TSTP Solution File: SEU239+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU239+1 : TPTP v5.0.0. Released v3.3.0.
% 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 06:15:03 EST 2010
% Result : Theorem 0.21s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 12 unt; 0 def)
% Number of atoms : 191 ( 6 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 228 ( 92 ~; 97 |; 28 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 39 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmp7nZtcr/sel_SEU239+1.p_1',commutativity_k2_tarski) ).
fof(13,conjecture,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> ! [X2] :
( in(X2,relation_field(X1))
=> in(ordered_pair(X2,X2),X1) ) ) ),
file('/tmp/tmp7nZtcr/sel_SEU239+1.p_1',l1_wellord1) ).
fof(18,axiom,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> is_reflexive_in(X1,relation_field(X1)) ) ),
file('/tmp/tmp7nZtcr/sel_SEU239+1.p_1',d9_relat_2) ).
fof(20,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_reflexive_in(X1,X2)
<=> ! [X3] :
( in(X3,X2)
=> in(ordered_pair(X3,X3),X1) ) ) ),
file('/tmp/tmp7nZtcr/sel_SEU239+1.p_1',d1_relat_2) ).
fof(28,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmp7nZtcr/sel_SEU239+1.p_1',d5_tarski) ).
fof(37,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> ! [X2] :
( in(X2,relation_field(X1))
=> in(ordered_pair(X2,X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[13]) ).
fof(45,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[2]) ).
cnf(46,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[45]) ).
fof(77,negated_conjecture,
? [X1] :
( relation(X1)
& ( ~ reflexive(X1)
| ? [X2] :
( in(X2,relation_field(X1))
& ~ in(ordered_pair(X2,X2),X1) ) )
& ( reflexive(X1)
| ! [X2] :
( ~ in(X2,relation_field(X1))
| in(ordered_pair(X2,X2),X1) ) ) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(78,negated_conjecture,
? [X3] :
( relation(X3)
& ( ~ reflexive(X3)
| ? [X4] :
( in(X4,relation_field(X3))
& ~ in(ordered_pair(X4,X4),X3) ) )
& ( reflexive(X3)
| ! [X5] :
( ~ in(X5,relation_field(X3))
| in(ordered_pair(X5,X5),X3) ) ) ),
inference(variable_rename,[status(thm)],[77]) ).
fof(79,negated_conjecture,
( relation(esk4_0)
& ( ~ reflexive(esk4_0)
| ( in(esk5_0,relation_field(esk4_0))
& ~ in(ordered_pair(esk5_0,esk5_0),esk4_0) ) )
& ( reflexive(esk4_0)
| ! [X5] :
( ~ in(X5,relation_field(esk4_0))
| in(ordered_pair(X5,X5),esk4_0) ) ) ),
inference(skolemize,[status(esa)],[78]) ).
fof(80,negated_conjecture,
! [X5] :
( ( ~ in(X5,relation_field(esk4_0))
| in(ordered_pair(X5,X5),esk4_0)
| reflexive(esk4_0) )
& ( ~ reflexive(esk4_0)
| ( in(esk5_0,relation_field(esk4_0))
& ~ in(ordered_pair(esk5_0,esk5_0),esk4_0) ) )
& relation(esk4_0) ),
inference(shift_quantors,[status(thm)],[79]) ).
fof(81,negated_conjecture,
! [X5] :
( ( ~ in(X5,relation_field(esk4_0))
| in(ordered_pair(X5,X5),esk4_0)
| reflexive(esk4_0) )
& ( in(esk5_0,relation_field(esk4_0))
| ~ reflexive(esk4_0) )
& ( ~ in(ordered_pair(esk5_0,esk5_0),esk4_0)
| ~ reflexive(esk4_0) )
& relation(esk4_0) ),
inference(distribute,[status(thm)],[80]) ).
cnf(82,negated_conjecture,
relation(esk4_0),
inference(split_conjunct,[status(thm)],[81]) ).
cnf(83,negated_conjecture,
( ~ reflexive(esk4_0)
| ~ in(ordered_pair(esk5_0,esk5_0),esk4_0) ),
inference(split_conjunct,[status(thm)],[81]) ).
cnf(84,negated_conjecture,
( in(esk5_0,relation_field(esk4_0))
| ~ reflexive(esk4_0) ),
inference(split_conjunct,[status(thm)],[81]) ).
