% Mizar problem: e1_36_1_2,pua2mss1,1159,22 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_36_type,type,( c1_36__pua2mss1: $i )).
thf(c2_36_type,type,( c2_36__pua2mss1: $i )).
thf(k10_xtuple_0_type,type,( k10_xtuple_0: $i > $i )).
thf(k13_finseq_1_type,type,( k13_finseq_1: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $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_pua2mss1_type,type,( k1_pua2mss1: $i > $i > $i )).
thf(k1_relset_1_type,type,( k1_relset_1: $i > $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_xcmplx_0_type,type,( k2_xcmplx_0: $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_finseq_2_type,type,( k3_finseq_2: $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k4_partfun1_type,type,( k4_partfun1: $i > $i > $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(k7_finseq_1_type,type,( k7_finseq_1: $i > $i > $i )).
thf(k9_finseq_1_type,type,( k9_finseq_1: $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(u1_unialg_1_type,type,( u1_unialg_1: $i > $i )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l1_unialg_1_type,type,( l1_unialg_1: $i > $o )).
thf(m1_finseq_1_type,type,( m1_finseq_1: $i > $i > $o )).
thf(m1_finseq_2_type,type,( m1_finseq_2: $i > $i > $o )).
thf(m1_pua2mss1_type,type,( m1_pua2mss1: $i > $i > $i > $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(r2_relset_1_type,type,( r2_relset_1: $i > $i > $i > $i > $o )).
thf(v13_struct_0_type,type,( v13_struct_0: $i > $i > $o )).
thf(v1_card_1_type,type,( v1_card_1: $i > $o )).
thf(v1_card_3_type,type,( v1_card_3: $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_funct_2_type,type,( v1_funct_2: $i > $i > $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_partfun1_type,type,( v1_partfun1: $i > $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_xtuple_0_type,type,( v1_xtuple_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_card_3_type,type,( v2_card_3: $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_margrel1_type,type,( v2_margrel1: $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_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v2_unialg_1_type,type,( v2_unialg_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_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(v3_xxreal_0_type,type,( v3_xxreal_0: $i > $o )).
thf(v4_card_3_type,type,( v4_card_3: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_margrel1_type,type,( v4_margrel1: $i > $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v4_unialg_1_type,type,( v4_unialg_1: $i > $o )).
thf(v5_card_3_type,type,( v5_card_3: $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_0: $i > $o )).
thf(commutativity_k2_xcmplx_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) ) => ( = @ ( k2_xcmplx_0 @ A @ B ) @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(xcmplx_0,k2_xcmplx_0)).
thf(dt_k2_xcmplx_0,axiom,( $true ),file(xcmplx_0,k2_xcmplx_0)).
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(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(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(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_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_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_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(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(cc2_card_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_setfam_1 @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) => ( ( v2_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) ) ) ) ),file(card_3,cc2_card_3)).
thf(cc2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_2 @ C @ A @ B ) => ( v1_partfun1 @ C @ A ) ) ) ) ),file(funct_2,cc2_funct_2)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc2_setfam_1,axiom,( ! [A: $i] : ( ~ ( v2_setfam_1 @ A ) => ~ ( v1_xboole_0 @ A ) ) ),file(setfam_1,cc2_setfam_1)).
thf(cc3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_2 @ C @ A @ B ) => ( v1_partfun1 @ C @ A ) ) ) ) ),file(funct_2,cc3_funct_2)).
thf(cc4_card_3,axiom,( ! [A: $i] : ( ( v5_card_3 @ A ) => ( ~ ( v1_finset_1 @ A ) & ( v4_card_3 @ A ) ) ) ),file(card_3,cc4_card_3)).
thf(cc4_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) => ( ( v1_funct_2 @ B @ A @ A ) => ( v1_partfun1 @ B @ A ) ) ) ),file(funct_2,cc4_funct_2)).
thf(cc4_setfam_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ~ ( v2_setfam_1 @ A ) ) ),file(setfam_1,cc4_setfam_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_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(cc8_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) => ( ( v1_funct_1 @ C ) & ~ ( v1_xboole_0 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) ) ) ) ),file(funct_2,cc8_funct_2)).
thf(fc18_funct_1,axiom,( ! [A: $i] : ( ( ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ~ ( v1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(funct_1,fc18_funct_1)).
thf(fc24_relat_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) ) => ( v1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc24_relat_1)).
