% Mizar problem: e3_22_1_2,vectsp_7,760,52 
include('Axioms/SET010^1.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_22_type,type,( c1_22__vectsp_7: $i )).
thf(c1_22_1_type,type,( c1_22_1__vectsp_7: $i )).
thf(c1_22_1_2_type,type,( c1_22_1_2__vectsp_7: $i )).
thf(c2_22_type,type,( c2_22__vectsp_7: $i )).
thf(c3_22_1_type,type,( c3_22_1__vectsp_7: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_funct_2_type,type,( k1_funct_2: $i > $i > $i )).
thf(k1_vectsp_6_type,type,( k1_vectsp_6: $i > $i > $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k9_funct_2_type,type,( k9_funct_2: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $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(l1_vectsp_1_type,type,( l1_vectsp_1: $i > $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_funct_2_type,type,( m1_funct_2: $i > $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m1_vectsp_6_type,type,( m1_vectsp_6: $i > $i > $i > $o )).
thf(m2_funct_2_type,type,( m2_funct_2: $i > $i > $i > $i > $o )).
thf(m2_vectsp_6_type,type,( m2_vectsp_6: $i > $i > $i > $i > $o )).
thf(v10_vectsp_1_type,type,( v10_vectsp_1: $i > $i > $o )).
thf(v11_vectsp_1_type,type,( v11_vectsp_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_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_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_7_type,type,( v1_vectsp_7: $i > $i > $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_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(v33_algstr_0_type,type,( v33_algstr_0: $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_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_finset_1_type,type,( v5_finset_1: $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_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(v8_vectsp_1_type,type,( v8_vectsp_1: $i > $i > $o )).
thf(v9_vectsp_1_type,type,( v9_vectsp_1: $i > $i > $o )).
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(rc5_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) ) ),file(finset_1,rc5_finset_1)).
thf(rc6_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ? [C: $i] : ( ~ ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) ) ) ),file(finset_1,rc6_finset_1)).
thf(dt_k1_funct_2,axiom,( $true ),file(funct_2,k1_funct_2)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_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(dt_m1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_funct_2 @ C @ A @ B ) => ~ ( v1_xboole_0 @ C ) ) ),file(funct_2,m1_funct_2)).
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_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(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_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_finset_1 @ A ) => ! [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_funct_2 @ C @ A @ B ) & ( v1_finset_1 @ C ) ) ) ) ) ),file(finset_1,cc3_finset_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(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_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(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(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(fc14_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_finset_1 @ A ) & ( v1_finset_1 @ B ) ) => ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(finset_1,fc14_finset_1)).
thf(fc8_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) => ( v1_relat_1 @ ( k9_xtuple_0 @ D ) ) ) ),file(relset_1,fc8_relset_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(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(redefinition_k9_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ( = @ ( k9_funct_2 @ A @ B ) @ ( k1_funct_2 @ A @ B ) ) ) ),file(funct_2,k9_funct_2)).
thf(redefinition_m2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( m1_funct_2 @ C @ A @ B ) ) => ! [D: $i] : ( ( m2_funct_2 @ D @ A @ B @ C ) <=> ( m1_subset_1 @ D @ C ) ) ) ),file(funct_2,m2_funct_2)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_k9_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ( m1_funct_2 @ ( k9_funct_2 @ A @ B ) @ A @ B ) ) ),file(funct_2,k9_funct_2)).
thf(dt_l1_algstr_0,axiom,( ! [A: $i] : ( ( l1_algstr_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(algstr_0,l1_algstr_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(dt_m2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( m1_funct_2 @ C @ A @ B ) ) => ! [D: $i] : ( ( m2_funct_2 @ D @ A @ B @ C ) => ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),file(funct_2,m2_funct_2)).
