% Mizar problem: e3_82,cgames_1,2224,8 
include('Axioms/SET010^0.ax').
thf(k13_cgames_1_type,type,( k13_cgames_1: $i > $i )).
thf(k8_cgames_1_type,type,( k8_cgames_1: $i > $i )).
thf(v2_cgames_1_type,type,( v2_cgames_1: $i > $o )).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k13_cgames_1,axiom,( $true ),file(cgames_1,k13_cgames_1)).
thf(dt_k8_cgames_1,axiom,( $true ),file(cgames_1,k8_cgames_1)).
thf(fc10_cgames_1,axiom,( ! [A: $i] : ( ( v2_cgames_1 @ A ) => ( v2_cgames_1 @ ( k13_cgames_1 @ A ) ) ) ),file(cgames_1,fc10_cgames_1)).
thf(rc4_cgames_1,axiom,( ? [A: $i] : ( v2_cgames_1 @ A ) ),file(cgames_1,rc4_cgames_1)).
thf(e2_82__cgames_1,axiom,( ? [A: $i] : ( ( v2_cgames_1 @ A ) & ~ ( = @ ( k13_cgames_1 @ ( k13_cgames_1 @ A ) ) @ A ) ) ),file(cgames_1,e2_82__cgames_1)).
thf(s2_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 @ C @ ( k8_cgames_1 @ B ) ) & ( A @ C ) ) ) ) ) ),file(cgames_1,s2_cgames_1)).
thf(e3_82__cgames_1,conjecture,( ? [A: $i] : ( ( v2_cgames_1 @ A ) & ~ ( = @ ( k13_cgames_1 @ ( k13_cgames_1 @ A ) ) @ A ) & ! [B: $i] : ( ( v2_cgames_1 @ B ) => ~ ( ( r2_hidden @ B @ ( k8_cgames_1 @ A ) ) & ~ ( = @ ( k13_cgames_1 @ ( k13_cgames_1 @ B ) ) @ B ) ) ) ) ),file(cgames_1,e3_82__cgames_1)).
