% Mizar problem: s3_substut2,substut2,729,9 
include('Axioms/SET010^0.ax').
thf(n0_type,type,( np__0: $i )).
thf(n1_type,type,( np__1: $i )).
thf(n2_type,type,( np__2: $i )).
thf(f1_s3_substut2_type,type,( f1_s3_substut2: $i )).
thf(k10_qc_lang1_type,type,( k10_qc_lang1: $i > $i > $i > $i )).
thf(k11_cqc_lang_type,type,( k11_cqc_lang: $i > $i > $i > $i )).
thf(k12_qc_lang1_type,type,( k12_qc_lang1: $i > $i )).
thf(k13_qc_lang1_type,type,( k13_qc_lang1: $i > $i > $i )).
thf(k14_qc_lang1_type,type,( k14_qc_lang1: $i > $i > $i > $i )).
thf(k15_qc_lang1_type,type,( k15_qc_lang1: $i > $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_nat_1_type,type,( k2_nat_1: $i > $i > $i )).
thf(k2_qc_lang1_type,type,( k2_qc_lang1: $i > $i )).
thf(k2_xcmplx_0_type,type,( k2_xcmplx_0: $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_cqc_lang_type,type,( k3_cqc_lang: $i > $i )).
thf(k3_qc_lang1_type,type,( k3_qc_lang1: $i > $i )).
thf(k4_cqc_lang_type,type,( k4_cqc_lang: $i > $i > $i > $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k4_xcmplx_0_type,type,( k4_xcmplx_0: $i > $i )).
thf(k5_cqc_lang_type,type,( k5_cqc_lang: $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_cqc_lang_type,type,( k6_cqc_lang: $i > $i > $i )).
thf(k6_numbers_type,type,( k6_numbers: $i )).
thf(k6_qc_lang1_type,type,( k6_qc_lang1: $i > $i )).
thf(k6_xcmplx_0_type,type,( k6_xcmplx_0: $i > $i > $i )).
thf(k7_cqc_lang_type,type,( k7_cqc_lang: $i > $i > $i > $i )).
thf(k7_cqc_sim1_type,type,( k7_cqc_sim1: $i > $i > $i )).
thf(k8_qc_lang1_type,type,( k8_qc_lang1: $i > $i > $i )).
thf(k9_qc_lang1_type,type,( k9_qc_lang1: $i > $i )).
thf(m1_finseq_1_type,type,( m1_finseq_1: $i > $i > $o )).
thf(m1_qc_lang1_type,type,( m1_qc_lang1: $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_finseq_1_type,type,( m2_finseq_1: $i > $i > $o )).
thf(m2_subset_1_type,type,( m2_subset_1: $i > $i > $i > $o )).
thf(p1_s3_substut2_type,type,( p1_s3_substut2: $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(v1_card_1_type,type,( v1_card_1: $i > $o )).
thf(v1_finseq_1_type,type,( v1_finseq_1: $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_funcop_1_type,type,( v1_funcop_1: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_int_1_type,type,( v1_int_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $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_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_card_1_type,type,( v2_card_1: $i > $o )).
thf(v2_funcop_1_type,type,( v2_funcop_1: $i > $o )).
thf(v2_funct_1_type,type,( v2_funct_1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $i > $o )).
thf(v3_card_1_type,type,( v3_card_1: $i > $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(v3_xxreal_0_type,type,( v3_xxreal_0: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $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_ordinal1_type,type,( v6_ordinal1: $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_card_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_zfmisc_1 @ A ) ) => ( v3_card_1 @ A @ np__1 ) ) ),file(card_1,cc10_card_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(cc1_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(card_1,cc1_card_1)).
thf(cc1_funcop_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_funcop_1 @ B ) ) ) ) ),file(funcop_1,cc1_funcop_1)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_1)).
thf(cc1_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) ) ),file(nat_1,cc1_nat_1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc1_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( ( v1_relat_1 @ A ) & ~ ( v1_xboole_0 @ A ) ) ) ),file(qc_lang1,cc1_qc_lang1)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_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(cc1_xreal_0,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc1_xreal_0)).
thf(cc2_card_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc2_card_1)).
thf(cc2_funcop_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funcop_1 @ A ) ) ) ),file(funcop_1,cc2_funcop_1)).
thf(cc2_funct_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) ) ) ),file(funct_1,cc2_funct_1)).
thf(cc2_int_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_int_1 @ A ) ) ),file(int_1,cc2_int_1)).
thf(cc2_nat_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ~ ( v3_xxreal_0 @ A ) ) ),file(nat_1,cc2_nat_1)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc2_relat_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_relat_1 @ B ) ) ) ),file(relat_1,cc2_relat_1)).
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(cc2_xreal_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc2_xreal_0)).
thf(cc2_xxreal_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,cc2_xxreal_0)).
thf(cc3_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc3_card_1)).
thf(cc3_funcop_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) ) ),file(funcop_1,cc3_funcop_1)).
thf(cc3_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_funct_1 @ B ) ) ) ),file(funct_1,cc3_funct_1)).
thf(cc3_int_1,axiom,( ! [A: $i] : ( ( v1_int_1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(int_1,cc3_int_1)).
thf(cc3_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v7_ordinal1 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(nat_1,cc3_nat_1)).
thf(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
thf(cc3_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) ) ) ),file(relat_1,cc3_relat_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(cc3_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xcmplx_0 @ A ) ) ),file(xreal_0,cc3_xreal_0)).
thf(cc3_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) ) => ( ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc3_xxreal_0)).
thf(cc4_card_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc4_card_1)).
thf(cc4_funct_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) ) ),file(funct_1,cc4_funct_1)).
thf(cc4_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
thf(cc4_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ) ),file(relat_1,cc4_relat_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(cc4_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xreal_0,cc4_xreal_0)).
thf(cc4_xxreal_0,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) => ( ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc4_xxreal_0)).
thf(cc5_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc5_card_1)).
thf(cc5_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) => ( ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ) ),file(funct_1,cc5_funct_1)).
