% Mizar problem: e1_22_1_1,heyting3,654,65 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(n2_type,type,( np__2: $i )).
thf(c1_22_type,type,( c1_22__heyting3: $i )).
thf(c2_22_type,type,( c2_22__heyting3: $i )).
thf(k1_domain_1_type,type,( k1_domain_1: $i > $i > $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_tarski_type,type,( k1_tarski: $i > $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_xcmplx_0_type,type,( k2_xcmplx_0: $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_xcmplx_0_type,type,( k3_xcmplx_0: $i > $i > $i )).
thf(k4_nat_1_type,type,( k4_nat_1: $i > $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_domain_1_type,type,( k6_domain_1: $i > $i > $i )).
thf(k8_mcart_1_type,type,( k8_mcart_1: $i > $i > $i > $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_subset_1_type,type,( m2_subset_1: $i > $i > $i > $o )).
thf(r1_xxreal_0_type,type,( r1_xxreal_0: $i > $i > $o )).
thf(v1_abian_type,type,( v1_abian: $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_finsub_1_type,type,( v1_finsub_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_membered_type,type,( v1_membered: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_partfun1_type,type,( v1_partfun1: $i > $i > $o )).
thf(v1_rat_1_type,type,( v1_rat_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_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_xxreal_2_type,type,( v1_xxreal_2: $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_finseq_1_type,type,( v2_finseq_1: $i > $o )).
thf(v2_finset_1_type,type,( v2_finset_1: $i > $o )).
thf(v2_membered_type,type,( v2_membered: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v2_setfam_1_type,type,( v2_setfam_1: $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $i > $o )).
thf(v2_xxreal_2_type,type,( v2_xxreal_2: $i > $o )).
thf(v3_finseq_1_type,type,( v3_finseq_1: $i > $o )).
thf(v3_finsub_1_type,type,( v3_finsub_1: $i > $o )).
thf(v3_membered_type,type,( v3_membered: $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(v3_xxreal_2_type,type,( v3_xxreal_2: $i > $o )).
thf(v4_finsub_1_type,type,( v4_finsub_1: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_membered_type,type,( v4_membered: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v4_xxreal_2_type,type,( v4_xxreal_2: $i > $o )).
thf(v5_finset_1_type,type,( v5_finset_1: $i > $o )).
thf(v5_membered_type,type,( v5_membered: $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v5_xxreal_2_type,type,( v5_xxreal_2: $i > $o )).
thf(v6_membered_type,type,( v6_membered: $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v6_xxreal_2_type,type,( v6_xxreal_2: $i > $o )).
thf(v7_membered_type,type,( v7_membered: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
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(fc10_membered,axiom,( ! [A: $i] : ( ( v1_rat_1 @ A ) => ( v4_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc10_membered)).
thf(rc1_abian,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) & ( v1_xxreal_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_int_1 @ A ) & ( v1_rat_1 @ A ) & ( v1_membered @ A ) & ( v2_membered @ A ) & ( v3_membered @ A ) & ( v4_membered @ A ) & ( v5_membered @ A ) & ( v6_membered @ A ) & ( v3_xxreal_2 @ A ) & ( v1_abian @ A ) ) ),file(abian,rc1_abian)).
thf(rc2_abian,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) & ( v1_xxreal_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_int_1 @ A ) & ( v1_rat_1 @ A ) & ( v1_membered @ A ) & ( v2_membered @ A ) & ( v3_membered @ A ) & ( v4_membered @ A ) & ( v5_membered @ A ) & ( v6_membered @ A ) & ( v3_xxreal_2 @ A ) & ~ ( v1_abian @ A ) ) ),file(abian,rc2_abian)).
