TSTP Solution File: SET578+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET578+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 02:57:32 EST 2010
% Result : Theorem 0.25s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 70 ( 21 unt; 0 def)
% Number of atoms : 205 ( 29 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 219 ( 84 ~; 86 |; 41 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 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 : 129 ( 9 sgn 55 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/tmp/tmpWL1qlm/sel_SET578+3.p_1',commutativity_of_intersection) ).
fof(2,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpWL1qlm/sel_SET578+3.p_1',subset_defn) ).
fof(3,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpWL1qlm/sel_SET578+3.p_1',equal_defn) ).
fof(5,conjecture,
! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
& member(X4,X3) ) )
=> X1 = intersection(X2,X3) ),
file('/tmp/tmpWL1qlm/sel_SET578+3.p_1',prove_th19) ).
fof(6,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpWL1qlm/sel_SET578+3.p_1',intersection_defn) ).
fof(8,negated_conjecture,
~ ! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
& member(X4,X3) ) )
=> X1 = intersection(X2,X3) ),
inference(assume_negation,[status(cth)],[5]) ).
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(34,negated_conjecture,
? [X1,X2,X3] :
( ! [X4] :
( ( ~ member(X4,X1)
| ( member(X4,X2)
& member(X4,X3) ) )
& ( ~ member(X4,X2)
| ~ member(X4,X3)
| member(X4,X1) ) )
& X1 != intersection(X2,X3) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(35,negated_conjecture,
? [X5,X6,X7] :
( ! [X8] :
( ( ~ member(X8,X5)
| ( member(X8,X6)
& member(X8,X7) ) )
& ( ~ member(X8,X6)
| ~ member(X8,X7)
| member(X8,X5) ) )
& X5 != intersection(X6,X7) ),
inference(variable_rename,[status(thm)],[34]) ).
fof(36,negated_conjecture,
( ! [X8] :
( ( ~ member(X8,esk3_0)
| ( member(X8,esk4_0)
& member(X8,esk5_0) ) )
& ( ~ member(X8,esk4_0)
| ~ member(X8,esk5_0)
| member(X8,esk3_0) ) )
& esk3_0 != intersection(esk4_0,esk5_0) ),
inference(skolemize,[status(esa)],[35]) ).
fof(37,negated_conjecture,
! [X8] :
( ( ~ member(X8,esk3_0)
| ( member(X8,esk4_0)
& member(X8,esk5_0) ) )
& ( ~ member(X8,esk4_0)
| ~ member(X8,esk5_0)
| member(X8,esk3_0) )
& esk3_0 != intersection(esk4_0,esk5_0) ),
inference(shift_quantors,[status(thm)],[36]) ).
fof(38,negated_conjecture,
! [X8] :
( ( member(X8,esk4_0)
| ~ member(X8,esk3_0) )
& ( member(X8,esk5_0)
| ~ member(X8,esk3_0) )
& ( ~ member(X8,esk4_0)
| ~ member(X8,esk5_0)
| member(X8,esk3_0) )
& esk3_0 != intersection(esk4_0,esk5_0) ),
inference(distribute,[status(thm)],[37]) ).
cnf(39,negated_conjecture,
esk3_0 != intersection(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[38]) ).
cnf(40,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk5_0)
| ~ member(X1,esk4_0) ),
inference(split_conjunct,[status(thm)],[38]) ).
cnf(41,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[38]) ).
cnf(42,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[38]) ).
fof(43,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(44,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)],[43]) ).
fof(45,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)],[44]) ).
cnf(46,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(47,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(48,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(59,plain,
( member(esk1_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[47,17,theory(equality)]) ).
cnf(62,plain,
( member(esk1_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[48,17,theory(equality)]) ).
cnf(63,negated_conjecture,
( subset(X1,esk4_0)
| ~ member(esk1_2(X1,esk4_0),esk3_0) ),
inference(spm,[status(thm)],[16,42,theory(equality)]) ).
cnf(64,negated_conjecture,
( subset(X1,esk5_0)
| ~ member(esk1_2(X1,esk5_0),esk3_0) ),
inference(spm,[status(thm)],[16,41,theory(equality)]) ).
cnf(72,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)],[16,46,theory(equality)]) ).
cnf(94,negated_conjecture,
( member(esk1_2(intersection(X1,esk5_0),X2),esk3_0)
| subset(intersection(X1,esk5_0),X2)
| ~ member(esk1_2(intersection(X1,esk5_0),X2),esk4_0) ),
inference(spm,[status(thm)],[40,59,theory(equality)]) ).
cnf(97,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[16,59,theory(equality)]) ).
cnf(98,negated_conjecture,
subset(intersection(X1,esk3_0),esk4_0),
inference(spm,[status(thm)],[63,59,theory(equality)]) ).
cnf(99,negated_conjecture,
subset(intersection(X1,esk3_0),esk5_0),
inference(spm,[status(thm)],[64,59,theory(equality)]) ).