cnf(85,negated_conjecture,
( reflexive(esk4_0)
| in(ordered_pair(X1,X1),esk4_0)
| ~ in(X1,relation_field(esk4_0)) ),
inference(split_conjunct,[status(thm)],[81]) ).
fof(97,plain,
! [X1] :
( ~ relation(X1)
| ( ( ~ reflexive(X1)
| is_reflexive_in(X1,relation_field(X1)) )
& ( ~ is_reflexive_in(X1,relation_field(X1))
| reflexive(X1) ) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(98,plain,
! [X2] :
( ~ relation(X2)
| ( ( ~ reflexive(X2)
| is_reflexive_in(X2,relation_field(X2)) )
& ( ~ is_reflexive_in(X2,relation_field(X2))
| reflexive(X2) ) ) ),
inference(variable_rename,[status(thm)],[97]) ).
fof(99,plain,
! [X2] :
( ( ~ reflexive(X2)
| is_reflexive_in(X2,relation_field(X2))
| ~ relation(X2) )
& ( ~ is_reflexive_in(X2,relation_field(X2))
| reflexive(X2)
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[98]) ).
cnf(100,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ is_reflexive_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[99]) ).
cnf(101,plain,
( is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ reflexive(X1) ),
inference(split_conjunct,[status(thm)],[99]) ).
fof(103,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ( ~ is_reflexive_in(X1,X2)
| ! [X3] :
( ~ in(X3,X2)
| in(ordered_pair(X3,X3),X1) ) )
& ( ? [X3] :
( in(X3,X2)
& ~ in(ordered_pair(X3,X3),X1) )
| is_reflexive_in(X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(104,plain,
! [X4] :
( ~ relation(X4)
| ! [X5] :
( ( ~ is_reflexive_in(X4,X5)
| ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X6,X6),X4) ) )
& ( ? [X7] :
( in(X7,X5)
& ~ in(ordered_pair(X7,X7),X4) )
| is_reflexive_in(X4,X5) ) ) ),
inference(variable_rename,[status(thm)],[103]) ).
fof(105,plain,
! [X4] :
( ~ relation(X4)
| ! [X5] :
( ( ~ is_reflexive_in(X4,X5)
| ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X6,X6),X4) ) )
& ( ( in(esk6_2(X4,X5),X5)
& ~ in(ordered_pair(esk6_2(X4,X5),esk6_2(X4,X5)),X4) )
| is_reflexive_in(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[104]) ).
fof(106,plain,
! [X4,X5,X6] :
( ( ( ~ in(X6,X5)
| in(ordered_pair(X6,X6),X4)
| ~ is_reflexive_in(X4,X5) )
& ( ( in(esk6_2(X4,X5),X5)
& ~ in(ordered_pair(esk6_2(X4,X5),esk6_2(X4,X5)),X4) )
| is_reflexive_in(X4,X5) ) )
| ~ relation(X4) ),
inference(shift_quantors,[status(thm)],[105]) ).
fof(107,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| in(ordered_pair(X6,X6),X4)
| ~ is_reflexive_in(X4,X5)
| ~ relation(X4) )
& ( in(esk6_2(X4,X5),X5)
| is_reflexive_in(X4,X5)
| ~ relation(X4) )
& ( ~ in(ordered_pair(esk6_2(X4,X5),esk6_2(X4,X5)),X4)
| is_reflexive_in(X4,X5)
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[106]) ).
cnf(108,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk6_2(X1,X2),esk6_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[107]) ).
cnf(109,plain,
( is_reflexive_in(X1,X2)
| in(esk6_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[107]) ).
cnf(110,plain,
( in(ordered_pair(X3,X3),X1)
| ~ relation(X1)
| ~ is_reflexive_in(X1,X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[107]) ).
fof(123,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[28]) ).
cnf(124,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[123]) ).
cnf(146,negated_conjecture,
( reflexive(esk4_0)
| in(unordered_pair(unordered_pair(X1,X1),singleton(X1)),esk4_0)
| ~ in(X1,relation_field(esk4_0)) ),
inference(rw,[status(thm)],[85,124,theory(equality)]),
[unfolding] ).
cnf(147,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk6_2(X1,X2),esk6_2(X1,X2)),singleton(esk6_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[108,124,theory(equality)]),
[unfolding] ).
cnf(148,plain,
( in(unordered_pair(unordered_pair(X3,X3),singleton(X3)),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ is_reflexive_in(X1,X2) ),
inference(rw,[status(thm)],[110,124,theory(equality)]),
[unfolding] ).