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(rc1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) ),file(funct_2,rc1_funct_2)).
thf(rc21_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_zfmisc_1 @ B ) ) ) ),file(struct_0,rc21_struct_0)).
thf(rc22_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_zfmisc_1 @ B ) ) ) ),file(struct_0,rc22_struct_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_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) ) ),file(ordinal1,rc2_ordinal1)).
thf(rc2_setfam_1,axiom,( ? [A: $i] : ~ ( v2_setfam_1 @ A ) ),file(setfam_1,rc2_setfam_1)).
thf(rc3_setfam_1,axiom,( ! [A: $i] : ( ~ ( v2_setfam_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ A ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(setfam_1,rc3_setfam_1)).
thf(rc5_card_3,axiom,( ? [A: $i] : ( v5_card_3 @ A ) ),file(card_3,rc5_card_3)).
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_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(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
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_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) => ( v13_struct_0 @ A @ np__1 ) ) ) ),file(struct_0,cc10_struct_0)).
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(cc11_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v13_struct_0 @ A @ np__1 ) => ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) ) ) ),file(struct_0,cc11_struct_0)).
thf(cc17_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v7_struct_0 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc17_struct_0)).
thf(cc1_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(card_1,cc1_card_1)).
thf(cc1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_partfun1 @ C @ A ) => ( v1_funct_2 @ C @ A @ B ) ) ) ),file(funct_2,cc1_funct_2)).
thf(cc1_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) ) ),file(nat_1,cc1_nat_1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc1_pboole,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_relat_1 @ B ) & ~ ( v3_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ) ) ),file(pboole,cc1_pboole)).
thf(cc1_pua2mss1,axiom,( ! [A: $i] : ( ( v1_setfam_1 @ A ) => ! [B: $i] : ( ( m1_finseq_1 @ B @ A ) => ( v2_relat_1 @ B ) ) ) ),file(pua2mss1,cc1_pua2mss1)).
thf(cc1_setfam_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_setfam_1 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ~ ( v1_xboole_0 @ B ) ) ) ),file(setfam_1,cc1_setfam_1)).
thf(cc2_pboole,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v3_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_relat_1 @ B ) & ~ ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ) ) ),file(pboole,cc2_pboole)).
thf(cc2_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v7_struct_0 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc2_struct_0)).
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(cc3_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc3_card_1)).
thf(cc3_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v7_ordinal1 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(nat_1,cc3_nat_1)).
thf(cc3_setfam_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_setfam_1 @ A ) ) => ~ ( v2_setfam_1 @ A ) ) ),file(setfam_1,cc3_setfam_1)).
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_pboole,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_relat_1 @ B ) & ~ ( v3_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ) ) ),file(pboole,cc4_pboole)).
thf(cc5_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc5_card_1)).
thf(cc5_card_3,axiom,( ! [A: $i] : ( ( ~ ( v1_finset_1 @ A ) & ( v4_card_3 @ A ) ) => ( v5_card_3 @ A ) ) ),file(card_3,cc5_card_3)).
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_pboole,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ~ ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ) ) ),file(pboole,cc5_pboole)).
thf(cc5_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ( ~ ( v2_struct_0 @ A ) & ~ ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc5_struct_0)).
thf(cc6_card_1,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v1_finset_1 @ A ) ) => ( v7_ordinal1 @ A ) ) ),file(card_1,cc6_card_1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(cc6_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v7_struct_0 @ A ) => ( v8_struct_0 @ A ) ) ) ),file(struct_0,cc6_struct_0)).
thf(cc7_card_1,axiom,( ! [A: $i] : ( ( v3_card_1 @ A @ k1_xboole_0 ) => ( v1_xboole_0 @ A ) ) ),file(card_1,cc7_card_1)).
thf(cc7_card_3,axiom,( ! [A: $i] : ( ( v4_card_3 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_card_3 @ B ) ) ) ),file(card_3,cc7_card_3)).
thf(cc7_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ~ ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc7_struct_0)).
thf(cc8_card_3,axiom,( ! [A: $i] : ( ( v2_card_3 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v2_card_3 @ B ) ) ) ),file(card_3,cc8_card_3)).
