TSTP Solution File: SET143+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET143+3 : TPTP v5.0.0. Released v2.2.0.
% 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 02:48:02 EST 2010
% Result : Theorem 10.88s
% Output : CNFRefutation 10.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 60 ( 26 unt; 0 def)
% Number of atoms : 148 ( 31 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 146 ( 58 ~; 60 |; 24 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 151 ( 6 sgn 48 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/tmp/tmpDbC0vJ/sel_SET143+3.p_1',commutativity_of_intersection) ).
fof(2,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpDbC0vJ/sel_SET143+3.p_1',subset_defn) ).
fof(3,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpDbC0vJ/sel_SET143+3.p_1',equal_defn) ).
fof(4,conjecture,
! [X1,X2,X3] : intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
file('/tmp/tmpDbC0vJ/sel_SET143+3.p_1',prove_associativity_of_intersection) ).
fof(6,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpDbC0vJ/sel_SET143+3.p_1',intersection_defn) ).
fof(8,negated_conjecture,
~ ! [X1,X2,X3] : intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
inference(assume_negation,[status(cth)],[4]) ).
fof(9,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(10,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[9]) ).
fof(11,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(12,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)],[11]) ).
fof(13,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)],[12]) ).
fof(14,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)],[13]) ).
fof(15,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)],[14]) ).
cnf(16,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(17,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(18,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[15]) ).
fof(19,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(20,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[19]) ).
fof(21,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)],[20]) ).
cnf(22,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[21]) ).
fof(25,negated_conjecture,
? [X1,X2,X3] : intersection(intersection(X1,X2),X3) != intersection(X1,intersection(X2,X3)),
inference(fof_nnf,[status(thm)],[8]) ).
fof(26,negated_conjecture,
? [X4,X5,X6] : intersection(intersection(X4,X5),X6) != intersection(X4,intersection(X5,X6)),
inference(variable_rename,[status(thm)],[25]) ).
fof(27,negated_conjecture,
intersection(intersection(esk2_0,esk3_0),esk4_0) != intersection(esk2_0,intersection(esk3_0,esk4_0)),
inference(skolemize,[status(esa)],[26]) ).
cnf(28,negated_conjecture,
intersection(intersection(esk2_0,esk3_0),esk4_0) != intersection(esk2_0,intersection(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[27]) ).
fof(38,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)],[6]) ).
fof(39,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)],[38]) ).
fof(40,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)],[39]) ).
cnf(41,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(42,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(43,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(46,negated_conjecture,
intersection(esk4_0,intersection(esk2_0,esk3_0)) != intersection(esk2_0,intersection(esk3_0,esk4_0)),
inference(rw,[status(thm)],[28,10,theory(equality)]) ).
cnf(55,plain,
( member(esk1_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[42,17,theory(equality)]) ).
cnf(56,plain,
( member(esk1_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[43,17,theory(equality)]) ).
cnf(64,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)],[16,41,theory(equality)]) ).
cnf(77,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[16,55,theory(equality)]) ).
cnf(95,plain,
( member(esk1_2(intersection(intersection(X1,X2),X3),X4),X2)
| subset(intersection(intersection(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[42,56,theory(equality)]) ).
cnf(114,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[64,17,theory(equality)]) ).
cnf(116,plain,
( subset(intersection(X1,X2),intersection(X3,X2))
| ~ member(esk1_2(intersection(X1,X2),intersection(X3,X2)),X3) ),
inference(spm,[status(thm)],[64,55,theory(equality)]) ).
cnf(117,plain,
( subset(intersection(X1,X2),intersection(X3,X1))
| ~ member(esk1_2(intersection(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[64,56,theory(equality)]) ).
cnf(395,plain,
subset(intersection(X1,X2),intersection(X2,intersection(X1,X2))),
inference(spm,[status(thm)],[114,55,theory(equality)]) ).