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(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(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(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(cc11_xxreal_2,axiom,( ! [A: $i] : ( ( ( v3_membered @ A ) & ( v2_xxreal_2 @ A ) ) => ( ( v3_membered @ A ) & ( v4_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc11_xxreal_2)).
thf(cc12_xxreal_2,axiom,( ! [A: $i] : ( ( ( v5_membered @ A ) & ( v5_xxreal_2 @ A ) ) => ( ( v5_membered @ A ) & ( v1_finset_1 @ A ) ) ) ),file(xxreal_2,cc12_xxreal_2)).
thf(cc14_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v5_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ( v3_membered @ A ) ) ) ),file(xxreal_2,cc14_xxreal_2)).
thf(cc15_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_rat_1 @ B ) ) ) ),file(membered,cc15_membered)).
thf(cc17_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v2_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) ) ) ),file(xxreal_2,cc17_xxreal_2)).
thf(cc22_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_membered @ B ) ) ) ),file(membered,cc22_membered)).
thf(cc2_abian,axiom,( ! [A: $i] : ( ( ( v1_int_1 @ A ) & ~ ( v1_abian @ A ) ) => ( ~ ( v1_xboole_0 @ A ) & ( v1_int_1 @ A ) ) ) ),file(abian,cc2_abian)).
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_finsub_1,axiom,( ! [A: $i] : ( ( ( v1_finsub_1 @ A ) & ( v3_finsub_1 @ A ) ) => ( v4_finsub_1 @ A ) ) ),file(finsub_1,cc2_finsub_1)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc3_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ( v3_membered @ A ) ) ),file(membered,cc3_membered)).
thf(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_1)).
thf(cc4_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v5_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ( v3_xxreal_2 @ A ) & ( v4_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc4_xxreal_2)).
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_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_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(fc10_abian,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ( v1_abian @ A ) & ( v1_int_1 @ B ) & ~ ( v1_abian @ B ) ) => ~ ( v1_abian @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(abian,fc10_abian)).
thf(fc11_abian,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ( v1_abian @ A ) & ( v1_int_1 @ B ) & ~ ( v1_abian @ B ) ) => ~ ( v1_abian @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(abian,fc11_abian)).
thf(fc11_membered,axiom,( ! [A: $i] : ( ( v1_int_1 @ A ) => ( v5_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc11_membered)).
thf(fc12_abian,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ~ ( v1_abian @ A ) & ( v1_int_1 @ B ) & ~ ( v1_abian @ B ) ) => ( v1_abian @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(abian,fc12_abian)).
thf(fc16_abian,axiom,( ! [A: $i] : ( ( ( v1_int_1 @ A ) & ( v1_abian @ A ) ) => ( v1_abian @ ( k2_xcmplx_0 @ A @ np__2 ) ) ) ),file(abian,fc16_abian)).
thf(fc17_abian,axiom,( ! [A: $i] : ( ( ( v1_int_1 @ A ) & ~ ( v1_abian @ A ) ) => ~ ( v1_abian @ ( k2_xcmplx_0 @ A @ np__2 ) ) ) ),file(abian,fc17_abian)).
thf(fc1_abian,axiom,( ! [A: $i] : ( ( v1_int_1 @ A ) => ( v1_abian @ ( k3_xcmplx_0 @ np__2 @ A ) ) ) ),file(abian,fc1_abian)).
thf(fc2_abian,axiom,( ! [A: $i] : ( ( ( v1_int_1 @ A ) & ( v1_abian @ A ) ) => ~ ( v1_abian @ ( k2_xcmplx_0 @ A @ np__1 ) ) ) ),file(abian,fc2_abian)).
thf(fc3_abian,axiom,( ! [A: $i] : ( ( ( v1_int_1 @ A ) & ~ ( v1_abian @ A ) ) => ( v1_abian @ ( k2_xcmplx_0 @ A @ np__1 ) ) ) ),file(abian,fc3_abian)).
thf(fc6_abian,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ( v1_abian @ A ) & ( v1_int_1 @ B ) ) => ( v1_abian @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(abian,fc6_abian)).
thf(fc7_abian,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ( v1_abian @ A ) & ( v1_int_1 @ B ) ) => ( v1_abian @ ( k3_xcmplx_0 @ B @ A ) ) ) ),file(abian,fc7_abian)).
thf(fc8_abian,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ~ ( v1_abian @ A ) & ( v1_int_1 @ B ) & ~ ( v1_abian @ B ) ) => ~ ( v1_abian @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(abian,fc8_abian)).
thf(fc9_abian,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ( v1_abian @ A ) & ( v1_int_1 @ B ) & ( v1_abian @ B ) ) => ( v1_abian @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(abian,fc9_abian)).
