% Mizar problem: e7_33,taxonom2,1161,62 
include('Axioms/SET010^0.ax').
thf(c1_33_type,type,( c1_33__taxonom2: $i )).
thf(c2_33_type,type,( c2_33__taxonom2: $i )).
thf(c3_33_type,type,( c3_33__taxonom2: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k9_setfam_1_type,type,( k9_setfam_1: $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m1_taxonom2_type,type,( m1_taxonom2: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $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(v3_abian_type,type,( v3_abian: $i > $i > $o )).
thf(v4_taxonom2_type,type,( v4_taxonom2: $i > $o )).
thf(v5_taxonom2_type,type,( v5_taxonom2: $i > $i > $o )).
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(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(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(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(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(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k9_setfam_1,axiom,( ! [A: $i] : ( = @ ( k9_setfam_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),file(setfam_1,k9_setfam_1)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k9_setfam_1,axiom,( ! [A: $i] : ( m1_subset_1 @ ( k9_setfam_1 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(setfam_1,k9_setfam_1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_m1_taxonom2,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_taxonom2 @ B @ A ) => ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ),file(taxonom2,m1_taxonom2)).
thf(dt_c1_33__taxonom2,axiom,( $true ),file(taxonom2,c1_33__taxonom2)).
thf(dt_c2_33__taxonom2,axiom,( ( v3_abian @ c2_33__taxonom2 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ c1_33__taxonom2 ) ) ) & ( v5_taxonom2 @ c2_33__taxonom2 @ c1_33__taxonom2 ) & ( m1_taxonom2 @ c2_33__taxonom2 @ c1_33__taxonom2 ) ),file(taxonom2,c2_33__taxonom2)).
thf(dt_c3_33__taxonom2,axiom,( m1_subset_1 @ c3_33__taxonom2 @ ( k1_zfmisc_1 @ c1_33__taxonom2 ) ),file(taxonom2,c3_33__taxonom2)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(rc3_taxonom2,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) & ( v4_taxonom2 @ B ) ) ),file(taxonom2,rc3_taxonom2)).
thf(rc4_taxonom2,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_taxonom2 @ B @ A ) & ( v3_abian @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) & ( v5_taxonom2 @ B @ A ) ) ),file(taxonom2,rc4_taxonom2)).
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(e7_33__taxonom2,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ( ( r2_hidden @ B @ ( k9_setfam_1 @ ( k9_setfam_1 @ c1_33__taxonom2 ) ) ) & ( r2_hidden @ c3_33__taxonom2 @ B ) & ( v4_taxonom2 @ B ) & ( r1_tarski @ B @ c2_33__taxonom2 ) ) ) ),file(taxonom2,e7_33__taxonom2)).
