% Mizar problem: e4_13,ring_1,210,9 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_13_type,type,( c1_13__ring_1: $i )).
thf(c2_13_type,type,( c2_13__ring_1: $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(k5_algstr_0_type,type,( k5_algstr_0: $i > $i > $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(l1_algstr_0_type,type,( l1_algstr_0: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l2_algstr_0_type,type,( l2_algstr_0: $i > $o )).
thf(l2_struct_0_type,type,( l2_struct_0: $i > $o )).
thf(l3_algstr_0_type,type,( l3_algstr_0: $i > $o )).
thf(l3_struct_0_type,type,( l3_struct_0: $i > $o )).
thf(l4_algstr_0_type,type,( l4_algstr_0: $i > $o )).
thf(l4_struct_0_type,type,( l4_struct_0: $i > $o )).
thf(l5_algstr_0_type,type,( l5_algstr_0: $i > $o )).
thf(l6_algstr_0_type,type,( l6_algstr_0: $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(v13_algstr_0_type,type,( v13_algstr_0: $i > $o )).
thf(v13_struct_0_type,type,( v13_struct_0: $i > $i > $o )).
thf(v1_algstr_1_type,type,( v1_algstr_1: $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_finsub_1_type,type,( v1_finsub_1: $i > $o )).
thf(v1_group_1_type,type,( v1_group_1: $i > $o )).
thf(v1_ideal_1_type,type,( v1_ideal_1: $i > $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_subset_1_type,type,( v1_subset_1: $i > $i > $o )).
thf(v1_vectsp_1_type,type,( v1_vectsp_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_algstr_1_type,type,( v2_algstr_1: $i > $o )).
thf(v2_group_1_type,type,( v2_group_1: $i > $o )).
thf(v2_ideal_1_type,type,( v2_ideal_1: $i > $i > $o )).
thf(v2_rlvect_1_type,type,( v2_rlvect_1: $i > $o )).
thf(v2_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v2_vectsp_1_type,type,( v2_vectsp_1: $i > $o )).
thf(v3_algstr_1_type,type,( v3_algstr_1: $i > $o )).
thf(v3_finsub_1_type,type,( v3_finsub_1: $i > $o )).
thf(v3_group_1_type,type,( v3_group_1: $i > $o )).
thf(v3_ideal_1_type,type,( v3_ideal_1: $i > $i > $o )).
thf(v3_relat_2_type,type,( v3_relat_2: $i > $o )).
thf(v3_rlvect_1_type,type,( v3_rlvect_1: $i > $o )).
thf(v3_vectsp_1_type,type,( v3_vectsp_1: $i > $o )).
thf(v4_algstr_1_type,type,( v4_algstr_1: $i > $o )).
thf(v4_finsub_1_type,type,( v4_finsub_1: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v4_rlvect_1_type,type,( v4_rlvect_1: $i > $o )).
thf(v4_vectsp_1_type,type,( v4_vectsp_1: $i > $o )).
thf(v5_algstr_0_type,type,( v5_algstr_0: $i > $o )).
thf(v5_group_1_type,type,( v5_group_1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v5_vectsp_1_type,type,( v5_vectsp_1: $i > $o )).
thf(v6_algstr_0_type,type,( v6_algstr_0: $i > $o )).
thf(v6_vectsp_1_type,type,( v6_vectsp_1: $i > $o )).
thf(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v8_relat_2_type,type,( v8_relat_2: $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_0: $i > $o )).
thf(cc1_ideal_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v5_group_1 @ A ) & ( l3_algstr_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( ~ ( v1_xboole_0 @ B ) & ( v2_ideal_1 @ B @ A ) ) => ( ~ ( v1_xboole_0 @ B ) & ( v3_ideal_1 @ B @ A ) ) ) ) ) ),file(ideal_1,cc1_ideal_1)).