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_subset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,cc5_subset_1)).
thf(cc5_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) => ( ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc5_xxreal_0)).
thf(cc6_card_1,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v1_finset_1 @ A ) ) => ( v7_ordinal1 @ A ) ) ),file(card_1,cc6_card_1)).
thf(cc6_funct_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) ) ),file(funct_1,cc6_funct_1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(cc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) => ( v5_relat_1 @ C @ A ) ) ) ),file(relat_1,cc6_relat_1)).
thf(cc6_xxreal_0,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) ) => ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc6_xxreal_0)).
thf(cc7_card_1,axiom,( ! [A: $i] : ( ( v3_card_1 @ A @ k1_xboole_0 ) => ( v1_xboole_0 @ A ) ) ),file(card_1,cc7_card_1)).
thf(cc7_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v4_funct_1 @ A ) ) ),file(funct_1,cc7_funct_1)).
thf(cc7_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
thf(cc7_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) => ( ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc7_xxreal_0)).
thf(cc8_card_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_card_1 @ A @ k1_xboole_0 ) ) ),file(card_1,cc8_card_1)).
thf(cc8_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) ) ) ),file(funct_1,cc8_funct_1)).
thf(cc8_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
thf(cc8_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) => ( ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) ) ) ),file(relat_1,cc8_relat_1)).
thf(cc8_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) => ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc8_xxreal_0)).
thf(cc9_card_1,axiom,( ! [A: $i] : ( ( v3_card_1 @ A @ np__1 ) => ( ~ ( v1_xboole_0 @ A ) & ( v1_zfmisc_1 @ A ) ) ) ),file(card_1,cc9_card_1)).
thf(cc9_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_funct_1 @ B ) ) ) ),file(funct_1,cc9_funct_1)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(commutativity_k2_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( v7_ordinal1 @ B ) ) => ( = @ ( k2_nat_1 @ A @ B ) @ ( k2_nat_1 @ B @ A ) ) ) ),file(nat_1,k2_nat_1)).
thf(commutativity_k2_xcmplx_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) ) => ( = @ ( k2_xcmplx_0 @ A @ B ) @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(xcmplx_0,k2_xcmplx_0)).
thf(dt_f1_s3_substut2,axiom,( m1_qc_lang1 @ f1_s3_substut2 ),file(substut2,f1_s3_substut2)).
thf(dt_k10_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k6_qc_lang1 @ A ) ) & ( m1_finseq_1 @ C @ ( k2_qc_lang1 @ A ) ) ) => ( m1_subset_1 @ ( k10_qc_lang1 @ A @ B @ C ) @ ( k9_qc_lang1 @ A ) ) ) ),file(qc_lang1,k10_qc_lang1)).
thf(dt_k11_cqc_lang,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k3_qc_lang1 @ A ) ) & ( m1_subset_1 @ C @ ( k3_cqc_lang @ A ) ) ) => ( m2_subset_1 @ ( k11_cqc_lang @ A @ B @ C ) @ ( k9_qc_lang1 @ A ) @ ( k3_cqc_lang @ A ) ) ) ),file(cqc_lang,k11_cqc_lang)).
thf(dt_k12_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( m1_subset_1 @ ( k12_qc_lang1 @ A ) @ ( k9_qc_lang1 @ A ) ) ) ),file(qc_lang1,k12_qc_lang1)).
thf(dt_k13_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) ) => ( m1_subset_1 @ ( k13_qc_lang1 @ A @ B ) @ ( k9_qc_lang1 @ A ) ) ) ),file(qc_lang1,k13_qc_lang1)).
thf(dt_k14_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) & ( m1_subset_1 @ C @ ( k9_qc_lang1 @ A ) ) ) => ( m1_subset_1 @ ( k14_qc_lang1 @ A @ B @ C ) @ ( k9_qc_lang1 @ A ) ) ) ),file(qc_lang1,k14_qc_lang1)).
thf(dt_k15_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k3_qc_lang1 @ A ) ) & ( m1_subset_1 @ C @ ( k9_qc_lang1 @ A ) ) ) => ( m1_subset_1 @ ( k15_qc_lang1 @ A @ B @ C ) @ ( k9_qc_lang1 @ A ) ) ) ),file(qc_lang1,k15_qc_lang1)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
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_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( v7_ordinal1 @ B ) ) => ( m2_subset_1 @ ( k2_nat_1 @ A @ B ) @ k1_numbers @ k5_numbers ) ) ),file(nat_1,k2_nat_1)).
thf(dt_k2_qc_lang1,axiom,( $true ),file(qc_lang1,k2_qc_lang1)).
thf(dt_k2_xcmplx_0,axiom,( $true ),file(xcmplx_0,k2_xcmplx_0)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_cqc_lang,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( m1_subset_1 @ ( k3_cqc_lang @ A ) @ ( k1_zfmisc_1 @ ( k9_qc_lang1 @ A ) ) ) ) ),file(cqc_lang,k3_cqc_lang)).
