ( k1_funct_1 @ C @ D ) @ E ) ) => ( ( v3_relat_2 @ E ) & ( v8_relat_2 @ E ) & ( v1_partfun1 @ E @ ( k1_funct_1 @ B @ D ) ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ B @ D ) ) ) ) ) ) ) ) ) ) ),file(msualg_4,d2_msualg_4)).
thf(d2_pralg_3,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ~ ( v2_struct_0 @ B ) & ~ ( v11_struct_0 @ B ) & ( l1_msualg_1 @ B ) ) => ! [C: $i] : ( ( m1_pralg_2 @ C @ A @ B ) => ! [D: $i] : ( ( m1_subset_1 @ D @ A ) => ! [E: $i] : ( ( m2_pboole @ E @ ( u1_struct_0 @ B ) @ ( u3_msualg_1 @ B @ ( k14_pralg_2 @ A @ B @ C ) ) @ ( u3_msualg_1 @ B @ ( k5_pralg_2 @ A @ B @ C @ D ) ) ) => ( ( = @ E @ ( k2_pralg_3 @ A @ B @ C @ D ) ) <=> ! [F: $i] : ( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) ) => ( = @ ( k1_msualg_3 @ ( u1_struct_0 @ B ) @ ( u3_msualg_1 @ B @ ( k14_pralg_2 @ A @ B @ C ) ) @ ( u3_msualg_1 @ B @ ( k5_pralg_2 @ A @ B @ C @ D ) ) @ E @ F ) @ ( k12_card_3 @ ( k9_pralg_2 @ A @ B @ F @ C ) @ D ) ) ) ) ) ) ) ) ) ),file(pralg_3,d2_pralg_3)).
thf(d2_relat_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ! [B: $i] : ( ( v1_relat_1 @ B ) => ( ( = @ A @ B ) <=> ! [C: $i] : ! [D: $i] : ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) <=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) ) ) ),file(relat_1,d2_relat_1)).
thf(d3_msualg_4,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( l3_msualg_1 @ B @ A ) => ! [C: $i] : ( ( m1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) => ( ( v2_msualg_4 @ C @ A @ B ) <=> ( v1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) ) ) ) ) ) ),file(msualg_4,d3_msualg_4)).
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(d5_msualg_5,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( ~ ( v2_struct_0 @ C ) & ( v3_lattices @ C ) & ( v10_lattices @ C ) & ( l3_lattices @ C ) ) => ( ( = @ C @ ( k5_msualg_5 @ A @ B ) ) <=> ( ! [D: $i] : ( ( r2_hidden @ D @ ( u1_struct_0 @ C ) ) <=> ( ( v1_msualg_4 @ D @ A @ B ) & ( m1_msualg_4 @ D @ A @ B @ B ) ) ) & ! [D: $i] : ( ( ( v1_msualg_4 @ D @ A @ B ) & ( m1_msualg_4 @ D @ A @ B @ B ) ) => ! [E: $i] : ( ( ( v1_msualg_4 @ E @ A @ B ) & ( m1_msualg_4 @ E @ A @ B @ B ) ) => ( ( = @ ( k1_binop_1 @ ( u1_lattices @ C ) @ D @ E ) @ ( k3_pboole @ A @ D @ E ) ) & ( = @ ( k1_binop_1 @ ( u2_lattices @ C ) @ D @ E ) @ ( k4_msualg_5 @ A @ B @ D @ E ) ) ) ) ) ) ) ) ) ) ),file(msualg_5,d5_msualg_5)).
thf(d5_pralg_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ B ) & ( l1_msualg_1 @ B ) ) => ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ( ( m1_pralg_2 @ C @ A @ B ) <=> ! [D: $i] : ( ( r2_hidden @ D @ A ) => ( ( v4_msualg_1 @ ( k1_funct_1 @ C @ D ) @ B ) & ( l3_msualg_1 @ ( k1_funct_1 @ C @ D ) @ B ) ) ) ) ) ) ),file(pralg_2,d5_pralg_2)).
thf(d5_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k4_tarski @ A @ B ) @ ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ) ),file(tarski,d5_tarski)).
thf(d6_funcop_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_funcop_1 @ A ) <=> ! [B: $i] : ( ( r2_hidden @ B @ ( k9_xtuple_0 @ A ) ) => ( ( v1_relat_1 @ ( k1_funct_1 @ A @ B ) ) & ( v1_funct_1 @ ( k1_funct_1 @ A @ B ) ) ) ) ) ) ),file(funcop_1,d6_funcop_1)).
thf(d6_msualg_5,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ! [C: $i] : ( ( ( v3_lattices @ C ) & ( m2_nat_lat @ C @ ( k5_msualg_5 @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) ) ) ) => ( ( = @ C @ ( k6_msualg_5 @ A @ B ) ) <=> ! [D: $i] : ( ( r2_hidden @ D @ ( u1_struct_0 @ C ) ) <=> ( ( v2_msualg_4 @ D @ A @ B ) & ( v3_msualg_4 @ D @ A @ B ) & ( m1_msualg_4 @ D @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) ) ) ) ) ) ),file(msualg_5,d6_msualg_5)).
thf(d8_msualg_3,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( l3_msualg_1 @ B @ A ) => ! [C: $i] : ( ( l3_msualg_1 @ C @ A ) => ! [D: $i] : ( ( m2_pboole @ D @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ C ) ) => ( ( r2_msualg_3 @ A @ B @ C @ D ) <=> ( ( r1_msualg_3 @ A @ B @ C @ D ) & ( v2_msualg_3 @ D @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ C ) ) ) ) ) ) ) ) ),file(msualg_3,d8_msualg_3)).
thf(d9_pralg_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ B ) & ( l1_msualg_1 @ B ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) => ! [D: $i] : ( ( m1_pralg_2 @ D @ A @ B ) => ! [E: $i] : ( ( ( v1_relat_1 @ E ) & ( v4_relat_1 @ E @ A ) & ( v1_funct_1 @ E ) & ( v1_partfun1 @ E @ A ) ) => ( ( ~ ( = @ A @ k1_xboole_0 ) => ( ( = @ E @ ( k9_pralg_2 @ A @ B @ C @ D ) ) <=> ! [F: $i] : ~ ( ( r2_hidden @ F @ A ) & ! [G: $i] : ( ( l3_msualg_1 @ G @ B ) => ~ ( ( = @ G @ ( k1_funct_1 @ D @ F ) ) & ( = @ ( k1_funct_1 @ E @ F ) @ ( k1_funct_1 @ ( u3_msualg_1 @ B @ G ) @ C ) ) ) ) ) ) ) & ( ( = @ A @ k1_xboole_0 ) => ( ( = @ E @ ( k9_pralg_2 @ A @ B @ C @ D ) ) <=> ( = @ E @ k1_xboole_0 ) ) ) ) ) ) ) ) ),file(pralg_2,d9_pralg_2)).
thf(dt_f1_s1_birkhoff,axiom,( ~ ( v2_struct_0 @ f1_s1_birkhoff ) & ~ ( v11_struct_0 @ f1_s1_birkhoff ) & ( l1_msualg_1 @ f1_s1_birkhoff ) ),file(birkhoff,f1_s1_birkhoff)).
thf(dt_f2_s1_birkhoff,axiom,( ( v4_msualg_1 @ f2_s1_birkhoff @ f1_s1_birkhoff ) & ( l3_msualg_1 @ f2_s1_birkhoff @ f1_s1_birkhoff ) ),file(birkhoff,f2_s1_birkhoff)).
thf(dt_g3_lattices,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ) => ( ( v3_lattices @ ( g3_lattices @ A @ B @ C ) ) & ( l3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ) ),file(lattices,g3_lattices)).
thf(dt_g3_msualg_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) ) & ( m2_pboole @ C @ ( u4_struct_0 @ A ) @ ( k3_relat_1 @ ( u1_msualg_1 @ A ) @ ( k6_finseq_2 @ ( u1_struct_0 @ A ) @ B ) ) @ ( k3_relat_1 @ ( u2_msualg_1 @ A ) @ B ) ) ) => ( ( v3_msualg_1 @ ( g3_msualg_1 @ A @ B @ C ) @ A ) & ( l3_msualg_1 @ ( g3_msualg_1 @ A @ B @ C ) @ A ) ) ) ),file(msualg_1,g3_msualg_1)).
thf(dt_k10_pralg_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ B ) & ( l1_msualg_1 @ B ) & ( m1_pralg_2 @ C @ A @ B ) ) => ( ( v1_relat_1 @ ( k10_pralg_2 @ A @ B @ C ) ) & ( v4_relat_1 @ ( k10_pralg_2 @ A @ B @ C ) @ ( u1_struct_0 @ B ) ) & ( v1_funct_1 @ ( k10_pralg_2 @ A @ B @ C ) ) & ( v1_partfun1 @ ( k10_pralg_2 @ A @ B @ C ) @ ( u1_struct_0 @ B ) ) ) ) ),file(pralg_2,k10_pralg_2)).
thf(dt_k12_card_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ ( k12_card_3 @ A @ B ) ) & ( v1_funct_1 @ ( k12_card_3 @ A @ B ) ) ) ) ),file(card_3,k12_card_3)).
thf(dt_k12_msualg_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) & ( v2_msualg_4 @ C @ A @ B ) & ( v3_msualg_4 @ C @ A @ B ) & ( m1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) => ( m2_pboole @ ( k12_msualg_4 @ A @ B @ C ) @ ( u4_struct_0 @ A ) @ ( k3_relat_1 @ ( u1_msualg_1 @ A ) @ ( k6_finseq_2 @ ( u1_struct_0 @ A ) @ ( k4_msualg_4 @ A @ B @ C ) ) ) @ ( k3_relat_1 @ ( u2_msualg_1 @ A ) @ ( k4_msualg_4 @ A @ B @ C ) ) ) ) ),file(msualg_4,k12_msualg_4)).
thf(dt_k13_finseq_1,axiom,( $true ),file(finseq_1,k13_finseq_1)).
thf(dt_k13_msualg_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) & ( v2_msualg_4 @ C @ A @ B ) & ( v3_msualg_4 @ C @ A @ B ) & ( m1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) => ( l3_msualg_1 @ ( k13_msualg_4 @ A @ B @ C ) @ A ) ) ),file(msualg_4,k13_msualg_4)).
