% Mizar problem: e2_92,cgames_1,2634,26 
include('Axioms/SET010^0.ax').
thf(k6_cgames_1_type,type,( k6_cgames_1: $i > $i )).
thf(k7_cgames_1_type,type,( k7_cgames_1: $i > $i )).
thf(k8_cgames_1_type,type,( k8_cgames_1: $i > $i )).
thf(v10_cgames_1_type,type,( v10_cgames_1: $i > $o )).
thf(v2_cgames_1_type,type,( v2_cgames_1: $i > $o )).
thf(v5_cgames_1_type,type,( v5_cgames_1: $i > $o )).
thf(v6_cgames_1_type,type,( v6_cgames_1: $i > $o )).
thf(v7_cgames_1_type,type,( v7_cgames_1: $i > $o )).
thf(v8_cgames_1_type,type,( v8_cgames_1: $i > $o )).
thf(v9_cgames_1_type,type,( v9_cgames_1: $i > $o )).
thf(cc10_cgames_1,axiom,( ! [A: $i] : ( ( ( v2_cgames_1 @ A ) & ( v5_cgames_1 @ A ) & ~ ( v7_cgames_1 @ A ) ) => ( ( v2_cgames_1 @ A ) & ( v9_cgames_1 @ A ) ) ) ),file(cgames_1,cc10_cgames_1)).
thf(cc5_cgames_1,axiom,( ! [A: $i] : ( ( ( v2_cgames_1 @ A ) & ( v7_cgames_1 @ A ) ) => ( ( v2_cgames_1 @ A ) & ( v5_cgames_1 @ A ) & ( v6_cgames_1 @ A ) ) ) ),file(cgames_1,cc5_cgames_1)).
thf(cc8_cgames_1,axiom,( ! [A: $i] : ( ( ( v2_cgames_1 @ A ) & ( v6_cgames_1 @ A ) & ~ ( v7_cgames_1 @ A ) ) => ( ( v2_cgames_1 @ A ) & ( v10_cgames_1 @ A ) ) ) ),file(cgames_1,cc8_cgames_1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k6_cgames_1,axiom,( $true ),file(cgames_1,k6_cgames_1)).
thf(dt_k7_cgames_1,axiom,( $true ),file(cgames_1,k7_cgames_1)).
thf(dt_k8_cgames_1,axiom,( $true ),file(cgames_1,k8_cgames_1)).
thf(cc11_cgames_1,axiom,( ! [A: $i] : ( ( ( v2_cgames_1 @ A ) & ( v8_cgames_1 @ A ) ) => ( ( v2_cgames_1 @ A ) & ~ ( v5_cgames_1 @ A ) & ~ ( v6_cgames_1 @ A ) ) ) ),file(cgames_1,cc11_cgames_1)).
thf(cc12_cgames_1,axiom,( ! [A: $i] : ( ( ( v2_cgames_1 @ A ) & ~ ( v5_cgames_1 @ A ) & ~ ( v6_cgames_1 @ A ) ) => ( ( v2_cgames_1 @ A ) & ( v8_cgames_1 @ A ) ) ) ),file(cgames_1,cc12_cgames_1)).
thf(cc6_cgames_1,axiom,( ! [A: $i] : ( ( ( v2_cgames_1 @ A ) & ( v5_cgames_1 @ A ) & ( v6_cgames_1 @ A ) ) => ( ( v2_cgames_1 @ A ) & ( v7_cgames_1 @ A ) ) ) ),file(cgames_1,cc6_cgames_1)).
thf(cc7_cgames_1,axiom,( ! [A: $i] : ( ( ( v2_cgames_1 @ A ) & ( v10_cgames_1 @ A ) ) => ( ( v2_cgames_1 @ A ) & ( v6_cgames_1 @ A ) & ~ ( v7_cgames_1 @ A ) ) ) ),file(cgames_1,cc7_cgames_1)).
thf(cc9_cgames_1,axiom,( ! [A: $i] : ( ( ( v2_cgames_1 @ A ) & ( v9_cgames_1 @ A ) ) => ( ( v2_cgames_1 @ A ) & ( v5_cgames_1 @ A ) & ~ ( v7_cgames_1 @ A ) ) ) ),file(cgames_1,cc9_cgames_1)).
thf(rc4_cgames_1,axiom,( ? [A: $i] : ( v2_cgames_1 @ A ) ),file(cgames_1,rc4_cgames_1)).
