% Mizar problem: e2_7_1,pboole,171,41 
include('Axioms/SET010^0.ax').
thf(f1_s2_pboole_type,type,( f1_s2_pboole: $i )).
thf(f2_s2_pboole_type,type,( f2_s2_pboole: $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(p1_s2_pboole_type,type,( p1_s2_pboole: $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(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(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_f1_s2_pboole,axiom,( $true ),file(pboole,f1_s2_pboole)).
thf(dt_f2_s2_pboole,axiom,( ( v1_relat_1 @ f2_s2_pboole ) & ( v4_relat_1 @ f2_s2_pboole @ f1_s2_pboole ) & ( v1_funct_1 @ f2_s2_pboole ) & ( v1_partfun1 @ f2_s2_pboole @ f1_s2_pboole ) ),file(pboole,f2_s2_pboole)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e1_7_1__pboole,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ f1_s2_pboole ) & ! [B: $i] : ~ ( ! [C: $i] : ( ( r2_hidden @ C @ B ) <=> ( ( r2_hidden @ C @ ( k1_funct_1 @ f2_s2_pboole @ A ) ) & ( p1_s2_pboole @ A @ C ) ) ) ) ) ),file(pboole,e1_7_1__pboole)).
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(e2_7_1__pboole,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ f1_s2_pboole ) & ! [B: $i] : ( ( r2_hidden @ B @ f1_s2_pboole ) => ! [C: $i] : ( ( r2_hidden @ C @ ( k1_funct_1 @ A @ B ) ) <=> ( ( r2_hidden @ C @ ( k1_funct_1 @ f2_s2_pboole @ B ) ) & ( p1_s2_pboole @ B @ C ) ) ) ) ) ),file(pboole,e2_7_1__pboole)).
