TSTP Solution File: SET985+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET985+1 : TPTP v5.0.0. Released v3.2.0.
% 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 04:03:12 EST 2010
% Result : Theorem 0.21s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 11 unt; 0 def)
% Number of atoms : 105 ( 46 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 98 ( 30 ~; 44 |; 16 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 57 ( 3 sgn 38 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1] :
( ~ empty(X1)
=> ! [X2,X3,X4] :
( ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| subset(cartesian_product2(X2,X1),cartesian_product2(X4,X3)) )
=> subset(X2,X4) ) ),
file('/tmp/tmpbsxeWs/sel_SET985+1.p_1',t139_zfmisc_1) ).
fof(3,axiom,
empty(empty_set),
file('/tmp/tmpbsxeWs/sel_SET985+1.p_1',fc1_xboole_0) ).
fof(4,axiom,
! [X1,X2,X3,X4] :
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
=> ( cartesian_product2(X1,X2) = empty_set
| ( subset(X1,X3)
& subset(X2,X4) ) ) ),
file('/tmp/tmpbsxeWs/sel_SET985+1.p_1',t138_zfmisc_1) ).
fof(6,axiom,
! [X1] : subset(empty_set,X1),
file('/tmp/tmpbsxeWs/sel_SET985+1.p_1',t2_xboole_1) ).
fof(7,axiom,
! [X1,X2] :
( cartesian_product2(X1,X2) = empty_set
<=> ( X1 = empty_set
| X2 = empty_set ) ),
file('/tmp/tmpbsxeWs/sel_SET985+1.p_1',t113_zfmisc_1) ).
fof(9,negated_conjecture,
~ ! [X1] :
( ~ empty(X1)
=> ! [X2,X3,X4] :
( ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| subset(cartesian_product2(X2,X1),cartesian_product2(X4,X3)) )
=> subset(X2,X4) ) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(10,negated_conjecture,
~ ! [X1] :
( ~ empty(X1)
=> ! [X2,X3,X4] :
( ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| subset(cartesian_product2(X2,X1),cartesian_product2(X4,X3)) )
=> subset(X2,X4) ) ),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(12,negated_conjecture,
? [X1] :
( ~ empty(X1)
& ? [X2,X3,X4] :
( ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| subset(cartesian_product2(X2,X1),cartesian_product2(X4,X3)) )
& ~ subset(X2,X4) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(13,negated_conjecture,
? [X5] :
( ~ empty(X5)
& ? [X6,X7,X8] :
( ( subset(cartesian_product2(X5,X6),cartesian_product2(X7,X8))
| subset(cartesian_product2(X6,X5),cartesian_product2(X8,X7)) )
& ~ subset(X6,X8) ) ),
inference(variable_rename,[status(thm)],[12]) ).
fof(14,negated_conjecture,
( ~ empty(esk1_0)
& ( subset(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0))
| subset(cartesian_product2(esk2_0,esk1_0),cartesian_product2(esk4_0,esk3_0)) )
& ~ subset(esk2_0,esk4_0) ),
inference(skolemize,[status(esa)],[13]) ).
cnf(15,negated_conjecture,
~ subset(esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(16,negated_conjecture,
( subset(cartesian_product2(esk2_0,esk1_0),cartesian_product2(esk4_0,esk3_0))
| subset(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(17,negated_conjecture,
~ empty(esk1_0),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(21,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[3]) ).
fof(22,plain,
! [X1,X2,X3,X4] :
( ~ subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| cartesian_product2(X1,X2) = empty_set
| ( subset(X1,X3)
& subset(X2,X4) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(23,plain,
! [X5,X6,X7,X8] :
( ~ subset(cartesian_product2(X5,X6),cartesian_product2(X7,X8))
| cartesian_product2(X5,X6) = empty_set
| ( subset(X5,X7)
& subset(X6,X8) ) ),
inference(variable_rename,[status(thm)],[22]) ).