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(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_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v13_struct_0 @ A @ k1_xboole_0 ) => ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc9_struct_0)).
thf(fc10_card_3,axiom,( v5_card_3 @ k4_ordinal1 ),file(card_3,fc10_card_3)).
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(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(fc14_card_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_card_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v3_card_1 @ B @ A ) ) => ( v3_card_1 @ ( k9_xtuple_0 @ B ) @ A ) ) ),file(card_1,fc14_card_1)).
thf(fc17_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v4_funct_1 @ A ) & ( v1_relat_1 @ C ) & ( v5_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) ) => ( ( v1_relat_1 @ ( k1_funct_1 @ C @ B ) ) & ( v1_funct_1 @ ( k1_funct_1 @ C @ B ) ) ) ) ),file(funct_1,fc17_funct_1)).
thf(fc19_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(funct_1,fc19_funct_1)).
thf(fc19_struct_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_card_1 @ A ) & ( v13_struct_0 @ B @ A ) & ( l1_struct_0 @ B ) ) => ( v3_card_1 @ ( u1_struct_0 @ B ) @ A ) ) ),file(struct_0,fc19_struct_0)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_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(fc29_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v3_finseq_1 @ A ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ( v1_finseq_1 @ ( k1_funct_1 @ B @ C ) ) ) ),file(finseq_1,fc29_finseq_1)).
thf(fc2_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( m1_subset_1 @ C @ A ) ) => ~ ( v1_xboole_0 @ ( k1_funct_1 @ B @ C ) ) ) ),file(pboole,fc2_pboole)).
thf(fc4_card_1,axiom,( v1_card_1 @ k4_ordinal1 ),file(card_1,fc4_card_1)).
thf(fc4_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v5_ordinal1 @ A ) ) => ( v3_ordinal1 @ ( k9_xtuple_0 @ A ) ) ) ),file(ordinal1,fc4_ordinal1)).
thf(fc5_card_1,axiom,( v2_card_1 @ k4_ordinal1 ),file(card_1,fc5_card_1)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
thf(fc6_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc6_struct_0)).
thf(fc7_card_1,axiom,( ~ ( v1_finset_1 @ k4_ordinal1 ) ),file(card_1,fc7_card_1)).
thf(fc7_margrel1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_margrel1 @ A ) ) => ( v2_card_3 @ ( k9_xtuple_0 @ A ) ) ) ),file(margrel1,fc7_margrel1)).
thf(fc7_struct_0,axiom,( ! [A: $i] : ( ( ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc7_struct_0)).
thf(fc8_struct_0,axiom,( ! [A: $i] : ( ( ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc8_struct_0)).
thf(fc9_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc9_struct_0)).
thf(rc1_card_1,axiom,( ? [A: $i] : ( v1_card_1 @ A ) ),file(card_1,rc1_card_1)).
thf(rc1_card_3,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_card_3 @ A ) ) ),file(card_3,rc1_card_3)).
thf(rc1_margrel1,axiom,( ? [A: $i] : ( ( v3_finseq_1 @ A ) & ( v2_card_3 @ A ) ) ),file(margrel1,rc1_margrel1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc1_pboole,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(pboole,rc1_pboole)).
thf(rc1_setfam_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_setfam_1 @ A ) ) ),file(setfam_1,rc1_setfam_1)).
thf(rc23_struct_0,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ? [B: $i] : ( ( l1_struct_0 @ B ) & ( v13_struct_0 @ B @ A ) ) ) ),file(struct_0,rc23_struct_0)).
thf(rc2_finseq_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ? [C: $i] : ( ( m1_finseq_1 @ C @ B ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ k5_numbers ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) & ( v3_card_1 @ C @ A ) & ( v1_finseq_1 @ C ) & ( v2_finseq_1 @ C ) & ( v4_card_3 @ C ) ) ) ),file(finseq_2,rc2_finseq_2)).
