% Mizar problem: s9_birkhoff,birkhoff,820,11 
include('Axioms/SET010^1.ax').
thf(n1_type,type,( np__1: $i )).
thf(f1_s9_birkhoff_type,type,( f1_s9_birkhoff: $i )).
thf(f2_s9_birkhoff_type,type,( f2_s9_birkhoff: $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_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_msualg_2_type,type,( k14_msualg_2: $i > $i > $i )).
thf(k14_pralg_2_type,type,( k14_pralg_2: $i > $i > $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_finseq_2_type,type,( k3_finseq_2: $i > $i )).
thf(k3_relat_1_type,type,( k3_relat_1: $i > $i > $i )).
thf(k4_msualg_4_type,type,( k4_msualg_4: $i > $i > $i > $i )).
thf(k6_finseq_2_type,type,( k6_finseq_2: $i > $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_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_msualg_1_type,type,( l1_msualg_1: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l2_msualg_1_type,type,( l2_msualg_1: $i > $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_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_pboole_type,type,( m2_pboole: $i > $i > $i > $i > $o )).
thf(p1_s9_birkhoff_type,type,( p1_s9_birkhoff: $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(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(v11_struct_0_type,type,( v11_struct_0: $i > $o )).
thf(v13_struct_0_type,type,( v13_struct_0: $i > $i > $o )).
thf(v14_struct_0_type,type,( v14_struct_0: $i > $o )).
thf(v15_struct_0_type,type,( v15_struct_0: $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_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_zfmisc_1_type,type,( v1_zfmisc_1: $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_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_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(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_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $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_struct_0_type,type,( v8_struct_0: $i > $o )).
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_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_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_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_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_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_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_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(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(d19_msualg_2,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( l3_msualg_1 @ B @ A ) => ! [C: $i] : ( ( = @ C @ ( k14_msualg_2 @ A @ B ) ) <=> ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( ( v3_msualg_1 @ D @ A ) & ( m1_msualg_2 @ D @ A @ B ) ) ) ) ) ) ),file(msualg_2,d19_msualg_2)).
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(dt_f1_s9_birkhoff,axiom,( ~ ( v2_struct_0 @ f1_s9_birkhoff ) & ~ ( v11_struct_0 @ f1_s9_birkhoff ) & ( l1_msualg_1 @ f1_s9_birkhoff ) ),file(birkhoff,f1_s9_birkhoff)).
thf(dt_f2_s9_birkhoff,axiom,( ( v4_msualg_1 @ f2_s9_birkhoff @ f1_s9_birkhoff ) & ( l3_msualg_1 @ f2_s9_birkhoff @ f1_s9_birkhoff ) ),file(birkhoff,f2_s9_birkhoff)).
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_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_msualg_2,axiom,( $true ),file(msualg_2,k14_msualg_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_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_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_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) ),file(relat_1,k3_relat_1)).
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_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_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_msualg_1,axiom,( $true ),file(msualg_1,l2_msualg_1)).
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_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_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_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_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_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_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_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_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_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(fc11_msualg_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( l3_msualg_1 @ B @ A ) ) => ~ ( v1_xboole_0 @ ( k14_msualg_2 @ A @ B ) ) ) ),file(msualg_2,fc11_msualg_2)).
thf(fc13_struct_0,axiom,( ! [A: $i] : ( ( ( v11_struct_0 @ A ) & ( l5_struct_0 @ A ) ) => ( v1_xboole_0 @ ( u4_struct_0 @ A ) ) ) ),file(struct_0,fc13_struct_0)).
thf(fc14_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v11_struct_0 @ A ) & ( l5_struct_0 @ A ) ) => ~ ( v1_xboole_0 @ ( u4_struct_0 @ A ) ) ) ),file(struct_0,fc14_struct_0)).
thf(fc1_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_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(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(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(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(fc4_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ A ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) ) => ( ( v1_funct_1 @ ( k3_relat_1 @ D @ C ) ) & ( v1_funct_2 @ ( k3_relat_1 @ D @ C ) @ A @ B ) ) ) ),file(funct_2,fc4_funct_2)).
