% Mizar problem: e1_26_1_2,nat_lat,376,29 
include('Axioms/SET010^0.ax').
thf(k1_binop_1_type,type,( k1_binop_1: $i > $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $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_int_2_type,type,( k3_int_2: $i > $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k5_binop_1_type,type,( k5_binop_1: $i > $i > $i > $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_nat_d_type,type,( k6_nat_d: $i > $i > $i )).
thf(k6_nat_lat_type,type,( k6_nat_lat: $i )).
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(r8_binop_1_type,type,( r8_binop_1: $i > $i > $i > $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_int_1_type,type,( v1_int_1: $i > $o )).
thf(v1_membered_type,type,( v1_membered: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_rat_1_type,type,( v1_rat_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_xcmplx_0_type,type,( v1_xcmplx_0: $i > $o )).
thf(v1_xreal_0_type,type,( v1_xreal_0: $i > $o )).
thf(v1_xxreal_0_type,type,( v1_xxreal_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_membered_type,type,( v2_membered: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v3_membered_type,type,( v3_membered: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v4_membered_type,type,( v4_membered: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_finset_1_type,type,( v5_finset_1: $i > $o )).
thf(v5_membered_type,type,( v5_membered: $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v6_membered_type,type,( v6_membered: $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v7_membered_type,type,( v7_membered: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(cc12_membered,axiom,( ! [A: $i] : ( ( v1_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xcmplx_0 @ B ) ) ) ),file(membered,cc12_membered)).
thf(cc13_membered,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xxreal_0 @ B ) ) ) ),file(membered,cc13_membered)).
thf(cc15_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_rat_1 @ B ) ) ) ),file(membered,cc15_membered)).
thf(cc19_membered,axiom,( ! [A: $i] : ( ( v1_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_membered @ B ) ) ) ),file(membered,cc19_membered)).
thf(cc20_membered,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v2_membered @ B ) ) ) ),file(membered,cc20_membered)).
thf(cc22_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_membered @ B ) ) ) ),file(membered,cc22_membered)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc3_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ( v3_membered @ A ) ) ),file(membered,cc3_membered)).
thf(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_1)).
thf(rc2_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) ) ),file(ordinal1,rc2_ordinal1)).
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(cc10_ordinal1,axiom,( ! [A: $i] : ( ( v6_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v6_ordinal1 @ B ) ) ) ),file(ordinal1,cc10_ordinal1)).
thf(cc14_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xreal_0 @ B ) ) ) ),file(membered,cc14_membered)).
thf(cc16_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_int_1 @ B ) ) ) ),file(membered,cc16_membered)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc21_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v3_membered @ B ) ) ) ),file(membered,cc21_membered)).
thf(cc23_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_membered @ B ) ) ) ),file(membered,cc23_membered)).
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_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ( v4_membered @ A ) ) ),file(membered,cc2_membered)).
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(cc4_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v2_membered @ A ) ) ),file(membered,cc4_membered)).
thf(cc5_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_1)).
thf(cc5_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v1_membered @ A ) ) ),file(membered,cc5_membered)).
thf(cc5_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal1,cc5_ordinal1)).
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(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(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(fc17_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc17_finset_1)).
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_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
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(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(rc3_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) & ( v7_membered @ A ) ) ),file(membered,rc3_membered)).
thf(rc3_ordinal1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v5_ordinal1 @ B ) ) ),file(ordinal1,rc3_ordinal1)).
thf(rc4_xreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc4_xreal_0)).
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(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(commutativity_k3_int_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ( v1_int_1 @ B ) ) => ( = @ ( k3_int_2 @ A @ B ) @ ( k3_int_2 @ B @ A ) ) ) ),file(int_2,k3_int_2)).
thf(dt_k1_binop_1,axiom,( $true ),file(binop_1,k1_binop_1)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k3_int_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ( v1_int_1 @ B ) ) => ( v7_ordinal1 @ ( k3_int_2 @ A @ B ) ) ) ),file(int_2,k3_int_2)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(cc17_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v7_ordinal1 @ B ) ) ) ),file(membered,cc17_membered)).
thf(cc18_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_membered @ A ) ) ),file(membered,cc18_membered)).
thf(cc1_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc1_finset_1)).
thf(cc1_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ( v5_membered @ A ) ) ),file(membered,cc1_membered)).
thf(cc1_nat_lat,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xreal_0 @ B ) ) ) ),file(nat_lat,cc1_nat_lat)).
thf(cc1_xreal_0,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc1_xreal_0)).
thf(cc24_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v6_membered @ B ) ) ) ),file(membered,cc24_membered)).
thf(cc26_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_membered @ A ) ) ),file(membered,cc26_membered)).
thf(cc2_xreal_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc2_xreal_0)).
thf(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
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_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xcmplx_0 @ A ) ) ),file(xreal_0,cc3_xreal_0)).
thf(cc4_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
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_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xreal_0,cc4_xreal_0)).
thf(cc6_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(cc7_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
thf(cc8_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) ) => ( v3_membered @ A ) ) ),file(membered,cc8_membered)).
thf(cc8_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
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(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(fc3_membered,axiom,( v3_membered @ k1_numbers ),file(membered,fc3_membered)).
thf(fc56_membered,axiom,( v7_membered @ k1_numbers ),file(membered,fc56_membered)).
thf(fc59_membered,axiom,( v7_membered @ k4_ordinal1 ),file(membered,fc59_membered)).
thf(fc6_membered,axiom,( v6_membered @ k4_ordinal1 ),file(membered,fc6_membered)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
thf(rc1_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc1_membered)).