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_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_pboole,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v3_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(pboole,rc2_pboole)).
thf(rc3_card_3,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) & ( v2_card_3 @ A ) ) ),file(card_3,rc3_card_3)).
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_pboole,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(pboole,rc3_pboole)).
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_margrel1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) & ( v2_margrel1 @ A ) ) ),file(margrel1,rc4_margrel1)).
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(rc5_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ? [B: $i] : ( v3_card_1 @ B @ A ) ) ),file(card_1,rc5_card_1)).
thf(rc5_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) ),file(funct_1,rc5_funct_1)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(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(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(rc7_pboole,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ B ) & ( v5_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ B ) ) ) ),file(pboole,rc7_pboole)).
thf(rc8_finseq_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v3_finseq_1 @ A ) ) ),file(finseq_1,rc8_finseq_1)).
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(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
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(dt_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
thf(dt_k13_finseq_1,axiom,( $true ),file(finseq_1,k13_finseq_1)).
thf(dt_k4_partfun1,axiom,( $true ),file(partfun1,k4_partfun1)).
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_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
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_finseq_2,axiom,( $true ),file(finseq_2,m1_finseq_2)).
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(cc1_card_3,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_card_3 @ A ) ) ) ),file(card_3,cc1_card_3)).
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_margrel1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v2_card_3 @ A ) ) ),file(margrel1,cc1_margrel1)).
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_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc1_struct_0)).
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(cc2_card_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc2_card_1)).
thf(cc2_finseq_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_finseq_2 @ B @ A ) => ( v4_funct_1 @ B ) ) ),file(finseq_2,cc2_finseq_2)).
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_nat_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ~ ( v3_xxreal_0 @ A ) ) ),file(nat_1,cc2_nat_1)).
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(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_finseq_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_finseq_2 @ B @ A ) => ( v3_finseq_1 @ B ) ) ),file(finseq_2,cc3_finseq_2)).
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_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(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_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_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc4_struct_0)).
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(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(cc6_card_3,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v4_card_3 @ A ) ) ),file(card_3,cc6_card_3)).
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_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_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_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v13_struct_0 @ A @ k1_xboole_0 ) ) ) ),file(struct_0,cc8_struct_0)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
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_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc10_relat_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(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_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( m1_subset_1 @ B @ ( k9_xtuple_0 @ A ) ) ) => ~ ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(funct_1,fc11_funct_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(fc12_finseq_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k13_finseq_1 @ A ) ) ),file(finseq_1,fc12_finseq_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_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ~ ( v1_xboole_0 @ ( k4_partfun1 @ A @ B ) ) ),file(partfun1,fc1_partfun1)).
thf(fc1_struct_0,axiom,( ! [A: $i] : ( ( ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc1_struct_0)).
thf(fc22_finseq_1,axiom,( ! [A: $i] : ( v4_funct_1 @ ( k13_finseq_1 @ A ) ) ),file(finseq_1,fc22_finseq_1)).
thf(fc24_finseq_1,axiom,( ! [A: $i] : ( v3_card_1 @ ( k5_finseq_1 @ A ) @ np__1 ) ),file(finseq_1,fc24_finseq_1)).
thf(fc27_finseq_1,axiom,( ! [A: $i] : ( v3_finseq_1 @ ( k13_finseq_1 @ A ) ) ),file(finseq_1,fc27_finseq_1)).
thf(fc2_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc2_struct_0)).
thf(fc4_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ( v4_funct_1 @ ( k4_partfun1 @ A @ B ) ) ),file(partfun1,fc4_partfun1)).
thf(fc4_xtuple_0,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(xtuple_0,fc4_xtuple_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_margrel1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k3_finseq_2 @ A ) @ A ) ) ) ) => ( v3_finseq_1 @ ( k9_xtuple_0 @ B ) ) ) ),file(margrel1,fc6_margrel1)).
