% Mizar problem: s12_birkhoff,birkhoff,1047,10 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(f1_s12_birkhoff_type,type,( f1_s12_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(k11_msafree_type,type,( k11_msafree: $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(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_msualg_3_type,type,( k1_msualg_3: $i > $i > $i > $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_tarski_type,type,( k1_tarski: $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_xtuple_0_type,type,( k1_xtuple_0: $i > $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_funcop_1_type,type,( k2_funcop_1: $i > $i > $i )).
thf(k2_xtuple_0_type,type,( k2_xtuple_0: $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_equation_type,type,( k3_equation: $i > $i )).
thf(k3_finseq_2_type,type,( k3_finseq_2: $i > $i )).
thf(k3_msualg_3_type,type,( k3_msualg_3: $i > $i > $i > $i > $i > $i > $i )).
thf(k3_relat_1_type,type,( k3_relat_1: $i > $i > $i )).
thf(k4_equation_type,type,( k4_equation: $i > $i )).
thf(k4_msualg_4_type,type,( k4_msualg_4: $i > $i > $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_finseq_2_type,type,( k6_finseq_2: $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(k8_funcop_1_type,type,( k8_funcop_1: $i > $i > $i > $i )).
thf(k8_pboole_type,type,( k8_pboole: $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(m3_pboole_type,type,( m3_pboole: $i > $i > $i > $o )).
thf(p1_s12_birkhoff_type,type,( p1_s12_birkhoff: $i > $o )).
thf(r1_equation_type,type,( r1_equation: $i > $i > $i > $i > $o )).
thf(r1_msualg_3_type,type,( r1_msualg_3: $i > $i > $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(r2_equation_type,type,( r2_equation: $i > $i > $i > $o )).
thf(r2_pboole_type,type,( r2_pboole: $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(r8_pboole_type,type,( r8_pboole: $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_msafree1_type,type,( v1_msafree1: $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_msafree_type,type,( v2_msafree: $i > $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_funct_1_type,type,( v3_funct_1: $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_trees_2_type,type,( v3_trees_2: $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_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_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_msafree2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ ( k11_msafree @ A @ B ) ) @ C ) ) => ( ~ ( v1_xboole_0 @ D ) & ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( v1_finset_1 @ D ) ) ) ) ),file(msafree2,cc3_msafree2)).
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_msafree2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_funct_1 @ ( u3_msualg_1 @ A @ ( k11_msafree @ A @ B ) ) @ C ) ) => ( ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) ) => ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( v3_trees_2 @ D ) ) ) ) ) ),file(msafree2,cc4_msafree2)).
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_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
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(d18_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 ) ) => ( ( m3_pboole @ C @ A @ B ) <=> ( r2_pboole @ A @ C @ B ) ) ) ) ),file(pboole,d18_pboole)).
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_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 ) ) => ( ( r2_pboole @ A @ B @ C ) <=> ! [D: $i] : ( ( r2_hidden @ D @ A ) => ( r1_tarski @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ) ) ) ),file(pboole,d2_pboole)).
thf(d3_equation,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ( = @ ( k3_equation @ A ) @ ( k11_msafree @ A @ ( k8_funcop_1 @ ( k1_zfmisc_1 @ k1_numbers ) @ ( u1_struct_0 @ A ) @ k5_numbers ) ) ) ) ),file(equation,d3_equation)).
thf(d3_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( ( r1_tarski @ A @ B ) <=> ! [C: $i] : ( ( r2_hidden @ C @ A ) => ( r2_hidden @ C @ B ) ) ) ),file(tarski,d3_tarski)).
thf(d4_equation,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ( = @ ( k4_equation @ A ) @ ( k6_pboole @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ ( k3_equation @ A ) ) @ ( u3_msualg_1 @ A @ ( k3_equation @ A ) ) ) ) ) ),file(equation,d4_equation)).