thf(dt_k13_pralg_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ B ) & ~ ( v11_struct_0 @ B ) & ( l1_msualg_1 @ B ) & ( m1_pralg_2 @ C @ A @ B ) ) => ( m2_pboole @ ( k13_pralg_2 @ A @ B @ C ) @ ( u4_struct_0 @ B ) @ ( k3_relat_1 @ ( u1_msualg_1 @ B ) @ ( k6_finseq_2 @ ( u1_struct_0 @ B ) @ ( k10_pralg_2 @ A @ B @ C ) ) ) @ ( k3_relat_1 @ ( u2_msualg_1 @ B ) @ ( k10_pralg_2 @ A @ B @ C ) ) ) ) ),file(pralg_2,k13_pralg_2)).
thf(dt_k14_pralg_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ B ) & ~ ( v11_struct_0 @ B ) & ( l1_msualg_1 @ B ) & ( m1_pralg_2 @ C @ A @ B ) ) => ( l3_msualg_1 @ ( k14_pralg_2 @ A @ B @ C ) @ B ) ) ),file(pralg_2,k14_pralg_2)).
thf(dt_k15_msualg_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) & ( v2_msualg_4 @ C @ A @ B ) & ( v3_msualg_4 @ C @ A @ B ) & ( m1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) => ( m2_pboole @ ( k15_msualg_4 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ ( k13_msualg_4 @ A @ B @ C ) ) ) ) ),file(msualg_4,k15_msualg_4)).
thf(dt_k16_msualg_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) & ( v4_msualg_1 @ C @ A ) & ( l3_msualg_1 @ C @ A ) & ( m2_pboole @ D @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ C ) ) & ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) ) ) => ( ( v3_relat_2 @ ( k16_msualg_4 @ A @ B @ C @ D @ E ) ) & ( v8_relat_2 @ ( k16_msualg_4 @ A @ B @ C @ D @ E ) ) & ( v1_partfun1 @ ( k16_msualg_4 @ A @ B @ C @ D @ E ) @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ E ) ) & ( m1_subset_1 @ ( k16_msualg_4 @ A @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ E ) @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ E ) ) ) ) ) ) ),file(msualg_4,k16_msualg_4)).
thf(dt_k17_msualg_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) & ( v4_msualg_1 @ C @ A ) & ( l3_msualg_1 @ C @ A ) & ( m2_pboole @ D @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ C ) ) ) => ( ( v2_msualg_4 @ ( k17_msualg_4 @ A @ B @ C @ D ) @ A @ B ) & ( v3_msualg_4 @ ( k17_msualg_4 @ A @ B @ C @ D ) @ A @ B ) & ( m1_msualg_4 @ ( k17_msualg_4 @ A @ B @ C @ D ) @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) ) ),file(msualg_4,k17_msualg_4)).
thf(dt_k19_msualg_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) & ( v4_msualg_1 @ C @ A ) & ( l3_msualg_1 @ C @ A ) & ( m2_pboole @ D @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ C ) ) ) => ( m2_pboole @ ( k19_msualg_4 @ A @ B @ C @ D ) @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ ( k13_msualg_4 @ A @ B @ ( k17_msualg_4 @ A @ B @ C @ D ) ) ) @ ( u3_msualg_1 @ A @ C ) ) ) ),file(msualg_4,k19_msualg_4)).
thf(dt_k1_binop_1,axiom,( $true ),file(binop_1,k1_binop_1)).
thf(dt_k1_closure2,axiom,( $true ),file(closure2,k1_closure2)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_mboolean,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_relat_1 @ ( k1_mboolean @ A @ B ) ) & ( v4_relat_1 @ ( k1_mboolean @ A @ B ) @ A ) & ( v1_funct_1 @ ( k1_mboolean @ A @ B ) ) & ( v1_partfun1 @ ( k1_mboolean @ A @ B ) @ A ) ) ) ),file(mboolean,k1_mboolean)).
thf(dt_k1_msualg_3,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) & ( m2_pboole @ D @ A @ B @ C ) & ( m1_subset_1 @ E @ A ) ) => ( ( v1_funct_1 @ ( k1_msualg_3 @ A @ B @ C @ D @ E ) ) & ( v1_funct_2 @ ( k1_msualg_3 @ A @ B @ C @ D @ E ) @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) ) & ( m1_subset_1 @ ( k1_msualg_3 @ A @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) ) ) ) ) ) ),file(msualg_3,k1_msualg_3)).
thf(dt_k1_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ( v1_funct_1 @ E ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_funct_1 @ F ) & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ C @ D ) ) ) ) => ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) ) & ( m1_subset_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ D ) ) ) ) ) ),file(partfun1,k1_partfun1)).
thf(dt_k1_pzfmisc1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_relat_1 @ ( k1_pzfmisc1 @ A @ B ) ) & ( v4_relat_1 @ ( k1_pzfmisc1 @ A @ B ) @ A ) & ( v1_funct_1 @ ( k1_pzfmisc1 @ A @ B ) ) & ( v1_partfun1 @ ( k1_pzfmisc1 @ A @ B ) @ A ) ) ) ),file(pzfmisc1,k1_pzfmisc1)).
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_tarski,axiom,( $true ),file(tarski,k1_tarski)).
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_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( m1_subset_1 @ ( k2_closure2 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) ) ),file(closure2,k2_closure2)).
thf(dt_k2_funcop_1,axiom,( $true ),file(funcop_1,k2_funcop_1)).
thf(dt_k2_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( m3_pboole @ C @ A @ ( k1_mboolean @ A @ B ) ) & ( m1_subset_1 @ D @ A ) ) => ( m1_subset_1 @ ( k2_mssubfam @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k1_funct_1 @ B @ D ) ) ) ) ) ),file(mssubfam,k2_mssubfam)).
thf(dt_k2_msualg_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( l3_msualg_1 @ B @ A ) & ( v2_msualg_4 @ C @ A @ B ) & ( m1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) & ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) ) ) => ( ( v3_relat_2 @ ( k2_msualg_4 @ A @ B @ C @ D ) ) & ( v8_relat_2 @ ( k2_msualg_4 @ A @ B @ C @ D ) ) & ( v1_partfun1 @ ( k2_msualg_4 @ A @ B @ C @ D ) @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ D ) ) & ( m1_subset_1 @ ( k2_msualg_4 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ D ) @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ D ) ) ) ) ) ) ),file(msualg_4,k2_msualg_4)).
thf(dt_k2_pralg_3,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v2_struct_0 @ B ) & ~ ( v11_struct_0 @ B ) & ( l1_msualg_1 @ B ) & ( m1_pralg_2 @ C @ A @ B ) & ( m1_subset_1 @ D @ A ) ) => ( m2_pboole @ ( k2_pralg_3 @ A @ B @ C @ D ) @ ( u1_struct_0 @ B ) @ ( u3_msualg_1 @ B @ ( k14_pralg_2 @ A @ B @ C ) ) @ ( u3_msualg_1 @ B @ ( k5_pralg_2 @ A @ B @ C @ D ) ) ) ) ),file(pralg_3,k2_pralg_3)).
thf(dt_k2_tarski,axiom,( $true ),file(tarski,k2_tarski)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_finseq_2,axiom,( ! [A: $i] : ( m1_finseq_2 @ ( k3_finseq_2 @ A ) @ A ) ),file(finseq_2,k3_finseq_2)).
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_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( m3_pboole @ C @ A @ ( k1_mboolean @ A @ B ) ) ) => ( ( v1_relat_1 @ ( k3_mssubfam @ A @ B @ C ) ) & ( v4_relat_1 @ ( k3_mssubfam @ A @ B @ C ) @ A ) & ( v1_funct_1 @ ( k3_mssubfam @ A @ B @ C ) ) & ( v1_partfun1 @ ( k3_mssubfam @ A @ B @ C ) @ A ) ) ) ),file(mssubfam,k3_mssubfam)).
thf(dt_k3_msualg_3,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v2_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) & ( v1_relat_1 @ D ) & ( v2_relat_1 @ D ) & ( v4_relat_1 @ D @ A ) & ( v1_funct_1 @ D ) & ( v1_partfun1 @ D @ A ) & ( m2_pboole @ E @ A @ B @ C ) & ( m2_pboole @ F @ A @ C @ D ) ) => ( m2_pboole @ ( k3_msualg_3 @ A @ B @ C @ D @ E @ F ) @ A @ B @ D ) ) ),file(msualg_3,k3_msualg_3)).
thf(dt_k3_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ( ( v1_relat_1 @ ( k3_pboole @ A @ B @ C ) ) & ( v4_relat_1 @ ( k3_pboole @ A @ B @ C ) @ A ) & ( v1_funct_1 @ ( k3_pboole @ A @ B @ C ) ) & ( v1_partfun1 @ ( k3_pboole @ A @ B @ C ) @ A ) ) ) ),file(pboole,k3_pboole)).
