TSTP Solution File: SET958+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET958+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 03:54:34 EST 2010
% Result : Theorem 0.27s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 10 unt; 0 def)
% Number of atoms : 94 ( 15 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 104 ( 42 ~; 34 |; 22 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 52 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2] :
( ( ! [X3] :
~ ( in(X3,X1)
& ! [X4,X5] : X3 != ordered_pair(X4,X5) )
& ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
=> in(ordered_pair(X3,X4),X2) ) )
=> subset(X1,X2) ),
file('/tmp/tmpiK4F-X/sel_SET958+1.p_1',t111_zfmisc_1) ).
fof(2,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpiK4F-X/sel_SET958+1.p_1',d5_tarski) ).
fof(5,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpiK4F-X/sel_SET958+1.p_1',commutativity_k2_tarski) ).
fof(8,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpiK4F-X/sel_SET958+1.p_1',d3_tarski) ).
fof(10,negated_conjecture,
~ ! [X1,X2] :
( ( ! [X3] :
~ ( in(X3,X1)
& ! [X4,X5] : X3 != ordered_pair(X4,X5) )
& ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
=> in(ordered_pair(X3,X4),X2) ) )
=> subset(X1,X2) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(14,negated_conjecture,
? [X1,X2] :
( ! [X3] :
( ~ in(X3,X1)
| ? [X4,X5] : X3 = ordered_pair(X4,X5) )
& ! [X3,X4] :
( ~ in(ordered_pair(X3,X4),X1)
| in(ordered_pair(X3,X4),X2) )
& ~ subset(X1,X2) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(15,negated_conjecture,
? [X6,X7] :
( ! [X8] :
( ~ in(X8,X6)
| ? [X9,X10] : X8 = ordered_pair(X9,X10) )
& ! [X11,X12] :
( ~ in(ordered_pair(X11,X12),X6)
| in(ordered_pair(X11,X12),X7) )
& ~ subset(X6,X7) ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,negated_conjecture,
( ! [X8] :
( ~ in(X8,esk1_0)
| X8 = ordered_pair(esk3_1(X8),esk4_1(X8)) )
& ! [X11,X12] :
( ~ in(ordered_pair(X11,X12),esk1_0)
| in(ordered_pair(X11,X12),esk2_0) )
& ~ subset(esk1_0,esk2_0) ),
inference(skolemize,[status(esa)],[15]) ).
fof(17,negated_conjecture,
! [X8,X11,X12] :
( ( ~ in(ordered_pair(X11,X12),esk1_0)
| in(ordered_pair(X11,X12),esk2_0) )
& ( ~ in(X8,esk1_0)
| X8 = ordered_pair(esk3_1(X8),esk4_1(X8)) )
& ~ subset(esk1_0,esk2_0) ),
inference(shift_quantors,[status(thm)],[16]) ).
cnf(18,negated_conjecture,
~ subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(19,negated_conjecture,
( X1 = ordered_pair(esk3_1(X1),esk4_1(X1))
| ~ in(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(20,negated_conjecture,
( in(ordered_pair(X1,X2),esk2_0)
| ~ in(ordered_pair(X1,X2),esk1_0) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(21,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[2]) ).
cnf(22,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[21]) ).
fof(28,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(29,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[28]) ).
fof(36,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ in(X3,X1)
| in(X3,X2) ) )
& ( ? [X3] :
( in(X3,X1)
& ~ in(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(37,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ? [X7] :
( in(X7,X4)
& ~ in(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[36]) ).
fof(38,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk7_2(X4,X5),X4)
& ~ in(esk7_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[37]) ).
fof(39,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk7_2(X4,X5),X4)
& ~ in(esk7_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[38]) ).
fof(40,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk7_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk7_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[39]) ).
cnf(41,plain,
( subset(X1,X2)
| ~ in(esk7_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(42,plain,
( subset(X1,X2)
| in(esk7_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(46,negated_conjecture,
( unordered_pair(unordered_pair(esk3_1(X1),esk4_1(X1)),singleton(esk3_1(X1))) = X1
| ~ in(X1,esk1_0) ),
inference(rw,[status(thm)],[19,22,theory(equality)]),
[unfolding] ).
cnf(47,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk2_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk1_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[20,22,theory(equality)]),22,theory(equality)]),
[unfolding] ).
cnf(57,negated_conjecture,
( unordered_pair(singleton(esk3_1(X1)),unordered_pair(esk3_1(X1),esk4_1(X1))) = X1
| ~ in(X1,esk1_0) ),
inference(rw,[status(thm)],[46,29,theory(equality)]) ).
cnf(60,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk2_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk1_0) ),
inference(spm,[status(thm)],[47,29,theory(equality)]) ).
cnf(77,negated_conjecture,
( in(X1,esk2_0)
| ~ in(X1,esk1_0) ),
inference(spm,[status(thm)],[60,57,theory(equality)]) ).
cnf(81,negated_conjecture,
( subset(X1,esk2_0)
| ~ in(esk7_2(X1,esk2_0),esk1_0) ),
inference(spm,[status(thm)],[41,77,theory(equality)]) ).
cnf(96,negated_conjecture,
subset(esk1_0,esk2_0),
inference(spm,[status(thm)],[81,42,theory(equality)]) ).
cnf(97,negated_conjecture,
$false,
inference(sr,[status(thm)],[96,18,theory(equality)]) ).
cnf(98,negated_conjecture,
$false,
97,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET958+1.p
% --creating new selector for []
% -running prover on /tmp/tmpiK4F-X/sel_SET958+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET958+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET958+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET958+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
%
%------------------------------------------------------------------------------