thf(cc2_ideal_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v5_group_1 @ A ) & ( l3_algstr_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( ~ ( v1_xboole_0 @ B ) & ( v3_ideal_1 @ B @ A ) ) => ( ~ ( v1_xboole_0 @ B ) & ( v2_ideal_1 @ B @ A ) ) ) ) ) ),file(ideal_1,cc2_ideal_1)).
thf(cc6_vectsp_1,axiom,( ! [A: $i] : ( ( l4_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v5_group_1 @ A ) & ( v6_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v3_vectsp_1 @ A ) ) ) ) ),file(vectsp_1,cc6_vectsp_1)).
thf(rc3_vectsp_1,axiom,( ? [A: $i] : ( ( l3_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v3_group_1 @ A ) & ( v5_group_1 @ A ) ) ),file(vectsp_1,rc3_vectsp_1)).
thf(rc4_vectsp_1,axiom,( ? [A: $i] : ( ( l4_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v1_group_1 @ A ) & ( v3_group_1 @ A ) & ( v5_group_1 @ A ) ) ),file(vectsp_1,rc4_vectsp_1)).
thf(dt_l3_algstr_0,axiom,( ! [A: $i] : ( ( l3_algstr_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(algstr_0,l3_algstr_0)).
thf(dt_l3_struct_0,axiom,( ! [A: $i] : ( ( l3_struct_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(struct_0,l3_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(cc2_algstr_1,axiom,( ! [A: $i] : ( ( l2_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v5_algstr_0 @ A ) & ( v6_algstr_0 @ A ) & ( v2_algstr_1 @ A ) & ( v3_algstr_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v4_algstr_1 @ A ) ) ) ) ),file(algstr_1,cc2_algstr_1)).
thf(cc4_vectsp_1,axiom,( ! [A: $i] : ( ( l4_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v3_vectsp_1 @ A ) & ( v6_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v1_group_1 @ A ) ) ) ) ),file(vectsp_1,cc4_vectsp_1)).
thf(cc5_subset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,cc5_subset_1)).
thf(cc7_algstr_1,axiom,( ! [A: $i] : ( ( l2_algstr_0 @ A ) => ( ( v13_struct_0 @ A @ np__1 ) => ( ( v13_struct_0 @ A @ np__1 ) & ( v13_algstr_0 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) ) ) ) ),file(algstr_1,cc7_algstr_1)).
thf(cc9_algstr_1,axiom,( ! [A: $i] : ( ( l3_algstr_0 @ A ) => ( ( v13_struct_0 @ A @ np__1 ) => ( ( v13_struct_0 @ A @ np__1 ) & ( v2_group_1 @ A ) & ( v3_group_1 @ A ) & ( v5_group_1 @ A ) ) ) ) ),file(algstr_1,cc9_algstr_1)).
thf(rc21_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_zfmisc_1 @ B ) ) ) ),file(struct_0,rc21_struct_0)).
thf(rc22_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_zfmisc_1 @ B ) ) ) ),file(struct_0,rc22_struct_0)).
thf(rc4_ideal_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l3_algstr_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v2_ideal_1 @ B @ A ) ) ) ),file(ideal_1,rc4_ideal_1)).
thf(rc5_ideal_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l3_algstr_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v3_ideal_1 @ B @ A ) ) ) ),file(ideal_1,rc5_ideal_1)).
thf(rc5_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,rc5_subset_1)).
thf(rc6_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,rc6_subset_1)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_l1_algstr_0,axiom,( ! [A: $i] : ( ( l1_algstr_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(algstr_0,l1_algstr_0)).
thf(dt_l2_struct_0,axiom,( ! [A: $i] : ( ( l2_struct_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(struct_0,l2_struct_0)).
thf(dt_l4_algstr_0,axiom,( ! [A: $i] : ( ( l4_algstr_0 @ A ) => ( ( l3_struct_0 @ A ) & ( l3_algstr_0 @ A ) ) ) ),file(algstr_0,l4_algstr_0)).
thf(dt_l4_struct_0,axiom,( ! [A: $i] : ( ( l4_struct_0 @ A ) => ( ( l2_struct_0 @ A ) & ( l3_struct_0 @ A ) ) ) ),file(struct_0,l4_struct_0)).
