TSTP Solution File: SET957+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET957+1 : TPTP v5.0.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 03:58:50 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 15 unt; 0 def)
% Number of atoms : 152 ( 32 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 164 ( 61 ~; 61 |; 36 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 126 ( 4 sgn 65 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2,X3,X4,X5,X6] :
( ( subset(X1,cartesian_product2(X2,X3))
& subset(X4,cartesian_product2(X5,X6))
& ! [X7,X8] :
( in(ordered_pair(X7,X8),X1)
<=> in(ordered_pair(X7,X8),X4) ) )
=> X1 = X4 ),
file('/tmp/tmp4YWQne/sel_SET957+1.p_1',t110_zfmisc_1) ).
fof(2,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmp4YWQne/sel_SET957+1.p_1',d5_tarski) ).
fof(3,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/tmp/tmp4YWQne/sel_SET957+1.p_1',t2_tarski) ).
fof(6,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmp4YWQne/sel_SET957+1.p_1',commutativity_k2_tarski) ).
fof(7,axiom,
! [X1,X2,X3,X4] :
~ ( subset(X1,cartesian_product2(X2,X3))
& in(X4,X1)
& ! [X5,X6] :
~ ( in(X5,X2)
& in(X6,X3)
& X4 = ordered_pair(X5,X6) ) ),
file('/tmp/tmp4YWQne/sel_SET957+1.p_1',t103_zfmisc_1) ).
fof(11,negated_conjecture,
~ ! [X1,X2,X3,X4,X5,X6] :
( ( subset(X1,cartesian_product2(X2,X3))
& subset(X4,cartesian_product2(X5,X6))
& ! [X7,X8] :
( in(ordered_pair(X7,X8),X1)
<=> in(ordered_pair(X7,X8),X4) ) )
=> X1 = X4 ),
inference(assume_negation,[status(cth)],[1]) ).
fof(15,negated_conjecture,
? [X1,X2,X3,X4,X5,X6] :
( subset(X1,cartesian_product2(X2,X3))
& subset(X4,cartesian_product2(X5,X6))
& ! [X7,X8] :
( ( ~ in(ordered_pair(X7,X8),X1)
| in(ordered_pair(X7,X8),X4) )
& ( ~ in(ordered_pair(X7,X8),X4)
| in(ordered_pair(X7,X8),X1) ) )
& X1 != X4 ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(16,negated_conjecture,
? [X9,X10,X11,X12,X13,X14] :
( subset(X9,cartesian_product2(X10,X11))
& subset(X12,cartesian_product2(X13,X14))
& ! [X15,X16] :
( ( ~ in(ordered_pair(X15,X16),X9)
| in(ordered_pair(X15,X16),X12) )
& ( ~ in(ordered_pair(X15,X16),X12)
| in(ordered_pair(X15,X16),X9) ) )
& X9 != X12 ),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,negated_conjecture,
( subset(esk1_0,cartesian_product2(esk2_0,esk3_0))
& subset(esk4_0,cartesian_product2(esk5_0,esk6_0))
& ! [X15,X16] :
( ( ~ in(ordered_pair(X15,X16),esk1_0)
| in(ordered_pair(X15,X16),esk4_0) )
& ( ~ in(ordered_pair(X15,X16),esk4_0)
| in(ordered_pair(X15,X16),esk1_0) ) )
& esk1_0 != esk4_0 ),
inference(skolemize,[status(esa)],[16]) ).
fof(18,negated_conjecture,
! [X15,X16] :
( ( ~ in(ordered_pair(X15,X16),esk1_0)
| in(ordered_pair(X15,X16),esk4_0) )
& ( ~ in(ordered_pair(X15,X16),esk4_0)
| in(ordered_pair(X15,X16),esk1_0) )
& subset(esk1_0,cartesian_product2(esk2_0,esk3_0))
& subset(esk4_0,cartesian_product2(esk5_0,esk6_0))
& esk1_0 != esk4_0 ),
inference(shift_quantors,[status(thm)],[17]) ).
cnf(19,negated_conjecture,
esk1_0 != esk4_0,
inference(split_conjunct,[status(thm)],[18]) ).
cnf(20,negated_conjecture,
subset(esk4_0,cartesian_product2(esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(21,negated_conjecture,
subset(esk1_0,cartesian_product2(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(22,negated_conjecture,
( in(ordered_pair(X1,X2),esk1_0)
| ~ in(ordered_pair(X1,X2),esk4_0) ),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(23,negated_conjecture,
( in(ordered_pair(X1,X2),esk4_0)
| ~ in(ordered_pair(X1,X2),esk1_0) ),
inference(split_conjunct,[status(thm)],[18]) ).
fof(24,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[2]) ).
cnf(25,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[24]) ).
fof(26,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(27,plain,
! [X4,X5] :
( ? [X6] :
( ( ~ in(X6,X4)
| ~ in(X6,X5) )
& ( in(X6,X4)
| in(X6,X5) ) )
| X4 = X5 ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,plain,
! [X4,X5] :
( ( ( ~ in(esk7_2(X4,X5),X4)
| ~ in(esk7_2(X4,X5),X5) )
& ( in(esk7_2(X4,X5),X4)
| in(esk7_2(X4,X5),X5) ) )
| X4 = X5 ),
inference(skolemize,[status(esa)],[27]) ).
fof(29,plain,
! [X4,X5] :
( ( ~ in(esk7_2(X4,X5),X4)
| ~ in(esk7_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk7_2(X4,X5),X4)
| in(esk7_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[28]) ).
cnf(30,plain,
( X1 = X2
| in(esk7_2(X1,X2),X2)
| in(esk7_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(31,plain,
( X1 = X2
| ~ in(esk7_2(X1,X2),X2)
| ~ in(esk7_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(37,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[6]) ).
