%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET011+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 02:36:46 EST 2010
% Result : Theorem 20.53s
% Output : CNFRefutation 20.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 15 unt; 0 def)
% Number of atoms : 170 ( 21 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 185 ( 72 ~; 75 |; 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 : 142 ( 5 sgn 61 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/tmp/tmpIvSK2K/sel_SET011+3.p_1',commutativity_of_intersection) ).
fof(2,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpIvSK2K/sel_SET011+3.p_1',subset_defn) ).
fof(3,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpIvSK2K/sel_SET011+3.p_1',equal_defn) ).
fof(6,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpIvSK2K/sel_SET011+3.p_1',intersection_defn) ).
fof(7,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/tmp/tmpIvSK2K/sel_SET011+3.p_1',difference_defn) ).
fof(8,conjecture,
! [X1,X2] : difference(X1,difference(X1,X2)) = intersection(X1,X2),
file('/tmp/tmpIvSK2K/sel_SET011+3.p_1',prove_difference_difference_intersection) ).
fof(9,negated_conjecture,
~ ! [X1,X2] : difference(X1,difference(X1,X2)) = intersection(X1,X2),
inference(assume_negation,[status(cth)],[8]) ).
fof(10,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
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(13,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(14,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)],[13]) ).
fof(15,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)],[14]) ).
fof(16,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)],[15]) ).
fof(17,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)],[16]) ).
cnf(18,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(19,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(21,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(22,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[21]) ).
fof(23,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)],[22]) ).
cnf(24,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[23]) ).
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]) ).
fof(44,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)],[10]) ).
fof(45,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)],[44]) ).
fof(46,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)],[45]) ).
cnf(47,plain,
( member(X1,difference(X2,X3))
| member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(48,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(49,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[46]) ).
fof(50,negated_conjecture,
? [X1,X2] : difference(X1,difference(X1,X2)) != intersection(X1,X2),
inference(fof_nnf,[status(thm)],[9]) ).
fof(51,negated_conjecture,
? [X3,X4] : difference(X3,difference(X3,X4)) != intersection(X3,X4),
inference(variable_rename,[status(thm)],[50]) ).
fof(52,negated_conjecture,
difference(esk3_0,difference(esk3_0,esk4_0)) != intersection(esk3_0,esk4_0),
inference(skolemize,[status(esa)],[51]) ).
cnf(53,negated_conjecture,
difference(esk3_0,difference(esk3_0,esk4_0)) != intersection(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[52]) ).
cnf(62,plain,
( member(esk1_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[42,19,theory(equality)]) ).
cnf(63,plain,
( member(esk1_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[43,19,theory(equality)]) ).
cnf(64,plain,
( member(esk1_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[49,19,theory(equality)]) ).
cnf(65,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[48,19,theory(equality)]) ).
cnf(71,plain,
( subset(X1,difference(X2,X3))
| member(esk1_2(X1,difference(X2,X3)),X3)
| ~ member(esk1_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[18,47,theory(equality)]) ).
cnf(76,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)],[18,41,theory(equality)]) ).
cnf(158,plain,
( subset(difference(X1,difference(X2,X3)),X4)
| member(esk1_2(difference(X1,difference(X2,X3)),X4),X3)
| ~ member(esk1_2(difference(X1,difference(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[65,47,theory(equality)]) ).
cnf(290,plain,
( member(esk1_2(intersection(X1,X2),difference(X1,X3)),X3)
| subset(intersection(X1,X2),difference(X1,X3)) ),
inference(spm,[status(thm)],[71,63,theory(equality)]) ).
cnf(321,plain,
( subset(difference(X1,X2),intersection(X3,X1))
| ~ member(esk1_2(difference(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[76,64,theory(equality)]) ).
cnf(4594,plain,
( member(esk1_2(difference(X1,difference(X1,X2)),X3),X2)
| subset(difference(X1,difference(X1,X2)),X3) ),
inference(spm,[status(thm)],[158,64,theory(equality)]) ).
cnf(5626,plain,
( subset(intersection(X1,X2),difference(X1,difference(X3,X4)))
| ~ member(esk1_2(intersection(X1,X2),difference(X1,difference(X3,X4))),X4) ),
inference(spm,[status(thm)],[48,290,theory(equality)]) ).
cnf(7300,plain,
( subset(difference(X1,X2),intersection(X1,X3))
| ~ member(esk1_2(difference(X1,X2),intersection(X1,X3)),X3) ),
inference(spm,[status(thm)],[321,12,theory(equality)]) ).
cnf(673840,plain,
subset(intersection(X1,X2),difference(X1,difference(X3,X2))),
inference(spm,[status(thm)],[5626,62,theory(equality)]) ).
cnf(791404,plain,
subset(difference(X1,difference(X1,X2)),intersection(X1,X2)),
inference(spm,[status(thm)],[7300,4594,theory(equality)]) ).
cnf(791774,plain,
( intersection(X1,X2) = difference(X1,difference(X1,X2))
| ~ subset(intersection(X1,X2),difference(X1,difference(X1,X2))) ),
inference(spm,[status(thm)],[24,791404,theory(equality)]) ).
cnf(791955,plain,
( intersection(X1,X2) = difference(X1,difference(X1,X2))
| $false ),
inference(rw,[status(thm)],[791774,673840,theory(equality)]) ).
cnf(791956,plain,
intersection(X1,X2) = difference(X1,difference(X1,X2)),
inference(cn,[status(thm)],[791955,theory(equality)]) ).
cnf(793013,negated_conjecture,
$false,
inference(rw,[status(thm)],[53,791956,theory(equality)]) ).
cnf(793014,negated_conjecture,
$false,
inference(cn,[status(thm)],[793013,theory(equality)]) ).
cnf(793015,negated_conjecture,
$false,
793014,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET011+3.p
% --creating new selector for []
% -running prover on /tmp/tmpIvSK2K/sel_SET011+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET011+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET011+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET011+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
%
%------------------------------------------------------------------------------