thf(d5_equation,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( l3_msualg_1 @ B @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_funct_1 @ ( k4_equation @ A ) @ C ) ) => ( ( r1_equation @ A @ B @ C @ D ) <=> ! [E: $i] : ( ( m2_pboole @ E @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ ( k3_equation @ A ) ) @ ( u3_msualg_1 @ A @ B ) ) => ( ( r1_msualg_3 @ A @ ( k3_equation @ A ) @ B @ E ) => ( = @ ( k1_funct_1 @ ( k1_msualg_3 @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ ( k3_equation @ A ) ) @ ( u3_msualg_1 @ A @ B ) @ E @ C ) @ ( k1_xtuple_0 @ D ) ) @ ( k1_funct_1 @ ( k1_msualg_3 @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ ( k3_equation @ A ) ) @ ( u3_msualg_1 @ A @ B ) @ E @ C ) @ ( k2_xtuple_0 @ D ) ) ) ) ) ) ) ) ) ) ),file(equation,d5_equation)).
thf(d6_equation,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ! [B: $i] : ( ( l3_msualg_1 @ B @ A ) => ! [C: $i] : ( ( m3_pboole @ C @ ( u1_struct_0 @ A ) @ ( k4_equation @ A ) ) => ( ( r2_equation @ A @ B @ C ) <=> ! [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) ) => ! [E: $i] : ( ( m1_subset_1 @ E @ ( k1_funct_1 @ ( k4_equation @ A ) @ D ) ) => ( ( r2_hidden @ E @ ( k1_funct_1 @ C @ D ) ) => ( r1_equation @ A @ B @ D @ E ) ) ) ) ) ) ) ) ),file(equation,d6_equation)).
thf(dt_f1_s12_birkhoff,axiom,( ~ ( v2_struct_0 @ f1_s12_birkhoff ) & ~ ( v11_struct_0 @ f1_s12_birkhoff ) & ( l1_msualg_1 @ f1_s12_birkhoff ) ),file(birkhoff,f1_s12_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_k11_msafree,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) ) ) => ( l3_msualg_1 @ ( k11_msafree @ A @ B ) @ A ) ) ),file(msafree,k11_msafree)).
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_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
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_numbers,axiom,( $true ),file(numbers,k1_numbers)).
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_xtuple_0,axiom,( $true ),file(xtuple_0,k1_xtuple_0)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_funcop_1,axiom,( $true ),file(funcop_1,k2_funcop_1)).
thf(dt_k2_xtuple_0,axiom,( $true ),file(xtuple_0,k2_xtuple_0)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_equation,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ( l3_msualg_1 @ ( k3_equation @ A ) @ A ) ) ),file(equation,k3_equation)).
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_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_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) ),file(relat_1,k3_relat_1)).
thf(dt_k4_equation,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ( ( v1_relat_1 @ ( k4_equation @ A ) ) & ( v4_relat_1 @ ( k4_equation @ A ) @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ ( k4_equation @ A ) ) & ( v1_partfun1 @ ( k4_equation @ A ) @ ( u1_struct_0 @ A ) ) ) ) ),file(equation,k4_equation)).
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_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
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_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_k8_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ C @ A ) ) => ( ( v1_funct_1 @ ( k8_funcop_1 @ A @ B @ C ) ) & ( v1_funct_2 @ ( k8_funcop_1 @ A @ B @ C ) @ B @ A ) & ( m1_subset_1 @ ( k8_funcop_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) ) ) ),file(funcop_1,k8_funcop_1)).
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_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_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_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(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(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_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_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_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_msualg_9,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) ) ) => ( v2_msafree @ ( k11_msafree @ A @ B ) @ A ) ) ),file(msualg_9,fc2_msualg_9)).
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_equation,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ( ( v3_msualg_1 @ ( k3_equation @ A ) @ A ) & ( v4_msualg_1 @ ( k3_equation @ A ) @ A ) & ( v2_msafree @ ( k3_equation @ A ) @ A ) ) ) ),file(equation,fc3_equation)).
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_msafree1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v1_msafree1 @ B @ A ) & ( l3_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 ) ) & ( v1_prob_2 @ ( u3_msualg_1 @ A @ B ) ) ) ) ),file(msafree1,fc3_msafree1)).
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(fc4_equation,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ( ( v1_relat_1 @ ( k4_equation @ A ) ) & ( v2_relat_1 @ ( k4_equation @ A ) ) & ( v4_relat_1 @ ( k4_equation @ A ) @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ ( k4_equation @ A ) ) & ( v1_partfun1 @ ( k4_equation @ A ) @ ( u1_struct_0 @ A ) ) ) ) ),file(equation,fc4_equation)).
