%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU156+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 04:54:38 EST 2010
% Result : Theorem 0.28s
% Output : CNFRefutation 0.28s
% 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(2,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmp6-9r-r/sel_SEU156+1.p_1',d5_tarski) ).
fof(4,axiom,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('/tmp/tmp6-9r-r/sel_SEU156+1.p_1',t9_zfmisc_1) ).
fof(6,conjecture,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('/tmp/tmp6-9r-r/sel_SEU156+1.p_1',t33_zfmisc_1) ).
fof(7,axiom,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
file('/tmp/tmp6-9r-r/sel_SEU156+1.p_1',t10_zfmisc_1) ).
fof(8,axiom,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/tmp/tmp6-9r-r/sel_SEU156+1.p_1',t8_zfmisc_1) ).
fof(10,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmp6-9r-r/sel_SEU156+1.p_1',commutativity_k2_tarski) ).
fof(13,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/tmp/tmp6-9r-r/sel_SEU156+1.p_1',t69_enumset1) ).
fof(16,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(20,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[2]) ).
cnf(21,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[20]) ).
fof(23,plain,
! [X1,X2,X3] :
( singleton(X1) != unordered_pair(X2,X3)
| X2 = X3 ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(24,plain,
! [X4,X5,X6] :
( singleton(X4) != unordered_pair(X5,X6)
| X5 = X6 ),
inference(variable_rename,[status(thm)],[23]) ).
cnf(25,plain,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(29,negated_conjecture,
? [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
& ( X1 != X3
| X2 != X4 ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(30,negated_conjecture,
? [X5,X6,X7,X8] :
( ordered_pair(X5,X6) = ordered_pair(X7,X8)
& ( X5 != X7
| X6 != X8 ) ),
inference(variable_rename,[status(thm)],[29]) ).
fof(31,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)],[30]) ).
cnf(32,negated_conjecture,
( esk3_0 != esk5_0
| esk2_0 != esk4_0 ),
inference(split_conjunct,[status(thm)],[31]) ).
cnf(33,negated_conjecture,
ordered_pair(esk2_0,esk3_0) = ordered_pair(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[31]) ).
fof(34,plain,
! [X1,X2,X3,X4] :
( unordered_pair(X1,X2) != unordered_pair(X3,X4)
| X1 = X3
| X1 = X4 ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(35,plain,
! [X5,X6,X7,X8] :
( unordered_pair(X5,X6) != unordered_pair(X7,X8)
| X5 = X7
| X5 = X8 ),
inference(variable_rename,[status(thm)],[34]) ).
cnf(36,plain,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X1,X2,X3] :
( singleton(X1) != unordered_pair(X2,X3)
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(38,plain,
! [X4,X5,X6] :
( singleton(X4) != unordered_pair(X5,X6)
| X4 = X5 ),
inference(variable_rename,[status(thm)],[37]) ).
cnf(39,plain,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[38]) ).
fof(42,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[10]) ).
cnf(43,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[42]) ).
fof(50,plain,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[13]) ).
cnf(51,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[50]) ).
cnf(55,plain,
unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[21,51,theory(equality)]),
[unfolding] ).
cnf(56,plain,
( X1 = X2
| unordered_pair(X2,X3) != unordered_pair(X1,X1) ),
inference(rw,[status(thm)],[39,51,theory(equality)]),
[unfolding] ).
cnf(57,plain,
( X1 = X2
| unordered_pair(X1,X2) != unordered_pair(X3,X3) ),
inference(rw,[status(thm)],[25,51,theory(equality)]),
[unfolding] ).
cnf(59,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)],[33,55,theory(equality)]),55,theory(equality)]),
[unfolding] ).
cnf(68,plain,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X3,X2) ),
inference(spm,[status(thm)],[56,43,theory(equality)]) ).
cnf(78,plain,
( X1 = X2
| X1 = X3
| unordered_pair(X4,X1) != unordered_pair(X3,X2) ),
inference(spm,[status(thm)],[36,43,theory(equality)]) ).
cnf(82,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)],[59,43,theory(equality)]) ).
cnf(83,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)],[82,43,theory(equality)]) ).
