TSTP Solution File: SET893+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET893+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 03:44:32 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 59 ( 10 unt; 0 def)
% Number of atoms : 204 ( 104 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 242 ( 97 ~; 108 |; 32 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 110 ( 10 sgn 50 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/tmp/tmpgUAiqE/sel_SET893+1.p_1',l55_zfmisc_1) ).
fof(2,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpgUAiqE/sel_SET893+1.p_1',d5_tarski) ).
fof(5,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpgUAiqE/sel_SET893+1.p_1',commutativity_k2_tarski) ).
fof(6,conjecture,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),singleton(X4)))
<=> ( X1 = X3
& X2 = X4 ) ),
file('/tmp/tmpgUAiqE/sel_SET893+1.p_1',t34_zfmisc_1) ).
fof(7,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpgUAiqE/sel_SET893+1.p_1',d1_tarski) ).
fof(10,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),singleton(X4)))
<=> ( X1 = X3
& X2 = X4 ) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(14,plain,
! [X1,X2,X3,X4] :
( ( ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ( in(X1,X3)
& in(X2,X4) ) )
& ( ~ in(X1,X3)
| ~ in(X2,X4)
| in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(15,plain,
! [X5,X6,X7,X8] :
( ( ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8))
| ( in(X5,X7)
& in(X6,X8) ) )
& ( ~ in(X5,X7)
| ~ in(X6,X8)
| in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) ) ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,plain,
! [X5,X6,X7,X8] :
( ( in(X5,X7)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( in(X6,X8)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( ~ in(X5,X7)
| ~ in(X6,X8)
| in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) ) ),
inference(distribute,[status(thm)],[15]) ).
cnf(17,plain,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(18,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(19,plain,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[16]) ).
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(27,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(28,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,negated_conjecture,
? [X1,X2,X3,X4] :
( ( ~ in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),singleton(X4)))
| X1 != X3
| X2 != X4 )
& ( in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),singleton(X4)))
| ( X1 = X3
& X2 = X4 ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(30,negated_conjecture,
? [X5,X6,X7,X8] :
( ( ~ in(ordered_pair(X5,X6),cartesian_product2(singleton(X7),singleton(X8)))
| X5 != X7
| X6 != X8 )
& ( in(ordered_pair(X5,X6),cartesian_product2(singleton(X7),singleton(X8)))
| ( X5 = X7
& X6 = X8 ) ) ),
inference(variable_rename,[status(thm)],[29]) ).
fof(31,negated_conjecture,
( ( ~ in(ordered_pair(esk2_0,esk3_0),cartesian_product2(singleton(esk4_0),singleton(esk5_0)))
| esk2_0 != esk4_0
| esk3_0 != esk5_0 )
& ( in(ordered_pair(esk2_0,esk3_0),cartesian_product2(singleton(esk4_0),singleton(esk5_0)))
| ( esk2_0 = esk4_0
& esk3_0 = esk5_0 ) ) ),
inference(skolemize,[status(esa)],[30]) ).
fof(32,negated_conjecture,
( ( ~ in(ordered_pair(esk2_0,esk3_0),cartesian_product2(singleton(esk4_0),singleton(esk5_0)))
| esk2_0 != esk4_0
| esk3_0 != esk5_0 )
& ( esk2_0 = esk4_0
| in(ordered_pair(esk2_0,esk3_0),cartesian_product2(singleton(esk4_0),singleton(esk5_0))) )
& ( esk3_0 = esk5_0
| in(ordered_pair(esk2_0,esk3_0),cartesian_product2(singleton(esk4_0),singleton(esk5_0))) ) ),
inference(distribute,[status(thm)],[31]) ).
cnf(33,negated_conjecture,
( in(ordered_pair(esk2_0,esk3_0),cartesian_product2(singleton(esk4_0),singleton(esk5_0)))
| esk3_0 = esk5_0 ),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(34,negated_conjecture,
( in(ordered_pair(esk2_0,esk3_0),cartesian_product2(singleton(esk4_0),singleton(esk5_0)))
| esk2_0 = esk4_0 ),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(35,negated_conjecture,
( esk3_0 != esk5_0
| esk2_0 != esk4_0
| ~ in(ordered_pair(esk2_0,esk3_0),cartesian_product2(singleton(esk4_0),singleton(esk5_0))) ),
inference(split_conjunct,[status(thm)],[32]) ).
fof(36,plain,
! [X1,X2] :
( ( X2 != singleton(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1 )
& ( X3 != X1
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| X3 != X1 )
& ( in(X3,X2)
| X3 = X1 ) )
| X2 = singleton(X1) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(37,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| X7 != X4 )
& ( in(X7,X5)
| X7 = X4 ) )
| X5 = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[36]) ).
fof(38,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk6_2(X4,X5),X5)
| esk6_2(X4,X5) != X4 )
& ( in(esk6_2(X4,X5),X5)
| esk6_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[37]) ).
fof(39,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk6_2(X4,X5),X5)
| esk6_2(X4,X5) != X4 )
& ( in(esk6_2(X4,X5),X5)
| esk6_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[38]) ).
fof(40,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk6_2(X4,X5),X5)
| esk6_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk6_2(X4,X5),X5)
| esk6_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[39]) ).
cnf(43,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(44,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(51,negated_conjecture,
( esk4_0 = esk2_0
| in(unordered_pair(unordered_pair(esk2_0,esk3_0),singleton(esk2_0)),cartesian_product2(singleton(esk4_0),singleton(esk5_0))) ),
inference(rw,[status(thm)],[34,21,theory(equality)]),
[unfolding] ).
