TSTP Solution File: SET598+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET598+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 03:00:03 EST 2010
% Result : Theorem 0.30s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 63 ( 16 unt; 0 def)
% Number of atoms : 220 ( 54 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 256 ( 99 ~; 112 |; 39 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 2 sgn 38 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/tmp/tmpF5SHZd/sel_SET598+3.p_1',commutativity_of_intersection) ).
fof(3,axiom,
! [X1,X2] : subset(intersection(X1,X2),X1),
file('/tmp/tmpF5SHZd/sel_SET598+3.p_1',intersection_is_subset) ).
fof(4,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,intersection(X2,X3)) ),
file('/tmp/tmpF5SHZd/sel_SET598+3.p_1',intersection_of_subsets) ).
fof(5,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpF5SHZd/sel_SET598+3.p_1',equal_defn) ).
fof(6,conjecture,
! [X1,X2,X3] :
( X1 = intersection(X2,X3)
<=> ( subset(X1,X2)
& subset(X1,X3)
& ! [X4] :
( ( subset(X4,X2)
& subset(X4,X3) )
=> subset(X4,X1) ) ) ),
file('/tmp/tmpF5SHZd/sel_SET598+3.p_1',prove_th57) ).
fof(10,negated_conjecture,
~ ! [X1,X2,X3] :
( X1 = intersection(X2,X3)
<=> ( subset(X1,X2)
& subset(X1,X3)
& ! [X4] :
( ( subset(X4,X2)
& subset(X4,X3) )
=> subset(X4,X1) ) ) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(11,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(12,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[11]) ).
fof(21,plain,
! [X3,X4] : subset(intersection(X3,X4),X3),
inference(variable_rename,[status(thm)],[3]) ).
cnf(22,plain,
subset(intersection(X1,X2),X1),
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,plain,
! [X1,X2,X3] :
( ~ subset(X1,X2)
| ~ subset(X1,X3)
| subset(X1,intersection(X2,X3)) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(24,plain,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X4,X6)
| subset(X4,intersection(X5,X6)) ),
inference(variable_rename,[status(thm)],[23]) ).
cnf(25,plain,
( subset(X1,intersection(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(26,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(27,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,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)],[27]) ).
cnf(29,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[28]) ).
fof(32,negated_conjecture,
? [X1,X2,X3] :
( ( X1 != intersection(X2,X3)
| ~ subset(X1,X2)
| ~ subset(X1,X3)
| ? [X4] :
( subset(X4,X2)
& subset(X4,X3)
& ~ subset(X4,X1) ) )
& ( X1 = intersection(X2,X3)
| ( subset(X1,X2)
& subset(X1,X3)
& ! [X4] :
( ~ subset(X4,X2)
| ~ subset(X4,X3)
| subset(X4,X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(33,negated_conjecture,
? [X5,X6,X7] :
( ( X5 != intersection(X6,X7)
| ~ subset(X5,X6)
| ~ subset(X5,X7)
| ? [X8] :
( subset(X8,X6)
& subset(X8,X7)
& ~ subset(X8,X5) ) )
& ( X5 = intersection(X6,X7)
| ( subset(X5,X6)
& subset(X5,X7)
& ! [X9] :
( ~ subset(X9,X6)
| ~ subset(X9,X7)
| subset(X9,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[32]) ).
fof(34,negated_conjecture,
( ( esk2_0 != intersection(esk3_0,esk4_0)
| ~ subset(esk2_0,esk3_0)
| ~ subset(esk2_0,esk4_0)
| ( subset(esk5_0,esk3_0)
& subset(esk5_0,esk4_0)
& ~ subset(esk5_0,esk2_0) ) )
& ( esk2_0 = intersection(esk3_0,esk4_0)
| ( subset(esk2_0,esk3_0)
& subset(esk2_0,esk4_0)
& ! [X9] :
( ~ subset(X9,esk3_0)
| ~ subset(X9,esk4_0)
| subset(X9,esk2_0) ) ) ) ),
inference(skolemize,[status(esa)],[33]) ).
fof(35,negated_conjecture,
! [X9] :
( ( ( ( ~ subset(X9,esk3_0)
| ~ subset(X9,esk4_0)
| subset(X9,esk2_0) )
& subset(esk2_0,esk3_0)
& subset(esk2_0,esk4_0) )
| esk2_0 = intersection(esk3_0,esk4_0) )
& ( esk2_0 != intersection(esk3_0,esk4_0)
| ~ subset(esk2_0,esk3_0)
| ~ subset(esk2_0,esk4_0)
| ( subset(esk5_0,esk3_0)
& subset(esk5_0,esk4_0)
& ~ subset(esk5_0,esk2_0) ) ) ),
inference(shift_quantors,[status(thm)],[34]) ).