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_card_3,axiom,( $true ),file(card_3,k4_card_3)).
thf(dt_k4_closure2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) ) => ( ( v1_relat_1 @ ( k4_closure2 @ A @ B @ C ) ) & ( v4_relat_1 @ ( k4_closure2 @ A @ B @ C ) @ A ) & ( v1_funct_1 @ ( k4_closure2 @ A @ B @ C ) ) & ( v1_partfun1 @ ( k4_closure2 @ A @ B @ C ) @ A ) ) ) ),file(closure2,k4_closure2)).
thf(dt_k4_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( m3_pboole @ C @ A @ ( k1_mboolean @ A @ B ) ) ) => ( m3_pboole @ ( k4_mssubfam @ A @ B @ C ) @ A @ B ) ) ),file(mssubfam,k4_mssubfam)).
thf(dt_k4_msualg_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) & ( v2_msualg_4 @ C @ A @ B ) & ( v3_msualg_4 @ C @ A @ B ) & ( m1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) => ( ( v1_relat_1 @ ( k4_msualg_4 @ A @ B @ C ) ) & ( v2_relat_1 @ ( k4_msualg_4 @ A @ B @ C ) ) & ( v4_relat_1 @ ( k4_msualg_4 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ ( k4_msualg_4 @ A @ B @ C ) ) & ( v1_partfun1 @ ( k4_msualg_4 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ) ) ),file(msualg_4,k4_msualg_4)).
thf(dt_k4_msualg_5,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_msualg_4 @ C @ A @ B ) & ( m1_msualg_4 @ C @ A @ B @ B ) & ( v1_msualg_4 @ D @ A @ B ) & ( m1_msualg_4 @ D @ A @ B @ B ) ) => ( ( v1_msualg_4 @ ( k4_msualg_5 @ A @ B @ C @ D ) @ A @ B ) & ( m1_msualg_4 @ ( k4_msualg_5 @ A @ B @ C @ D ) @ A @ B @ B ) ) ) ),file(msualg_5,k4_msualg_5)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_k5_closure2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) ) => ( m3_pboole @ ( k5_closure2 @ A @ B @ C ) @ A @ ( k1_mboolean @ A @ B ) ) ) ),file(closure2,k5_closure2)).
thf(dt_k5_msualg_5,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ~ ( v2_struct_0 @ ( k5_msualg_5 @ A @ B ) ) & ( v3_lattices @ ( k5_msualg_5 @ A @ B ) ) & ( v10_lattices @ ( k5_msualg_5 @ A @ B ) ) & ( l3_lattices @ ( k5_msualg_5 @ A @ B ) ) ) ) ),file(msualg_5,k5_msualg_5)).
thf(dt_k5_pralg_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v2_struct_0 @ B ) & ( l1_msualg_1 @ B ) & ( m1_pralg_2 @ C @ A @ B ) & ( m1_subset_1 @ D @ A ) ) => ( ( v4_msualg_1 @ ( k5_pralg_2 @ A @ B @ C @ D ) @ B ) & ( l3_msualg_1 @ ( k5_pralg_2 @ A @ B @ C @ D ) @ B ) ) ) ),file(pralg_2,k5_pralg_2)).
thf(dt_k6_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_closure2 @ ( k6_closure2 @ A @ B ) @ A @ B ) & ( v2_closure2 @ ( k6_closure2 @ A @ B ) @ A @ B ) & ( v3_closure2 @ ( k6_closure2 @ A @ B ) @ A @ B ) & ( v4_closure2 @ ( k6_closure2 @ A @ B ) @ A @ B ) & ( v5_closure2 @ ( k6_closure2 @ A @ B ) @ A @ B ) & ( v6_closure2 @ ( k6_closure2 @ A @ B ) @ A @ B ) & ( m1_subset_1 @ ( k6_closure2 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) ) ) ),file(closure2,k6_closure2)).
thf(dt_k6_finseq_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_relat_1 @ ( k6_finseq_2 @ A @ B ) ) & ( v4_relat_1 @ ( k6_finseq_2 @ A @ B ) @ ( k3_finseq_2 @ A ) ) & ( v1_funct_1 @ ( k6_finseq_2 @ A @ B ) ) & ( v1_partfun1 @ ( k6_finseq_2 @ A @ B ) @ ( k3_finseq_2 @ A ) ) ) ) ),file(finseq_2,k6_finseq_2)).
thf(dt_k6_msualg_3,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) & ( v4_msualg_1 @ C @ A ) & ( l3_msualg_1 @ C @ A ) & ( m2_pboole @ D @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ C ) ) ) => ( ( v3_msualg_1 @ ( k6_msualg_3 @ A @ B @ C @ D ) @ A ) & ( v4_msualg_1 @ ( k6_msualg_3 @ A @ B @ C @ D ) @ A ) & ( m1_msualg_2 @ ( k6_msualg_3 @ A @ B @ C @ D ) @ A @ C ) ) ) ),file(msualg_3,k6_msualg_3)).
thf(dt_k6_msualg_5,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ( ( v3_lattices @ ( k6_msualg_5 @ A @ B ) ) & ( m2_nat_lat @ ( k6_msualg_5 @ A @ B ) @ ( k5_msualg_5 @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) ) ) ) ) ),file(msualg_5,k6_msualg_5)).
thf(dt_k6_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ( ( v1_relat_1 @ ( k6_pboole @ A @ B @ C ) ) & ( v4_relat_1 @ ( k6_pboole @ A @ B @ C ) @ A ) & ( v1_funct_1 @ ( k6_pboole @ A @ B @ C ) ) & ( v1_partfun1 @ ( k6_pboole @ A @ B @ C ) @ A ) ) ) ),file(pboole,k6_pboole)).
thf(dt_k7_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_funct_1 @ ( k7_funcop_1 @ A @ B ) ) & ( v1_funct_2 @ ( k7_funcop_1 @ A @ B ) @ A @ ( k1_tarski @ B ) ) & ( m1_subset_1 @ ( k7_funcop_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) ) ) ) ) ),file(funcop_1,k7_funcop_1)).
thf(dt_k7_msafree2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ( ( v3_msualg_1 @ ( k7_msafree2 @ A ) @ A ) & ( l3_msualg_1 @ ( k7_msafree2 @ A ) @ A ) ) ) ),file(msafree2,k7_msafree2)).
thf(dt_k8_pboole,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_funcop_1 @ B ) ) => ( ( v1_relat_1 @ ( k8_pboole @ A @ B ) ) & ( v1_funct_1 @ ( k8_pboole @ A @ B ) ) ) ) ),file(pboole,k8_pboole)).
thf(dt_k8_setfam_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) => ( m1_subset_1 @ ( k8_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(setfam_1,k8_setfam_1)).
thf(dt_k9_pralg_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v2_struct_0 @ B ) & ( l1_msualg_1 @ B ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) & ( m1_pralg_2 @ D @ A @ B ) ) => ( ( v1_relat_1 @ ( k9_pralg_2 @ A @ B @ C @ D ) ) & ( v4_relat_1 @ ( k9_pralg_2 @ A @ B @ C @ D ) @ A ) & ( v1_funct_1 @ ( k9_pralg_2 @ A @ B @ C @ D ) ) & ( v1_partfun1 @ ( k9_pralg_2 @ A @ B @ C @ D ) @ A ) ) ) ),file(pralg_2,k9_pralg_2)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_l1_lattices,axiom,( ! [A: $i] : ( ( l1_lattices @ A ) => ( l1_struct_0 @ A ) ) ),file(lattices,l1_lattices)).
thf(dt_l1_msualg_1,axiom,( ! [A: $i] : ( ( l1_msualg_1 @ A ) => ( l5_struct_0 @ A ) ) ),file(msualg_1,l1_msualg_1)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_l2_lattices,axiom,( ! [A: $i] : ( ( l2_lattices @ A ) => ( l1_struct_0 @ A ) ) ),file(lattices,l2_lattices)).
thf(dt_l2_msualg_1,axiom,( $true ),file(msualg_1,l2_msualg_1)).
thf(dt_l3_lattices,axiom,( ! [A: $i] : ( ( l3_lattices @ A ) => ( ( l1_lattices @ A ) & ( l2_lattices @ A ) ) ) ),file(lattices,l3_lattices)).
thf(dt_l3_msualg_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( l3_msualg_1 @ B @ A ) => ( l2_msualg_1 @ B @ A ) ) ) ),file(msualg_1,l3_msualg_1)).
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_closure2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ~ ( v1_xboole_0 @ C ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) ) => ! [D: $i] : ( ( m1_closure2 @ D @ A @ B @ C ) => ( m3_pboole @ D @ A @ B ) ) ) ),file(closure2,m1_closure2)).
thf(dt_m1_finseq_2,axiom,( $true ),file(finseq_2,m1_finseq_2)).
thf(dt_m1_msualg_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( l3_msualg_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_msualg_2 @ C @ A @ B ) => ( l3_msualg_1 @ C @ A ) ) ) ),file(msualg_2,m1_msualg_2)).
thf(dt_m1_msualg_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ! [D: $i] : ( ( m1_msualg_4 @ D @ A @ B @ C ) => ( ( v1_relat_1 @ D ) & ( v4_relat_1 @ D @ A ) & ( v1_funct_1 @ D ) & ( v1_partfun1 @ D @ A ) ) ) ) ),file(msualg_4,m1_msualg_4)).
thf(dt_m1_pralg_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ B ) & ( l1_msualg_1 @ B ) ) => ! [C: $i] : ( ( m1_pralg_2 @ C @ A @ B ) => ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) ) ) ),file(pralg_2,m1_pralg_2)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_m2_nat_lat,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( l3_lattices @ A ) ) => ! [B: $i] : ( ( m2_nat_lat @ B @ A ) => ( ~ ( v2_struct_0 @ B ) & ( v10_lattices @ B ) & ( l3_lattices @ B ) ) ) ) ),file(nat_lat,m2_nat_lat)).
thf(dt_m2_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ! [D: $i] : ( ( m2_pboole @ D @ A @ B @ C ) => ( ( v1_relat_1 @ D ) & ( v4_relat_1 @ D @ A ) & ( v1_funct_1 @ D ) & ( v1_partfun1 @ D @ A ) ) ) ) ),file(pboole,m2_pboole)).
thf(dt_m3_pboole,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( m3_pboole @ C @ A @ B ) => ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) ) ) ),file(pboole,m3_pboole)).
thf(dt_u1_lattices,axiom,( ! [A: $i] : ( ( l1_lattices @ A ) => ( ( v1_funct_1 @ ( u1_lattices @ A ) ) & ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ ( u1_lattices @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),file(lattices,u1_lattices)).
thf(dt_u1_msualg_1,axiom,( ! [A: $i] : ( ( l1_msualg_1 @ A ) => ( ( v1_funct_1 @ ( u1_msualg_1 @ A ) ) & ( v1_funct_2 @ ( u1_msualg_1 @ A ) @ ( u4_struct_0 @ A ) @ ( k3_finseq_2 @ ( u1_struct_0 @ A ) ) ) & ( m1_subset_1 @ ( u1_msualg_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u4_struct_0 @ A ) @ ( k3_finseq_2 @ ( u1_struct_0 @ A ) ) ) ) ) ) ) ),file(msualg_1,u1_msualg_1)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_u2_lattices,axiom,( ! [A: $i] : ( ( l2_lattices @ A ) => ( ( v1_funct_1 @ ( u2_lattices @ A ) ) & ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ ( u2_lattices @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),file(lattices,u2_lattices)).
