TSTP Solution File: SET959+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET959+1 : TPTP v5.0.0. Bugfixed v4.0.0.
% 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 03:54:43 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 13 unt; 0 def)
% Number of atoms : 139 ( 46 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 150 ( 58 ~; 58 |; 28 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 55 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpWS8PbJ/sel_SET959+1.p_1',d5_tarski) ).
fof(2,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/tmp/tmpWS8PbJ/sel_SET959+1.p_1',t2_tarski) ).
fof(5,conjecture,
! [X1,X2] :
( ( ! [X3] :
~ ( in(X3,X1)
& ! [X4,X5] : X3 != ordered_pair(X4,X5) )
& ! [X3] :
~ ( in(X3,X2)
& ! [X4,X5] : X3 != ordered_pair(X4,X5) )
& ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
<=> in(ordered_pair(X3,X4),X2) ) )
=> X1 = X2 ),
file('/tmp/tmpWS8PbJ/sel_SET959+1.p_1',t112_zfmisc_1) ).
fof(6,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpWS8PbJ/sel_SET959+1.p_1',commutativity_k2_tarski) ).
fof(9,negated_conjecture,
~ ! [X1,X2] :
( ( ! [X3] :
~ ( in(X3,X1)
& ! [X4,X5] : X3 != ordered_pair(X4,X5) )
& ! [X3] :
~ ( in(X3,X2)
& ! [X4,X5] : X3 != ordered_pair(X4,X5) )
& ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
<=> in(ordered_pair(X3,X4),X2) ) )
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[5]) ).
fof(13,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[1]) ).
cnf(14,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[13]) ).
fof(15,plain,
! [X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X2) ) )
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(16,plain,
! [X4,X5] :
( ? [X6] :
( ( ~ in(X6,X4)
| ~ in(X6,X5) )
& ( in(X6,X4)
| in(X6,X5) ) )
| X4 = X5 ),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,plain,
! [X4,X5] :
( ( ( ~ in(esk1_2(X4,X5),X4)
| ~ in(esk1_2(X4,X5),X5) )
& ( in(esk1_2(X4,X5),X4)
| in(esk1_2(X4,X5),X5) ) )
| X4 = X5 ),
inference(skolemize,[status(esa)],[16]) ).
fof(18,plain,
! [X4,X5] :
( ( ~ in(esk1_2(X4,X5),X4)
| ~ in(esk1_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk1_2(X4,X5),X4)
| in(esk1_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[17]) ).
cnf(19,plain,
( X1 = X2
| in(esk1_2(X1,X2),X2)
| in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(20,plain,
( X1 = X2
| ~ in(esk1_2(X1,X2),X2)
| ~ in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[18]) ).
fof(26,negated_conjecture,
? [X1,X2] :
( ! [X3] :
( ~ in(X3,X1)
| ? [X4,X5] : X3 = ordered_pair(X4,X5) )
& ! [X3] :
( ~ in(X3,X2)
| ? [X4,X5] : X3 = ordered_pair(X4,X5) )
& ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X1)
| in(ordered_pair(X3,X4),X2) )
& ( ~ in(ordered_pair(X3,X4),X2)
| in(ordered_pair(X3,X4),X1) ) )
& X1 != X2 ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(27,negated_conjecture,
? [X6,X7] :
( ! [X8] :
( ~ in(X8,X6)
| ? [X9,X10] : X8 = ordered_pair(X9,X10) )
& ! [X11] :
( ~ in(X11,X7)
| ? [X12,X13] : X11 = ordered_pair(X12,X13) )
& ! [X14,X15] :
( ( ~ in(ordered_pair(X14,X15),X6)
| in(ordered_pair(X14,X15),X7) )
& ( ~ in(ordered_pair(X14,X15),X7)
| in(ordered_pair(X14,X15),X6) ) )
& X6 != X7 ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,negated_conjecture,
( ! [X8] :
( ~ in(X8,esk3_0)
| X8 = ordered_pair(esk5_1(X8),esk6_1(X8)) )
& ! [X11] :
( ~ in(X11,esk4_0)
| X11 = ordered_pair(esk7_1(X11),esk8_1(X11)) )
& ! [X14,X15] :
( ( ~ in(ordered_pair(X14,X15),esk3_0)
| in(ordered_pair(X14,X15),esk4_0) )
& ( ~ in(ordered_pair(X14,X15),esk4_0)
| in(ordered_pair(X14,X15),esk3_0) ) )
& esk3_0 != esk4_0 ),
inference(skolemize,[status(esa)],[27]) ).
fof(29,negated_conjecture,
! [X8,X11,X14,X15] :
( ( ~ in(ordered_pair(X14,X15),esk3_0)
| in(ordered_pair(X14,X15),esk4_0) )
& ( ~ in(ordered_pair(X14,X15),esk4_0)
| in(ordered_pair(X14,X15),esk3_0) )
& ( ~ in(X11,esk4_0)
| X11 = ordered_pair(esk7_1(X11),esk8_1(X11)) )
& ( ~ in(X8,esk3_0)
| X8 = ordered_pair(esk5_1(X8),esk6_1(X8)) )
& esk3_0 != esk4_0 ),
inference(shift_quantors,[status(thm)],[28]) ).
cnf(30,negated_conjecture,
esk3_0 != esk4_0,
inference(split_conjunct,[status(thm)],[29]) ).