thf(fc7_finseq_1,axiom,( ! [A: $i] : ( v1_finseq_1 @ ( k5_finseq_1 @ A ) ) ),file(finseq_1,fc7_finseq_1)).
thf(fc8_margrel1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v4_margrel1 @ B @ A ) & ( m1_finseq_1 @ B @ ( k4_partfun1 @ ( k3_finseq_2 @ A ) @ A ) ) ) => ( v2_margrel1 @ ( k1_funct_1 @ B @ C ) ) ) ),file(margrel1,fc8_margrel1)).
thf(fc8_relat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ~ ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc8_relat_1)).
thf(fc8_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) => ( v1_relat_1 @ ( k9_xtuple_0 @ D ) ) ) ),file(relset_1,fc8_relset_1)).
thf(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_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) ) => ( v1_relat_1 @ ( k10_xtuple_0 @ D ) ) ) ),file(relset_1,fc9_relset_1)).
thf(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_finseq_2,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_finseq_2 @ B @ A ) & ~ ( v1_xboole_0 @ B ) ) ),file(finseq_2,rc1_finseq_2)).
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_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_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_0)).
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_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(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_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(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_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(struct_0,rc4_struct_0)).
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(rc6_card_3,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v1_finset_1 @ A ) ) ),file(card_3,rc6_card_3)).
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(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(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(symmetry_r2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( r2_relset_1 @ A @ B @ C @ D ) => ( r2_relset_1 @ A @ B @ D @ C ) ) ) ),file(relset_1,r2_relset_1)).
thf(reflexivity_r2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( r2_relset_1 @ A @ B @ C @ C ) ) ),file(relset_1,r2_relset_1)).
thf(redefinition_k1_pua2mss1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_finseq_1 @ B @ ( k4_partfun1 @ ( k3_finseq_2 @ A ) @ A ) ) ) => ( = @ ( k1_pua2mss1 @ A @ B ) @ ( k10_xtuple_0 @ B ) ) ) ),file(pua2mss1,k1_pua2mss1)).
thf(redefinition_k1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( = @ ( k1_relset_1 @ A @ B ) @ ( k9_xtuple_0 @ B ) ) ) ),file(relset_1,k1_relset_1)).
thf(redefinition_k3_finseq_2,axiom,( ! [A: $i] : ( = @ ( k3_finseq_2 @ A ) @ ( k13_finseq_1 @ A ) ) ),file(finseq_2,k3_finseq_2)).
thf(redefinition_k9_finseq_1,axiom,( ! [A: $i] : ( = @ ( k9_finseq_1 @ A ) @ ( k5_finseq_1 @ A ) ) ),file(finseq_1,k9_finseq_1)).
thf(redefinition_m1_pua2mss1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k4_partfun1 @ A @ B ) ) ) ) => ! [D: $i] : ( ( m1_pua2mss1 @ D @ A @ B @ C ) <=> ( m1_subset_1 @ D @ C ) ) ) ),file(pua2mss1,m1_pua2mss1)).
thf(redefinition_r2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( r2_relset_1 @ A @ B @ C @ D ) <=> ( = @ C @ D ) ) ) ),file(relset_1,r2_relset_1)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_pua2mss1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_finseq_1 @ B @ ( k4_partfun1 @ ( k3_finseq_2 @ A ) @ A ) ) ) => ( m1_subset_1 @ ( k1_pua2mss1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k4_partfun1 @ ( k3_finseq_2 @ A ) @ A ) ) ) ) ),file(pua2mss1,k1_pua2mss1)).
thf(dt_k1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( m1_subset_1 @ ( k1_relset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(relset_1,k1_relset_1)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_finseq_2,axiom,( ! [A: $i] : ( m1_finseq_2 @ ( k3_finseq_2 @ A ) @ A ) ),file(finseq_2,k3_finseq_2)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
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_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_l1_unialg_1,axiom,( ! [A: $i] : ( ( l1_unialg_1 @ A ) => ( l1_struct_0 @ A ) ) ),file(unialg_1,l1_unialg_1)).
