% Mizar problem: s2_seq_1,seq_1,181,14 
include('Axioms/SET010^0.ax').
thf(f1_s2_seq_1_type,type,( f1_s2_seq_1: $i )).
thf(f2_s2_seq_1_type,type,( f2_s2_seq_1: $i )).
thf(k10_xtuple_0_type,type,( k10_xtuple_0: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_relset_1_type,type,( k1_relset_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_partfun1_type,type,( k2_partfun1: $i > $i > $i > $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(k3_numbers_type,type,( k3_numbers: $i )).
thf(k3_xboole_0_type,type,( k3_xboole_0: $i > $i > $i )).
thf(k4_numbers_type,type,( k4_numbers: $i )).
thf(k5_relat_1_type,type,( k5_relat_1: $i > $i > $i )).
thf(k9_subset_1_type,type,( k9_subset_1: $i > $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(p1_s2_seq_1_type,type,( p1_s2_seq_1: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $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_partfun1_type,type,( v1_partfun1: $i > $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_valued_0_type,type,( v1_valued_0: $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(v2_membered_type,type,( v2_membered: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_valued_0_type,type,( v2_valued_0: $i > $o )).
thf(v3_membered_type,type,( v3_membered: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_valued_0_type,type,( v3_valued_0: $i > $o )).
thf(v4_membered_type,type,( v4_membered: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v4_valued_0_type,type,( v4_valued_0: $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(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(cc10_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k4_numbers ) ) => ( v5_membered @ A ) ) ),file(membered,cc10_membered)).
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(cc10_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_valued_0 @ B ) ) ) ),file(valued_0,cc10_valued_0)).
thf(cc11_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v2_valued_0 @ B ) ) ) ),file(valued_0,cc11_valued_0)).
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(cc12_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v3_valued_0 @ B ) ) ) ),file(valued_0,cc12_valued_0)).
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(cc13_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_relat_1 @ B @ k3_numbers ) ) ) ),file(valued_0,cc13_valued_0)).
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(cc14_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_relat_1 @ B @ k4_numbers ) ) ) ),file(valued_0,cc14_valued_0)).
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(cc15_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_valued_0 @ B ) ) ) ),file(valued_0,cc15_valued_0)).
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(cc16_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_membered @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_valued_0 @ C ) ) ) ),file(valued_0,cc16_valued_0)).
thf(cc17_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v7_ordinal1 @ B ) ) ) ),file(membered,cc17_membered)).
thf(cc17_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v2_membered @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v2_valued_0 @ C ) ) ) ),file(valued_0,cc17_valued_0)).
thf(cc18_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_membered @ A ) ) ),file(membered,cc18_membered)).
thf(cc18_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v3_membered @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v3_valued_0 @ C ) ) ) ),file(valued_0,cc18_valued_0)).
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(cc19_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v4_membered @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v5_relat_1 @ C @ k3_numbers ) ) ) ),file(valued_0,cc19_valued_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_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ( v5_membered @ A ) ) ),file(membered,cc1_membered)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
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_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) ) ),file(valued_0,cc1_valued_0)).
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(cc20_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v5_membered @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v5_relat_1 @ C @ k4_numbers ) ) ) ),file(valued_0,cc20_valued_0)).
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(cc21_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v6_membered @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v4_valued_0 @ C ) ) ) ),file(valued_0,cc21_valued_0)).
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(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(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_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_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ( v4_membered @ A ) ) ),file(membered,cc2_membered)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
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(cc2_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) ) ),file(valued_0,cc2_valued_0)).
thf(cc2_xreal_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc2_xreal_0)).
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_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ( v3_membered @ A ) ) ),file(membered,cc3_membered)).
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_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc3_valued_0)).
thf(cc3_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xcmplx_0 @ A ) ) ),file(xreal_0,cc3_xreal_0)).
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_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v2_membered @ A ) ) ),file(membered,cc4_membered)).
