TSTP Solution File: SEU165+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU165+1 : TPTP v5.0.0. Released v3.3.0.
% 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 04:59:19 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 9 unt; 0 def)
% Number of atoms : 94 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 102 ( 41 ~; 41 |; 17 &)
% ( 3 <=>; 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 7 sgn 28 !; 8 ?)
% 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/tmp-_Pdn6/sel_SEU165+1.p_1',l55_zfmisc_1) ).
fof(11,conjecture,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/tmp/tmp-_Pdn6/sel_SEU165+1.p_1',t106_zfmisc_1) ).
fof(12,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmp-_Pdn6/sel_SEU165+1.p_1',d5_tarski) ).
fof(13,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
inference(assume_negation,[status(cth)],[11]) ).
fof(17,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(18,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)],[17]) ).
fof(19,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)],[18]) ).
cnf(20,plain,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(21,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(22,plain,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[19]) ).
fof(40,negated_conjecture,
? [X1,X2,X3,X4] :
( ( ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X1,X3)
| ~ in(X2,X4) )
& ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ( in(X1,X3)
& in(X2,X4) ) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(41,negated_conjecture,
? [X5,X6,X7,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))
| ( in(X5,X7)
& in(X6,X8) ) ) ),
inference(variable_rename,[status(thm)],[40]) ).
fof(42,negated_conjecture,
( ( ~ in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
| ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk6_0) )
& ( in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
| ( in(esk3_0,esk5_0)
& in(esk4_0,esk6_0) ) ) ),
inference(skolemize,[status(esa)],[41]) ).
fof(43,negated_conjecture,
( ( ~ in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
| ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk6_0) )
& ( in(esk3_0,esk5_0)
| in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) )
& ( in(esk4_0,esk6_0)
| in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) ) ),
inference(distribute,[status(thm)],[42]) ).
cnf(44,negated_conjecture,
( in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
| in(esk4_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(45,negated_conjecture,
( in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
| in(esk3_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(46,negated_conjecture,
( ~ in(esk4_0,esk6_0)
| ~ in(esk3_0,esk5_0)
| ~ in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(47,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[12]) ).
cnf(48,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[47]) ).
cnf(49,negated_conjecture,
( in(esk3_0,esk5_0)
| in(unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0)),cartesian_product2(esk5_0,esk6_0)) ),
inference(rw,[status(thm)],[45,48,theory(equality)]),
[unfolding] ).
cnf(50,negated_conjecture,
( in(esk4_0,esk6_0)
| in(unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0)),cartesian_product2(esk5_0,esk6_0)) ),
inference(rw,[status(thm)],[44,48,theory(equality)]),
[unfolding] ).
cnf(51,plain,
( in(X2,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[21,48,theory(equality)]),
[unfolding] ).
cnf(52,plain,
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[22,48,theory(equality)]),
[unfolding] ).
cnf(53,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[20,48,theory(equality)]),
[unfolding] ).
cnf(55,negated_conjecture,
( ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk6_0)
| ~ in(unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0)),cartesian_product2(esk5_0,esk6_0)) ),
inference(rw,[status(thm)],[46,48,theory(equality)]),
[unfolding] ).
cnf(63,negated_conjecture,
in(esk4_0,esk6_0),
inference(spm,[status(thm)],[51,50,theory(equality)]) ).
cnf(74,negated_conjecture,
( ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk6_0) ),
inference(csr,[status(thm)],[55,53]) ).
cnf(79,negated_conjecture,
in(esk3_0,esk5_0),
inference(spm,[status(thm)],[52,49,theory(equality)]) ).
cnf(91,negated_conjecture,
( ~ in(esk3_0,esk5_0)
| $false ),
inference(rw,[status(thm)],[74,63,theory(equality)]) ).
cnf(92,negated_conjecture,
~ in(esk3_0,esk5_0),
inference(cn,[status(thm)],[91,theory(equality)]) ).
cnf(101,negated_conjecture,
$false,
inference(rw,[status(thm)],[92,79,theory(equality)]) ).
cnf(102,negated_conjecture,
$false,
inference(cn,[status(thm)],[101,theory(equality)]) ).
cnf(103,negated_conjecture,
$false,
102,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU165+1.p
% --creating new selector for []
% -running prover on /tmp/tmp-_Pdn6/sel_SEU165+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU165+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU165+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU165+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
%
%------------------------------------------------------------------------------