TSTP Solution File: SET961+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET961+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 03:54:52 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 14 unt; 0 def)
% Number of atoms : 155 ( 53 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 164 ( 65 ~; 68 |; 24 &)
% ( 4 <=>; 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 101 ( 13 sgn 47 !; 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/tmpLt7HeR/sel_SET961+1.p_1',l55_zfmisc_1) ).
fof(2,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpLt7HeR/sel_SET961+1.p_1',d5_tarski) ).
fof(3,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/tmp/tmpLt7HeR/sel_SET961+1.p_1',t2_tarski) ).
fof(7,conjecture,
! [X1,X2] :
( cartesian_product2(X1,X2) = cartesian_product2(X2,X1)
=> ( X1 = empty_set
| X2 = empty_set
| X1 = X2 ) ),
file('/tmp/tmpLt7HeR/sel_SET961+1.p_1',t114_zfmisc_1) ).
fof(10,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/tmp/tmpLt7HeR/sel_SET961+1.p_1',d1_xboole_0) ).
fof(12,negated_conjecture,
~ ! [X1,X2] :
( cartesian_product2(X1,X2) = cartesian_product2(X2,X1)
=> ( X1 = empty_set
| X2 = empty_set
| X1 = X2 ) ),
inference(assume_negation,[status(cth)],[7]) ).
fof(16,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
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(23,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[2]) ).
cnf(24,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[23]) ).
fof(25,plain,
! [X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X2) ) )
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(26,plain,
! [X4,X5] :
( ? [X6] :
( ( ~ in(X6,X4)
| ~ in(X6,X5) )
& ( in(X6,X4)
| in(X6,X5) ) )
| X4 = X5 ),
inference(variable_rename,[status(thm)],[25]) ).
fof(27,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)],[26]) ).
fof(28,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)],[27]) ).
cnf(29,plain,
( X1 = X2
| in(esk1_2(X1,X2),X2)
| in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(30,plain,
( X1 = X2
| ~ in(esk1_2(X1,X2),X2)
| ~ in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[28]) ).
fof(38,negated_conjecture,
? [X1,X2] :
( cartesian_product2(X1,X2) = cartesian_product2(X2,X1)
& X1 != empty_set
& X2 != empty_set
& X1 != X2 ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(39,negated_conjecture,
? [X3,X4] :
( cartesian_product2(X3,X4) = cartesian_product2(X4,X3)
& X3 != empty_set
& X4 != empty_set
& X3 != X4 ),
inference(variable_rename,[status(thm)],[38]) ).
fof(40,negated_conjecture,
( cartesian_product2(esk3_0,esk4_0) = cartesian_product2(esk4_0,esk3_0)
& esk3_0 != empty_set
& esk4_0 != empty_set
& esk3_0 != esk4_0 ),
inference(skolemize,[status(esa)],[39]) ).
cnf(41,negated_conjecture,
esk3_0 != esk4_0,
inference(split_conjunct,[status(thm)],[40]) ).
cnf(42,negated_conjecture,
esk4_0 != empty_set,
inference(split_conjunct,[status(thm)],[40]) ).
cnf(43,negated_conjecture,
esk3_0 != empty_set,
inference(split_conjunct,[status(thm)],[40]) ).
cnf(44,negated_conjecture,
cartesian_product2(esk3_0,esk4_0) = cartesian_product2(esk4_0,esk3_0),
inference(split_conjunct,[status(thm)],[40]) ).
fof(51,plain,
! [X1] :
( ( X1 != empty_set
| ! [X2] : ~ in(X2,X1) )
& ( ? [X2] : in(X2,X1)
| X1 = empty_set ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(52,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( ? [X5] : in(X5,X3)
| X3 = empty_set ) ),
inference(variable_rename,[status(thm)],[51]) ).
fof(53,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( in(esk6_1(X3),X3)
| X3 = empty_set ) ),
inference(skolemize,[status(esa)],[52]) ).
fof(54,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| X3 != empty_set )
& ( in(esk6_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[53]) ).
cnf(55,plain,
( X1 = empty_set
| in(esk6_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[54]) ).
cnf(58,plain,
( in(X2,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[21,24,theory(equality)]),
[unfolding] ).
