% Mizar problem: e2_4_1,yellow18,292,31 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(f1_s4_yellow18_type,type,( f1_s4_yellow18: $i )).
thf(f2_s4_yellow18_type,type,( f2_s4_yellow18: $i > $i > $i )).
thf(f3_s4_yellow18_type,type,( f3_s4_yellow18: $i > $i > $i > $i > $i > $i )).
thf(g2_altcat_1_type,type,( g2_altcat_1: $i > $i > $i > $i )).
thf(k1_altcat_1_type,type,( k1_altcat_1: $i > $i > $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k2_altcat_1_type,type,( k2_altcat_1: $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_altcat_1_type,type,( k3_altcat_1: $i > $i > $i > $i )).
thf(k3_zfmisc_1_type,type,( k3_zfmisc_1: $i > $i > $i > $i )).
thf(k5_altcat_1_type,type,( k5_altcat_1: $i > $i > $i > $i > $i > $i > $i )).
thf(u1_altcat_1_type,type,( u1_altcat_1: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(u2_altcat_1_type,type,( u2_altcat_1: $i > $i )).
thf(l1_altcat_1_type,type,( l1_altcat_1: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l2_altcat_1_type,type,( l2_altcat_1: $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(v13_altcat_1_type,type,( v13_altcat_1: $i > $o )).
thf(v13_struct_0_type,type,( v13_struct_0: $i > $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_funcop_1_type,type,( v1_funcop_1: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_partfun1_type,type,( v1_partfun1: $i > $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_altcat_1_type,type,( v2_altcat_1: $i > $o )).
thf(v2_funcop_1_type,type,( v2_funcop_1: $i > $o )).
thf(v2_funct_1_type,type,( v2_funct_1: $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_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v6_altcat_1_type,type,( v6_altcat_1: $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(cc4_altcat_1,axiom,( ! [A: $i] : ( ( l2_altcat_1 @ A ) => ( ( v13_altcat_1 @ A ) => ( v2_altcat_1 @ A ) ) ) ),file(altcat_1,cc4_altcat_1)).
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(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(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_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(cc3_altcat_1,axiom,( ! [A: $i] : ( ( l2_altcat_1 @ A ) => ( ( v13_struct_0 @ A @ np__1 ) => ( v13_altcat_1 @ A ) ) ) ),file(altcat_1,cc3_altcat_1)).
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(cc5_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) => ( ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ) ),file(funct_1,cc5_funct_1)).
thf(cc6_funct_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) ) ),file(funct_1,cc6_funct_1)).
thf(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(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_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) ) ),file(funct_1,rc2_funct_1)).
thf(rc2_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_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
thf(rc3_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc3_funct_1)).
thf(rc3_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_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc4_funct_1)).
thf(rc4_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(rc5_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) ),file(funct_1,rc5_funct_1)).
thf(rc9_funct_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) ),file(funct_1,rc9_funct_1)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(dt_k2_altcat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ ( k2_zfmisc_1 @ A @ A ) ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ ( k2_zfmisc_1 @ A @ A ) ) ) => ( ( v1_relat_1 @ ( k2_altcat_1 @ A @ B ) ) & ( v4_relat_1 @ ( k2_altcat_1 @ A @ B ) @ ( k3_zfmisc_1 @ A @ A @ A ) ) & ( v1_funct_1 @ ( k2_altcat_1 @ A @ B ) ) & ( v1_partfun1 @ ( k2_altcat_1 @ A @ B ) @ ( k3_zfmisc_1 @ A @ A @ A ) ) ) ) ),file(altcat_1,k2_altcat_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_altcat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ ( k2_zfmisc_1 @ A @ A ) ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ ( k2_zfmisc_1 @ A @ A ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ ( k2_zfmisc_1 @ A @ A ) ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ ( k2_zfmisc_1 @ A @ A ) ) ) => ( ( v1_relat_1 @ ( k3_altcat_1 @ A @ B @ C ) ) & ( v4_relat_1 @ ( k3_altcat_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ A @ A @ A ) ) & ( v1_funct_1 @ ( k3_altcat_1 @ A @ B @ C ) ) & ( v1_partfun1 @ ( k3_altcat_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ A @ A @ A ) ) ) ) ),file(altcat_1,k3_altcat_1)).
