TSTP Solution File: SEU186+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU186+2 : TPTP v5.0.0. Released v3.3.0.
% 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 05:17:24 EST 2010
% Result : Theorem 0.52s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 18 unt; 0 def)
% Number of atoms : 114 ( 45 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 128 ( 59 ~; 37 |; 23 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 97 ( 4 sgn 63 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(25,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/tmp/tmpjxhKK_/sel_SEU186+2.p_1',d1_xboole_0) ).
fof(43,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/tmp/tmpjxhKK_/sel_SEU186+2.p_1',t69_enumset1) ).
fof(60,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
file('/tmp/tmpjxhKK_/sel_SEU186+2.p_1',d1_relat_1) ).
fof(85,conjecture,
! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
file('/tmp/tmpjxhKK_/sel_SEU186+2.p_1',t56_relat_1) ).
fof(93,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpjxhKK_/sel_SEU186+2.p_1',commutativity_k2_tarski) ).
fof(115,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpjxhKK_/sel_SEU186+2.p_1',d5_tarski) ).
fof(165,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
inference(assume_negation,[status(cth)],[85]) ).
fof(171,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[25,theory(equality)]) ).
fof(176,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
inference(fof_simplification,[status(thm)],[165,theory(equality)]) ).
fof(285,plain,
! [X1] :
( ( X1 != empty_set
| ! [X2] : ~ in(X2,X1) )
& ( ? [X2] : in(X2,X1)
| X1 = empty_set ) ),
inference(fof_nnf,[status(thm)],[171]) ).
fof(286,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( ? [X5] : in(X5,X3)
| X3 = empty_set ) ),
inference(variable_rename,[status(thm)],[285]) ).
fof(287,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( in(esk10_1(X3),X3)
| X3 = empty_set ) ),
inference(skolemize,[status(esa)],[286]) ).
fof(288,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| X3 != empty_set )
& ( in(esk10_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[287]) ).
cnf(289,plain,
( X1 = empty_set
| in(esk10_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[288]) ).
fof(341,plain,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[43]) ).
cnf(342,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[341]) ).
fof(418,plain,
! [X1] :
( ( ~ relation(X1)
| ! [X2] :
( ~ in(X2,X1)
| ? [X3,X4] : X2 = ordered_pair(X3,X4) ) )
& ( ? [X2] :
( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
| relation(X1) ) ),
inference(fof_nnf,[status(thm)],[60]) ).
fof(419,plain,
! [X5] :
( ( ~ relation(X5)
| ! [X6] :
( ~ in(X6,X5)
| ? [X7,X8] : X6 = ordered_pair(X7,X8) ) )
& ( ? [X9] :
( in(X9,X5)
& ! [X10,X11] : X9 != ordered_pair(X10,X11) )
| relation(X5) ) ),
inference(variable_rename,[status(thm)],[418]) ).
fof(420,plain,
! [X5] :
( ( ~ relation(X5)
| ! [X6] :
( ~ in(X6,X5)
| X6 = ordered_pair(esk20_2(X5,X6),esk21_2(X5,X6)) ) )
& ( ( in(esk22_1(X5),X5)
& ! [X10,X11] : esk22_1(X5) != ordered_pair(X10,X11) )
| relation(X5) ) ),
inference(skolemize,[status(esa)],[419]) ).
fof(421,plain,
! [X5,X6,X10,X11] :
( ( ( esk22_1(X5) != ordered_pair(X10,X11)
& in(esk22_1(X5),X5) )
| relation(X5) )
& ( ~ in(X6,X5)
| X6 = ordered_pair(esk20_2(X5,X6),esk21_2(X5,X6))
| ~ relation(X5) ) ),
inference(shift_quantors,[status(thm)],[420]) ).
fof(422,plain,
! [X5,X6,X10,X11] :
( ( esk22_1(X5) != ordered_pair(X10,X11)
| relation(X5) )
& ( in(esk22_1(X5),X5)
| relation(X5) )
& ( ~ in(X6,X5)
| X6 = ordered_pair(esk20_2(X5,X6),esk21_2(X5,X6))
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[421]) ).
