% Mizar problem: e1_74_1,cgames_1,1456,8 
include('Axioms/SET010^0.ax').
thf(k9_cgames_1_type,type,( k9_cgames_1: $i > $i )).
thf(p1_s4_cgames_1_type,type,( p1_s4_cgames_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v2_cgames_1_type,type,( v2_cgames_1: $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_k9_cgames_1,axiom,( ! [A: $i] : ( v3_ordinal1 @ ( k9_cgames_1 @ A ) ) ),file(cgames_1,k9_cgames_1)).
thf(rc4_cgames_1,axiom,( ? [A: $i] : ( v2_cgames_1 @ A ) ),file(cgames_1,rc4_cgames_1)).
thf(e1_74__cgames_1,axiom,( ? [A: $i] : ( ( v2_cgames_1 @ A ) & ( p1_s4_cgames_1 @ A ) ) ),file(cgames_1,e1_74__cgames_1)).
thf(s1_cgames_1,axiom,( ! [A: $i > $o] : ( ? [B: $i] : ( ( v2_cgames_1 @ B ) & ( A @ B ) ) => ? [B: $i] : ( ( v2_cgames_1 @ B ) & ( A @ B ) & ! [C: $i] : ( ( v2_cgames_1 @ C ) => ~ ( ( r2_hidden @ ( k9_cgames_1 @ C ) @ ( k9_cgames_1 @ B ) ) & ( A @ C ) ) ) ) ) ),file(cgames_1,s1_cgames_1)).
thf(e1_74_1__cgames_1,conjecture,( ? [A: $i] : ( ( v2_cgames_1 @ A ) & ( p1_s4_cgames_1 @ A ) & ! [B: $i] : ( ( v2_cgames_1 @ B ) => ~ ( ( r2_hidden @ ( k9_cgames_1 @ B ) @ ( k9_cgames_1 @ A ) ) & ( p1_s4_cgames_1 @ B ) ) ) ) ),file(cgames_1,e1_74_1__cgames_1)).