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_xxreal_2,axiom,( ? [A: $i] : ( ( v1_membered @ A ) & ( v2_membered @ A ) & ( v3_membered @ A ) & ( v4_membered @ A ) & ( v5_membered @ A ) & ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) & ( v2_xxreal_2 @ A ) ) ),file(xxreal_2,rc1_xxreal_2)).
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(rc3_abian,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_int_1 @ A ) & ( v1_abian @ A ) ) ),file(abian,rc3_abian)).
thf(rc3_xxreal_2,axiom,( ? [A: $i] : ( ( v1_membered @ A ) & ( v2_membered @ A ) & ( v3_membered @ A ) & ( v4_membered @ A ) & ( v5_membered @ A ) & ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) & ( v5_xxreal_2 @ A ) ) ),file(xxreal_2,rc3_xxreal_2)).
thf(rc4_abian,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_int_1 @ A ) & ~ ( v1_abian @ A ) ) ),file(abian,rc4_abian)).
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(rc5_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ( v1_xxreal_2 @ A ) & ( v2_xxreal_2 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc5_xxreal_2)).
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(rc6_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ~ ( v1_xxreal_2 @ A ) & ( v2_xxreal_2 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc6_xxreal_2)).
thf(rc7_abian,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_int_1 @ A ) & ~ ( v1_abian @ A ) ) ),file(abian,rc7_abian)).
thf(rc7_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_zfmisc_1 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(finset_1,rc7_finset_1)).
thf(rc7_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ( v1_xxreal_2 @ A ) & ~ ( v2_xxreal_2 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc7_xxreal_2)).
thf(rc8_abian,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_int_1 @ A ) & ( v1_abian @ A ) ) ),file(abian,rc8_abian)).
thf(rc8_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ~ ( v1_xxreal_2 @ A ) & ~ ( v2_xxreal_2 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc8_xxreal_2)).
thf(rc9_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finset_1 @ A ) ) ),file(finset_1,rc9_finset_1)).
thf(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(cc10_xxreal_2,axiom,( ! [A: $i] : ( ( ( v3_membered @ A ) & ( v1_xxreal_2 @ A ) ) => ( ( v3_membered @ A ) & ( v3_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc10_xxreal_2)).
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(cc12_membered,axiom,( ! [A: $i] : ( ( v1_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xcmplx_0 @ B ) ) ) ),file(membered,cc12_membered)).
thf(cc13_membered,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xxreal_0 @ B ) ) ) ),file(membered,cc13_membered)).
thf(cc15_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v2_membered @ A ) & ( v6_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc15_xxreal_2)).
thf(cc16_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_int_1 @ B ) ) ) ),file(membered,cc16_membered)).
thf(cc16_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v1_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) ) ) ),file(xxreal_2,cc16_xxreal_2)).
thf(cc19_membered,axiom,( ! [A: $i] : ( ( v1_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_membered @ B ) ) ) ),file(membered,cc19_membered)).
thf(cc1_abian,axiom,( ! [A: $i] : ( ( v2_setfam_1 @ A ) => ( v1_zfmisc_1 @ A ) ) ),file(abian,cc1_abian)).
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_finsub_1,axiom,( ! [A: $i] : ( ( v4_finsub_1 @ A ) => ( ( v1_finsub_1 @ A ) & ( v3_finsub_1 @ A ) ) ) ),file(finsub_1,cc1_finsub_1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc20_membered,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v2_membered @ B ) ) ) ),file(membered,cc20_membered)).
thf(cc23_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_membered @ B ) ) ) ),file(membered,cc23_membered)).
thf(cc2_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_finset_1 @ B ) ) ) ),file(finset_1,cc2_finset_1)).
thf(cc2_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ( v4_membered @ A ) ) ),file(membered,cc2_membered)).
thf(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_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) => ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) & ( v2_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc2_xxreal_2)).
