TSTP Solution File: SET606+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET606+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 03:00:45 EST 2010
% Result : Theorem 23.41s
% Output : CNFRefutation 23.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 73 ( 25 unt; 0 def)
% Number of atoms : 192 ( 30 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 194 ( 75 ~; 81 |; 32 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 175 ( 11 sgn 61 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/tmp/tmproBbu6/sel_SET606+3.p_1',commutativity_of_intersection) ).
fof(3,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmproBbu6/sel_SET606+3.p_1',equal_defn) ).
fof(4,conjecture,
! [X1,X2] : difference(X1,intersection(X1,X2)) = difference(X1,X2),
file('/tmp/tmproBbu6/sel_SET606+3.p_1',prove_difference_into_intersection) ).
fof(6,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmproBbu6/sel_SET606+3.p_1',subset_defn) ).
fof(8,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmproBbu6/sel_SET606+3.p_1',intersection_defn) ).
fof(9,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/tmp/tmproBbu6/sel_SET606+3.p_1',difference_defn) ).
fof(10,negated_conjecture,
~ ! [X1,X2] : difference(X1,intersection(X1,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)],[9,theory(equality)]) ).
fof(12,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(13,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[12]) ).
fof(20,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(21,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[20]) ).
fof(22,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)],[21]) ).
cnf(23,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(26,negated_conjecture,
? [X1,X2] : difference(X1,intersection(X1,X2)) != difference(X1,X2),
inference(fof_nnf,[status(thm)],[10]) ).
fof(27,negated_conjecture,
? [X3,X4] : difference(X3,intersection(X3,X4)) != difference(X3,X4),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,negated_conjecture,
difference(esk2_0,intersection(esk2_0,esk3_0)) != difference(esk2_0,esk3_0),
inference(skolemize,[status(esa)],[27]) ).
cnf(29,negated_conjecture,
difference(esk2_0,intersection(esk2_0,esk3_0)) != difference(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[28]) ).
fof(32,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)],[6]) ).
fof(33,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)],[32]) ).
fof(34,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk4_2(X4,X5),X4)
& ~ member(esk4_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[33]) ).
fof(35,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk4_2(X4,X5),X4)
& ~ member(esk4_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[34]) ).
fof(36,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk4_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk4_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[35]) ).
cnf(37,plain,
( subset(X1,X2)
| ~ member(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(38,plain,
( subset(X1,X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[36]) ).
fof(49,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)],[8]) ).
fof(50,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)],[49]) ).
fof(51,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)],[50]) ).
cnf(52,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[51]) ).
cnf(53,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[51]) ).
cnf(54,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[51]) ).
fof(55,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(56,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)],[55]) ).
fof(57,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)],[56]) ).
cnf(58,plain,
( member(X1,difference(X2,X3))
| member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(59,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(60,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(69,plain,
( member(esk4_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[53,38,theory(equality)]) ).
cnf(70,plain,
( member(esk4_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[54,38,theory(equality)]) ).
cnf(71,plain,
( member(esk4_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[60,38,theory(equality)]) ).
cnf(74,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk4_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[59,38,theory(equality)]) ).
cnf(77,plain,
( subset(X1,difference(X2,X3))
| member(esk4_2(X1,difference(X2,X3)),X3)
| ~ member(esk4_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[37,58,theory(equality)]) ).
cnf(83,plain,
( subset(X1,intersection(X2,X3))
| ~ member(esk4_2(X1,intersection(X2,X3)),X3)
| ~ member(esk4_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[37,52,theory(equality)]) ).
cnf(115,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[37,69,theory(equality)]) ).
cnf(138,plain,
( subset(intersection(difference(X1,X2),X3),X4)
| ~ member(esk4_2(intersection(difference(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[59,70,theory(equality)]) ).
cnf(143,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[37,71,theory(equality)]) ).
cnf(147,plain,
( subset(difference(X1,difference(X2,X3)),X4)
| member(esk4_2(difference(X1,difference(X2,X3)),X4),X3)
| ~ member(esk4_2(difference(X1,difference(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[74,58,theory(equality)]) ).
cnf(150,plain,
( subset(X1,difference(X1,X2))
| member(esk4_2(X1,difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[77,38,theory(equality)]) ).
cnf(153,plain,
( subset(intersection(X1,X2),difference(X2,X3))
| member(esk4_2(intersection(X1,X2),difference(X2,X3)),X3) ),
inference(spm,[status(thm)],[77,69,theory(equality)]) ).
