TSTP Solution File: SET877+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET877+1 : TPTP v5.0.0. Released v3.2.0.
% 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 03:42:48 EST 2010
% Result : Theorem 0.19s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 89 ( 59 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 100 ( 38 ~; 39 |; 18 &)
% ( 2 <=>; 3 =>; 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 : 48 ( 0 sgn 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/tmp/tmpzkM5NS/sel_SET877+1.p_1',commutativity_k3_xboole_0) ).
fof(3,conjecture,
! [X1,X2] :
( set_intersection2(singleton(X1),singleton(X2)) = singleton(X1)
=> X1 = X2 ),
file('/tmp/tmpzkM5NS/sel_SET877+1.p_1',t18_zfmisc_1) ).
fof(5,axiom,
! [X1,X2] :
( set_intersection2(X1,singleton(X2)) = singleton(X2)
=> in(X2,X1) ),
file('/tmp/tmpzkM5NS/sel_SET877+1.p_1',l30_zfmisc_1) ).
fof(6,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpzkM5NS/sel_SET877+1.p_1',d1_tarski) ).
fof(9,negated_conjecture,
~ ! [X1,X2] :
( set_intersection2(singleton(X1),singleton(X2)) = singleton(X1)
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[3]) ).
fof(12,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(13,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[12]) ).
fof(16,negated_conjecture,
? [X1,X2] :
( set_intersection2(singleton(X1),singleton(X2)) = singleton(X1)
& X1 != X2 ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(17,negated_conjecture,
? [X3,X4] :
( set_intersection2(singleton(X3),singleton(X4)) = singleton(X3)
& X3 != X4 ),
inference(variable_rename,[status(thm)],[16]) ).
fof(18,negated_conjecture,
( set_intersection2(singleton(esk1_0),singleton(esk2_0)) = singleton(esk1_0)
& esk1_0 != esk2_0 ),
inference(skolemize,[status(esa)],[17]) ).
cnf(19,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[18]) ).
cnf(20,negated_conjecture,
set_intersection2(singleton(esk1_0),singleton(esk2_0)) = singleton(esk1_0),
inference(split_conjunct,[status(thm)],[18]) ).
fof(24,plain,
! [X1,X2] :
( set_intersection2(X1,singleton(X2)) != singleton(X2)
| in(X2,X1) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(25,plain,
! [X3,X4] :
( set_intersection2(X3,singleton(X4)) != singleton(X4)
| in(X4,X3) ),
inference(variable_rename,[status(thm)],[24]) ).
cnf(26,plain,
( in(X1,X2)
| set_intersection2(X2,singleton(X1)) != singleton(X1) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(27,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)],[6]) ).
fof(28,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)],[27]) ).
fof(29,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) != X4 )
& ( in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[28]) ).
fof(30,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) != X4 )
& ( in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[29]) ).
fof(31,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[30]) ).
cnf(35,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[31]) ).
cnf(49,plain,
( in(X1,X2)
| set_intersection2(singleton(X1),X2) != singleton(X1) ),
inference(spm,[status(thm)],[26,13,theory(equality)]) ).
cnf(70,negated_conjecture,
in(esk1_0,singleton(esk2_0)),
inference(spm,[status(thm)],[49,20,theory(equality)]) ).
cnf(75,negated_conjecture,
( X1 = esk1_0
| singleton(X1) != singleton(esk2_0) ),
inference(spm,[status(thm)],[35,70,theory(equality)]) ).
cnf(78,negated_conjecture,
esk2_0 = esk1_0,
inference(er,[status(thm)],[75,theory(equality)]) ).
cnf(79,negated_conjecture,
$false,
inference(sr,[status(thm)],[78,19,theory(equality)]) ).
cnf(80,negated_conjecture,
$false,
79,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET877+1.p
% --creating new selector for []
% -running prover on /tmp/tmpzkM5NS/sel_SET877+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET877+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET877+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET877+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
%
%------------------------------------------------------------------------------