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_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc4_valued_0)).
thf(cc4_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xreal_0,cc4_xreal_0)).
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(cc5_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_valued_0 @ A ) ) ) ),file(valued_0,cc5_valued_0)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(cc6_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_valued_0 @ A ) ) ) ),file(valued_0,cc6_valued_0)).
thf(cc7_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
thf(cc7_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) ) ),file(valued_0,cc7_valued_0)).
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(cc8_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc8_valued_0)).
thf(cc9_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k3_numbers ) ) => ( v4_membered @ A ) ) ),file(membered,cc9_membered)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(cc9_valued_0,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) ) ),file(valued_0,cc9_valued_0)).
thf(commutativity_k3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ A ) ) ),file(xboole_0,k3_xboole_0)).
thf(commutativity_k9_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) => ( = @ ( k9_subset_1 @ A @ B @ C ) @ ( k9_subset_1 @ A @ C @ B ) ) ) ),file(subset_1,k9_subset_1)).
thf(d1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ~ ( = @ B @ k1_xboole_0 ) => ( ( v1_funct_2 @ C @ A @ B ) <=> ( = @ A @ ( k1_relset_1 @ A @ C ) ) ) ) & ( ( = @ B @ k1_xboole_0 ) => ( ( v1_funct_2 @ C @ A @ B ) <=> ( = @ C @ k1_xboole_0 ) ) ) ) ) ),file(funct_2,d1_funct_2)).
thf(d3_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( ( r1_tarski @ A @ B ) <=> ! [C: $i] : ( ( r2_hidden @ C @ A ) => ( r2_hidden @ C @ B ) ) ) ),file(tarski,d3_tarski)).
thf(d4_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( = @ C @ ( k3_xboole_0 @ A @ B ) ) <=> ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( ( r2_hidden @ D @ A ) & ( r2_hidden @ D @ B ) ) ) ) ),file(xboole_0,d4_xboole_0)).
thf(dt_f1_s2_seq_1,axiom,( ~ ( v1_xboole_0 @ f1_s2_seq_1 ) ),file(seq_1,f1_s2_seq_1)).
thf(dt_f2_s2_seq_1,axiom,( ~ ( v1_xboole_0 @ f2_s2_seq_1 ) ),file(seq_1,f2_s2_seq_1)).
thf(dt_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_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_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ C ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ C @ D ) ) & ( m1_subset_1 @ ( k2_partfun1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ),file(partfun1,k2_partfun1)).
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_k3_numbers,axiom,( $true ),file(numbers,k3_numbers)).
thf(dt_k3_xboole_0,axiom,( $true ),file(xboole_0,k3_xboole_0)).
thf(dt_k4_numbers,axiom,( $true ),file(numbers,k4_numbers)).
thf(dt_k5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ),file(relat_1,k5_relat_1)).
thf(dt_k9_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) => ( m1_subset_1 @ ( k9_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(subset_1,k9_subset_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(existence_m1_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( m1_subset_1 @ B @ A ) ),file(subset_1,m1_subset_1)).
thf(fc10_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ) => ( ~ ( v1_xboole_0 @ ( k5_relat_1 @ A @ B ) ) & ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(relset_1,fc10_relset_1)).
thf(fc13_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_valued_0 @ A ) & ( v1_relat_1 @ B ) ) => ( v1_valued_0 @ ( k3_xboole_0 @ A @ B ) ) ) ),file(valued_0,fc13_valued_0)).
thf(fc15_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_valued_0 @ A ) & ( v1_relat_1 @ B ) ) => ( v2_valued_0 @ ( k3_xboole_0 @ A @ B ) ) ) ),file(valued_0,fc15_valued_0)).
thf(fc17_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) & ( v1_relat_1 @ B ) ) => ( v3_valued_0 @ ( k3_xboole_0 @ A @ B ) ) ) ),file(valued_0,fc17_valued_0)).
