% Mizar problem: e4_5,ordinal3,76,18 
include('Axioms/SET010^0.ax').
thf(c2_5_type,type,( c2_5__ordinal3: $i )).
thf(k2_ordinal1_type,type,( k2_ordinal1: $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(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k2_ordinal1,axiom,( $true ),file(ordinal1,k2_ordinal1)).
thf(dt_c2_5__ordinal3,axiom,( $true ),file(ordinal3,c2_5__ordinal3)).
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(e3_5__ordinal3,axiom,( ! [A: $i] : ( ( r2_hidden @ A @ ( k2_ordinal1 @ c2_5__ordinal3 ) ) <=> ( ( r2_hidden @ A @ c2_5__ordinal3 ) & ( v3_ordinal1 @ A ) ) ) ),file(ordinal3,e3_5__ordinal3)).
thf(e2_5__ordinal3,axiom,( ! [A: $i] : ( ( r2_hidden @ A @ c2_5__ordinal3 ) <=> ( ( r2_hidden @ A @ c2_5__ordinal3 ) & ( v3_ordinal1 @ A ) ) ) ),file(ordinal3,e2_5__ordinal3)).
thf(s2_xboole_0,axiom,( ! [A: $i] : ! [B: $i > $o] : ! [C: $i] : ( ( ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( B @ D ) ) & ! [D: $i] : ( ( r2_hidden @ D @ A ) <=> ( B @ D ) ) ) => ( = @ C @ A ) ) ),file(xboole_0,s2_xboole_0)).
thf(e4_5__ordinal3,conjecture,( = @ ( k2_ordinal1 @ c2_5__ordinal3 ) @ c2_5__ordinal3 ),file(ordinal3,e4_5__ordinal3)).
