% Mizar problem: e2_38_1_1_6,ordinal2,839,32 
include('Axioms/SET010^0.ax').
thf(c1_38_1_1_type,type,( c1_38_1_1__ordinal2: $i )).
thf(c2_38_1_1_type,type,( c2_38_1_1__ordinal2: $i )).
thf(c4_38_1_1_type,type,( c4_38_1_1__ordinal2: $i )).
thf(k10_xtuple_0_type,type,( k10_xtuple_0: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k5_relat_1_type,type,( k5_relat_1: $i > $i > $i )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_ordinal2_type,type,( v1_ordinal2: $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(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(fc1_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v1_ordinal2 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(ordinal2,fc1_ordinal2)).
thf(fc2_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) & ( v3_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(ordinal2,fc2_ordinal2)).
thf(rc2_ordinal2,axiom,( ? [A: $i] : ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) ) ),file(ordinal2,rc2_ordinal2)).
thf(dt_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
thf(cc1_ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( ( v5_ordinal1 @ B ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ( ( v5_ordinal1 @ B ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_ordinal2 @ B ) ) ) ) ),file(ordinal2,cc1_ordinal2)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(rc3_ordinal1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v5_ordinal1 @ B ) ) ),file(ordinal1,rc3_ordinal1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ),file(relat_1,k5_relat_1)).
thf(dt_c1_38_1_1__ordinal2,axiom,( v3_ordinal1 @ c1_38_1_1__ordinal2 ),file(ordinal2,c1_38_1_1__ordinal2)).
thf(dt_c2_38_1_1__ordinal2,axiom,( ( v1_relat_1 @ c2_38_1_1__ordinal2 ) & ( v1_funct_1 @ c2_38_1_1__ordinal2 ) ),file(ordinal2,c2_38_1_1__ordinal2)).
thf(dt_c4_38_1_1__ordinal2,axiom,( ( v5_ordinal1 @ c4_38_1_1__ordinal2 ) & ( v1_relat_1 @ c4_38_1_1__ordinal2 ) & ( v1_funct_1 @ c4_38_1_1__ordinal2 ) ),file(ordinal2,c4_38_1_1__ordinal2)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(fc5_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v5_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v5_relat_1 @ ( k5_relat_1 @ A @ B ) @ ( k10_xtuple_0 @ A ) ) & ( v5_ordinal1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(ordinal1,fc5_ordinal1)).
thf(fc8_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(funct_1,fc8_funct_1)).
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(e1_38_1_1_6__ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r2_hidden @ B @ A ) => ! [C: $i] : ( ( ( v5_ordinal1 @ C ) & ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) ) => ( ( ( r2_hidden @ B @ c1_38_1_1__ordinal2 ) & ( = @ C @ ( k1_funct_1 @ c2_38_1_1__ordinal2 @ B ) ) ) => ( = @ ( k5_relat_1 @ c4_38_1_1__ordinal2 @ B ) @ C ) ) ) ) ) => ! [B: $i] : ( ( ( v5_ordinal1 @ B ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( ( ( r2_hidden @ A @ c1_38_1_1__ordinal2 ) & ( = @ B @ ( k1_funct_1 @ c2_38_1_1__ordinal2 @ A ) ) ) => ( = @ ( k5_relat_1 @ c4_38_1_1__ordinal2 @ A ) @ B ) ) ) ) ) ),file(ordinal2,e1_38_1_1_6__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_38_1_1_6__ordinal2,conjecture,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( ( v5_ordinal1 @ B ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( ( ( r2_hidden @ A @ c1_38_1_1__ordinal2 ) & ( = @ B @ ( k1_funct_1 @ c2_38_1_1__ordinal2 @ A ) ) ) => ( = @ ( k5_relat_1 @ c4_38_1_1__ordinal2 @ A ) @ B ) ) ) ) ),file(ordinal2,e2_38_1_1_6__ordinal2)).