fof(36,negated_conjecture,
! [X9] :
( ( ~ subset(X9,esk3_0)
| ~ subset(X9,esk4_0)
| subset(X9,esk2_0)
| esk2_0 = intersection(esk3_0,esk4_0) )
& ( subset(esk2_0,esk3_0)
| esk2_0 = intersection(esk3_0,esk4_0) )
& ( subset(esk2_0,esk4_0)
| esk2_0 = intersection(esk3_0,esk4_0) )
& ( subset(esk5_0,esk3_0)
| ~ subset(esk2_0,esk3_0)
| ~ subset(esk2_0,esk4_0)
| esk2_0 != intersection(esk3_0,esk4_0) )
& ( subset(esk5_0,esk4_0)
| ~ subset(esk2_0,esk3_0)
| ~ subset(esk2_0,esk4_0)
| esk2_0 != intersection(esk3_0,esk4_0) )
& ( ~ subset(esk5_0,esk2_0)
| ~ subset(esk2_0,esk3_0)
| ~ subset(esk2_0,esk4_0)
| esk2_0 != intersection(esk3_0,esk4_0) ) ),
inference(distribute,[status(thm)],[35]) ).
cnf(37,negated_conjecture,
( esk2_0 != intersection(esk3_0,esk4_0)
| ~ subset(esk2_0,esk4_0)
| ~ subset(esk2_0,esk3_0)
| ~ subset(esk5_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(38,negated_conjecture,
( subset(esk5_0,esk4_0)
| esk2_0 != intersection(esk3_0,esk4_0)
| ~ subset(esk2_0,esk4_0)
| ~ subset(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(39,negated_conjecture,
( subset(esk5_0,esk3_0)
| esk2_0 != intersection(esk3_0,esk4_0)
| ~ subset(esk2_0,esk4_0)
| ~ subset(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(40,negated_conjecture,
( esk2_0 = intersection(esk3_0,esk4_0)
| subset(esk2_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(41,negated_conjecture,
( esk2_0 = intersection(esk3_0,esk4_0)
| subset(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(42,negated_conjecture,
( esk2_0 = intersection(esk3_0,esk4_0)
| subset(X1,esk2_0)
| ~ subset(X1,esk4_0)
| ~ subset(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(60,negated_conjecture,
subset(esk2_0,esk3_0),
inference(spm,[status(thm)],[22,41,theory(equality)]) ).
cnf(66,plain,
subset(intersection(X2,X1),X1),
inference(spm,[status(thm)],[22,12,theory(equality)]) ).
cnf(88,negated_conjecture,
( intersection(esk3_0,esk4_0) = esk2_0
| subset(intersection(esk4_0,X1),esk2_0)
| ~ subset(intersection(esk4_0,X1),esk3_0) ),
inference(spm,[status(thm)],[42,22,theory(equality)]) ).
cnf(114,negated_conjecture,
( intersection(esk3_0,esk4_0) != esk2_0
| $false
| ~ subset(esk2_0,esk4_0)
| ~ subset(esk5_0,esk2_0) ),
inference(rw,[status(thm)],[37,60,theory(equality)]) ).
cnf(115,negated_conjecture,
( intersection(esk3_0,esk4_0) != esk2_0
| ~ subset(esk2_0,esk4_0)
| ~ subset(esk5_0,esk2_0) ),
inference(cn,[status(thm)],[114,theory(equality)]) ).
cnf(116,negated_conjecture,
( subset(esk5_0,esk4_0)
| intersection(esk3_0,esk4_0) != esk2_0
| $false
| ~ subset(esk2_0,esk4_0) ),
inference(rw,[status(thm)],[38,60,theory(equality)]) ).
cnf(117,negated_conjecture,
( subset(esk5_0,esk4_0)
| intersection(esk3_0,esk4_0) != esk2_0
| ~ subset(esk2_0,esk4_0) ),
inference(cn,[status(thm)],[116,theory(equality)]) ).
cnf(118,negated_conjecture,
( subset(esk5_0,esk3_0)
| intersection(esk3_0,esk4_0) != esk2_0
| $false
| ~ subset(esk2_0,esk4_0) ),
inference(rw,[status(thm)],[39,60,theory(equality)]) ).
cnf(119,negated_conjecture,
( subset(esk5_0,esk3_0)
| intersection(esk3_0,esk4_0) != esk2_0
| ~ subset(esk2_0,esk4_0) ),
inference(cn,[status(thm)],[118,theory(equality)]) ).
cnf(136,negated_conjecture,
subset(esk2_0,esk4_0),
inference(spm,[status(thm)],[66,40,theory(equality)]) ).
cnf(146,negated_conjecture,
( subset(esk5_0,esk3_0)
| intersection(esk3_0,esk4_0) != esk2_0
| $false ),
inference(rw,[status(thm)],[119,136,theory(equality)]) ).
