% Mizar problem: s2_qc_lang1,qc_lang1,1286,8 
include('Axioms/SET010^2.ax').
thf(n1_type,type,( np__1: $i )).
thf(n2_type,type,( np__2: $i )).
thf(n3_type,type,( np__3: $i )).
thf(n4_type,type,( np__4: $i )).
thf(n5_type,type,( np__5: $i )).
thf(n6_type,type,( np__6: $i )).
thf(n7_type,type,( np__7: $i )).
thf(f1_s2_qc_lang1_type,type,( f1_s2_qc_lang1: $i )).
thf(k10_qc_lang1_type,type,( k10_qc_lang1: $i > $i > $i > $i )).
thf(k10_xtuple_0_type,type,( k10_xtuple_0: $i > $i )).
thf(k11_qc_lang1_type,type,( k11_qc_lang1: $i > $i > $i )).
thf(k12_finseq_1_type,type,( k12_finseq_1: $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(k18_qc_lang1_type,type,( k18_qc_lang1: $i > $i > $i )).
thf(k19_qc_lang1_type,type,( k19_qc_lang1: $i > $i > $i )).
thf(k1_nat_1_type,type,( k1_nat_1: $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_qc_lang1_type,type,( k1_qc_lang1: $i > $i )).
thf(k1_tarski_type,type,( k1_tarski: $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k20_qc_lang1_type,type,( k20_qc_lang1: $i > $i > $i )).
thf(k22_qc_lang1_type,type,( k22_qc_lang1: $i > $i > $i )).
thf(k2_qc_lang1_type,type,( k2_qc_lang1: $i > $i )).
thf(k2_tarski_type,type,( k2_tarski: $i > $i > $i )).
thf(k2_xboole_0_type,type,( k2_xboole_0: $i > $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_qc_lang1_type,type,( k3_qc_lang1: $i > $i )).
thf(k3_xcmplx_0_type,type,( k3_xcmplx_0: $i > $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(k5_finseq_1_type,type,( k5_finseq_1: $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_numbers_type,type,( k6_numbers: $i )).
thf(k6_qc_lang1_type,type,( k6_qc_lang1: $i > $i )).
thf(k7_finseq_1_type,type,( k7_finseq_1: $i > $i > $i )).
thf(k7_qc_lang1_type,type,( k7_qc_lang1: $i > $i > $i )).
thf(k8_qc_lang1_type,type,( k8_qc_lang1: $i > $i > $i )).
thf(k9_finseq_1_type,type,( k9_finseq_1: $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_s2_qc_lang1_type,type,( p1_s2_qc_lang1: $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(r1_xxreal_0_type,type,( r1_xxreal_0: $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_funct_1_type,type,( v1_funct_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_setfam_1_type,type,( v1_setfam_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_xtuple_0_type,type,( v1_xtuple_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_finseq_1_type,type,( v2_finseq_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_qc_lang1_type,type,( v2_qc_lang1: $i > $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_finseq_1_type,type,( v3_finseq_1: $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_qc_lang1_type,type,( v3_qc_lang1: $i > $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(v4_qc_lang1_type,type,( v4_qc_lang1: $i > $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v5_qc_lang1_type,type,( v5_qc_lang1: $i > $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_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_finseq_1 @ B ) ) ) ),file(finseq_1,cc10_finseq_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(cc11_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v3_finseq_1 @ B ) ) ) ),file(finseq_1,cc11_finseq_1)).
thf(cc1_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(card_1,cc1_card_1)).
thf(cc1_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_finseq_1 @ A ) ) ) ),file(finseq_1,cc1_finseq_1)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_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_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) ) ),file(finseq_1,cc2_finseq_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_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(cc3_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc3_card_1)).
thf(cc3_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_finseq_1 @ B @ A ) => ( v5_relat_1 @ B @ A ) ) ),file(finseq_1,cc3_finseq_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_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(cc4_card_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc4_card_1)).
thf(cc4_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_finseq_1 @ A ) ) ) ),file(finseq_1,cc4_finseq_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(cc5_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc5_card_1)).
thf(cc5_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) ) ),file(finseq_1,cc5_finseq_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_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) => ( v4_relat_1 @ C @ A ) ) ) ),file(relat_1,cc5_relat_1)).
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(cc6_card_1,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v1_finset_1 @ A ) ) => ( v7_ordinal1 @ A ) ) ),file(card_1,cc6_card_1)).
thf(cc6_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finseq_1 @ A ) ) ) ),file(finseq_1,cc6_finseq_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(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_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ( v2_finseq_1 @ A ) ) ) ),file(finseq_1,cc7_finseq_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_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) ) ) ),file(relat_1,cc7_relat_1)).
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_finseq_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_finseq_1 @ A ) ) ),file(finseq_1,cc8_finseq_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(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_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ( v4_funct_1 @ A ) ) ),file(finseq_1,cc9_finseq_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_k1_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ( = @ ( k1_nat_1 @ A @ B ) @ ( k1_nat_1 @ B @ A ) ) ) ),file(nat_1,k1_nat_1)).
thf(commutativity_k2_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ B @ A ) ) ),file(tarski,k2_tarski)).
thf(commutativity_k2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ A ) ) ),file(xboole_0,k2_xboole_0)).
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(commutativity_k3_xcmplx_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) ) => ( = @ ( k3_xcmplx_0 @ A @ B ) @ ( k3_xcmplx_0 @ B @ A ) ) ) ),file(xcmplx_0,k3_xcmplx_0)).
thf(connectedness_r1_xxreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v1_xxreal_0 @ B ) ) => ( ( r1_xxreal_0 @ A @ B ) | ( r1_xxreal_0 @ B @ A ) ) ) ),file(xxreal_0,r1_xxreal_0)).
thf(d13_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) => ( = @ ( k11_qc_lang1 @ A @ B ) @ B ) ) ) ),file(qc_lang1,d13_qc_lang1)).
thf(d14_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( = @ ( k12_qc_lang1 @ A ) @ ( k9_finseq_1 @ ( k4_tarski @ k6_numbers @ k6_numbers ) ) ) ) ),file(qc_lang1,d14_qc_lang1)).
thf(d15_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) => ( = @ ( k13_qc_lang1 @ A @ B ) @ ( k7_finseq_1 @ ( k9_finseq_1 @ ( k4_tarski @ np__1 @ k6_numbers ) ) @ ( k11_qc_lang1 @ A @ B ) ) ) ) ) ),file(qc_lang1,d15_qc_lang1)).
