TSTP Solution File: SET980+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET980+1 : TPTP v5.0.0. Bugfixed v4.0.0.
% 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 03:58:07 EST 2010
% Result : Theorem 0.26s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 6
% Syntax : Number of formulae : 85 ( 18 unt; 0 def)
% Number of atoms : 237 ( 112 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 255 ( 103 ~; 112 |; 32 &)
% ( 5 <=>; 3 =>; 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 : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 134 ( 16 sgn 59 !; 12 ?)
% 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/tmpqlCqBZ/sel_SET980+1.p_1',l55_zfmisc_1) ).
fof(2,conjecture,
! [X1,X2,X3,X4] :
( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
=> ( X1 = empty_set
| X2 = empty_set
| ( X1 = X3
& X2 = X4 ) ) ),
file('/tmp/tmpqlCqBZ/sel_SET980+1.p_1',t134_zfmisc_1) ).
fof(3,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpqlCqBZ/sel_SET980+1.p_1',d5_tarski) ).
fof(4,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/tmp/tmpqlCqBZ/sel_SET980+1.p_1',t2_tarski) ).
fof(6,axiom,
! [X1,X2] :
( cartesian_product2(X1,X2) = empty_set
<=> ( X1 = empty_set
| X2 = empty_set ) ),
file('/tmp/tmpqlCqBZ/sel_SET980+1.p_1',t113_zfmisc_1) ).
fof(11,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/tmp/tmpqlCqBZ/sel_SET980+1.p_1',d1_xboole_0) ).
fof(13,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
=> ( X1 = empty_set
| X2 = empty_set
| ( X1 = X3
& X2 = X4 ) ) ),
inference(assume_negation,[status(cth)],[2]) ).
fof(17,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
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)],[1]) ).
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,negated_conjecture,
? [X1,X2,X3,X4] :
( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
& X1 != empty_set
& X2 != empty_set
& ( X1 != X3
| X2 != X4 ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(25,negated_conjecture,
? [X5,X6,X7,X8] :
( cartesian_product2(X5,X6) = cartesian_product2(X7,X8)
& X5 != empty_set
& X6 != empty_set
& ( X5 != X7
| X6 != X8 ) ),
inference(variable_rename,[status(thm)],[24]) ).
fof(26,negated_conjecture,
( cartesian_product2(esk1_0,esk2_0) = cartesian_product2(esk3_0,esk4_0)
& esk1_0 != empty_set
& esk2_0 != empty_set
& ( esk1_0 != esk3_0
| esk2_0 != esk4_0 ) ),
inference(skolemize,[status(esa)],[25]) ).
cnf(27,negated_conjecture,
( esk2_0 != esk4_0
| esk1_0 != esk3_0 ),
inference(split_conjunct,[status(thm)],[26]) ).
cnf(28,negated_conjecture,
esk2_0 != empty_set,
inference(split_conjunct,[status(thm)],[26]) ).
cnf(29,negated_conjecture,
esk1_0 != empty_set,
inference(split_conjunct,[status(thm)],[26]) ).
cnf(30,negated_conjecture,
cartesian_product2(esk1_0,esk2_0) = cartesian_product2(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[26]) ).
fof(31,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(32,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[31]) ).
fof(33,plain,
! [X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X2) ) )
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(34,plain,
! [X4,X5] :
( ? [X6] :
( ( ~ in(X6,X4)
| ~ in(X6,X5) )
& ( in(X6,X4)
| in(X6,X5) ) )
| X4 = X5 ),
inference(variable_rename,[status(thm)],[33]) ).
fof(35,plain,
! [X4,X5] :
( ( ( ~ in(esk5_2(X4,X5),X4)
| ~ in(esk5_2(X4,X5),X5) )
& ( in(esk5_2(X4,X5),X4)
| in(esk5_2(X4,X5),X5) ) )
| X4 = X5 ),
inference(skolemize,[status(esa)],[34]) ).
fof(36,plain,
! [X4,X5] :
( ( ~ in(esk5_2(X4,X5),X4)
| ~ in(esk5_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk5_2(X4,X5),X4)
| in(esk5_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[35]) ).
cnf(37,plain,
( X1 = X2
| in(esk5_2(X1,X2),X2)
| in(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(38,plain,
( X1 = X2
| ~ in(esk5_2(X1,X2),X2)
| ~ in(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[36]) ).
fof(42,plain,
! [X1,X2] :
( ( cartesian_product2(X1,X2) != empty_set
| X1 = empty_set
| X2 = empty_set )
& ( ( X1 != empty_set
& X2 != empty_set )
| cartesian_product2(X1,X2) = empty_set ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(43,plain,
! [X3,X4] :
( ( cartesian_product2(X3,X4) != empty_set
| X3 = empty_set
| X4 = empty_set )
& ( ( X3 != empty_set
& X4 != empty_set )
| cartesian_product2(X3,X4) = empty_set ) ),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,plain,
! [X3,X4] :
( ( cartesian_product2(X3,X4) != empty_set
| X3 = empty_set
| X4 = empty_set )
& ( X3 != empty_set
| cartesian_product2(X3,X4) = empty_set )
& ( X4 != empty_set
| cartesian_product2(X3,X4) = empty_set ) ),
inference(distribute,[status(thm)],[43]) ).