thf(dt_k3_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( m1_subset_1 @ ( k3_qc_lang1 @ A ) @ ( k1_zfmisc_1 @ ( k2_qc_lang1 @ A ) ) ) ) ),file(qc_lang1,k3_qc_lang1)).
thf(dt_k4_cqc_lang,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( m1_qc_lang1 @ B ) & ( m1_subset_1 @ C @ ( k8_qc_lang1 @ B @ A ) ) & ( v5_relat_1 @ D @ ( k3_qc_lang1 @ B ) ) & ( v3_card_1 @ D @ A ) & ( m1_finseq_1 @ D @ ( k2_qc_lang1 @ B ) ) ) => ( m2_subset_1 @ ( k4_cqc_lang @ A @ B @ C @ D ) @ ( k9_qc_lang1 @ B ) @ ( k3_cqc_lang @ B ) ) ) ),file(cqc_lang,k4_cqc_lang)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(dt_k4_xcmplx_0,axiom,( ! [A: $i] : ( ( v1_xcmplx_0 @ A ) => ( v1_xcmplx_0 @ ( k4_xcmplx_0 @ A ) ) ) ),file(xcmplx_0,k4_xcmplx_0)).
thf(dt_k5_cqc_lang,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( m2_subset_1 @ ( k5_cqc_lang @ A ) @ ( k9_qc_lang1 @ A ) @ ( k3_cqc_lang @ A ) ) ) ),file(cqc_lang,k5_cqc_lang)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_k6_cqc_lang,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k3_cqc_lang @ A ) ) ) => ( m2_subset_1 @ ( k6_cqc_lang @ A @ B ) @ ( k9_qc_lang1 @ A ) @ ( k3_cqc_lang @ A ) ) ) ),file(cqc_lang,k6_cqc_lang)).
thf(dt_k6_numbers,axiom,( m2_subset_1 @ k6_numbers @ k1_numbers @ k5_numbers ),file(numbers,k6_numbers)).
thf(dt_k6_qc_lang1,axiom,( $true ),file(qc_lang1,k6_qc_lang1)).
thf(dt_k6_xcmplx_0,axiom,( $true ),file(xcmplx_0,k6_xcmplx_0)).
thf(dt_k7_cqc_lang,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k3_cqc_lang @ A ) ) & ( m1_subset_1 @ C @ ( k3_cqc_lang @ A ) ) ) => ( m2_subset_1 @ ( k7_cqc_lang @ A @ B @ C ) @ ( k9_qc_lang1 @ A ) @ ( k3_cqc_lang @ A ) ) ) ),file(cqc_lang,k7_cqc_lang)).
thf(dt_k7_cqc_sim1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k3_cqc_lang @ A ) ) ) => ( m1_subset_1 @ ( k7_cqc_sim1 @ A @ B ) @ k5_numbers ) ) ),file(cqc_sim1,k7_cqc_sim1)).
thf(dt_k8_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ( m1_subset_1 @ ( k8_qc_lang1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k6_qc_lang1 @ A ) ) ) ) ),file(qc_lang1,k8_qc_lang1)).
thf(dt_k9_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ~ ( v1_xboole_0 @ ( k9_qc_lang1 @ A ) ) ) ),file(qc_lang1,k9_qc_lang1)).
thf(dt_m1_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_finseq_1 @ B @ A ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_finseq_1 @ B ) ) ) ),file(finseq_1,m1_finseq_1)).
thf(dt_m1_qc_lang1,axiom,( $true ),file(qc_lang1,m1_qc_lang1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_m2_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m2_finseq_1 @ B @ A ) => ( ( v1_funct_1 @ B ) & ( v1_finseq_1 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ A ) ) ) ) ) ),file(finseq_1,m2_finseq_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(existence_m1_finseq_1,axiom,( ! [A: $i] : ? [B: $i] : ( m1_finseq_1 @ B @ A ) ),file(finseq_1,m1_finseq_1)).
thf(existence_m1_qc_lang1,axiom,( ? [A: $i] : ( m1_qc_lang1 @ A ) ),file(qc_lang1,m1_qc_lang1)).
thf(existence_m1_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( m1_subset_1 @ B @ A ) ),file(subset_1,m1_subset_1)).
thf(existence_m2_finseq_1,axiom,( ! [A: $i] : ? [B: $i] : ( m2_finseq_1 @ B @ A ) ),file(finseq_1,m2_finseq_1)).
thf(existence_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 ) ) ),file(subset_1,m2_subset_1)).
thf(fc10_card_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_finset_1 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(card_1,fc10_card_1)).
thf(fc10_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(subset_1,fc10_subset_1)).
thf(fc10_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v2_xxreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc10_xreal_0)).
thf(fc11_card_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_finset_1 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_finset_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) ),file(card_1,fc11_card_1)).
thf(fc11_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v3_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v2_xxreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc11_xreal_0)).
thf(fc12_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v3_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v2_xxreal_0 @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc12_xreal_0)).
thf(fc13_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v3_xxreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc13_xreal_0)).
thf(fc14_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v3_xxreal_0 @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc14_xreal_0)).
thf(fc15_xreal_0,axiom,( ! [A: $i] : ( ( ~ ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) => ( ( v1_xcmplx_0 @ ( k4_xcmplx_0 @ A ) ) & ~ ( v3_xxreal_0 @ ( k4_xcmplx_0 @ A ) ) ) ) ),file(xreal_0,fc15_xreal_0)).
thf(fc16_xreal_0,axiom,( ! [A: $i] : ( ( ~ ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) => ( ( v1_xcmplx_0 @ ( k4_xcmplx_0 @ A ) ) & ~ ( v2_xxreal_0 @ ( k4_xcmplx_0 @ A ) ) ) ) ),file(xreal_0,fc16_xreal_0)).
