% Mizar problem: e5_15,wellord2,326,65 
include('Axioms/SET010^0.ax').
thf(c1_15_type,type,( c1_15__wellord2: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_relat_1_type,type,( k1_relat_1: $i > $i )).
thf(k1_wellord1_type,type,( k1_wellord1: $i > $i > $i )).
thf(k1_wellord2_type,type,( k1_wellord2: $i > $i )).
thf(k2_wellord1_type,type,( k2_wellord1: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(r4_wellord1_type,type,( r4_wellord1: $i > $i > $o )).
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(v1_relat_2_type,type,( v1_relat_2: $i > $o )).
thf(v1_wellord1_type,type,( v1_wellord1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_wellord1_type,type,( v2_wellord1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v4_relat_2_type,type,( v4_relat_2: $i > $o )).
thf(v6_relat_2_type,type,( v6_relat_2: $i > $o )).
thf(v8_relat_2_type,type,( v8_relat_2: $i > $o )).
thf(cc1_wellord1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_wellord1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_relat_2 @ A ) & ( v4_relat_2 @ A ) & ( v6_relat_2 @ A ) & ( v8_relat_2 @ A ) & ( v1_wellord1 @ A ) ) ) ),file(wellord1,cc1_wellord1)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc2_wellord1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_2 @ A ) & ( v4_relat_2 @ A ) & ( v6_relat_2 @ A ) & ( v8_relat_2 @ A ) & ( v1_wellord1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_wellord1 @ A ) ) ) ),file(wellord1,cc2_wellord1)).
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_k1_relat_1,axiom,( $true ),file(relat_1,k1_relat_1)).
thf(dt_k1_wellord1,axiom,( $true ),file(wellord1,k1_wellord1)).
thf(dt_k1_wellord2,axiom,( ! [A: $i] : ( v1_relat_1 @ ( k1_wellord2 @ A ) ) ),file(wellord2,k1_wellord2)).
thf(dt_k2_wellord1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( v1_relat_1 @ ( k2_wellord1 @ A @ B ) ) ) ),file(wellord1,k2_wellord1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_15__wellord2,axiom,( v1_relat_1 @ c1_15__wellord2 ),file(wellord2,c1_15__wellord2)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(fc1_wellord2,axiom,( ! [A: $i] : ( ( v1_relat_1 @ ( k1_wellord2 @ A ) ) & ( v1_relat_2 @ ( k1_wellord2 @ A ) ) ) ),file(wellord2,fc1_wellord2)).
thf(fc2_wellord2,axiom,( ! [A: $i] : ( ( v1_relat_1 @ ( k1_wellord2 @ A ) ) & ( v8_relat_2 @ ( k1_wellord2 @ A ) ) ) ),file(wellord2,fc2_wellord2)).
thf(fc3_wellord2,axiom,( ! [A: $i] : ( ( v1_relat_1 @ ( k1_wellord2 @ A ) ) & ( v4_relat_2 @ ( k1_wellord2 @ A ) ) ) ),file(wellord2,fc3_wellord2)).
thf(fc4_wellord2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_relat_1 @ ( k1_wellord2 @ A ) ) & ( v6_relat_2 @ ( k1_wellord2 @ A ) ) ) ) ),file(wellord2,fc4_wellord2)).
thf(fc5_wellord2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_relat_1 @ ( k1_wellord2 @ A ) ) & ( v1_wellord1 @ ( k1_wellord2 @ A ) ) ) ) ),file(wellord2,fc5_wellord2)).
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(e4_15__wellord2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ A @ ( k1_relat_1 @ c1_15__wellord2 ) ) & ! [D: $i] : ( ( v3_ordinal1 @ D ) => ( ( = @ D @ B ) <=> ( r4_wellord1 @ ( k2_wellord1 @ c1_15__wellord2 @ ( k1_wellord1 @ c1_15__wellord2 @ A ) ) @ ( k1_wellord2 @ D ) ) ) ) & ! [D: $i] : ( ( v3_ordinal1 @ D ) => ( ( = @ D @ C ) <=> ( r4_wellord1 @ ( k2_wellord1 @ c1_15__wellord2 @ ( k1_wellord1 @ c1_15__wellord2 @ A ) ) @ ( k1_wellord2 @ D ) ) ) ) ) => ( = @ B @ C ) ) ),file(wellord2,e4_15__wellord2)).
thf(e3_15__wellord2,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ c1_15__wellord2 ) ) & ! [B: $i] : ~ ( ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( = @ C @ B ) <=> ( r4_wellord1 @ ( k2_wellord1 @ c1_15__wellord2 @ ( k1_wellord1 @ c1_15__wellord2 @ A ) ) @ ( k1_wellord2 @ C ) ) ) ) ) ) ),file(wellord2,e3_15__wellord2)).
thf(s2_funct_1,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ( ( ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( r2_hidden @ C @ B ) & ( A @ C @ D ) & ( A @ C @ E ) ) => ( = @ D @ E ) ) & ! [C: $i] : ~ ( ( r2_hidden @ C @ B ) & ! [D: $i] : ~ ( A @ C @ D ) ) ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( A @ D @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),file(funct_1,s2_funct_1)).
thf(e5_15__wellord2,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k1_relat_1 @ c1_15__wellord2 ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k1_relat_1 @ c1_15__wellord2 ) ) => ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( = @ C @ ( k1_funct_1 @ A @ B ) ) <=> ( r4_wellord1 @ ( k2_wellord1 @ c1_15__wellord2 @ ( k1_wellord1 @ c1_15__wellord2 @ B ) ) @ ( k1_wellord2 @ C ) ) ) ) ) ) ),file(wellord2,e5_15__wellord2)).
