TSTP Solution File: SET984+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET984+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 03:58:31 EST 2010
% Result : Theorem 0.86s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 23 unt; 0 def)
% Number of atoms : 150 ( 117 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 142 ( 51 ~; 68 |; 18 &)
% ( 1 <=>; 4 =>; 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 120 ( 19 sgn 54 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/tmp/tmp2ycPs2/sel_SET984+1.p_1',commutativity_k3_xboole_0) ).
fof(3,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/tmp/tmp2ycPs2/sel_SET984+1.p_1',t28_xboole_1) ).
fof(5,axiom,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('/tmp/tmp2ycPs2/sel_SET984+1.p_1',t17_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/tmp2ycPs2/sel_SET984+1.p_1',t123_zfmisc_1) ).
fof(7,axiom,
! [X1,X2] :
( cartesian_product2(X1,X2) = empty_set
<=> ( X1 = empty_set
| X2 = empty_set ) ),
file('/tmp/tmp2ycPs2/sel_SET984+1.p_1',t113_zfmisc_1) ).
fof(8,conjecture,
! [X1,X2,X3,X4] :
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
=> ( cartesian_product2(X1,X2) = empty_set
| ( subset(X1,X3)
& subset(X2,X4) ) ) ),
file('/tmp/tmp2ycPs2/sel_SET984+1.p_1',t138_zfmisc_1) ).
fof(10,axiom,
! [X1,X2,X3,X4] :
( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
=> ( X1 = empty_set
| X2 = empty_set
| ( X1 = X3
& X2 = X4 ) ) ),
file('/tmp/tmp2ycPs2/sel_SET984+1.p_1',t134_zfmisc_1) ).
fof(13,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
=> ( cartesian_product2(X1,X2) = empty_set
| ( subset(X1,X3)
& subset(X2,X4) ) ) ),
inference(assume_negation,[status(cth)],[8]) ).
fof(15,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(16,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[15]) ).
fof(19,plain,
! [X1,X2] :
( ~ subset(X1,X2)
| set_intersection2(X1,X2) = X1 ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(20,plain,
! [X3,X4] :
( ~ subset(X3,X4)
| set_intersection2(X3,X4) = X3 ),
inference(variable_rename,[status(thm)],[19]) ).
cnf(21,plain,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(25,plain,
! [X3,X4] : subset(set_intersection2(X3,X4),X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(26,plain,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[25]) ).
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]) ).
fof(29,plain,
! [X1,X2] :
( ( cartesian_product2(X1,X2) != empty_set
| X1 = empty_set
| X2 = empty_set )
& ( ( X1 != empty_set
& X2 != empty_set )
| cartesian_product2(X1,X2) = empty_set ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(30,plain,
! [X3,X4] :
( ( cartesian_product2(X3,X4) != empty_set
| X3 = empty_set
| X4 = empty_set )
& ( ( X3 != empty_set
& X4 != empty_set )
| cartesian_product2(X3,X4) = empty_set ) ),
inference(variable_rename,[status(thm)],[29]) ).
fof(31,plain,
! [X3,X4] :
( ( cartesian_product2(X3,X4) != empty_set
| X3 = empty_set
| X4 = empty_set )
& ( X3 != empty_set
| cartesian_product2(X3,X4) = empty_set )
& ( X4 != empty_set
| cartesian_product2(X3,X4) = empty_set ) ),
inference(distribute,[status(thm)],[30]) ).
cnf(32,plain,
( cartesian_product2(X1,X2) = empty_set
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[31]) ).
cnf(33,plain,
( cartesian_product2(X1,X2) = empty_set
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[31]) ).
fof(35,negated_conjecture,
? [X1,X2,X3,X4] :
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
& cartesian_product2(X1,X2) != empty_set
& ( ~ subset(X1,X3)
| ~ subset(X2,X4) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(36,negated_conjecture,
? [X5,X6,X7,X8] :
( subset(cartesian_product2(X5,X6),cartesian_product2(X7,X8))
& cartesian_product2(X5,X6) != empty_set
& ( ~ subset(X5,X7)
| ~ subset(X6,X8) ) ),
inference(variable_rename,[status(thm)],[35]) ).