cnf(45,plain,
( cartesian_product2(X1,X2) = empty_set
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(46,plain,
( cartesian_product2(X1,X2) = empty_set
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(47,plain,
( X1 = empty_set
| X2 = empty_set
| cartesian_product2(X2,X1) != empty_set ),
inference(split_conjunct,[status(thm)],[44]) ).
fof(58,plain,
! [X1] :
( ( X1 != empty_set
| ! [X2] : ~ in(X2,X1) )
& ( ? [X2] : in(X2,X1)
| X1 = empty_set ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(59,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( ? [X5] : in(X5,X3)
| X3 = empty_set ) ),
inference(variable_rename,[status(thm)],[58]) ).
fof(60,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( in(esk8_1(X3),X3)
| X3 = empty_set ) ),
inference(skolemize,[status(esa)],[59]) ).
fof(61,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| X3 != empty_set )
& ( in(esk8_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[60]) ).
cnf(62,plain,
( X1 = empty_set
| in(esk8_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[61]) ).
cnf(65,plain,
( in(X2,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[22,32,theory(equality)]),
[unfolding] ).
cnf(66,plain,
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[23,32,theory(equality)]),
[unfolding] ).
cnf(67,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[21,32,theory(equality)]),
[unfolding] ).
cnf(69,negated_conjecture,
( empty_set = cartesian_product2(esk1_0,esk2_0)
| empty_set != esk4_0 ),
inference(spm,[status(thm)],[30,45,theory(equality)]) ).
cnf(70,negated_conjecture,
( empty_set = cartesian_product2(esk1_0,esk2_0)
| empty_set != esk3_0 ),
inference(spm,[status(thm)],[30,46,theory(equality)]) ).
cnf(80,negated_conjecture,
( in(X1,esk4_0)
| ~ in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),cartesian_product2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[65,30,theory(equality)]) ).
cnf(94,negated_conjecture,
( in(X1,esk3_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[66,30,theory(equality)]) ).
cnf(101,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk1_0,esk2_0))
| ~ in(X2,esk4_0)
| ~ in(X1,esk3_0) ),
inference(spm,[status(thm)],[67,30,theory(equality)]) ).
cnf(116,negated_conjecture,
( empty_set = esk2_0
| empty_set = esk1_0
| esk4_0 != empty_set ),
inference(spm,[status(thm)],[47,69,theory(equality)]) ).
cnf(120,negated_conjecture,
( esk1_0 = empty_set
| esk4_0 != empty_set ),
inference(sr,[status(thm)],[116,28,theory(equality)]) ).
cnf(121,negated_conjecture,
esk4_0 != empty_set,
inference(sr,[status(thm)],[120,29,theory(equality)]) ).
cnf(122,negated_conjecture,
( empty_set = esk2_0
| empty_set = esk1_0
| esk3_0 != empty_set ),
inference(spm,[status(thm)],[47,70,theory(equality)]) ).
cnf(126,negated_conjecture,
( esk1_0 = empty_set
| esk3_0 != empty_set ),
inference(sr,[status(thm)],[122,28,theory(equality)]) ).
cnf(127,negated_conjecture,
esk3_0 != empty_set,
inference(sr,[status(thm)],[126,29,theory(equality)]) ).
cnf(151,negated_conjecture,
( in(X1,esk4_0)
| ~ in(X1,esk2_0)
| ~ in(X2,esk1_0) ),
inference(spm,[status(thm)],[80,67,theory(equality)]) ).
cnf(169,negated_conjecture,
( in(X1,esk4_0)
| empty_set = esk1_0
| ~ in(X1,esk2_0) ),
inference(spm,[status(thm)],[151,62,theory(equality)]) ).
cnf(174,negated_conjecture,
( in(X1,esk4_0)
| ~ in(X1,esk2_0) ),
inference(sr,[status(thm)],[169,29,theory(equality)]) ).
cnf(518,negated_conjecture,
( in(X1,esk3_0)
| ~ in(X2,esk2_0)
| ~ in(X1,esk1_0) ),
inference(spm,[status(thm)],[94,67,theory(equality)]) ).
cnf(521,negated_conjecture,
( in(X1,esk3_0)
| empty_set = esk2_0
| ~ in(X1,esk1_0) ),
inference(spm,[status(thm)],[518,62,theory(equality)]) ).
cnf(526,negated_conjecture,
( in(X1,esk3_0)
| ~ in(X1,esk1_0) ),
inference(sr,[status(thm)],[521,28,theory(equality)]) ).
cnf(611,negated_conjecture,
( in(X1,esk2_0)
| ~ in(X1,esk4_0)
| ~ in(X2,esk3_0) ),
inference(spm,[status(thm)],[65,101,theory(equality)]) ).
