% Mizar problem: e4_67_1,circcmb3,1616,8 
include('Axioms/SET010^0.ax').
thf(c1_67_1_type,type,( c1_67_1__circcmb3: $i )).
thf(k6_classes1_type,type,( k6_classes1: $i > $i )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k6_classes1,axiom,( ! [A: $i] : ( v3_ordinal1 @ ( k6_classes1 @ A ) ) ),file(classes1,k6_classes1)).
thf(dt_c1_67_1__circcmb3,axiom,( $true ),file(circcmb3,c1_67_1__circcmb3)).
thf(e3_67_1__circcmb3,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( = @ B @ ( k6_classes1 @ A ) ) & ( = @ C @ ( k6_classes1 @ A ) ) ) => ( = @ B @ C ) ) ),file(circcmb3,e3_67_1__circcmb3)).
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(e4_67_1__circcmb3,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ? [C: $i] : ( ( r2_hidden @ C @ c1_67_1__circcmb3 ) & ( = @ B @ ( k6_classes1 @ C ) ) ) ) ),file(circcmb3,e4_67_1__circcmb3)).