cnf(90,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)],[36,83,theory(equality)]) ).
cnf(128,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)],[78,83,theory(equality)]) ).
cnf(129,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)],[78,83,theory(equality)]) ).
cnf(214,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)],[90,theory(equality)]) ).
cnf(224,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)],[57,214,theory(equality)]) ).
cnf(272,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)],[128,theory(equality)]) ).
cnf(323,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)],[129,theory(equality)]) ).
cnf(394,negated_conjecture,
( unordered_pair(esk2_0,esk2_0) = unordered_pair(esk4_0,esk4_0)
| esk3_0 = esk2_0 ),
inference(er,[status(thm)],[224,theory(equality)]) ).
cnf(414,negated_conjecture,
( esk2_0 = X1
| esk3_0 = esk2_0
| unordered_pair(esk4_0,esk4_0) != unordered_pair(X1,X2) ),
inference(spm,[status(thm)],[56,394,theory(equality)]) ).
cnf(447,negated_conjecture,
( esk3_0 = esk2_0
| esk2_0 = esk4_0 ),
inference(er,[status(thm)],[414,theory(equality)]) ).
cnf(460,negated_conjecture,
( unordered_pair(esk2_0,esk2_0) = unordered_pair(esk4_0,esk5_0)
| esk2_0 = esk4_0 ),
inference(spm,[status(thm)],[323,447,theory(equality)]) ).
cnf(464,negated_conjecture,
esk2_0 = esk4_0,
inference(csr,[status(thm)],[460,56]) ).
cnf(485,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)],[323,464,theory(equality)]),464,theory(equality)]) ).
cnf(486,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)],[485,464,theory(equality)]) ).
cnf(492,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)],[272,464,theory(equality)]) ).
cnf(493,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)],[492,464,theory(equality)]) ).
cnf(517,negated_conjecture,
( $false
| esk3_0 != esk5_0 ),
inference(rw,[status(thm)],[32,464,theory(equality)]) ).
cnf(518,negated_conjecture,
esk3_0 != esk5_0,
inference(cn,[status(thm)],[517,theory(equality)]) ).
cnf(528,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)],[78,486,theory(equality)]) ).
cnf(550,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)],[57,493,theory(equality)]) ).
cnf(611,negated_conjecture,
( esk3_0 = esk4_0
| unordered_pair(esk4_0,esk5_0) != unordered_pair(X1,X1) ),
inference(csr,[status(thm)],[550,68]) ).
cnf(632,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)],[528,theory(equality)]) ).
cnf(636,negated_conjecture,
( unordered_pair(esk4_0,esk5_0) = unordered_pair(esk4_0,esk4_0)
| esk3_0 = esk4_0 ),
inference(sr,[status(thm)],[632,518,theory(equality)]) ).
cnf(637,negated_conjecture,
esk3_0 = esk4_0,
inference(csr,[status(thm)],[636,611]) ).
cnf(640,negated_conjecture,
esk4_0 != esk5_0,
inference(rw,[status(thm)],[518,637,theory(equality)]) ).
cnf(664,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)],[486,637,theory(equality)]) ).
cnf(665,negated_conjecture,
unordered_pair(esk4_0,esk5_0) = unordered_pair(esk4_0,esk4_0),
inference(cn,[status(thm)],[664,theory(equality)]) ).
cnf(671,negated_conjecture,
( esk4_0 = esk5_0
| unordered_pair(esk4_0,esk4_0) != unordered_pair(X1,X1) ),
inference(spm,[status(thm)],[57,665,theory(equality)]) ).
cnf(679,negated_conjecture,
unordered_pair(esk4_0,esk4_0) != unordered_pair(X1,X1),
inference(sr,[status(thm)],[671,640,theory(equality)]) ).
cnf(682,negated_conjecture,
$false,
inference(er,[status(thm)],[679,theory(equality)]) ).
cnf(687,negated_conjecture,
$false,
682,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU156+1.p
% --creating new selector for []
% -running prover on /tmp/tmp6-9r-r/sel_SEU156+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU156+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU156+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU156+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
%
%------------------------------------------------------------------------------