% Mizar problem: e5_16_2_1,ordinal2,256,69 
include('Axioms/SET010^0.ax').
thf(c1_16_type,type,( c1_16__ordinal2: $i )).
thf(k2_ordinal1_type,type,( k2_ordinal1: $i > $i )).
thf(r1_ordinal1_type,type,( r1_ordinal1: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
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(reflexivity_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( r1_ordinal1 @ A @ A ) ) ),file(ordinal1,r1_ordinal1)).
thf(connectedness_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( r1_ordinal1 @ A @ B ) | ( r1_ordinal1 @ B @ A ) ) ) ),file(ordinal1,r1_ordinal1)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(redefinition_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( r1_ordinal1 @ A @ B ) <=> ( r1_tarski @ A @ B ) ) ) ),file(ordinal1,r1_ordinal1)).
thf(dt_k2_ordinal1,axiom,( $true ),file(ordinal1,k2_ordinal1)).
thf(dt_c1_16__ordinal2,axiom,( $true ),file(ordinal2,c1_16__ordinal2)).
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(e4_16_2_1__ordinal2,axiom,( ? [A: $i] : ( ( v3_ordinal1 @ A ) & ( r1_tarski @ ( k2_ordinal1 @ c1_16__ordinal2 ) @ A ) ) ),file(ordinal2,e4_16_2_1__ordinal2)).
thf(s1_ordinal1,axiom,( ! [A: $i > $o] : ( ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( A @ B ) ) => ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( A @ B ) & ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( A @ C ) => ( r1_ordinal1 @ B @ C ) ) ) ) ) ),file(ordinal1,s1_ordinal1)).
thf(e5_16_2_1__ordinal2,conjecture,( ? [A: $i] : ( ( v3_ordinal1 @ A ) & ( r1_tarski @ ( k2_ordinal1 @ c1_16__ordinal2 ) @ A ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r1_tarski @ ( k2_ordinal1 @ c1_16__ordinal2 ) @ B ) => ( r1_ordinal1 @ A @ B ) ) ) ) ),file(ordinal2,e5_16_2_1__ordinal2)).
