% Mizar problem: e2_67_1_1,ringcat1,1156,68 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_67_type,type,( c1_67__ringcat1: $i )).
thf(g1_ringcat1_type,type,( g1_ringcat1: $i > $i > $i > $i )).
thf(k10_ringcat1_type,type,( k10_ringcat1: $i > $i )).
thf(k11_ringcat1_type,type,( k11_ringcat1: $i > $i > $i )).
thf(k12_ringcat1_type,type,( k12_ringcat1: $i > $i > $i )).
thf(k1_binop_1_type,type,( k1_binop_1: $i > $i > $i > $i )).
thf(k1_relset_1_type,type,( k1_relset_1: $i > $i > $i )).
thf(k1_ringcat1_type,type,( k1_ringcat1: $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_ringcat1_type,type,( k2_ringcat1: $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(k6_ringcat1_type,type,( k6_ringcat1: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(u1_ringcat1_type,type,( u1_ringcat1: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(u2_ringcat1_type,type,( u2_ringcat1: $i > $i )).
thf(u3_ringcat1_type,type,( u3_ringcat1: $i > $i )).
thf(l1_algstr_0_type,type,( l1_algstr_0: $i > $o )).
thf(l1_ringcat1_type,type,( l1_ringcat1: $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_ringcat1_type,type,( m2_ringcat1: $i > $i > $o )).
thf(m3_ringcat1_type,type,( m3_ringcat1: $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_partfun1_type,type,( v1_partfun1: $i > $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $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_xtuple_0_type,type,( v1_xtuple_0: $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_ringcat1_type,type,( v2_ringcat1: $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_group_1_type,type,( v3_group_1: $i > $o )).
thf(v3_ringcat1_type,type,( v3_ringcat1: $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_ringcat1_type,type,( v4_ringcat1: $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_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v5_ringcat1_type,type,( v5_ringcat1: $i > $o )).
thf(v5_vectsp_1_type,type,( v5_vectsp_1: $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(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(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(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(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(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(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_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_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(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_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_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(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(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(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
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_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(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(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(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(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(free_g1_ringcat1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v3_group_1 @ A ) & ( v4_vectsp_1 @ A ) & ( v5_vectsp_1 @ A ) & ( l6_algstr_0 @ A ) & ~ ( v2_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v2_rlvect_1 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( v3_group_1 @ B ) & ( v4_vectsp_1 @ B ) & ( v5_vectsp_1 @ B ) & ( l6_algstr_0 @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ) => ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( = @ ( g1_ringcat1 @ A @ B @ C ) @ ( g1_ringcat1 @ D @ E @ F ) ) => ( ( = @ A @ D ) & ( = @ B @ E ) & ( = @ C @ F ) ) ) ) ),file(ringcat1,g1_ringcat1)).
thf(dt_g1_ringcat1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v3_group_1 @ A ) & ( v4_vectsp_1 @ A ) & ( v5_vectsp_1 @ A ) & ( l6_algstr_0 @ A ) & ~ ( v2_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v2_rlvect_1 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( v3_group_1 @ B ) & ( v4_vectsp_1 @ B ) & ( v5_vectsp_1 @ B ) & ( l6_algstr_0 @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ) => ( ( v2_ringcat1 @ ( g1_ringcat1 @ A @ B @ C ) ) & ( l1_ringcat1 @ ( g1_ringcat1 @ A @ B @ C ) ) ) ) ),file(ringcat1,g1_ringcat1)).
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_u1_ringcat1,axiom,( ! [A: $i] : ( ( l1_ringcat1 @ A ) => ( ~ ( v2_struct_0 @ ( u1_ringcat1 @ A ) ) & ( v13_algstr_0 @ ( u1_ringcat1 @ A ) ) & ( v2_rlvect_1 @ ( u1_ringcat1 @ A ) ) & ( v3_rlvect_1 @ ( u1_ringcat1 @ A ) ) & ( v4_rlvect_1 @ ( u1_ringcat1 @ A ) ) & ( v3_group_1 @ ( u1_ringcat1 @ A ) ) & ( v4_vectsp_1 @ ( u1_ringcat1 @ A ) ) & ( v5_vectsp_1 @ ( u1_ringcat1 @ A ) ) & ( l6_algstr_0 @ ( u1_ringcat1 @ A ) ) ) ) ),file(ringcat1,u1_ringcat1)).
