TSTP Solution File: SET954+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET954+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 03:54:04 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 17 unt; 0 def)
% Number of atoms : 65 ( 6 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 58 ( 26 ~; 19 |; 10 &)
% ( 1 <=>; 2 =>; 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 7 sgn 32 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
=> in(ordered_pair(X2,X1),cartesian_product2(X4,X3)) ),
file('/tmp/tmppYR2kK/sel_SET954+1.p_1',t107_zfmisc_1) ).
fof(2,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/tmp/tmppYR2kK/sel_SET954+1.p_1',l55_zfmisc_1) ).
fof(3,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmppYR2kK/sel_SET954+1.p_1',d5_tarski) ).
fof(6,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmppYR2kK/sel_SET954+1.p_1',commutativity_k2_tarski) ).
fof(9,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
=> in(ordered_pair(X2,X1),cartesian_product2(X4,X3)) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(13,negated_conjecture,
? [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
& ~ in(ordered_pair(X2,X1),cartesian_product2(X4,X3)) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(14,negated_conjecture,
? [X5,X6,X7,X8] :
( in(ordered_pair(X5,X6),cartesian_product2(X7,X8))
& ~ in(ordered_pair(X6,X5),cartesian_product2(X8,X7)) ),
inference(variable_rename,[status(thm)],[13]) ).
fof(15,negated_conjecture,
( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0))
& ~ in(ordered_pair(esk2_0,esk1_0),cartesian_product2(esk4_0,esk3_0)) ),
inference(skolemize,[status(esa)],[14]) ).
cnf(16,negated_conjecture,
~ in(ordered_pair(esk2_0,esk1_0),cartesian_product2(esk4_0,esk3_0)),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(17,negated_conjecture,
in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[15]) ).
fof(18,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)],[2]) ).
fof(19,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)],[18]) ).
fof(20,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)],[19]) ).
cnf(21,plain,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(22,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(23,plain,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(24,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(25,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[24]) ).
fof(31,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[6]) ).
cnf(32,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[31]) ).
cnf(39,negated_conjecture,
in(unordered_pair(unordered_pair(esk1_0,esk2_0),singleton(esk1_0)),cartesian_product2(esk3_0,esk4_0)),
inference(rw,[status(thm)],[17,25,theory(equality)]),
[unfolding] ).
cnf(40,plain,
( in(X2,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[22,25,theory(equality)]),
[unfolding] ).
cnf(41,plain,
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[23,25,theory(equality)]),
[unfolding] ).
cnf(42,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[21,25,theory(equality)]),
[unfolding] ).
cnf(44,negated_conjecture,
~ in(unordered_pair(unordered_pair(esk2_0,esk1_0),singleton(esk2_0)),cartesian_product2(esk4_0,esk3_0)),
inference(rw,[status(thm)],[16,25,theory(equality)]),
[unfolding] ).
cnf(49,negated_conjecture,
~ in(unordered_pair(unordered_pair(esk1_0,esk2_0),singleton(esk2_0)),cartesian_product2(esk4_0,esk3_0)),
inference(rw,[status(thm)],[44,32,theory(equality)]) ).
cnf(52,negated_conjecture,
in(esk2_0,esk4_0),
inference(spm,[status(thm)],[40,39,theory(equality)]) ).
cnf(57,negated_conjecture,
in(esk1_0,esk3_0),
inference(spm,[status(thm)],[41,39,theory(equality)]) ).
cnf(65,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,esk1_0),singleton(X1)),cartesian_product2(X2,esk3_0))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[42,57,theory(equality)]) ).
cnf(132,negated_conjecture,
in(unordered_pair(unordered_pair(esk2_0,esk1_0),singleton(esk2_0)),cartesian_product2(esk4_0,esk3_0)),
inference(spm,[status(thm)],[65,52,theory(equality)]) ).
cnf(136,negated_conjecture,
in(unordered_pair(unordered_pair(esk1_0,esk2_0),singleton(esk2_0)),cartesian_product2(esk4_0,esk3_0)),
inference(rw,[status(thm)],[132,32,theory(equality)]) ).
cnf(137,negated_conjecture,
$false,
inference(sr,[status(thm)],[136,49,theory(equality)]) ).
cnf(138,negated_conjecture,
$false,
137,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET954+1.p
% --creating new selector for []
% -running prover on /tmp/tmppYR2kK/sel_SET954+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET954+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET954+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET954+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
%
%------------------------------------------------------------------------------