%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU156+3 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 04:54:54 EST 2010
% Result : Theorem 0.19s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 7
% Syntax : Number of formulae : 67 ( 22 unt; 0 def)
% Number of atoms : 131 ( 128 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 102 ( 38 ~; 53 |; 7 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 101 ( 9 sgn 48 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('/tmp/tmpp3tTEV/sel_SEU156+3.p_1',t9_zfmisc_1) ).
fof(2,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpp3tTEV/sel_SEU156+3.p_1',d5_tarski) ).
fof(4,conjecture,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('/tmp/tmpp3tTEV/sel_SEU156+3.p_1',t33_zfmisc_1) ).
fof(5,axiom,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
file('/tmp/tmpp3tTEV/sel_SEU156+3.p_1',t10_zfmisc_1) ).
fof(6,axiom,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/tmp/tmpp3tTEV/sel_SEU156+3.p_1',t8_zfmisc_1) ).
fof(8,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpp3tTEV/sel_SEU156+3.p_1',commutativity_k2_tarski) ).
fof(10,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/tmp/tmpp3tTEV/sel_SEU156+3.p_1',t69_enumset1) ).
fof(13,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(16,plain,
! [X1,X2,X3] :
( singleton(X1) != unordered_pair(X2,X3)
| X2 = X3 ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(17,plain,
! [X4,X5,X6] :
( singleton(X4) != unordered_pair(X5,X6)
| X5 = X6 ),
inference(variable_rename,[status(thm)],[16]) ).
cnf(18,plain,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(19,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[2]) ).
cnf(20,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[19]) ).
fof(24,negated_conjecture,
? [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
& ( X1 != X3
| X2 != X4 ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(25,negated_conjecture,
? [X5,X6,X7,X8] :
( ordered_pair(X5,X6) = ordered_pair(X7,X8)
& ( X5 != X7
| X6 != X8 ) ),
inference(variable_rename,[status(thm)],[24]) ).
fof(26,negated_conjecture,
( ordered_pair(esk2_0,esk3_0) = ordered_pair(esk4_0,esk5_0)
& ( esk2_0 != esk4_0
| esk3_0 != esk5_0 ) ),
inference(skolemize,[status(esa)],[25]) ).
cnf(27,negated_conjecture,
( esk3_0 != esk5_0
| esk2_0 != esk4_0 ),
inference(split_conjunct,[status(thm)],[26]) ).
cnf(28,negated_conjecture,
ordered_pair(esk2_0,esk3_0) = ordered_pair(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[26]) ).
fof(29,plain,
! [X1,X2,X3,X4] :
( unordered_pair(X1,X2) != unordered_pair(X3,X4)
| X1 = X3
| X1 = X4 ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(30,plain,
! [X5,X6,X7,X8] :
( unordered_pair(X5,X6) != unordered_pair(X7,X8)
| X5 = X7
| X5 = X8 ),
inference(variable_rename,[status(thm)],[29]) ).
cnf(31,plain,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(32,plain,
! [X1,X2,X3] :
( singleton(X1) != unordered_pair(X2,X3)
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(33,plain,
! [X4,X5,X6] :
( singleton(X4) != unordered_pair(X5,X6)
| X4 = X5 ),
inference(variable_rename,[status(thm)],[32]) ).
cnf(34,plain,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(37,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[8]) ).
cnf(38,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[37]) ).
fof(42,plain,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[10]) ).
cnf(43,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[42]) ).
cnf(49,plain,
unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[20,43,theory(equality)]),
[unfolding] ).
cnf(50,plain,
( X1 = X2
| unordered_pair(X2,X3) != unordered_pair(X1,X1) ),
inference(rw,[status(thm)],[34,43,theory(equality)]),
[unfolding] ).
cnf(51,plain,
( X1 = X2
| unordered_pair(X1,X2) != unordered_pair(X3,X3) ),
inference(rw,[status(thm)],[18,43,theory(equality)]),
[unfolding] ).
cnf(53,negated_conjecture,
unordered_pair(unordered_pair(esk4_0,esk5_0),unordered_pair(esk4_0,esk4_0)) = unordered_pair(unordered_pair(esk2_0,esk3_0),unordered_pair(esk2_0,esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[28,49,theory(equality)]),49,theory(equality)]),
[unfolding] ).
cnf(62,plain,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X3,X2) ),
inference(spm,[status(thm)],[50,38,theory(equality)]) ).