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(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_msafree1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) ) ) => ( v4_msualg_1 @ ( k11_msafree @ A @ B ) @ A ) ) ),file(msafree1,fc5_msafree1)).
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_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
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_msafree1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) ) ) => ( ( v1_relat_1 @ ( u3_msualg_1 @ A @ ( k11_msafree @ A @ B ) ) ) & ( v4_relat_1 @ ( u3_msualg_1 @ A @ ( k11_msafree @ A @ B ) ) @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ ( u3_msualg_1 @ A @ ( k11_msafree @ A @ B ) ) ) & ( v1_partfun1 @ ( u3_msualg_1 @ A @ ( k11_msafree @ A @ B ) ) @ ( u1_struct_0 @ A ) ) & ( v1_prob_2 @ ( u3_msualg_1 @ A @ ( k11_msafree @ A @ B ) ) ) ) ) ),file(msafree1,fc8_msafree1)).
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_msafree1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) & ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) ) ) => ( v1_msafree1 @ ( k11_msafree @ A @ B ) @ A ) ) ),file(msafree1,fc9_msafree1)).
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_equation,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v11_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ? [B: $i] : ( ( l3_msualg_1 @ B @ A ) & ( v3_msualg_1 @ B @ A ) & ( v4_msualg_1 @ B @ A ) & ( v2_msafree @ B @ A ) ) ) ),file(equation,rc1_equation)).
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_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_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_msafree1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_msualg_1 @ A ) ) => ? [B: $i] : ( ( l3_msualg_1 @ B @ A ) & ( v4_msualg_1 @ B @ A ) & ( v1_msafree1 @ B @ A ) ) ) ),file(msafree1,rc2_msafree1)).
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_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(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_k3_finseq_2,axiom,( ! [A: $i] : ( = @ ( k3_finseq_2 @ A ) @ ( k13_finseq_1 @ A ) ) ),file(finseq_2,k3_finseq_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_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
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_k8_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ C @ A ) ) => ( = @ ( k8_funcop_1 @ A @ B @ C ) @ ( k2_funcop_1 @ B @ C ) ) ) ),file(funcop_1,k8_funcop_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_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_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_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_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(t1_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ( m1_subset_1 @ A @ B ) ) ),file(subset,t1_subset)).
thf(t2_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ A @ B ) => ( ( v1_xboole_0 @ B ) | ( r2_hidden @ A @ B ) ) ) ),file(subset,t2_subset)).
thf(t32_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] : ( ( m3_pboole @ C @ ( u1_struct_0 @ A ) @ ( k4_equation @ A ) ) => ! [D: $i] : ( ( ( v3_msualg_1 @ D @ A ) & ( v4_msualg_1 @ D @ A ) & ( m1_msualg_2 @ D @ A @ B ) ) => ( ( r2_equation @ A @ B @ C ) => ( r2_equation @ A @ D @ C ) ) ) ) ) ) ),file(equation,t32_equation)).
thf(t34_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] : ( ( ( v4_msualg_1 @ C @ A ) & ( l3_msualg_1 @ C @ A ) ) => ! [D: $i] : ( ( m3_pboole @ D @ ( u1_struct_0 @ A ) @ ( k4_equation @ A ) ) => ( ( ( r6_msualg_3 @ A @ B @ C ) & ( r2_equation @ A @ B @ D ) ) => ( r2_equation @ A @ C @ D ) ) ) ) ) ) ),file(equation,t34_equation)).
thf(t38_equation,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ B ) & ~ ( v11_struct_0 @ B ) & ( l1_msualg_1 @ B ) ) => ! [C: $i] : ( ( m3_pboole @ C @ ( u1_struct_0 @ B ) @ ( k4_equation @ B ) ) => ! [D: $i] : ( ( m1_pralg_2 @ D @ A @ B ) => ( ! [E: $i] : ~ ( ( r2_hidden @ E @ A ) & ! [F: $i] : ( ( l3_msualg_1 @ F @ B ) => ~ ( ( = @ F @ ( k1_funct_1 @ D @ E ) ) & ( r2_equation @ B @ F @ C ) ) ) ) => ( r2_equation @ B @ ( k14_pralg_2 @ A @ B @ D ) @ C ) ) ) ) ) ),file(equation,t38_equation)).
