TSTP Solution File: SET597+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET597+3 : TPTP v5.0.0. Released v2.2.0.
% 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 03:04:20 EST 2010
% Result : Theorem 0.24s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 63 ( 16 unt; 0 def)
% Number of atoms : 220 ( 54 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 256 ( 99 ~; 112 |; 39 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 2 sgn 38 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2,X3] :
( X1 = union(X2,X3)
<=> ( subset(X2,X1)
& subset(X3,X1)
& ! [X4] :
( ( subset(X2,X4)
& subset(X3,X4) )
=> subset(X1,X4) ) ) ),
file('/tmp/tmpMnkTUX/sel_SET597+3.p_1',prove_th56) ).
fof(3,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpMnkTUX/sel_SET597+3.p_1',equal_defn) ).
fof(6,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(union(X1,X3),X2) ),
file('/tmp/tmpMnkTUX/sel_SET597+3.p_1',union_subset) ).
fof(7,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/tmp/tmpMnkTUX/sel_SET597+3.p_1',commutativity_of_union) ).
fof(9,axiom,
! [X1,X2] : subset(X1,union(X1,X2)),
file('/tmp/tmpMnkTUX/sel_SET597+3.p_1',subset_of_union) ).
fof(10,negated_conjecture,
~ ! [X1,X2,X3] :
( X1 = union(X2,X3)
<=> ( subset(X2,X1)
& subset(X3,X1)
& ! [X4] :
( ( subset(X2,X4)
& subset(X3,X4) )
=> subset(X1,X4) ) ) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(11,negated_conjecture,
? [X1,X2,X3] :
( ( X1 != union(X2,X3)
| ~ subset(X2,X1)
| ~ subset(X3,X1)
| ? [X4] :
( subset(X2,X4)
& subset(X3,X4)
& ~ subset(X1,X4) ) )
& ( X1 = union(X2,X3)
| ( subset(X2,X1)
& subset(X3,X1)
& ! [X4] :
( ~ subset(X2,X4)
| ~ subset(X3,X4)
| subset(X1,X4) ) ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(12,negated_conjecture,
? [X5,X6,X7] :
( ( X5 != union(X6,X7)
| ~ subset(X6,X5)
| ~ subset(X7,X5)
| ? [X8] :
( subset(X6,X8)
& subset(X7,X8)
& ~ subset(X5,X8) ) )
& ( X5 = union(X6,X7)
| ( subset(X6,X5)
& subset(X7,X5)
& ! [X9] :
( ~ subset(X6,X9)
| ~ subset(X7,X9)
| subset(X5,X9) ) ) ) ),
inference(variable_rename,[status(thm)],[11]) ).
fof(13,negated_conjecture,
( ( esk1_0 != union(esk2_0,esk3_0)
| ~ subset(esk2_0,esk1_0)
| ~ subset(esk3_0,esk1_0)
| ( subset(esk2_0,esk4_0)
& subset(esk3_0,esk4_0)
& ~ subset(esk1_0,esk4_0) ) )
& ( esk1_0 = union(esk2_0,esk3_0)
| ( subset(esk2_0,esk1_0)
& subset(esk3_0,esk1_0)
& ! [X9] :
( ~ subset(esk2_0,X9)
| ~ subset(esk3_0,X9)
| subset(esk1_0,X9) ) ) ) ),
inference(skolemize,[status(esa)],[12]) ).
fof(14,negated_conjecture,
! [X9] :
( ( ( ( ~ subset(esk2_0,X9)
| ~ subset(esk3_0,X9)
| subset(esk1_0,X9) )
& subset(esk2_0,esk1_0)
& subset(esk3_0,esk1_0) )
| esk1_0 = union(esk2_0,esk3_0) )
& ( esk1_0 != union(esk2_0,esk3_0)
| ~ subset(esk2_0,esk1_0)
| ~ subset(esk3_0,esk1_0)
| ( subset(esk2_0,esk4_0)
& subset(esk3_0,esk4_0)
& ~ subset(esk1_0,esk4_0) ) ) ),
inference(shift_quantors,[status(thm)],[13]) ).
fof(15,negated_conjecture,
! [X9] :
( ( ~ subset(esk2_0,X9)
| ~ subset(esk3_0,X9)
| subset(esk1_0,X9)
| esk1_0 = union(esk2_0,esk3_0) )
& ( subset(esk2_0,esk1_0)
| esk1_0 = union(esk2_0,esk3_0) )
& ( subset(esk3_0,esk1_0)
| esk1_0 = union(esk2_0,esk3_0) )
& ( subset(esk2_0,esk4_0)
| ~ subset(esk2_0,esk1_0)
| ~ subset(esk3_0,esk1_0)
| esk1_0 != union(esk2_0,esk3_0) )
& ( subset(esk3_0,esk4_0)
| ~ subset(esk2_0,esk1_0)
| ~ subset(esk3_0,esk1_0)
| esk1_0 != union(esk2_0,esk3_0) )
& ( ~ subset(esk1_0,esk4_0)
| ~ subset(esk2_0,esk1_0)
| ~ subset(esk3_0,esk1_0)
| esk1_0 != union(esk2_0,esk3_0) ) ),
inference(distribute,[status(thm)],[14]) ).