thf(dt_m1_pua2mss1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k4_partfun1 @ A @ B ) ) ) ) => ! [D: $i] : ( ( m1_pua2mss1 @ D @ A @ B @ C ) => ( ( v1_funct_1 @ D ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),file(pua2mss1,m1_pua2mss1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_u1_unialg_1,axiom,( ! [A: $i] : ( ( l1_unialg_1 @ A ) => ( m2_finseq_1 @ ( u1_unialg_1 @ A ) @ ( k4_partfun1 @ ( k3_finseq_2 @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ) ),file(unialg_1,u1_unialg_1)).
thf(dt_c1_36__pua2mss1,axiom,( ( v2_unialg_1 @ c1_36__pua2mss1 ) & ( v4_unialg_1 @ c1_36__pua2mss1 ) & ( l1_unialg_1 @ c1_36__pua2mss1 ) ),file(pua2mss1,c1_36__pua2mss1)).
thf(dt_c2_36__pua2mss1,axiom,( m1_subset_1 @ c2_36__pua2mss1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_36__pua2mss1 ) @ ( u1_struct_0 @ c1_36__pua2mss1 ) ) ) ),file(pua2mss1,c2_36__pua2mss1)).
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(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_pua2mss1,axiom,( ! [A: $i] : ( ( l1_unialg_1 @ A ) => ( ( v4_unialg_1 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(pua2mss1,cc2_pua2mss1)).
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_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ) ),file(relset_1,cc2_relset_1)).
thf(cc3_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(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(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(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_unialg_1,axiom,( ! [A: $i] : ( ( ( v2_unialg_1 @ A ) & ( l1_unialg_1 @ A ) ) => ( v4_margrel1 @ ( u1_unialg_1 @ A ) @ ( u1_struct_0 @ A ) ) ) ),file(unialg_1,fc2_unialg_1)).
thf(fc4_unialg_1,axiom,( ! [A: $i] : ( ( ( v4_unialg_1 @ A ) & ( l1_unialg_1 @ A ) ) => ( ( v2_relat_1 @ ( u1_unialg_1 @ A ) ) & ~ ( v1_xboole_0 @ ( u1_unialg_1 @ A ) ) ) ) ),file(unialg_1,fc4_unialg_1)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(s2_pua2mss1,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ C ) & ~ ( v1_xboole_0 @ B ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ C @ B ) ) ) => ! [E: $i] : ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ C @ B ) ) ) => ( ( ! [F: $i] : ( ( m1_subset_1 @ F @ C ) => ! [G: $i] : ( ( m1_subset_1 @ G @ B ) => ( ( r2_hidden @ ( k4_tarski @ F @ G ) @ D ) <=> ( A @ F @ G ) ) ) ) & ! [F: $i] : ( ( m1_subset_1 @ F @ C ) => ! [G: $i] : ( ( m1_subset_1 @ G @ B ) => ( ( r2_hidden @ ( k4_tarski @ F @ G ) @ E ) <=> ( A @ F @ G ) ) ) ) ) => ( r2_relset_1 @ C @ B @ D @ E ) ) ) ) ) ),file(pua2mss1,s2_pua2mss1)).
