% Mizar problem: e1_20,numbers,363,37 
include('Axioms/SET010^1.ax').
thf(c2_type,type,( c2__numbers: $i )).
thf(k10_arytm_3_type,type,( k10_arytm_3: $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(k5_arytm_3_type,type,( k5_arytm_3: $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(r3_arytm_3_type,type,( r3_arytm_3: $i > $i > $o )).
thf(v1_card_1_type,type,( v1_card_1: $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v3_card_1_type,type,( v3_card_1: $i > $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(rc2_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(cc10_ordinal1,axiom,( ! [A: $i] : ( ( v6_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v6_ordinal1 @ B ) ) ) ),file(ordinal1,cc10_ordinal1)).
thf(cc1_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(card_1,cc1_card_1)).
thf(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(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(cc6_card_1,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v1_finset_1 @ A ) ) => ( v7_ordinal1 @ A ) ) ),file(card_1,cc6_card_1)).
thf(cc7_card_1,axiom,( ! [A: $i] : ( ( v3_card_1 @ A @ k1_xboole_0 ) => ( v1_xboole_0 @ A ) ) ),file(card_1,cc7_card_1)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc9_card_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(card_1,fc9_card_1)).
thf(rc1_card_1,axiom,( ? [A: $i] : ( v1_card_1 @ A ) ),file(card_1,rc1_card_1)).
thf(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_1)).
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(rc3_card_1,axiom,( ? [A: $i] : ~ ( v1_finset_1 @ A ) ),file(card_1,rc3_card_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(rc5_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ? [B: $i] : ( v3_card_1 @ B @ A ) ) ),file(card_1,rc5_card_1)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_1)).
thf(cc2_card_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc2_card_1)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc3_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc3_card_1)).
thf(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
thf(cc4_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
thf(cc5_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc5_card_1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(cc7_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
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(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(rc1_arytm_3,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ k5_arytm_3 ) & ~ ( v1_xboole_0 @ A ) & ( v3_ordinal1 @ A ) ) ),file(arytm_3,rc1_arytm_3)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc2_arytm_3,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ k5_arytm_3 ) & ( v1_xboole_0 @ A ) ) ),file(arytm_3,rc2_arytm_3)).
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_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(commutativity_k10_arytm_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_arytm_3 ) & ( m1_subset_1 @ B @ k5_arytm_3 ) ) => ( = @ ( k10_arytm_3 @ A @ B ) @ ( k10_arytm_3 @ B @ A ) ) ) ),file(arytm_3,k10_arytm_3)).
thf(connectedness_r3_arytm_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_arytm_3 ) & ( m1_subset_1 @ B @ k5_arytm_3 ) ) => ( ( r3_arytm_3 @ A @ B ) | ( r3_arytm_3 @ B @ A ) ) ) ),file(arytm_3,r3_arytm_3)).
thf(dt_k10_arytm_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_arytm_3 ) & ( m1_subset_1 @ B @ k5_arytm_3 ) ) => ( m1_subset_1 @ ( k10_arytm_3 @ A @ B ) @ k5_arytm_3 ) ) ),file(arytm_3,k10_arytm_3)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k5_arytm_3,axiom,( $true ),file(arytm_3,k5_arytm_3)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_c2__numbers,axiom,( ( v3_ordinal1 @ c2__numbers ) & ( m1_subset_1 @ c2__numbers @ k5_arytm_3 ) ),file(numbers,c2__numbers)).
thf(cc1_arytm_3,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_arytm_3 ) => ( ( v3_ordinal1 @ A ) => ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) ) ) ),file(arytm_3,cc1_arytm_3)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc2_ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal2,cc2_ordinal2)).
thf(cc5_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal1,cc5_ordinal1)).
thf(fc3_arytm_3,axiom,( ~ ( v1_xboole_0 @ k5_arytm_3 ) ),file(arytm_3,fc3_arytm_3)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(s7_domain_1,axiom,( ! [A: $i > $o] : ! [B: $i] : ( m1_subset_1 @ ( replSep1 @ ^ [C: $i] : ( m1_subset_1 @ C @ B ) @ ^ [C: $i] : C @ ^ [C: $i] : ( A @ C ) ) @ ( k1_zfmisc_1 @ B ) ) ),file(domain_1,s7_domain_1)).
thf(e1_20__numbers,conjecture,( m1_subset_1 @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ k5_arytm_3 ) @ ^ [A: $i] : A @ ^ [A: $i] : ~ ( r3_arytm_3 @ c2__numbers @ ( k10_arytm_3 @ A @ A ) ) ) @ ( k1_zfmisc_1 @ k5_arytm_3 ) ),file(numbers,e1_20__numbers)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
