TSTP Solution File: SEU186+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU186+1 : 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 05:17:05 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 19 unt; 0 def)
% Number of atoms : 113 ( 33 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 118 ( 52 ~; 38 |; 19 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 95 ( 4 sgn 61 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,conjecture,
! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
file('/tmp/tmpUM9HV5/sel_SEU186+1.p_1',t56_relat_1) ).
fof(8,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpUM9HV5/sel_SEU186+1.p_1',commutativity_k2_tarski) ).
fof(14,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
file('/tmp/tmpUM9HV5/sel_SEU186+1.p_1',d1_relat_1) ).
fof(15,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/tmp/tmpUM9HV5/sel_SEU186+1.p_1',t2_subset) ).
fof(21,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpUM9HV5/sel_SEU186+1.p_1',d5_tarski) ).
fof(22,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/tmp/tmpUM9HV5/sel_SEU186+1.p_1',t6_boole) ).
fof(23,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/tmp/tmpUM9HV5/sel_SEU186+1.p_1',existence_m1_subset_1) ).
fof(27,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(29,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
inference(fof_simplification,[status(thm)],[27,theory(equality)]) ).
fof(45,negated_conjecture,
? [X1] :
( relation(X1)
& ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
& X1 != empty_set ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(46,negated_conjecture,
? [X4] :
( relation(X4)
& ! [X5,X6] : ~ in(ordered_pair(X5,X6),X4)
& X4 != empty_set ),
inference(variable_rename,[status(thm)],[45]) ).
fof(47,negated_conjecture,
( relation(esk3_0)
& ! [X5,X6] : ~ in(ordered_pair(X5,X6),esk3_0)
& esk3_0 != empty_set ),
inference(skolemize,[status(esa)],[46]) ).
fof(48,negated_conjecture,
! [X5,X6] :
( ~ in(ordered_pair(X5,X6),esk3_0)
& esk3_0 != empty_set
& relation(esk3_0) ),
inference(shift_quantors,[status(thm)],[47]) ).
cnf(49,negated_conjecture,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(50,negated_conjecture,
esk3_0 != empty_set,
inference(split_conjunct,[status(thm)],[48]) ).
cnf(51,negated_conjecture,
~ in(ordered_pair(X1,X2),esk3_0),
inference(split_conjunct,[status(thm)],[48]) ).
fof(59,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[8]) ).
cnf(60,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[59]) ).
fof(74,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)],[14]) ).
fof(75,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)],[74]) ).
fof(76,plain,
! [X5] :
( ( ~ relation(X5)
| ! [X6] :
( ~ in(X6,X5)
| X6 = ordered_pair(esk5_2(X5,X6),esk6_2(X5,X6)) ) )
& ( ( in(esk7_1(X5),X5)
& ! [X10,X11] : esk7_1(X5) != ordered_pair(X10,X11) )
| relation(X5) ) ),
inference(skolemize,[status(esa)],[75]) ).
fof(77,plain,
! [X5,X6,X10,X11] :
( ( ( esk7_1(X5) != ordered_pair(X10,X11)
& in(esk7_1(X5),X5) )
| relation(X5) )
& ( ~ in(X6,X5)
| X6 = ordered_pair(esk5_2(X5,X6),esk6_2(X5,X6))
| ~ relation(X5) ) ),
inference(shift_quantors,[status(thm)],[76]) ).
fof(78,plain,
! [X5,X6,X10,X11] :
( ( esk7_1(X5) != ordered_pair(X10,X11)
| relation(X5) )
& ( in(esk7_1(X5),X5)
| relation(X5) )
& ( ~ in(X6,X5)
| X6 = ordered_pair(esk5_2(X5,X6),esk6_2(X5,X6))
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[77]) ).
cnf(79,plain,
( X2 = ordered_pair(esk5_2(X1,X2),esk6_2(X1,X2))
| ~ relation(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[78]) ).
fof(82,plain,
! [X1,X2] :
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(83,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[82]) ).
cnf(84,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[83]) ).
fof(91,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[21]) ).
cnf(92,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[91]) ).
fof(93,plain,
! [X1] :
( ~ empty(X1)
| X1 = empty_set ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(94,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[93]) ).
cnf(95,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[94]) ).
fof(96,plain,
! [X3] :
? [X4] : element(X4,X3),
inference(variable_rename,[status(thm)],[23]) ).
fof(97,plain,
! [X3] : element(esk8_1(X3),X3),
inference(skolemize,[status(esa)],[96]) ).
cnf(98,plain,
element(esk8_1(X1),X1),
inference(split_conjunct,[status(thm)],[97]) ).
cnf(107,plain,
( unordered_pair(unordered_pair(esk5_2(X1,X2),esk6_2(X1,X2)),singleton(esk5_2(X1,X2))) = X2
| ~ relation(X1)
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[79,92,theory(equality)]),
[unfolding] ).
cnf(109,negated_conjecture,
~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk3_0),
inference(rw,[status(thm)],[51,92,theory(equality)]),
[unfolding] ).
cnf(124,plain,
( in(esk8_1(X1),X1)
| empty(X1) ),
inference(spm,[status(thm)],[84,98,theory(equality)]) ).
cnf(126,plain,
( unordered_pair(singleton(esk5_2(X1,X2)),unordered_pair(esk5_2(X1,X2),esk6_2(X1,X2))) = X2
| ~ relation(X1)
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[107,60,theory(equality)]) ).
cnf(130,negated_conjecture,
~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk3_0),
inference(spm,[status(thm)],[109,60,theory(equality)]) ).
cnf(159,negated_conjecture,
( ~ in(X2,esk3_0)
| ~ in(X2,X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[130,126,theory(equality)]) ).
cnf(171,negated_conjecture,
( empty(esk3_0)
| ~ in(esk8_1(esk3_0),X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[159,124,theory(equality)]) ).
cnf(173,negated_conjecture,
( empty(esk3_0)
| ~ relation(esk3_0) ),
inference(spm,[status(thm)],[171,124,theory(equality)]) ).
cnf(174,negated_conjecture,
empty(esk3_0),
inference(spm,[status(thm)],[173,49,theory(equality)]) ).
cnf(176,negated_conjecture,
empty_set = esk3_0,
inference(spm,[status(thm)],[95,174,theory(equality)]) ).
cnf(180,negated_conjecture,
$false,
inference(sr,[status(thm)],[176,50,theory(equality)]) ).
cnf(181,negated_conjecture,
$false,
180,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU186+1.p
% --creating new selector for []
% -running prover on /tmp/tmpUM9HV5/sel_SEU186+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU186+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU186+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU186+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
%
%------------------------------------------------------------------------------