cnf(59,plain,
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[22,24,theory(equality)]),
[unfolding] ).
cnf(60,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[20,24,theory(equality)]),
[unfolding] ).
cnf(75,negated_conjecture,
( in(X1,esk4_0)
| ~ in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),cartesian_product2(esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[58,44,theory(equality)]) ).
cnf(80,negated_conjecture,
( in(X1,esk3_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[59,44,theory(equality)]) ).
cnf(116,negated_conjecture,
( in(X1,esk4_0)
| ~ in(X1,esk3_0)
| ~ in(X2,esk4_0) ),
inference(spm,[status(thm)],[75,60,theory(equality)]) ).
cnf(117,negated_conjecture,
( in(esk6_1(esk3_0),esk4_0)
| empty_set = esk3_0
| ~ in(X1,esk4_0) ),
inference(spm,[status(thm)],[116,55,theory(equality)]) ).
cnf(118,negated_conjecture,
( in(esk1_2(esk3_0,X1),esk4_0)
| esk3_0 = X1
| in(esk1_2(esk3_0,X1),X1)
| ~ in(X2,esk4_0) ),
inference(spm,[status(thm)],[116,29,theory(equality)]) ).
cnf(122,negated_conjecture,
( in(esk6_1(esk3_0),esk4_0)
| ~ in(X1,esk4_0) ),
inference(sr,[status(thm)],[117,43,theory(equality)]) ).
cnf(123,negated_conjecture,
( in(esk6_1(esk3_0),esk4_0)
| empty_set = esk4_0 ),
inference(spm,[status(thm)],[122,55,theory(equality)]) ).
cnf(128,negated_conjecture,
in(esk6_1(esk3_0),esk4_0),
inference(sr,[status(thm)],[123,42,theory(equality)]) ).
cnf(168,negated_conjecture,
( in(X1,esk3_0)
| ~ in(X2,esk3_0)
| ~ in(X1,esk4_0) ),
inference(spm,[status(thm)],[80,60,theory(equality)]) ).
cnf(169,negated_conjecture,
( in(X1,esk3_0)
| empty_set = esk3_0
| ~ in(X1,esk4_0) ),
inference(spm,[status(thm)],[168,55,theory(equality)]) ).
cnf(174,negated_conjecture,
( in(X1,esk3_0)
| ~ in(X1,esk4_0) ),
inference(sr,[status(thm)],[169,43,theory(equality)]) ).
cnf(330,negated_conjecture,
( esk3_0 = X1
| in(esk1_2(esk3_0,X1),esk4_0)
| in(esk1_2(esk3_0,X1),X1) ),
inference(spm,[status(thm)],[118,128,theory(equality)]) ).
cnf(339,negated_conjecture,
( esk3_0 = esk4_0
| in(esk1_2(esk3_0,esk4_0),esk4_0) ),
inference(ef,[status(thm)],[330,theory(equality)]) ).
cnf(347,negated_conjecture,
in(esk1_2(esk3_0,esk4_0),esk4_0),
inference(sr,[status(thm)],[339,41,theory(equality)]) ).
cnf(351,negated_conjecture,
( esk3_0 = esk4_0
| ~ in(esk1_2(esk3_0,esk4_0),esk3_0) ),
inference(spm,[status(thm)],[30,347,theory(equality)]) ).
cnf(352,negated_conjecture,
~ in(esk1_2(esk3_0,esk4_0),esk3_0),
inference(sr,[status(thm)],[351,41,theory(equality)]) ).
cnf(370,negated_conjecture,
~ in(esk1_2(esk3_0,esk4_0),esk4_0),
inference(spm,[status(thm)],[352,174,theory(equality)]) ).
cnf(374,negated_conjecture,
$false,
inference(rw,[status(thm)],[370,347,theory(equality)]) ).
cnf(375,negated_conjecture,
$false,
inference(cn,[status(thm)],[374,theory(equality)]) ).
cnf(376,negated_conjecture,
$false,
375,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET961+1.p
% --creating new selector for []
% -running prover on /tmp/tmpLt7HeR/sel_SET961+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET961+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET961+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET961+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
%
%------------------------------------------------------------------------------