thf(fc19_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) & ( v1_relat_1 @ B ) ) => ( v5_relat_1 @ ( k3_xboole_0 @ A @ B ) @ k3_numbers ) ) ),file(valued_0,fc19_valued_0)).
thf(fc1_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_valued_0 @ A ) ) => ( v1_membered @ ( k10_xtuple_0 @ A ) ) ) ),file(valued_0,fc1_valued_0)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc21_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) & ( v1_relat_1 @ B ) ) => ( v5_relat_1 @ ( k3_xboole_0 @ A @ B ) @ k4_numbers ) ) ),file(valued_0,fc21_valued_0)).
thf(fc23_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) & ( v1_relat_1 @ B ) ) => ( v4_valued_0 @ ( k3_xboole_0 @ A @ B ) ) ) ),file(valued_0,fc23_valued_0)).
thf(fc2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_relat_1 @ C ) ) => ( v4_relat_1 @ ( k3_xboole_0 @ B @ C ) @ A ) ) ),file(relset_1,fc2_relset_1)).
thf(fc2_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_valued_0 @ A ) ) => ( v2_membered @ ( k10_xtuple_0 @ A ) ) ) ),file(valued_0,fc2_valued_0)).
thf(fc31_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_membered @ A ) => ( v1_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),file(membered,fc31_membered)).
thf(fc32_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_membered @ A ) => ( v1_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),file(membered,fc32_membered)).
thf(fc33_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v2_membered @ A ) => ( v2_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),file(membered,fc33_membered)).
thf(fc34_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v2_membered @ A ) => ( v2_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),file(membered,fc34_membered)).
thf(fc35_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v3_membered @ A ) => ( v3_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),file(membered,fc35_membered)).
thf(fc36_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v3_membered @ A ) => ( v3_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),file(membered,fc36_membered)).
thf(fc37_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v4_membered @ A ) => ( v4_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),file(membered,fc37_membered)).
thf(fc38_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v4_membered @ A ) => ( v4_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),file(membered,fc38_membered)).
thf(fc39_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v5_membered @ A ) => ( v5_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),file(membered,fc39_membered)).
thf(fc3_numbers,axiom,( ~ ( v1_xboole_0 @ k3_numbers ) ),file(numbers,fc3_numbers)).
thf(fc3_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) => ( v3_membered @ ( k10_xtuple_0 @ A ) ) ) ),file(valued_0,fc3_valued_0)).
thf(fc40_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v5_membered @ A ) => ( v5_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),file(membered,fc40_membered)).
thf(fc41_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v6_membered @ A ) => ( v6_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),file(membered,fc41_membered)).
thf(fc42_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( v6_membered @ A ) => ( v6_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),file(membered,fc42_membered)).
thf(fc43_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_valued_0 @ A ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v1_valued_0 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc43_valued_0)).
thf(fc44_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_valued_0 @ A ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v2_valued_0 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc44_valued_0)).
thf(fc45_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v3_valued_0 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc45_valued_0)).
thf(fc46_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v5_relat_1 @ ( k5_relat_1 @ A @ B ) @ k3_numbers ) ) ) ),file(valued_0,fc46_valued_0)).
thf(fc47_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v5_relat_1 @ ( k5_relat_1 @ A @ B ) @ k4_numbers ) ) ) ),file(valued_0,fc47_valued_0)).
thf(fc48_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v4_valued_0 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(valued_0,fc48_valued_0)).
thf(fc4_membered,axiom,( v4_membered @ k3_numbers ),file(membered,fc4_membered)).
thf(fc4_numbers,axiom,( ~ ( v1_xboole_0 @ k4_numbers ) ),file(numbers,fc4_numbers)).
thf(fc4_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v5_ordinal1 @ A ) ) => ( v3_ordinal1 @ ( k9_xtuple_0 @ A ) ) ) ),file(ordinal1,fc4_ordinal1)).