thf(e1_36_1_2__pua2mss1,conjecture,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_36__pua2mss1 ) @ ( u1_struct_0 @ c1_36__pua2mss1 ) ) ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ c1_36__pua2mss1 ) @ ( u1_struct_0 @ c1_36__pua2mss1 ) ) ) ) => ( ( ! [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ c1_36__pua2mss1 ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ c1_36__pua2mss1 ) ) => ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) <=> ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ c2_36__pua2mss1 ) & ! [E: $i] : ( ( m1_pua2mss1 @ E @ ( k3_finseq_2 @ ( u1_struct_0 @ c1_36__pua2mss1 ) ) @ ( u1_struct_0 @ c1_36__pua2mss1 ) @ ( k1_pua2mss1 @ ( u1_struct_0 @ c1_36__pua2mss1 ) @ ( u1_unialg_1 @ c1_36__pua2mss1 ) ) ) => ! [F: $i] : ( ( ( v1_relat_1 @ F ) & ( v1_funct_1 @ F ) & ( v1_finseq_1 @ F ) ) => ! [G: $i] : ( ( ( v1_relat_1 @ G ) & ( v1_funct_1 @ G ) & ( v1_finseq_1 @ G ) ) => ( ( ( r2_hidden @ ( k7_finseq_1 @ ( k7_finseq_1 @ F @ ( k9_finseq_1 @ C ) ) @ G ) @ ( k1_relset_1 @ ( k3_finseq_2 @ ( u1_struct_0 @ c1_36__pua2mss1 ) ) @ E ) ) & ( r2_hidden @ ( k7_finseq_1 @ ( k7_finseq_1 @ F @ ( k9_finseq_1 @ D ) ) @ G ) @ ( k1_relset_1 @ ( k3_finseq_2 @ ( u1_struct_0 @ c1_36__pua2mss1 ) ) @ E ) ) ) => ( r2_hidden @ ( k4_tarski @ ( k1_funct_1 @ E @ ( k7_finseq_1 @ ( k7_finseq_1 @ F @ ( k9_finseq_1 @ C ) ) @ G ) ) @ ( k1_funct_1 @ E @ ( k7_finseq_1 @ ( k7_finseq_1 @ F @ ( k9_finseq_1 @ D ) ) @ G ) ) ) @ c2_36__pua2mss1 ) ) ) ) ) ) ) ) ) & ! [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ c1_36__pua2mss1 ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( u1_struct_0 @ c1_36__pua2mss1 ) ) => ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) <=> ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ c2_36__pua2mss1 ) & ! [E: $i] : ( ( m1_pua2mss1 @ E @ ( k3_finseq_2 @ ( u1_struct_0 @ c1_36__pua2mss1 ) ) @ ( u1_struct_0 @ c1_36__pua2mss1 ) @ ( k1_pua2mss1 @ ( u1_struct_0 @ c1_36__pua2mss1 ) @ ( u1_unialg_1 @ c1_36__pua2mss1 ) ) ) => ! [F: $i] : ( ( ( v1_relat_1 @ F ) & ( v1_funct_1 @ F ) & ( v1_finseq_1 @ F ) ) => ! [G: $i] : ( ( ( v1_relat_1 @ G ) & ( v1_funct_1 @ G ) & ( v1_finseq_1 @ G ) ) => ( ( ( r2_hidden @ ( k7_finseq_1 @ ( k7_finseq_1 @ F @ ( k9_finseq_1 @ C ) ) @ G ) @ ( k1_relset_1 @ ( k3_finseq_2 @ ( u1_struct_0 @ c1_36__pua2mss1 ) ) @ E ) ) & ( r2_hidden @ ( k7_finseq_1 @ ( k7_finseq_1 @ F @ ( k9_finseq_1 @ D ) ) @ G ) @ ( k1_relset_1 @ ( k3_finseq_2 @ ( u1_struct_0 @ c1_36__pua2mss1 ) ) @ E ) ) ) => ( r2_hidden @ ( k4_tarski @ ( k1_funct_1 @ E @ ( k7_finseq_1 @ ( k7_finseq_1 @ F @ ( k9_finseq_1 @ C ) ) @ G ) ) @ ( k1_funct_1 @ E @ ( k7_finseq_1 @ ( k7_finseq_1 @ F @ ( k9_finseq_1 @ D ) ) @ G ) ) ) @ c2_36__pua2mss1 ) ) ) ) ) ) ) ) ) ) => ( r2_relset_1 @ ( u1_struct_0 @ c1_36__pua2mss1 ) @ ( u1_struct_0 @ c1_36__pua2mss1 ) @ A @ B ) ) ) ) ),file(pua2mss1,e1_36_1_2__pua2mss1)).