thf(dt_k3_zfmisc_1,axiom,( $true ),file(zfmisc_1,k3_zfmisc_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(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(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_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc2_funct_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) ) ) ),file(funct_1,cc2_funct_1)).
thf(cc2_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_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_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) ) ) ),file(relat_1,cc3_relat_1)).
thf(cc4_funct_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) ) ),file(funct_1,cc4_funct_1)).
thf(cc4_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ) ),file(relat_1,cc4_relat_1)).
thf(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_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) ) ) ),file(relat_1,cc7_relat_1)).
thf(cc7_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ~ ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc7_struct_0)).
thf(cc8_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) ) ) ),file(funct_1,cc8_funct_1)).
thf(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(fc10_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(subset_1,fc10_subset_1)).
thf(fc11_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) ) => ~ ( v1_xboole_0 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) ),file(subset_1,fc11_subset_1)).
thf(fc1_altcat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ ( k2_zfmisc_1 @ A @ A ) ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ ( k2_zfmisc_1 @ A @ A ) ) & ( m2_pboole @ C @ ( k3_zfmisc_1 @ A @ A @ A ) @ ( k3_altcat_1 @ A @ B @ B ) @ ( k2_altcat_1 @ A @ B ) ) ) => ( ~ ( v2_struct_0 @ ( g2_altcat_1 @ A @ B @ C ) ) & ( v6_altcat_1 @ ( g2_altcat_1 @ A @ B @ C ) ) ) ) ),file(altcat_1,fc1_altcat_1)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(fc6_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc6_struct_0)).
thf(fc7_struct_0,axiom,( ! [A: $i] : ( ( ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc7_struct_0)).
thf(fc8_struct_0,axiom,( ! [A: $i] : ( ( ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc8_struct_0)).
thf(fc9_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc9_struct_0)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
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_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_1)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(free_g2_altcat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ ( k2_zfmisc_1 @ A @ A ) ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ ( k2_zfmisc_1 @ A @ A ) ) & ( m2_pboole @ C @ ( k3_zfmisc_1 @ A @ A @ A ) @ ( k3_altcat_1 @ A @ B @ B ) @ ( k2_altcat_1 @ A @ B ) ) ) => ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( = @ ( g2_altcat_1 @ A @ B @ C ) @ ( g2_altcat_1 @ D @ E @ F ) ) => ( ( = @ A @ D ) & ( = @ B @ E ) & ( = @ C @ F ) ) ) ) ),file(altcat_1,g2_altcat_1)).
thf(dt_g2_altcat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ ( k2_zfmisc_1 @ A @ A ) ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ ( k2_zfmisc_1 @ A @ A ) ) & ( m2_pboole @ C @ ( k3_zfmisc_1 @ A @ A @ A ) @ ( k3_altcat_1 @ A @ B @ B ) @ ( k2_altcat_1 @ A @ B ) ) ) => ( ( v6_altcat_1 @ ( g2_altcat_1 @ A @ B @ C ) ) & ( l2_altcat_1 @ ( g2_altcat_1 @ A @ B @ C ) ) ) ) ),file(altcat_1,g2_altcat_1)).
thf(dt_l1_altcat_1,axiom,( ! [A: $i] : ( ( l1_altcat_1 @ A ) => ( l1_struct_0 @ A ) ) ),file(altcat_1,l1_altcat_1)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_u1_altcat_1,axiom,( ! [A: $i] : ( ( l1_altcat_1 @ A ) => ( ( v1_relat_1 @ ( u1_altcat_1 @ A ) ) & ( v4_relat_1 @ ( u1_altcat_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) & ( v1_funct_1 @ ( u1_altcat_1 @ A ) ) & ( v1_partfun1 @ ( u1_altcat_1 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ) ) ),file(altcat_1,u1_altcat_1)).