thf(dt_u2_msualg_1,axiom,( ! [A: $i] : ( ( l1_msualg_1 @ A ) => ( ( v1_funct_1 @ ( u2_msualg_1 @ A ) ) & ( v1_funct_2 @ ( u2_msualg_1 @ A ) @ ( u4_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ ( u2_msualg_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u4_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),file(msualg_1,u2_msualg_1)).
thf(dt_u3_msualg_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_struct_0 @ A ) & ( l2_msualg_1 @ B @ A ) ) => ( ( v1_relat_1 @ ( u3_msualg_1 @ A @ B ) ) & ( v4_relat_1 @ ( u3_msualg_1 @ A @ B ) @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ ( u3_msualg_1 @ A @ B ) ) & ( v1_partfun1 @ ( u3_msualg_1 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ) ),file(msualg_1,u3_msualg_1)).
thf(dt_u4_msualg_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( l3_msualg_1 @ B @ A ) ) => ( m2_pboole @ ( u4_msualg_1 @ A @ B ) @ ( u4_struct_0 @ A ) @ ( k3_relat_1 @ ( u1_msualg_1 @ A ) @ ( k6_finseq_2 @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) ) ) @ ( k3_relat_1 @ ( u2_msualg_1 @ A ) @ ( u3_msualg_1 @ A @ B ) ) ) ) ),file(msualg_1,u4_msualg_1)).
thf(dt_u4_struct_0,axiom,( $true ),file(struct_0,u4_struct_0)).
thf(existence_l1_lattices,axiom,( ? [A: $i] : ( l1_lattices @ A ) ),file(lattices,l1_lattices)).
thf(existence_l1_msualg_1,axiom,( ? [A: $i] : ( l1_msualg_1 @ A ) ),file(msualg_1,l1_msualg_1)).
thf(existence_l1_struct_0,axiom,( ? [A: $i] : ( l1_struct_0 @ A ) ),file(struct_0,l1_struct_0)).
thf(existence_l2_lattices,axiom,( ? [A: $i] : ( l2_lattices @ A ) ),file(lattices,l2_lattices)).
thf(existence_l2_msualg_1,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ? [B: $i] : ( l2_msualg_1 @ B @ A ) ) ),file(msualg_1,l2_msualg_1)).
thf(existence_l3_lattices,axiom,( ? [A: $i] : ( l3_lattices @ A ) ),file(lattices,l3_lattices)).
thf(existence_l3_msualg_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ? [B: $i] : ( l3_msualg_1 @ B @ A ) ) ),file(msualg_1,l3_msualg_1)).
thf(existence_l5_struct_0,axiom,( ? [A: $i] : ( l5_struct_0 @ A ) ),file(struct_0,l5_struct_0)).
thf(existence_m1_closure2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ~ ( v1_xboole_0 @ C ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) ) => ? [D: $i] : ( m1_closure2 @ D @ A @ B @ C ) ) ),file(closure2,m1_closure2)).
thf(existence_m1_finseq_2,axiom,( ! [A: $i] : ? [B: $i] : ( m1_finseq_2 @ B @ A ) ),file(finseq_2,m1_finseq_2)).
thf(existence_m1_msualg_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( l3_msualg_1 @ B @ A ) ) => ? [C: $i] : ( m1_msualg_2 @ C @ A @ B ) ) ),file(msualg_2,m1_msualg_2)).
thf(existence_m1_msualg_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ? [D: $i] : ( m1_msualg_4 @ D @ A @ B @ C ) ) ),file(msualg_4,m1_msualg_4)).
thf(existence_m1_pralg_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ B ) & ( l1_msualg_1 @ B ) ) => ? [C: $i] : ( m1_pralg_2 @ C @ A @ B ) ) ),file(pralg_2,m1_pralg_2)).
thf(existence_m1_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( m1_subset_1 @ B @ A ) ),file(subset_1,m1_subset_1)).
thf(existence_m2_nat_lat,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v10_lattices @ A ) & ( l3_lattices @ A ) ) => ? [B: $i] : ( m2_nat_lat @ B @ A ) ) ),file(nat_lat,m2_nat_lat)).
thf(existence_m2_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ? [D: $i] : ( m2_pboole @ D @ A @ B @ C ) ) ),file(pboole,m2_pboole)).
thf(existence_m3_pboole,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ? [C: $i] : ( m3_pboole @ C @ A @ B ) ) ),file(pboole,m3_pboole)).
thf(fc10_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ( v2_relat_1 @ ( k2_funcop_1 @ A @ B ) ) ) ),file(funcop_1,fc10_funcop_1)).
thf(fc11_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v2_finset_1 @ B ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) & ( v2_finset_1 @ C ) ) => ( ( v1_relat_1 @ ( k6_pboole @ A @ B @ C ) ) & ( v4_relat_1 @ ( k6_pboole @ A @ B @ C ) @ A ) & ( v1_funct_1 @ ( k6_pboole @ A @ B @ C ) ) & ( v1_partfun1 @ ( k6_pboole @ A @ B @ C ) @ A ) & ( v2_finset_1 @ ( k6_pboole @ A @ B @ C ) ) ) ) ),file(mssubfam,fc11_mssubfam)).
thf(fc12_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v2_finset_1 @ B ) ) => ( ( v1_relat_1 @ ( k1_mboolean @ A @ B ) ) & ( v4_relat_1 @ ( k1_mboolean @ A @ B ) @ A ) & ( v1_funct_1 @ ( k1_mboolean @ A @ B ) ) & ( v1_partfun1 @ ( k1_mboolean @ A @ B ) @ A ) & ( v2_finset_1 @ ( k1_mboolean @ A @ B ) ) ) ) ),file(mssubfam,fc12_mssubfam)).
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_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( v1_funcop_1 @ ( k2_funcop_1 @ A @ B ) ) ) ),file(funcop_1,fc14_funcop_1)).
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(fc15_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( v3_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ),file(funcop_1,fc15_funcop_1)).
thf(fc17_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( v4_relat_1 @ ( k2_funcop_1 @ A @ B ) @ A ) ),file(funcop_1,fc17_funcop_1)).
thf(fc1_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ~ ( v1_xboole_0 @ ( k1_closure2 @ A @ B ) ) & ( v4_funct_1 @ ( k1_closure2 @ A @ B ) ) & ( v2_card_3 @ ( k1_closure2 @ A @ B ) ) ) ) ),file(closure2,fc1_closure2)).
thf(fc1_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) ) & ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ) ),file(funcop_1,fc1_funcop_1)).
thf(fc1_msualg_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_struct_0 @ A ) & ( v4_msualg_1 @ B @ A ) & ( l2_msualg_1 @ B @ A ) ) => ( ( v1_relat_1 @ ( u3_msualg_1 @ A @ B ) ) & ( v2_relat_1 @ ( u3_msualg_1 @ A @ B ) ) & ( v4_relat_1 @ ( u3_msualg_1 @ A @ B ) @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ ( u3_msualg_1 @ A @ B ) ) & ( v1_partfun1 @ ( u3_msualg_1 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ) ),file(msualg_1,fc1_msualg_1)).
thf(fc1_msualg_5,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ( ( v3_lattices @ ( k6_msualg_5 @ A @ B ) ) & ( v15_lattices @ ( k6_msualg_5 @ A @ B ) ) ) ) ),file(msualg_5,fc1_msualg_5)).
thf(fc1_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_relat_1 @ D ) & ( v4_relat_1 @ D @ B ) & ( v1_funct_1 @ D ) & ( v1_partfun1 @ D @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ C @ D ) ) & ( v4_relat_1 @ ( k3_relat_1 @ C @ D ) @ A ) & ( v1_funct_1 @ ( k3_relat_1 @ C @ D ) ) & ( v1_partfun1 @ ( k3_relat_1 @ C @ D ) @ A ) ) ) ),file(pboole,fc1_pboole)).
thf(fc1_pralg_3,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ B ) & ~ ( v11_struct_0 @ B ) & ( l1_msualg_1 @ B ) & ( m1_pralg_2 @ C @ A @ B ) ) => ( v4_msualg_1 @ ( k14_pralg_2 @ A @ B @ C ) @ B ) ) ),file(pralg_3,fc1_pralg_3)).
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_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( v1_xtuple_0 @ ( k4_tarski @ A @ B ) ) ),file(xtuple_0,fc1_xtuple_0)).
thf(fc20_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) ) & ( v4_relat_1 @ ( k2_funcop_1 @ A @ B ) @ A ) & ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) & ( v1_partfun1 @ ( k2_funcop_1 @ A @ B ) @ A ) ) ),file(funcop_1,fc20_funcop_1)).
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(fc22_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ C @ B ) ) => ( v5_relat_1 @ ( k2_funcop_1 @ A @ C ) @ B ) ) ),file(funcop_1,fc22_funcop_1)).
thf(fc2_funcop_1,axiom,( ! [A: $i] : ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) ) ),file(funcop_1,fc2_funcop_1)).
thf(fc2_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( m1_subset_1 @ C @ A ) ) => ~ ( v1_xboole_0 @ ( k1_funct_1 @ B @ C ) ) ) ),file(pboole,fc2_pboole)).