thf(dt_u2_ringcat1,axiom,( ! [A: $i] : ( ( l1_ringcat1 @ A ) => ( ~ ( v2_struct_0 @ ( u2_ringcat1 @ A ) ) & ( v13_algstr_0 @ ( u2_ringcat1 @ A ) ) & ( v2_rlvect_1 @ ( u2_ringcat1 @ A ) ) & ( v3_rlvect_1 @ ( u2_ringcat1 @ A ) ) & ( v4_rlvect_1 @ ( u2_ringcat1 @ A ) ) & ( v3_group_1 @ ( u2_ringcat1 @ A ) ) & ( v4_vectsp_1 @ ( u2_ringcat1 @ A ) ) & ( v5_vectsp_1 @ ( u2_ringcat1 @ A ) ) & ( l6_algstr_0 @ ( u2_ringcat1 @ A ) ) ) ) ),file(ringcat1,u2_ringcat1)).
thf(dt_u3_ringcat1,axiom,( ! [A: $i] : ( ( l1_ringcat1 @ A ) => ( ( v1_funct_1 @ ( u3_ringcat1 @ A ) ) & ( v1_funct_2 @ ( u3_ringcat1 @ A ) @ ( u1_struct_0 @ ( u1_ringcat1 @ A ) ) @ ( u1_struct_0 @ ( u2_ringcat1 @ A ) ) ) & ( m1_subset_1 @ ( u3_ringcat1 @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ ( u1_ringcat1 @ A ) ) @ ( u1_struct_0 @ ( u2_ringcat1 @ A ) ) ) ) ) ) ) ),file(ringcat1,u3_ringcat1)).
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(abstractness_v2_ringcat1,axiom,( ! [A: $i] : ( ( l1_ringcat1 @ A ) => ( ( v2_ringcat1 @ A ) => ( = @ A @ ( g1_ringcat1 @ ( u1_ringcat1 @ A ) @ ( u2_ringcat1 @ A ) @ ( u3_ringcat1 @ A ) ) ) ) ) ),file(ringcat1,v2_ringcat1)).
thf(redefinition_m2_ringcat1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v4_ringcat1 @ A ) ) => ! [B: $i] : ( ( m2_ringcat1 @ B @ A ) <=> ( m1_subset_1 @ B @ A ) ) ) ),file(ringcat1,m2_ringcat1)).
thf(dt_k1_ringcat1,axiom,( ! [A: $i] : ( ( l1_ringcat1 @ A ) => ( ~ ( v2_struct_0 @ ( k1_ringcat1 @ A ) ) & ( v13_algstr_0 @ ( k1_ringcat1 @ A ) ) & ( v2_rlvect_1 @ ( k1_ringcat1 @ A ) ) & ( v3_rlvect_1 @ ( k1_ringcat1 @ A ) ) & ( v4_rlvect_1 @ ( k1_ringcat1 @ A ) ) & ( v3_group_1 @ ( k1_ringcat1 @ A ) ) & ( v4_vectsp_1 @ ( k1_ringcat1 @ A ) ) & ( v5_vectsp_1 @ ( k1_ringcat1 @ A ) ) & ( l6_algstr_0 @ ( k1_ringcat1 @ A ) ) ) ) ),file(ringcat1,k1_ringcat1)).
thf(dt_k2_ringcat1,axiom,( ! [A: $i] : ( ( l1_ringcat1 @ A ) => ( ~ ( v2_struct_0 @ ( k2_ringcat1 @ A ) ) & ( v13_algstr_0 @ ( k2_ringcat1 @ A ) ) & ( v2_rlvect_1 @ ( k2_ringcat1 @ A ) ) & ( v3_rlvect_1 @ ( k2_ringcat1 @ A ) ) & ( v4_rlvect_1 @ ( k2_ringcat1 @ A ) ) & ( v3_group_1 @ ( k2_ringcat1 @ A ) ) & ( v4_vectsp_1 @ ( k2_ringcat1 @ A ) ) & ( v5_vectsp_1 @ ( k2_ringcat1 @ A ) ) & ( l6_algstr_0 @ ( k2_ringcat1 @ A ) ) ) ) ),file(ringcat1,k2_ringcat1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_l1_ringcat1,axiom,( $true ),file(ringcat1,l1_ringcat1)).
thf(dt_m2_ringcat1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v4_ringcat1 @ A ) ) => ! [B: $i] : ( ( m2_ringcat1 @ B @ A ) => ( ~ ( v2_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v2_rlvect_1 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( v3_group_1 @ B ) & ( v4_vectsp_1 @ B ) & ( v5_vectsp_1 @ B ) & ( l6_algstr_0 @ B ) ) ) ) ),file(ringcat1,m2_ringcat1)).
thf(fc4_xtuple_0,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(xtuple_0,fc4_xtuple_0)).