fof(37,negated_conjecture,
( subset(cartesian_product2(esk2_0,esk3_0),cartesian_product2(esk4_0,esk5_0))
& cartesian_product2(esk2_0,esk3_0) != empty_set
& ( ~ subset(esk2_0,esk4_0)
| ~ subset(esk3_0,esk5_0) ) ),
inference(skolemize,[status(esa)],[36]) ).
cnf(38,negated_conjecture,
( ~ subset(esk3_0,esk5_0)
| ~ subset(esk2_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(39,negated_conjecture,
cartesian_product2(esk2_0,esk3_0) != empty_set,
inference(split_conjunct,[status(thm)],[37]) ).
cnf(40,negated_conjecture,
subset(cartesian_product2(esk2_0,esk3_0),cartesian_product2(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[37]) ).
fof(44,plain,
! [X1,X2,X3,X4] :
( cartesian_product2(X1,X2) != cartesian_product2(X3,X4)
| X1 = empty_set
| X2 = empty_set
| ( X1 = X3
& X2 = X4 ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(45,plain,
! [X5,X6,X7,X8] :
( cartesian_product2(X5,X6) != cartesian_product2(X7,X8)
| X5 = empty_set
| X6 = empty_set
| ( X5 = X7
& X6 = X8 ) ),
inference(variable_rename,[status(thm)],[44]) ).
fof(46,plain,
! [X5,X6,X7,X8] :
( ( X5 = X7
| X5 = empty_set
| X6 = empty_set
| cartesian_product2(X5,X6) != cartesian_product2(X7,X8) )
& ( X6 = X8
| X5 = empty_set
| X6 = empty_set
| cartesian_product2(X5,X6) != cartesian_product2(X7,X8) ) ),
inference(distribute,[status(thm)],[45]) ).
cnf(47,plain,
( X2 = empty_set
| X1 = empty_set
| X2 = X4
| cartesian_product2(X1,X2) != cartesian_product2(X3,X4) ),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(48,plain,
( X2 = empty_set
| X1 = empty_set
| X1 = X3
| cartesian_product2(X1,X2) != cartesian_product2(X3,X4) ),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(54,negated_conjecture,
empty_set != esk3_0,
inference(spm,[status(thm)],[39,32,theory(equality)]) ).
cnf(61,negated_conjecture,
set_intersection2(cartesian_product2(esk2_0,esk3_0),cartesian_product2(esk4_0,esk5_0)) = cartesian_product2(esk2_0,esk3_0),
inference(spm,[status(thm)],[21,40,theory(equality)]) ).
cnf(68,plain,
subset(set_intersection2(X2,X1),X1),
inference(spm,[status(thm)],[26,16,theory(equality)]) ).
cnf(88,plain,
( set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) = empty_set
| empty_set != set_intersection2(X3,X4) ),
inference(spm,[status(thm)],[32,28,theory(equality)]) ).
cnf(89,plain,
( set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) = empty_set
| empty_set != set_intersection2(X1,X2) ),
inference(spm,[status(thm)],[33,28,theory(equality)]) ).
cnf(91,plain,
( empty_set = set_intersection2(X1,X2)
| empty_set = set_intersection2(X3,X4)
| set_intersection2(X3,X4) = X5
| set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) != cartesian_product2(X6,X5) ),
inference(spm,[status(thm)],[47,28,theory(equality)]) ).
cnf(93,plain,
( empty_set = set_intersection2(X1,X2)
| empty_set = set_intersection2(X3,X4)
| set_intersection2(X1,X2) = X5
| set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) != cartesian_product2(X5,X6) ),
inference(spm,[status(thm)],[48,28,theory(equality)]) ).
cnf(691,negated_conjecture,
( empty_set = cartesian_product2(esk2_0,esk3_0)
| set_intersection2(esk3_0,esk5_0) != empty_set ),
inference(spm,[status(thm)],[61,88,theory(equality)]) ).
cnf(713,negated_conjecture,
set_intersection2(esk3_0,esk5_0) != empty_set,
inference(sr,[status(thm)],[691,39,theory(equality)]) ).