thf(cc10_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) => ( v13_struct_0 @ A @ np__1 ) ) ) ),file(struct_0,cc10_struct_0)).
thf(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_algstr_1,axiom,( ! [A: $i] : ( ( l2_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v4_algstr_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v5_algstr_0 @ A ) & ( v6_algstr_0 @ A ) & ( v2_algstr_1 @ A ) & ( v3_algstr_1 @ A ) ) ) ) ),file(algstr_1,cc1_algstr_1)).
thf(cc2_finsub_1,axiom,( ! [A: $i] : ( ( ( v1_finsub_1 @ A ) & ( v3_finsub_1 @ A ) ) => ( v4_finsub_1 @ A ) ) ),file(finsub_1,cc2_finsub_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_algstr_1,axiom,( ! [A: $i] : ( ( l2_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v4_algstr_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_algstr_1 @ A ) ) ) ) ),file(algstr_1,cc3_algstr_1)).
thf(cc3_vectsp_1,axiom,( ! [A: $i] : ( ( l4_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v4_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v3_vectsp_1 @ A ) & ( v6_vectsp_1 @ A ) ) ) ) ),file(vectsp_1,cc3_vectsp_1)).
thf(cc5_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ( ~ ( v2_struct_0 @ A ) & ~ ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc5_struct_0)).
thf(cc5_vectsp_1,axiom,( ! [A: $i] : ( ( l4_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v4_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v1_group_1 @ A ) ) ) ) ),file(vectsp_1,cc5_vectsp_1)).
thf(cc6_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v7_struct_0 @ A ) => ( v8_struct_0 @ A ) ) ) ),file(struct_0,cc6_struct_0)).
thf(cc7_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ~ ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc7_struct_0)).
thf(cc8_algstr_1,axiom,( ! [A: $i] : ( ( l6_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v1_vectsp_1 @ A ) & ( v4_vectsp_1 @ A ) ) ) ) ),file(algstr_1,cc8_algstr_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(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc6_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc6_struct_0)).
thf(fc7_struct_0,axiom,( ! [A: $i] : ( ( ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc7_struct_0)).
thf(fc8_struct_0,axiom,( ! [A: $i] : ( ( ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc8_struct_0)).
thf(fc9_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc9_struct_0)).
thf(rc11_vectsp_1,axiom,( ? [A: $i] : ( ( l4_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v4_vectsp_1 @ A ) ) ),file(vectsp_1,rc11_vectsp_1)).
thf(rc1_ideal_1,axiom,( ? [A: $i] : ( ( l2_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v1_algstr_1 @ A ) ) ),file(ideal_1,rc1_ideal_1)).
thf(rc20_struct_0,axiom,( ? [A: $i] : ( ( l2_struct_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) ),file(struct_0,rc20_struct_0)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_l2_algstr_0,axiom,( ! [A: $i] : ( ( l2_algstr_0 @ A ) => ( ( l2_struct_0 @ A ) & ( l1_algstr_0 @ A ) ) ) ),file(algstr_0,l2_algstr_0)).
thf(dt_l5_algstr_0,axiom,( ! [A: $i] : ( ( l5_algstr_0 @ A ) => ( ( l4_algstr_0 @ A ) & ( l4_struct_0 @ A ) ) ) ),file(algstr_0,l5_algstr_0)).
thf(cc1_finsub_1,axiom,( ! [A: $i] : ( ( v4_finsub_1 @ A ) => ( ( v1_finsub_1 @ A ) & ( v3_finsub_1 @ A ) ) ) ),file(finsub_1,cc1_finsub_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_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ~ ( v1_subset_1 @ B @ A ) => ~ ( v1_xboole_0 @ B ) ) ) ) ),file(subset_1,cc2_subset_1)).
thf(cc2_vectsp_1,axiom,( ! [A: $i] : ( ( l6_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v1_vectsp_1 @ A ) & ( v2_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v5_vectsp_1 @ A ) ) ) ) ),file(vectsp_1,cc2_vectsp_1)).
