TSTP Solution File: SET183+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET183+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 02:54:03 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 17 unt; 0 def)
% Number of atoms : 143 ( 24 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 146 ( 56 ~; 57 |; 27 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 95 ( 4 sgn 50 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/tmp/tmp27CJ_-/sel_SET183+3.p_1',commutativity_of_intersection) ).
fof(2,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmp27CJ_-/sel_SET183+3.p_1',subset_defn) ).
fof(3,axiom,
! [X1,X2] : subset(intersection(X1,X2),X1),
file('/tmp/tmp27CJ_-/sel_SET183+3.p_1',intersection_is_subset) ).
fof(4,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmp27CJ_-/sel_SET183+3.p_1',equal_defn) ).
fof(5,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> intersection(X1,X2) = X1 ),
file('/tmp/tmp27CJ_-/sel_SET183+3.p_1',prove_subset_intersection) ).
fof(7,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmp27CJ_-/sel_SET183+3.p_1',intersection_defn) ).
fof(9,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> intersection(X1,X2) = X1 ),
inference(assume_negation,[status(cth)],[5]) ).
fof(10,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(11,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[10]) ).
fof(12,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ member(X3,X1)
| member(X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ member(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(13,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( member(X7,X4)
& ~ member(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[12]) ).
fof(14,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[13]) ).
fof(15,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[14]) ).
fof(16,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk1_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[15]) ).
cnf(17,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(18,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(19,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[16]) ).
fof(20,plain,
! [X3,X4] : subset(intersection(X3,X4),X3),
inference(variable_rename,[status(thm)],[3]) ).
cnf(21,plain,
subset(intersection(X1,X2),X1),
inference(split_conjunct,[status(thm)],[20]) ).
fof(22,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(23,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[22]) ).
fof(24,plain,
! [X3,X4] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(distribute,[status(thm)],[23]) ).
cnf(25,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(28,negated_conjecture,
? [X1,X2] :
( subset(X1,X2)
& intersection(X1,X2) != X1 ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(29,negated_conjecture,
? [X3,X4] :
( subset(X3,X4)
& intersection(X3,X4) != X3 ),
inference(variable_rename,[status(thm)],[28]) ).
fof(30,negated_conjecture,
( subset(esk2_0,esk3_0)
& intersection(esk2_0,esk3_0) != esk2_0 ),
inference(skolemize,[status(esa)],[29]) ).
cnf(31,negated_conjecture,
intersection(esk2_0,esk3_0) != esk2_0,
inference(split_conjunct,[status(thm)],[30]) ).
cnf(32,negated_conjecture,
subset(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[30]) ).
fof(42,plain,
! [X1,X2,X3] :
( ( ~ member(X3,intersection(X1,X2))
| ( member(X3,X1)
& member(X3,X2) ) )
& ( ~ member(X3,X1)
| ~ member(X3,X2)
| member(X3,intersection(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(43,plain,
! [X4,X5,X6] :
( ( ~ member(X6,intersection(X4,X5))
| ( member(X6,X4)
& member(X6,X5) ) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,plain,
! [X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,intersection(X4,X5)) )
& ( member(X6,X5)
| ~ member(X6,intersection(X4,X5)) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) ),
inference(distribute,[status(thm)],[43]) ).
cnf(45,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(46,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(60,plain,
( member(esk1_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[46,18,theory(equality)]) ).
cnf(66,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[19,32,theory(equality)]) ).
cnf(73,plain,
( subset(X1,intersection(X2,X3))
| ~ member(esk1_2(X1,intersection(X2,X3)),X3)
| ~ member(esk1_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[17,45,theory(equality)]) ).
cnf(89,negated_conjecture,
( subset(X1,esk3_0)
| ~ member(esk1_2(X1,esk3_0),esk2_0) ),
inference(spm,[status(thm)],[17,66,theory(equality)]) ).
cnf(102,negated_conjecture,
subset(intersection(X1,esk2_0),esk3_0),
inference(spm,[status(thm)],[89,60,theory(equality)]) ).
cnf(107,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,intersection(X2,esk2_0)) ),
inference(spm,[status(thm)],[19,102,theory(equality)]) ).
cnf(129,negated_conjecture,
( member(esk1_2(intersection(X1,esk2_0),X2),esk3_0)
| subset(intersection(X1,esk2_0),X2) ),
inference(spm,[status(thm)],[107,18,theory(equality)]) ).
cnf(155,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[73,18,theory(equality)]) ).
cnf(773,plain,
subset(X1,intersection(X1,X1)),
inference(spm,[status(thm)],[155,18,theory(equality)]) ).
cnf(778,negated_conjecture,
subset(intersection(X1,esk2_0),intersection(esk3_0,intersection(X1,esk2_0))),
inference(spm,[status(thm)],[155,129,theory(equality)]) ).
cnf(790,plain,
( intersection(X1,X1) = X1
| ~ subset(intersection(X1,X1),X1) ),
inference(spm,[status(thm)],[25,773,theory(equality)]) ).
cnf(796,plain,
( intersection(X1,X1) = X1
| $false ),
inference(rw,[status(thm)],[790,21,theory(equality)]) ).
cnf(797,plain,
intersection(X1,X1) = X1,
inference(cn,[status(thm)],[796,theory(equality)]) ).
cnf(931,negated_conjecture,
subset(esk2_0,intersection(esk3_0,esk2_0)),
inference(spm,[status(thm)],[778,797,theory(equality)]) ).
cnf(937,negated_conjecture,
subset(esk2_0,intersection(esk2_0,esk3_0)),
inference(rw,[status(thm)],[931,11,theory(equality)]) ).
cnf(940,negated_conjecture,
( intersection(esk2_0,esk3_0) = esk2_0
| ~ subset(intersection(esk2_0,esk3_0),esk2_0) ),
inference(spm,[status(thm)],[25,937,theory(equality)]) ).
cnf(943,negated_conjecture,
( intersection(esk2_0,esk3_0) = esk2_0
| $false ),
inference(rw,[status(thm)],[940,21,theory(equality)]) ).
cnf(944,negated_conjecture,
intersection(esk2_0,esk3_0) = esk2_0,
inference(cn,[status(thm)],[943,theory(equality)]) ).
cnf(945,negated_conjecture,
$false,
inference(sr,[status(thm)],[944,31,theory(equality)]) ).
cnf(946,negated_conjecture,
$false,
945,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET183+3.p
% --creating new selector for []
% -running prover on /tmp/tmp27CJ_-/sel_SET183+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET183+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET183+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET183+3.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
%
%------------------------------------------------------------------------------