cnf(38,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,plain,
! [X1,X2,X3,X4] :
( ~ subset(X1,cartesian_product2(X2,X3))
| ~ in(X4,X1)
| ? [X5,X6] :
( in(X5,X2)
& in(X6,X3)
& X4 = ordered_pair(X5,X6) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(40,plain,
! [X7,X8,X9,X10] :
( ~ subset(X7,cartesian_product2(X8,X9))
| ~ in(X10,X7)
| ? [X11,X12] :
( in(X11,X8)
& in(X12,X9)
& X10 = ordered_pair(X11,X12) ) ),
inference(variable_rename,[status(thm)],[39]) ).
fof(41,plain,
! [X7,X8,X9,X10] :
( ~ subset(X7,cartesian_product2(X8,X9))
| ~ in(X10,X7)
| ( in(esk9_4(X7,X8,X9,X10),X8)
& in(esk10_4(X7,X8,X9,X10),X9)
& X10 = ordered_pair(esk9_4(X7,X8,X9,X10),esk10_4(X7,X8,X9,X10)) ) ),
inference(skolemize,[status(esa)],[40]) ).
fof(42,plain,
! [X7,X8,X9,X10] :
( ( in(esk9_4(X7,X8,X9,X10),X8)
| ~ subset(X7,cartesian_product2(X8,X9))
| ~ in(X10,X7) )
& ( in(esk10_4(X7,X8,X9,X10),X9)
| ~ subset(X7,cartesian_product2(X8,X9))
| ~ in(X10,X7) )
& ( X10 = ordered_pair(esk9_4(X7,X8,X9,X10),esk10_4(X7,X8,X9,X10))
| ~ subset(X7,cartesian_product2(X8,X9))
| ~ in(X10,X7) ) ),
inference(distribute,[status(thm)],[41]) ).
cnf(43,plain,
( X1 = ordered_pair(esk9_4(X2,X3,X4,X1),esk10_4(X2,X3,X4,X1))
| ~ in(X1,X2)
| ~ subset(X2,cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[42]) ).
cnf(54,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk1_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk4_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[22,25,theory(equality)]),25,theory(equality)]),
[unfolding] ).
cnf(55,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk4_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk1_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[23,25,theory(equality)]),25,theory(equality)]),
[unfolding] ).
cnf(56,plain,
( unordered_pair(unordered_pair(esk9_4(X2,X3,X4,X1),esk10_4(X2,X3,X4,X1)),singleton(esk9_4(X2,X3,X4,X1))) = X1
| ~ in(X1,X2)
| ~ subset(X2,cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[43,25,theory(equality)]),
[unfolding] ).
cnf(70,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk1_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk4_0) ),
inference(spm,[status(thm)],[54,38,theory(equality)]) ).
cnf(74,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk4_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk1_0) ),
inference(spm,[status(thm)],[55,38,theory(equality)]) ).
cnf(79,plain,
( unordered_pair(singleton(esk9_4(X2,X3,X4,X1)),unordered_pair(esk9_4(X2,X3,X4,X1),esk10_4(X2,X3,X4,X1))) = X1
| ~ in(X1,X2)
| ~ subset(X2,cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[56,38,theory(equality)]) ).
cnf(106,negated_conjecture,
( in(X4,esk1_0)
| ~ in(X4,esk4_0)
| ~ in(X4,X1)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
inference(spm,[status(thm)],[70,79,theory(equality)]) ).
cnf(111,negated_conjecture,
( in(X1,esk1_0)
| ~ in(X1,esk4_0) ),
inference(spm,[status(thm)],[106,20,theory(equality)]) ).
cnf(112,negated_conjecture,
( in(esk7_2(esk4_0,X1),esk1_0)
| esk4_0 = X1
| in(esk7_2(esk4_0,X1),X1) ),
inference(spm,[status(thm)],[111,30,theory(equality)]) ).
cnf(123,negated_conjecture,
( esk4_0 = esk1_0
| in(esk7_2(esk4_0,esk1_0),esk1_0) ),
inference(ef,[status(thm)],[112,theory(equality)]) ).
cnf(129,negated_conjecture,
in(esk7_2(esk4_0,esk1_0),esk1_0),
inference(sr,[status(thm)],[123,19,theory(equality)]) ).
cnf(132,negated_conjecture,
( esk4_0 = esk1_0
| ~ in(esk7_2(esk4_0,esk1_0),esk4_0) ),
inference(spm,[status(thm)],[31,129,theory(equality)]) ).
cnf(133,negated_conjecture,
~ in(esk7_2(esk4_0,esk1_0),esk4_0),
inference(sr,[status(thm)],[132,19,theory(equality)]) ).
cnf(172,negated_conjecture,
( in(X4,esk4_0)
| ~ in(X4,esk1_0)
| ~ in(X4,X1)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
inference(spm,[status(thm)],[74,79,theory(equality)]) ).
cnf(177,negated_conjecture,
( in(X1,esk4_0)
| ~ in(X1,esk1_0) ),
inference(spm,[status(thm)],[172,21,theory(equality)]) ).
cnf(187,negated_conjecture,
~ in(esk7_2(esk4_0,esk1_0),esk1_0),
inference(spm,[status(thm)],[133,177,theory(equality)]) ).
cnf(193,negated_conjecture,
$false,
inference(rw,[status(thm)],[187,129,theory(equality)]) ).
cnf(194,negated_conjecture,
$false,
inference(cn,[status(thm)],[193,theory(equality)]) ).
cnf(195,negated_conjecture,
$false,
194,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET957+1.p
% --creating new selector for []
% -running prover on /tmp/tmp4YWQne/sel_SET957+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET957+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET957+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET957+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
%
%------------------------------------------------------------------------------