cnf(31,negated_conjecture,
( X1 = ordered_pair(esk5_1(X1),esk6_1(X1))
| ~ in(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(32,negated_conjecture,
( X1 = ordered_pair(esk7_1(X1),esk8_1(X1))
| ~ in(X1,esk4_0) ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(33,negated_conjecture,
( in(ordered_pair(X1,X2),esk3_0)
| ~ in(ordered_pair(X1,X2),esk4_0) ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(34,negated_conjecture,
( in(ordered_pair(X1,X2),esk4_0)
| ~ in(ordered_pair(X1,X2),esk3_0) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(35,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[6]) ).
cnf(36,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(43,negated_conjecture,
( unordered_pair(unordered_pair(esk5_1(X1),esk6_1(X1)),singleton(esk5_1(X1))) = X1
| ~ in(X1,esk3_0) ),
inference(rw,[status(thm)],[31,14,theory(equality)]),
[unfolding] ).
cnf(44,negated_conjecture,
( unordered_pair(unordered_pair(esk7_1(X1),esk8_1(X1)),singleton(esk7_1(X1))) = X1
| ~ in(X1,esk4_0) ),
inference(rw,[status(thm)],[32,14,theory(equality)]),
[unfolding] ).
cnf(45,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk3_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk4_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[33,14,theory(equality)]),14,theory(equality)]),
[unfolding] ).
cnf(46,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk4_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk3_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[34,14,theory(equality)]),14,theory(equality)]),
[unfolding] ).
cnf(53,negated_conjecture,
( unordered_pair(singleton(esk5_1(X1)),unordered_pair(esk5_1(X1),esk6_1(X1))) = X1
| ~ in(X1,esk3_0) ),
inference(rw,[status(thm)],[43,36,theory(equality)]) ).
cnf(54,negated_conjecture,
( unordered_pair(singleton(esk5_1(esk1_2(esk3_0,X1))),unordered_pair(esk5_1(esk1_2(esk3_0,X1)),esk6_1(esk1_2(esk3_0,X1)))) = esk1_2(esk3_0,X1)
| esk3_0 = X1
| in(esk1_2(esk3_0,X1),X1) ),
inference(spm,[status(thm)],[53,19,theory(equality)]) ).
cnf(56,negated_conjecture,
( unordered_pair(singleton(esk7_1(X1)),unordered_pair(esk7_1(X1),esk8_1(X1))) = X1
| ~ in(X1,esk4_0) ),
inference(rw,[status(thm)],[44,36,theory(equality)]) ).
cnf(59,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk4_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk3_0) ),
inference(rw,[status(thm)],[46,36,theory(equality)]) ).
cnf(60,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk4_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk3_0) ),
inference(rw,[status(thm)],[59,36,theory(equality)]) ).
cnf(64,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk3_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk4_0) ),
inference(rw,[status(thm)],[45,36,theory(equality)]) ).
cnf(65,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk3_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk4_0) ),
inference(rw,[status(thm)],[64,36,theory(equality)]) ).
cnf(80,negated_conjecture,
( in(esk1_2(esk3_0,X1),esk4_0)
| esk3_0 = X1
| in(esk1_2(esk3_0,X1),X1)
| ~ in(esk1_2(esk3_0,X1),esk3_0) ),
inference(spm,[status(thm)],[60,54,theory(equality)]) ).
cnf(95,negated_conjecture,
( esk3_0 = X1
| in(esk1_2(esk3_0,X1),esk4_0)
| in(esk1_2(esk3_0,X1),X1) ),
inference(csr,[status(thm)],[80,19]) ).
cnf(96,negated_conjecture,
( esk3_0 = esk4_0
| in(esk1_2(esk3_0,esk4_0),esk4_0) ),
inference(ef,[status(thm)],[95,theory(equality)]) ).
cnf(102,negated_conjecture,
in(esk1_2(esk3_0,esk4_0),esk4_0),
inference(sr,[status(thm)],[96,30,theory(equality)]) ).
cnf(105,negated_conjecture,
unordered_pair(singleton(esk7_1(esk1_2(esk3_0,esk4_0))),unordered_pair(esk7_1(esk1_2(esk3_0,esk4_0)),esk8_1(esk1_2(esk3_0,esk4_0)))) = esk1_2(esk3_0,esk4_0),
inference(spm,[status(thm)],[56,102,theory(equality)]) ).
cnf(106,negated_conjecture,
( esk3_0 = esk4_0
| ~ in(esk1_2(esk3_0,esk4_0),esk3_0) ),
inference(spm,[status(thm)],[20,102,theory(equality)]) ).
cnf(107,negated_conjecture,
~ in(esk1_2(esk3_0,esk4_0),esk3_0),
inference(sr,[status(thm)],[106,30,theory(equality)]) ).
cnf(116,negated_conjecture,
( in(esk1_2(esk3_0,esk4_0),esk3_0)
| ~ in(esk1_2(esk3_0,esk4_0),esk4_0) ),
inference(spm,[status(thm)],[65,105,theory(equality)]) ).
cnf(126,negated_conjecture,
( in(esk1_2(esk3_0,esk4_0),esk3_0)
| $false ),
inference(rw,[status(thm)],[116,102,theory(equality)]) ).
cnf(127,negated_conjecture,
in(esk1_2(esk3_0,esk4_0),esk3_0),
inference(cn,[status(thm)],[126,theory(equality)]) ).
cnf(128,negated_conjecture,
$false,
inference(sr,[status(thm)],[127,107,theory(equality)]) ).
cnf(129,negated_conjecture,
$false,
128,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET959+1.p
% --creating new selector for []
% -running prover on /tmp/tmpWS8PbJ/sel_SET959+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET959+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET959+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET959+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
%
%------------------------------------------------------------------------------