thf(fc17_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v3_xxreal_0 @ ( k6_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc17_xreal_0)).
thf(fc18_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v2_xxreal_0 @ ( k6_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc18_xreal_0)).
thf(fc19_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v2_xxreal_0 @ ( k6_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc19_xreal_0)).
thf(fc1_int_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ( v1_int_1 @ B ) ) => ( v1_int_1 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(int_1,fc1_int_1)).
thf(fc1_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( v7_ordinal1 @ B ) ) => ( v7_ordinal1 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(nat_1,fc1_nat_1)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc20_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v3_xxreal_0 @ ( k6_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc20_xreal_0)).
thf(fc21_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v3_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v3_xxreal_0 @ ( k6_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc21_xreal_0)).
thf(fc22_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v3_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v2_xxreal_0 @ ( k6_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc22_xreal_0)).
thf(fc2_cqc_lang,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ~ ( v1_xboole_0 @ ( k3_cqc_lang @ A ) ) ) ),file(cqc_lang,fc2_cqc_lang)).
thf(fc2_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ~ ( v1_xboole_0 @ ( k2_qc_lang1 @ A ) ) ) ),file(qc_lang1,fc2_qc_lang1)).
thf(fc3_int_1,axiom,( ! [A: $i] : ( ( v1_int_1 @ A ) => ( ( v1_xcmplx_0 @ ( k4_xcmplx_0 @ A ) ) & ( v1_int_1 @ ( k4_xcmplx_0 @ A ) ) ) ) ),file(int_1,fc3_int_1)).
thf(fc3_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v7_ordinal1 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(nat_1,fc3_nat_1)).
thf(fc3_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ~ ( v1_xboole_0 @ ( k3_qc_lang1 @ A ) ) ) ),file(qc_lang1,fc3_qc_lang1)).
thf(fc3_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( ( v1_xcmplx_0 @ ( k4_xcmplx_0 @ A ) ) & ( v1_xreal_0 @ ( k4_xcmplx_0 @ A ) ) ) ) ),file(xreal_0,fc3_xreal_0)).
thf(fc4_card_1,axiom,( v1_card_1 @ k4_ordinal1 ),file(card_1,fc4_card_1)).
thf(fc4_int_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ( v1_int_1 @ B ) ) => ( v1_int_1 @ ( k6_xcmplx_0 @ A @ B ) ) ) ),file(int_1,fc4_int_1)).
thf(fc4_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v7_ordinal1 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(nat_1,fc4_nat_1)).
thf(fc5_card_1,axiom,( v2_card_1 @ k4_ordinal1 ),file(card_1,fc5_card_1)).
thf(fc5_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xreal_0 @ A ) & ( v1_xreal_0 @ B ) ) => ( v1_xreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc5_xreal_0)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
thf(fc6_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ~ ( v1_xboole_0 @ ( k6_qc_lang1 @ A ) ) ) ),file(qc_lang1,fc6_qc_lang1)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(fc7_card_1,axiom,( ~ ( v1_finset_1 @ k4_ordinal1 ) ),file(card_1,fc7_card_1)).
thf(fc7_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( m1_qc_lang1 @ B ) ) => ~ ( v1_xboole_0 @ ( k8_qc_lang1 @ B @ A ) ) ) ),file(qc_lang1,fc7_qc_lang1)).
thf(fc7_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xreal_0 @ A ) & ( v1_xreal_0 @ B ) ) => ( v1_xreal_0 @ ( k6_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc7_xreal_0)).
thf(fc9_card_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(card_1,fc9_card_1)).
thf(fc9_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v3_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v3_xxreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc9_xreal_0)).
thf(involutiveness_k4_xcmplx_0,axiom,( ! [A: $i] : ( ( v1_xcmplx_0 @ A ) => ( = @ ( k4_xcmplx_0 @ ( k4_xcmplx_0 @ A ) ) @ A ) ) ),file(xcmplx_0,k4_xcmplx_0)).
thf(rc1_card_1,axiom,( ? [A: $i] : ( v1_card_1 @ A ) ),file(card_1,rc1_card_1)).
thf(rc1_funcop_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) ),file(funcop_1,rc1_funcop_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_int_1,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) & ( v1_xxreal_0 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_int_1 @ A ) ) ),file(int_1,rc1_int_1)).
thf(rc1_nat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) ),file(nat_1,rc1_nat_1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_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(rc1_xreal_0,axiom,( ? [A: $i] : ( v1_xreal_0 @ A ) ),file(xreal_0,rc1_xreal_0)).
thf(rc1_xxreal_0,axiom,( ? [A: $i] : ( v1_xxreal_0 @ A ) ),file(xxreal_0,rc1_xxreal_0)).
thf(rc2_card_1,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) ),file(card_1,rc2_card_1)).
thf(rc2_funcop_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) ) ),file(funcop_1,rc2_funcop_1)).
thf(rc2_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) ) ),file(funct_1,rc2_funct_1)).
thf(rc2_int_1,axiom,( ? [A: $i] : ( v1_int_1 @ A ) ),file(int_1,rc2_int_1)).
thf(rc2_nat_1,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) ) & ~ ( v1_xboole_0 @ A ) & ( v3_ordinal1 @ A ) ) ),file(nat_1,rc2_nat_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(rc2_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
thf(rc2_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v1_xboole_0 @ B ) ) ),file(subset_1,rc2_subset_1)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc2_xreal_0,axiom,( ? [A: $i] : ( ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc2_xreal_0)).
thf(rc2_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) ) ),file(xxreal_0,rc2_xxreal_0)).
thf(rc3_card_1,axiom,( ? [A: $i] : ~ ( v1_finset_1 @ A ) ),file(card_1,rc3_card_1)).
thf(rc3_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc3_funct_1)).
thf(rc3_nat_1,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) & ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) ),file(nat_1,rc3_nat_1)).
