TSTP Solution File: SET610+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET610+3 : TPTP v5.0.0. Released v2.2.0.
% 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 03:01:28 EST 2010
% Result : Theorem 80.07s
% Output : CNFRefutation 80.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of formulae : 92 ( 33 unt; 0 def)
% Number of atoms : 225 ( 33 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 209 ( 76 ~; 96 |; 31 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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; 2 con; 0-2 aty)
% Number of variables : 230 ( 24 sgn 61 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpNrGUZj/sel_SET610+3.p_2',equal_defn) ).
fof(3,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/tmp/tmpNrGUZj/sel_SET610+3.p_2',union_defn) ).
fof(4,conjecture,
! [X1,X2] : difference(union(X1,X2),X2) = difference(X1,X2),
file('/tmp/tmpNrGUZj/sel_SET610+3.p_2',prove_th83) ).
fof(5,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/tmp/tmpNrGUZj/sel_SET610+3.p_2',commutativity_of_union) ).
fof(7,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpNrGUZj/sel_SET610+3.p_2',subset_defn) ).
fof(8,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/tmp/tmpNrGUZj/sel_SET610+3.p_2',difference_defn) ).
fof(10,negated_conjecture,
~ ! [X1,X2] : difference(union(X1,X2),X2) = difference(X1,X2),
inference(assume_negation,[status(cth)],[4]) ).
fof(11,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).
fof(18,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(19,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[18]) ).
fof(20,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)],[19]) ).
cnf(21,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(24,plain,
! [X1,X2,X3] :
( ( ~ member(X3,union(X1,X2))
| member(X3,X1)
| member(X3,X2) )
& ( ( ~ member(X3,X1)
& ~ member(X3,X2) )
| member(X3,union(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(25,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ( ~ member(X6,X4)
& ~ member(X6,X5) )
| member(X6,union(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[24]) ).
fof(26,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X4)
| member(X6,union(X4,X5)) )
& ( ~ member(X6,X5)
| member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[25]) ).
cnf(27,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[26]) ).
cnf(28,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[26]) ).
cnf(29,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[26]) ).
fof(30,negated_conjecture,
? [X1,X2] : difference(union(X1,X2),X2) != difference(X1,X2),
inference(fof_nnf,[status(thm)],[10]) ).
fof(31,negated_conjecture,
? [X3,X4] : difference(union(X3,X4),X4) != difference(X3,X4),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,negated_conjecture,
difference(union(esk2_0,esk3_0),esk3_0) != difference(esk2_0,esk3_0),
inference(skolemize,[status(esa)],[31]) ).
cnf(33,negated_conjecture,
difference(union(esk2_0,esk3_0),esk3_0) != difference(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[32]) ).
fof(34,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(35,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[34]) ).
fof(45,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)],[7]) ).
fof(46,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)],[45]) ).
fof(47,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk5_2(X4,X5),X4)
& ~ member(esk5_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[46]) ).
fof(48,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk5_2(X4,X5),X4)
& ~ member(esk5_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[47]) ).
fof(49,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk5_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk5_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[48]) ).
cnf(50,plain,
( subset(X1,X2)
| ~ member(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(51,plain,
( subset(X1,X2)
| member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(52,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[49]) ).
fof(53,plain,
! [X1,X2,X3] :
( ( ~ member(X3,difference(X1,X2))
| ( member(X3,X1)
& ~ member(X3,X2) ) )
& ( ~ member(X3,X1)
| member(X3,X2)
| member(X3,difference(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(54,plain,
! [X4,X5,X6] :
( ( ~ member(X6,difference(X4,X5))
| ( member(X6,X4)
& ~ member(X6,X5) ) )
& ( ~ member(X6,X4)
| member(X6,X5)
| member(X6,difference(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[53]) ).
fof(55,plain,
! [X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X5)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X4)
| member(X6,X5)
| member(X6,difference(X4,X5)) ) ),
inference(distribute,[status(thm)],[54]) ).
cnf(56,plain,
( member(X1,difference(X2,X3))
| member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(57,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(58,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(61,negated_conjecture,
difference(union(esk3_0,esk2_0),esk3_0) != difference(esk2_0,esk3_0),
inference(rw,[status(thm)],[33,35,theory(equality)]) ).
cnf(70,plain,
( member(esk5_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[58,51,theory(equality)]) ).
cnf(71,plain,
( subset(X1,union(X2,X3))
| ~ member(esk5_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[50,27,theory(equality)]) ).
cnf(72,plain,
( subset(X1,union(X2,X3))
| ~ member(esk5_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[50,28,theory(equality)]) ).
cnf(75,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk5_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[57,51,theory(equality)]) ).