thf(dt_u2_altcat_1,axiom,( ! [A: $i] : ( ( l2_altcat_1 @ A ) => ( m2_pboole @ ( u2_altcat_1 @ A ) @ ( k3_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( k3_altcat_1 @ ( u1_struct_0 @ A ) @ ( u1_altcat_1 @ A ) @ ( u1_altcat_1 @ A ) ) @ ( k2_altcat_1 @ ( u1_struct_0 @ A ) @ ( u1_altcat_1 @ A ) ) ) ) ),file(altcat_1,u2_altcat_1)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_1)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_1)).
thf(cc1_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc1_struct_0)).
thf(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
thf(cc4_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
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(cc7_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v4_funct_1 @ A ) ) ),file(funct_1,cc7_funct_1)).
thf(cc7_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_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(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(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(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(abstractness_v6_altcat_1,axiom,( ! [A: $i] : ( ( l2_altcat_1 @ A ) => ( ( v6_altcat_1 @ A ) => ( = @ A @ ( g2_altcat_1 @ ( u1_struct_0 @ A ) @ ( u1_altcat_1 @ A ) @ ( u2_altcat_1 @ A ) ) ) ) ) ),file(altcat_1,v6_altcat_1)).
thf(dt_k1_altcat_1,axiom,( $true ),file(altcat_1,k1_altcat_1)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_k5_altcat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l2_altcat_1 @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ E @ ( k1_altcat_1 @ A @ B @ C ) ) & ( m1_subset_1 @ F @ ( k1_altcat_1 @ A @ C @ D ) ) ) => ( m1_subset_1 @ ( k5_altcat_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_altcat_1 @ A @ B @ D ) ) ) ),file(altcat_1,k5_altcat_1)).
thf(dt_l2_altcat_1,axiom,( ! [A: $i] : ( ( l2_altcat_1 @ A ) => ( l1_altcat_1 @ A ) ) ),file(altcat_1,l2_altcat_1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_f1_s4_yellow18,axiom,( ~ ( v1_xboole_0 @ f1_s4_yellow18 ) ),file(yellow18,f1_s4_yellow18)).
thf(dt_f2_s4_yellow18,axiom,( $true ),file(yellow18,f2_s4_yellow18)).
thf(dt_f3_s4_yellow18,axiom,( $true ),file(yellow18,f3_s4_yellow18)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(rc2_altcat_1,axiom,( ? [A: $i] : ( ( l2_altcat_1 @ A ) & ( v6_altcat_1 @ A ) ) ),file(altcat_1,rc2_altcat_1)).
thf(rc3_altcat_1,axiom,( ? [A: $i] : ( ( l2_altcat_1 @ A ) & ~ ( v2_struct_0 @ A ) & ( v6_altcat_1 @ A ) ) ),file(altcat_1,rc3_altcat_1)).
thf(rc4_altcat_2,axiom,( ? [A: $i] : ( ( l2_altcat_1 @ A ) & ( v2_struct_0 @ A ) & ( v6_altcat_1 @ A ) ) ),file(altcat_2,rc4_altcat_2)).
thf(e1_4_1__yellow18,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ f1_s4_yellow18 ) => ! [B: $i] : ( ( m1_subset_1 @ B @ f1_s4_yellow18 ) => ! [C: $i] : ( ( m1_subset_1 @ C @ f1_s4_yellow18 ) => ! [D: $i] : ! [E: $i] : ( ( ( r2_hidden @ D @ ( f2_s4_yellow18 @ A @ B ) ) & ( r2_hidden @ E @ ( f2_s4_yellow18 @ B @ C ) ) ) => ( r2_hidden @ ( f3_s4_yellow18 @ A @ B @ C @ D @ E ) @ ( f2_s4_yellow18 @ A @ C ) ) ) ) ) ) ),file(yellow18,e1_4_1__yellow18)).