cnf(72,plain,
( X1 = X2
| X1 = X3
| unordered_pair(X4,X1) != unordered_pair(X3,X2) ),
inference(spm,[status(thm)],[31,38,theory(equality)]) ).
cnf(76,negated_conjecture,
unordered_pair(unordered_pair(esk4_0,esk4_0),unordered_pair(esk4_0,esk5_0)) = unordered_pair(unordered_pair(esk2_0,esk3_0),unordered_pair(esk2_0,esk2_0)),
inference(rw,[status(thm)],[53,38,theory(equality)]) ).
cnf(77,negated_conjecture,
unordered_pair(unordered_pair(esk4_0,esk4_0),unordered_pair(esk4_0,esk5_0)) = unordered_pair(unordered_pair(esk2_0,esk2_0),unordered_pair(esk2_0,esk3_0)),
inference(rw,[status(thm)],[76,38,theory(equality)]) ).
cnf(84,negated_conjecture,
( X1 = unordered_pair(esk2_0,esk3_0)
| X1 = unordered_pair(esk2_0,esk2_0)
| unordered_pair(X1,X2) != unordered_pair(unordered_pair(esk4_0,esk4_0),unordered_pair(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[31,77,theory(equality)]) ).
cnf(122,negated_conjecture,
( unordered_pair(esk2_0,esk3_0) = X1
| unordered_pair(esk2_0,esk3_0) = X2
| unordered_pair(unordered_pair(esk4_0,esk4_0),unordered_pair(esk4_0,esk5_0)) != unordered_pair(X1,X2) ),
inference(spm,[status(thm)],[72,77,theory(equality)]) ).
cnf(123,negated_conjecture,
( X1 = unordered_pair(esk2_0,esk2_0)
| X1 = unordered_pair(esk2_0,esk3_0)
| unordered_pair(X2,X1) != unordered_pair(unordered_pair(esk4_0,esk4_0),unordered_pair(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[72,77,theory(equality)]) ).
cnf(208,negated_conjecture,
( unordered_pair(esk4_0,esk4_0) = unordered_pair(esk2_0,esk2_0)
| unordered_pair(esk4_0,esk4_0) = unordered_pair(esk2_0,esk3_0) ),
inference(er,[status(thm)],[84,theory(equality)]) ).
cnf(218,negated_conjecture,
( esk2_0 = esk3_0
| unordered_pair(esk2_0,esk2_0) = unordered_pair(esk4_0,esk4_0)
| unordered_pair(esk4_0,esk4_0) != unordered_pair(X1,X1) ),
inference(spm,[status(thm)],[51,208,theory(equality)]) ).
cnf(266,negated_conjecture,
( unordered_pair(esk2_0,esk3_0) = unordered_pair(esk4_0,esk5_0)
| unordered_pair(esk2_0,esk3_0) = unordered_pair(esk4_0,esk4_0) ),
inference(er,[status(thm)],[122,theory(equality)]) ).
cnf(317,negated_conjecture,
( unordered_pair(esk4_0,esk5_0) = unordered_pair(esk2_0,esk3_0)
| unordered_pair(esk4_0,esk5_0) = unordered_pair(esk2_0,esk2_0) ),
inference(er,[status(thm)],[123,theory(equality)]) ).
cnf(388,negated_conjecture,
( unordered_pair(esk2_0,esk2_0) = unordered_pair(esk4_0,esk4_0)
| esk3_0 = esk2_0 ),
inference(er,[status(thm)],[218,theory(equality)]) ).
cnf(408,negated_conjecture,
( esk2_0 = X1
| esk3_0 = esk2_0
| unordered_pair(esk4_0,esk4_0) != unordered_pair(X1,X2) ),
inference(spm,[status(thm)],[50,388,theory(equality)]) ).
cnf(441,negated_conjecture,
( esk3_0 = esk2_0
| esk2_0 = esk4_0 ),
inference(er,[status(thm)],[408,theory(equality)]) ).
cnf(454,negated_conjecture,
( unordered_pair(esk2_0,esk2_0) = unordered_pair(esk4_0,esk5_0)
| esk2_0 = esk4_0 ),
inference(spm,[status(thm)],[317,441,theory(equality)]) ).
cnf(458,negated_conjecture,
esk2_0 = esk4_0,
inference(csr,[status(thm)],[454,50]) ).
cnf(479,negated_conjecture,
( unordered_pair(esk4_0,esk4_0) = unordered_pair(esk4_0,esk5_0)
| unordered_pair(esk2_0,esk3_0) = unordered_pair(esk4_0,esk5_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[317,458,theory(equality)]),458,theory(equality)]) ).