thf(cc4_algstr_1,axiom,( ! [A: $i] : ( ( l2_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v1_algstr_1 @ A ) & ( v4_algstr_1 @ A ) ) ) ) ),file(algstr_1,cc4_algstr_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(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(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_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(rc2_vectsp_1,axiom,( ? [A: $i] : ( ( l5_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v4_vectsp_1 @ A ) ) ),file(vectsp_1,rc2_vectsp_1)).
thf(rc3_ideal_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l2_algstr_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_ideal_1 @ B @ A ) ) ) ),file(ideal_1,rc3_ideal_1)).
thf(rc3_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_subset_1 @ B @ A ) ) ),file(subset_1,rc3_subset_1)).
thf(rc4_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(rc4_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v1_subset_1 @ B @ A ) ) ) ),file(subset_1,rc4_subset_1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_k5_algstr_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( l2_algstr_0 @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) => ( m1_subset_1 @ ( k5_algstr_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ) ),file(algstr_0,k5_algstr_0)).
thf(dt_l6_algstr_0,axiom,( ! [A: $i] : ( ( l6_algstr_0 @ A ) => ( ( l2_algstr_0 @ A ) & ( l5_algstr_0 @ A ) ) ) ),file(algstr_0,l6_algstr_0)).
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_c1_13__ring_1,axiom,( ~ ( v2_struct_0 @ c1_13__ring_1 ) & ( v13_algstr_0 @ c1_13__ring_1 ) & ( v3_group_1 @ c1_13__ring_1 ) & ( v4_vectsp_1 @ c1_13__ring_1 ) & ( v5_vectsp_1 @ c1_13__ring_1 ) & ( v2_rlvect_1 @ c1_13__ring_1 ) & ( v3_rlvect_1 @ c1_13__ring_1 ) & ( v4_rlvect_1 @ c1_13__ring_1 ) & ( l6_algstr_0 @ c1_13__ring_1 ) ),file(ring_1,c1_13__ring_1)).
thf(dt_c2_13__ring_1,axiom,( ~ ( v1_xboole_0 @ c2_13__ring_1 ) & ( v1_ideal_1 @ c2_13__ring_1 @ c1_13__ring_1 ) & ( v2_ideal_1 @ c2_13__ring_1 @ c1_13__ring_1 ) & ( v3_ideal_1 @ c2_13__ring_1 @ c1_13__ring_1 ) & ( m1_subset_1 @ c2_13__ring_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c1_13__ring_1 ) ) ) ),file(ring_1,c2_13__ring_1)).
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_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_xboole_0 @ B ) ) ) ),file(subset_1,cc1_subset_1)).
thf(cc1_vectsp_1,axiom,( ! [A: $i] : ( ( l6_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v5_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v1_vectsp_1 @ A ) & ( v2_vectsp_1 @ A ) ) ) ) ),file(vectsp_1,cc1_vectsp_1)).
thf(cc2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ) ),file(relset_1,cc2_relset_1)).
thf(cc3_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc3_relset_1)).
thf(cc3_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ( v1_xboole_0 @ B ) => ( v1_subset_1 @ B @ A ) ) ) ) ),file(subset_1,cc3_subset_1)).
thf(cc4_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc4_relset_1)).
thf(cc4_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ~ ( v1_subset_1 @ B @ A ) ) ) ),file(subset_1,cc4_subset_1)).
thf(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(fc1_finsub_1,axiom,( ! [A: $i] : ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ) ),file(finsub_1,fc1_finsub_1)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(rc1_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(subset_1,rc1_subset_1)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc2_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v1_xboole_0 @ B ) ) ),file(subset_1,rc2_subset_1)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc6_ideal_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l6_algstr_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_ideal_1 @ B @ A ) & ( v2_ideal_1 @ B @ A ) & ( v3_ideal_1 @ B @ A ) ) ) ),file(ideal_1,rc6_ideal_1)).