cnf(52,negated_conjecture,
( esk5_0 = esk3_0
| in(unordered_pair(unordered_pair(esk2_0,esk3_0),singleton(esk2_0)),cartesian_product2(singleton(esk4_0),singleton(esk5_0))) ),
inference(rw,[status(thm)],[33,21,theory(equality)]),
[unfolding] ).
cnf(53,plain,
( in(X2,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[18,21,theory(equality)]),
[unfolding] ).
cnf(54,plain,
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[19,21,theory(equality)]),
[unfolding] ).
cnf(55,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[17,21,theory(equality)]),
[unfolding] ).
cnf(57,negated_conjecture,
( esk4_0 != esk2_0
| esk5_0 != esk3_0
| ~ in(unordered_pair(unordered_pair(esk2_0,esk3_0),singleton(esk2_0)),cartesian_product2(singleton(esk4_0),singleton(esk5_0))) ),
inference(rw,[status(thm)],[35,21,theory(equality)]),
[unfolding] ).
cnf(58,plain,
( in(X1,X2)
| singleton(X1) != X2 ),
inference(er,[status(thm)],[43,theory(equality)]) ).
cnf(59,negated_conjecture,
( esk4_0 = esk2_0
| in(unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0)),cartesian_product2(singleton(esk4_0),singleton(esk5_0))) ),
inference(rw,[status(thm)],[51,28,theory(equality)]) ).
cnf(67,negated_conjecture,
( esk5_0 = esk3_0
| in(unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0)),cartesian_product2(singleton(esk4_0),singleton(esk5_0))) ),
inference(rw,[status(thm)],[52,28,theory(equality)]) ).
cnf(70,negated_conjecture,
( esk4_0 != esk2_0
| esk5_0 != esk3_0
| ~ in(unordered_pair(singleton(esk2_0),unordered_pair(esk2_0,esk3_0)),cartesian_product2(singleton(esk4_0),singleton(esk5_0))) ),
inference(rw,[status(thm)],[57,28,theory(equality)]) ).
cnf(73,plain,
( in(X2,X4)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[53,28,theory(equality)]) ).
cnf(77,negated_conjecture,
( in(esk3_0,singleton(esk5_0))
| esk5_0 = esk3_0 ),
inference(spm,[status(thm)],[73,67,theory(equality)]) ).
cnf(78,plain,
( in(X1,X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[54,28,theory(equality)]) ).
cnf(81,negated_conjecture,
( in(esk2_0,singleton(esk4_0))
| esk4_0 = esk2_0 ),
inference(spm,[status(thm)],[78,59,theory(equality)]) ).
cnf(84,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[55,28,theory(equality)]) ).
cnf(89,negated_conjecture,
( esk4_0 != esk2_0
| esk5_0 != esk3_0
| ~ in(esk3_0,singleton(esk5_0))
| ~ in(esk2_0,singleton(esk4_0)) ),
inference(spm,[status(thm)],[70,84,theory(equality)]) ).
cnf(109,negated_conjecture,
( X1 = esk3_0
| esk5_0 = esk3_0
| singleton(X1) != singleton(esk5_0) ),
inference(spm,[status(thm)],[44,77,theory(equality)]) ).
cnf(112,negated_conjecture,
( X1 = esk2_0
| esk4_0 = esk2_0
| singleton(X1) != singleton(esk4_0) ),
inference(spm,[status(thm)],[44,81,theory(equality)]) ).
cnf(124,negated_conjecture,
( esk4_0 != esk2_0
| esk5_0 != esk3_0
| ~ in(esk2_0,singleton(esk4_0))
| singleton(esk3_0) != singleton(esk5_0) ),
inference(spm,[status(thm)],[89,58,theory(equality)]) ).
cnf(126,negated_conjecture,
( singleton(esk5_0) != singleton(esk3_0)
| esk4_0 != esk2_0
| esk5_0 != esk3_0
| singleton(esk2_0) != singleton(esk4_0) ),
inference(spm,[status(thm)],[124,58,theory(equality)]) ).
cnf(148,negated_conjecture,
esk5_0 = esk3_0,
inference(er,[status(thm)],[109,theory(equality)]) ).
cnf(156,negated_conjecture,
( $false
| singleton(esk4_0) != singleton(esk2_0)
| esk4_0 != esk2_0
| esk5_0 != esk3_0 ),
inference(rw,[status(thm)],[126,148,theory(equality)]) ).
cnf(157,negated_conjecture,
( $false
| singleton(esk4_0) != singleton(esk2_0)
| esk4_0 != esk2_0
| $false ),
inference(rw,[status(thm)],[156,148,theory(equality)]) ).
cnf(158,negated_conjecture,
( singleton(esk4_0) != singleton(esk2_0)
| esk4_0 != esk2_0 ),
inference(cn,[status(thm)],[157,theory(equality)]) ).
cnf(190,negated_conjecture,
esk4_0 = esk2_0,
inference(er,[status(thm)],[112,theory(equality)]) ).
cnf(193,negated_conjecture,
( $false
| esk4_0 != esk2_0 ),
inference(rw,[status(thm)],[158,190,theory(equality)]) ).
cnf(194,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[193,190,theory(equality)]) ).
cnf(195,negated_conjecture,
$false,
inference(cn,[status(thm)],[194,theory(equality)]) ).
cnf(196,negated_conjecture,
$false,
195,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET893+1.p
% --creating new selector for []
% -running prover on /tmp/tmpgUAiqE/sel_SET893+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET893+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET893+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET893+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
%
%------------------------------------------------------------------------------