cnf(613,negated_conjecture,
( in(X1,esk1_0)
| ~ in(X2,esk4_0)
| ~ in(X1,esk3_0) ),
inference(spm,[status(thm)],[66,101,theory(equality)]) ).
cnf(1811,negated_conjecture,
( in(X1,esk1_0)
| empty_set = esk4_0
| ~ in(X1,esk3_0) ),
inference(spm,[status(thm)],[613,62,theory(equality)]) ).
cnf(1817,negated_conjecture,
( in(X1,esk1_0)
| ~ in(X1,esk3_0) ),
inference(sr,[status(thm)],[1811,121,theory(equality)]) ).
cnf(1818,negated_conjecture,
( in(esk8_1(esk3_0),esk1_0)
| empty_set = esk3_0 ),
inference(spm,[status(thm)],[1817,62,theory(equality)]) ).
cnf(1819,negated_conjecture,
( in(esk5_2(esk3_0,X1),esk1_0)
| esk3_0 = X1
| in(esk5_2(esk3_0,X1),X1) ),
inference(spm,[status(thm)],[1817,37,theory(equality)]) ).
cnf(1824,negated_conjecture,
in(esk8_1(esk3_0),esk1_0),
inference(sr,[status(thm)],[1818,127,theory(equality)]) ).
cnf(1847,negated_conjecture,
( esk3_0 = esk1_0
| in(esk5_2(esk3_0,esk1_0),esk1_0) ),
inference(ef,[status(thm)],[1819,theory(equality)]) ).
cnf(1857,negated_conjecture,
( esk3_0 = esk1_0
| ~ in(esk5_2(esk3_0,esk1_0),esk3_0) ),
inference(spm,[status(thm)],[38,1847,theory(equality)]) ).
cnf(1861,negated_conjecture,
( esk3_0 = esk1_0
| ~ in(esk5_2(esk3_0,esk1_0),esk1_0) ),
inference(spm,[status(thm)],[1857,526,theory(equality)]) ).
cnf(1862,negated_conjecture,
esk3_0 = esk1_0,
inference(csr,[status(thm)],[1861,1847]) ).
cnf(1863,negated_conjecture,
in(esk8_1(esk1_0),esk1_0),
inference(rw,[status(thm)],[1824,1862,theory(equality)]) ).
cnf(1886,negated_conjecture,
( in(X1,esk2_0)
| ~ in(X1,esk4_0)
| ~ in(X2,esk1_0) ),
inference(rw,[status(thm)],[611,1862,theory(equality)]) ).
cnf(1903,negated_conjecture,
( $false
| esk4_0 != esk2_0 ),
inference(rw,[status(thm)],[27,1862,theory(equality)]) ).
cnf(1904,negated_conjecture,
esk4_0 != esk2_0,
inference(cn,[status(thm)],[1903,theory(equality)]) ).
cnf(1946,negated_conjecture,
( in(esk5_2(esk4_0,X1),esk2_0)
| esk4_0 = X1
| in(esk5_2(esk4_0,X1),X1)
| ~ in(X2,esk1_0) ),
inference(spm,[status(thm)],[1886,37,theory(equality)]) ).
cnf(2485,negated_conjecture,
( esk4_0 = X1
| in(esk5_2(esk4_0,X1),esk2_0)
| in(esk5_2(esk4_0,X1),X1) ),
inference(spm,[status(thm)],[1946,1863,theory(equality)]) ).
cnf(2492,negated_conjecture,
( esk4_0 = esk2_0
| in(esk5_2(esk4_0,esk2_0),esk2_0) ),
inference(ef,[status(thm)],[2485,theory(equality)]) ).
cnf(2500,negated_conjecture,
in(esk5_2(esk4_0,esk2_0),esk2_0),
inference(sr,[status(thm)],[2492,1904,theory(equality)]) ).
cnf(2503,negated_conjecture,
( esk4_0 = esk2_0
| ~ in(esk5_2(esk4_0,esk2_0),esk4_0) ),
inference(spm,[status(thm)],[38,2500,theory(equality)]) ).
cnf(2505,negated_conjecture,
~ in(esk5_2(esk4_0,esk2_0),esk4_0),
inference(sr,[status(thm)],[2503,1904,theory(equality)]) ).
cnf(2509,negated_conjecture,
~ in(esk5_2(esk4_0,esk2_0),esk2_0),
inference(spm,[status(thm)],[2505,174,theory(equality)]) ).
cnf(2513,negated_conjecture,
$false,
inference(rw,[status(thm)],[2509,2500,theory(equality)]) ).
cnf(2514,negated_conjecture,
$false,
inference(cn,[status(thm)],[2513,theory(equality)]) ).
cnf(2515,negated_conjecture,
$false,
2514,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET980+1.p
% --creating new selector for []
% -running prover on /tmp/tmpqlCqBZ/sel_SET980+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET980+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET980+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET980+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
%
%------------------------------------------------------------------------------