cnf(78,plain,
( subset(X1,difference(X2,X3))
| member(esk5_2(X1,difference(X2,X3)),X3)
| ~ member(esk5_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[50,56,theory(equality)]) ).
cnf(84,plain,
( member(esk5_2(union(X1,X2),X3),X2)
| member(esk5_2(union(X1,X2),X3),X1)
| subset(union(X1,X2),X3) ),
inference(spm,[status(thm)],[29,51,theory(equality)]) ).
cnf(110,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[50,70,theory(equality)]) ).
cnf(112,plain,
( member(esk5_2(difference(union(X1,X2),X3),X4),X2)
| member(esk5_2(difference(union(X1,X2),X3),X4),X1)
| subset(difference(union(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[29,70,theory(equality)]) ).
cnf(117,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk5_2(X1,union(X2,union(X3,X4))),X4) ),
inference(spm,[status(thm)],[71,27,theory(equality)]) ).
cnf(121,plain,
subset(difference(X1,X2),union(X3,X1)),
inference(spm,[status(thm)],[71,70,theory(equality)]) ).
cnf(130,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[72,51,theory(equality)]) ).
cnf(131,plain,
( subset(X1,union(difference(X2,X3),X4))
| member(esk5_2(X1,union(difference(X2,X3),X4)),X3)
| ~ member(esk5_2(X1,union(difference(X2,X3),X4)),X2) ),
inference(spm,[status(thm)],[72,56,theory(equality)]) ).
cnf(142,plain,
( member(X1,union(X2,X3))
| ~ member(X1,difference(X3,X4)) ),
inference(spm,[status(thm)],[52,121,theory(equality)]) ).
cnf(234,plain,
( subset(X1,difference(X1,X2))
| member(esk5_2(X1,difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[78,51,theory(equality)]) ).
cnf(269,plain,
( member(esk5_2(union(difference(X1,X2),X3),X4),X1)
| subset(union(difference(X1,X2),X3),X4)
| member(esk5_2(union(difference(X1,X2),X3),X4),X3) ),
inference(spm,[status(thm)],[58,84,theory(equality)]) ).
cnf(277,plain,
( subset(union(X1,X2),union(X3,X1))
| member(esk5_2(union(X1,X2),union(X3,X1)),X2) ),
inference(spm,[status(thm)],[71,84,theory(equality)]) ).
cnf(279,plain,
( subset(union(X1,X2),union(X1,X3))
| member(esk5_2(union(X1,X2),union(X1,X3)),X2) ),
inference(spm,[status(thm)],[72,84,theory(equality)]) ).
cnf(290,plain,
( subset(X1,difference(X1,difference(X2,X3)))
| ~ member(esk5_2(X1,difference(X1,difference(X2,X3))),X3) ),
inference(spm,[status(thm)],[57,234,theory(equality)]) ).
cnf(446,plain,
( member(esk5_2(difference(X1,X2),X3),union(X4,X1))
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[142,51,theory(equality)]) ).
cnf(671,plain,
( subset(difference(X1,X2),difference(union(X3,X1),X4))
| member(esk5_2(difference(X1,X2),difference(union(X3,X1),X4)),X4) ),
inference(spm,[status(thm)],[78,446,theory(equality)]) ).
cnf(2624,plain,
( subset(difference(union(X1,X2),X3),X1)
| member(esk5_2(difference(union(X1,X2),X3),X1),X2) ),
inference(spm,[status(thm)],[50,112,theory(equality)]) ).
cnf(9417,plain,
( subset(union(difference(X5,X6),X5),X7)
| member(esk5_2(union(difference(X5,X6),X5),X7),X5) ),
inference(ef,[status(thm)],[269,theory(equality)]) ).
cnf(9510,plain,
( subset(union(X5,difference(X5,X6)),X7)
| member(esk5_2(union(difference(X5,X6),X5),X7),X5) ),
inference(rw,[status(thm)],[9417,35,theory(equality)]) ).
cnf(9511,plain,
( subset(union(X5,difference(X5,X6)),X7)
| member(esk5_2(union(X5,difference(X5,X6)),X7),X5) ),
inference(rw,[status(thm)],[9510,35,theory(equality)]) ).
cnf(11915,plain,
( subset(union(X1,X2),union(difference(X2,X3),X1))
| member(esk5_2(union(X1,X2),union(difference(X2,X3),X1)),X3) ),
inference(spm,[status(thm)],[131,277,theory(equality)]) ).
cnf(12395,plain,
subset(union(X1,X2),union(X1,union(X3,X2))),
inference(spm,[status(thm)],[117,279,theory(equality)]) ).
cnf(13832,plain,
subset(X1,difference(X1,difference(X2,X1))),
inference(spm,[status(thm)],[290,51,theory(equality)]) ).