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(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(rc3_xreal_0,axiom,( ? [A: $i] : ( ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc3_xreal_0)).
thf(rc3_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) ),file(xxreal_0,rc3_xxreal_0)).
thf(rc4_card_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_finset_1 @ B ) ) ) ),file(card_1,rc4_card_1)).
thf(rc4_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc4_funct_1)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
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(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(rc4_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,rc4_xxreal_0)).
thf(rc5_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ? [B: $i] : ( v3_card_1 @ B @ A ) ) ),file(card_1,rc5_card_1)).
thf(rc5_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) ),file(funct_1,rc5_funct_1)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
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_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v3_card_1 @ B @ A ) ) ) ),file(card_1,rc6_card_1)).
thf(rc6_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,rc6_subset_1)).
thf(rc7_card_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v3_card_1 @ B @ np__1 ) ) ) ),file(card_1,rc7_card_1)).
thf(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(redefinition_k11_cqc_lang,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k3_qc_lang1 @ A ) ) & ( m1_subset_1 @ C @ ( k3_cqc_lang @ A ) ) ) => ( = @ ( k11_cqc_lang @ A @ B @ C ) @ ( k15_qc_lang1 @ A @ B @ C ) ) ) ),file(cqc_lang,k11_cqc_lang)).
thf(redefinition_k2_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( v7_ordinal1 @ B ) ) => ( = @ ( k2_nat_1 @ A @ B ) @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(nat_1,k2_nat_1)).
thf(redefinition_k4_cqc_lang,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( m1_qc_lang1 @ B ) & ( m1_subset_1 @ C @ ( k8_qc_lang1 @ B @ A ) ) & ( v5_relat_1 @ D @ ( k3_qc_lang1 @ B ) ) & ( v3_card_1 @ D @ A ) & ( m1_finseq_1 @ D @ ( k2_qc_lang1 @ B ) ) ) => ( = @ ( k4_cqc_lang @ A @ B @ C @ D ) @ ( k10_qc_lang1 @ B @ C @ D ) ) ) ),file(cqc_lang,k4_cqc_lang)).
thf(redefinition_k5_cqc_lang,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( = @ ( k5_cqc_lang @ A ) @ ( k12_qc_lang1 @ A ) ) ) ),file(cqc_lang,k5_cqc_lang)).
thf(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
thf(redefinition_k6_cqc_lang,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k3_cqc_lang @ A ) ) ) => ( = @ ( k6_cqc_lang @ A @ B ) @ ( k13_qc_lang1 @ A @ B ) ) ) ),file(cqc_lang,k6_cqc_lang)).
thf(redefinition_k6_numbers,axiom,( = @ k6_numbers @ k1_xboole_0 ),file(numbers,k6_numbers)).
thf(redefinition_k7_cqc_lang,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k3_cqc_lang @ A ) ) & ( m1_subset_1 @ C @ ( k3_cqc_lang @ A ) ) ) => ( = @ ( k7_cqc_lang @ A @ B @ C ) @ ( k14_qc_lang1 @ A @ B @ C ) ) ) ),file(cqc_lang,k7_cqc_lang)).
thf(redefinition_m2_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m2_finseq_1 @ B @ A ) <=> ( m1_finseq_1 @ B @ A ) ) ),file(finseq_1,m2_finseq_1)).
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(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(rqRealAdd__k2_xcmplx_0__r0_r0_r0,axiom,( = @ ( k2_xcmplx_0 @ np__0 @ np__0 ) @ np__0 ),file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0)).
thf(rqRealAdd__k2_xcmplx_0__r0_r1_r1,axiom,( = @ ( k2_xcmplx_0 @ np__0 @ np__1 ) @ np__1 ),file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1)).
thf(rqRealAdd__k2_xcmplx_0__r0_r2_r2,axiom,( = @ ( k2_xcmplx_0 @ np__0 @ np__2 ) @ np__2 ),file(arithm,rqRealAdd__k2_xcmplx_0__r0_r2_r2)).
thf(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,axiom,( = @ ( k2_xcmplx_0 @ np__0 @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k4_xcmplx_0 @ np__1 ) ),file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,axiom,( = @ ( k2_xcmplx_0 @ np__0 @ ( k4_xcmplx_0 @ np__2 ) ) @ ( k4_xcmplx_0 @ np__2 ) ),file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2)).
thf(rqRealAdd__k2_xcmplx_0__r1_r0_r1,axiom,( = @ ( k2_xcmplx_0 @ np__1 @ np__0 ) @ np__1 ),file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1)).
thf(rqRealAdd__k2_xcmplx_0__r1_r1_r2,axiom,( = @ ( k2_xcmplx_0 @ np__1 @ np__1 ) @ np__2 ),file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2)).
thf(rqRealAdd__k2_xcmplx_0__r1_rm1_r0,axiom,( = @ ( k2_xcmplx_0 @ np__1 @ ( k4_xcmplx_0 @ np__1 ) ) @ np__0 ),file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm1_r0)).