thf(d16_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k9_qc_lang1 @ A ) ) => ( = @ ( k14_qc_lang1 @ A @ B @ C ) @ ( k7_finseq_1 @ ( k7_finseq_1 @ ( k9_finseq_1 @ ( k4_tarski @ np__2 @ k6_numbers ) ) @ ( k11_qc_lang1 @ A @ B ) ) @ ( k11_qc_lang1 @ A @ C ) ) ) ) ) ) ),file(qc_lang1,d16_qc_lang1)).
thf(d17_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ! [B: $i] : ( ( m2_subset_1 @ B @ ( k2_qc_lang1 @ A ) @ ( k3_qc_lang1 @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k9_qc_lang1 @ A ) ) => ( = @ ( k15_qc_lang1 @ A @ B @ C ) @ ( k7_finseq_1 @ ( k7_finseq_1 @ ( k9_finseq_1 @ ( k4_tarski @ np__3 @ k6_numbers ) ) @ ( k12_finseq_1 @ ( k3_qc_lang1 @ A ) @ B ) ) @ ( k11_qc_lang1 @ A @ C ) ) ) ) ) ) ),file(qc_lang1,d17_qc_lang1)).
thf(d18_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) => ( ( v2_qc_lang1 @ B @ A ) <=> ? [C: $i] : ( ( m1_subset_1 @ C @ k5_numbers ) & ? [D: $i] : ( ( m2_subset_1 @ D @ ( k6_qc_lang1 @ A ) @ ( k8_qc_lang1 @ A @ C ) ) & ? [E: $i] : ( ( v3_card_1 @ E @ C ) & ( m2_finseq_1 @ E @ ( k2_qc_lang1 @ A ) ) & ( = @ B @ ( k10_qc_lang1 @ A @ D @ E ) ) ) ) ) ) ) ) ),file(qc_lang1,d18_qc_lang1)).
thf(d19_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) => ( ( v3_qc_lang1 @ B @ A ) <=> ? [C: $i] : ( ( m1_subset_1 @ C @ ( k9_qc_lang1 @ A ) ) & ( = @ B @ ( k13_qc_lang1 @ A @ C ) ) ) ) ) ) ),file(qc_lang1,d19_qc_lang1)).
thf(d20_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) => ( ( v4_qc_lang1 @ B @ A ) <=> ? [C: $i] : ( ( m1_subset_1 @ C @ ( k9_qc_lang1 @ A ) ) & ? [D: $i] : ( ( m1_subset_1 @ D @ ( k9_qc_lang1 @ A ) ) & ( = @ B @ ( k14_qc_lang1 @ A @ C @ D ) ) ) ) ) ) ) ),file(qc_lang1,d20_qc_lang1)).
thf(d21_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) => ( ( v5_qc_lang1 @ B @ A ) <=> ? [C: $i] : ( ( m2_subset_1 @ C @ ( k2_qc_lang1 @ A ) @ ( k3_qc_lang1 @ A ) ) & ? [D: $i] : ( ( m1_subset_1 @ D @ ( k9_qc_lang1 @ A ) ) & ( = @ B @ ( k15_qc_lang1 @ A @ C @ D ) ) ) ) ) ) ) ),file(qc_lang1,d21_qc_lang1)).
thf(d24_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) => ( ( v3_qc_lang1 @ B @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k9_qc_lang1 @ A ) ) => ( ( = @ C @ ( k18_qc_lang1 @ A @ B ) ) <=> ( = @ B @ ( k13_qc_lang1 @ A @ C ) ) ) ) ) ) ) ),file(qc_lang1,d24_qc_lang1)).
thf(d25_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) => ( ( v4_qc_lang1 @ B @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k9_qc_lang1 @ A ) ) => ( ( = @ C @ ( k19_qc_lang1 @ A @ B ) ) <=> ? [D: $i] : ( ( m1_subset_1 @ D @ ( k9_qc_lang1 @ A ) ) & ( = @ B @ ( k14_qc_lang1 @ A @ C @ D ) ) ) ) ) ) ) ) ),file(qc_lang1,d25_qc_lang1)).
thf(d26_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) => ( ( v4_qc_lang1 @ B @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k9_qc_lang1 @ A ) ) => ( ( = @ C @ ( k20_qc_lang1 @ A @ B ) ) <=> ? [D: $i] : ( ( m1_subset_1 @ D @ ( k9_qc_lang1 @ A ) ) & ( = @ B @ ( k14_qc_lang1 @ A @ D @ C ) ) ) ) ) ) ) ) ),file(qc_lang1,d26_qc_lang1)).
thf(d28_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) => ( ( v5_qc_lang1 @ B @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k9_qc_lang1 @ A ) ) => ( ( = @ C @ ( k22_qc_lang1 @ A @ B ) ) <=> ? [D: $i] : ( ( m2_subset_1 @ D @ ( k2_qc_lang1 @ A ) @ ( k3_qc_lang1 @ A ) ) & ( = @ B @ ( k15_qc_lang1 @ A @ D @ C ) ) ) ) ) ) ) ) ),file(qc_lang1,d28_qc_lang1)).
thf(d2_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( = @ ( k1_qc_lang1 @ A ) @ ( k10_xtuple_0 @ A ) ) ) ),file(qc_lang1,d2_qc_lang1)).
thf(d2_xboole_0,axiom,( = @ k1_xboole_0 @ ( eps @ ^ [A: $i] : ( v1_xboole_0 @ A ) ) ),file(xboole_0,d2_xboole_0)).
thf(d3_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( = @ ( k2_qc_lang1 @ A ) @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ np__6 ) @ k5_numbers ) @ ( k2_zfmisc_1 @ ( k2_tarski @ np__4 @ np__5 ) @ ( k1_qc_lang1 @ A ) ) ) ) ) ),file(qc_lang1,d3_qc_lang1)).
thf(d4_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( = @ ( k3_qc_lang1 @ A ) @ ( k2_zfmisc_1 @ ( k1_tarski @ np__4 ) @ ( k1_qc_lang1 @ A ) ) ) ) ),file(qc_lang1,d4_qc_lang1)).
thf(d5_finseq_1,axiom,( ! [A: $i] : ( = @ ( k5_finseq_1 @ A ) @ ( k1_tarski @ ( k4_tarski @ np__1 @ A ) ) ) ),file(finseq_1,d5_finseq_1)).
thf(d5_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k4_tarski @ A @ B ) @ ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ) ),file(tarski,d5_tarski)).