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(fc2_xboole_0,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ) ),file(xboole_0,fc2_xboole_0)).
thf(fc3_closure2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_xboole_0 @ C ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) ) => ( ( v1_relat_1 @ ( k4_closure2 @ A @ B @ C ) ) & ( v3_relat_1 @ ( k4_closure2 @ A @ B @ C ) ) & ( v4_relat_1 @ ( k4_closure2 @ A @ B @ C ) @ A ) & ( v1_funct_1 @ ( k4_closure2 @ A @ B @ C ) ) & ( v1_partfun1 @ ( k4_closure2 @ A @ B @ C ) @ A ) ) ) ),file(closure2,fc3_closure2)).
thf(fc3_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ B ) => ( v1_xboole_0 @ ( k2_funcop_1 @ B @ A ) ) ) ),file(funcop_1,fc3_funcop_1)).
thf(fc3_msualg_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) & ( v2_msualg_4 @ C @ A @ B ) & ( v3_msualg_4 @ C @ A @ B ) & ( m1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) => ( ( v3_msualg_1 @ ( k13_msualg_4 @ A @ B @ C ) @ A ) & ( v4_msualg_1 @ ( k13_msualg_4 @ A @ B @ C ) @ A ) ) ) ),file(msualg_4,fc3_msualg_4)).
thf(fc3_pboole,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_funcop_1 @ B ) ) => ( ( v1_relat_1 @ ( k8_pboole @ A @ B ) ) & ( v1_funct_1 @ ( k8_pboole @ A @ B ) ) & ( v1_funcop_1 @ ( k8_pboole @ A @ B ) ) ) ) ),file(pboole,fc3_pboole)).
thf(fc3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ) ),file(xboole_0,fc3_xboole_0)).
thf(fc4_closure2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ~ ( v1_xboole_0 @ C ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) ) => ( ( v1_relat_1 @ ( k4_closure2 @ A @ B @ C ) ) & ( v2_relat_1 @ ( k4_closure2 @ A @ B @ C ) ) & ( v4_relat_1 @ ( k4_closure2 @ A @ B @ C ) @ A ) & ( v1_funct_1 @ ( k4_closure2 @ A @ B @ C ) ) & ( v1_partfun1 @ ( k4_closure2 @ A @ B @ C ) @ A ) ) ) ),file(closure2,fc4_closure2)).
thf(fc4_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ~ ( v1_xboole_0 @ ( k2_funcop_1 @ B @ A ) ) ) ),file(funcop_1,fc4_funcop_1)).
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(fc4_msualg_9,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ( ( v1_relat_1 @ ( u3_msualg_1 @ A @ ( k7_msafree2 @ A ) ) ) & ( v2_relat_1 @ ( u3_msualg_1 @ A @ ( k7_msafree2 @ A ) ) ) & ( v4_relat_1 @ ( u3_msualg_1 @ A @ ( k7_msafree2 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ ( u3_msualg_1 @ A @ ( k7_msafree2 @ A ) ) ) & ( v1_partfun1 @ ( u3_msualg_1 @ A @ ( k7_msafree2 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( v2_finset_1 @ ( u3_msualg_1 @ A @ ( k7_msafree2 @ A ) ) ) ) ) ),file(msualg_9,fc4_msualg_9)).
thf(fc4_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v5_ordinal1 @ A ) ) => ( v3_ordinal1 @ ( k9_xtuple_0 @ A ) ) ) ),file(ordinal1,fc4_ordinal1)).
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_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(fc5_msualg_9,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ( ( v3_msualg_1 @ ( k7_msafree2 @ A ) @ A ) & ( v4_msualg_1 @ ( k7_msafree2 @ A ) @ A ) & ( v4_msafree2 @ ( k7_msafree2 @ A ) @ A ) ) ) ),file(msualg_9,fc5_msualg_9)).
thf(fc6_msualg_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ( ( v3_msualg_1 @ ( g3_msualg_1 @ A @ ( u3_msualg_1 @ A @ B ) @ ( u4_msualg_1 @ A @ B ) ) @ A ) & ( v4_msualg_1 @ ( g3_msualg_1 @ A @ ( u3_msualg_1 @ A @ B ) @ ( u4_msualg_1 @ A @ B ) ) @ A ) ) ) ),file(msualg_2,fc6_msualg_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_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) & ( v2_finset_1 @ C ) ) => ( ( v1_relat_1 @ ( k3_pboole @ A @ B @ C ) ) & ( v4_relat_1 @ ( k3_pboole @ A @ B @ C ) @ A ) & ( v1_funct_1 @ ( k3_pboole @ A @ B @ C ) ) & ( v1_partfun1 @ ( k3_pboole @ A @ B @ C ) @ A ) & ( v2_finset_1 @ ( k3_pboole @ A @ B @ C ) ) ) ) ),file(mssubfam,fc7_mssubfam)).
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_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) => ( ( v1_relat_1 @ ( k1_funct_1 @ A @ B ) ) & ( v1_funct_1 @ ( k1_funct_1 @ A @ B ) ) ) ) ),file(funcop_1,fc8_funcop_1)).
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_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) & ( v2_finset_1 @ C ) ) => ( ( v1_relat_1 @ ( k3_pboole @ A @ C @ B ) ) & ( v4_relat_1 @ ( k3_pboole @ A @ C @ B ) @ A ) & ( v1_funct_1 @ ( k3_pboole @ A @ C @ B ) ) & ( v1_partfun1 @ ( k3_pboole @ A @ C @ B ) @ A ) & ( v2_finset_1 @ ( k3_pboole @ A @ C @ B ) ) ) ) ),file(mssubfam,fc8_mssubfam)).
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_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ B @ A ) ) & ( v1_funcop_1 @ ( k3_relat_1 @ B @ A ) ) ) ) ),file(funcop_1,fc9_funcop_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(free_g3_lattices,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ) => ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( = @ ( g3_lattices @ A @ B @ C ) @ ( g3_lattices @ D @ E @ F ) ) => ( ( = @ A @ D ) & ( = @ B @ E ) & ( = @ C @ F ) ) ) ) ),file(lattices,g3_lattices)).
thf(free_g3_msualg_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) ) & ( m2_pboole @ C @ ( u4_struct_0 @ A ) @ ( k3_relat_1 @ ( u1_msualg_1 @ A ) @ ( k6_finseq_2 @ ( u1_struct_0 @ A ) @ B ) ) @ ( k3_relat_1 @ ( u2_msualg_1 @ A ) @ B ) ) ) => ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( = @ ( g3_msualg_1 @ A @ B @ C ) @ ( g3_msualg_1 @ D @ E @ F ) ) => ( ( = @ A @ D ) & ( = @ B @ E ) & ( = @ C @ F ) ) ) ) ),file(msualg_1,g3_msualg_1)).
thf(idempotence_k3_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ( = @ ( k3_pboole @ A @ B @ B ) @ B ) ) ),file(pboole,k3_pboole)).
thf(rc1_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) & ~ ( v1_xboole_0 @ C ) & ( v4_funct_1 @ C ) & ( v2_card_3 @ C ) ) ) ),file(closure2,rc1_closure2)).
thf(rc1_funcop_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) ),file(funcop_1,rc1_funcop_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_msafree1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_prob_2 @ B ) ) ),file(msafree1,rc1_msafree1)).
thf(rc1_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ? [C: $i] : ( ( m3_pboole @ C @ A @ B ) & ( v1_relat_1 @ C ) & ( v3_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) & ( v2_finset_1 @ C ) ) ) ),file(mssubfam,rc1_mssubfam)).
thf(rc1_msualg_4,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v2_funcop_1 @ B ) ) ),file(msualg_4,rc1_msualg_4)).
thf(rc1_msualg_5,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ? [C: $i] : ( ( m1_msualg_4 @ C @ A @ B @ B ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) & ( v2_funcop_1 @ C ) & ( v1_msualg_4 @ C @ A @ B ) ) ) ),file(msualg_5,rc1_msualg_5)).
thf(rc1_msualg_9,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( k6_closure2 @ A @ B ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) & ( v2_finset_1 @ C ) ) ) ),file(msualg_9,rc1_msualg_9)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc1_pboole,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(pboole,rc1_pboole)).
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_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc1_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_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_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) & ( v1_xboole_0 @ C ) & ( v4_funct_1 @ C ) & ( v1_finset_1 @ C ) ) ) ),file(closure2,rc2_closure2)).
thf(rc2_equation,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ? [C: $i] : ( ( m1_msualg_2 @ C @ A @ B ) & ( v3_msualg_1 @ C @ A ) & ( v4_msualg_1 @ C @ A ) & ( v3_msafree2 @ C @ A ) ) ) ),file(equation,rc2_equation)).
thf(rc2_funcop_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) ) ),file(funcop_1,rc2_funcop_1)).
thf(rc2_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ? [C: $i] : ( ( m3_pboole @ C @ A @ ( k1_mboolean @ A @ B ) ) & ( v1_relat_1 @ C ) & ( v2_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) ) ),file(mssubfam,rc2_mssubfam)).
thf(rc2_msualg_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( l3_msualg_1 @ B @ A ) ) => ? [C: $i] : ( ( m1_msualg_2 @ C @ A @ B ) & ( v3_msualg_1 @ C @ A ) ) ) ),file(msualg_2,rc2_msualg_2)).
thf(rc2_msualg_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( l3_msualg_1 @ B @ A ) ) => ? [C: $i] : ( ( m1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) & ~ ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) ) & ( v2_funcop_1 @ C ) & ( v2_msualg_4 @ C @ A @ B ) ) ) ),file(msualg_4,rc2_msualg_4)).
thf(rc2_msualg_9,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ? [C: $i] : ( ( m3_pboole @ C @ A @ B ) & ( v1_relat_1 @ C ) & ( v2_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) & ( v2_finset_1 @ C ) ) ) ),file(msualg_9,rc2_msualg_9)).
thf(rc2_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) ) ),file(ordinal1,rc2_ordinal1)).
thf(rc2_pboole,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v3_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(pboole,rc2_pboole)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc3_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) & ~ ( v1_xboole_0 @ C ) & ( v4_funct_1 @ C ) & ( v2_card_3 @ C ) & ( v1_closure2 @ C @ A @ B ) & ( v2_closure2 @ C @ A @ B ) & ( v3_closure2 @ C @ A @ B ) & ( v4_closure2 @ C @ A @ B ) & ( v5_closure2 @ C @ A @ B ) & ( v6_closure2 @ C @ A @ B ) ) ) ),file(closure2,rc3_closure2)).
thf(rc3_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( 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_partfun1 @ C @ A ) ) ) ),file(funcop_1,rc3_funcop_1)).
thf(rc3_msafree2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ? [B: $i] : ( ( l3_msualg_1 @ B @ A ) & ( v3_msualg_1 @ B @ A ) & ( v4_msualg_1 @ B @ A ) & ( v4_msafree2 @ B @ A ) ) ) ),file(msafree2,rc3_msafree2)).
