% Mizar problem: e2_80,ordinal2,2229,29 
include('Axioms/SET010^0.ax').
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(v4_ordinal1_type,type,( v4_ordinal1: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(rc1_ordinal2,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v4_ordinal1 @ A ) ) ),file(ordinal2,rc1_ordinal2)).
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(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(e1_80__ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r2_hidden @ B @ A ) => ? [C: $i] : ( ( v3_ordinal1 @ C ) & ? [D: $i] : ( ( v3_ordinal1 @ D ) & ( v4_ordinal1 @ C ) & ( v7_ordinal1 @ D ) & ( = @ B @ ( k10_ordinal2 @ C @ D ) ) ) ) ) ) => ? [B: $i] : ( ( v3_ordinal1 @ B ) & ? [C: $i] : ( ( v3_ordinal1 @ C ) & ( v4_ordinal1 @ B ) & ( v7_ordinal1 @ C ) & ( = @ A @ ( k10_ordinal2 @ B @ C ) ) ) ) ) ) ),file(ordinal2,e1_80__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_80__ordinal2,conjecture,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ? [B: $i] : ( ( v3_ordinal1 @ B ) & ? [C: $i] : ( ( v3_ordinal1 @ C ) & ( v4_ordinal1 @ B ) & ( v7_ordinal1 @ C ) & ( = @ A @ ( k10_ordinal2 @ B @ C ) ) ) ) ) ),file(ordinal2,e2_80__ordinal2)).