thf(d7_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( = @ ( k6_qc_lang1 @ A ) @ ( replSep2 @ ^ [B: $i] : ( m1_subset_1 @ B @ k5_numbers ) @ ^ [B: $i] : ^ [C: $i] : ( m1_subset_1 @ C @ ( k1_qc_lang1 @ A ) ) @ ^ [B: $i] : ^ [C: $i] : ( k4_tarski @ B @ C ) @ ^ [B: $i] : ^ [C: $i] : ( r1_xxreal_0 @ np__7 @ B ) ) ) ) ),file(qc_lang1,d7_qc_lang1)).
thf(d9_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ k5_numbers ) => ( = @ ( k8_qc_lang1 @ A @ B ) @ ( replSep1 @ ^ [C: $i] : ( m1_subset_1 @ C @ ( k6_qc_lang1 @ A ) ) @ ^ [C: $i] : C @ ^ [C: $i] : ( = @ ( k7_qc_lang1 @ A @ C ) @ B ) ) ) ) ) ),file(qc_lang1,d9_qc_lang1)).
thf(dt_f1_s2_qc_lang1,axiom,( m1_qc_lang1 @ f1_s2_qc_lang1 ),file(qc_lang1,f1_s2_qc_lang1)).
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_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
thf(dt_k11_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) ) => ( m2_finseq_1 @ ( k11_qc_lang1 @ A @ B ) @ ( k2_zfmisc_1 @ k5_numbers @ ( k1_qc_lang1 @ A ) ) ) ) ),file(qc_lang1,k11_qc_lang1)).
thf(dt_k12_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) ) => ( m2_finseq_1 @ ( k12_finseq_1 @ A @ B ) @ A ) ) ),file(finseq_1,k12_finseq_1)).
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_k18_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) ) => ( m1_subset_1 @ ( k18_qc_lang1 @ A @ B ) @ ( k9_qc_lang1 @ A ) ) ) ),file(qc_lang1,k18_qc_lang1)).
thf(dt_k19_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) ) => ( m1_subset_1 @ ( k19_qc_lang1 @ A @ B ) @ ( k9_qc_lang1 @ A ) ) ) ),file(qc_lang1,k19_qc_lang1)).
thf(dt_k1_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ( m2_subset_1 @ ( k1_nat_1 @ A @ B ) @ k1_numbers @ k5_numbers ) ) ),file(nat_1,k1_nat_1)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k1_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ~ ( v1_xboole_0 @ ( k1_qc_lang1 @ A ) ) ) ),file(qc_lang1,k1_qc_lang1)).
thf(dt_k1_tarski,axiom,( $true ),file(tarski,k1_tarski)).
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_k20_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) ) => ( m1_subset_1 @ ( k20_qc_lang1 @ A @ B ) @ ( k9_qc_lang1 @ A ) ) ) ),file(qc_lang1,k20_qc_lang1)).
thf(dt_k22_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) ) => ( m1_subset_1 @ ( k22_qc_lang1 @ A @ B ) @ ( k9_qc_lang1 @ A ) ) ) ),file(qc_lang1,k22_qc_lang1)).
thf(dt_k2_qc_lang1,axiom,( $true ),file(qc_lang1,k2_qc_lang1)).
thf(dt_k2_tarski,axiom,( $true ),file(tarski,k2_tarski)).
thf(dt_k2_xboole_0,axiom,( $true ),file(xboole_0,k2_xboole_0)).
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_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_k3_xcmplx_0,axiom,( $true ),file(xcmplx_0,k3_xcmplx_0)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_k5_finseq_1,axiom,( $true ),file(finseq_1,k5_finseq_1)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
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_k7_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_finseq_1 @ B ) ) => ( ( v1_relat_1 @ ( k7_finseq_1 @ A @ B ) ) & ( v1_funct_1 @ ( k7_finseq_1 @ A @ B ) ) & ( v1_finseq_1 @ ( k7_finseq_1 @ A @ B ) ) ) ) ),file(finseq_1,k7_finseq_1)).
thf(dt_k7_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k6_qc_lang1 @ A ) ) ) => ( m1_subset_1 @ ( k7_qc_lang1 @ A @ B ) @ k5_numbers ) ) ),file(qc_lang1,k7_qc_lang1)).
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_finseq_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ ( k9_finseq_1 @ A ) ) & ( v1_funct_1 @ ( k9_finseq_1 @ A ) ) ) ),file(finseq_1,k9_finseq_1)).
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_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( v1_setfam_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(funct_1,fc10_funct_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_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k10_xtuple_0 @ A ) ) ) ),file(relat_1,fc11_relat_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_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) => ( v1_zfmisc_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(funct_1,fc12_funct_1)).
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_card_1,axiom,( ! [A: $i] : ( v3_card_1 @ ( k1_tarski @ A ) @ np__1 ) ),file(card_1,fc13_card_1)).
thf(fc13_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) => ~ ( v1_zfmisc_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(funct_1,fc13_funct_1)).
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_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( v4_funct_1 @ ( k1_tarski @ A ) ) ) ),file(funct_1,fc14_funct_1)).
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_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( v4_funct_1 @ ( k2_tarski @ A @ B ) ) ) ),file(funct_1,fc15_funct_1)).
thf(fc16_finseq_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k5_finseq_1 @ A ) ) ),file(finseq_1,fc16_finseq_1)).
thf(fc17_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ~ ( v1_xboole_0 @ B ) & ( v1_finseq_1 @ B ) ) => ( ( v1_relat_1 @ ( k7_finseq_1 @ A @ B ) ) & ( v1_funct_1 @ ( k7_finseq_1 @ A @ B ) ) & ~ ( v1_xboole_0 @ ( k7_finseq_1 @ A @ B ) ) & ( v1_finseq_1 @ ( k7_finseq_1 @ A @ B ) ) ) ) ),file(finseq_1,fc17_finseq_1)).
thf(fc18_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ~ ( v1_xboole_0 @ B ) & ( v1_finseq_1 @ B ) ) => ( ( v1_relat_1 @ ( k7_finseq_1 @ B @ A ) ) & ( v1_funct_1 @ ( k7_finseq_1 @ B @ A ) ) & ~ ( v1_xboole_0 @ ( k7_finseq_1 @ B @ A ) ) & ( v1_finseq_1 @ ( k7_finseq_1 @ B @ A ) ) ) ) ),file(finseq_1,fc18_finseq_1)).
thf(fc1_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_funct_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ) ),file(funct_1,fc1_funct_1)).
thf(fc1_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ~ ( v1_xboole_0 @ ( k1_qc_lang1 @ A ) ) ) ),file(qc_lang1,fc1_qc_lang1)).