cnf(16,negated_conjecture,
( esk1_0 != union(esk2_0,esk3_0)
| ~ subset(esk3_0,esk1_0)
| ~ subset(esk2_0,esk1_0)
| ~ subset(esk1_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(17,negated_conjecture,
( subset(esk3_0,esk4_0)
| esk1_0 != union(esk2_0,esk3_0)
| ~ subset(esk3_0,esk1_0)
| ~ subset(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(18,negated_conjecture,
( subset(esk2_0,esk4_0)
| esk1_0 != union(esk2_0,esk3_0)
| ~ subset(esk3_0,esk1_0)
| ~ subset(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(19,negated_conjecture,
( esk1_0 = union(esk2_0,esk3_0)
| subset(esk3_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(20,negated_conjecture,
( esk1_0 = union(esk2_0,esk3_0)
| subset(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(21,negated_conjecture,
( esk1_0 = union(esk2_0,esk3_0)
| subset(esk1_0,X1)
| ~ subset(esk3_0,X1)
| ~ subset(esk2_0,X1) ),
inference(split_conjunct,[status(thm)],[15]) ).
fof(30,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(31,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,plain,
! [X3,X4] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(distribute,[status(thm)],[31]) ).
cnf(33,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[32]) ).
fof(44,plain,
! [X1,X2,X3] :
( ~ subset(X1,X2)
| ~ subset(X3,X2)
| subset(union(X1,X3),X2) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(45,plain,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X6,X5)
| subset(union(X4,X6),X5) ),
inference(variable_rename,[status(thm)],[44]) ).
cnf(46,plain,
( subset(union(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[45]) ).
fof(47,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[7]) ).
cnf(48,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[47]) ).
fof(58,plain,
! [X3,X4] : subset(X3,union(X3,X4)),
inference(variable_rename,[status(thm)],[9]) ).
cnf(59,plain,
subset(X1,union(X1,X2)),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(60,negated_conjecture,
subset(esk2_0,esk1_0),
inference(spm,[status(thm)],[59,20,theory(equality)]) ).
cnf(66,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[59,48,theory(equality)]) ).
cnf(88,negated_conjecture,
( union(esk2_0,esk3_0) = esk1_0
| subset(esk1_0,union(esk3_0,X1))
| ~ subset(esk2_0,union(esk3_0,X1)) ),
inference(spm,[status(thm)],[21,59,theory(equality)]) ).
cnf(113,negated_conjecture,
( union(esk2_0,esk3_0) != esk1_0
| ~ subset(esk1_0,esk4_0)
| $false
| ~ subset(esk3_0,esk1_0) ),
inference(rw,[status(thm)],[16,60,theory(equality)]) ).
cnf(114,negated_conjecture,
( union(esk2_0,esk3_0) != esk1_0
| ~ subset(esk1_0,esk4_0)
| ~ subset(esk3_0,esk1_0) ),
inference(cn,[status(thm)],[113,theory(equality)]) ).
cnf(115,negated_conjecture,
( subset(esk3_0,esk4_0)
| union(esk2_0,esk3_0) != esk1_0
| $false
| ~ subset(esk3_0,esk1_0) ),
inference(rw,[status(thm)],[17,60,theory(equality)]) ).
cnf(116,negated_conjecture,
( subset(esk3_0,esk4_0)
| union(esk2_0,esk3_0) != esk1_0
| ~ subset(esk3_0,esk1_0) ),
inference(cn,[status(thm)],[115,theory(equality)]) ).
cnf(117,negated_conjecture,
( subset(esk2_0,esk4_0)
| union(esk2_0,esk3_0) != esk1_0
| $false
| ~ subset(esk3_0,esk1_0) ),
inference(rw,[status(thm)],[18,60,theory(equality)]) ).
cnf(118,negated_conjecture,
( subset(esk2_0,esk4_0)
| union(esk2_0,esk3_0) != esk1_0
| ~ subset(esk3_0,esk1_0) ),
inference(cn,[status(thm)],[117,theory(equality)]) ).
cnf(135,negated_conjecture,
subset(esk3_0,esk1_0),
inference(spm,[status(thm)],[66,19,theory(equality)]) ).
