TSTP Solution File: SET879+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET879+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 03:43:03 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 7 unt; 0 def)
% Number of atoms : 116 ( 76 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 136 ( 54 ~; 56 |; 20 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 30 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpwgv-D1/sel_SET879+1.p_1',d1_tarski) ).
fof(3,conjecture,
! [X1,X2] :
( set_difference(singleton(X1),singleton(X2)) = singleton(X1)
<=> X1 != X2 ),
file('/tmp/tmpwgv-D1/sel_SET879+1.p_1',t20_zfmisc_1) ).
fof(6,axiom,
! [X1,X2] :
( set_difference(singleton(X1),X2) = singleton(X1)
<=> ~ in(X1,X2) ),
file('/tmp/tmpwgv-D1/sel_SET879+1.p_1',l34_zfmisc_1) ).
fof(7,negated_conjecture,
~ ! [X1,X2] :
( set_difference(singleton(X1),singleton(X2)) = singleton(X1)
<=> X1 != X2 ),
inference(assume_negation,[status(cth)],[3]) ).
fof(10,plain,
! [X1,X2] :
( set_difference(singleton(X1),X2) = singleton(X1)
<=> ~ in(X1,X2) ),
inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).
fof(14,plain,
! [X1,X2] :
( ( X2 != singleton(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1 )
& ( X3 != X1
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| X3 != X1 )
& ( in(X3,X2)
| X3 = X1 ) )
| X2 = singleton(X1) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(15,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| X7 != X4 )
& ( in(X7,X5)
| X7 = X4 ) )
| X5 = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) != X4 )
& ( in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[15]) ).
fof(17,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) != X4 )
& ( in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[16]) ).
fof(18,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[17]) ).
cnf(21,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(22,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[18]) ).
fof(23,negated_conjecture,
? [X1,X2] :
( ( set_difference(singleton(X1),singleton(X2)) != singleton(X1)
| X1 = X2 )
& ( set_difference(singleton(X1),singleton(X2)) = singleton(X1)
| X1 != X2 ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(24,negated_conjecture,
? [X3,X4] :
( ( set_difference(singleton(X3),singleton(X4)) != singleton(X3)
| X3 = X4 )
& ( set_difference(singleton(X3),singleton(X4)) = singleton(X3)
| X3 != X4 ) ),
inference(variable_rename,[status(thm)],[23]) ).
fof(25,negated_conjecture,
( ( set_difference(singleton(esk3_0),singleton(esk4_0)) != singleton(esk3_0)
| esk3_0 = esk4_0 )
& ( set_difference(singleton(esk3_0),singleton(esk4_0)) = singleton(esk3_0)
| esk3_0 != esk4_0 ) ),
inference(skolemize,[status(esa)],[24]) ).
cnf(26,negated_conjecture,
( set_difference(singleton(esk3_0),singleton(esk4_0)) = singleton(esk3_0)
| esk3_0 != esk4_0 ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(27,negated_conjecture,
( esk3_0 = esk4_0
| set_difference(singleton(esk3_0),singleton(esk4_0)) != singleton(esk3_0) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(34,plain,
! [X1,X2] :
( ( set_difference(singleton(X1),X2) != singleton(X1)
| ~ in(X1,X2) )
& ( in(X1,X2)
| set_difference(singleton(X1),X2) = singleton(X1) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(35,plain,
! [X3,X4] :
( ( set_difference(singleton(X3),X4) != singleton(X3)
| ~ in(X3,X4) )
& ( in(X3,X4)
| set_difference(singleton(X3),X4) = singleton(X3) ) ),
inference(variable_rename,[status(thm)],[34]) ).
cnf(36,plain,
( set_difference(singleton(X1),X2) = singleton(X1)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(37,plain,
( ~ in(X1,X2)
| set_difference(singleton(X1),X2) != singleton(X1) ),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(40,negated_conjecture,
( esk3_0 = esk4_0
| in(esk3_0,singleton(esk4_0)) ),
inference(spm,[status(thm)],[27,36,theory(equality)]) ).
cnf(41,plain,
( in(X1,X2)
| singleton(X1) != X2 ),
inference(er,[status(thm)],[21,theory(equality)]) ).
cnf(42,plain,
( X1 = X2
| ~ in(X2,singleton(X1)) ),
inference(er,[status(thm)],[22,theory(equality)]) ).
cnf(44,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[41,theory(equality)]) ).
cnf(46,negated_conjecture,
esk3_0 = esk4_0,
inference(csr,[status(thm)],[40,42]) ).
cnf(50,negated_conjecture,
( set_difference(singleton(esk4_0),singleton(esk4_0)) = singleton(esk3_0)
| esk3_0 != esk4_0 ),
inference(rw,[status(thm)],[26,46,theory(equality)]) ).
cnf(51,negated_conjecture,
( set_difference(singleton(esk4_0),singleton(esk4_0)) = singleton(esk4_0)
| esk3_0 != esk4_0 ),
inference(rw,[status(thm)],[50,46,theory(equality)]) ).
cnf(52,negated_conjecture,
( set_difference(singleton(esk4_0),singleton(esk4_0)) = singleton(esk4_0)
| $false ),
inference(rw,[status(thm)],[51,46,theory(equality)]) ).
cnf(53,negated_conjecture,
set_difference(singleton(esk4_0),singleton(esk4_0)) = singleton(esk4_0),
inference(cn,[status(thm)],[52,theory(equality)]) ).
cnf(54,negated_conjecture,
~ in(esk4_0,singleton(esk4_0)),
inference(spm,[status(thm)],[37,53,theory(equality)]) ).
cnf(55,negated_conjecture,
$false,
inference(rw,[status(thm)],[54,44,theory(equality)]) ).
cnf(56,negated_conjecture,
$false,
inference(cn,[status(thm)],[55,theory(equality)]) ).
cnf(57,negated_conjecture,
$false,
56,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET879+1.p
% --creating new selector for []
% -running prover on /tmp/tmpwgv-D1/sel_SET879+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET879+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET879+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET879+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
%
%------------------------------------------------------------------------------