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(fc1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( v1_xtuple_0 @ ( k4_tarski @ A @ B ) ) ),file(xtuple_0,fc1_xtuple_0)).
thf(fc23_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 @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc23_xreal_0)).
thf(fc24_finseq_1,axiom,( ! [A: $i] : ( v3_card_1 @ ( k5_finseq_1 @ A ) @ np__1 ) ),file(finseq_1,fc24_finseq_1)).
thf(fc24_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 @ ( k3_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc24_xreal_0)).
thf(fc25_relat_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) ) => ( v1_zfmisc_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(relat_1,fc25_relat_1)).
thf(fc25_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 @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc25_xreal_0)).
thf(fc26_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 @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc26_xreal_0)).
thf(fc28_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v7_ordinal1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) & ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( v3_card_1 @ C @ A ) & ( v1_finseq_1 @ C ) & ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( v3_card_1 @ D @ B ) & ( v1_finseq_1 @ D ) ) => ( ( v1_relat_1 @ ( k7_finseq_1 @ C @ D ) ) & ( v1_funct_1 @ ( k7_finseq_1 @ C @ D ) ) & ( v3_card_1 @ ( k7_finseq_1 @ C @ D ) @ ( k1_nat_1 @ A @ B ) ) & ( v1_finseq_1 @ ( k7_finseq_1 @ C @ D ) ) ) ) ),file(finseq_1,fc28_finseq_1)).
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(fc2_xboole_0,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ) ),file(xboole_0,fc2_xboole_0)).
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_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) ) => ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),file(relat_1,fc3_relat_1)).
thf(fc3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ) ),file(xboole_0,fc3_xboole_0)).
thf(fc4_card_1,axiom,( v1_card_1 @ k4_ordinal1 ),file(card_1,fc4_card_1)).
thf(fc4_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ A ) => ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ) ),file(xboole_0,fc4_xboole_0)).
thf(fc5_card_1,axiom,( v2_card_1 @ k4_ordinal1 ),file(card_1,fc5_card_1)).
thf(fc5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ) ),file(relat_1,fc5_relat_1)).
thf(fc5_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ A ) => ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ) ),file(xboole_0,fc5_xboole_0)).
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(fc5_xtuple_0,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k10_xtuple_0 @ A ) ) ) ),file(xtuple_0,fc5_xtuple_0)).
thf(fc6_finseq_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ ( k5_finseq_1 @ A ) ) & ( v1_funct_1 @ ( k5_finseq_1 @ A ) ) ) ),file(finseq_1,fc6_finseq_1)).
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(fc6_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xreal_0 @ A ) & ( v1_xreal_0 @ B ) ) => ( v1_xreal_0 @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc6_xreal_0)).
thf(fc7_card_1,axiom,( ~ ( v1_finset_1 @ k4_ordinal1 ) ),file(card_1,fc7_card_1)).
thf(fc7_finseq_1,axiom,( ! [A: $i] : ( v1_finseq_1 @ ( k5_finseq_1 @ A ) ) ),file(finseq_1,fc7_finseq_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_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( v1_relat_1 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) ) ),file(relat_1,fc7_relat_1)).
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_relat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ~ ( v1_xboole_0 @ ( k10_xtuple_0 @ A ) ) ) ),file(relat_1,fc9_relat_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(idempotence_k2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k2_xboole_0)).
thf(rc1_card_1,axiom,( ? [A: $i] : ( v1_card_1 @ A ) ),file(card_1,rc1_card_1)).
thf(rc1_finseq_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ A ) ) ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_finseq_1 @ B ) ) ),file(finseq_1,rc1_finseq_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc1_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( m1_qc_lang1 @ B ) ) => ? [C: $i] : ( ( m1_finseq_1 @ C @ ( k2_qc_lang1 @ B ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ k5_numbers ) & ( v5_relat_1 @ C @ ( k2_qc_lang1 @ B ) ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) & ( v3_card_1 @ C @ A ) & ( v1_finseq_1 @ C ) & ( v2_finseq_1 @ C ) ) ) ),file(qc_lang1,rc1_qc_lang1)).
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_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_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_finseq_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_finseq_1 @ B @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) & ( v1_finseq_1 @ B ) ) ),file(finseq_1,rc2_finseq_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_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(rc3_card_1,axiom,( ? [A: $i] : ~ ( v1_finset_1 @ A ) ),file(card_1,rc3_card_1)).
thf(rc3_finseq_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finseq_1 @ A ) ) ),file(finseq_1,rc3_finseq_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_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_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relat_1,rc3_relat_1)).
thf(rc3_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_subset_1 @ B @ A ) ) ),file(subset_1,rc3_subset_1)).
thf(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(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_finseq_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v1_finseq_1 @ A ) & ( v2_finseq_1 @ A ) ) ),file(finseq_1,rc4_finseq_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(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_finseq_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v1_finseq_1 @ A ) & ( v2_finseq_1 @ A ) ) ),file(finseq_1,rc5_finseq_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_finseq_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_finseq_1 @ B @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ~ ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) & ( v1_finseq_1 @ B ) & ( v2_finseq_1 @ B ) ) ) ),file(finseq_1,rc6_finseq_1)).
thf(rc6_funct_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 ) ) ),file(funct_1,rc6_funct_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_finseq_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v3_card_1 @ B @ A ) & ( v1_finseq_1 @ B ) & ( v2_finseq_1 @ B ) ) ) ),file(finseq_1,rc7_finseq_1)).
thf(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(rc8_finseq_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v3_finseq_1 @ A ) ) ),file(finseq_1,rc8_finseq_1)).
thf(rc9_finseq_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v1_finseq_1 @ B ) & ( v2_finseq_1 @ B ) ) ),file(finseq_1,rc9_finseq_1)).
thf(rc9_funct_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) ),file(funct_1,rc9_funct_1)).
thf(redefinition_k12_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) ) => ( = @ ( k12_finseq_1 @ A @ B ) @ ( k5_finseq_1 @ B ) ) ) ),file(finseq_1,k12_finseq_1)).
thf(redefinition_k1_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ( = @ ( k1_nat_1 @ A @ B ) @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(nat_1,k1_nat_1)).
thf(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
thf(redefinition_k6_numbers,axiom,( = @ k6_numbers @ k1_xboole_0 ),file(numbers,k6_numbers)).
thf(redefinition_k9_finseq_1,axiom,( ! [A: $i] : ( = @ ( k9_finseq_1 @ A ) @ ( k5_finseq_1 @ A ) ) ),file(finseq_1,k9_finseq_1)).