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(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_ringcat1,axiom,( ? [A: $i] : ( ( l1_ringcat1 @ A ) & ( v2_ringcat1 @ A ) ) ),file(ringcat1,rc1_ringcat1)).
thf(rc1_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_0)).
thf(rc2_ringcat1,axiom,( ? [A: $i] : ( ( l1_ringcat1 @ A ) & ( v2_ringcat1 @ A ) & ( v3_ringcat1 @ A ) ) ),file(ringcat1,rc2_ringcat1)).
thf(rc6_ringcat1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v5_ringcat1 @ A ) ) ),file(ringcat1,rc6_ringcat1)).
thf(rc7_ringcat1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v5_ringcat1 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ A ) & ( v2_ringcat1 @ B ) & ( v3_ringcat1 @ B ) ) ) ),file(ringcat1,rc7_ringcat1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k11_ringcat1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v4_ringcat1 @ A ) & ( m1_subset_1 @ B @ ( k10_ringcat1 @ A ) ) ) => ( = @ ( k11_ringcat1 @ A @ B ) @ ( k1_ringcat1 @ B ) ) ) ),file(ringcat1,k11_ringcat1)).
thf(redefinition_k12_ringcat1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v4_ringcat1 @ A ) & ( m1_subset_1 @ B @ ( k10_ringcat1 @ A ) ) ) => ( = @ ( k12_ringcat1 @ A @ B ) @ ( k2_ringcat1 @ B ) ) ) ),file(ringcat1,k12_ringcat1)).
thf(redefinition_k1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( = @ ( k1_relset_1 @ A @ B ) @ ( k9_xtuple_0 @ B ) ) ) ),file(relset_1,k1_relset_1)).
thf(redefinition_m3_ringcat1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v5_ringcat1 @ A ) ) => ! [B: $i] : ( ( m3_ringcat1 @ B @ A ) <=> ( m1_subset_1 @ B @ A ) ) ) ),file(ringcat1,m3_ringcat1)).
thf(dt_k10_ringcat1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v4_ringcat1 @ A ) ) => ( ~ ( v1_xboole_0 @ ( k10_ringcat1 @ A ) ) & ( v5_ringcat1 @ ( k10_ringcat1 @ A ) ) ) ) ),file(ringcat1,k10_ringcat1)).
thf(dt_k11_ringcat1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v4_ringcat1 @ A ) & ( m1_subset_1 @ B @ ( k10_ringcat1 @ A ) ) ) => ( m2_ringcat1 @ ( k11_ringcat1 @ A @ B ) @ A ) ) ),file(ringcat1,k11_ringcat1)).
thf(dt_k12_ringcat1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v4_ringcat1 @ A ) & ( m1_subset_1 @ B @ ( k10_ringcat1 @ A ) ) ) => ( m2_ringcat1 @ ( k12_ringcat1 @ A @ B ) @ A ) ) ),file(ringcat1,k12_ringcat1)).
thf(dt_k1_binop_1,axiom,( $true ),file(binop_1,k1_binop_1)).
thf(dt_k1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( m1_subset_1 @ ( k1_relset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(relset_1,k1_relset_1)).
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_k6_ringcat1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ringcat1 @ A ) & ( l1_ringcat1 @ A ) & ( v3_ringcat1 @ B ) & ( l1_ringcat1 @ B ) ) => ( ( v2_ringcat1 @ ( k6_ringcat1 @ A @ B ) ) & ( v3_ringcat1 @ ( k6_ringcat1 @ A @ B ) ) & ( l1_ringcat1 @ ( k6_ringcat1 @ A @ B ) ) ) ) ),file(ringcat1,k6_ringcat1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_m3_ringcat1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v5_ringcat1 @ A ) ) => ! [B: $i] : ( ( m3_ringcat1 @ B @ A ) => ( ( v3_ringcat1 @ B ) & ( l1_ringcat1 @ B ) ) ) ) ),file(ringcat1,m3_ringcat1)).
thf(dt_c1_67__ringcat1,axiom,( ~ ( v1_xboole_0 @ c1_67__ringcat1 ) & ( v4_ringcat1 @ c1_67__ringcat1 ) ),file(ringcat1,c1_67__ringcat1)).