thf(e1_92__cgames_1,axiom,( ! [A: $i] : ( ( v2_cgames_1 @ A ) => ( ! [B: $i] : ( ( v2_cgames_1 @ B ) => ( ( r2_hidden @ B @ ( k8_cgames_1 @ A ) ) => ( ( ( v5_cgames_1 @ B ) => ! [C: $i] : ( ( v2_cgames_1 @ C ) => ~ ( ( r2_hidden @ C @ ( k7_cgames_1 @ B ) ) & ~ ( v8_cgames_1 @ C ) & ~ ( v9_cgames_1 @ C ) ) ) ) & ( ! [C: $i] : ( ( v2_cgames_1 @ C ) => ~ ( ( r2_hidden @ C @ ( k7_cgames_1 @ B ) ) & ~ ( v8_cgames_1 @ C ) & ~ ( v9_cgames_1 @ C ) ) ) => ( v5_cgames_1 @ B ) ) & ( ( v6_cgames_1 @ B ) => ! [C: $i] : ( ( v2_cgames_1 @ C ) => ~ ( ( r2_hidden @ C @ ( k6_cgames_1 @ B ) ) & ~ ( v8_cgames_1 @ C ) & ~ ( v10_cgames_1 @ C ) ) ) ) & ( ! [C: $i] : ( ( v2_cgames_1 @ C ) => ~ ( ( r2_hidden @ C @ ( k6_cgames_1 @ B ) ) & ~ ( v8_cgames_1 @ C ) & ~ ( v10_cgames_1 @ C ) ) ) => ( v6_cgames_1 @ B ) ) ) ) ) => ( ( ( v5_cgames_1 @ A ) => ! [B: $i] : ( ( v2_cgames_1 @ B ) => ~ ( ( r2_hidden @ B @ ( k7_cgames_1 @ A ) ) & ~ ( v8_cgames_1 @ B ) & ~ ( v9_cgames_1 @ B ) ) ) ) & ( ! [B: $i] : ( ( v2_cgames_1 @ B ) => ~ ( ( r2_hidden @ B @ ( k7_cgames_1 @ A ) ) & ~ ( v8_cgames_1 @ B ) & ~ ( v9_cgames_1 @ B ) ) ) => ( v5_cgames_1 @ A ) ) & ( ( v6_cgames_1 @ A ) => ! [B: $i] : ( ( v2_cgames_1 @ B ) => ~ ( ( r2_hidden @ B @ ( k6_cgames_1 @ A ) ) & ~ ( v8_cgames_1 @ B ) & ~ ( v10_cgames_1 @ B ) ) ) ) & ( ! [B: $i] : ( ( v2_cgames_1 @ B ) => ~ ( ( r2_hidden @ B @ ( k6_cgames_1 @ A ) ) & ~ ( v8_cgames_1 @ B ) & ~ ( v10_cgames_1 @ B ) ) ) => ( v6_cgames_1 @ A ) ) ) ) ) ),file(cgames_1,e1_92__cgames_1)).
thf(s3_cgames_1,axiom,( ! [A: $i > $o] : ( ! [B: $i] : ( ( v2_cgames_1 @ B ) => ( ! [C: $i] : ( ( v2_cgames_1 @ C ) => ( ( r2_hidden @ C @ ( k8_cgames_1 @ B ) ) => ( A @ C ) ) ) => ( A @ B ) ) ) => ! [B: $i] : ( ( v2_cgames_1 @ B ) => ( A @ B ) ) ) ),file(cgames_1,s3_cgames_1)).
thf(e2_92__cgames_1,conjecture,( ! [A: $i] : ( ( v2_cgames_1 @ A ) => ( ( ( v5_cgames_1 @ A ) => ! [B: $i] : ( ( v2_cgames_1 @ B ) => ~ ( ( r2_hidden @ B @ ( k7_cgames_1 @ A ) ) & ~ ( v8_cgames_1 @ B ) & ~ ( v9_cgames_1 @ B ) ) ) ) & ( ! [B: $i] : ( ( v2_cgames_1 @ B ) => ~ ( ( r2_hidden @ B @ ( k7_cgames_1 @ A ) ) & ~ ( v8_cgames_1 @ B ) & ~ ( v9_cgames_1 @ B ) ) ) => ( v5_cgames_1 @ A ) ) & ( ( v6_cgames_1 @ A ) => ! [B: $i] : ( ( v2_cgames_1 @ B ) => ~ ( ( r2_hidden @ B @ ( k6_cgames_1 @ A ) ) & ~ ( v8_cgames_1 @ B ) & ~ ( v10_cgames_1 @ B ) ) ) ) & ( ! [B: $i] : ( ( v2_cgames_1 @ B ) => ~ ( ( r2_hidden @ B @ ( k6_cgames_1 @ A ) ) & ~ ( v8_cgames_1 @ B ) & ~ ( v10_cgames_1 @ B ) ) ) => ( v6_cgames_1 @ A ) ) ) ) ),file(cgames_1,e2_92__cgames_1)).