thf(rc7_ideal_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l6_algstr_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_ideal_1 @ B @ A ) & ( v3_ideal_1 @ B @ A ) ) ) ),file(ideal_1,rc7_ideal_1)).
thf(rc8_ideal_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l6_algstr_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_ideal_1 @ B @ A ) & ( v2_ideal_1 @ B @ A ) ) ) ),file(ideal_1,rc8_ideal_1)).
thf(e3_13__ring_1,axiom,( ! [A: $i] : ( ( r2_hidden @ A @ ( u1_struct_0 @ c1_13__ring_1 ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ? [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ( = @ B @ A ) & ( = @ C @ A ) & ( r2_hidden @ ( k5_algstr_0 @ c1_13__ring_1 @ B @ C ) @ c2_13__ring_1 ) ) ) ) ),file(ring_1,e3_13__ring_1)).
thf(e1_13__ring_1,axiom,( ! [A: $i] : ! [B: $i] : ( ? [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ? [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ( = @ C @ A ) & ( = @ D @ B ) & ( r2_hidden @ ( k5_algstr_0 @ c1_13__ring_1 @ C @ D ) @ c2_13__ring_1 ) ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ? [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ( = @ C @ B ) & ( = @ D @ A ) & ( r2_hidden @ ( k5_algstr_0 @ c1_13__ring_1 @ C @ D ) @ c2_13__ring_1 ) ) ) ) ),file(ring_1,e1_13__ring_1)).
thf(e2_13__ring_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ? [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ? [E: $i] : ( ( m1_subset_1 @ E @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ( = @ D @ A ) & ( = @ E @ B ) & ( r2_hidden @ ( k5_algstr_0 @ c1_13__ring_1 @ D @ E ) @ c2_13__ring_1 ) ) ) & ? [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ? [E: $i] : ( ( m1_subset_1 @ E @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ( = @ D @ B ) & ( = @ E @ C ) & ( r2_hidden @ ( k5_algstr_0 @ c1_13__ring_1 @ D @ E ) @ c2_13__ring_1 ) ) ) ) => ? [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ? [E: $i] : ( ( m1_subset_1 @ E @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ( = @ D @ A ) & ( = @ E @ C ) & ( r2_hidden @ ( k5_algstr_0 @ c1_13__ring_1 @ D @ E ) @ c2_13__ring_1 ) ) ) ) ),file(ring_1,e2_13__ring_1)).
thf(s1_eqrel_1,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ( ( ! [C: $i] : ( ( r2_hidden @ C @ B ) => ( A @ C @ C ) ) & ! [C: $i] : ! [D: $i] : ( ( A @ C @ D ) => ( A @ D @ C ) ) & ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( A @ C @ D ) & ( A @ D @ E ) ) => ( A @ C @ E ) ) ) => ? [C: $i] : ( ( v3_relat_2 @ C ) & ( v8_relat_2 @ C ) & ( v1_partfun1 @ C @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ B ) ) ) & ! [D: $i] : ! [E: $i] : ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) <=> ( ( r2_hidden @ D @ B ) & ( r2_hidden @ E @ B ) & ( A @ D @ E ) ) ) ) ) ),file(eqrel_1,s1_eqrel_1)).
thf(e4_13__ring_1,conjecture,( ? [A: $i] : ( ( v1_partfun1 @ A @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ( v3_relat_2 @ A ) & ( v8_relat_2 @ A ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_13__ring_1 ) @ ( u1_struct_0 @ c1_13__ring_1 ) ) ) ) & ! [B: $i] : ! [C: $i] : ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) <=> ( ( r2_hidden @ B @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ( r2_hidden @ C @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ? [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ? [E: $i] : ( ( m1_subset_1 @ E @ ( u1_struct_0 @ c1_13__ring_1 ) ) & ( = @ D @ B ) & ( = @ E @ C ) & ( r2_hidden @ ( k5_algstr_0 @ c1_13__ring_1 @ D @ E ) @ c2_13__ring_1 ) ) ) ) ) ) ),file(ring_1,e4_13__ring_1)).