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(reflexivity_r1_xxreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v1_xxreal_0 @ B ) ) => ( r1_xxreal_0 @ A @ A ) ) ),file(xxreal_0,r1_xxreal_0)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r1,axiom,( r1_xxreal_0 @ np__1 @ np__1 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r1_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r2,axiom,( r1_xxreal_0 @ np__1 @ np__2 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r1_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r3,axiom,( r1_xxreal_0 @ np__1 @ np__3 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r1_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r4,axiom,( r1_xxreal_0 @ np__1 @ np__4 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r1_r4)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r5,axiom,( r1_xxreal_0 @ np__1 @ np__5 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r1_r5)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r6,axiom,( r1_xxreal_0 @ np__1 @ np__6 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r1_r6)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r7,axiom,( r1_xxreal_0 @ np__1 @ np__7 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r1_r7)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r1,axiom,( ~ ( r1_xxreal_0 @ np__2 @ np__1 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r2_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r2,axiom,( r1_xxreal_0 @ np__2 @ np__2 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r2_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r3,axiom,( r1_xxreal_0 @ np__2 @ np__3 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r2_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r4,axiom,( r1_xxreal_0 @ np__2 @ np__4 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r2_r4)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r5,axiom,( r1_xxreal_0 @ np__2 @ np__5 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r2_r5)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r6,axiom,( r1_xxreal_0 @ np__2 @ np__6 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r2_r6)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r7,axiom,( r1_xxreal_0 @ np__2 @ np__7 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r2_r7)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r1,axiom,( ~ ( r1_xxreal_0 @ np__3 @ np__1 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r3_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r2,axiom,( ~ ( r1_xxreal_0 @ np__3 @ np__2 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r3_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r3,axiom,( r1_xxreal_0 @ np__3 @ np__3 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r3_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r4,axiom,( r1_xxreal_0 @ np__3 @ np__4 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r3_r4)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r5,axiom,( r1_xxreal_0 @ np__3 @ np__5 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r3_r5)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r6,axiom,( r1_xxreal_0 @ np__3 @ np__6 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r3_r6)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r7,axiom,( r1_xxreal_0 @ np__3 @ np__7 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r3_r7)).
thf(rqLessOrEqual__r1_xxreal_0__r4_r1,axiom,( ~ ( r1_xxreal_0 @ np__4 @ np__1 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r4_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r4_r2,axiom,( ~ ( r1_xxreal_0 @ np__4 @ np__2 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r4_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r4_r3,axiom,( ~ ( r1_xxreal_0 @ np__4 @ np__3 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r4_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r4_r4,axiom,( r1_xxreal_0 @ np__4 @ np__4 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r4_r4)).
thf(rqLessOrEqual__r1_xxreal_0__r4_r5,axiom,( r1_xxreal_0 @ np__4 @ np__5 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r4_r5)).
thf(rqLessOrEqual__r1_xxreal_0__r4_r6,axiom,( r1_xxreal_0 @ np__4 @ np__6 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r4_r6)).
thf(rqLessOrEqual__r1_xxreal_0__r4_r7,axiom,( r1_xxreal_0 @ np__4 @ np__7 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r4_r7)).
thf(rqLessOrEqual__r1_xxreal_0__r5_r1,axiom,( ~ ( r1_xxreal_0 @ np__5 @ np__1 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r5_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r5_r2,axiom,( ~ ( r1_xxreal_0 @ np__5 @ np__2 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r5_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r5_r3,axiom,( ~ ( r1_xxreal_0 @ np__5 @ np__3 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r5_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r5_r4,axiom,( ~ ( r1_xxreal_0 @ np__5 @ np__4 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r5_r4)).
thf(rqLessOrEqual__r1_xxreal_0__r5_r5,axiom,( r1_xxreal_0 @ np__5 @ np__5 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r5_r5)).
thf(rqLessOrEqual__r1_xxreal_0__r5_r6,axiom,( r1_xxreal_0 @ np__5 @ np__6 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r5_r6)).
thf(rqLessOrEqual__r1_xxreal_0__r5_r7,axiom,( r1_xxreal_0 @ np__5 @ np__7 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r5_r7)).
thf(rqLessOrEqual__r1_xxreal_0__r6_r1,axiom,( ~ ( r1_xxreal_0 @ np__6 @ np__1 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r6_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r6_r2,axiom,( ~ ( r1_xxreal_0 @ np__6 @ np__2 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r6_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r6_r3,axiom,( ~ ( r1_xxreal_0 @ np__6 @ np__3 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r6_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r6_r4,axiom,( ~ ( r1_xxreal_0 @ np__6 @ np__4 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r6_r4)).
thf(rqLessOrEqual__r1_xxreal_0__r6_r5,axiom,( ~ ( r1_xxreal_0 @ np__6 @ np__5 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r6_r5)).
thf(rqLessOrEqual__r1_xxreal_0__r6_r6,axiom,( r1_xxreal_0 @ np__6 @ np__6 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r6_r6)).
thf(rqLessOrEqual__r1_xxreal_0__r6_r7,axiom,( r1_xxreal_0 @ np__6 @ np__7 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r6_r7)).
thf(rqLessOrEqual__r1_xxreal_0__r7_r1,axiom,( ~ ( r1_xxreal_0 @ np__7 @ np__1 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r7_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r7_r2,axiom,( ~ ( r1_xxreal_0 @ np__7 @ np__2 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r7_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r7_r3,axiom,( ~ ( r1_xxreal_0 @ np__7 @ np__3 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r7_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r7_r4,axiom,( ~ ( r1_xxreal_0 @ np__7 @ np__4 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r7_r4)).
thf(rqLessOrEqual__r1_xxreal_0__r7_r5,axiom,( ~ ( r1_xxreal_0 @ np__7 @ np__5 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r7_r5)).
thf(rqLessOrEqual__r1_xxreal_0__r7_r6,axiom,( ~ ( r1_xxreal_0 @ np__7 @ np__6 ) ),file(arithm,rqLessOrEqual__r1_xxreal_0__r7_r6)).
thf(rqLessOrEqual__r1_xxreal_0__r7_r7,axiom,( r1_xxreal_0 @ np__7 @ np__7 ),file(arithm,rqLessOrEqual__r1_xxreal_0__r7_r7)).