cnf(145,negated_conjecture,
( subset(esk2_0,esk4_0)
| union(esk2_0,esk3_0) != esk1_0
| $false ),
inference(rw,[status(thm)],[118,135,theory(equality)]) ).
cnf(146,negated_conjecture,
( subset(esk2_0,esk4_0)
| union(esk2_0,esk3_0) != esk1_0 ),
inference(cn,[status(thm)],[145,theory(equality)]) ).
cnf(147,negated_conjecture,
( subset(esk3_0,esk4_0)
| union(esk2_0,esk3_0) != esk1_0
| $false ),
inference(rw,[status(thm)],[116,135,theory(equality)]) ).
cnf(148,negated_conjecture,
( subset(esk3_0,esk4_0)
| union(esk2_0,esk3_0) != esk1_0 ),
inference(cn,[status(thm)],[147,theory(equality)]) ).
cnf(149,negated_conjecture,
( union(esk2_0,esk3_0) != esk1_0
| ~ subset(esk1_0,esk4_0)
| $false ),
inference(rw,[status(thm)],[114,135,theory(equality)]) ).
cnf(150,negated_conjecture,
( union(esk2_0,esk3_0) != esk1_0
| ~ subset(esk1_0,esk4_0) ),
inference(cn,[status(thm)],[149,theory(equality)]) ).
cnf(403,negated_conjecture,
( union(esk2_0,esk3_0) = esk1_0
| subset(esk1_0,union(esk3_0,esk2_0)) ),
inference(spm,[status(thm)],[88,66,theory(equality)]) ).
cnf(410,negated_conjecture,
( union(esk2_0,esk3_0) = esk1_0
| subset(esk1_0,union(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[403,48,theory(equality)]) ).
cnf(413,negated_conjecture,
( union(esk2_0,esk3_0) = esk1_0
| ~ subset(union(esk2_0,esk3_0),esk1_0) ),
inference(spm,[status(thm)],[33,410,theory(equality)]) ).
cnf(420,negated_conjecture,
( union(esk2_0,esk3_0) = esk1_0
| ~ subset(esk3_0,esk1_0)
| ~ subset(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[413,46,theory(equality)]) ).
cnf(423,negated_conjecture,
( union(esk2_0,esk3_0) = esk1_0
| $false
| ~ subset(esk2_0,esk1_0) ),
inference(rw,[status(thm)],[420,135,theory(equality)]) ).
cnf(424,negated_conjecture,
( union(esk2_0,esk3_0) = esk1_0
| $false
| $false ),
inference(rw,[status(thm)],[423,60,theory(equality)]) ).
cnf(425,negated_conjecture,
union(esk2_0,esk3_0) = esk1_0,
inference(cn,[status(thm)],[424,theory(equality)]) ).
cnf(434,negated_conjecture,
( subset(esk1_0,X1)
| ~ subset(esk3_0,X1)
| ~ subset(esk2_0,X1) ),
inference(spm,[status(thm)],[46,425,theory(equality)]) ).
cnf(451,negated_conjecture,
( $false
| ~ subset(esk1_0,esk4_0) ),
inference(rw,[status(thm)],[150,425,theory(equality)]) ).
cnf(452,negated_conjecture,
~ subset(esk1_0,esk4_0),
inference(cn,[status(thm)],[451,theory(equality)]) ).
cnf(453,negated_conjecture,
( subset(esk3_0,esk4_0)
| $false ),
inference(rw,[status(thm)],[148,425,theory(equality)]) ).
cnf(454,negated_conjecture,
subset(esk3_0,esk4_0),
inference(cn,[status(thm)],[453,theory(equality)]) ).
cnf(455,negated_conjecture,
( subset(esk2_0,esk4_0)
| $false ),
inference(rw,[status(thm)],[146,425,theory(equality)]) ).
cnf(456,negated_conjecture,
subset(esk2_0,esk4_0),
inference(cn,[status(thm)],[455,theory(equality)]) ).
cnf(604,negated_conjecture,
( subset(esk1_0,esk4_0)
| ~ subset(esk2_0,esk4_0) ),
inference(spm,[status(thm)],[434,454,theory(equality)]) ).
cnf(616,negated_conjecture,
( subset(esk1_0,esk4_0)
| $false ),
inference(rw,[status(thm)],[604,456,theory(equality)]) ).
cnf(617,negated_conjecture,
subset(esk1_0,esk4_0),
inference(cn,[status(thm)],[616,theory(equality)]) ).
cnf(618,negated_conjecture,
$false,
inference(sr,[status(thm)],[617,452,theory(equality)]) ).
cnf(619,negated_conjecture,
$false,
618,
[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/SET/SET597+3.p
% --creating new selector for []
% -running prover on /tmp/tmpMnkTUX/sel_SET597+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET597+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET597+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET597+3.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
%
%------------------------------------------------------------------------------