thf(rc3_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ? [C: $i] : ( ( m3_pboole @ C @ A @ ( k1_mboolean @ A @ B ) ) & ( v1_relat_1 @ C ) & ( v3_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) & ( v2_finset_1 @ C ) ) ) ),file(mssubfam,rc3_mssubfam)).
thf(rc3_msualg_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ? [C: $i] : ( ( m1_msualg_2 @ C @ A @ B ) & ( v3_msualg_1 @ C @ A ) & ( v4_msualg_1 @ C @ A ) ) ) ),file(msualg_2,rc3_msualg_2)).
thf(rc3_msualg_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ? [C: $i] : ( ( m1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) & ~ ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) ) & ( v2_funcop_1 @ C ) & ( v2_msualg_4 @ C @ A @ B ) & ( v3_msualg_4 @ C @ A @ B ) ) ) ),file(msualg_4,rc3_msualg_4)).
thf(rc3_ordinal1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v5_ordinal1 @ B ) ) ),file(ordinal1,rc3_ordinal1)).
thf(rc3_pboole,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(pboole,rc3_pboole)).
thf(rc4_funcop_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(funcop_1,rc4_funcop_1)).
thf(rc4_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v2_finset_1 @ B ) ) => ? [C: $i] : ( ( m3_pboole @ C @ A @ ( k1_mboolean @ A @ B ) ) & ( v1_relat_1 @ C ) & ( v2_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) & ( v2_finset_1 @ C ) ) ) ),file(mssubfam,rc4_mssubfam)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(rc4_pboole,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_funcop_1 @ B ) ) ),file(pboole,rc4_pboole)).
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_msualg_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ? [B: $i] : ( ( l3_msualg_1 @ B @ A ) & ( v3_msualg_1 @ B @ A ) ) ) ),file(msualg_1,rc5_msualg_1)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(rc5_pboole,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ? [C: $i] : ( ( m3_pboole @ C @ A @ B ) & ( v1_relat_1 @ C ) & ( v2_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) ) ),file(pboole,rc5_pboole)).
thf(rc6_msualg_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ? [B: $i] : ( ( l3_msualg_1 @ B @ A ) & ( v3_msualg_1 @ B @ A ) & ( v4_msualg_1 @ B @ A ) ) ) ),file(msualg_1,rc6_msualg_1)).
thf(rc7_pboole,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ B ) & ( v5_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ B ) ) ) ),file(pboole,rc7_pboole)).
thf(redefinition_k1_msualg_3,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) & ( m2_pboole @ D @ A @ B @ C ) & ( m1_subset_1 @ E @ A ) ) => ( = @ ( k1_msualg_3 @ A @ B @ C @ D @ E ) @ ( k1_funct_1 @ D @ E ) ) ) ),file(msualg_3,k1_msualg_3)).
thf(redefinition_k1_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ( v1_funct_1 @ E ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_funct_1 @ F ) & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ C @ D ) ) ) ) => ( = @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) @ ( k3_relat_1 @ E @ F ) ) ) ),file(partfun1,k1_partfun1)).
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_k2_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( = @ ( k2_closure2 @ A @ B ) @ ( k1_closure2 @ A @ B ) ) ) ),file(closure2,k2_closure2)).
thf(redefinition_k2_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( m3_pboole @ C @ A @ ( k1_mboolean @ A @ B ) ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k2_mssubfam @ A @ B @ C @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ),file(mssubfam,k2_mssubfam)).
thf(redefinition_k2_msualg_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( l3_msualg_1 @ B @ A ) & ( v2_msualg_4 @ C @ A @ B ) & ( m1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) & ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) ) ) => ( = @ ( k2_msualg_4 @ A @ B @ C @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ),file(msualg_4,k2_msualg_4)).
thf(redefinition_k3_finseq_2,axiom,( ! [A: $i] : ( = @ ( k3_finseq_2 @ A ) @ ( k13_finseq_1 @ A ) ) ),file(finseq_2,k3_finseq_2)).
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_msualg_3,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v2_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) & ( v1_relat_1 @ D ) & ( v2_relat_1 @ D ) & ( v4_relat_1 @ D @ A ) & ( v1_funct_1 @ D ) & ( v1_partfun1 @ D @ A ) & ( m2_pboole @ E @ A @ B @ C ) & ( m2_pboole @ F @ A @ C @ D ) ) => ( = @ ( k3_msualg_3 @ A @ B @ C @ D @ E @ F ) @ ( k8_pboole @ E @ F ) ) ) ),file(msualg_3,k3_msualg_3)).
thf(redefinition_k4_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( m3_pboole @ C @ A @ ( k1_mboolean @ A @ B ) ) ) => ( = @ ( k4_mssubfam @ A @ B @ C ) @ ( k3_mssubfam @ A @ B @ C ) ) ) ),file(mssubfam,k4_mssubfam)).
thf(redefinition_k5_closure2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) ) => ( = @ ( k5_closure2 @ A @ B @ C ) @ ( k4_closure2 @ A @ B @ C ) ) ) ),file(closure2,k5_closure2)).
thf(redefinition_k5_pralg_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v2_struct_0 @ B ) & ( l1_msualg_1 @ B ) & ( m1_pralg_2 @ C @ A @ B ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k5_pralg_2 @ A @ B @ C @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ),file(pralg_2,k5_pralg_2)).
thf(redefinition_k6_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( = @ ( k6_closure2 @ A @ B ) @ ( k1_closure2 @ A @ B ) ) ) ),file(closure2,k6_closure2)).
thf(redefinition_k7_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k7_funcop_1 @ A @ B ) @ ( k2_funcop_1 @ A @ B ) ) ),file(funcop_1,k7_funcop_1)).
thf(redefinition_m1_closure2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ~ ( v1_xboole_0 @ C ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) ) => ! [D: $i] : ( ( m1_closure2 @ D @ A @ B @ C ) <=> ( m1_subset_1 @ D @ C ) ) ) ),file(closure2,m1_closure2)).
thf(redefinition_r2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( r2_relset_1 @ A @ B @ C @ D ) <=> ( = @ C @ D ) ) ) ),file(relset_1,r2_relset_1)).
thf(redefinition_r6_msualg_3,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( l3_msualg_1 @ B @ A ) & ( l3_msualg_1 @ C @ A ) ) => ( ( r6_msualg_3 @ A @ B @ C ) <=> ( r5_msualg_3 @ A @ B @ C ) ) ) ),file(msualg_3,r6_msualg_3)).
thf(redefinition_r6_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ( ( r6_pboole @ A @ B @ C ) <=> ( = @ B @ C ) ) ) ),file(pboole,r6_pboole)).
thf(redefinition_r8_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ( ( r8_pboole @ A @ B @ C ) <=> ( = @ B @ C ) ) ) ),file(pboole,r8_pboole)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(reflexivity_r2_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ( r2_pboole @ A @ B @ B ) ) ),file(pboole,r2_pboole)).
thf(reflexivity_r2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( r2_relset_1 @ A @ B @ C @ C ) ) ),file(relset_1,r2_relset_1)).
thf(reflexivity_r6_msualg_3,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( l3_msualg_1 @ B @ A ) & ( l3_msualg_1 @ C @ A ) ) => ( r6_msualg_3 @ A @ B @ B ) ) ),file(msualg_3,r6_msualg_3)).
thf(reflexivity_r6_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ( r6_pboole @ A @ B @ B ) ) ),file(pboole,r6_pboole)).
thf(reflexivity_r8_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ( r8_pboole @ A @ B @ B ) ) ),file(pboole,r8_pboole)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(symmetry_r2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( r2_relset_1 @ A @ B @ C @ D ) => ( r2_relset_1 @ A @ B @ D @ C ) ) ) ),file(relset_1,r2_relset_1)).
thf(symmetry_r6_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ( ( r6_pboole @ A @ B @ C ) => ( r6_pboole @ A @ C @ B ) ) ) ),file(pboole,r6_pboole)).
thf(symmetry_r8_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ( ( r8_pboole @ A @ B @ C ) => ( r8_pboole @ A @ C @ B ) ) ) ),file(pboole,r8_pboole)).
thf(t10_card_3,axiom,( = @ ( k4_card_3 @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ),file(card_3,t10_card_3)).
thf(t12_extens_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v2_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ! [D: $i] : ( ( m2_pboole @ D @ A @ B @ C ) => ( ( v2_msualg_3 @ D @ A @ B @ C ) <=> ! [E: $i] : ( ( ( v1_relat_1 @ E ) & ( v2_relat_1 @ E ) & ( v4_relat_1 @ E @ A ) & ( v1_funct_1 @ E ) & ( v1_partfun1 @ E @ A ) ) => ! [F: $i] : ( ( m2_pboole @ F @ A @ C @ E ) => ! [G: $i] : ( ( m2_pboole @ G @ A @ C @ E ) => ( ( r6_pboole @ A @ ( k3_msualg_3 @ A @ B @ C @ E @ D @ F ) @ ( k3_msualg_3 @ A @ B @ C @ E @ D @ G ) ) => ( r6_pboole @ A @ F @ G ) ) ) ) ) ) ) ) ) ),file(extens_1,t12_extens_1)).
thf(t14_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) => ( ~ ( v1_xboole_0 @ C ) => ! [D: $i] : ( ( r2_hidden @ D @ A ) => ( = @ ( k1_funct_1 @ ( k4_closure2 @ A @ B @ C ) @ D ) @ ( replSep1 @ ^ [E: $i] : ( m1_closure2 @ E @ A @ B @ ( k2_closure2 @ A @ B ) ) @ ^ [E: $i] : ( k1_funct_1 @ E @ D ) @ ^ [E: $i] : ( r2_hidden @ E @ C ) ) ) ) ) ) ) ),file(closure2,t14_closure2)).