cnf(423,plain,
( X2 = ordered_pair(esk20_2(X1,X2),esk21_2(X1,X2))
| ~ relation(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[422]) ).
fof(521,negated_conjecture,
? [X1] :
( relation(X1)
& ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
& X1 != empty_set ),
inference(fof_nnf,[status(thm)],[176]) ).
fof(522,negated_conjecture,
? [X4] :
( relation(X4)
& ! [X5,X6] : ~ in(ordered_pair(X5,X6),X4)
& X4 != empty_set ),
inference(variable_rename,[status(thm)],[521]) ).
fof(523,negated_conjecture,
( relation(esk27_0)
& ! [X5,X6] : ~ in(ordered_pair(X5,X6),esk27_0)
& esk27_0 != empty_set ),
inference(skolemize,[status(esa)],[522]) ).
fof(524,negated_conjecture,
! [X5,X6] :
( ~ in(ordered_pair(X5,X6),esk27_0)
& esk27_0 != empty_set
& relation(esk27_0) ),
inference(shift_quantors,[status(thm)],[523]) ).
cnf(525,negated_conjecture,
relation(esk27_0),
inference(split_conjunct,[status(thm)],[524]) ).
cnf(526,negated_conjecture,
esk27_0 != empty_set,
inference(split_conjunct,[status(thm)],[524]) ).
cnf(527,negated_conjecture,
~ in(ordered_pair(X1,X2),esk27_0),
inference(split_conjunct,[status(thm)],[524]) ).
fof(552,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[93]) ).
cnf(553,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[552]) ).
fof(627,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[115]) ).
cnf(628,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[627]) ).
cnf(832,plain,
unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[628,342,theory(equality)]),
[unfolding] ).
cnf(886,plain,
( unordered_pair(unordered_pair(esk20_2(X1,X2),esk21_2(X1,X2)),unordered_pair(esk20_2(X1,X2),esk20_2(X1,X2))) = X2
| ~ relation(X1)
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[423,832,theory(equality)]),
[unfolding] ).
cnf(913,negated_conjecture,
~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),esk27_0),
inference(rw,[status(thm)],[527,832,theory(equality)]),
[unfolding] ).
cnf(1013,negated_conjecture,
~ in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X2)),esk27_0),
inference(spm,[status(thm)],[913,553,theory(equality)]) ).
cnf(3208,plain,
( unordered_pair(unordered_pair(esk20_2(X1,X2),esk20_2(X1,X2)),unordered_pair(esk20_2(X1,X2),esk21_2(X1,X2))) = X2
| ~ relation(X1)
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[886,553,theory(equality)]) ).
cnf(5272,negated_conjecture,
( ~ in(X2,esk27_0)
| ~ in(X2,X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[1013,3208,theory(equality)]) ).
cnf(5283,negated_conjecture,
( empty_set = esk27_0
| ~ in(esk10_1(esk27_0),X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[5272,289,theory(equality)]) ).
cnf(5320,negated_conjecture,
( ~ in(esk10_1(esk27_0),X1)
| ~ relation(X1) ),
inference(sr,[status(thm)],[5283,526,theory(equality)]) ).
cnf(5336,negated_conjecture,
( empty_set = esk27_0
| ~ relation(esk27_0) ),
inference(spm,[status(thm)],[5320,289,theory(equality)]) ).
cnf(5342,negated_conjecture,
~ relation(esk27_0),
inference(sr,[status(thm)],[5336,526,theory(equality)]) ).
cnf(5344,negated_conjecture,
$false,
inference(sr,[status(thm)],[525,5342,theory(equality)]) ).
cnf(5345,negated_conjecture,
$false,
5344,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU186+2.p
% --creating new selector for []
% -running prover on /tmp/tmpjxhKK_/sel_SEU186+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU186+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU186+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU186+2.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
%
%------------------------------------------------------------------------------