cnf(260,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk4_2(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[83,38,theory(equality)]) ).
cnf(265,plain,
( subset(difference(X1,X2),intersection(X3,X1))
| ~ member(esk4_2(difference(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[83,71,theory(equality)]) ).
cnf(321,plain,
( subset(X1,difference(X1,difference(X2,X3)))
| ~ member(esk4_2(X1,difference(X1,difference(X2,X3))),X3) ),
inference(spm,[status(thm)],[59,150,theory(equality)]) ).
cnf(749,plain,
subset(difference(X1,X2),intersection(X1,difference(X1,X2))),
inference(spm,[status(thm)],[260,71,theory(equality)]) ).
cnf(934,plain,
( intersection(X1,difference(X1,X2)) = difference(X1,X2)
| ~ subset(intersection(X1,difference(X1,X2)),difference(X1,X2)) ),
inference(spm,[status(thm)],[23,749,theory(equality)]) ).
cnf(944,plain,
( intersection(X1,difference(X1,X2)) = difference(X1,X2)
| $false ),
inference(rw,[status(thm)],[934,115,theory(equality)]) ).
cnf(945,plain,
intersection(X1,difference(X1,X2)) = difference(X1,X2),
inference(cn,[status(thm)],[944,theory(equality)]) ).
cnf(5540,plain,
( subset(difference(X1,difference(X1,X2)),X3)
| member(esk4_2(difference(X1,difference(X1,X2)),X3),X2) ),
inference(spm,[status(thm)],[147,71,theory(equality)]) ).
cnf(6274,plain,
subset(intersection(difference(X1,X2),X3),difference(X3,X2)),
inference(spm,[status(thm)],[138,153,theory(equality)]) ).
cnf(16519,plain,
subset(X1,difference(X1,difference(X2,X1))),
inference(spm,[status(thm)],[321,38,theory(equality)]) ).
cnf(16614,plain,
( difference(X1,difference(X2,X1)) = X1
| ~ subset(difference(X1,difference(X2,X1)),X1) ),
inference(spm,[status(thm)],[23,16519,theory(equality)]) ).
cnf(16647,plain,
( difference(X1,difference(X2,X1)) = X1
| $false ),
inference(rw,[status(thm)],[16614,143,theory(equality)]) ).
cnf(16648,plain,
difference(X1,difference(X2,X1)) = X1,
inference(cn,[status(thm)],[16647,theory(equality)]) ).
cnf(16685,plain,
subset(intersection(X1,X3),difference(X3,difference(X2,X1))),
inference(spm,[status(thm)],[6274,16648,theory(equality)]) ).
cnf(903532,plain,
subset(difference(X1,difference(X1,X2)),intersection(X2,X1)),
inference(spm,[status(thm)],[265,5540,theory(equality)]) ).
cnf(904344,plain,
( intersection(X1,X2) = difference(X2,difference(X2,X1))
| ~ subset(intersection(X1,X2),difference(X2,difference(X2,X1))) ),
inference(spm,[status(thm)],[23,903532,theory(equality)]) ).
cnf(904614,plain,
( intersection(X1,X2) = difference(X2,difference(X2,X1))
| $false ),
inference(rw,[status(thm)],[904344,16685,theory(equality)]) ).
cnf(904615,plain,
intersection(X1,X2) = difference(X2,difference(X2,X1)),
inference(cn,[status(thm)],[904614,theory(equality)]) ).
cnf(905119,plain,
difference(X1,intersection(X2,X1)) = intersection(difference(X1,X2),X1),
inference(spm,[status(thm)],[904615,904615,theory(equality)]) ).
cnf(906019,plain,
difference(X1,intersection(X2,X1)) = difference(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[905119,13,theory(equality)]),945,theory(equality)]) ).
cnf(907400,plain,
difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(spm,[status(thm)],[906019,13,theory(equality)]) ).
cnf(909250,negated_conjecture,
$false,
inference(rw,[status(thm)],[29,907400,theory(equality)]) ).
cnf(909251,negated_conjecture,
$false,
inference(cn,[status(thm)],[909250,theory(equality)]) ).
cnf(909252,negated_conjecture,
$false,
909251,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET606+3.p
% --creating new selector for []
% -running prover on /tmp/tmproBbu6/sel_SET606+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET606+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET606+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET606+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
%
%------------------------------------------------------------------------------