cnf(480,plain,
( intersection(X1,intersection(X2,X1)) = intersection(X2,X1)
| ~ subset(intersection(X1,intersection(X2,X1)),intersection(X2,X1)) ),
inference(spm,[status(thm)],[22,395,theory(equality)]) ).
cnf(484,plain,
( intersection(X1,intersection(X2,X1)) = intersection(X2,X1)
| $false ),
inference(rw,[status(thm)],[480,77,theory(equality)]) ).
cnf(485,plain,
intersection(X1,intersection(X2,X1)) = intersection(X2,X1),
inference(cn,[status(thm)],[484,theory(equality)]) ).
cnf(1534,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X2,X3)),
inference(spm,[status(thm)],[116,95,theory(equality)]) ).
cnf(1575,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,X2)),
inference(spm,[status(thm)],[1534,10,theory(equality)]) ).
cnf(1580,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,intersection(intersection(X4,X2),X3)) ),
inference(spm,[status(thm)],[18,1534,theory(equality)]) ).
cnf(22858,plain,
( member(esk1_2(intersection(intersection(X1,X2),X3),X4),intersection(X2,X3))
| subset(intersection(intersection(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[1580,17,theory(equality)]) ).
cnf(351459,plain,
subset(intersection(intersection(X1,X2),X3),intersection(intersection(X2,X3),intersection(X1,X2))),
inference(spm,[status(thm)],[117,22858,theory(equality)]) ).
cnf(352430,plain,
( intersection(intersection(X1,X2),intersection(X3,X1)) = intersection(intersection(X3,X1),X2)
| ~ subset(intersection(intersection(X1,X2),intersection(X3,X1)),intersection(intersection(X3,X1),X2)) ),
inference(spm,[status(thm)],[22,351459,theory(equality)]) ).
cnf(352682,plain,
( intersection(intersection(X1,X2),intersection(X3,X1)) = intersection(intersection(X3,X1),X2)
| $false ),
inference(rw,[status(thm)],[352430,1575,theory(equality)]) ).
cnf(352683,plain,
intersection(intersection(X1,X2),intersection(X3,X1)) = intersection(intersection(X3,X1),X2),
inference(cn,[status(thm)],[352682,theory(equality)]) ).
cnf(355270,plain,
intersection(intersection(X2,X1),intersection(X3,X1)) = intersection(intersection(X3,X1),X2),
inference(spm,[status(thm)],[352683,10,theory(equality)]) ).
cnf(365905,plain,
intersection(intersection(X3,X2),X1) = intersection(intersection(X3,X2),intersection(X1,X2)),
inference(spm,[status(thm)],[10,355270,theory(equality)]) ).
cnf(368565,plain,
intersection(intersection(X3,X2),X1) = intersection(intersection(X1,X2),X3),
inference(rw,[status(thm)],[365905,355270,theory(equality)]) ).
cnf(373561,plain,
intersection(intersection(X3,X2),X1) = intersection(X3,intersection(X1,X2)),
inference(spm,[status(thm)],[10,368565,theory(equality)]) ).
cnf(377161,plain,
intersection(X1,intersection(X3,X2)) = intersection(intersection(X3,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[355270,373561,theory(equality)]),10,theory(equality)]),485,theory(equality)]) ).
cnf(377162,plain,
intersection(X1,intersection(X3,X2)) = intersection(X3,intersection(X1,X2)),
inference(rw,[status(thm)],[377161,373561,theory(equality)]) ).
cnf(379839,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[46,377162,theory(equality)]),10,theory(equality)]) ).
cnf(379840,negated_conjecture,
$false,
inference(cn,[status(thm)],[379839,theory(equality)]) ).
cnf(379841,negated_conjecture,
$false,
379840,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET143+3.p
% --creating new selector for []
% -running prover on /tmp/tmpDbC0vJ/sel_SET143+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET143+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET143+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET143+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
%
%------------------------------------------------------------------------------