thf(t14_msualg_9,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) => ! [D: $i] : ( ( m1_pralg_2 @ D @ B @ A ) => ! [E: $i] : ( ( m1_subset_1 @ E @ ( k4_card_3 @ ( k9_pralg_2 @ B @ A @ C @ D ) ) ) => ! [F: $i] : ( ( m1_subset_1 @ F @ ( k4_card_3 @ ( k9_pralg_2 @ B @ A @ C @ D ) ) ) => ( ! [G: $i] : ( ( m1_subset_1 @ G @ B ) => ( = @ ( k1_funct_1 @ ( k12_card_3 @ ( k9_pralg_2 @ B @ A @ C @ D ) @ G ) @ E ) @ ( k1_funct_1 @ ( k12_card_3 @ ( k9_pralg_2 @ B @ A @ C @ D ) @ G ) @ F ) ) ) => ( r8_pboole @ B @ E @ F ) ) ) ) ) ) ) ) ),file(msualg_9,t14_msualg_9)).
thf(t15_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ! [E: $i] : ( ( ( v1_relat_1 @ E ) & ( v1_funct_1 @ E ) ) => ( ( r2_hidden @ C @ A ) => ( ( = @ B @ k1_xboole_0 ) | ( = @ ( k1_funct_1 @ ( k3_relat_1 @ D @ E ) @ C ) @ ( k1_funct_1 @ E @ ( k1_funct_1 @ D @ C ) ) ) ) ) ) ) ),file(funct_2,t15_funct_2)).
thf(t16_msualg_9,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ! [C: $i] : ( ( ( v4_msualg_1 @ C @ A ) & ( l3_msualg_1 @ C @ A ) ) => ! [D: $i] : ( ( m2_pboole @ D @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ C ) ) => ( ( r3_msualg_3 @ A @ B @ C @ D ) => ( r6_msualg_3 @ A @ B @ ( k6_msualg_3 @ A @ B @ C @ D ) ) ) ) ) ) ) ),file(msualg_9,t16_msualg_9)).
thf(t17_msualg_3,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ! [C: $i] : ( ( ( v4_msualg_1 @ C @ A ) & ( l3_msualg_1 @ C @ A ) ) => ( ( r6_msualg_3 @ A @ B @ C ) => ( r6_msualg_3 @ A @ C @ B ) ) ) ) ) ),file(msualg_3,t17_msualg_3)).
thf(t18_msualg_5,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ( ( v2_msualg_4 @ ( k6_pboole @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) @ A @ B ) & ( v3_msualg_4 @ ( k6_pboole @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) @ A @ B ) & ( m1_msualg_4 @ ( k6_pboole @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) ) ) ),file(msualg_5,t18_msualg_5)).
thf(t1_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ( m1_subset_1 @ A @ B ) ) ),file(subset,t1_subset)).
thf(t21_closure2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) => ( ( r2_hidden @ C @ D ) => ( r1_pboole @ A @ C @ ( k5_closure2 @ A @ B @ D ) ) ) ) ) ) ),file(closure2,t21_closure2)).
thf(t26_msualg_9,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( l3_msualg_1 @ B @ A ) => ( ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ ( u1_struct_0 @ A ) ) & ( r8_pboole @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( k1_pzfmisc1 @ ( u1_struct_0 @ A ) @ C ) ) ) => ( r6_msualg_3 @ A @ B @ ( k7_msafree2 @ A ) ) ) ) ) ),file(msualg_9,t26_msualg_9)).
thf(t28_msualg_9,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_msualg_5 @ A @ B ) ) ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_closure2 @ ( u1_struct_0 @ A ) @ ( k6_pboole @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) ) ) => ( ( = @ C @ D ) => ( ( v2_msualg_4 @ ( k4_mssubfam @ ( u1_struct_0 @ A ) @ ( k6_pboole @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) @ ( k5_closure2 @ ( u1_struct_0 @ A ) @ ( k6_pboole @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) @ D ) ) @ A @ B ) & ( v3_msualg_4 @ ( k4_mssubfam @ ( u1_struct_0 @ A ) @ ( k6_pboole @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) @ ( k5_closure2 @ ( u1_struct_0 @ A ) @ ( k6_pboole @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) @ D ) ) @ A @ B ) & ( m1_msualg_4 @ ( k4_mssubfam @ ( u1_struct_0 @ A ) @ ( k6_pboole @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) @ ( k5_closure2 @ ( u1_struct_0 @ A ) @ ( k6_pboole @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) @ D ) ) @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) ) ) ) ) ) ),file(msualg_9,t28_msualg_9)).
thf(t29_msualg_9,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ! [C: $i] : ( ( ( v2_msualg_4 @ C @ A @ B ) & ( v3_msualg_4 @ C @ A @ B ) & ( m1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) => ( ( r8_pboole @ ( u1_struct_0 @ A ) @ C @ ( k6_pboole @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) => ( r8_pboole @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ ( k13_msualg_4 @ A @ B @ C ) ) @ ( k1_pzfmisc1 @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) ) ) ) ) ) ) ),file(msualg_9,t29_msualg_9)).
thf(t29_pralg_3,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ~ ( v2_struct_0 @ B ) & ~ ( v11_struct_0 @ B ) & ( l1_msualg_1 @ B ) ) => ! [C: $i] : ( ( m1_pralg_2 @ C @ A @ B ) => ! [D: $i] : ( ( ( v4_msualg_1 @ D @ B ) & ( l3_msualg_1 @ D @ B ) ) => ! [E: $i] : ( ( ( v1_relat_1 @ E ) & ( v4_relat_1 @ E @ A ) & ( v1_funct_1 @ E ) & ( v1_partfun1 @ E @ A ) & ( v1_funcop_1 @ E ) ) => ~ ( ! [F: $i] : ( ( m1_subset_1 @ F @ A ) => ? [G: $i] : ( ( m2_pboole @ G @ ( u1_struct_0 @ B ) @ ( u3_msualg_1 @ B @ D ) @ ( u3_msualg_1 @ B @ ( k5_pralg_2 @ A @ B @ C @ F ) ) ) & ( = @ G @ ( k1_funct_1 @ E @ F ) ) & ( r1_msualg_3 @ B @ D @ ( k5_pralg_2 @ A @ B @ C @ F ) @ G ) ) ) & ! [F: $i] : ( ( m2_pboole @ F @ ( u1_struct_0 @ B ) @ ( u3_msualg_1 @ B @ D ) @ ( u3_msualg_1 @ B @ ( k14_pralg_2 @ A @ B @ C ) ) ) => ~ ( ( r1_msualg_3 @ B @ D @ ( k14_pralg_2 @ A @ B @ C ) @ F ) & ! [G: $i] : ( ( m1_subset_1 @ G @ A ) => ( = @ ( k3_msualg_3 @ ( u1_struct_0 @ B ) @ ( u3_msualg_1 @ B @ D ) @ ( u3_msualg_1 @ B @ ( k14_pralg_2 @ A @ B @ C ) ) @ ( u3_msualg_1 @ B @ ( k5_pralg_2 @ A @ B @ C @ G ) ) @ F @ ( k2_pralg_3 @ A @ B @ C @ G ) ) @ ( k1_funct_1 @ E @ G ) ) ) ) ) ) ) ) ) ) ) ),file(pralg_3,t29_pralg_3)).
thf(t2_msualg_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ! [D: $i] : ( ( ( v1_relat_1 @ D ) & ( v4_relat_1 @ D @ A ) & ( v1_funct_1 @ D ) & ( v1_partfun1 @ D @ A ) ) => ! [E: $i] : ( ( m2_pboole @ E @ A @ B @ C ) => ! [F: $i] : ( ( m2_pboole @ F @ A @ C @ D ) => ( ( = @ ( k9_xtuple_0 @ ( k8_pboole @ E @ F ) ) @ A ) & ! [G: $i] : ( ( r2_hidden @ G @ A ) => ( = @ ( k1_funct_1 @ ( k8_pboole @ E @ F ) @ G ) @ ( k3_relat_1 @ ( k1_funct_1 @ E @ G ) @ ( k1_funct_1 @ F @ G ) ) ) ) ) ) ) ) ) ) ),file(msualg_3,t2_msualg_3)).
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(t33_msualg_9,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ! [C: $i] : ( ( ( v2_msualg_4 @ C @ A @ B ) & ( v3_msualg_4 @ C @ A @ B ) & ( m1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) ) => ! [E: $i] : ( ( m1_subset_1 @ E @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ D ) ) => ! [F: $i] : ( ( m1_subset_1 @ F @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ D ) ) => ( ( = @ ( k3_funct_2 @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ D ) @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ ( k13_msualg_4 @ A @ B @ C ) ) @ D ) @ ( k1_msualg_3 @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ ( k13_msualg_4 @ A @ B @ C ) ) @ ( k15_msualg_4 @ A @ B @ C ) @ D ) @ E ) @ ( k3_funct_2 @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ B ) @ D ) @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ ( k13_msualg_4 @ A @ B @ C ) ) @ D ) @ ( k1_msualg_3 @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ ( k13_msualg_4 @ A @ B @ C ) ) @ ( k15_msualg_4 @ A @ B @ C ) @ D ) @ F ) ) <=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_msualg_4 @ A @ B @ C @ D ) ) ) ) ) ) ) ) ) ),file(msualg_9,t33_msualg_9)).
thf(t36_msualg_9,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ! [C: $i] : ( ( ( v4_msualg_1 @ C @ A ) & ( l3_msualg_1 @ C @ A ) ) => ! [D: $i] : ( ( m2_pboole @ D @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ C ) ) => ( ( r1_msualg_3 @ A @ B @ C @ D ) => ! [E: $i] : ( ( ( v2_msualg_4 @ E @ A @ B ) & ( v3_msualg_4 @ E @ A @ B ) & ( m1_msualg_4 @ E @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) => ~ ( ( r2_pboole @ ( u1_struct_0 @ A ) @ E @ ( k17_msualg_4 @ A @ B @ C @ D ) ) & ! [F: $i] : ( ( m2_pboole @ F @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ ( k13_msualg_4 @ A @ B @ E ) ) @ ( u3_msualg_1 @ A @ C ) ) => ~ ( ( r1_msualg_3 @ A @ ( k13_msualg_4 @ A @ B @ E ) @ C @ F ) & ( r8_pboole @ ( u1_struct_0 @ A ) @ D @ ( k3_msualg_3 @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ ( k13_msualg_4 @ A @ B @ E ) ) @ ( u3_msualg_1 @ A @ C ) @ ( k15_msualg_4 @ A @ B @ E ) @ F ) ) ) ) ) ) ) ) ) ) ) ),file(msualg_9,t36_msualg_9)).
thf(t3_msualg_4,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ! [C: $i] : ( ( ( v2_msualg_4 @ C @ A @ B ) & ( v3_msualg_4 @ C @ A @ B ) & ( m1_msualg_4 @ C @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ B ) ) ) => ( r2_msualg_3 @ A @ B @ ( k13_msualg_4 @ A @ B @ C ) @ ( k15_msualg_4 @ A @ B @ C ) ) ) ) ) ),file(msualg_4,t3_msualg_4)).
thf(t3_pboole,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ( ! [D: $i] : ( ( r2_hidden @ D @ A ) => ( = @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ C @ D ) ) ) => ( = @ B @ C ) ) ) ) ),file(pboole,t3_pboole)).
