% Mizar problem: e4_45_1,trees_2,1179,51 
include('Axioms/SET010^0.ax').
thf(c1_45_1_type,type,( c1_45_1__trees_2: $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(p2_s5_trees_2_type,type,( p2_s5_trees_2: $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_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_45_1__trees_2,axiom,( $true ),file(trees_2,c1_45_1__trees_2)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e3_45_1__trees_2,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ c1_45_1__trees_2 ) & ! [B: $i] : ~ ( ( r2_hidden @ B @ c1_45_1__trees_2 ) & ( p2_s5_trees_2 @ A @ B ) ) ) ),file(trees_2,e3_45_1__trees_2)).
thf(s1_classes1,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ( ! [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(classes1,s1_classes1)).
thf(e4_45_1__trees_2,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ c1_45_1__trees_2 ) & ! [B: $i] : ( ( r2_hidden @ B @ c1_45_1__trees_2 ) => ( ( r2_hidden @ ( k1_funct_1 @ A @ B ) @ c1_45_1__trees_2 ) & ( p2_s5_trees_2 @ B @ ( k1_funct_1 @ A @ B ) ) ) ) ) ),file(trees_2,e4_45_1__trees_2)).