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_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(fc1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( v1_xtuple_0 @ ( k4_tarski @ A @ B ) ) ),file(xtuple_0,fc1_xtuple_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(rc4_ringcat1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_ringcat1 @ A ) ) ),file(ringcat1,rc4_ringcat1)).
thf(e1_67_1_1__ringcat1,axiom,( ! [A: $i] : ( ( m3_ringcat1 @ A @ ( k10_ringcat1 @ c1_67__ringcat1 ) ) => ! [B: $i] : ( ( m3_ringcat1 @ B @ ( k10_ringcat1 @ c1_67__ringcat1 ) ) => ( ( = @ ( k11_ringcat1 @ c1_67__ringcat1 @ A ) @ ( k12_ringcat1 @ c1_67__ringcat1 @ B ) ) => ( r2_hidden @ ( k6_ringcat1 @ A @ B ) @ ( k10_ringcat1 @ c1_67__ringcat1 ) ) ) ) ) ),file(ringcat1,e1_67_1_1__ringcat1)).
thf(s8_binop_1,axiom,( ! [A: $i] : ! [B: $i > $i > $i] : ! [C: $i > $i > $o] : ! [D: $i] : ! [E: $i] : ( ! [F: $i] : ( ( m1_subset_1 @ F @ E ) => ! [G: $i] : ( ( m1_subset_1 @ G @ D ) => ( ( C @ F @ G ) => ( r2_hidden @ ( B @ F @ G ) @ A ) ) ) ) => ? [F: $i] : ( ( v1_funct_1 @ F ) & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ E @ D ) @ A ) ) ) & ! [G: $i] : ( ( m1_subset_1 @ G @ E ) => ! [H: $i] : ( ( m1_subset_1 @ H @ D ) => ( ( r2_hidden @ ( k4_tarski @ G @ H ) @ ( k1_relset_1 @ ( k2_zfmisc_1 @ E @ D ) @ F ) ) <=> ( C @ G @ H ) ) ) ) & ! [G: $i] : ( ( m1_subset_1 @ G @ E ) => ! [H: $i] : ( ( m1_subset_1 @ H @ D ) => ( ( r2_hidden @ ( k4_tarski @ G @ H ) @ ( k1_relset_1 @ ( k2_zfmisc_1 @ E @ D ) @ F ) ) => ( = @ ( k1_binop_1 @ F @ G @ H ) @ ( B @ G @ H ) ) ) ) ) ) ) ),file(binop_1,s8_binop_1)).
thf(e2_67_1_1__ringcat1,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( k10_ringcat1 @ c1_67__ringcat1 ) @ ( k10_ringcat1 @ c1_67__ringcat1 ) ) @ ( k10_ringcat1 @ c1_67__ringcat1 ) ) ) ) & ! [B: $i] : ( ( m3_ringcat1 @ B @ ( k10_ringcat1 @ c1_67__ringcat1 ) ) => ! [C: $i] : ( ( m3_ringcat1 @ C @ ( k10_ringcat1 @ c1_67__ringcat1 ) ) => ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( k1_relset_1 @ ( k2_zfmisc_1 @ ( k10_ringcat1 @ c1_67__ringcat1 ) @ ( k10_ringcat1 @ c1_67__ringcat1 ) ) @ A ) ) <=> ( = @ ( k11_ringcat1 @ c1_67__ringcat1 @ B ) @ ( k12_ringcat1 @ c1_67__ringcat1 @ C ) ) ) ) ) & ! [B: $i] : ( ( m3_ringcat1 @ B @ ( k10_ringcat1 @ c1_67__ringcat1 ) ) => ! [C: $i] : ( ( m3_ringcat1 @ C @ ( k10_ringcat1 @ c1_67__ringcat1 ) ) => ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( k1_relset_1 @ ( k2_zfmisc_1 @ ( k10_ringcat1 @ c1_67__ringcat1 ) @ ( k10_ringcat1 @ c1_67__ringcat1 ) ) @ A ) ) => ( = @ ( k1_binop_1 @ A @ B @ C ) @ ( k6_ringcat1 @ B @ C ) ) ) ) ) ) ),file(ringcat1,e2_67_1_1__ringcat1)).
