% Mizar problem: e1_81_1_1,grcat_1,1172,58 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_81_type,type,( c1_81__grcat_1: $i )).
thf(g2_algstr_0_type,type,( g2_algstr_0: $i > $i > $i > $i )).
thf(k18_grcat_1_type,type,( k18_grcat_1: $i > $i )).
thf(k19_grcat_1_type,type,( k19_grcat_1: $i > $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $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(k3_funct_2_type,type,( k3_funct_2: $i > $i > $i > $i > $i )).
thf(k7_grcat_1_type,type,( k7_grcat_1: $i > $i )).
thf(u1_algstr_0_type,type,( u1_algstr_0: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(u2_struct_0_type,type,( u2_struct_0: $i > $i )).
thf(l1_algstr_0_type,type,( l1_algstr_0: $i > $o )).
thf(l1_grcat_1_type,type,( l1_grcat_1: $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(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_grcat_1_type,type,( m2_grcat_1: $i > $i > $o )).
thf(m3_grcat_1_type,type,( m3_grcat_1: $i > $i > $o )).
thf(v10_algstr_0_type,type,( v10_algstr_0: $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_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_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_algstr_0_type,type,( v2_algstr_0: $i > $i > $o )).
thf(v2_algstr_1_type,type,( v2_algstr_1: $i > $o )).
thf(v2_grcat_1_type,type,( v2_grcat_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(v3_algstr_0_type,type,( v3_algstr_0: $i > $i > $o )).
thf(v3_algstr_1_type,type,( v3_algstr_1: $i > $o )).
thf(v3_grcat_1_type,type,( v3_grcat_1: $i > $o )).
thf(v3_rlvect_1_type,type,( v3_rlvect_1: $i > $o )).
thf(v4_algstr_0_type,type,( v4_algstr_0: $i > $i > $o )).
thf(v4_algstr_1_type,type,( v4_algstr_1: $i > $o )).
thf(v4_grcat_1_type,type,( v4_grcat_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(v5_algstr_0_type,type,( v5_algstr_0: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v6_algstr_0_type,type,( v6_algstr_0: $i > $o )).
thf(v7_algstr_0_type,type,( v7_algstr_0: $i > $o )).
thf(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v8_algstr_0_type,type,( v8_algstr_0: $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_0: $i > $o )).
thf(cc2_algstr_0,axiom,( ! [A: $i] : ( ( l1_algstr_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) => ( ( v4_algstr_0 @ B @ A ) => ( ( v2_algstr_0 @ B @ A ) & ( v3_algstr_0 @ B @ A ) ) ) ) ) ),file(algstr_0,cc2_algstr_0)).
thf(rc3_algstr_1,axiom,( ? [A: $i] : ( ( l2_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v5_algstr_0 @ A ) & ( v6_algstr_0 @ A ) & ( v7_algstr_0 @ A ) & ( v8_algstr_0 @ A ) & ( v13_algstr_0 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v1_algstr_1 @ A ) & ( v2_algstr_1 @ A ) & ( v3_algstr_1 @ A ) & ( v4_algstr_1 @ A ) ) ),file(algstr_1,rc3_algstr_1)).
thf(cc11_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v13_struct_0 @ A @ np__1 ) => ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) ) ) ),file(struct_0,cc11_struct_0)).
thf(cc1_algstr_0,axiom,( ! [A: $i] : ( ( l1_algstr_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) => ( ( ( v2_algstr_0 @ B @ A ) & ( v3_algstr_0 @ B @ A ) ) => ( v4_algstr_0 @ B @ A ) ) ) ) ),file(algstr_0,cc1_algstr_0)).
thf(cc4_algstr_0,axiom,( ! [A: $i] : ( ( l1_algstr_0 @ A ) => ( ( v7_algstr_0 @ A ) => ( ( v5_algstr_0 @ A ) & ( v6_algstr_0 @ A ) ) ) ) ),file(algstr_0,cc4_algstr_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(fc7_algstr_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( 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 ) ) => ( ( v7_struct_0 @ ( g2_algstr_0 @ A @ B @ C ) ) & ( v8_algstr_0 @ ( g2_algstr_0 @ A @ B @ C ) ) ) ) ),file(algstr_0,fc7_algstr_0)).
thf(fc8_algstr_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_zfmisc_1 @ A ) & ( 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 ) ) => ( ~ ( v7_struct_0 @ ( g2_algstr_0 @ A @ B @ C ) ) & ( v8_algstr_0 @ ( g2_algstr_0 @ A @ B @ C ) ) ) ) ),file(algstr_0,fc8_algstr_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(rc2_algstr_1,axiom,( ? [A: $i] : ( ( l2_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v5_algstr_0 @ A ) & ( v6_algstr_0 @ A ) & ( v7_algstr_0 @ A ) & ( v8_algstr_0 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( v1_algstr_1 @ A ) & ( v2_algstr_1 @ A ) & ( v3_algstr_1 @ A ) & ( v4_algstr_1 @ A ) ) ),file(algstr_1,rc2_algstr_1)).