thf(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,axiom,( = @ ( k2_xcmplx_0 @ np__1 @ ( k4_xcmplx_0 @ np__2 ) ) @ ( k4_xcmplx_0 @ np__1 ) ),file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r2_r0_r2,axiom,( = @ ( k2_xcmplx_0 @ np__2 @ np__0 ) @ np__2 ),file(arithm,rqRealAdd__k2_xcmplx_0__r2_r0_r2)).
thf(rqRealAdd__k2_xcmplx_0__r2_rm1_r1,axiom,( = @ ( k2_xcmplx_0 @ np__2 @ ( k4_xcmplx_0 @ np__1 ) ) @ np__1 ),file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm1_r1)).
thf(rqRealAdd__k2_xcmplx_0__r2_rm2_r0,axiom,( = @ ( k2_xcmplx_0 @ np__2 @ ( k4_xcmplx_0 @ np__2 ) ) @ np__0 ),file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm2_r0)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,axiom,( = @ ( k2_xcmplx_0 @ ( k4_xcmplx_0 @ np__1 ) @ np__0 ) @ ( k4_xcmplx_0 @ np__1 ) ),file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r1_r0,axiom,( = @ ( k2_xcmplx_0 @ ( k4_xcmplx_0 @ np__1 ) @ np__1 ) @ np__0 ),file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r1_r0)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r2_r1,axiom,( = @ ( k2_xcmplx_0 @ ( k4_xcmplx_0 @ np__1 ) @ np__2 ) @ np__1 ),file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r2_r1)).
thf(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,axiom,( = @ ( k2_xcmplx_0 @ ( k4_xcmplx_0 @ np__1 ) @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k4_xcmplx_0 @ np__2 ) ),file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2)).
thf(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,axiom,( = @ ( k2_xcmplx_0 @ ( k4_xcmplx_0 @ np__2 ) @ np__1 ) @ ( k4_xcmplx_0 @ np__1 ) ),file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1)).
thf(rqRealAdd__k2_xcmplx_0__rm2_r2_r0,axiom,( = @ ( k2_xcmplx_0 @ ( k4_xcmplx_0 @ np__2 ) @ np__2 ) @ np__0 ),file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r2_r0)).
thf(rqRealDiff__k6_xcmplx_0__r0_r0_r0,axiom,( = @ ( k6_xcmplx_0 @ np__0 @ np__0 ) @ np__0 ),file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0)).
thf(rqRealDiff__k6_xcmplx_0__r0_r1_rm1,axiom,( = @ ( k6_xcmplx_0 @ np__0 @ np__1 ) @ ( k4_xcmplx_0 @ np__1 ) ),file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r0_r2_rm2,axiom,( = @ ( k6_xcmplx_0 @ np__0 @ np__2 ) @ ( k4_xcmplx_0 @ np__2 ) ),file(arithm,rqRealDiff__k6_xcmplx_0__r0_r2_rm2)).
thf(rqRealDiff__k6_xcmplx_0__r0_rm1_r1,axiom,( = @ ( k6_xcmplx_0 @ np__0 @ ( k4_xcmplx_0 @ np__1 ) ) @ np__1 ),file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1)).
thf(rqRealDiff__k6_xcmplx_0__r0_rm2_r2,axiom,( = @ ( k6_xcmplx_0 @ np__0 @ ( k4_xcmplx_0 @ np__2 ) ) @ np__2 ),file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm2_r2)).
thf(rqRealDiff__k6_xcmplx_0__r1_r0_r1,axiom,( = @ ( k6_xcmplx_0 @ np__1 @ np__0 ) @ np__1 ),file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1)).
thf(rqRealDiff__k6_xcmplx_0__r1_r1_r0,axiom,( = @ ( k6_xcmplx_0 @ np__1 @ np__1 ) @ np__0 ),file(arithm,rqRealDiff__k6_xcmplx_0__r1_r1_r0)).
thf(rqRealDiff__k6_xcmplx_0__r1_r2_rm1,axiom,( = @ ( k6_xcmplx_0 @ np__1 @ np__2 ) @ ( k4_xcmplx_0 @ np__1 ) ),file(arithm,rqRealDiff__k6_xcmplx_0__r1_r2_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r1_rm1_r2,axiom,( = @ ( k6_xcmplx_0 @ np__1 @ ( k4_xcmplx_0 @ np__1 ) ) @ np__2 ),file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm1_r2)).
thf(rqRealDiff__k6_xcmplx_0__r2_r0_r2,axiom,( = @ ( k6_xcmplx_0 @ np__2 @ np__0 ) @ np__2 ),file(arithm,rqRealDiff__k6_xcmplx_0__r2_r0_r2)).
thf(rqRealDiff__k6_xcmplx_0__r2_r1_r1,axiom,( = @ ( k6_xcmplx_0 @ np__2 @ np__1 ) @ np__1 ),file(arithm,rqRealDiff__k6_xcmplx_0__r2_r1_r1)).
thf(rqRealDiff__k6_xcmplx_0__r2_r2_r0,axiom,( = @ ( k6_xcmplx_0 @ np__2 @ np__2 ) @ np__0 ),file(arithm,rqRealDiff__k6_xcmplx_0__r2_r2_r0)).
thf(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,axiom,( = @ ( k6_xcmplx_0 @ ( k4_xcmplx_0 @ np__1 ) @ np__0 ) @ ( k4_xcmplx_0 @ np__1 ) ),file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,axiom,( = @ ( k6_xcmplx_0 @ ( k4_xcmplx_0 @ np__1 ) @ np__1 ) @ ( k4_xcmplx_0 @ np__2 ) ),file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2)).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,axiom,( = @ ( k6_xcmplx_0 @ ( k4_xcmplx_0 @ np__1 ) @ ( k4_xcmplx_0 @ np__1 ) ) @ np__0 ),file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,axiom,( = @ ( k6_xcmplx_0 @ ( k4_xcmplx_0 @ np__1 ) @ ( k4_xcmplx_0 @ np__2 ) ) @ np__1 ),file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1)).
