TSTP Solution File: SET971+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET971+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 03:56:06 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 16 unt; 0 def)
% Number of atoms : 39 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 10 ~; 3 |; 8 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 26 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/tmp/tmp0YZ5s5/sel_SET971+1.p_1',commutativity_k3_xboole_0) ).
fof(2,conjecture,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X3)) = cartesian_product2(X1,X3) ),
file('/tmp/tmp0YZ5s5/sel_SET971+1.p_1',t124_zfmisc_1) ).
fof(4,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/tmp/tmp0YZ5s5/sel_SET971+1.p_1',t28_xboole_1) ).
fof(6,axiom,
! [X1,X2,X3,X4] : cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
file('/tmp/tmp0YZ5s5/sel_SET971+1.p_1',t123_zfmisc_1) ).
fof(9,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X3)) = cartesian_product2(X1,X3) ),
inference(assume_negation,[status(cth)],[2]) ).
fof(11,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(12,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[11]) ).
fof(13,negated_conjecture,
? [X1,X2,X3,X4] :
( subset(X1,X2)
& subset(X3,X4)
& set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X3)) != cartesian_product2(X1,X3) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(14,negated_conjecture,
? [X5,X6,X7,X8] :
( subset(X5,X6)
& subset(X7,X8)
& set_intersection2(cartesian_product2(X5,X8),cartesian_product2(X6,X7)) != cartesian_product2(X5,X7) ),
inference(variable_rename,[status(thm)],[13]) ).
fof(15,negated_conjecture,
( subset(esk1_0,esk2_0)
& subset(esk3_0,esk4_0)
& set_intersection2(cartesian_product2(esk1_0,esk4_0),cartesian_product2(esk2_0,esk3_0)) != cartesian_product2(esk1_0,esk3_0) ),
inference(skolemize,[status(esa)],[14]) ).
cnf(16,negated_conjecture,
set_intersection2(cartesian_product2(esk1_0,esk4_0),cartesian_product2(esk2_0,esk3_0)) != cartesian_product2(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(17,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(18,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[15]) ).
fof(21,plain,
! [X1,X2] :
( ~ subset(X1,X2)
| set_intersection2(X1,X2) = X1 ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(22,plain,
! [X3,X4] :
( ~ subset(X3,X4)
| set_intersection2(X3,X4) = X3 ),
inference(variable_rename,[status(thm)],[21]) ).
cnf(23,plain,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(27,plain,
! [X5,X6,X7,X8] : cartesian_product2(set_intersection2(X5,X6),set_intersection2(X7,X8)) = set_intersection2(cartesian_product2(X5,X7),cartesian_product2(X6,X8)),
inference(variable_rename,[status(thm)],[6]) ).
cnf(28,plain,
cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(38,negated_conjecture,
set_intersection2(esk1_0,esk2_0) = esk1_0,
inference(spm,[status(thm)],[23,18,theory(equality)]) ).
cnf(39,negated_conjecture,
set_intersection2(esk3_0,esk4_0) = esk3_0,
inference(spm,[status(thm)],[23,17,theory(equality)]) ).
cnf(45,negated_conjecture,
cartesian_product2(set_intersection2(esk1_0,esk2_0),set_intersection2(esk3_0,esk4_0)) != cartesian_product2(esk1_0,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[16,28,theory(equality)]),12,theory(equality)]) ).
cnf(49,negated_conjecture,
cartesian_product2(esk1_0,set_intersection2(esk3_0,esk4_0)) != cartesian_product2(esk1_0,esk3_0),
inference(rw,[status(thm)],[45,38,theory(equality)]) ).
cnf(50,negated_conjecture,
$false,
inference(rw,[status(thm)],[49,39,theory(equality)]) ).
cnf(51,negated_conjecture,
$false,
inference(cn,[status(thm)],[50,theory(equality)]) ).
cnf(52,negated_conjecture,
$false,
51,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET971+1.p
% --creating new selector for []
% -running prover on /tmp/tmp0YZ5s5/sel_SET971+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET971+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET971+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET971+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
%
%------------------------------------------------------------------------------