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(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_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(cc5_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_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_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v3_xxreal_2 @ A ) & ( v4_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ( v5_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc5_xxreal_2)).
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_2,axiom,( ! [A: $i] : ( ( ( v3_membered @ A ) & ( v1_finset_1 @ A ) ) => ( ( v3_membered @ A ) & ( v5_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc6_xxreal_2)).
thf(cc7_finset_1,axiom,( ! [A: $i] : ( ( v5_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_finset_1 @ B ) ) ) ),file(finset_1,cc7_finset_1)).
thf(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(cc7_xxreal_2,axiom,( ! [A: $i] : ( ( ( v5_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v4_xxreal_2 @ A ) ) => ( ( v5_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v2_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc7_xxreal_2)).
thf(cc8_finset_1,axiom,( ! [A: $i] : ( ( v5_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_finset_1 @ B ) ) ) ),file(finset_1,cc8_finset_1)).
thf(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_2,axiom,( ! [A: $i] : ( ( ( v5_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v3_xxreal_2 @ A ) ) => ( ( v5_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc8_xxreal_2)).
thf(cc9_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ( v4_funct_1 @ A ) ) ),file(finseq_1,cc9_finseq_1)).
thf(cc9_finset_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_finset_1 @ A ) ) ) ),file(finset_1,cc9_finset_1)).
thf(fc14_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_finset_1 @ A ) & ( v1_finset_1 @ B ) ) => ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(finset_1,fc14_finset_1)).
thf(fc17_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc17_finset_1)).
thf(fc30_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v5_finset_1 @ ( k1_tarski @ A ) ) ) ),file(finset_1,fc30_finset_1)).
thf(fc31_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v5_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc31_finset_1)).
thf(fc7_membered,axiom,( ! [A: $i] : ( ( v1_xcmplx_0 @ A ) => ( v1_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc7_membered)).
thf(fc9_membered,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v3_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc9_membered)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc1_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) ) ),file(partfun1,rc1_partfun1)).
thf(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_1)).
thf(rc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relset_1,rc1_relset_1)).
thf(rc1_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_0)).
thf(rc2_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(finset_1,rc2_finset_1)).
thf(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_xxreal_2,axiom,( ? [A: $i] : ( ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(xxreal_2,rc2_xxreal_2)).
thf(rc3_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc3_finset_1)).
thf(rc3_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_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ~ ( v1_xboole_0 @ C ) ) ) ),file(partfun1,rc3_partfun1)).
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(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_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc4_xxreal_2)).
thf(rc5_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) ) ),file(finset_1,rc5_finset_1)).
thf(rc6_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ? [C: $i] : ( ~ ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) ) ) ),file(finset_1,rc6_finset_1)).
thf(rc8_finseq_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v3_finseq_1 @ A ) ) ),file(finseq_1,rc8_finseq_1)).
thf(rc8_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v5_finset_1 @ A ) ) ),file(finset_1,rc8_finset_1)).
thf(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(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(dt_k1_tarski,axiom,( $true ),file(tarski,k1_tarski)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
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_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_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) => ( m1_subset_1 @ C @ A ) ) ) ),file(subset_1,m2_subset_1)).
thf(cc11_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k5_numbers ) ) => ( v6_membered @ A ) ) ),file(membered,cc11_membered)).
thf(cc13_xxreal_2,axiom,( ! [A: $i] : ( ( ( v6_membered @ A ) & ( v4_xxreal_2 @ A ) ) => ( ( v6_membered @ A ) & ( v1_finset_1 @ A ) & ( v4_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc13_xxreal_2)).
thf(cc14_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xreal_0 @ B ) ) ) ),file(membered,cc14_membered)).
thf(cc17_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v7_ordinal1 @ B ) ) ) ),file(membered,cc17_membered)).
thf(cc18_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_membered @ A ) ) ),file(membered,cc18_membered)).
thf(cc1_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc1_finset_1)).