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_r2_r3,axiom,( = @ ( k2_xcmplx_0 @ np__1 @ np__2 ) @ np__3 ),file(arithm,rqRealAdd__k2_xcmplx_0__r1_r2_r3)).
thf(rqRealAdd__k2_xcmplx_0__r1_r3_r4,axiom,( = @ ( k2_xcmplx_0 @ np__1 @ np__3 ) @ np__4 ),file(arithm,rqRealAdd__k2_xcmplx_0__r1_r3_r4)).
thf(rqRealAdd__k2_xcmplx_0__r1_r4_r5,axiom,( = @ ( k2_xcmplx_0 @ np__1 @ np__4 ) @ np__5 ),file(arithm,rqRealAdd__k2_xcmplx_0__r1_r4_r5)).
thf(rqRealAdd__k2_xcmplx_0__r1_r5_r6,axiom,( = @ ( k2_xcmplx_0 @ np__1 @ np__5 ) @ np__6 ),file(arithm,rqRealAdd__k2_xcmplx_0__r1_r5_r6)).
thf(rqRealAdd__k2_xcmplx_0__r1_r6_r7,axiom,( = @ ( k2_xcmplx_0 @ np__1 @ np__6 ) @ np__7 ),file(arithm,rqRealAdd__k2_xcmplx_0__r1_r6_r7)).
thf(rqRealAdd__k2_xcmplx_0__r2_r1_r3,axiom,( = @ ( k2_xcmplx_0 @ np__2 @ np__1 ) @ np__3 ),file(arithm,rqRealAdd__k2_xcmplx_0__r2_r1_r3)).
thf(rqRealAdd__k2_xcmplx_0__r2_r2_r4,axiom,( = @ ( k2_xcmplx_0 @ np__2 @ np__2 ) @ np__4 ),file(arithm,rqRealAdd__k2_xcmplx_0__r2_r2_r4)).
thf(rqRealAdd__k2_xcmplx_0__r2_r3_r5,axiom,( = @ ( k2_xcmplx_0 @ np__2 @ np__3 ) @ np__5 ),file(arithm,rqRealAdd__k2_xcmplx_0__r2_r3_r5)).
thf(rqRealAdd__k2_xcmplx_0__r2_r4_r6,axiom,( = @ ( k2_xcmplx_0 @ np__2 @ np__4 ) @ np__6 ),file(arithm,rqRealAdd__k2_xcmplx_0__r2_r4_r6)).
thf(rqRealAdd__k2_xcmplx_0__r2_r5_r7,axiom,( = @ ( k2_xcmplx_0 @ np__2 @ np__5 ) @ np__7 ),file(arithm,rqRealAdd__k2_xcmplx_0__r2_r5_r7)).
thf(rqRealAdd__k2_xcmplx_0__r3_r1_r4,axiom,( = @ ( k2_xcmplx_0 @ np__3 @ np__1 ) @ np__4 ),file(arithm,rqRealAdd__k2_xcmplx_0__r3_r1_r4)).
thf(rqRealAdd__k2_xcmplx_0__r3_r2_r5,axiom,( = @ ( k2_xcmplx_0 @ np__3 @ np__2 ) @ np__5 ),file(arithm,rqRealAdd__k2_xcmplx_0__r3_r2_r5)).
thf(rqRealAdd__k2_xcmplx_0__r3_r3_r6,axiom,( = @ ( k2_xcmplx_0 @ np__3 @ np__3 ) @ np__6 ),file(arithm,rqRealAdd__k2_xcmplx_0__r3_r3_r6)).
thf(rqRealAdd__k2_xcmplx_0__r3_r4_r7,axiom,( = @ ( k2_xcmplx_0 @ np__3 @ np__4 ) @ np__7 ),file(arithm,rqRealAdd__k2_xcmplx_0__r3_r4_r7)).
thf(rqRealAdd__k2_xcmplx_0__r4_r1_r5,axiom,( = @ ( k2_xcmplx_0 @ np__4 @ np__1 ) @ np__5 ),file(arithm,rqRealAdd__k2_xcmplx_0__r4_r1_r5)).
thf(rqRealAdd__k2_xcmplx_0__r4_r2_r6,axiom,( = @ ( k2_xcmplx_0 @ np__4 @ np__2 ) @ np__6 ),file(arithm,rqRealAdd__k2_xcmplx_0__r4_r2_r6)).
thf(rqRealAdd__k2_xcmplx_0__r4_r3_r7,axiom,( = @ ( k2_xcmplx_0 @ np__4 @ np__3 ) @ np__7 ),file(arithm,rqRealAdd__k2_xcmplx_0__r4_r3_r7)).
thf(rqRealAdd__k2_xcmplx_0__r5_r1_r6,axiom,( = @ ( k2_xcmplx_0 @ np__5 @ np__1 ) @ np__6 ),file(arithm,rqRealAdd__k2_xcmplx_0__r5_r1_r6)).
thf(rqRealAdd__k2_xcmplx_0__r5_r2_r7,axiom,( = @ ( k2_xcmplx_0 @ np__5 @ np__2 ) @ np__7 ),file(arithm,rqRealAdd__k2_xcmplx_0__r5_r2_r7)).
thf(rqRealAdd__k2_xcmplx_0__r6_r1_r7,axiom,( = @ ( k2_xcmplx_0 @ np__6 @ np__1 ) @ np__7 ),file(arithm,rqRealAdd__k2_xcmplx_0__r6_r1_r7)).
thf(rqRealMult__k3_xcmplx_0__r1_r1_r1,axiom,( = @ ( k3_xcmplx_0 @ np__1 @ np__1 ) @ np__1 ),file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1)).
thf(rqRealMult__k3_xcmplx_0__r1_r2_r2,axiom,( = @ ( k3_xcmplx_0 @ np__1 @ np__2 ) @ np__2 ),file(arithm,rqRealMult__k3_xcmplx_0__r1_r2_r2)).
thf(rqRealMult__k3_xcmplx_0__r1_r3_r3,axiom,( = @ ( k3_xcmplx_0 @ np__1 @ np__3 ) @ np__3 ),file(arithm,rqRealMult__k3_xcmplx_0__r1_r3_r3)).
thf(rqRealMult__k3_xcmplx_0__r1_r4_r4,axiom,( = @ ( k3_xcmplx_0 @ np__1 @ np__4 ) @ np__4 ),file(arithm,rqRealMult__k3_xcmplx_0__r1_r4_r4)).
thf(rqRealMult__k3_xcmplx_0__r1_r5_r5,axiom,( = @ ( k3_xcmplx_0 @ np__1 @ np__5 ) @ np__5 ),file(arithm,rqRealMult__k3_xcmplx_0__r1_r5_r5)).
