TSTP Solution File: SEU148+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU148+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 04:52:41 EST 2010
% Result : Theorem 2.36s
% Output : CNFRefutation 2.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 18 unt; 0 def)
% Number of atoms : 137 ( 74 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 150 ( 58 ~; 60 |; 26 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 3 sgn 44 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(9,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/tmp/tmpXkWtL9/sel_SEU148+2.p_1',t69_enumset1) ).
fof(11,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/tmp/tmpXkWtL9/sel_SEU148+2.p_1',l4_zfmisc_1) ).
fof(15,axiom,
! [X1,X2] : subset(X1,X1),
file('/tmp/tmpXkWtL9/sel_SEU148+2.p_1',reflexivity_r1_tarski) ).
fof(24,conjecture,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('/tmp/tmpXkWtL9/sel_SEU148+2.p_1',t6_zfmisc_1) ).
fof(64,axiom,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/tmp/tmpXkWtL9/sel_SEU148+2.p_1',l2_zfmisc_1) ).
fof(66,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpXkWtL9/sel_SEU148+2.p_1',d1_tarski) ).
fof(67,axiom,
! [X1] : singleton(X1) != empty_set,
file('/tmp/tmpXkWtL9/sel_SEU148+2.p_1',l1_zfmisc_1) ).
fof(72,negated_conjecture,
~ ! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[24]) ).
fof(105,plain,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[9]) ).
cnf(106,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[105]) ).
fof(109,plain,
! [X1,X2] :
( ( ~ subset(X1,singleton(X2))
| X1 = empty_set
| X1 = singleton(X2) )
& ( ( X1 != empty_set
& X1 != singleton(X2) )
| subset(X1,singleton(X2)) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(110,plain,
! [X3,X4] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( ( X3 != empty_set
& X3 != singleton(X4) )
| subset(X3,singleton(X4)) ) ),
inference(variable_rename,[status(thm)],[109]) ).
fof(111,plain,
! [X3,X4] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( X3 != empty_set
| subset(X3,singleton(X4)) )
& ( X3 != singleton(X4)
| subset(X3,singleton(X4)) ) ),
inference(distribute,[status(thm)],[110]) ).
cnf(114,plain,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[111]) ).
fof(124,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[15]) ).
cnf(125,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[124]) ).
fof(154,negated_conjecture,
? [X1,X2] :
( subset(singleton(X1),singleton(X2))
& X1 != X2 ),
inference(fof_nnf,[status(thm)],[72]) ).
fof(155,negated_conjecture,
? [X3,X4] :
( subset(singleton(X3),singleton(X4))
& X3 != X4 ),
inference(variable_rename,[status(thm)],[154]) ).
fof(156,negated_conjecture,
( subset(singleton(esk4_0),singleton(esk5_0))
& esk4_0 != esk5_0 ),
inference(skolemize,[status(esa)],[155]) ).
cnf(157,negated_conjecture,
esk4_0 != esk5_0,
inference(split_conjunct,[status(thm)],[156]) ).
cnf(158,negated_conjecture,
subset(singleton(esk4_0),singleton(esk5_0)),
inference(split_conjunct,[status(thm)],[156]) ).
fof(288,plain,
! [X1,X2] :
( ( ~ subset(singleton(X1),X2)
| in(X1,X2) )
& ( ~ in(X1,X2)
| subset(singleton(X1),X2) ) ),
inference(fof_nnf,[status(thm)],[64]) ).
fof(289,plain,
! [X3,X4] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X3,X4)
| subset(singleton(X3),X4) ) ),
inference(variable_rename,[status(thm)],[288]) ).
cnf(291,plain,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[289]) ).
fof(294,plain,
! [X1,X2] :
( ( X2 != singleton(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1 )
& ( X3 != X1
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| X3 != X1 )
& ( in(X3,X2)
| X3 = X1 ) )
| X2 = singleton(X1) ) ),
inference(fof_nnf,[status(thm)],[66]) ).
fof(295,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| X7 != X4 )
& ( in(X7,X5)
| X7 = X4 ) )
| X5 = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[294]) ).
fof(296,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk12_2(X4,X5),X5)
| esk12_2(X4,X5) != X4 )
& ( in(esk12_2(X4,X5),X5)
| esk12_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[295]) ).
fof(297,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk12_2(X4,X5),X5)
| esk12_2(X4,X5) != X4 )
& ( in(esk12_2(X4,X5),X5)
| esk12_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[296]) ).
fof(298,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk12_2(X4,X5),X5)
| esk12_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk12_2(X4,X5),X5)
| esk12_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[297]) ).
cnf(302,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[298]) ).
fof(303,plain,
! [X2] : singleton(X2) != empty_set,
inference(variable_rename,[status(thm)],[67]) ).
cnf(304,plain,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[303]) ).
cnf(338,negated_conjecture,
subset(unordered_pair(esk4_0,esk4_0),unordered_pair(esk5_0,esk5_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[158,106,theory(equality)]),106,theory(equality)]),
[unfolding] ).
cnf(342,plain,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[291,106,theory(equality)]),
[unfolding] ).
cnf(344,plain,
( empty_set = X1
| unordered_pair(X2,X2) = X1
| ~ subset(X1,unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[114,106,theory(equality)]),106,theory(equality)]),
[unfolding] ).
cnf(346,plain,
( X2 = X3
| unordered_pair(X2,X2) != X1
| ~ in(X3,X1) ),
inference(rw,[status(thm)],[302,106,theory(equality)]),
[unfolding] ).
cnf(349,plain,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[304,106,theory(equality)]),
[unfolding] ).
cnf(563,negated_conjecture,
( unordered_pair(esk5_0,esk5_0) = unordered_pair(esk4_0,esk4_0)
| empty_set = unordered_pair(esk4_0,esk4_0) ),
inference(spm,[status(thm)],[344,338,theory(equality)]) ).
cnf(569,negated_conjecture,
unordered_pair(esk5_0,esk5_0) = unordered_pair(esk4_0,esk4_0),
inference(sr,[status(thm)],[563,349,theory(equality)]) ).
cnf(914,plain,
( X1 = X2
| ~ in(X2,unordered_pair(X1,X1)) ),
inference(er,[status(thm)],[346,theory(equality)]) ).
cnf(1305,negated_conjecture,
( in(esk5_0,X1)
| ~ subset(unordered_pair(esk4_0,esk4_0),X1) ),
inference(spm,[status(thm)],[342,569,theory(equality)]) ).
cnf(1464,negated_conjecture,
in(esk5_0,unordered_pair(esk4_0,esk4_0)),
inference(spm,[status(thm)],[1305,125,theory(equality)]) ).
cnf(36017,negated_conjecture,
esk4_0 = esk5_0,
inference(spm,[status(thm)],[914,1464,theory(equality)]) ).
cnf(36095,negated_conjecture,
$false,
inference(sr,[status(thm)],[36017,157,theory(equality)]) ).
cnf(36096,negated_conjecture,
$false,
36095,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU148+2.p
% --creating new selector for []
% -running prover on /tmp/tmpXkWtL9/sel_SEU148+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU148+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU148+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU148+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
%
%------------------------------------------------------------------------------