cnf(747,negated_conjecture,
( empty_set = cartesian_product2(esk2_0,esk3_0)
| set_intersection2(esk2_0,esk4_0) != empty_set ),
inference(spm,[status(thm)],[61,89,theory(equality)]) ).
cnf(769,negated_conjecture,
set_intersection2(esk2_0,esk4_0) != empty_set,
inference(sr,[status(thm)],[747,39,theory(equality)]) ).
cnf(834,negated_conjecture,
( set_intersection2(esk3_0,esk5_0) = empty_set
| set_intersection2(esk2_0,esk4_0) = empty_set
| set_intersection2(esk3_0,esk5_0) = X1
| cartesian_product2(esk2_0,esk3_0) != cartesian_product2(X2,X1) ),
inference(spm,[status(thm)],[91,61,theory(equality)]) ).
cnf(857,negated_conjecture,
( set_intersection2(esk2_0,esk4_0) = empty_set
| set_intersection2(esk3_0,esk5_0) = X1
| cartesian_product2(esk2_0,esk3_0) != cartesian_product2(X2,X1) ),
inference(sr,[status(thm)],[834,713,theory(equality)]) ).
cnf(858,negated_conjecture,
( set_intersection2(esk3_0,esk5_0) = X1
| cartesian_product2(esk2_0,esk3_0) != cartesian_product2(X2,X1) ),
inference(sr,[status(thm)],[857,769,theory(equality)]) ).
cnf(865,negated_conjecture,
set_intersection2(esk3_0,esk5_0) = esk3_0,
inference(er,[status(thm)],[858,theory(equality)]) ).
cnf(876,negated_conjecture,
subset(esk3_0,esk5_0),
inference(spm,[status(thm)],[68,865,theory(equality)]) ).
cnf(889,negated_conjecture,
( ~ subset(esk2_0,esk4_0)
| $false ),
inference(rw,[status(thm)],[38,876,theory(equality)]) ).
cnf(890,negated_conjecture,
~ subset(esk2_0,esk4_0),
inference(cn,[status(thm)],[889,theory(equality)]) ).
cnf(1065,negated_conjecture,
( set_intersection2(esk3_0,esk5_0) = empty_set
| set_intersection2(esk2_0,esk4_0) = empty_set
| set_intersection2(esk2_0,esk4_0) = X1
| cartesian_product2(esk2_0,esk3_0) != cartesian_product2(X1,X2) ),
inference(spm,[status(thm)],[93,61,theory(equality)]) ).
cnf(1088,negated_conjecture,
( esk3_0 = empty_set
| set_intersection2(esk2_0,esk4_0) = empty_set
| set_intersection2(esk2_0,esk4_0) = X1
| cartesian_product2(esk2_0,esk3_0) != cartesian_product2(X1,X2) ),
inference(rw,[status(thm)],[1065,865,theory(equality)]) ).
cnf(1089,negated_conjecture,
( set_intersection2(esk2_0,esk4_0) = empty_set
| set_intersection2(esk2_0,esk4_0) = X1
| cartesian_product2(esk2_0,esk3_0) != cartesian_product2(X1,X2) ),
inference(sr,[status(thm)],[1088,54,theory(equality)]) ).
cnf(1090,negated_conjecture,
( set_intersection2(esk2_0,esk4_0) = X1
| cartesian_product2(esk2_0,esk3_0) != cartesian_product2(X1,X2) ),
inference(sr,[status(thm)],[1089,769,theory(equality)]) ).
cnf(17578,negated_conjecture,
set_intersection2(esk2_0,esk4_0) = esk2_0,
inference(er,[status(thm)],[1090,theory(equality)]) ).
cnf(17600,negated_conjecture,
subset(esk2_0,esk4_0),
inference(spm,[status(thm)],[68,17578,theory(equality)]) ).
cnf(17640,negated_conjecture,
$false,
inference(sr,[status(thm)],[17600,890,theory(equality)]) ).
cnf(17641,negated_conjecture,
$false,
17640,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET984+1.p
% --creating new selector for []
% -running prover on /tmp/tmp2ycPs2/sel_SET984+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET984+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET984+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET984+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
%
%------------------------------------------------------------------------------