fof(24,plain,
! [X5,X6,X7,X8] :
( ( subset(X5,X7)
| cartesian_product2(X5,X6) = empty_set
| ~ subset(cartesian_product2(X5,X6),cartesian_product2(X7,X8)) )
& ( subset(X6,X8)
| cartesian_product2(X5,X6) = empty_set
| ~ subset(cartesian_product2(X5,X6),cartesian_product2(X7,X8)) ) ),
inference(distribute,[status(thm)],[23]) ).
cnf(25,plain,
( cartesian_product2(X1,X2) = empty_set
| subset(X2,X4)
| ~ subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[24]) ).
cnf(26,plain,
( cartesian_product2(X1,X2) = empty_set
| subset(X1,X3)
| ~ subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(30,plain,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[6]) ).
cnf(31,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[30]) ).
fof(32,plain,
! [X1,X2] :
( ( cartesian_product2(X1,X2) != empty_set
| X1 = empty_set
| X2 = empty_set )
& ( ( X1 != empty_set
& X2 != empty_set )
| cartesian_product2(X1,X2) = empty_set ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(33,plain,
! [X3,X4] :
( ( cartesian_product2(X3,X4) != empty_set
| X3 = empty_set
| X4 = empty_set )
& ( ( X3 != empty_set
& X4 != empty_set )
| cartesian_product2(X3,X4) = empty_set ) ),
inference(variable_rename,[status(thm)],[32]) ).
fof(34,plain,
! [X3,X4] :
( ( cartesian_product2(X3,X4) != empty_set
| X3 = empty_set
| X4 = empty_set )
& ( X3 != empty_set
| cartesian_product2(X3,X4) = empty_set )
& ( X4 != empty_set
| cartesian_product2(X3,X4) = empty_set ) ),
inference(distribute,[status(thm)],[33]) ).
cnf(37,plain,
( X1 = empty_set
| X2 = empty_set
| cartesian_product2(X2,X1) != empty_set ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(56,negated_conjecture,
( cartesian_product2(esk2_0,esk1_0) = empty_set
| subset(esk2_0,esk4_0)
| subset(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[26,16,theory(equality)]) ).
cnf(58,negated_conjecture,
( cartesian_product2(esk2_0,esk1_0) = empty_set
| subset(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) ),
inference(sr,[status(thm)],[56,15,theory(equality)]) ).
cnf(63,negated_conjecture,
( cartesian_product2(esk1_0,esk2_0) = empty_set
| subset(esk2_0,esk4_0)
| cartesian_product2(esk2_0,esk1_0) = empty_set ),
inference(spm,[status(thm)],[25,58,theory(equality)]) ).
cnf(67,negated_conjecture,
( cartesian_product2(esk1_0,esk2_0) = empty_set
| cartesian_product2(esk2_0,esk1_0) = empty_set ),
inference(sr,[status(thm)],[63,15,theory(equality)]) ).
cnf(68,negated_conjecture,
( empty_set = esk1_0
| empty_set = esk2_0
| cartesian_product2(esk1_0,esk2_0) = empty_set ),
inference(spm,[status(thm)],[37,67,theory(equality)]) ).
cnf(73,negated_conjecture,
( esk1_0 = empty_set
| esk2_0 = empty_set ),
inference(csr,[status(thm)],[68,37]) ).
cnf(74,negated_conjecture,
( esk1_0 = empty_set
| ~ subset(empty_set,esk4_0) ),
inference(spm,[status(thm)],[15,73,theory(equality)]) ).
cnf(78,negated_conjecture,
( esk1_0 = empty_set
| $false ),
inference(rw,[status(thm)],[74,31,theory(equality)]) ).
cnf(79,negated_conjecture,
esk1_0 = empty_set,
inference(cn,[status(thm)],[78,theory(equality)]) ).
cnf(80,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[17,79,theory(equality)]),21,theory(equality)]) ).
cnf(81,negated_conjecture,
$false,
inference(cn,[status(thm)],[80,theory(equality)]) ).
cnf(82,negated_conjecture,
$false,
81,
[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/SET985+1.p
% --creating new selector for []
% -running prover on /tmp/tmpbsxeWs/sel_SET985+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET985+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET985+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET985+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
%
%------------------------------------------------------------------------------