% Mizar problem: e2_30,domain_1,493,20 
include('Axioms/SET010^4.ax').
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k4_zfmisc_1_type,type,( k4_zfmisc_1: $i > $i > $i > $i > $i )).
thf(k5_domain_1_type,type,( k5_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i )).
thf(k6_xtuple_0_type,type,( k6_xtuple_0: $i > $i > $i > $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $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_xtuple_0_type,type,( v1_xtuple_0: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v2_xtuple_0_type,type,( v2_xtuple_0: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(v3_xtuple_0_type,type,( v3_xtuple_0: $i > $o )).
thf(rc1_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_0)).
thf(cc1_xtuple_0,axiom,( ! [A: $i] : ( ( v2_xtuple_0 @ A ) => ( v1_xtuple_0 @ A ) ) ),file(xtuple_0,cc1_xtuple_0)).
thf(rc2_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
thf(rc2_xtuple_0,axiom,( ? [A: $i] : ( v2_xtuple_0 @ A ) ),file(xtuple_0,rc2_xtuple_0)).
thf(dt_k6_xtuple_0,axiom,( $true ),file(xtuple_0,k6_xtuple_0)).
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_xtuple_0,axiom,( ! [A: $i] : ( ( v3_xtuple_0 @ A ) => ( v2_xtuple_0 @ A ) ) ),file(xtuple_0,cc2_xtuple_0)).
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_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(fc3_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( v3_xtuple_0 @ ( k6_xtuple_0 @ A @ B @ C @ D ) ) ),file(xtuple_0,fc3_xtuple_0)).
thf(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_1)).
thf(rc3_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_subset_1 @ B @ A ) ) ),file(subset_1,rc3_subset_1)).
thf(rc3_xtuple_0,axiom,( ? [A: $i] : ( v3_xtuple_0 @ A ) ),file(xtuple_0,rc3_xtuple_0)).
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(redefinition_k5_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ! [G: $i] : ! [H: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ~ ( v1_xboole_0 @ D ) & ( m1_subset_1 @ E @ A ) & ( m1_subset_1 @ F @ B ) & ( m1_subset_1 @ G @ C ) & ( m1_subset_1 @ H @ D ) ) => ( = @ ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k6_xtuple_0 @ E @ F @ G @ H ) ) ) ),file(domain_1,k5_domain_1)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k4_zfmisc_1,axiom,( $true ),file(zfmisc_1,k4_zfmisc_1)).
thf(dt_k5_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ! [G: $i] : ! [H: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ~ ( v1_xboole_0 @ D ) & ( m1_subset_1 @ E @ A ) & ( m1_subset_1 @ F @ B ) & ( m1_subset_1 @ G @ C ) & ( m1_subset_1 @ H @ D ) ) => ( m1_subset_1 @ ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ),file(domain_1,k5_domain_1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_1)).
thf(cc1_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_xboole_0 @ B ) ) ) ),file(subset_1,cc1_subset_1)).
thf(cc2_mcart_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ~ ( v1_xboole_0 @ D ) ) => ! [E: $i] : ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) => ( v3_xtuple_0 @ E ) ) ) ),file(mcart_1,cc2_mcart_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_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(fc12_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ~ ( v1_xboole_0 @ D ) ) => ~ ( v1_xboole_0 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ),file(subset_1,fc12_subset_1)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_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(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(s4_domain_1,axiom,( ! [A: $i > $i > $i > $i > $o] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ! [C: $i] : ( ~ ( v1_xboole_0 @ C ) => ! [D: $i] : ( ~ ( v1_xboole_0 @ D ) => ! [E: $i] : ( ~ ( v1_xboole_0 @ E ) => ( m1_subset_1 @ ( replSep4 @ ^ [F: $i] : ( m1_subset_1 @ F @ B ) @ ^ [F: $i] : ^ [G: $i] : ( m1_subset_1 @ G @ C ) @ ^ [F: $i] : ^ [G: $i] : ^ [H: $i] : ( m1_subset_1 @ H @ D ) @ ^ [F: $i] : ^ [G: $i] : ^ [H: $i] : ^ [I: $i] : ( m1_subset_1 @ I @ E ) @ ^ [F: $i] : ^ [G: $i] : ^ [H: $i] : ^ [I: $i] : ( k5_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) @ ^ [F: $i] : ^ [G: $i] : ^ [H: $i] : ^ [I: $i] : ( A @ F @ G @ H @ I ) ) @ ( k1_zfmisc_1 @ ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ),file(domain_1,s4_domain_1)).
thf(e2_30__domain_1,conjecture,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ! [C: $i] : ( ~ ( v1_xboole_0 @ C ) => ! [D: $i] : ( ~ ( v1_xboole_0 @ D ) => ( m1_subset_1 @ ( replSep4 @ ^ [E: $i] : ( m1_subset_1 @ E @ A ) @ ^ [E: $i] : ^ [F: $i] : ( m1_subset_1 @ F @ B ) @ ^ [E: $i] : ^ [F: $i] : ^ [G: $i] : ( m1_subset_1 @ G @ C ) @ ^ [E: $i] : ^ [F: $i] : ^ [G: $i] : ^ [H: $i] : ( m1_subset_1 @ H @ D ) @ ^ [E: $i] : ^ [F: $i] : ^ [G: $i] : ^ [H: $i] : ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ^ [E: $i] : ^ [F: $i] : ^ [G: $i] : ^ [H: $i] : $true ) @ ( k1_zfmisc_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ) ) ) ) ),file(domain_1,e2_30__domain_1)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
