%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU326+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 07:22:26 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 11 unt; 0 def)
% Number of atoms : 106 ( 60 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 111 ( 49 ~; 33 |; 23 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 3 sgn 28 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(6,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
file('/tmp/tmp0ZR74g/sel_SEU326+1.p_1',involutiveness_k7_setfam_1) ).
fof(19,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
file('/tmp/tmp0ZR74g/sel_SEU326+1.p_1',t46_setfam_1) ).
fof(23,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
file('/tmp/tmp0ZR74g/sel_SEU326+1.p_1',dt_k7_setfam_1) ).
fof(29,conjecture,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set )
& ~ ( complements_of_subsets(X1,X2) != empty_set
& X2 = empty_set ) ) ),
file('/tmp/tmp0ZR74g/sel_SEU326+1.p_1',t10_tops_2) ).
fof(32,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/tmp/tmp0ZR74g/sel_SEU326+1.p_1',t6_boole) ).
fof(35,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/tmp/tmp0ZR74g/sel_SEU326+1.p_1',rc2_subset_1) ).
fof(39,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set )
& ~ ( complements_of_subsets(X1,X2) != empty_set
& X2 = empty_set ) ) ),
inference(assume_negation,[status(cth)],[29]) ).
fof(65,plain,
! [X1,X2] :
( ~ element(X2,powerset(powerset(X1)))
| complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(66,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| complements_of_subsets(X3,complements_of_subsets(X3,X4)) = X4 ),
inference(variable_rename,[status(thm)],[65]) ).
cnf(67,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[66]) ).
fof(118,plain,
! [X1,X2] :
( ~ element(X2,powerset(powerset(X1)))
| X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(119,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| X4 = empty_set
| complements_of_subsets(X3,X4) != empty_set ),
inference(variable_rename,[status(thm)],[118]) ).
cnf(120,plain,
( X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[119]) ).
fof(140,plain,
! [X1,X2] :
( ~ element(X2,powerset(powerset(X1)))
| element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(141,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| element(complements_of_subsets(X3,X4),powerset(powerset(X3))) ),
inference(variable_rename,[status(thm)],[140]) ).
cnf(142,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[141]) ).
fof(162,negated_conjecture,
? [X1,X2] :
( element(X2,powerset(powerset(X1)))
& ( ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set )
| ( complements_of_subsets(X1,X2) != empty_set
& X2 = empty_set ) ) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(163,negated_conjecture,
? [X3,X4] :
( element(X4,powerset(powerset(X3)))
& ( ( X4 != empty_set
& complements_of_subsets(X3,X4) = empty_set )
| ( complements_of_subsets(X3,X4) != empty_set
& X4 = empty_set ) ) ),
inference(variable_rename,[status(thm)],[162]) ).
fof(164,negated_conjecture,
( element(esk4_0,powerset(powerset(esk3_0)))
& ( ( esk4_0 != empty_set
& complements_of_subsets(esk3_0,esk4_0) = empty_set )
| ( complements_of_subsets(esk3_0,esk4_0) != empty_set
& esk4_0 = empty_set ) ) ),
inference(skolemize,[status(esa)],[163]) ).
fof(165,negated_conjecture,
( element(esk4_0,powerset(powerset(esk3_0)))
& ( complements_of_subsets(esk3_0,esk4_0) != empty_set
| esk4_0 != empty_set )
& ( esk4_0 = empty_set
| esk4_0 != empty_set )
& ( complements_of_subsets(esk3_0,esk4_0) != empty_set
| complements_of_subsets(esk3_0,esk4_0) = empty_set )
& ( esk4_0 = empty_set
| complements_of_subsets(esk3_0,esk4_0) = empty_set ) ),
inference(distribute,[status(thm)],[164]) ).
cnf(166,negated_conjecture,
( complements_of_subsets(esk3_0,esk4_0) = empty_set
| esk4_0 = empty_set ),
inference(split_conjunct,[status(thm)],[165]) ).
cnf(169,negated_conjecture,
( esk4_0 != empty_set
| complements_of_subsets(esk3_0,esk4_0) != empty_set ),
inference(split_conjunct,[status(thm)],[165]) ).
cnf(170,negated_conjecture,
element(esk4_0,powerset(powerset(esk3_0))),
inference(split_conjunct,[status(thm)],[165]) ).
fof(175,plain,
! [X1] :
( ~ empty(X1)
| X1 = empty_set ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(176,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[175]) ).
cnf(177,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[176]) ).
fof(187,plain,
! [X3] :
? [X4] :
( element(X4,powerset(X3))
& empty(X4) ),
inference(variable_rename,[status(thm)],[35]) ).
fof(188,plain,
! [X3] :
( element(esk6_1(X3),powerset(X3))
& empty(esk6_1(X3)) ),
inference(skolemize,[status(esa)],[187]) ).
cnf(189,plain,
empty(esk6_1(X1)),
inference(split_conjunct,[status(thm)],[188]) ).
cnf(190,plain,
element(esk6_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[188]) ).
cnf(212,plain,
empty_set = esk6_1(X1),
inference(spm,[status(thm)],[177,189,theory(equality)]) ).
cnf(221,negated_conjecture,
( empty_set = esk4_0
| ~ element(esk4_0,powerset(powerset(esk3_0))) ),
inference(spm,[status(thm)],[120,166,theory(equality)]) ).
cnf(222,negated_conjecture,
( empty_set = esk4_0
| $false ),
inference(rw,[status(thm)],[221,170,theory(equality)]) ).
cnf(223,negated_conjecture,
empty_set = esk4_0,
inference(cn,[status(thm)],[222,theory(equality)]) ).
cnf(235,plain,
( empty_set = complements_of_subsets(X1,X2)
| X2 != empty_set
| ~ element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(spm,[status(thm)],[120,67,theory(equality)]) ).
cnf(399,negated_conjecture,
( complements_of_subsets(esk3_0,empty_set) != empty_set
| esk4_0 != empty_set ),
inference(rw,[status(thm)],[169,223,theory(equality)]) ).
cnf(400,negated_conjecture,
( complements_of_subsets(esk3_0,empty_set) != empty_set
| $false ),
inference(rw,[status(thm)],[399,223,theory(equality)]) ).
cnf(401,negated_conjecture,
complements_of_subsets(esk3_0,empty_set) != empty_set,
inference(cn,[status(thm)],[400,theory(equality)]) ).
cnf(483,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[190,212,theory(equality)]) ).
cnf(583,plain,
( complements_of_subsets(X1,X2) = empty_set
| X2 != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(csr,[status(thm)],[235,142]) ).
cnf(584,negated_conjecture,
~ element(empty_set,powerset(powerset(esk3_0))),
inference(spm,[status(thm)],[401,583,theory(equality)]) ).
cnf(591,negated_conjecture,
$false,
inference(rw,[status(thm)],[584,483,theory(equality)]) ).
cnf(592,negated_conjecture,
$false,
inference(cn,[status(thm)],[591,theory(equality)]) ).
cnf(593,negated_conjecture,
$false,
592,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU326+1.p
% --creating new selector for []
% -running prover on /tmp/tmp0ZR74g/sel_SEU326+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU326+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU326+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU326+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------