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(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(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_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_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_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_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(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_finset_1,axiom,( ! [A: $i] : ( ( v5_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_finset_1 @ B ) ) ) ),file(finset_1,cc7_finset_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_finset_1,axiom,( ! [A: $i] : ( ( v5_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_finset_1 @ B ) ) ) ),file(finset_1,cc8_finset_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(fc35_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finset_1 @ A ) ) => ( v1_finset_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(finset_1,fc35_finset_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(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_vectsp_7,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v6_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v33_algstr_0 @ A ) & ( v3_group_1 @ A ) & ( v5_group_1 @ A ) & ( v4_vectsp_1 @ A ) & ( v5_vectsp_1 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( l6_algstr_0 @ A ) & ~ ( v2_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v8_vectsp_1 @ B @ A ) & ( v9_vectsp_1 @ B @ A ) & ( v10_vectsp_1 @ B @ A ) & ( v11_vectsp_1 @ B @ A ) & ( v2_rlvect_1 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( l1_vectsp_1 @ B @ A ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) & ( v1_finset_1 @ C ) & ( v1_vectsp_7 @ C @ A @ B ) ) ) ),file(vectsp_7,rc1_vectsp_7)).
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(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(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_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(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(rc7_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_zfmisc_1 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(finset_1,rc7_finset_1)).
thf(rc8_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v5_finset_1 @ A ) ) ),file(finset_1,rc8_finset_1)).
thf(rc9_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finset_1 @ A ) ) ),file(finset_1,rc9_finset_1)).
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_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_m1_vectsp_6,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l2_struct_0 @ A ) & ~ ( v2_struct_0 @ B ) & ( l1_vectsp_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_vectsp_6 @ C @ A @ B ) => ( m2_funct_2 @ C @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ ( k9_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) ) ) ) ),file(vectsp_6,m1_vectsp_6)).
thf(dt_c3_22_1__vectsp_7,axiom,( m1_subset_1 @ c3_22_1__vectsp_7 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c2_22__vectsp_7 ) ) ),file(vectsp_7,c3_22_1__vectsp_7)).
thf(cc1_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc1_finset_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(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_7,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v6_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v33_algstr_0 @ A ) & ( v3_group_1 @ A ) & ( v5_group_1 @ A ) & ( v4_vectsp_1 @ A ) & ( v5_vectsp_1 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( l6_algstr_0 @ A ) & ~ ( v2_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v8_vectsp_1 @ B @ A ) & ( v9_vectsp_1 @ B @ A ) & ( v10_vectsp_1 @ B @ A ) & ( v11_vectsp_1 @ B @ A ) & ( v2_rlvect_1 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( l1_vectsp_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) => ( ( v1_xboole_0 @ C ) => ( v1_vectsp_7 @ C @ A @ B ) ) ) ) ),file(vectsp_7,cc1_vectsp_7)).
thf(cc2_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_finset_1 @ B ) ) ) ),file(finset_1,cc2_finset_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_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_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(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(cc5_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_1)).
thf(cc6_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_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(cc9_finset_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_finset_1 @ A ) ) ) ),file(finset_1,cc9_finset_1)).
thf(fc17_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc17_finset_1)).
thf(fc19_finset_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_finset_1 @ A ) ) => ( v1_finset_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(finset_1,fc19_finset_1)).
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(fc31_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v5_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc31_finset_1)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_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_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(finset_1,rc2_finset_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(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc3_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc3_finset_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(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_vectsp_6,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l2_struct_0 @ A ) & ~ ( v2_struct_0 @ B ) & ( l1_vectsp_1 @ B @ A ) & ( m1_vectsp_6 @ C @ A @ B ) ) => ( ( v1_finset_1 @ ( k1_vectsp_6 @ A @ B @ C ) ) & ( m1_subset_1 @ ( k1_vectsp_6 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) ) ) ),file(vectsp_6,k1_vectsp_6)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_l1_vectsp_1,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ! [B: $i] : ( ( l1_vectsp_1 @ B @ A ) => ( l2_algstr_0 @ B ) ) ) ),file(vectsp_1,l1_vectsp_1)).
