TSTP Solution File: SET968+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET968+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 03:55:35 EST 2010
% Result : Theorem 0.16s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 15 unt; 0 def)
% Number of atoms : 19 ( 16 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 20 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& cartesian_product2(X3,set_union2(X1,X2)) = set_union2(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ),
file('/tmp/tmpapIoUe/sel_SET968+1.p_1',t120_zfmisc_1) ).
fof(8,conjecture,
! [X1,X2,X3,X4] : cartesian_product2(set_union2(X1,X2),set_union2(X3,X4)) = set_union2(set_union2(set_union2(cartesian_product2(X1,X3),cartesian_product2(X1,X4)),cartesian_product2(X2,X3)),cartesian_product2(X2,X4)),
file('/tmp/tmpapIoUe/sel_SET968+1.p_1',t121_zfmisc_1) ).
fof(9,axiom,
! [X1,X2,X3] : set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
file('/tmp/tmpapIoUe/sel_SET968+1.p_1',t4_xboole_1) ).
fof(10,negated_conjecture,
~ ! [X1,X2,X3,X4] : cartesian_product2(set_union2(X1,X2),set_union2(X3,X4)) = set_union2(set_union2(set_union2(cartesian_product2(X1,X3),cartesian_product2(X1,X4)),cartesian_product2(X2,X3)),cartesian_product2(X2,X4)),
inference(assume_negation,[status(cth)],[8]) ).
fof(14,plain,
! [X4,X5,X6] :
( cartesian_product2(set_union2(X4,X5),X6) = set_union2(cartesian_product2(X4,X6),cartesian_product2(X5,X6))
& cartesian_product2(X6,set_union2(X4,X5)) = set_union2(cartesian_product2(X6,X4),cartesian_product2(X6,X5)) ),
inference(variable_rename,[status(thm)],[1]) ).
cnf(15,plain,
cartesian_product2(X1,set_union2(X2,X3)) = set_union2(cartesian_product2(X1,X2),cartesian_product2(X1,X3)),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(16,plain,
cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3)),
inference(split_conjunct,[status(thm)],[14]) ).
fof(33,negated_conjecture,
? [X1,X2,X3,X4] : cartesian_product2(set_union2(X1,X2),set_union2(X3,X4)) != set_union2(set_union2(set_union2(cartesian_product2(X1,X3),cartesian_product2(X1,X4)),cartesian_product2(X2,X3)),cartesian_product2(X2,X4)),
inference(fof_nnf,[status(thm)],[10]) ).
fof(34,negated_conjecture,
? [X5,X6,X7,X8] : cartesian_product2(set_union2(X5,X6),set_union2(X7,X8)) != set_union2(set_union2(set_union2(cartesian_product2(X5,X7),cartesian_product2(X5,X8)),cartesian_product2(X6,X7)),cartesian_product2(X6,X8)),
inference(variable_rename,[status(thm)],[33]) ).
fof(35,negated_conjecture,
cartesian_product2(set_union2(esk3_0,esk4_0),set_union2(esk5_0,esk6_0)) != set_union2(set_union2(set_union2(cartesian_product2(esk3_0,esk5_0),cartesian_product2(esk3_0,esk6_0)),cartesian_product2(esk4_0,esk5_0)),cartesian_product2(esk4_0,esk6_0)),
inference(skolemize,[status(esa)],[34]) ).
cnf(36,negated_conjecture,
cartesian_product2(set_union2(esk3_0,esk4_0),set_union2(esk5_0,esk6_0)) != set_union2(set_union2(set_union2(cartesian_product2(esk3_0,esk5_0),cartesian_product2(esk3_0,esk6_0)),cartesian_product2(esk4_0,esk5_0)),cartesian_product2(esk4_0,esk6_0)),
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X4,X5,X6] : set_union2(set_union2(X4,X5),X6) = set_union2(X4,set_union2(X5,X6)),
inference(variable_rename,[status(thm)],[9]) ).
cnf(38,plain,
set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(50,negated_conjecture,
cartesian_product2(set_union2(esk3_0,esk4_0),set_union2(esk5_0,esk6_0)) != set_union2(cartesian_product2(esk3_0,esk5_0),set_union2(cartesian_product2(esk3_0,esk6_0),set_union2(cartesian_product2(esk4_0,esk5_0),cartesian_product2(esk4_0,esk6_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[36,38,theory(equality)]),38,theory(equality)]),38,theory(equality)]) ).
cnf(160,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[50,16,theory(equality)]),15,theory(equality)]),15,theory(equality)]),38,theory(equality)]) ).
cnf(161,negated_conjecture,
$false,
inference(cn,[status(thm)],[160,theory(equality)]) ).
cnf(162,negated_conjecture,
$false,
161,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET968+1.p
% --creating new selector for []
% -running prover on /tmp/tmpapIoUe/sel_SET968+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET968+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET968+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET968+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
%
%------------------------------------------------------------------------------