% Mizar problem: e2_73_1_1,grcat_1,1004,56 
include('Axioms/SET010^0.ax').
thf(c1_73_type,type,( c1_73__grcat_1: $i )).
thf(r1_grcat_1_type,type,( r1_grcat_1: $i > $i > $o )).
thf(v1_classes1_type,type,( v1_classes1: $i > $o )).
thf(v1_classes2_type,type,( v1_classes2: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v2_classes1_type,type,( v2_classes1: $i > $o )).
thf(cc1_classes2,axiom,( ! [A: $i] : ( ( v2_classes1 @ A ) => ( v1_classes1 @ A ) ) ),file(classes2,cc1_classes2)).
thf(cc3_classes2,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_classes1 @ A ) ) => ( v1_classes2 @ A ) ) ),file(classes2,cc3_classes2)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_c1_73__grcat_1,axiom,( ~ ( v1_xboole_0 @ c1_73__grcat_1 ) & ( v1_classes2 @ c1_73__grcat_1 ) ),file(grcat_1,c1_73__grcat_1)).
thf(cc2_classes2,axiom,( ! [A: $i] : ( ( v1_classes2 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_classes1 @ A ) ) ) ),file(classes2,cc2_classes2)).
thf(rc1_classes2,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_classes2 @ A ) ) ),file(classes2,rc1_classes2)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(e1_73_1_1__grcat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r1_grcat_1 @ A @ B ) & ( r1_grcat_1 @ A @ C ) ) => ( = @ B @ C ) ) ),file(grcat_1,e1_73_1_1__grcat_1)).
thf(s1_tarski,axiom,( ! [A: $i] : ! [B: $i > $i > $o] : ( ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( B @ C @ D ) & ( B @ C @ E ) ) => ( = @ D @ E ) ) => ? [C: $i] : ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ? [E: $i] : ( ( r2_hidden @ E @ A ) & ( B @ E @ D ) ) ) ) ),file(tarski,s1_tarski)).
thf(e2_73_1_1__grcat_1,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ? [C: $i] : ( ( r2_hidden @ C @ c1_73__grcat_1 ) & ( r1_grcat_1 @ C @ B ) ) ) ),file(grcat_1,e2_73_1_1__grcat_1)).