thf(rqRealMult__k3_xcmplx_0__r1_r6_r6,axiom,( = @ ( k3_xcmplx_0 @ np__1 @ np__6 ) @ np__6 ),file(arithm,rqRealMult__k3_xcmplx_0__r1_r6_r6)).
thf(rqRealMult__k3_xcmplx_0__r1_r7_r7,axiom,( = @ ( k3_xcmplx_0 @ np__1 @ np__7 ) @ np__7 ),file(arithm,rqRealMult__k3_xcmplx_0__r1_r7_r7)).
thf(rqRealMult__k3_xcmplx_0__r2_r1_r2,axiom,( = @ ( k3_xcmplx_0 @ np__2 @ np__1 ) @ np__2 ),file(arithm,rqRealMult__k3_xcmplx_0__r2_r1_r2)).
thf(rqRealMult__k3_xcmplx_0__r2_r2_r4,axiom,( = @ ( k3_xcmplx_0 @ np__2 @ np__2 ) @ np__4 ),file(arithm,rqRealMult__k3_xcmplx_0__r2_r2_r4)).
thf(rqRealMult__k3_xcmplx_0__r2_r3_r6,axiom,( = @ ( k3_xcmplx_0 @ np__2 @ np__3 ) @ np__6 ),file(arithm,rqRealMult__k3_xcmplx_0__r2_r3_r6)).
thf(rqRealMult__k3_xcmplx_0__r3_r1_r3,axiom,( = @ ( k3_xcmplx_0 @ np__3 @ np__1 ) @ np__3 ),file(arithm,rqRealMult__k3_xcmplx_0__r3_r1_r3)).
thf(rqRealMult__k3_xcmplx_0__r3_r2_r6,axiom,( = @ ( k3_xcmplx_0 @ np__3 @ np__2 ) @ np__6 ),file(arithm,rqRealMult__k3_xcmplx_0__r3_r2_r6)).
thf(rqRealMult__k3_xcmplx_0__r4_r1_r4,axiom,( = @ ( k3_xcmplx_0 @ np__4 @ np__1 ) @ np__4 ),file(arithm,rqRealMult__k3_xcmplx_0__r4_r1_r4)).
thf(rqRealMult__k3_xcmplx_0__r5_r1_r5,axiom,( = @ ( k3_xcmplx_0 @ np__5 @ np__1 ) @ np__5 ),file(arithm,rqRealMult__k3_xcmplx_0__r5_r1_r5)).
thf(rqRealMult__k3_xcmplx_0__r6_r1_r6,axiom,( = @ ( k3_xcmplx_0 @ np__6 @ np__1 ) @ np__6 ),file(arithm,rqRealMult__k3_xcmplx_0__r6_r1_r6)).
thf(rqRealMult__k3_xcmplx_0__r7_r1_r7,axiom,( = @ ( k3_xcmplx_0 @ np__7 @ np__1 ) @ np__7 ),file(arithm,rqRealMult__k3_xcmplx_0__r7_r1_r7)).
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(spc3_boole,axiom,( ~ ( v1_xboole_0 @ np__3 ) ),file(boole,spc3_boole)).
thf(spc3_numerals,axiom,( ( v2_xxreal_0 @ np__3 ) & ( m2_subset_1 @ np__3 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__3 @ k5_numbers ) & ( m1_subset_1 @ np__3 @ k1_numbers ) ),file(numerals,spc3_numerals)).
thf(spc4_boole,axiom,( ~ ( v1_xboole_0 @ np__4 ) ),file(boole,spc4_boole)).
thf(spc4_numerals,axiom,( ( v2_xxreal_0 @ np__4 ) & ( m2_subset_1 @ np__4 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__4 @ k5_numbers ) & ( m1_subset_1 @ np__4 @ k1_numbers ) ),file(numerals,spc4_numerals)).
thf(spc5_arithm,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) & ( v1_xcmplx_0 @ C ) ) => ( = @ ( k3_xcmplx_0 @ ( k2_xcmplx_0 @ A @ B ) @ C ) @ ( k2_xcmplx_0 @ ( k3_xcmplx_0 @ A @ C ) @ ( k3_xcmplx_0 @ B @ C ) ) ) ) ),file(arithm,spc5_arithm)).
thf(spc5_boole,axiom,( ~ ( v1_xboole_0 @ np__5 ) ),file(boole,spc5_boole)).
thf(spc5_numerals,axiom,( ( v2_xxreal_0 @ np__5 ) & ( m2_subset_1 @ np__5 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__5 @ k5_numbers ) & ( m1_subset_1 @ np__5 @ k1_numbers ) ),file(numerals,spc5_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(spc6_boole,axiom,( ~ ( v1_xboole_0 @ np__6 ) ),file(boole,spc6_boole)).
thf(spc6_numerals,axiom,( ( v2_xxreal_0 @ np__6 ) & ( m2_subset_1 @ np__6 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__6 @ k5_numbers ) & ( m1_subset_1 @ np__6 @ k1_numbers ) ),file(numerals,spc6_numerals)).
thf(spc7_arithm,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) & ( v1_xcmplx_0 @ C ) ) => ( = @ ( k3_xcmplx_0 @ ( k3_xcmplx_0 @ A @ B ) @ C ) @ ( k3_xcmplx_0 @ A @ ( k3_xcmplx_0 @ B @ C ) ) ) ) ),file(arithm,spc6_arithm)).
thf(spc7_boole,axiom,( ~ ( v1_xboole_0 @ np__7 ) ),file(boole,spc7_boole)).
thf(spc7_numerals,axiom,( ( v2_xxreal_0 @ np__7 ) & ( m2_subset_1 @ np__7 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__7 @ k5_numbers ) & ( m1_subset_1 @ np__7 @ k1_numbers ) ),file(numerals,spc7_numerals)).
thf(t1_arithm,axiom,( ! [A: $i] : ( ( v1_xcmplx_0 @ A ) => ( = @ ( k2_xcmplx_0 @ A @ k6_numbers ) @ A ) ) ),file(arithm,t1_arithm)).
thf(t1_boole,axiom,( ! [A: $i] : ( = @ ( k2_xboole_0 @ A @ k1_xboole_0 ) @ A ) ),file(boole,t1_boole)).
thf(t1_numerals,axiom,( m1_subset_1 @ k1_xboole_0 @ k4_ordinal1 ),file(numerals,t1_numerals)).
thf(t1_real,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ! [B: $i] : ( ( v1_xreal_0 @ B ) => ( ( ( r1_xxreal_0 @ A @ B ) & ( v2_xxreal_0 @ A ) ) => ( v2_xxreal_0 @ B ) ) ) ) ),file(real,t1_real)).
thf(t1_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ( m1_subset_1 @ A @ B ) ) ),file(subset,t1_subset)).
thf(t2_arithm,axiom,( ! [A: $i] : ( ( v1_xcmplx_0 @ A ) => ( = @ ( k3_xcmplx_0 @ A @ k6_numbers ) @ k6_numbers ) ) ),file(arithm,t2_arithm)).
thf(t2_real,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ! [B: $i] : ( ( v1_xreal_0 @ B ) => ( ( ( r1_xxreal_0 @ A @ B ) & ( v3_xxreal_0 @ B ) ) => ( v3_xxreal_0 @ A ) ) ) ) ),file(real,t2_real)).