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(s11_birkhoff,axiom,( ! [A: $i > $o] : ! [B: $i > $o] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ~ ( v2_struct_0 @ E ) & ~ ( v11_struct_0 @ E ) & ( l1_msualg_1 @ E ) & ( v3_msualg_1 @ D @ E ) & ( v4_msualg_1 @ D @ E ) & ( l3_msualg_1 @ D @ E ) & ( m2_pboole @ C @ ( u1_struct_0 @ E ) @ ( k7_funcop_1 @ ( u1_struct_0 @ E ) @ k5_numbers ) @ ( u3_msualg_1 @ E @ D ) ) ) => ( ( ! [F: $i] : ( ( ( v4_msualg_1 @ F @ E ) & ( l3_msualg_1 @ F @ E ) ) => ( ( B @ F ) <=> ! [G: $i] : ( ( m1_subset_1 @ G @ ( u1_struct_0 @ E ) ) => ! [H: $i] : ( ( m1_subset_1 @ H @ ( k1_funct_1 @ ( k4_equation @ E ) @ G ) ) => ( ! [I: $i] : ( ( ( v4_msualg_1 @ I @ E ) & ( l3_msualg_1 @ I @ E ) ) => ( ( A @ I ) => ( r1_equation @ E @ I @ G @ H ) ) ) => ( r1_equation @ E @ F @ G @ H ) ) ) ) ) ) & ! [F: $i] : ( ( ( v4_msualg_1 @ F @ E ) & ( l3_msualg_1 @ F @ E ) ) => ! [G: $i] : ( ( m2_pboole @ G @ ( u1_struct_0 @ E ) @ ( k7_funcop_1 @ ( u1_struct_0 @ E ) @ k5_numbers ) @ ( u3_msualg_1 @ E @ F ) ) => ~ ( ( B @ F ) & ! [H: $i] : ( ( m2_pboole @ H @ ( u1_struct_0 @ E ) @ ( u3_msualg_1 @ E @ D ) @ ( u3_msualg_1 @ E @ F ) ) => ~ ( ( r1_msualg_3 @ E @ D @ F @ H ) & ( r8_pboole @ ( u1_struct_0 @ E ) @ ( k3_msualg_3 @ ( u1_struct_0 @ E ) @ ( k7_funcop_1 @ ( u1_struct_0 @ E ) @ k5_numbers ) @ ( u3_msualg_1 @ E @ D ) @ ( u3_msualg_1 @ E @ F ) @ C @ H ) @ G ) & ! [I: $i] : ( ( m2_pboole @ I @ ( u1_struct_0 @ E ) @ ( u3_msualg_1 @ E @ D ) @ ( u3_msualg_1 @ E @ F ) ) => ( ( ( r1_msualg_3 @ E @ D @ F @ I ) & ( r8_pboole @ ( u1_struct_0 @ E ) @ ( k3_msualg_3 @ ( u1_struct_0 @ E ) @ ( k7_funcop_1 @ ( u1_struct_0 @ E ) @ k5_numbers ) @ ( u3_msualg_1 @ E @ D ) @ ( u3_msualg_1 @ E @ F ) @ C @ I ) @ G ) ) => ( r8_pboole @ ( u1_struct_0 @ E ) @ H @ I ) ) ) ) ) ) ) ) & ( B @ D ) & ! [F: $i] : ( ( ( v4_msualg_1 @ F @ E ) & ( l3_msualg_1 @ F @ E ) ) => ! [G: $i] : ( ( ( v4_msualg_1 @ G @ E ) & ( l3_msualg_1 @ G @ E ) ) => ( ( ( r6_msualg_3 @ E @ F @ G ) & ( A @ F ) ) => ( A @ G ) ) ) ) & ! [F: $i] : ( ( ( v4_msualg_1 @ F @ E ) & ( l3_msualg_1 @ F @ E ) ) => ! [G: $i] : ( ( ( v3_msualg_1 @ G @ E ) & ( v4_msualg_1 @ G @ E ) & ( m1_msualg_2 @ G @ E @ F ) ) => ( ( A @ F ) => ( A @ G ) ) ) ) & ! [F: $i] : ! [G: $i] : ( ( m1_pralg_2 @ G @ F @ E ) => ( ! [H: $i] : ~ ( ( r2_hidden @ H @ F ) & ! [I: $i] : ( ( l3_msualg_1 @ I @ E ) => ~ ( ( = @ I @ ( k1_funct_1 @ G @ H ) ) & ( A @ I ) ) ) ) => ( A @ ( k14_pralg_2 @ F @ E @ G ) ) ) ) ) => ( A @ D ) ) ) ),file(birkhoff,s11_birkhoff)).