thf(rc5_algstr_0,axiom,( ? [A: $i] : ( ( l2_algstr_0 @ A ) & ( v13_struct_0 @ A @ np__1 ) & ( v8_algstr_0 @ A ) ) ),file(algstr_0,rc5_algstr_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_grcat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v3_grcat_1 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ A ) & ~ ( v2_struct_0 @ B ) & ( v5_algstr_0 @ B ) & ( v6_algstr_0 @ B ) & ( v7_algstr_0 @ B ) & ( v8_algstr_0 @ B ) & ( v13_algstr_0 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( v1_algstr_1 @ B ) & ( v2_algstr_1 @ B ) & ( v3_algstr_1 @ B ) & ( v4_algstr_1 @ B ) ) ) ),file(grcat_1,rc6_grcat_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(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_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(cc3_algstr_0,axiom,( ! [A: $i] : ( ( l1_algstr_0 @ A ) => ( ( ( v5_algstr_0 @ A ) & ( v6_algstr_0 @ A ) ) => ( v7_algstr_0 @ A ) ) ) ),file(algstr_0,cc3_algstr_0)).
thf(cc5_algstr_0,axiom,( ! [A: $i] : ( ( ( v5_algstr_0 @ A ) & ( l1_algstr_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) => ( v2_algstr_0 @ B @ A ) ) ) ),file(algstr_0,cc5_algstr_0)).
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_algstr_0,axiom,( ! [A: $i] : ( ( ( v6_algstr_0 @ A ) & ( l1_algstr_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) => ( v3_algstr_0 @ B @ A ) ) ) ),file(algstr_0,cc6_algstr_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(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(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(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_algstr_1,axiom,( ? [A: $i] : ( ( l2_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v8_algstr_0 @ A ) & ( v4_rlvect_1 @ A ) & ( v1_algstr_1 @ A ) & ( v4_algstr_1 @ A ) ) ),file(algstr_1,rc1_algstr_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(free_g2_algstr_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $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 ) ) => ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( = @ ( g2_algstr_0 @ A @ B @ C ) @ ( g2_algstr_0 @ D @ E @ F ) ) => ( ( = @ A @ D ) & ( = @ B @ E ) & ( = @ C @ F ) ) ) ) ),file(algstr_0,g2_algstr_0)).
thf(dt_g2_algstr_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $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 ) ) => ( ( v8_algstr_0 @ ( g2_algstr_0 @ A @ B @ C ) ) & ( l2_algstr_0 @ ( g2_algstr_0 @ A @ B @ C ) ) ) ) ),file(algstr_0,g2_algstr_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_u1_algstr_0,axiom,( ! [A: $i] : ( ( l1_algstr_0 @ A ) => ( ( v1_funct_1 @ ( u1_algstr_0 @ A ) ) & ( v1_funct_2 @ ( u1_algstr_0 @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ ( u1_algstr_0 @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ) ) ) ),file(algstr_0,u1_algstr_0)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_u2_struct_0,axiom,( ! [A: $i] : ( ( l2_struct_0 @ A ) => ( m1_subset_1 @ ( u2_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,u2_struct_0)).
thf(cc12_algstr_0,axiom,( ! [A: $i] : ( ( ( v13_algstr_0 @ A ) & ( l2_algstr_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) => ( v10_algstr_0 @ B @ A ) ) ) ),file(algstr_0,cc12_algstr_0)).
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(fc6_algstr_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( 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 ) ) => ( ~ ( v2_struct_0 @ ( g2_algstr_0 @ A @ B @ C ) ) & ( v8_algstr_0 @ ( g2_algstr_0 @ A @ B @ C ) ) ) ) ),file(algstr_0,fc6_algstr_0)).
thf(rc4_algstr_0,axiom,( ? [A: $i] : ( ( l2_algstr_0 @ A ) & ( v8_algstr_0 @ A ) ) ),file(algstr_0,rc4_algstr_0)).
thf(abstractness_v8_algstr_0,axiom,( ! [A: $i] : ( ( l2_algstr_0 @ A ) => ( ( v8_algstr_0 @ A ) => ( = @ A @ ( g2_algstr_0 @ ( u1_struct_0 @ A ) @ ( u1_algstr_0 @ A ) @ ( u2_struct_0 @ A ) ) ) ) ) ),file(algstr_0,v8_algstr_0)).
