%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU255+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 06:21:00 EST 2010
% Result : Theorem 0.51s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 11 unt; 0 def)
% Number of atoms : 197 ( 24 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 239 ( 95 ~; 105 |; 29 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 99 ( 3 sgn 48 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpXULTW7/sel_SEU255+1.p_1',commutativity_k2_tarski) ).
fof(5,axiom,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X3,X2),X1) )
=> X2 = X3 ) ) ),
file('/tmp/tmpXULTW7/sel_SEU255+1.p_1',l3_wellord1) ).
fof(8,axiom,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
file('/tmp/tmpXULTW7/sel_SEU255+1.p_1',t16_wellord1) ).
fof(22,conjecture,
! [X1,X2] :
( relation(X2)
=> ( antisymmetric(X2)
=> antisymmetric(relation_restriction(X2,X1)) ) ),
file('/tmp/tmpXULTW7/sel_SEU255+1.p_1',t25_wellord1) ).
fof(24,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_restriction(X1,X2)) ),
file('/tmp/tmpXULTW7/sel_SEU255+1.p_1',dt_k2_wellord1) ).
fof(28,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpXULTW7/sel_SEU255+1.p_1',d5_tarski) ).
fof(34,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> ( antisymmetric(X2)
=> antisymmetric(relation_restriction(X2,X1)) ) ),
inference(assume_negation,[status(cth)],[22]) ).
fof(40,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[2]) ).
cnf(41,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[40]) ).
fof(49,plain,
! [X1] :
( ~ relation(X1)
| ( ( ~ antisymmetric(X1)
| ! [X2,X3] :
( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X1)
| X2 = X3 ) )
& ( ? [X2,X3] :
( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X3,X2),X1)
& X2 != X3 )
| antisymmetric(X1) ) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(50,plain,
! [X4] :
( ~ relation(X4)
| ( ( ~ antisymmetric(X4)
| ! [X5,X6] :
( ~ in(ordered_pair(X5,X6),X4)
| ~ in(ordered_pair(X6,X5),X4)
| X5 = X6 ) )
& ( ? [X7,X8] :
( in(ordered_pair(X7,X8),X4)
& in(ordered_pair(X8,X7),X4)
& X7 != X8 )
| antisymmetric(X4) ) ) ),
inference(variable_rename,[status(thm)],[49]) ).
fof(51,plain,
! [X4] :
( ~ relation(X4)
| ( ( ~ antisymmetric(X4)
| ! [X5,X6] :
( ~ in(ordered_pair(X5,X6),X4)
| ~ in(ordered_pair(X6,X5),X4)
| X5 = X6 ) )
& ( ( in(ordered_pair(esk2_1(X4),esk3_1(X4)),X4)
& in(ordered_pair(esk3_1(X4),esk2_1(X4)),X4)
& esk2_1(X4) != esk3_1(X4) )
| antisymmetric(X4) ) ) ),
inference(skolemize,[status(esa)],[50]) ).
fof(52,plain,
! [X4,X5,X6] :
( ( ( ~ in(ordered_pair(X5,X6),X4)
| ~ in(ordered_pair(X6,X5),X4)
| X5 = X6
| ~ antisymmetric(X4) )
& ( ( in(ordered_pair(esk2_1(X4),esk3_1(X4)),X4)
& in(ordered_pair(esk3_1(X4),esk2_1(X4)),X4)
& esk2_1(X4) != esk3_1(X4) )
| antisymmetric(X4) ) )
| ~ relation(X4) ),
inference(shift_quantors,[status(thm)],[51]) ).
fof(53,plain,
! [X4,X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X4)
| ~ in(ordered_pair(X6,X5),X4)
| X5 = X6
| ~ antisymmetric(X4)
| ~ relation(X4) )
& ( in(ordered_pair(esk2_1(X4),esk3_1(X4)),X4)
| antisymmetric(X4)
| ~ relation(X4) )
& ( in(ordered_pair(esk3_1(X4),esk2_1(X4)),X4)
| antisymmetric(X4)
| ~ relation(X4) )
& ( esk2_1(X4) != esk3_1(X4)
| antisymmetric(X4)
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[52]) ).