cnf(147,negated_conjecture,
( subset(esk5_0,esk3_0)
| intersection(esk3_0,esk4_0) != esk2_0 ),
inference(cn,[status(thm)],[146,theory(equality)]) ).
cnf(148,negated_conjecture,
( subset(esk5_0,esk4_0)
| intersection(esk3_0,esk4_0) != esk2_0
| $false ),
inference(rw,[status(thm)],[117,136,theory(equality)]) ).
cnf(149,negated_conjecture,
( subset(esk5_0,esk4_0)
| intersection(esk3_0,esk4_0) != esk2_0 ),
inference(cn,[status(thm)],[148,theory(equality)]) ).
cnf(150,negated_conjecture,
( intersection(esk3_0,esk4_0) != esk2_0
| $false
| ~ subset(esk5_0,esk2_0) ),
inference(rw,[status(thm)],[115,136,theory(equality)]) ).
cnf(151,negated_conjecture,
( intersection(esk3_0,esk4_0) != esk2_0
| ~ subset(esk5_0,esk2_0) ),
inference(cn,[status(thm)],[150,theory(equality)]) ).
cnf(409,negated_conjecture,
( intersection(esk3_0,esk4_0) = esk2_0
| subset(intersection(esk4_0,esk3_0),esk2_0) ),
inference(spm,[status(thm)],[88,66,theory(equality)]) ).
cnf(418,negated_conjecture,
( intersection(esk3_0,esk4_0) = esk2_0
| subset(intersection(esk3_0,esk4_0),esk2_0) ),
inference(rw,[status(thm)],[409,12,theory(equality)]) ).
cnf(424,negated_conjecture,
( esk2_0 = intersection(esk3_0,esk4_0)
| ~ subset(esk2_0,intersection(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[29,418,theory(equality)]) ).
cnf(431,negated_conjecture,
( intersection(esk3_0,esk4_0) = esk2_0
| ~ subset(esk2_0,esk4_0)
| ~ subset(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[424,25,theory(equality)]) ).
cnf(434,negated_conjecture,
( intersection(esk3_0,esk4_0) = esk2_0
| $false
| ~ subset(esk2_0,esk3_0) ),
inference(rw,[status(thm)],[431,136,theory(equality)]) ).
cnf(435,negated_conjecture,
( intersection(esk3_0,esk4_0) = esk2_0
| $false
| $false ),
inference(rw,[status(thm)],[434,60,theory(equality)]) ).
cnf(436,negated_conjecture,
intersection(esk3_0,esk4_0) = esk2_0,
inference(cn,[status(thm)],[435,theory(equality)]) ).
cnf(445,negated_conjecture,
( subset(X1,esk2_0)
| ~ subset(X1,esk4_0)
| ~ subset(X1,esk3_0) ),
inference(spm,[status(thm)],[25,436,theory(equality)]) ).
cnf(460,negated_conjecture,
( $false
| ~ subset(esk5_0,esk2_0) ),
inference(rw,[status(thm)],[151,436,theory(equality)]) ).
cnf(461,negated_conjecture,
~ subset(esk5_0,esk2_0),
inference(cn,[status(thm)],[460,theory(equality)]) ).
cnf(462,negated_conjecture,
( subset(esk5_0,esk4_0)
| $false ),
inference(rw,[status(thm)],[149,436,theory(equality)]) ).
cnf(463,negated_conjecture,
subset(esk5_0,esk4_0),
inference(cn,[status(thm)],[462,theory(equality)]) ).
cnf(464,negated_conjecture,
( subset(esk5_0,esk3_0)
| $false ),
inference(rw,[status(thm)],[147,436,theory(equality)]) ).
cnf(465,negated_conjecture,
subset(esk5_0,esk3_0),
inference(cn,[status(thm)],[464,theory(equality)]) ).
cnf(636,negated_conjecture,
( subset(esk5_0,esk2_0)
| ~ subset(esk5_0,esk3_0) ),
inference(spm,[status(thm)],[445,463,theory(equality)]) ).
cnf(647,negated_conjecture,
( subset(esk5_0,esk2_0)
| $false ),
inference(rw,[status(thm)],[636,465,theory(equality)]) ).
cnf(648,negated_conjecture,
subset(esk5_0,esk2_0),
inference(cn,[status(thm)],[647,theory(equality)]) ).
cnf(649,negated_conjecture,
$false,
inference(sr,[status(thm)],[648,461,theory(equality)]) ).
cnf(650,negated_conjecture,
$false,
649,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET598+3.p
% --creating new selector for []
% -running prover on /tmp/tmpF5SHZd/sel_SET598+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET598+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET598+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET598+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
%
%------------------------------------------------------------------------------