thf(fc4_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) => ( v4_membered @ ( k10_xtuple_0 @ A ) ) ) ),file(valued_0,fc4_valued_0)).
thf(fc57_membered,axiom,( v7_membered @ k3_numbers ),file(membered,fc57_membered)).
thf(fc58_membered,axiom,( v7_membered @ k4_numbers ),file(membered,fc58_membered)).
thf(fc5_membered,axiom,( v5_membered @ k4_numbers ),file(membered,fc5_membered)).
thf(fc5_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v5_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v5_relat_1 @ ( k5_relat_1 @ A @ B ) @ ( k10_xtuple_0 @ A ) ) & ( v5_ordinal1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(ordinal1,fc5_ordinal1)).
thf(fc5_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_relat_1 @ C ) ) => ( v5_relat_1 @ ( k3_xboole_0 @ B @ C ) @ A ) ) ),file(relset_1,fc5_relset_1)).
thf(fc5_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) => ( v5_membered @ ( k10_xtuple_0 @ A ) ) ) ),file(valued_0,fc5_valued_0)).
thf(fc61_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_valued_0 @ A ) ) => ( v1_xcmplx_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc61_valued_0)).
thf(fc62_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) ) => ( v1_xxreal_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc62_valued_0)).
thf(fc63_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_valued_0 @ A ) ) => ( v1_xreal_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc63_valued_0)).
thf(fc64_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) & ( v1_funct_1 @ A ) ) => ( v1_rat_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc64_valued_0)).
thf(fc65_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) & ( v1_funct_1 @ A ) ) => ( v1_int_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc65_valued_0)).
thf(fc66_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v4_valued_0 @ A ) ) => ( v7_ordinal1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc66_valued_0)).
thf(fc6_numbers,axiom,( ~ ( v1_finset_1 @ k4_numbers ) ),file(numbers,fc6_numbers)).
thf(fc6_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( v6_membered @ ( k10_xtuple_0 @ A ) ) ) ),file(valued_0,fc6_valued_0)).
thf(fc7_numbers,axiom,( ~ ( v1_finset_1 @ k3_numbers ) ),file(numbers,fc7_numbers)).
thf(fc85_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_membered @ B ) => ( v1_valued_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(valued_0,fc85_valued_0)).
thf(fc86_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v2_membered @ B ) => ( v2_valued_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(valued_0,fc86_valued_0)).
thf(fc87_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v3_membered @ B ) => ( v3_valued_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(valued_0,fc87_valued_0)).
thf(fc88_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v4_membered @ B ) => ( v5_relat_1 @ ( k2_zfmisc_1 @ A @ B ) @ k3_numbers ) ) ),file(valued_0,fc88_valued_0)).
thf(fc89_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v5_membered @ B ) => ( v5_relat_1 @ ( k2_zfmisc_1 @ A @ B ) @ k4_numbers ) ) ),file(valued_0,fc89_valued_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(fc90_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v6_membered @ B ) => ( v4_valued_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(valued_0,fc90_valued_0)).
thf(fc9_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) ) => ( v1_relat_1 @ ( k10_xtuple_0 @ D ) ) ) ),file(relset_1,fc9_relset_1)).
thf(idempotence_k3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k3_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k3_xboole_0)).
thf(idempotence_k9_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) => ( = @ ( k9_subset_1 @ A @ B @ B ) @ B ) ) ),file(subset_1,k9_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_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc1_membered)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
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_valued_0,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v4_valued_0 @ A ) ) ),file(valued_0,rc1_valued_0)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
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(rc2_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) ) ),file(ordinal1,rc2_ordinal1)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
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_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_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_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(rc5_valued_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v5_relat_1 @ B @ k3_numbers ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_valued_0 @ B ) & ( v2_valued_0 @ B ) & ( v3_valued_0 @ B ) & ( v4_valued_0 @ B ) ) ),file(valued_1,rc5_valued_1)).
thf(rc6_valued_0,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v4_valued_0 @ B ) ) ),file(valued_0,rc6_valued_0)).