cnf(100,negated_conjecture,
subset(intersection(esk3_0,X1),esk4_0),
inference(spm,[status(thm)],[98,10,theory(equality)]) ).
cnf(107,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,intersection(X2,esk3_0)) ),
inference(spm,[status(thm)],[18,99,theory(equality)]) ).
cnf(115,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,intersection(esk3_0,X2)) ),
inference(spm,[status(thm)],[18,100,theory(equality)]) ).
cnf(123,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[16,62,theory(equality)]) ).
cnf(158,negated_conjecture,
( member(esk1_2(intersection(X1,esk3_0),X2),esk5_0)
| subset(intersection(X1,esk3_0),X2) ),
inference(spm,[status(thm)],[107,17,theory(equality)]) ).
cnf(168,negated_conjecture,
( member(esk1_2(intersection(esk3_0,X1),X2),esk4_0)
| subset(intersection(esk3_0,X1),X2) ),
inference(spm,[status(thm)],[115,17,theory(equality)]) ).
cnf(188,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[72,17,theory(equality)]) ).
cnf(190,plain,
( subset(intersection(X1,X2),intersection(X3,X2))
| ~ member(esk1_2(intersection(X1,X2),intersection(X3,X2)),X3) ),
inference(spm,[status(thm)],[72,59,theory(equality)]) ).
cnf(443,negated_conjecture,
( member(esk1_2(intersection(esk4_0,esk5_0),X1),esk3_0)
| subset(intersection(esk4_0,esk5_0),X1) ),
inference(spm,[status(thm)],[94,62,theory(equality)]) ).
cnf(445,negated_conjecture,
subset(intersection(esk4_0,esk5_0),esk3_0),
inference(spm,[status(thm)],[16,443,theory(equality)]) ).
cnf(451,negated_conjecture,
( esk3_0 = intersection(esk4_0,esk5_0)
| ~ subset(esk3_0,intersection(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[22,445,theory(equality)]) ).
cnf(453,negated_conjecture,
~ subset(esk3_0,intersection(esk4_0,esk5_0)),
inference(sr,[status(thm)],[451,39,theory(equality)]) ).
cnf(1389,plain,
subset(X1,intersection(X1,X1)),
inference(spm,[status(thm)],[188,17,theory(equality)]) ).
cnf(1394,negated_conjecture,
subset(intersection(X1,esk3_0),intersection(esk5_0,intersection(X1,esk3_0))),
inference(spm,[status(thm)],[188,158,theory(equality)]) ).
cnf(1424,plain,
( intersection(X1,X1) = X1
| ~ subset(intersection(X1,X1),X1) ),
inference(spm,[status(thm)],[22,1389,theory(equality)]) ).
cnf(1430,plain,
( intersection(X1,X1) = X1
| $false ),
inference(rw,[status(thm)],[1424,123,theory(equality)]) ).
cnf(1431,plain,
intersection(X1,X1) = X1,
inference(cn,[status(thm)],[1430,theory(equality)]) ).
cnf(2000,negated_conjecture,
( intersection(esk5_0,intersection(X1,esk3_0)) = intersection(X1,esk3_0)
| ~ subset(intersection(esk5_0,intersection(X1,esk3_0)),intersection(X1,esk3_0)) ),
inference(spm,[status(thm)],[22,1394,theory(equality)]) ).
cnf(2004,negated_conjecture,
( intersection(esk5_0,intersection(X1,esk3_0)) = intersection(X1,esk3_0)
| $false ),
inference(rw,[status(thm)],[2000,97,theory(equality)]) ).
cnf(2005,negated_conjecture,
intersection(esk5_0,intersection(X1,esk3_0)) = intersection(X1,esk3_0),
inference(cn,[status(thm)],[2004,theory(equality)]) ).
cnf(2019,negated_conjecture,
intersection(esk5_0,esk3_0) = esk3_0,
inference(spm,[status(thm)],[2005,1431,theory(equality)]) ).
cnf(2077,negated_conjecture,
intersection(esk3_0,esk5_0) = esk3_0,
inference(rw,[status(thm)],[2019,10,theory(equality)]) ).
cnf(2197,negated_conjecture,
subset(intersection(esk3_0,X1),intersection(esk4_0,X1)),
inference(spm,[status(thm)],[190,168,theory(equality)]) ).
cnf(2234,negated_conjecture,
subset(esk3_0,intersection(esk4_0,esk5_0)),
inference(spm,[status(thm)],[2197,2077,theory(equality)]) ).
cnf(2245,negated_conjecture,
$false,
inference(sr,[status(thm)],[2234,453,theory(equality)]) ).
cnf(2246,negated_conjecture,
$false,
2245,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET578+3.p
% --creating new selector for []
% -running prover on /tmp/tmpWL1qlm/sel_SET578+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET578+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET578+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET578+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
%
%------------------------------------------------------------------------------