cnf(150,negated_conjecture,
( ~ reflexive(esk4_0)
| ~ in(unordered_pair(unordered_pair(esk5_0,esk5_0),singleton(esk5_0)),esk4_0) ),
inference(rw,[status(thm)],[83,124,theory(equality)]),
[unfolding] ).
cnf(157,negated_conjecture,
( reflexive(esk4_0)
| in(unordered_pair(singleton(X1),unordered_pair(X1,X1)),esk4_0)
| ~ in(X1,relation_field(esk4_0)) ),
inference(spm,[status(thm)],[146,46,theory(equality)]) ).
cnf(194,plain,
( in(unordered_pair(unordered_pair(X1,X1),singleton(X1)),X2)
| ~ in(X1,relation_field(X2))
| ~ relation(X2)
| ~ reflexive(X2) ),
inference(spm,[status(thm)],[148,101,theory(equality)]) ).
cnf(195,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(singleton(esk6_2(X1,X2)),unordered_pair(esk6_2(X1,X2),esk6_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[147,46,theory(equality)]) ).
cnf(230,negated_conjecture,
( is_reflexive_in(esk4_0,X1)
| reflexive(esk4_0)
| ~ relation(esk4_0)
| ~ in(esk6_2(esk4_0,X1),relation_field(esk4_0)) ),
inference(spm,[status(thm)],[195,157,theory(equality)]) ).
cnf(231,negated_conjecture,
( is_reflexive_in(esk4_0,X1)
| reflexive(esk4_0)
| $false
| ~ in(esk6_2(esk4_0,X1),relation_field(esk4_0)) ),
inference(rw,[status(thm)],[230,82,theory(equality)]) ).
cnf(232,negated_conjecture,
( is_reflexive_in(esk4_0,X1)
| reflexive(esk4_0)
| ~ in(esk6_2(esk4_0,X1),relation_field(esk4_0)) ),
inference(cn,[status(thm)],[231,theory(equality)]) ).
cnf(268,negated_conjecture,
( ~ reflexive(esk4_0)
| ~ in(esk5_0,relation_field(esk4_0))
| ~ relation(esk4_0) ),
inference(spm,[status(thm)],[150,194,theory(equality)]) ).
cnf(271,negated_conjecture,
( ~ reflexive(esk4_0)
| ~ in(esk5_0,relation_field(esk4_0))
| $false ),
inference(rw,[status(thm)],[268,82,theory(equality)]) ).
cnf(272,negated_conjecture,
( ~ reflexive(esk4_0)
| ~ in(esk5_0,relation_field(esk4_0)) ),
inference(cn,[status(thm)],[271,theory(equality)]) ).
cnf(274,negated_conjecture,
~ reflexive(esk4_0),
inference(csr,[status(thm)],[272,84]) ).
cnf(330,negated_conjecture,
( is_reflexive_in(esk4_0,X1)
| ~ in(esk6_2(esk4_0,X1),relation_field(esk4_0)) ),
inference(sr,[status(thm)],[232,274,theory(equality)]) ).
cnf(331,negated_conjecture,
( is_reflexive_in(esk4_0,relation_field(esk4_0))
| ~ relation(esk4_0) ),
inference(spm,[status(thm)],[330,109,theory(equality)]) ).
cnf(332,negated_conjecture,
( is_reflexive_in(esk4_0,relation_field(esk4_0))
| $false ),
inference(rw,[status(thm)],[331,82,theory(equality)]) ).
cnf(333,negated_conjecture,
is_reflexive_in(esk4_0,relation_field(esk4_0)),
inference(cn,[status(thm)],[332,theory(equality)]) ).
cnf(334,negated_conjecture,
( reflexive(esk4_0)
| ~ relation(esk4_0) ),
inference(spm,[status(thm)],[100,333,theory(equality)]) ).
cnf(336,negated_conjecture,
( reflexive(esk4_0)
| $false ),
inference(rw,[status(thm)],[334,82,theory(equality)]) ).
cnf(337,negated_conjecture,
reflexive(esk4_0),
inference(cn,[status(thm)],[336,theory(equality)]) ).
cnf(338,negated_conjecture,
$false,
inference(sr,[status(thm)],[337,274,theory(equality)]) ).
cnf(339,negated_conjecture,
$false,
338,
[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/SEU/SEU239+1.p
% --creating new selector for []
% -running prover on /tmp/tmp7nZtcr/sel_SEU239+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU239+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU239+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU239+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
%
%------------------------------------------------------------------------------