% Mizar problem: e1_5_1_2,closure2,139,60 
include('Axioms/SET010^0.ax').
thf(c1_5_type,type,( c1_5__closure2: $i )).
thf(c2_5_type,type,( c2_5__closure2: $i )).
thf(m3_pboole_type,type,( m3_pboole: $i > $i > $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_partfun1_type,type,( v1_partfun1: $i > $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $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_m3_pboole,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( m3_pboole @ C @ A @ B ) => ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) ) ) ),file(pboole,m3_pboole)).
thf(dt_c1_5__closure2,axiom,( $true ),file(closure2,c1_5__closure2)).
thf(dt_c2_5__closure2,axiom,( ( v1_relat_1 @ c2_5__closure2 ) & ( v4_relat_1 @ c2_5__closure2 @ c1_5__closure2 ) & ( v1_funct_1 @ c2_5__closure2 ) & ( v1_partfun1 @ c2_5__closure2 @ c1_5__closure2 ) ),file(closure2,c2_5__closure2)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_pboole,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(pboole,rc1_pboole)).
thf(s3_xboole_0,axiom,( ! [A: $i > $o] : ! [B: $i] : ! [C: $i] : ( ( ! [D: $i] : ( ( r2_hidden @ D @ B ) <=> ( A @ D ) ) & ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( A @ D ) ) ) => ( = @ B @ C ) ) ),file(xboole_0,s3_xboole_0)).
thf(e1_5_1_2__closure2,conjecture,( ! [A: $i] : ! [B: $i] : ( ( ! [C: $i] : ( ( r2_hidden @ C @ A ) <=> ( m3_pboole @ C @ c1_5__closure2 @ c2_5__closure2 ) ) & ! [C: $i] : ( ( r2_hidden @ C @ B ) <=> ( m3_pboole @ C @ c1_5__closure2 @ c2_5__closure2 ) ) ) => ( = @ A @ B ) ) ),file(closure2,e1_5_1_2__closure2)).