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_arithm,axiom,( ! [A: $i] : ( ( v1_xcmplx_0 @ A ) => ( = @ ( k3_xcmplx_0 @ np__1 @ A ) @ A ) ) ),file(arithm,t3_arithm)).
thf(t3_real,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ! [B: $i] : ( ( v1_xreal_0 @ B ) => ~ ( ( r1_xxreal_0 @ A @ B ) & ~ ( v3_xxreal_0 @ A ) & ( v3_xxreal_0 @ B ) ) ) ) ),file(real,t3_real)).
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_real,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ! [B: $i] : ( ( v1_xreal_0 @ B ) => ~ ( ( r1_xxreal_0 @ A @ B ) & ~ ( v2_xxreal_0 @ B ) & ( v2_xxreal_0 @ A ) ) ) ) ),file(real,t4_real)).
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_real,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ! [B: $i] : ( ( v1_xreal_0 @ B ) => ( ( r1_xxreal_0 @ A @ B ) => ( ( v1_xboole_0 @ B ) | ( v3_xxreal_0 @ A ) | ( v2_xxreal_0 @ B ) ) ) ) ) ),file(real,t5_real)).
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(t6_real,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ! [B: $i] : ( ( v1_xreal_0 @ B ) => ( ( r1_xxreal_0 @ A @ B ) => ( ( v1_xboole_0 @ A ) | ( v2_xxreal_0 @ B ) | ( v3_xxreal_0 @ A ) ) ) ) ) ),file(real,t6_real)).
thf(t7_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( r2_hidden @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t7_boole)).
thf(t7_real,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ! [B: $i] : ( ( v1_xreal_0 @ B ) => ~ ( ~ ( r1_xxreal_0 @ A @ B ) & ~ ( v2_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ B ) ) ) ) ),file(real,t7_real)).
thf(t8_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( v1_xboole_0 @ A ) & ~ ( = @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t8_boole)).
thf(t8_real,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ! [B: $i] : ( ( v1_xreal_0 @ B ) => ~ ( ~ ( r1_xxreal_0 @ A @ B ) & ~ ( v3_xxreal_0 @ B ) & ~ ( v2_xxreal_0 @ A ) ) ) ) ),file(real,t8_real)).
thf(s1_qc_lang1,axiom,( ! [A: $i > $o] : ! [B: $i] : ( ( m1_qc_lang1 @ B ) => ( ( ! [C: $i] : ( ( m1_subset_1 @ C @ k5_numbers ) => ! [D: $i] : ( ( m2_subset_1 @ D @ ( k6_qc_lang1 @ B ) @ ( k8_qc_lang1 @ B @ C ) ) => ! [E: $i] : ( ( ( v3_card_1 @ E @ C ) & ( m2_finseq_1 @ E @ ( k2_qc_lang1 @ B ) ) ) => ( A @ ( k10_qc_lang1 @ B @ D @ E ) ) ) ) ) & ( A @ ( k12_qc_lang1 @ B ) ) & ! [C: $i] : ( ( m1_subset_1 @ C @ ( k9_qc_lang1 @ B ) ) => ( ( A @ C ) => ( A @ ( k13_qc_lang1 @ B @ C ) ) ) ) & ! [C: $i] : ( ( m1_subset_1 @ C @ ( k9_qc_lang1 @ B ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( k9_qc_lang1 @ B ) ) => ( ( ( A @ C ) & ( A @ D ) ) => ( A @ ( k14_qc_lang1 @ B @ C @ D ) ) ) ) ) & ! [C: $i] : ( ( m2_subset_1 @ C @ ( k2_qc_lang1 @ B ) @ ( k3_qc_lang1 @ B ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( k9_qc_lang1 @ B ) ) => ( ( A @ D ) => ( A @ ( k15_qc_lang1 @ B @ C @ D ) ) ) ) ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k9_qc_lang1 @ B ) ) => ( A @ C ) ) ) ) ),file(qc_lang1,s1_qc_lang1)).
thf(s2_qc_lang1,conjecture,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k9_qc_lang1 @ f1_s2_qc_lang1 ) ) => ( ( ( v2_qc_lang1 @ A @ f1_s2_qc_lang1 ) => ( p1_s2_qc_lang1 @ A ) ) & ( p1_s2_qc_lang1 @ ( k12_qc_lang1 @ f1_s2_qc_lang1 ) ) & ( ( ( v3_qc_lang1 @ A @ f1_s2_qc_lang1 ) & ( p1_s2_qc_lang1 @ ( k18_qc_lang1 @ f1_s2_qc_lang1 @ A ) ) ) => ( p1_s2_qc_lang1 @ A ) ) & ( ( ( v4_qc_lang1 @ A @ f1_s2_qc_lang1 ) & ( p1_s2_qc_lang1 @ ( k19_qc_lang1 @ f1_s2_qc_lang1 @ A ) ) & ( p1_s2_qc_lang1 @ ( k20_qc_lang1 @ f1_s2_qc_lang1 @ A ) ) ) => ( p1_s2_qc_lang1 @ A ) ) & ( ( ( v5_qc_lang1 @ A @ f1_s2_qc_lang1 ) & ( p1_s2_qc_lang1 @ ( k22_qc_lang1 @ f1_s2_qc_lang1 @ A ) ) ) => ( p1_s2_qc_lang1 @ A ) ) ) ) => ! [A: $i] : ( ( m1_subset_1 @ A @ ( k9_qc_lang1 @ f1_s2_qc_lang1 ) ) => ( p1_s2_qc_lang1 @ A ) ) ),file(qc_lang1,s2_qc_lang1)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
