% Mizar problem: e1_38_1_1,quofield,1878,63 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_38_type,type,( c1_38__quofield: $i )).
thf(k1_binop_1_type,type,( k1_binop_1: $i > $i > $i > $i )).
thf(k1_quofield_type,type,( k1_quofield: $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_binop_1_type,type,( k2_binop_1: $i > $i > $i > $i > $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k5_binop_1_type,type,( k5_binop_1: $i > $i > $i > $i > $i )).
thf(k7_quofield_type,type,( k7_quofield: $i > $i )).
thf(k9_quofield_type,type,( k9_quofield: $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(m2_subset_1_type,type,( m2_subset_1: $i > $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_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_funct_2_type,type,( v1_funct_2: $i > $i > $i > $o )).
thf(v1_group_1_type,type,( v1_group_1: $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_vectsp_2_type,type,( v1_vectsp_2: $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_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_group_1_type,type,( v3_group_1: $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_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_struct_0_type,type,( v6_struct_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_struct_0_type,type,( v8_struct_0: $i > $o )).
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(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(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_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(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_gcd_1,axiom,( ! [A: $i] : ( ( l4_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v5_group_1 @ A ) & ( v3_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v6_vectsp_1 @ A ) ) ) ) ),file(gcd_1,cc1_gcd_1)).
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(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(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_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_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v7_struct_0 @ A ) => ( v8_struct_0 @ A ) ) ) ),file(struct_0,cc6_struct_0)).
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(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(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(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(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_l1_algstr_0,axiom,( ! [A: $i] : ( ( l1_algstr_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(algstr_0,l1_algstr_0)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_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(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(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(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_struct_0,axiom,( ! [A: $i] : ( ( l4_struct_0 @ A ) => ( ~ ( v6_struct_0 @ A ) => ~ ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc3_struct_0)).
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(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_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(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(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(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(dt_k1_binop_1,axiom,( $true ),file(binop_1,k1_binop_1)).
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_l2_struct_0,axiom,( ! [A: $i] : ( ( l2_struct_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(struct_0,l2_struct_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(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_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_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(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_gcd_1,axiom,( ! [A: $i] : ( ( l6_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v5_group_1 @ A ) & ( v1_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v5_vectsp_1 @ A ) ) ) ) ),file(gcd_1,cc2_gcd_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(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_gcd_1,axiom,( ! [A: $i] : ( ( l6_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v5_group_1 @ A ) & ( v2_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v5_vectsp_1 @ A ) ) ) ) ),file(gcd_1,cc3_gcd_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_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_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(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(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_quofield,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v6_struct_0 @ A ) & ( l5_algstr_0 @ A ) ) => ~ ( v1_xboole_0 @ ( k1_quofield @ A ) ) ) ),file(quofield,fc1_quofield)).
thf(fc3_quofield,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v6_struct_0 @ A ) & ( l5_algstr_0 @ A ) ) => ~ ( v1_xboole_0 @ ( k7_quofield @ A ) ) ) ),file(quofield,fc3_quofield)).
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_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_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(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_vectsp_1,axiom,( ? [A: $i] : ( ( l5_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v4_vectsp_1 @ A ) ) ),file(vectsp_1,rc2_vectsp_1)).
thf(redefinition_k2_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) & ( m1_subset_1 @ E @ A ) & ( m1_subset_1 @ F @ B ) ) => ( = @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_binop_1 @ D @ E @ F ) ) ) ),file(binop_1,k2_binop_1)).
thf(redefinition_k5_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) & ( m1_subset_1 @ C @ A ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k5_binop_1 @ A @ B @ C @ D ) @ ( k1_binop_1 @ B @ C @ D ) ) ) ),file(binop_1,k5_binop_1)).
thf(redefinition_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) <=> ( m1_subset_1 @ C @ B ) ) ) ),file(subset_1,m2_subset_1)).