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_xreal_0,axiom,( ? [A: $i] : ( v1_xreal_0 @ A ) ),file(xreal_0,rc1_xreal_0)).
thf(rc2_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc2_membered)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(commutativity_k6_nat_d,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( v7_ordinal1 @ B ) ) => ( = @ ( k6_nat_d @ A @ B ) @ ( k6_nat_d @ B @ A ) ) ) ),file(nat_d,k6_nat_d)).
thf(symmetry_r8_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( 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 ) ) ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) ) => ( ( r8_binop_1 @ A @ B @ C @ D @ E ) => ( r8_binop_1 @ A @ B @ C @ E @ D ) ) ) ),file(binop_1,r8_binop_1)).
thf(reflexivity_r8_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( 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 ) ) ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) ) => ( r8_binop_1 @ A @ B @ C @ D @ D ) ) ),file(binop_1,r8_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_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
thf(redefinition_k6_nat_d,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( v7_ordinal1 @ B ) ) => ( = @ ( k6_nat_d @ A @ B ) @ ( k3_int_2 @ A @ B ) ) ) ),file(nat_d,k6_nat_d)).
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(redefinition_r8_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( 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 ) ) ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) ) => ( ( r8_binop_1 @ A @ B @ C @ D @ E ) <=> ( = @ D @ E ) ) ) ),file(binop_1,r8_binop_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_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_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_k6_nat_d,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( v7_ordinal1 @ B ) ) => ( m1_subset_1 @ ( k6_nat_d @ A @ B ) @ k5_numbers ) ) ),file(nat_d,k6_nat_d)).
thf(dt_k6_nat_lat,axiom,( m1_subset_1 @ k6_nat_lat @ ( k1_zfmisc_1 @ k5_numbers ) ),file(nat_lat,k6_nat_lat)).
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(cc11_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k5_numbers ) ) => ( v6_membered @ A ) ) ),file(membered,cc11_membered)).
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(cc25_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ( v6_membered @ A ) ) ),file(membered,cc25_membered)).
thf(cc2_nat_lat,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k5_numbers ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xreal_0 @ B ) ) ) ),file(nat_lat,cc2_nat_lat)).
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_nat_lat,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k6_nat_lat ) => ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ) ),file(nat_lat,cc3_nat_lat)).
thf(fc5_nat_lat,axiom,( ~ ( v1_xboole_0 @ k6_nat_lat ) ),file(nat_lat,fc5_nat_lat)).
thf(s2_binop_2,axiom,( ! [A: $i > $i > $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) ) => ! [D: $i] : ( ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) ) => ( ( ! [E: $i] : ( ( m1_subset_1 @ E @ B ) => ! [F: $i] : ( ( m1_subset_1 @ F @ B ) => ( = @ ( k5_binop_1 @ B @ C @ E @ F ) @ ( A @ E @ F ) ) ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ B ) => ! [F: $i] : ( ( m1_subset_1 @ F @ B ) => ( = @ ( k5_binop_1 @ B @ D @ E @ F ) @ ( A @ E @ F ) ) ) ) ) => ( r8_binop_1 @ B @ B @ B @ C @ D ) ) ) ) ),file(binop_2,s2_binop_2)).
thf(e1_26_1_2__nat_lat,conjecture,( ! [A: $i] : ( ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k6_nat_lat @ k6_nat_lat ) @ k6_nat_lat ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ k6_nat_lat @ k6_nat_lat ) @ k6_nat_lat ) ) ) ) => ! [B: $i] : ( ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ k6_nat_lat @ k6_nat_lat ) @ k6_nat_lat ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ k6_nat_lat @ k6_nat_lat ) @ k6_nat_lat ) ) ) ) => ( ( ! [C: $i] : ( ( m2_subset_1 @ C @ k5_numbers @ k6_nat_lat ) => ! [D: $i] : ( ( m2_subset_1 @ D @ k5_numbers @ k6_nat_lat ) => ( = @ ( k5_binop_1 @ k6_nat_lat @ A @ C @ D ) @ ( k6_nat_d @ C @ D ) ) ) ) & ! [C: $i] : ( ( m2_subset_1 @ C @ k5_numbers @ k6_nat_lat ) => ! [D: $i] : ( ( m2_subset_1 @ D @ k5_numbers @ k6_nat_lat ) => ( = @ ( k5_binop_1 @ k6_nat_lat @ B @ C @ D ) @ ( k6_nat_d @ C @ D ) ) ) ) ) => ( = @ A @ B ) ) ) ) ),file(nat_lat,e1_26_1_2__nat_lat)).