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(t43_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ! [D: $i] : ( ( m3_pboole @ D @ A @ ( k1_mboolean @ A @ B ) ) => ( ( r1_pboole @ A @ C @ D ) => ( r2_pboole @ A @ ( k4_mssubfam @ A @ B @ D ) @ C ) ) ) ) ) ),file(mssubfam,t43_mssubfam)).
thf(t43_setfam_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) => ( ( r2_hidden @ B @ A ) => ( ( r2_hidden @ B @ ( k8_setfam_1 @ A @ C ) ) <=> ! [D: $i] : ( ( r2_hidden @ D @ C ) => ( r2_hidden @ B @ D ) ) ) ) ) ),file(setfam_1,t43_setfam_1)).
thf(t4_msualg_4,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( ( v4_msualg_1 @ B @ A ) & ( l3_msualg_1 @ B @ A ) ) => ! [C: $i] : ( ( ( v4_msualg_1 @ C @ A ) & ( l3_msualg_1 @ C @ A ) ) => ! [D: $i] : ( ( m2_pboole @ D @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) @ ( u3_msualg_1 @ A @ C ) ) => ( ( r1_msualg_3 @ A @ B @ C @ D ) => ( r3_msualg_3 @ A @ ( k13_msualg_4 @ A @ B @ ( k17_msualg_4 @ A @ B @ C @ D ) ) @ C @ ( k19_msualg_4 @ A @ B @ C @ D ) ) ) ) ) ) ) ),file(msualg_4,t4_msualg_4)).
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_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( r2_hidden @ C @ A ) => ( ( = @ B @ k1_xboole_0 ) | ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ) ) ),file(funct_2,t5_funct_2)).
thf(t5_msualg_7,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k5_msualg_5 @ A @ B ) ) ) ) => ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ ( k6_pboole @ A @ B @ B ) ) ) ) ) ) ) ),file(msualg_7,t5_msualg_7)).
thf(t5_msualg_9,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) & ( r6_pboole @ A @ ( k1_pzfmisc1 @ A @ C ) @ ( k7_funcop_1 @ A @ ( k1_tarski @ B ) ) ) ) ),file(msualg_9,t5_msualg_9)).
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(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(t7_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( r2_hidden @ B @ A ) => ( = @ ( k1_funct_1 @ ( k2_funcop_1 @ A @ C ) @ B ) @ C ) ) ),file(funcop_1,t7_funcop_1)).
thf(t87_zfmisc_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) ) <=> ( ( r2_hidden @ A @ C ) & ( r2_hidden @ B @ D ) ) ) ),file(zfmisc_1,t87_zfmisc_1)).
thf(t8_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( v1_xboole_0 @ A ) & ~ ( = @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t8_boole)).
thf(t8_msualg_7,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k5_msualg_5 @ A @ B ) ) ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ ( k6_pboole @ A @ B @ B ) ) ) ) => ( ( = @ D @ C ) => ( ( v1_xboole_0 @ C ) | ( ( v1_msualg_4 @ ( k4_mssubfam @ A @ ( k6_pboole @ A @ B @ B ) @ ( k5_closure2 @ A @ ( k6_pboole @ A @ B @ B ) @ D ) ) @ A @ B ) & ( m1_msualg_4 @ ( k4_mssubfam @ A @ ( k6_pboole @ A @ B @ B ) @ ( k5_closure2 @ A @ ( k6_pboole @ A @ B @ B ) @ D ) ) @ A @ B @ B ) ) ) ) ) ) ) ) ),file(msualg_7,t8_msualg_7)).
thf(s3_pboole,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ( ! [C: $i] : ~ ( ( r2_hidden @ C @ B ) & ! [D: $i] : ~ ( A @ C @ D ) ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( A @ D @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),file(pboole,s3_pboole)).
thf(s6_pboole,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ( ! [C: $i] : ( ( m1_subset_1 @ C @ B ) => ? [D: $i] : ( A @ C @ D ) ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ B ) & ! [D: $i] : ( ( m1_subset_1 @ D @ B ) => ( A @ D @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),file(pboole,s6_pboole)).
thf(s7_domain_1,axiom,( ! [A: $i > $o] : ! [B: $i] : ( m1_subset_1 @ ( replSep1 @ ^ [C: $i] : ( m1_subset_1 @ C @ B ) @ ^ [C: $i] : C @ ^ [C: $i] : ( A @ C ) ) @ ( k1_zfmisc_1 @ B ) ) ),file(domain_1,s7_domain_1)).
thf(s1_birkhoff,conjecture,( ( ! [A: $i] : ( ( ( v4_msualg_1 @ A @ f1_s1_birkhoff ) & ( l3_msualg_1 @ A @ f1_s1_birkhoff ) ) => ! [B: $i] : ( ( ( v4_msualg_1 @ B @ f1_s1_birkhoff ) & ( l3_msualg_1 @ B @ f1_s1_birkhoff ) ) => ( ( ( r6_msualg_3 @ f1_s1_birkhoff @ A @ B ) & ( p1_s1_birkhoff @ A ) ) => ( p1_s1_birkhoff @ B ) ) ) ) & ! [A: $i] : ( ( ( v4_msualg_1 @ A @ f1_s1_birkhoff ) & ( l3_msualg_1 @ A @ f1_s1_birkhoff ) ) => ! [B: $i] : ( ( ( v3_msualg_1 @ B @ f1_s1_birkhoff ) & ( v4_msualg_1 @ B @ f1_s1_birkhoff ) & ( m1_msualg_2 @ B @ f1_s1_birkhoff @ A ) ) => ( ( p1_s1_birkhoff @ A ) => ( p1_s1_birkhoff @ B ) ) ) ) & ! [A: $i] : ! [B: $i] : ( ( m1_pralg_2 @ B @ A @ f1_s1_birkhoff ) => ( ! [C: $i] : ~ ( ( r2_hidden @ C @ A ) & ! [D: $i] : ( ( l3_msualg_1 @ D @ f1_s1_birkhoff ) => ~ ( ( = @ D @ ( k1_funct_1 @ B @ C ) ) & ( p1_s1_birkhoff @ D ) ) ) ) => ( p1_s1_birkhoff @ ( k14_pralg_2 @ A @ f1_s1_birkhoff @ B ) ) ) ) ) => ? [A: $i] : ( ( v3_msualg_1 @ A @ f1_s1_birkhoff ) & ( v4_msualg_1 @ A @ f1_s1_birkhoff ) & ( l3_msualg_1 @ A @ f1_s1_birkhoff ) & ? [B: $i] : ( ( m2_pboole @ B @ ( u1_struct_0 @ f1_s1_birkhoff ) @ ( u3_msualg_1 @ f1_s1_birkhoff @ f2_s1_birkhoff ) @ ( u3_msualg_1 @ f1_s1_birkhoff @ A ) ) & ( p1_s1_birkhoff @ A ) & ( r2_msualg_3 @ f1_s1_birkhoff @ f2_s1_birkhoff @ A @ B ) & ! [C: $i] : ( ( ( v4_msualg_1 @ C @ f1_s1_birkhoff ) & ( l3_msualg_1 @ C @ f1_s1_birkhoff ) ) => ! [D: $i] : ( ( m2_pboole @ D @ ( u1_struct_0 @ f1_s1_birkhoff ) @ ( u3_msualg_1 @ f1_s1_birkhoff @ f2_s1_birkhoff ) @ ( u3_msualg_1 @ f1_s1_birkhoff @ C ) ) => ~ ( ( r1_msualg_3 @ f1_s1_birkhoff @ f2_s1_birkhoff @ C @ D ) & ( p1_s1_birkhoff @ C ) & ! [E: $i] : ( ( m2_pboole @ E @ ( u1_struct_0 @ f1_s1_birkhoff ) @ ( u3_msualg_1 @ f1_s1_birkhoff @ A ) @ ( u3_msualg_1 @ f1_s1_birkhoff @ C ) ) => ~ ( ( r1_msualg_3 @ f1_s1_birkhoff @ A @ C @ E ) & ( r8_pboole @ ( u1_struct_0 @ f1_s1_birkhoff ) @ ( k3_msualg_3 @ ( u1_struct_0 @ f1_s1_birkhoff ) @ ( u3_msualg_1 @ f1_s1_birkhoff @ f2_s1_birkhoff ) @ ( u3_msualg_1 @ f1_s1_birkhoff @ A ) @ ( u3_msualg_1 @ f1_s1_birkhoff @ C ) @ B @ E ) @ D ) & ! [F: $i] : ( ( m2_pboole @ F @ ( u1_struct_0 @ f1_s1_birkhoff ) @ ( u3_msualg_1 @ f1_s1_birkhoff @ A ) @ ( u3_msualg_1 @ f1_s1_birkhoff @ C ) ) => ( ( r8_pboole @ ( u1_struct_0 @ f1_s1_birkhoff ) @ ( k3_msualg_3 @ ( u1_struct_0 @ f1_s1_birkhoff ) @ ( u3_msualg_1 @ f1_s1_birkhoff @ f2_s1_birkhoff ) @ ( u3_msualg_1 @ f1_s1_birkhoff @ A ) @ ( u3_msualg_1 @ f1_s1_birkhoff @ C ) @ B @ F ) @ D ) => ( r8_pboole @ ( u1_struct_0 @ f1_s1_birkhoff ) @ E @ F ) ) ) ) ) ) ) ) ) ) ),file(birkhoff,s1_birkhoff)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