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_k2_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ C ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( = @ ( k2_partfun1 @ A @ B @ C @ D ) @ ( k5_relat_1 @ C @ D ) ) ) ),file(partfun1,k2_partfun1)).
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_k9_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) => ( = @ ( k9_subset_1 @ A @ B @ C ) @ ( k3_xboole_0 @ B @ C ) ) ) ),file(subset_1,k9_subset_1)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(t1_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ( m1_subset_1 @ A @ B ) ) ),file(subset,t1_subset)).
thf(t2_boole,axiom,( ! [A: $i] : ( = @ ( k3_xboole_0 @ A @ k1_xboole_0 ) @ k1_xboole_0 ) ),file(boole,t2_boole)).
thf(t2_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ A @ B ) => ( ( v1_xboole_0 @ B ) | ( r2_hidden @ A @ B ) ) ) ),file(subset,t2_subset)).
thf(t3_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) <=> ( r1_tarski @ A @ B ) ) ),file(subset,t3_subset)).
thf(t47_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) ) => ( ( r2_hidden @ A @ ( k9_xtuple_0 @ ( k5_relat_1 @ C @ B ) ) ) => ( = @ ( k1_funct_1 @ ( k5_relat_1 @ C @ B ) @ A ) @ ( k1_funct_1 @ C @ A ) ) ) ) ),file(funct_1,t47_funct_1)).
thf(t4_subset,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ A @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) ) => ( m1_subset_1 @ A @ C ) ) ),file(subset,t4_subset)).
thf(t58_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ B ) => ( r1_tarski @ ( k9_xtuple_0 @ ( k5_relat_1 @ B @ A ) ) @ A ) ) ),file(relat_1,t58_relat_1)).
thf(t5_subset,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ~ ( ( r2_hidden @ A @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) & ( v1_xboole_0 @ C ) ) ),file(subset,t5_subset)).
thf(t61_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ B ) => ( = @ ( k9_xtuple_0 @ ( k5_relat_1 @ B @ A ) ) @ ( k3_xboole_0 @ ( k9_xtuple_0 @ B ) @ A ) ) ) ),file(relat_1,t61_relat_1)).
thf(t6_boole,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( = @ A @ k1_xboole_0 ) ) ),file(boole,t6_boole)).
thf(t7_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( r2_hidden @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t7_boole)).
thf(t8_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( v1_xboole_0 @ A ) & ~ ( = @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t8_boole)).
thf(s1_xboole_0,axiom,( ! [A: $i > $o] : ! [B: $i] : ? [C: $i] : ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( ( r2_hidden @ D @ B ) & ( A @ D ) ) ) ),file(xboole_0,s1_xboole_0)).
thf(s3_funct_2,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ! [C: $i] : ( ! [D: $i] : ( ( m1_subset_1 @ D @ C ) => ? [E: $i] : ( ( m1_subset_1 @ E @ B ) & ( A @ D @ E ) ) ) => ? [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 ) => ( A @ E @ ( k3_funct_2 @ C @ B @ D @ E ) ) ) ) ) ),file(funct_2,s3_funct_2)).
thf(s2_seq_1,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ f1_s2_seq_1 @ f2_s2_seq_1 ) ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ f1_s2_seq_1 ) => ( ( r2_hidden @ B @ ( k1_relset_1 @ f1_s2_seq_1 @ A ) ) <=> ? [C: $i] : ( ( m1_subset_1 @ C @ f2_s2_seq_1 ) & ( p1_s2_seq_1 @ B @ C ) ) ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ f1_s2_seq_1 ) => ( ( r2_hidden @ B @ ( k1_relset_1 @ f1_s2_seq_1 @ A ) ) => ( p1_s2_seq_1 @ B @ ( k1_funct_1 @ A @ B ) ) ) ) ) ),file(seq_1,s2_seq_1)).