thf(s1_yellow18,axiom,( ! [A: $i > $i > $i > $i > $i > $i] : ! [B: $i > $i > $i] : ! [C: $i] : ( ~ ( v1_xboole_0 @ C ) => ( ! [D: $i] : ( ( m1_subset_1 @ D @ C ) => ! [E: $i] : ( ( m1_subset_1 @ E @ C ) => ! [F: $i] : ( ( m1_subset_1 @ F @ C ) => ! [G: $i] : ! [H: $i] : ( ( ( r2_hidden @ G @ ( B @ D @ E ) ) & ( r2_hidden @ H @ ( B @ E @ F ) ) ) => ( r2_hidden @ ( A @ D @ E @ F @ G @ H ) @ ( B @ D @ F ) ) ) ) ) ) => ? [D: $i] : ( ~ ( v2_struct_0 @ D ) & ( v2_altcat_1 @ D ) & ( v6_altcat_1 @ D ) & ( l2_altcat_1 @ D ) & ( = @ ( u1_struct_0 @ D ) @ C ) & ! [E: $i] : ( ( m1_subset_1 @ E @ ( u1_struct_0 @ D ) ) => ! [F: $i] : ( ( m1_subset_1 @ F @ ( u1_struct_0 @ D ) ) => ( = @ ( k1_altcat_1 @ D @ E @ F ) @ ( B @ E @ F ) ) ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ ( u1_struct_0 @ D ) ) => ! [F: $i] : ( ( m1_subset_1 @ F @ ( u1_struct_0 @ D ) ) => ! [G: $i] : ( ( m1_subset_1 @ G @ ( u1_struct_0 @ D ) ) => ~ ( ~ ( = @ ( k1_altcat_1 @ D @ E @ F ) @ k1_xboole_0 ) & ~ ( = @ ( k1_altcat_1 @ D @ F @ G ) @ k1_xboole_0 ) & ~ ( ! [H: $i] : ( ( m1_subset_1 @ H @ ( k1_altcat_1 @ D @ E @ F ) ) => ! [I: $i] : ( ( m1_subset_1 @ I @ ( k1_altcat_1 @ D @ F @ G ) ) => ( = @ ( k5_altcat_1 @ D @ E @ F @ G @ H @ I ) @ ( A @ E @ F @ G @ H @ I ) ) ) ) ) ) ) ) ) ) ) ) ),file(yellow18,s1_yellow18)).
thf(e2_4_1__yellow18,conjecture,( ? [A: $i] : ( ~ ( v2_struct_0 @ A ) & ( v2_altcat_1 @ A ) & ( v6_altcat_1 @ A ) & ( l2_altcat_1 @ A ) & ( = @ ( u1_struct_0 @ A ) @ f1_s4_yellow18 ) & ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) => ( = @ ( k1_altcat_1 @ A @ B @ C ) @ ( f2_s4_yellow18 @ B @ C ) ) ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) ) => ~ ( ~ ( = @ ( k1_altcat_1 @ A @ B @ C ) @ k1_xboole_0 ) & ~ ( = @ ( k1_altcat_1 @ A @ C @ D ) @ k1_xboole_0 ) & ~ ( ! [E: $i] : ( ( m1_subset_1 @ E @ ( k1_altcat_1 @ A @ B @ C ) ) => ! [F: $i] : ( ( m1_subset_1 @ F @ ( k1_altcat_1 @ A @ C @ D ) ) => ( = @ ( k5_altcat_1 @ A @ B @ C @ D @ E @ F ) @ ( f3_s4_yellow18 @ B @ C @ D @ E @ F ) ) ) ) ) ) ) ) ) ) ),file(yellow18,e2_4_1__yellow18)).
