TSTP Solution File: SEU162+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU162+3 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 04:57:46 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 8 unt; 0 def)
% Number of atoms : 76 ( 21 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 71 ( 32 ~; 26 |; 6 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 32 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('/tmp/tmpi5-a2n/sel_SEU162+3.p_1',t65_zfmisc_1) ).
fof(3,axiom,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('/tmp/tmpi5-a2n/sel_SEU162+3.p_1',l25_zfmisc_1) ).
fof(5,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/tmp/tmpi5-a2n/sel_SEU162+3.p_1',symmetry_r1_xboole_0) ).
fof(6,axiom,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/tmp/tmpi5-a2n/sel_SEU162+3.p_1',l28_zfmisc_1) ).
fof(8,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/tmp/tmpi5-a2n/sel_SEU162+3.p_1',t83_xboole_1) ).
fof(9,negated_conjecture,
~ ! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(10,negated_conjecture,
~ ! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(12,plain,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).
fof(14,negated_conjecture,
? [X1,X2] :
( ( set_difference(X1,singleton(X2)) != X1
| in(X2,X1) )
& ( set_difference(X1,singleton(X2)) = X1
| ~ in(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(15,negated_conjecture,
? [X3,X4] :
( ( set_difference(X3,singleton(X4)) != X3
| in(X4,X3) )
& ( set_difference(X3,singleton(X4)) = X3
| ~ in(X4,X3) ) ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,negated_conjecture,
( ( set_difference(esk1_0,singleton(esk2_0)) != esk1_0
| in(esk2_0,esk1_0) )
& ( set_difference(esk1_0,singleton(esk2_0)) = esk1_0
| ~ in(esk2_0,esk1_0) ) ),
inference(skolemize,[status(esa)],[15]) ).
cnf(17,negated_conjecture,
( set_difference(esk1_0,singleton(esk2_0)) = esk1_0
| ~ in(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(18,negated_conjecture,
( in(esk2_0,esk1_0)
| set_difference(esk1_0,singleton(esk2_0)) != esk1_0 ),
inference(split_conjunct,[status(thm)],[16]) ).
fof(22,plain,
! [X1,X2] :
( ~ disjoint(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(23,plain,
! [X3,X4] :
( ~ disjoint(singleton(X3),X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[22]) ).
cnf(24,plain,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(28,plain,
! [X1,X2] :
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(29,plain,
! [X3,X4] :
( ~ disjoint(X3,X4)
| disjoint(X4,X3) ),
inference(variable_rename,[status(thm)],[28]) ).
cnf(30,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X1,X2] :
( in(X1,X2)
| disjoint(singleton(X1),X2) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(32,plain,
! [X3,X4] :
( in(X3,X4)
| disjoint(singleton(X3),X4) ),
inference(variable_rename,[status(thm)],[31]) ).
cnf(33,plain,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[32]) ).
fof(37,plain,
! [X1,X2] :
( ( ~ disjoint(X1,X2)
| set_difference(X1,X2) = X1 )
& ( set_difference(X1,X2) != X1
| disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(38,plain,
! [X3,X4] :
( ( ~ disjoint(X3,X4)
| set_difference(X3,X4) = X3 )
& ( set_difference(X3,X4) != X3
| disjoint(X3,X4) ) ),
inference(variable_rename,[status(thm)],[37]) ).
cnf(39,plain,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[38]) ).
cnf(40,plain,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[38]) ).
cnf(43,plain,
( disjoint(X1,singleton(X2))
| in(X2,X1) ),
inference(spm,[status(thm)],[30,33,theory(equality)]) ).
cnf(45,plain,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
inference(spm,[status(thm)],[40,43,theory(equality)]) ).
cnf(47,negated_conjecture,
in(esk2_0,esk1_0),
inference(spm,[status(thm)],[18,45,theory(equality)]) ).
cnf(51,negated_conjecture,
( set_difference(esk1_0,singleton(esk2_0)) = esk1_0
| $false ),
inference(rw,[status(thm)],[17,47,theory(equality)]) ).
cnf(52,negated_conjecture,
set_difference(esk1_0,singleton(esk2_0)) = esk1_0,
inference(cn,[status(thm)],[51,theory(equality)]) ).
cnf(53,negated_conjecture,
disjoint(esk1_0,singleton(esk2_0)),
inference(spm,[status(thm)],[39,52,theory(equality)]) ).
cnf(55,negated_conjecture,
disjoint(singleton(esk2_0),esk1_0),
inference(spm,[status(thm)],[30,53,theory(equality)]) ).
cnf(57,negated_conjecture,
~ in(esk2_0,esk1_0),
inference(spm,[status(thm)],[24,55,theory(equality)]) ).
cnf(60,negated_conjecture,
$false,
inference(rw,[status(thm)],[57,47,theory(equality)]) ).
cnf(61,negated_conjecture,
$false,
inference(cn,[status(thm)],[60,theory(equality)]) ).
cnf(62,negated_conjecture,
$false,
61,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU162+3.p
% --creating new selector for []
% -running prover on /tmp/tmpi5-a2n/sel_SEU162+3.p_1 with time limit 29
% -prover status Theorem
% Problem SEU162+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU162+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU162+3.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
%
%------------------------------------------------------------------------------