thf(s2_birkhoff,axiom,( ! [A: $i > $o] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ C ) & ~ ( v11_struct_0 @ C ) & ( l1_msualg_1 @ C ) & ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ ( u1_struct_0 @ C ) ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ ( u1_struct_0 @ C ) ) ) => ( ( ! [D: $i] : ( ( ( v4_msualg_1 @ D @ C ) & ( l3_msualg_1 @ D @ C ) ) => ! [E: $i] : ( ( ( v4_msualg_1 @ E @ C ) & ( l3_msualg_1 @ E @ C ) ) => ( ( ( r6_msualg_3 @ C @ D @ E ) & ( A @ D ) ) => ( A @ E ) ) ) ) & ! [D: $i] : ( ( ( v4_msualg_1 @ D @ C ) & ( l3_msualg_1 @ D @ C ) ) => ! [E: $i] : ( ( ( v3_msualg_1 @ E @ C ) & ( v4_msualg_1 @ E @ C ) & ( m1_msualg_2 @ E @ C @ D ) ) => ( ( A @ D ) => ( A @ E ) ) ) ) & ! [D: $i] : ! [E: $i] : ( ( m1_pralg_2 @ E @ D @ C ) => ( ! [F: $i] : ~ ( ( r2_hidden @ F @ D ) & ! [G: $i] : ( ( l3_msualg_1 @ G @ C ) => ~ ( ( = @ G @ ( k1_funct_1 @ E @ F ) ) & ( A @ G ) ) ) ) => ( A @ ( k14_pralg_2 @ D @ C @ E ) ) ) ) ) => ? [D: $i] : ( ( v3_msualg_1 @ D @ C ) & ( v4_msualg_1 @ D @ C ) & ( l3_msualg_1 @ D @ C ) & ? [E: $i] : ( ( m2_pboole @ E @ ( u1_struct_0 @ C ) @ B @ ( u3_msualg_1 @ C @ D ) ) & ( A @ D ) & ! [F: $i] : ( ( ( v4_msualg_1 @ F @ C ) & ( l3_msualg_1 @ F @ C ) ) => ! [G: $i] : ( ( m2_pboole @ G @ ( u1_struct_0 @ C ) @ B @ ( u3_msualg_1 @ C @ F ) ) => ~ ( ( A @ F ) & ! [H: $i] : ( ( m2_pboole @ H @ ( u1_struct_0 @ C ) @ ( u3_msualg_1 @ C @ D ) @ ( u3_msualg_1 @ C @ F ) ) => ~ ( ( r1_msualg_3 @ C @ D @ F @ H ) & ( r8_pboole @ ( u1_struct_0 @ C ) @ ( k3_msualg_3 @ ( u1_struct_0 @ C ) @ B @ ( u3_msualg_1 @ C @ D ) @ ( u3_msualg_1 @ C @ F ) @ E @ H ) @ G ) & ! [I: $i] : ( ( m2_pboole @ I @ ( u1_struct_0 @ C ) @ ( u3_msualg_1 @ C @ D ) @ ( u3_msualg_1 @ C @ F ) ) => ( ( ( r1_msualg_3 @ C @ D @ F @ I ) & ( r8_pboole @ ( u1_struct_0 @ C ) @ ( k3_msualg_3 @ ( u1_struct_0 @ C ) @ B @ ( u3_msualg_1 @ C @ D ) @ ( u3_msualg_1 @ C @ F ) @ E @ I ) @ G ) ) => ( r8_pboole @ ( u1_struct_0 @ C ) @ H @ I ) ) ) ) ) ) ) ) ) ) ) ) ),file(birkhoff,s2_birkhoff)).
