% Mizar problem: e4_69_1_1_2,classes2,1607,55 
include('Axioms/SET010^0.ax').
thf(c1_69_1_1_2_type,type,( c1_69_1_1_2__classes2: $i )).
thf(k16_classes2_type,type,( k16_classes2: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v5_ordinal1_type,type,( v5_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_k16_classes2,axiom,( $true ),file(classes2,k16_classes2)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_69_1_1_2__classes2,axiom,( v3_ordinal1 @ c1_69_1_1_2__classes2 ),file(classes2,c1_69_1_1_2__classes2)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(fc4_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v5_ordinal1 @ A ) ) => ( v3_ordinal1 @ ( k9_xtuple_0 @ A ) ) ) ),file(ordinal1,fc4_ordinal1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(s2_ordinal2,axiom,( ! [A: $i > $i] : ! [B: $i] : ? [C: $i] : ( ( v5_ordinal1 @ C ) & ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( v3_ordinal1 @ D ) => ( ( r2_hidden @ D @ B ) => ( = @ ( k1_funct_1 @ C @ D ) @ ( A @ D ) ) ) ) ) ),file(ordinal2,s2_ordinal2)).
thf(e4_69_1_1_2__classes2,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ c1_69_1_1_2__classes2 ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r2_hidden @ B @ c1_69_1_1_2__classes2 ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k16_classes2 @ B ) ) ) ) ) ),file(classes2,e4_69_1_1_2__classes2)).
