% Mizar problem: e2_65,ordinal2,1712,23 
include('Axioms/SET010^0.ax').
thf(c1_65_type,type,( c1_65__ordinal2: $i )).
thf(c3_65_type,type,( c3_65__ordinal2: $i )).
thf(k10_ordinal2_type,type,( k10_ordinal2: $i > $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_k10_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k10_ordinal2 @ A @ B ) ) ) ),file(ordinal2,k10_ordinal2)).
thf(dt_c1_65__ordinal2,axiom,( v3_ordinal1 @ c1_65__ordinal2 ),file(ordinal2,c1_65__ordinal2)).
thf(dt_c3_65__ordinal2,axiom,( v3_ordinal1 @ c3_65__ordinal2 ),file(ordinal2,c3_65__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(e1_65__ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r2_hidden @ B @ A ) => ( ( r2_hidden @ c1_65__ordinal2 @ B ) => ( r2_hidden @ ( k10_ordinal2 @ c3_65__ordinal2 @ c1_65__ordinal2 ) @ ( k10_ordinal2 @ c3_65__ordinal2 @ B ) ) ) ) ) => ( ( r2_hidden @ c1_65__ordinal2 @ A ) => ( r2_hidden @ ( k10_ordinal2 @ c3_65__ordinal2 @ c1_65__ordinal2 ) @ ( k10_ordinal2 @ c3_65__ordinal2 @ A ) ) ) ) ) ),file(ordinal2,e1_65__ordinal2)).
thf(s2_ordinal1,axiom,( ! [A: $i > $o] : ( ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( r2_hidden @ C @ B ) => ( A @ C ) ) ) => ( A @ B ) ) ) => ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( A @ B ) ) ) ),file(ordinal1,s2_ordinal1)).
thf(e2_65__ordinal2,conjecture,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( r2_hidden @ c1_65__ordinal2 @ A ) => ( r2_hidden @ ( k10_ordinal2 @ c3_65__ordinal2 @ c1_65__ordinal2 ) @ ( k10_ordinal2 @ c3_65__ordinal2 @ A ) ) ) ) ),file(ordinal2,e2_65__ordinal2)).