cnf(480,negated_conjecture,
( unordered_pair(esk4_0,esk4_0) = unordered_pair(esk4_0,esk5_0)
| unordered_pair(esk4_0,esk3_0) = unordered_pair(esk4_0,esk5_0) ),
inference(rw,[status(thm)],[479,458,theory(equality)]) ).
cnf(486,negated_conjecture,
( unordered_pair(esk4_0,esk3_0) = unordered_pair(esk4_0,esk4_0)
| unordered_pair(esk2_0,esk3_0) = unordered_pair(esk4_0,esk5_0) ),
inference(rw,[status(thm)],[266,458,theory(equality)]) ).
cnf(487,negated_conjecture,
( unordered_pair(esk4_0,esk3_0) = unordered_pair(esk4_0,esk4_0)
| unordered_pair(esk4_0,esk3_0) = unordered_pair(esk4_0,esk5_0) ),
inference(rw,[status(thm)],[486,458,theory(equality)]) ).
cnf(511,negated_conjecture,
( $false
| esk3_0 != esk5_0 ),
inference(rw,[status(thm)],[27,458,theory(equality)]) ).
cnf(512,negated_conjecture,
esk3_0 != esk5_0,
inference(cn,[status(thm)],[511,theory(equality)]) ).
cnf(522,negated_conjecture,
( esk3_0 = X1
| esk3_0 = X2
| unordered_pair(esk4_0,esk5_0) = unordered_pair(esk4_0,esk4_0)
| unordered_pair(esk4_0,esk5_0) != unordered_pair(X1,X2) ),
inference(spm,[status(thm)],[72,480,theory(equality)]) ).
cnf(544,negated_conjecture,
( esk4_0 = esk3_0
| unordered_pair(esk4_0,esk3_0) = unordered_pair(esk4_0,esk4_0)
| unordered_pair(esk4_0,esk5_0) != unordered_pair(X1,X1) ),
inference(spm,[status(thm)],[51,487,theory(equality)]) ).
cnf(605,negated_conjecture,
( esk3_0 = esk4_0
| unordered_pair(esk4_0,esk5_0) != unordered_pair(X1,X1) ),
inference(csr,[status(thm)],[544,62]) ).
cnf(626,negated_conjecture,
( unordered_pair(esk4_0,esk5_0) = unordered_pair(esk4_0,esk4_0)
| esk3_0 = esk5_0
| esk3_0 = esk4_0 ),
inference(er,[status(thm)],[522,theory(equality)]) ).
cnf(630,negated_conjecture,
( unordered_pair(esk4_0,esk5_0) = unordered_pair(esk4_0,esk4_0)
| esk3_0 = esk4_0 ),
inference(sr,[status(thm)],[626,512,theory(equality)]) ).
cnf(631,negated_conjecture,
esk3_0 = esk4_0,
inference(csr,[status(thm)],[630,605]) ).
cnf(634,negated_conjecture,
esk4_0 != esk5_0,
inference(rw,[status(thm)],[512,631,theory(equality)]) ).
cnf(658,negated_conjecture,
( unordered_pair(esk4_0,esk4_0) = unordered_pair(esk4_0,esk5_0)
| unordered_pair(esk4_0,esk5_0) = unordered_pair(esk4_0,esk4_0) ),
inference(rw,[status(thm)],[480,631,theory(equality)]) ).
cnf(659,negated_conjecture,
unordered_pair(esk4_0,esk5_0) = unordered_pair(esk4_0,esk4_0),
inference(cn,[status(thm)],[658,theory(equality)]) ).
cnf(665,negated_conjecture,
( esk4_0 = esk5_0
| unordered_pair(esk4_0,esk4_0) != unordered_pair(X1,X1) ),
inference(spm,[status(thm)],[51,659,theory(equality)]) ).
cnf(673,negated_conjecture,
unordered_pair(esk4_0,esk4_0) != unordered_pair(X1,X1),
inference(sr,[status(thm)],[665,634,theory(equality)]) ).
cnf(676,negated_conjecture,
$false,
inference(er,[status(thm)],[673,theory(equality)]) ).
cnf(681,negated_conjecture,
$false,
676,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU156+3.p
% --creating new selector for []
% -running prover on /tmp/tmpp3tTEV/sel_SEU156+3.p_1 with time limit 29
% -prover status Theorem
% Problem SEU156+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU156+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU156+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
%
%------------------------------------------------------------------------------