thf(cc1_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ( v5_membered @ A ) ) ),file(membered,cc1_membered)).
thf(cc1_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) ) ),file(nat_1,cc1_nat_1)).
thf(cc1_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_partfun1 @ C @ A ) ) ) ),file(partfun1,cc1_partfun1)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_1)).
thf(cc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_relat_1 @ C ) ) ),file(relset_1,cc1_relset_1)).
thf(cc1_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_xboole_0 @ B ) ) ) ),file(subset_1,cc1_subset_1)).
thf(cc21_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v3_membered @ B ) ) ) ),file(membered,cc21_membered)).
thf(cc24_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v6_membered @ B ) ) ) ),file(membered,cc24_membered)).
thf(cc26_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_membered @ A ) ) ),file(membered,cc26_membered)).
thf(cc2_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_xboole_0 @ B ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ~ ( v1_partfun1 @ C @ A ) ) ) ),file(partfun1,cc2_partfun1)).
thf(cc2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ) ),file(relset_1,cc2_relset_1)).
thf(cc2_xxreal_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,cc2_xxreal_0)).
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_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc3_relset_1)).
thf(cc3_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ( v1_xboole_0 @ B ) => ( v1_subset_1 @ B @ A ) ) ) ) ),file(subset_1,cc3_subset_1)).
thf(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(cc3_xxreal_2,axiom,( ! [A: $i] : ( ( ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) ) => ( ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc3_xxreal_2)).
thf(cc4_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v2_membered @ A ) ) ),file(membered,cc4_membered)).
thf(cc4_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
thf(cc4_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc4_relset_1)).
thf(cc4_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_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_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v1_membered @ A ) ) ),file(membered,cc5_membered)).
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_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(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_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_finseq_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_finseq_1 @ A ) ) ),file(finseq_1,cc8_finseq_1)).
thf(cc8_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) ) => ( v3_membered @ A ) ) ),file(membered,cc8_membered)).
thf(cc8_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
thf(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_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(cc9_xxreal_2,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ( ( v6_membered @ A ) & ( v3_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc9_xxreal_2)).
thf(fc10_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(subset_1,fc10_subset_1)).
thf(fc12_membered,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v6_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc12_membered)).
thf(fc19_abian,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ~ ( v2_setfam_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(abian,fc19_abian)).
thf(fc1_finset_1,axiom,( ! [A: $i] : ( v1_finset_1 @ ( k1_tarski @ A ) ) ),file(finset_1,fc1_finset_1)).
thf(fc1_finsub_1,axiom,( ! [A: $i] : ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ) ),file(finsub_1,fc1_finsub_1)).
thf(fc1_heyting3,axiom,( ! [A: $i] : ! [B: $i] : ( v1_funct_1 @ ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) ) ) ),file(heyting3,fc1_heyting3)).
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_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( v1_xtuple_0 @ ( k4_tarski @ A @ B ) ) ),file(xtuple_0,fc1_xtuple_0)).
thf(fc2_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( v7_ordinal1 @ B ) ) => ( v7_ordinal1 @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(nat_1,fc2_nat_1)).
thf(fc2_xboole_0,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ) ),file(xboole_0,fc2_xboole_0)).
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(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(fc59_membered,axiom,( v7_membered @ k4_ordinal1 ),file(membered,fc59_membered)).
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(fc6_membered,axiom,( v6_membered @ k4_ordinal1 ),file(membered,fc6_membered)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(fc8_membered,axiom,( ! [A: $i] : ( ( v1_xxreal_0 @ A ) => ( v2_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc8_membered)).
thf(rc1_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc1_membered)).
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_xxreal_0,axiom,( ? [A: $i] : ( v1_xxreal_0 @ A ) ),file(xxreal_0,rc1_xxreal_0)).
thf(rc2_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc2_membered)).
