TSTP Solution File: SEU154+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU154+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 04:54:11 EST 2010
% Result : Theorem 79.87s
% Output : CNFRefutation 79.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 26 unt; 0 def)
% Number of atoms : 96 ( 41 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 83 ( 36 ~; 28 |; 13 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 1 sgn 42 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(10,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',t69_enumset1) ).
fof(11,axiom,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',t36_xboole_1) ).
fof(12,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',l4_zfmisc_1) ).
fof(21,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',t3_boole) ).
fof(47,axiom,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',t48_xboole_1) ).
fof(51,conjecture,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',l28_zfmisc_1) ).
fof(55,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',commutativity_k3_xboole_0) ).
fof(69,axiom,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',l2_zfmisc_1) ).
fof(76,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',t83_xboole_1) ).
fof(78,negated_conjecture,
~ ! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(assume_negation,[status(cth)],[51]) ).
fof(86,negated_conjecture,
~ ! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[78,theory(equality)]) ).
fof(120,plain,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[10]) ).
cnf(121,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[120]) ).
fof(122,plain,
! [X3,X4] : subset(set_difference(X3,X4),X3),
inference(variable_rename,[status(thm)],[11]) ).
cnf(123,plain,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[122]) ).
fof(124,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)],[12]) ).
fof(125,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)],[124]) ).
fof(126,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)],[125]) ).
cnf(129,plain,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[126]) ).
fof(151,plain,
! [X2] : set_difference(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[21]) ).
cnf(152,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[151]) ).
fof(244,plain,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[47]) ).
cnf(245,plain,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[244]) ).
fof(254,negated_conjecture,
? [X1,X2] :
( ~ in(X1,X2)
& ~ disjoint(singleton(X1),X2) ),
inference(fof_nnf,[status(thm)],[86]) ).
fof(255,negated_conjecture,
? [X3,X4] :
( ~ in(X3,X4)
& ~ disjoint(singleton(X3),X4) ),
inference(variable_rename,[status(thm)],[254]) ).
fof(256,negated_conjecture,
( ~ in(esk8_0,esk9_0)
& ~ disjoint(singleton(esk8_0),esk9_0) ),
inference(skolemize,[status(esa)],[255]) ).
cnf(257,negated_conjecture,
~ disjoint(singleton(esk8_0),esk9_0),
inference(split_conjunct,[status(thm)],[256]) ).
cnf(258,negated_conjecture,
~ in(esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[256]) ).
fof(274,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[55]) ).
cnf(275,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[274]) ).
fof(309,plain,
! [X1,X2] :
( ( ~ subset(singleton(X1),X2)
| in(X1,X2) )
& ( ~ in(X1,X2)
| subset(singleton(X1),X2) ) ),
inference(fof_nnf,[status(thm)],[69]) ).
fof(310,plain,
! [X3,X4] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X3,X4)
| subset(singleton(X3),X4) ) ),
inference(variable_rename,[status(thm)],[309]) ).
cnf(312,plain,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[310]) ).
fof(356,plain,
! [X1,X2] :
( ( ~ disjoint(X1,X2)
| set_difference(X1,X2) = X1 )
& ( set_difference(X1,X2) != X1
| disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[76]) ).
fof(357,plain,
! [X3,X4] :
( ( ~ disjoint(X3,X4)
| set_difference(X3,X4) = X3 )
& ( set_difference(X3,X4) != X3
| disjoint(X3,X4) ) ),
inference(variable_rename,[status(thm)],[356]) ).
cnf(358,plain,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[357]) ).
cnf(370,plain,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[312,121,theory(equality)]),
[unfolding] ).
cnf(372,plain,
( empty_set = X1
| unordered_pair(X2,X2) = X1
| ~ subset(X1,unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[129,121,theory(equality)]),121,theory(equality)]),
[unfolding] ).
cnf(378,negated_conjecture,
~ disjoint(unordered_pair(esk8_0,esk8_0),esk9_0),
inference(rw,[status(thm)],[257,121,theory(equality)]),
[unfolding] ).
cnf(382,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[275,245,theory(equality)]),245,theory(equality)]),
[unfolding] ).
cnf(591,plain,
( unordered_pair(X1,X1) = set_difference(unordered_pair(X1,X1),X2)
| empty_set = set_difference(unordered_pair(X1,X1),X2) ),
inference(spm,[status(thm)],[372,123,theory(equality)]) ).
cnf(876,plain,
subset(set_difference(X2,set_difference(X2,X1)),X1),
inference(spm,[status(thm)],[123,382,theory(equality)]) ).
cnf(5878,plain,
( disjoint(unordered_pair(X1,X1),X2)
| set_difference(unordered_pair(X1,X1),X2) = empty_set ),
inference(spm,[status(thm)],[358,591,theory(equality)]) ).
cnf(548236,plain,
set_difference(unordered_pair(esk8_0,esk8_0),esk9_0) = empty_set,
inference(spm,[status(thm)],[378,5878,theory(equality)]) ).
cnf(548381,plain,
subset(set_difference(unordered_pair(esk8_0,esk8_0),empty_set),esk9_0),
inference(spm,[status(thm)],[876,548236,theory(equality)]) ).
cnf(548688,plain,
subset(unordered_pair(esk8_0,esk8_0),esk9_0),
inference(rw,[status(thm)],[548381,152,theory(equality)]) ).
cnf(549053,plain,
in(esk8_0,esk9_0),
inference(spm,[status(thm)],[370,548688,theory(equality)]) ).
cnf(549095,plain,
$false,
inference(sr,[status(thm)],[549053,258,theory(equality)]) ).
cnf(549096,plain,
$false,
549095,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU154+2.p
% --creating new selector for []
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpWqZsKp/sel_SEU154+2.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpWqZsKp/sel_SEU154+2.p_2 with time limit 80
% -prover status Theorem
% Problem SEU154+2.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU154+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU154+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
%
%------------------------------------------------------------------------------