cnf(13966,plain,
( difference(X1,difference(X2,X1)) = X1
| ~ subset(difference(X1,difference(X2,X1)),X1) ),
inference(spm,[status(thm)],[21,13832,theory(equality)]) ).
cnf(14011,plain,
( difference(X1,difference(X2,X1)) = X1
| $false ),
inference(rw,[status(thm)],[13966,110,theory(equality)]) ).
cnf(14012,plain,
difference(X1,difference(X2,X1)) = X1,
inference(cn,[status(thm)],[14011,theory(equality)]) ).
cnf(92719,plain,
subset(difference(X1,X2),difference(union(X3,X1),X2)),
inference(spm,[status(thm)],[75,671,theory(equality)]) ).
cnf(92874,plain,
subset(X1,difference(union(X3,X1),difference(X2,X1))),
inference(spm,[status(thm)],[92719,14012,theory(equality)]) ).
cnf(135908,plain,
subset(X1,difference(union(X1,X2),difference(X3,X1))),
inference(spm,[status(thm)],[92874,35,theory(equality)]) ).
cnf(246969,plain,
subset(difference(union(X1,X2),X2),X1),
inference(spm,[status(thm)],[75,2624,theory(equality)]) ).
cnf(846589,plain,
subset(union(X1,difference(X1,X2)),X1),
inference(spm,[status(thm)],[50,9511,theory(equality)]) ).
cnf(847394,plain,
( X1 = union(X1,difference(X1,X2))
| ~ subset(X1,union(X1,difference(X1,X2))) ),
inference(spm,[status(thm)],[21,846589,theory(equality)]) ).
cnf(847630,plain,
( X1 = union(X1,difference(X1,X2))
| $false ),
inference(rw,[status(thm)],[847394,130,theory(equality)]) ).
cnf(847631,plain,
X1 = union(X1,difference(X1,X2)),
inference(cn,[status(thm)],[847630,theory(equality)]) ).
cnf(847724,plain,
subset(union(X1,difference(X2,X3)),union(X1,X2)),
inference(spm,[status(thm)],[12395,847631,theory(equality)]) ).
cnf(1313864,plain,
subset(union(X1,X2),union(difference(X2,X1),X1)),
inference(spm,[status(thm)],[71,11915,theory(equality)]) ).
cnf(1314510,plain,
subset(union(X1,X2),union(X1,difference(X2,X1))),
inference(rw,[status(thm)],[1313864,35,theory(equality)]) ).
cnf(1314926,plain,
( union(X1,difference(X2,X1)) = union(X1,X2)
| ~ subset(union(X1,difference(X2,X1)),union(X1,X2)) ),
inference(spm,[status(thm)],[21,1314510,theory(equality)]) ).
cnf(1315316,plain,
( union(X1,difference(X2,X1)) = union(X1,X2)
| $false ),
inference(rw,[status(thm)],[1314926,847724,theory(equality)]) ).
cnf(1315317,plain,
union(X1,difference(X2,X1)) = union(X1,X2),
inference(cn,[status(thm)],[1315316,theory(equality)]) ).
cnf(1315560,plain,
subset(difference(union(X1,X2),difference(X2,X1)),X1),
inference(spm,[status(thm)],[246969,1315317,theory(equality)]) ).
cnf(1700541,plain,
( X1 = difference(union(X1,X2),difference(X2,X1))
| ~ subset(X1,difference(union(X1,X2),difference(X2,X1))) ),
inference(spm,[status(thm)],[21,1315560,theory(equality)]) ).
cnf(1700906,plain,
( X1 = difference(union(X1,X2),difference(X2,X1))
| $false ),
inference(rw,[status(thm)],[1700541,135908,theory(equality)]) ).
cnf(1700907,plain,
X1 = difference(union(X1,X2),difference(X2,X1)),
inference(cn,[status(thm)],[1700906,theory(equality)]) ).
cnf(1700974,plain,
difference(union(difference(X1,X2),X2),X2) = difference(X1,X2),
inference(spm,[status(thm)],[1700907,14012,theory(equality)]) ).
cnf(1702725,plain,
difference(union(X2,X1),X2) = difference(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1700974,35,theory(equality)]),1315317,theory(equality)]) ).
cnf(1705066,negated_conjecture,
$false,
inference(rw,[status(thm)],[61,1702725,theory(equality)]) ).
cnf(1705067,negated_conjecture,
$false,
inference(cn,[status(thm)],[1705066,theory(equality)]) ).
cnf(1705068,negated_conjecture,
$false,
1705067,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET610+3.p
% --creating new selector for []
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpNrGUZj/sel_SET610+3.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpNrGUZj/sel_SET610+3.p_2 with time limit 80
% -prover status Theorem
% Problem SET610+3.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET610+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET610+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
%
%------------------------------------------------------------------------------