thf(fc5_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ B @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ B ) ) ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( v1_funct_1 @ ( k3_relat_1 @ D @ C ) ) & ( v1_funct_2 @ ( k3_relat_1 @ D @ C ) @ A @ B ) ) ) ),file(funct_2,fc5_funct_2)).
thf(fc6_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_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_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_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(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_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_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(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_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_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_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_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_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_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(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_k3_finseq_2,axiom,( ! [A: $i] : ( = @ ( k3_finseq_2 @ A ) @ ( k13_finseq_1 @ A ) ) ),file(finseq_2,k3_finseq_2)).
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(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
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(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(t1_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ( m1_subset_1 @ A @ B ) ) ),file(subset,t1_subset)).
thf(t27_equation,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] : ( ( = @ C @ ( replSep1 @ ^ [D: $i] : ( m1_subset_1 @ D @ ( k14_msualg_2 @ A @ B ) ) @ ^ [D: $i] : D @ ^ [D: $i] : ? [E: $i] : ( ( v3_msualg_1 @ E @ A ) & ( v4_msualg_1 @ E @ A ) & ( v3_msafree2 @ E @ A ) & ( m1_msualg_2 @ E @ A @ B ) & ( = @ E @ D ) ) ) ) => ! [D: $i] : ( ( m1_pralg_2 @ D @ C @ A ) => ~ ( ! [E: $i] : ( ( r2_hidden @ E @ C ) => ( = @ E @ ( k1_funct_1 @ D @ E ) ) ) & ! [E: $i] : ( ( ( v3_msualg_1 @ E @ A ) & ( v4_msualg_1 @ E @ A ) & ( m1_msualg_2 @ E @ A @ ( k14_pralg_2 @ C @ A @ D ) ) ) => ! [F: $i] : ( ( m2_pboole @ F @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ E ) @ ( u3_msualg_1 @ A @ B ) ) => ~ ( r2_msualg_3 @ A @ E @ B @ F ) ) ) ) ) ) ) ) ),file(equation,t27_equation)).
thf(t2_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ A @ B ) => ( ( v1_xboole_0 @ B ) | ( r2_hidden @ A @ B ) ) ) ),file(subset,t2_subset)).
thf(t3_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) <=> ( r1_tarski @ A @ B ) ) ),file(subset,t3_subset)).
thf(t4_subset,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ A @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) ) => ( m1_subset_1 @ A @ C ) ) ),file(subset,t4_subset)).
thf(t5_subset,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ~ ( ( r2_hidden @ A @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) & ( v1_xboole_0 @ C ) ) ),file(subset,t5_subset)).
thf(t6_boole,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( = @ A @ k1_xboole_0 ) ) ),file(boole,t6_boole)).
thf(t7_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( r2_hidden @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t7_boole)).
thf(t8_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( v1_xboole_0 @ A ) & ~ ( = @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t8_boole)).
thf(s3_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(s8_birkhoff,axiom,( ! [A: $i > $o] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v2_struct_0 @ D ) & ~ ( v11_struct_0 @ D ) & ( l1_msualg_1 @ D ) & ( v4_msualg_1 @ C @ D ) & ( l3_msualg_1 @ C @ D ) & ( v4_msualg_1 @ B @ D ) & ( l3_msualg_1 @ B @ D ) ) => ( ( ? [E: $i] : ( ( m2_pboole @ E @ ( u1_struct_0 @ D ) @ ( u3_msualg_1 @ D @ C ) @ ( u3_msualg_1 @ D @ B ) ) & ( r2_msualg_3 @ D @ C @ B @ E ) ) & ( A @ C ) & ! [E: $i] : ( ( ( v4_msualg_1 @ E @ D ) & ( l3_msualg_1 @ E @ D ) ) => ! [F: $i] : ( ( ( v4_msualg_1 @ F @ D ) & ( l3_msualg_1 @ F @ D ) ) => ( ( ( r6_msualg_3 @ D @ E @ F ) & ( A @ E ) ) => ( A @ F ) ) ) ) & ! [E: $i] : ( ( ( v4_msualg_1 @ E @ D ) & ( l3_msualg_1 @ E @ D ) ) => ! [F: $i] : ( ( ( v2_msualg_4 @ F @ D @ E ) & ( v3_msualg_4 @ F @ D @ E ) & ( m1_msualg_4 @ F @ ( u1_struct_0 @ D ) @ ( u3_msualg_1 @ D @ E ) @ ( u3_msualg_1 @ D @ E ) ) ) => ( ( A @ E ) => ( A @ ( k13_msualg_4 @ D @ E @ F ) ) ) ) ) ) => ( A @ B ) ) ) ),file(birkhoff,s8_birkhoff)).