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_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) ) ),file(xxreal_0,rc2_xxreal_0)).
thf(rc3_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) & ( v7_membered @ A ) ) ),file(membered,rc3_membered)).
thf(rc3_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) ),file(xxreal_0,rc3_xxreal_0)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(rc4_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,rc4_xxreal_0)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_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_k4_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( v7_ordinal1 @ B ) ) => ( = @ ( k4_nat_1 @ A @ B ) @ ( k4_nat_1 @ B @ A ) ) ) ),file(nat_1,k4_nat_1)).
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(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(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k1_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ C @ A ) & ( m1_subset_1 @ D @ B ) ) => ( = @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k4_tarski @ C @ D ) ) ) ),file(domain_1,k1_domain_1)).
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_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( v7_ordinal1 @ B ) ) => ( = @ ( k4_nat_1 @ A @ B ) @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(nat_1,k4_nat_1)).
thf(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
thf(redefinition_k6_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) ) => ( = @ ( k6_domain_1 @ A @ B ) @ ( k1_tarski @ B ) ) ) ),file(domain_1,k6_domain_1)).
thf(redefinition_k8_mcart_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) ) => ( = @ ( k8_mcart_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ C @ D ) ) ) ),file(mcart_1,k8_mcart_1)).
thf(dt_k1_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ C @ A ) & ( m1_subset_1 @ D @ B ) ) => ( m1_subset_1 @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(domain_1,k1_domain_1)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
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_k4_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( v7_ordinal1 @ B ) ) => ( m2_subset_1 @ ( k4_nat_1 @ A @ B ) @ k1_numbers @ k5_numbers ) ) ),file(nat_1,k4_nat_1)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_k6_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) ) => ( m1_subset_1 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(domain_1,k6_domain_1)).
thf(dt_k8_mcart_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) ) => ( m1_subset_1 @ ( k8_mcart_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ),file(mcart_1,k8_mcart_1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_c1_22__heyting3,axiom,( m1_subset_1 @ c1_22__heyting3 @ k5_numbers ),file(heyting3,c1_22__heyting3)).
thf(dt_c2_22__heyting3,axiom,( m1_subset_1 @ c2_22__heyting3 @ k5_numbers ),file(heyting3,c2_22__heyting3)).
thf(cc25_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ( v6_membered @ A ) ) ),file(membered,cc25_membered)).
thf(cc2_nat_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ~ ( v3_xxreal_0 @ A ) ) ),file(nat_1,cc2_nat_1)).
thf(fc11_xxreal_2,axiom,( ~ ( v3_xxreal_2 @ k1_numbers ) & ~ ( v4_xxreal_2 @ k1_numbers ) ),file(xxreal_2,fc11_xxreal_2)).
thf(fc17_xxreal_2,axiom,( v6_xxreal_2 @ k1_numbers ),file(xxreal_2,fc17_xxreal_2)).
thf(fc3_membered,axiom,( v3_membered @ k1_numbers ),file(membered,fc3_membered)).
thf(fc56_membered,axiom,( v7_membered @ k1_numbers ),file(membered,fc56_membered)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(spc2_boole,axiom,( ~ ( v1_xboole_0 @ np__2 ) ),file(boole,spc2_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_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(s1_xboole_0,axiom,( ! [A: $i > $o] : ! [B: $i] : ? [C: $i] : ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( ( r2_hidden @ D @ B ) & ( A @ D ) ) ) ),file(xboole_0,s1_xboole_0)).
thf(e1_22_1_1__heyting3,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ( ( r2_hidden @ B @ ( k8_mcart_1 @ k1_numbers @ k5_numbers @ k5_numbers @ ( k6_domain_1 @ k5_numbers @ c2_22__heyting3 ) ) ) & ? [C: $i] : ( ~ ( v1_abian @ C ) & ( m1_subset_1 @ C @ k5_numbers ) & ( r1_xxreal_0 @ C @ ( k2_nat_1 @ ( k4_nat_1 @ np__2 @ c1_22__heyting3 ) @ np__1 ) ) & ( = @ ( k1_domain_1 @ k5_numbers @ k5_numbers @ C @ c2_22__heyting3 ) @ B ) ) ) ) ),file(heyting3,e1_22_1_1__heyting3)).