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(s7_birkhoff,axiom,( ! [A: $i > $o] : ! [B: $i > $o] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ~ ( v2_struct_0 @ F ) & ~ ( v11_struct_0 @ F ) & ( l1_msualg_1 @ F ) & ( v3_msualg_1 @ E @ F ) & ( v4_msualg_1 @ E @ F ) & ( v3_msafree2 @ E @ F ) & ( l3_msualg_1 @ E @ F ) & ( v4_msualg_1 @ D @ F ) & ( l3_msualg_1 @ D @ F ) & ( m2_pboole @ C @ ( u1_struct_0 @ F ) @ ( k7_funcop_1 @ ( u1_struct_0 @ F ) @ k5_numbers ) @ ( u3_msualg_1 @ F @ D ) ) ) => ( ( ( B @ E ) & ( A @ D ) & ! [G: $i] : ( ( ( v4_msualg_1 @ G @ F ) & ( l3_msualg_1 @ G @ F ) ) => ! [H: $i] : ( ( m2_pboole @ H @ ( u1_struct_0 @ F ) @ ( k7_funcop_1 @ ( u1_struct_0 @ F ) @ k5_numbers ) @ ( u3_msualg_1 @ F @ G ) ) => ~ ( ( B @ G ) & ! [I: $i] : ( ( m2_pboole @ I @ ( u1_struct_0 @ F ) @ ( u3_msualg_1 @ F @ D ) @ ( u3_msualg_1 @ F @ G ) ) => ~ ( ( r1_msualg_3 @ F @ D @ G @ I ) & ( r8_pboole @ ( u1_struct_0 @ F ) @ H @ ( k3_msualg_3 @ ( u1_struct_0 @ F ) @ ( k7_funcop_1 @ ( u1_struct_0 @ F ) @ k5_numbers ) @ ( u3_msualg_1 @ F @ D ) @ ( u3_msualg_1 @ F @ G ) @ C @ I ) ) ) ) ) ) ) & ! [G: $i] : ( ( ( v4_msualg_1 @ G @ F ) & ( l3_msualg_1 @ G @ F ) ) => ! [H: $i] : ( ( ( v4_msualg_1 @ H @ F ) & ( l3_msualg_1 @ H @ F ) ) => ( ( ( r6_msualg_3 @ F @ G @ H ) & ( A @ G ) ) => ( A @ H ) ) ) ) & ! [G: $i] : ( ( ( v4_msualg_1 @ G @ F ) & ( l3_msualg_1 @ G @ F ) ) => ! [H: $i] : ( ( ( v2_msualg_4 @ H @ F @ G ) & ( v3_msualg_4 @ H @ F @ G ) & ( m1_msualg_4 @ H @ ( u1_struct_0 @ F ) @ ( u3_msualg_1 @ F @ G ) @ ( u3_msualg_1 @ F @ G ) ) ) => ( ( A @ G ) => ( A @ ( k13_msualg_4 @ F @ G @ H ) ) ) ) ) ) => ( A @ E ) ) ) ),file(birkhoff,s7_birkhoff)).
thf(s9_birkhoff,axiom,( ! [A: $i > $o] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ C ) & ~ ( v11_struct_0 @ C ) & ( l1_msualg_1 @ C ) & ( v4_msualg_1 @ B @ C ) & ( l3_msualg_1 @ B @ C ) ) => ( ( ! [D: $i] : ( ( ( v3_msualg_1 @ D @ C ) & ( v4_msualg_1 @ D @ C ) & ( v3_msafree2 @ D @ C ) & ( m1_msualg_2 @ D @ C @ B ) ) => ( A @ D ) ) & ! [D: $i] : ( ( ( v4_msualg_1 @ D @ C ) & ( l3_msualg_1 @ D @ C ) ) => ! [E: $i] : ( ( ( v4_msualg_1 @ E @ C ) & ( l3_msualg_1 @ E @ C ) ) => ( ( ( r6_msualg_3 @ C @ D @ E ) & ( A @ D ) ) => ( A @ E ) ) ) ) & ! [D: $i] : ( ( ( v4_msualg_1 @ D @ C ) & ( l3_msualg_1 @ D @ C ) ) => ! [E: $i] : ( ( ( v3_msualg_1 @ E @ C ) & ( v4_msualg_1 @ E @ C ) & ( m1_msualg_2 @ E @ C @ D ) ) => ( ( A @ D ) => ( A @ E ) ) ) ) & ! [D: $i] : ( ( ( v4_msualg_1 @ D @ C ) & ( l3_msualg_1 @ D @ C ) ) => ! [E: $i] : ( ( ( v2_msualg_4 @ E @ C @ D ) & ( v3_msualg_4 @ E @ C @ D ) & ( m1_msualg_4 @ E @ ( u1_struct_0 @ C ) @ ( u3_msualg_1 @ C @ D ) @ ( u3_msualg_1 @ C @ D ) ) ) => ( ( A @ D ) => ( A @ ( k13_msualg_4 @ C @ D @ E ) ) ) ) ) & ! [D: $i] : ! [E: $i] : ( ( m1_pralg_2 @ E @ D @ C ) => ( ! [F: $i] : ~ ( ( r2_hidden @ F @ D ) & ! [G: $i] : ( ( l3_msualg_1 @ G @ C ) => ~ ( ( = @ G @ ( k1_funct_1 @ E @ F ) ) & ( A @ G ) ) ) ) => ( A @ ( k14_pralg_2 @ D @ C @ E ) ) ) ) ) => ( A @ B ) ) ) ),file(birkhoff,s9_birkhoff)).