thf(s9_birkhoff,conjecture,( ( ! [A: $i] : ( ( ( v3_msualg_1 @ A @ f1_s9_birkhoff ) & ( v4_msualg_1 @ A @ f1_s9_birkhoff ) & ( v3_msafree2 @ A @ f1_s9_birkhoff ) & ( m1_msualg_2 @ A @ f1_s9_birkhoff @ f2_s9_birkhoff ) ) => ( p1_s9_birkhoff @ A ) ) & ! [A: $i] : ( ( ( v4_msualg_1 @ A @ f1_s9_birkhoff ) & ( l3_msualg_1 @ A @ f1_s9_birkhoff ) ) => ! [B: $i] : ( ( ( v4_msualg_1 @ B @ f1_s9_birkhoff ) & ( l3_msualg_1 @ B @ f1_s9_birkhoff ) ) => ( ( ( r6_msualg_3 @ f1_s9_birkhoff @ A @ B ) & ( p1_s9_birkhoff @ A ) ) => ( p1_s9_birkhoff @ B ) ) ) ) & ! [A: $i] : ( ( ( v4_msualg_1 @ A @ f1_s9_birkhoff ) & ( l3_msualg_1 @ A @ f1_s9_birkhoff ) ) => ! [B: $i] : ( ( ( v3_msualg_1 @ B @ f1_s9_birkhoff ) & ( v4_msualg_1 @ B @ f1_s9_birkhoff ) & ( m1_msualg_2 @ B @ f1_s9_birkhoff @ A ) ) => ( ( p1_s9_birkhoff @ A ) => ( p1_s9_birkhoff @ B ) ) ) ) & ! [A: $i] : ( ( ( v4_msualg_1 @ A @ f1_s9_birkhoff ) & ( l3_msualg_1 @ A @ f1_s9_birkhoff ) ) => ! [B: $i] : ( ( ( v2_msualg_4 @ B @ f1_s9_birkhoff @ A ) & ( v3_msualg_4 @ B @ f1_s9_birkhoff @ A ) & ( m1_msualg_4 @ B @ ( u1_struct_0 @ f1_s9_birkhoff ) @ ( u3_msualg_1 @ f1_s9_birkhoff @ A ) @ ( u3_msualg_1 @ f1_s9_birkhoff @ A ) ) ) => ( ( p1_s9_birkhoff @ A ) => ( p1_s9_birkhoff @ ( k13_msualg_4 @ f1_s9_birkhoff @ A @ B ) ) ) ) ) & ! [A: $i] : ! [B: $i] : ( ( m1_pralg_2 @ B @ A @ f1_s9_birkhoff ) => ( ! [C: $i] : ~ ( ( r2_hidden @ C @ A ) & ! [D: $i] : ( ( l3_msualg_1 @ D @ f1_s9_birkhoff ) => ~ ( ( = @ D @ ( k1_funct_1 @ B @ C ) ) & ( p1_s9_birkhoff @ D ) ) ) ) => ( p1_s9_birkhoff @ ( k14_pralg_2 @ A @ f1_s9_birkhoff @ B ) ) ) ) ) => ( p1_s9_birkhoff @ f2_s9_birkhoff ) ),file(birkhoff,s9_birkhoff)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