thf(redefinition_m2_grcat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v3_grcat_1 @ A ) ) => ! [B: $i] : ( ( m2_grcat_1 @ B @ A ) <=> ( m1_subset_1 @ B @ A ) ) ) ),file(grcat_1,m2_grcat_1)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k7_grcat_1,axiom,( ! [A: $i] : ( ( l1_grcat_1 @ A ) => ( ~ ( v2_struct_0 @ ( k7_grcat_1 @ A ) ) & ( v13_algstr_0 @ ( k7_grcat_1 @ A ) ) & ( v3_rlvect_1 @ ( k7_grcat_1 @ A ) ) & ( v4_rlvect_1 @ ( k7_grcat_1 @ A ) ) & ( l2_algstr_0 @ ( k7_grcat_1 @ A ) ) ) ) ),file(grcat_1,k7_grcat_1)).
thf(dt_l1_grcat_1,axiom,( $true ),file(grcat_1,l1_grcat_1)).
thf(dt_m2_grcat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v3_grcat_1 @ A ) ) => ! [B: $i] : ( ( m2_grcat_1 @ B @ A ) => ( ~ ( v2_struct_0 @ B ) & ( v13_algstr_0 @ B ) & ( v3_rlvect_1 @ B ) & ( v4_rlvect_1 @ B ) & ( l2_algstr_0 @ B ) ) ) ) ),file(grcat_1,m2_grcat_1)).
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(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(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(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(rc7_grcat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_grcat_1 @ A ) ) ),file(grcat_1,rc7_grcat_1)).
thf(redefinition_k19_grcat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v3_grcat_1 @ A ) & ( m1_subset_1 @ B @ ( k18_grcat_1 @ A ) ) ) => ( = @ ( k19_grcat_1 @ A @ B ) @ ( k7_grcat_1 @ B ) ) ) ),file(grcat_1,k19_grcat_1)).
thf(redefinition_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ),file(funct_2,k3_funct_2)).
thf(redefinition_m3_grcat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v4_grcat_1 @ A ) ) => ! [B: $i] : ( ( m3_grcat_1 @ B @ A ) <=> ( m1_subset_1 @ B @ A ) ) ) ),file(grcat_1,m3_grcat_1)).
thf(dt_k18_grcat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v3_grcat_1 @ A ) ) => ( ~ ( v1_xboole_0 @ ( k18_grcat_1 @ A ) ) & ( v4_grcat_1 @ ( k18_grcat_1 @ A ) ) ) ) ),file(grcat_1,k18_grcat_1)).
thf(dt_k19_grcat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v3_grcat_1 @ A ) & ( m1_subset_1 @ B @ ( k18_grcat_1 @ A ) ) ) => ( ( v8_algstr_0 @ ( k19_grcat_1 @ A @ B ) ) & ( m2_grcat_1 @ ( k19_grcat_1 @ A @ B ) @ A ) ) ) ),file(grcat_1,k19_grcat_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_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ B ) ) ),file(funct_2,k3_funct_2)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_m3_grcat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v4_grcat_1 @ A ) ) => ! [B: $i] : ( ( m3_grcat_1 @ B @ A ) => ( ( v2_grcat_1 @ B ) & ( l1_grcat_1 @ B ) ) ) ) ),file(grcat_1,m3_grcat_1)).
thf(dt_c1_81__grcat_1,axiom,( ~ ( v1_xboole_0 @ c1_81__grcat_1 ) & ( v3_grcat_1 @ c1_81__grcat_1 ) ),file(grcat_1,c1_81__grcat_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(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_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_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_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_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_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_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(rc5_grcat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v3_grcat_1 @ A ) ) ),file(grcat_1,rc5_grcat_1)).
thf(s4_funct_2,axiom,( ! [A: $i > $i] : ! [B: $i] : ! [C: $i] : ? [D: $i] : ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ C @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ C @ B ) ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ C ) => ( = @ ( k3_funct_2 @ C @ B @ D @ E ) @ ( A @ E ) ) ) ) ),file(funct_2,s4_funct_2)).
thf(e1_81_1_1__grcat_1,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ ( k18_grcat_1 @ c1_81__grcat_1 ) @ c1_81__grcat_1 ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k18_grcat_1 @ c1_81__grcat_1 ) @ c1_81__grcat_1 ) ) ) & ! [B: $i] : ( ( m3_grcat_1 @ B @ ( k18_grcat_1 @ c1_81__grcat_1 ) ) => ( = @ ( k3_funct_2 @ ( k18_grcat_1 @ c1_81__grcat_1 ) @ c1_81__grcat_1 @ A @ B ) @ ( k19_grcat_1 @ c1_81__grcat_1 @ B ) ) ) ) ),file(grcat_1,e1_81_1_1__grcat_1)).