thf(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,axiom,( = @ ( k6_xcmplx_0 @ ( k4_xcmplx_0 @ np__2 ) @ np__0 ) @ ( k4_xcmplx_0 @ np__2 ) ),file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2)).
thf(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,axiom,( = @ ( k6_xcmplx_0 @ ( k4_xcmplx_0 @ np__2 ) @ ( k4_xcmplx_0 @ np__1 ) ) @ ( k4_xcmplx_0 @ np__1 ) ),file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,axiom,( = @ ( k6_xcmplx_0 @ ( k4_xcmplx_0 @ np__2 ) @ ( k4_xcmplx_0 @ np__2 ) ) @ np__0 ),file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0)).
thf(rqRealNeg__k4_xcmplx_0__r0_r0,axiom,( = @ ( k4_xcmplx_0 @ np__0 ) @ np__0 ),file(arithm,rqRealNeg__k4_xcmplx_0__r0_r0)).
thf(rqRealNeg__k4_xcmplx_0__r1_rm1,axiom,( = @ ( k4_xcmplx_0 @ np__1 ) @ ( k4_xcmplx_0 @ np__1 ) ),file(arithm,rqRealNeg__k4_xcmplx_0__r1_rm1)).
thf(rqRealNeg__k4_xcmplx_0__r2_rm2,axiom,( = @ ( k4_xcmplx_0 @ np__2 ) @ ( k4_xcmplx_0 @ np__2 ) ),file(arithm,rqRealNeg__k4_xcmplx_0__r2_rm2)).
thf(rqRealNeg__k4_xcmplx_0__rm1_r1,axiom,( = @ ( k4_xcmplx_0 @ ( k4_xcmplx_0 @ np__1 ) ) @ np__1 ),file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1)).
thf(rqRealNeg__k4_xcmplx_0__rm2_r2,axiom,( = @ ( k4_xcmplx_0 @ ( k4_xcmplx_0 @ np__2 ) ) @ np__2 ),file(arithm,rqRealNeg__k4_xcmplx_0__rm2_r2)).
thf(spc0_boole,axiom,( v1_xboole_0 @ np__0 ),file(boole,spc0_boole)).
thf(spc0_numerals,axiom,( ( m2_subset_1 @ np__0 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__0 @ k5_numbers ) & ( m1_subset_1 @ np__0 @ k1_numbers ) ),file(numerals,spc0_numerals)).
thf(spc1_arithm,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) ) => ( = @ ( k2_xcmplx_0 @ A @ ( k4_xcmplx_0 @ B ) ) @ ( k6_xcmplx_0 @ A @ B ) ) ) ),file(arithm,spc1_arithm)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(spc1_numerals,axiom,( ( v2_xxreal_0 @ np__1 ) & ( m2_subset_1 @ np__1 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__1 @ k5_numbers ) & ( m1_subset_1 @ np__1 @ k1_numbers ) ),file(numerals,spc1_numerals)).
thf(spc2_boole,axiom,( ~ ( v1_xboole_0 @ np__2 ) ),file(boole,spc2_boole)).
thf(spc2_numerals,axiom,( ( v2_xxreal_0 @ np__2 ) & ( m2_subset_1 @ np__2 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__2 @ k5_numbers ) & ( m1_subset_1 @ np__2 @ k1_numbers ) ),file(numerals,spc2_numerals)).
thf(spc6_arithm,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) & ( v1_xcmplx_0 @ C ) ) => ( = @ ( k2_xcmplx_0 @ ( k2_xcmplx_0 @ A @ B ) @ C ) @ ( k2_xcmplx_0 @ A @ ( k2_xcmplx_0 @ B @ C ) ) ) ) ),file(arithm,spc6_arithm)).
thf(spc8_arithm,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) ) => ( = @ ( k2_xcmplx_0 @ ( k4_xcmplx_0 @ A ) @ ( k4_xcmplx_0 @ B ) ) @ ( k4_xcmplx_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ) ),file(arithm,spc8_arithm)).
thf(spc9_arithm,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) ) => ( = @ ( k6_xcmplx_0 @ ( k4_xcmplx_0 @ A ) @ ( k4_xcmplx_0 @ B ) ) @ ( k6_xcmplx_0 @ B @ A ) ) ) ),file(arithm,spc9_arithm)).
thf(t16_cqc_sim1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ! [B: $i] : ( ( m2_subset_1 @ B @ ( k9_qc_lang1 @ A ) @ ( k3_cqc_lang @ A ) ) => ( = @ ( k7_cqc_sim1 @ A @ ( k6_cqc_lang @ A @ B ) ) @ ( k7_cqc_sim1 @ A @ B ) ) ) ) ),file(cqc_sim1,t16_cqc_sim1)).
thf(t17_cqc_sim1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ! [B: $i] : ( ( m2_subset_1 @ B @ ( k9_qc_lang1 @ A ) @ ( k3_cqc_lang @ A ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ ( k9_qc_lang1 @ A ) @ ( k3_cqc_lang @ A ) ) => ( = @ ( k7_cqc_sim1 @ A @ ( k7_cqc_lang @ A @ B @ C ) ) @ ( k2_nat_1 @ ( k7_cqc_sim1 @ A @ B ) @ ( k7_cqc_sim1 @ A @ C ) ) ) ) ) ) ),file(cqc_sim1,t17_cqc_sim1)).