thf(s12_birkhoff,conjecture,( ( ! [A: $i] : ( ( ( v4_msualg_1 @ A @ f1_s12_birkhoff ) & ( l3_msualg_1 @ A @ f1_s12_birkhoff ) ) => ! [B: $i] : ( ( ( v4_msualg_1 @ B @ f1_s12_birkhoff ) & ( l3_msualg_1 @ B @ f1_s12_birkhoff ) ) => ( ( ( r6_msualg_3 @ f1_s12_birkhoff @ A @ B ) & ( p1_s12_birkhoff @ A ) ) => ( p1_s12_birkhoff @ B ) ) ) ) & ! [A: $i] : ( ( ( v4_msualg_1 @ A @ f1_s12_birkhoff ) & ( l3_msualg_1 @ A @ f1_s12_birkhoff ) ) => ! [B: $i] : ( ( ( v3_msualg_1 @ B @ f1_s12_birkhoff ) & ( v4_msualg_1 @ B @ f1_s12_birkhoff ) & ( m1_msualg_2 @ B @ f1_s12_birkhoff @ A ) ) => ( ( p1_s12_birkhoff @ A ) => ( p1_s12_birkhoff @ B ) ) ) ) & ! [A: $i] : ( ( ( v4_msualg_1 @ A @ f1_s12_birkhoff ) & ( l3_msualg_1 @ A @ f1_s12_birkhoff ) ) => ! [B: $i] : ( ( ( v2_msualg_4 @ B @ f1_s12_birkhoff @ A ) & ( v3_msualg_4 @ B @ f1_s12_birkhoff @ A ) & ( m1_msualg_4 @ B @ ( u1_struct_0 @ f1_s12_birkhoff ) @ ( u3_msualg_1 @ f1_s12_birkhoff @ A ) @ ( u3_msualg_1 @ f1_s12_birkhoff @ A ) ) ) => ( ( p1_s12_birkhoff @ A ) => ( p1_s12_birkhoff @ ( k13_msualg_4 @ f1_s12_birkhoff @ A @ B ) ) ) ) ) & ! [A: $i] : ! [B: $i] : ( ( m1_pralg_2 @ B @ A @ f1_s12_birkhoff ) => ( ! [C: $i] : ~ ( ( r2_hidden @ C @ A ) & ! [D: $i] : ( ( l3_msualg_1 @ D @ f1_s12_birkhoff ) => ~ ( ( = @ D @ ( k1_funct_1 @ B @ C ) ) & ( p1_s12_birkhoff @ D ) ) ) ) => ( p1_s12_birkhoff @ ( k14_pralg_2 @ A @ f1_s12_birkhoff @ B ) ) ) ) ) => ? [A: $i] : ( ( m3_pboole @ A @ ( u1_struct_0 @ f1_s12_birkhoff ) @ ( k4_equation @ f1_s12_birkhoff ) ) & ! [B: $i] : ( ( ( v4_msualg_1 @ B @ f1_s12_birkhoff ) & ( l3_msualg_1 @ B @ f1_s12_birkhoff ) ) => ( ( p1_s12_birkhoff @ B ) <=> ( r2_equation @ f1_s12_birkhoff @ B @ A ) ) ) ) ),file(birkhoff,s12_birkhoff)).