cnf(54,plain,
( antisymmetric(X1)
| ~ relation(X1)
| esk2_1(X1) != esk3_1(X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(55,plain,
( antisymmetric(X1)
| in(ordered_pair(esk3_1(X1),esk2_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(56,plain,
( antisymmetric(X1)
| in(ordered_pair(esk2_1(X1),esk3_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(57,plain,
( X2 = X3
| ~ relation(X1)
| ~ antisymmetric(X1)
| ~ in(ordered_pair(X3,X2),X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
fof(65,plain,
! [X1,X2,X3] :
( ~ relation(X3)
| ( ( ~ in(X1,relation_restriction(X3,X2))
| ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) )
& ( ~ in(X1,X3)
| ~ in(X1,cartesian_product2(X2,X2))
| in(X1,relation_restriction(X3,X2)) ) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(66,plain,
! [X4,X5,X6] :
( ~ relation(X6)
| ( ( ~ in(X4,relation_restriction(X6,X5))
| ( in(X4,X6)
& in(X4,cartesian_product2(X5,X5)) ) )
& ( ~ in(X4,X6)
| ~ in(X4,cartesian_product2(X5,X5))
| in(X4,relation_restriction(X6,X5)) ) ) ),
inference(variable_rename,[status(thm)],[65]) ).
fof(67,plain,
! [X4,X5,X6] :
( ( in(X4,X6)
| ~ in(X4,relation_restriction(X6,X5))
| ~ relation(X6) )
& ( in(X4,cartesian_product2(X5,X5))
| ~ in(X4,relation_restriction(X6,X5))
| ~ relation(X6) )
& ( ~ in(X4,X6)
| ~ in(X4,cartesian_product2(X5,X5))
| in(X4,relation_restriction(X6,X5))
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[66]) ).
cnf(70,plain,
( in(X2,X1)
| ~ relation(X1)
| ~ in(X2,relation_restriction(X1,X3)) ),
inference(split_conjunct,[status(thm)],[67]) ).
fof(102,negated_conjecture,
? [X1,X2] :
( relation(X2)
& antisymmetric(X2)
& ~ antisymmetric(relation_restriction(X2,X1)) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(103,negated_conjecture,
? [X3,X4] :
( relation(X4)
& antisymmetric(X4)
& ~ antisymmetric(relation_restriction(X4,X3)) ),
inference(variable_rename,[status(thm)],[102]) ).
fof(104,negated_conjecture,
( relation(esk7_0)
& antisymmetric(esk7_0)
& ~ antisymmetric(relation_restriction(esk7_0,esk6_0)) ),
inference(skolemize,[status(esa)],[103]) ).
cnf(105,negated_conjecture,
~ antisymmetric(relation_restriction(esk7_0,esk6_0)),
inference(split_conjunct,[status(thm)],[104]) ).
cnf(106,negated_conjecture,
antisymmetric(esk7_0),
inference(split_conjunct,[status(thm)],[104]) ).
cnf(107,negated_conjecture,
relation(esk7_0),
inference(split_conjunct,[status(thm)],[104]) ).
fof(110,plain,
! [X1,X2] :
( ~ relation(X1)
| relation(relation_restriction(X1,X2)) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(111,plain,
! [X3,X4] :
( ~ relation(X3)
| relation(relation_restriction(X3,X4)) ),
inference(variable_rename,[status(thm)],[110]) ).
cnf(112,plain,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[111]) ).
fof(117,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[28]) ).
cnf(118,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[117]) ).
cnf(136,plain,
( antisymmetric(X1)
| in(unordered_pair(unordered_pair(esk2_1(X1),esk3_1(X1)),singleton(esk2_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[56,118,theory(equality)]),
[unfolding] ).
cnf(137,plain,
( antisymmetric(X1)
| in(unordered_pair(unordered_pair(esk3_1(X1),esk2_1(X1)),singleton(esk3_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[55,118,theory(equality)]),
[unfolding] ).
cnf(138,plain,
( X2 = X3
| ~ relation(X1)
| ~ antisymmetric(X1)
| ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[57,118,theory(equality)]),118,theory(equality)]),
[unfolding] ).
