% Mizar problem: e5_13_1,recdef_2,199,53 
include('Axioms/SET010^0.ax').
thf(c1_13_1_type,type,( c1_13_1__recdef_2: $i )).
thf(f2_s1_recdef_2_type,type,( f2_s1_recdef_2: $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_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_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_13_1__recdef_2,axiom,( $true ),file(recdef_2,c1_13_1__recdef_2)).
thf(dt_f2_s1_recdef_2,axiom,( $true ),file(recdef_2,f2_s1_recdef_2)).
thf(s3_funct_1,axiom,( ! [A: $i > $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( = @ ( k1_funct_1 @ C @ D ) @ ( A @ D ) ) ) ) ),file(funct_1,s3_funct_1)).
thf(e5_13_1__recdef_2,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ c1_13_1__recdef_2 ) & ! [B: $i] : ( ( r2_hidden @ B @ c1_13_1__recdef_2 ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( f2_s1_recdef_2 @ B ) ) ) ) ),file(recdef_2,e5_13_1__recdef_2)).