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_vectsp_6,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l2_struct_0 @ A ) & ~ ( v2_struct_0 @ B ) & ( l1_vectsp_1 @ B @ A ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) ) => ! [D: $i] : ( ( m2_vectsp_6 @ D @ A @ B @ C ) => ( m1_vectsp_6 @ D @ A @ B ) ) ) ),file(vectsp_6,m2_vectsp_6)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_c1_22__vectsp_7,axiom,( ~ ( v2_struct_0 @ c1_22__vectsp_7 ) & ~ ( v6_struct_0 @ c1_22__vectsp_7 ) & ( v13_algstr_0 @ c1_22__vectsp_7 ) & ( v33_algstr_0 @ c1_22__vectsp_7 ) & ( v3_group_1 @ c1_22__vectsp_7 ) & ( v5_group_1 @ c1_22__vectsp_7 ) & ( v4_vectsp_1 @ c1_22__vectsp_7 ) & ( v5_vectsp_1 @ c1_22__vectsp_7 ) & ( v2_rlvect_1 @ c1_22__vectsp_7 ) & ( v3_rlvect_1 @ c1_22__vectsp_7 ) & ( v4_rlvect_1 @ c1_22__vectsp_7 ) & ( l6_algstr_0 @ c1_22__vectsp_7 ) ),file(vectsp_7,c1_22__vectsp_7)).
thf(dt_c1_22_1__vectsp_7,axiom,( $true ),file(vectsp_7,c1_22_1__vectsp_7)).
thf(dt_c1_22_1_2__vectsp_7,axiom,( m2_vectsp_6 @ c1_22_1_2__vectsp_7 @ c1_22__vectsp_7 @ c2_22__vectsp_7 @ c3_22_1__vectsp_7 ),file(vectsp_7,c1_22_1_2__vectsp_7)).
thf(dt_c2_22__vectsp_7,axiom,( ~ ( v2_struct_0 @ c2_22__vectsp_7 ) & ( v13_algstr_0 @ c2_22__vectsp_7 ) & ( v8_vectsp_1 @ c2_22__vectsp_7 @ c1_22__vectsp_7 ) & ( v9_vectsp_1 @ c2_22__vectsp_7 @ c1_22__vectsp_7 ) & ( v10_vectsp_1 @ c2_22__vectsp_7 @ c1_22__vectsp_7 ) & ( v11_vectsp_1 @ c2_22__vectsp_7 @ c1_22__vectsp_7 ) & ( v2_rlvect_1 @ c2_22__vectsp_7 ) & ( v3_rlvect_1 @ c2_22__vectsp_7 ) & ( v4_rlvect_1 @ c2_22__vectsp_7 ) & ( l1_vectsp_1 @ c2_22__vectsp_7 @ c1_22__vectsp_7 ) ),file(vectsp_7,c2_22__vectsp_7)).
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(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(s3_funct_1,axiom,( ! [A: $i > $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( = @ ( k1_funct_1 @ C @ D ) @ ( A @ D ) ) ) ) ),file(funct_1,s3_funct_1)).
thf(e3_22_1_2__vectsp_7,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k1_vectsp_6 @ c1_22__vectsp_7 @ c2_22__vectsp_7 @ c1_22_1_2__vectsp_7 ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k1_vectsp_6 @ c1_22__vectsp_7 @ c2_22__vectsp_7 @ c1_22_1_2__vectsp_7 ) ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( replSep1 @ ^ [C: $i] : ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ c2_22__vectsp_7 ) ) ) @ ^ [C: $i] : C @ ^ [C: $i] : ( ( r2_hidden @ B @ C ) & ( r2_hidden @ C @ c1_22_1__vectsp_7 ) ) ) ) ) ) ),file(vectsp_7,e3_22_1_2__vectsp_7)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
