% Mizar problem: e7_64,wellord1,1540,45 
include('Axioms/SET010^0.ax').
thf(c1_64_type,type,( c1_64__wellord1: $i )).
thf(c2_64_type,type,( c2_64__wellord1: $i )).
thf(k1_relat_1_type,type,( k1_relat_1: $i > $i )).
thf(k1_wellord1_type,type,( k1_wellord1: $i > $i > $i )).
thf(k2_wellord1_type,type,( k2_wellord1: $i > $i > $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $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_relat_1_type,type,( v1_relat_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_k1_relat_1,axiom,( $true ),file(relat_1,k1_relat_1)).
thf(dt_k1_wellord1,axiom,( $true ),file(wellord1,k1_wellord1)).
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_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_c1_64__wellord1,axiom,( v1_relat_1 @ c1_64__wellord1 ),file(wellord1,c1_64__wellord1)).
thf(dt_c2_64__wellord1,axiom,( v1_relat_1 @ c2_64__wellord1 ),file(wellord1,c2_64__wellord1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e6_64__wellord1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ B @ ( k1_relat_1 @ c2_64__wellord1 ) ) & ( r4_wellord1 @ ( k2_wellord1 @ c1_64__wellord1 @ ( k1_wellord1 @ c1_64__wellord1 @ A ) ) @ ( k2_wellord1 @ c2_64__wellord1 @ ( k1_wellord1 @ c2_64__wellord1 @ B ) ) ) & ( r2_hidden @ C @ ( k1_relat_1 @ c2_64__wellord1 ) ) & ( r4_wellord1 @ ( k2_wellord1 @ c1_64__wellord1 @ ( k1_wellord1 @ c1_64__wellord1 @ A ) ) @ ( k2_wellord1 @ c2_64__wellord1 @ ( k1_wellord1 @ c2_64__wellord1 @ C ) ) ) ) => ( = @ B @ C ) ) ),file(wellord1,e6_64__wellord1)).
thf(s1_funct_1,axiom,( ! [A: $i] : ! [B: $i > $i > $o] : ( ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( B @ C @ D ) & ( B @ C @ E ) ) => ( = @ D @ E ) ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ! [D: $i] : ! [E: $i] : ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) <=> ( ( r2_hidden @ D @ A ) & ( B @ D @ E ) ) ) ) ) ),file(funct_1,s1_funct_1)).
thf(e7_64__wellord1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ! [B: $i] : ! [C: $i] : ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) <=> ( ( r2_hidden @ B @ ( k1_relat_1 @ c1_64__wellord1 ) ) & ( r2_hidden @ C @ ( k1_relat_1 @ c2_64__wellord1 ) ) & ( r4_wellord1 @ ( k2_wellord1 @ c1_64__wellord1 @ ( k1_wellord1 @ c1_64__wellord1 @ B ) ) @ ( k2_wellord1 @ c2_64__wellord1 @ ( k1_wellord1 @ c2_64__wellord1 @ C ) ) ) ) ) ) ),file(wellord1,e7_64__wellord1)).