thf(dt_k1_quofield,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l2_struct_0 @ A ) ) => ( m1_subset_1 @ ( k1_quofield @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ) ) ),file(quofield,k1_quofield)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) & ( m1_subset_1 @ E @ A ) & ( m1_subset_1 @ F @ B ) ) => ( m1_subset_1 @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ C ) ) ),file(binop_1,k2_binop_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k5_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) & ( m1_subset_1 @ C @ A ) & ( m1_subset_1 @ D @ A ) ) => ( m1_subset_1 @ ( k5_binop_1 @ A @ B @ C @ D ) @ A ) ) ),file(binop_1,k5_binop_1)).
thf(dt_k7_quofield,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v6_struct_0 @ A ) & ( l5_algstr_0 @ A ) ) => ( m1_subset_1 @ ( k7_quofield @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k1_quofield @ A ) ) ) ) ) ),file(quofield,k7_quofield)).
thf(dt_k9_quofield,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v6_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v3_group_1 @ A ) & ( v5_group_1 @ A ) & ( v4_vectsp_1 @ A ) & ( v5_vectsp_1 @ A ) & ( v1_vectsp_2 @ A ) & ( l6_algstr_0 @ A ) & ( m1_subset_1 @ B @ ( k7_quofield @ A ) ) & ( m1_subset_1 @ C @ ( k7_quofield @ A ) ) ) => ( m2_subset_1 @ ( k9_quofield @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k1_quofield @ A ) ) @ ( k7_quofield @ A ) ) ) ),file(quofield,k9_quofield)).
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_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) => ( m1_subset_1 @ C @ A ) ) ) ),file(subset_1,m2_subset_1)).
thf(dt_c1_38__quofield,axiom,( ~ ( v2_struct_0 @ c1_38__quofield ) & ~ ( v6_struct_0 @ c1_38__quofield ) & ( v13_algstr_0 @ c1_38__quofield ) & ( v2_rlvect_1 @ c1_38__quofield ) & ( v3_rlvect_1 @ c1_38__quofield ) & ( v4_rlvect_1 @ c1_38__quofield ) & ( v3_group_1 @ c1_38__quofield ) & ( v5_group_1 @ c1_38__quofield ) & ( v4_vectsp_1 @ c1_38__quofield ) & ( v5_vectsp_1 @ c1_38__quofield ) & ( v1_vectsp_2 @ c1_38__quofield ) & ( l6_algstr_0 @ c1_38__quofield ) ),file(quofield,c1_38__quofield)).
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_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(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_gcd_1,axiom,( ! [A: $i] : ( ( l6_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v3_group_1 @ A ) & ( v4_vectsp_1 @ A ) & ( v5_vectsp_1 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v3_group_1 @ A ) & ( v4_vectsp_1 @ A ) & ( v5_vectsp_1 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) ) ) ) ),file(gcd_1,cc4_gcd_1)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(s4_binop_1,axiom,( ! [A: $i > $i > $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ? [E: $i] : ( ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ D @ C ) @ B ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ D @ C ) @ B ) ) ) & ! [F: $i] : ( ( m1_subset_1 @ F @ D ) => ! [G: $i] : ( ( m1_subset_1 @ G @ C ) => ( = @ ( k2_binop_1 @ D @ C @ B @ E @ F @ G ) @ ( A @ F @ G ) ) ) ) ) ),file(binop_1,s4_binop_1)).
thf(e1_38_1_1__quofield,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ ( k7_quofield @ c1_38__quofield ) @ ( k7_quofield @ c1_38__quofield ) ) @ ( k7_quofield @ c1_38__quofield ) ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( k7_quofield @ c1_38__quofield ) @ ( k7_quofield @ c1_38__quofield ) ) @ ( k7_quofield @ c1_38__quofield ) ) ) ) & ! [B: $i] : ( ( m2_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_quofield @ c1_38__quofield ) ) @ ( k7_quofield @ c1_38__quofield ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_quofield @ c1_38__quofield ) ) @ ( k7_quofield @ c1_38__quofield ) ) => ( = @ ( k5_binop_1 @ ( k7_quofield @ c1_38__quofield ) @ A @ B @ C ) @ ( k9_quofield @ c1_38__quofield @ B @ C ) ) ) ) ) ),file(quofield,e1_38_1_1__quofield)).