thf(t18_cqc_sim1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ! [B: $i] : ( ( m2_subset_1 @ B @ ( k9_qc_lang1 @ A ) @ ( k3_cqc_lang @ A ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ ( k2_qc_lang1 @ A ) @ ( k3_qc_lang1 @ A ) ) => ( = @ ( k7_cqc_sim1 @ A @ ( k11_cqc_lang @ A @ C @ B ) ) @ ( k2_nat_1 @ ( k7_cqc_sim1 @ A @ B ) @ np__1 ) ) ) ) ) ),file(cqc_sim1,t18_cqc_sim1)).
thf(t1_arithm,axiom,( ! [A: $i] : ( ( v1_xcmplx_0 @ A ) => ( = @ ( k2_xcmplx_0 @ A @ k6_numbers ) @ A ) ) ),file(arithm,t1_arithm)).
thf(t1_numerals,axiom,( m1_subset_1 @ k1_xboole_0 @ k4_ordinal1 ),file(numerals,t1_numerals)).
thf(t1_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ( m1_subset_1 @ A @ B ) ) ),file(subset,t1_subset)).
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(t4_arithm,axiom,( ! [A: $i] : ( ( v1_xcmplx_0 @ A ) => ( = @ ( k6_xcmplx_0 @ A @ k6_numbers ) @ A ) ) ),file(arithm,t4_arithm)).
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(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(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_cqc_lang,axiom,( ! [A: $i > $o] : ! [B: $i] : ( ! [C: $i] : ( ( m2_subset_1 @ C @ ( k9_qc_lang1 @ B ) @ ( k3_cqc_lang @ B ) ) => ! [D: $i] : ( ( m2_subset_1 @ D @ ( k9_qc_lang1 @ B ) @ ( k3_cqc_lang @ B ) ) => ! [E: $i] : ( ( m2_subset_1 @ E @ ( k2_qc_lang1 @ B ) @ ( k3_qc_lang1 @ B ) ) => ! [F: $i] : ( ( m1_subset_1 @ F @ k5_numbers ) => ! [G: $i] : ( ( ( v5_relat_1 @ G @ ( k3_qc_lang1 @ B ) ) & ( v3_card_1 @ G @ F ) & ( m2_finseq_1 @ G @ ( k2_qc_lang1 @ B ) ) ) => ! [H: $i] : ( ( m2_subset_1 @ H @ ( k6_qc_lang1 @ B ) @ ( k8_qc_lang1 @ B @ F ) ) => ( ( A @ ( k5_cqc_lang @ B ) ) & ( A @ ( k4_cqc_lang @ F @ B @ H @ G ) ) & ( ( A @ C ) => ( A @ ( k6_cqc_lang @ B @ C ) ) ) & ( ( ( A @ C ) & ( A @ D ) ) => ( A @ ( k7_cqc_lang @ B @ C @ D ) ) ) & ( ( A @ C ) => ( A @ ( k11_cqc_lang @ B @ E @ C ) ) ) ) ) ) ) ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ ( k9_qc_lang1 @ B ) @ ( k3_cqc_lang @ B ) ) => ( A @ C ) ) ) ),file(cqc_lang,s1_cqc_lang)).
thf(s3_substut2,conjecture,( ! [A: $i] : ( ( m2_subset_1 @ A @ ( k9_qc_lang1 @ f1_s3_substut2 ) @ ( k3_cqc_lang @ f1_s3_substut2 ) ) => ! [B: $i] : ( ( m2_subset_1 @ B @ ( k9_qc_lang1 @ f1_s3_substut2 ) @ ( k3_cqc_lang @ f1_s3_substut2 ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ ( k2_qc_lang1 @ f1_s3_substut2 ) @ ( k3_qc_lang1 @ f1_s3_substut2 ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ k5_numbers ) => ! [E: $i] : ( ( ( v5_relat_1 @ E @ ( k3_qc_lang1 @ f1_s3_substut2 ) ) & ( v3_card_1 @ E @ D ) & ( m2_finseq_1 @ E @ ( k2_qc_lang1 @ f1_s3_substut2 ) ) ) => ! [F: $i] : ( ( m2_subset_1 @ F @ ( k6_qc_lang1 @ f1_s3_substut2 ) @ ( k8_qc_lang1 @ f1_s3_substut2 @ D ) ) => ( ( p1_s3_substut2 @ ( k5_cqc_lang @ f1_s3_substut2 ) ) & ( p1_s3_substut2 @ ( k4_cqc_lang @ D @ f1_s3_substut2 @ F @ E ) ) & ( ( p1_s3_substut2 @ A ) => ( p1_s3_substut2 @ ( k6_cqc_lang @ f1_s3_substut2 @ A ) ) ) & ( ( ( p1_s3_substut2 @ A ) & ( p1_s3_substut2 @ B ) ) => ( p1_s3_substut2 @ ( k7_cqc_lang @ f1_s3_substut2 @ A @ B ) ) ) ) ) ) ) ) ) ) => ! [A: $i] : ( ( m2_subset_1 @ A @ ( k9_qc_lang1 @ f1_s3_substut2 ) @ ( k3_cqc_lang @ f1_s3_substut2 ) ) => ( ( = @ ( k7_cqc_sim1 @ f1_s3_substut2 @ A ) @ k6_numbers ) => ( p1_s3_substut2 @ A ) ) ) ),file(substut2,s3_substut2)).
