% Mizar problem: e1_38_1,relset_1,591,66 
include('Axioms/SET010^0.ax').
thf(f1_s1_relset_1_type,type,( f1_s1_relset_1: $i )).
thf(f2_s1_relset_1_type,type,( f2_s1_relset_1: $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(p1_s1_relset_1_type,type,( p1_s1_relset_1: $i > $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_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_f1_s1_relset_1,axiom,( $true ),file(relset_1,f1_s1_relset_1)).
thf(dt_f2_s1_relset_1,axiom,( $true ),file(relset_1,f2_s1_relset_1)).
thf(s1_relat_1,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ! [C: $i] : ? [D: $i] : ( ( v1_relat_1 @ D ) & ! [E: $i] : ! [F: $i] : ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) <=> ( ( r2_hidden @ E @ C ) & ( r2_hidden @ F @ B ) & ( A @ E @ F ) ) ) ) ),file(relat_1,s1_relat_1)).
thf(e1_38_1__relset_1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ! [B: $i] : ! [C: $i] : ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) <=> ( ( r2_hidden @ B @ f1_s1_relset_1 ) & ( r2_hidden @ C @ f2_s1_relset_1 ) & ( p1_s1_relset_1 @ B @ C ) ) ) ) ),file(relset_1,e1_38_1__relset_1)).