cnf(161,plain,
( antisymmetric(X1)
| in(unordered_pair(singleton(esk2_1(X1)),unordered_pair(esk2_1(X1),esk3_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[136,41,theory(equality)]) ).
cnf(164,plain,
( in(unordered_pair(singleton(esk2_1(relation_restriction(X1,X2))),unordered_pair(esk2_1(relation_restriction(X1,X2)),esk3_1(relation_restriction(X1,X2)))),X1)
| antisymmetric(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ relation(relation_restriction(X1,X2)) ),
inference(spm,[status(thm)],[70,161,theory(equality)]) ).
cnf(167,plain,
( antisymmetric(X1)
| in(unordered_pair(singleton(esk3_1(X1)),unordered_pair(esk2_1(X1),esk3_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[137,41,theory(equality)]),41,theory(equality)]) ).
cnf(170,plain,
( in(unordered_pair(singleton(esk3_1(relation_restriction(X1,X2))),unordered_pair(esk2_1(relation_restriction(X1,X2)),esk3_1(relation_restriction(X1,X2)))),X1)
| antisymmetric(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ relation(relation_restriction(X1,X2)) ),
inference(spm,[status(thm)],[70,167,theory(equality)]) ).
cnf(174,plain,
( X1 = X2
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ antisymmetric(X3)
| ~ relation(X3) ),
inference(spm,[status(thm)],[138,41,theory(equality)]) ).
cnf(234,plain,
( in(unordered_pair(singleton(esk2_1(relation_restriction(X1,X2))),unordered_pair(esk2_1(relation_restriction(X1,X2)),esk3_1(relation_restriction(X1,X2)))),X1)
| antisymmetric(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(csr,[status(thm)],[164,112]) ).
cnf(406,plain,
( in(unordered_pair(singleton(esk3_1(relation_restriction(X1,X2))),unordered_pair(esk2_1(relation_restriction(X1,X2)),esk3_1(relation_restriction(X1,X2)))),X1)
| antisymmetric(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(csr,[status(thm)],[170,112]) ).
cnf(557,plain,
( esk3_1(relation_restriction(X1,X2)) = esk2_1(relation_restriction(X1,X2))
| antisymmetric(relation_restriction(X1,X2))
| ~ in(unordered_pair(unordered_pair(esk3_1(relation_restriction(X1,X2)),esk2_1(relation_restriction(X1,X2))),singleton(esk3_1(relation_restriction(X1,X2)))),X1)
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[174,234,theory(equality)]) ).
cnf(561,plain,
( esk3_1(relation_restriction(X1,X2)) = esk2_1(relation_restriction(X1,X2))
| antisymmetric(relation_restriction(X1,X2))
| ~ in(unordered_pair(singleton(esk3_1(relation_restriction(X1,X2))),unordered_pair(esk2_1(relation_restriction(X1,X2)),esk3_1(relation_restriction(X1,X2)))),X1)
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[557,41,theory(equality)]),41,theory(equality)]) ).
cnf(5202,plain,
( esk3_1(relation_restriction(X1,X2)) = esk2_1(relation_restriction(X1,X2))
| antisymmetric(relation_restriction(X1,X2))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[561,406]) ).
cnf(5204,plain,
( antisymmetric(relation_restriction(X1,X2))
| ~ relation(relation_restriction(X1,X2))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[54,5202,theory(equality)]) ).
cnf(5254,plain,
( antisymmetric(relation_restriction(X1,X2))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[5204,112]) ).
cnf(5256,negated_conjecture,
( ~ antisymmetric(esk7_0)
| ~ relation(esk7_0) ),
inference(spm,[status(thm)],[105,5254,theory(equality)]) ).
cnf(5281,negated_conjecture,
( $false
| ~ relation(esk7_0) ),
inference(rw,[status(thm)],[5256,106,theory(equality)]) ).
cnf(5282,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[5281,107,theory(equality)]) ).
cnf(5283,negated_conjecture,
$false,
inference(cn,[status(thm)],[5282,theory(equality)]) ).
cnf(5284,negated_conjecture,
$false,
5283,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU255+1.p
% --creating new selector for []
% -running prover on /tmp/tmpXULTW7/sel_SEU255+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU255+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU255+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU255+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
%
%------------------------------------------------------------------------------