TSTP Solution File: SET699+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET699+4 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 03:12:52 EST 2010
% Result : Theorem 0.54s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 63 ( 10 unt; 0 def)
% Number of atoms : 193 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 206 ( 76 ~; 85 |; 36 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 131 ( 10 sgn 51 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpFZicfr/sel_SET699+4.p_1',subset) ).
fof(2,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/tmp/tmpFZicfr/sel_SET699+4.p_1',difference) ).
fof(3,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpFZicfr/sel_SET699+4.p_1',intersection) ).
fof(4,conjecture,
! [X1,X2,X4] :
( ( subset(X1,X4)
& subset(X2,X4) )
=> ( subset(X1,X2)
<=> subset(intersection(X1,difference(X4,X2)),difference(X4,X1)) ) ),
file('/tmp/tmpFZicfr/sel_SET699+4.p_1',thI33) ).
fof(5,negated_conjecture,
~ ! [X1,X2,X4] :
( ( subset(X1,X4)
& subset(X2,X4) )
=> ( subset(X1,X2)
<=> subset(intersection(X1,difference(X4,X2)),difference(X4,X1)) ) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(6,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).
fof(7,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)],[1]) ).
fof(8,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)],[7]) ).
fof(9,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)],[8]) ).
fof(10,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)],[9]) ).
fof(11,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)],[10]) ).
cnf(12,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[11]) ).
cnf(13,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[11]) ).
cnf(14,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[11]) ).
fof(15,plain,
! [X2,X1,X4] :
( ( ~ member(X2,difference(X4,X1))
| ( member(X2,X4)
& ~ member(X2,X1) ) )
& ( ~ member(X2,X4)
| member(X2,X1)
| member(X2,difference(X4,X1)) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(16,plain,
! [X5,X6,X7] :
( ( ~ member(X5,difference(X7,X6))
| ( member(X5,X7)
& ~ member(X5,X6) ) )
& ( ~ member(X5,X7)
| member(X5,X6)
| member(X5,difference(X7,X6)) ) ),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,plain,
! [X5,X6,X7] :
( ( member(X5,X7)
| ~ member(X5,difference(X7,X6)) )
& ( ~ member(X5,X6)
| ~ member(X5,difference(X7,X6)) )
& ( ~ member(X5,X7)
| member(X5,X6)
| member(X5,difference(X7,X6)) ) ),
inference(distribute,[status(thm)],[16]) ).
cnf(18,plain,
( member(X1,difference(X2,X3))
| member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(19,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(20,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(21,plain,
! [X3,X1,X2] :
( ( ~ 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)],[3]) ).
fof(22,plain,
! [X4,X5,X6] :
( ( ~ member(X4,intersection(X5,X6))
| ( member(X4,X5)
& member(X4,X6) ) )
& ( ~ member(X4,X5)
| ~ member(X4,X6)
| member(X4,intersection(X5,X6)) ) ),
inference(variable_rename,[status(thm)],[21]) ).
fof(23,plain,
! [X4,X5,X6] :
( ( member(X4,X5)
| ~ member(X4,intersection(X5,X6)) )
& ( member(X4,X6)
| ~ member(X4,intersection(X5,X6)) )
& ( ~ member(X4,X5)
| ~ member(X4,X6)
| member(X4,intersection(X5,X6)) ) ),
inference(distribute,[status(thm)],[22]) ).
cnf(24,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(25,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(26,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(27,negated_conjecture,
? [X1,X2,X4] :
( subset(X1,X4)
& subset(X2,X4)
& ( ~ subset(X1,X2)
| ~ subset(intersection(X1,difference(X4,X2)),difference(X4,X1)) )
& ( subset(X1,X2)
| subset(intersection(X1,difference(X4,X2)),difference(X4,X1)) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(28,negated_conjecture,
? [X5,X6,X7] :
( subset(X5,X7)
& subset(X6,X7)
& ( ~ subset(X5,X6)
| ~ subset(intersection(X5,difference(X7,X6)),difference(X7,X5)) )
& ( subset(X5,X6)
| subset(intersection(X5,difference(X7,X6)),difference(X7,X5)) ) ),
inference(variable_rename,[status(thm)],[27]) ).
fof(29,negated_conjecture,
( subset(esk2_0,esk4_0)
& subset(esk3_0,esk4_0)
& ( ~ subset(esk2_0,esk3_0)
| ~ subset(intersection(esk2_0,difference(esk4_0,esk3_0)),difference(esk4_0,esk2_0)) )
& ( subset(esk2_0,esk3_0)
| subset(intersection(esk2_0,difference(esk4_0,esk3_0)),difference(esk4_0,esk2_0)) ) ),
inference(skolemize,[status(esa)],[28]) ).
cnf(30,negated_conjecture,
( subset(intersection(esk2_0,difference(esk4_0,esk3_0)),difference(esk4_0,esk2_0))
| subset(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(31,negated_conjecture,
( ~ subset(intersection(esk2_0,difference(esk4_0,esk3_0)),difference(esk4_0,esk2_0))
| ~ subset(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(33,negated_conjecture,
subset(esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(35,plain,
( member(esk1_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[25,13,theory(equality)]) ).
cnf(36,plain,
( member(esk1_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[20,13,theory(equality)]) ).
cnf(37,plain,
( member(esk1_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[26,13,theory(equality)]) ).
cnf(38,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[14,33,theory(equality)]) ).
cnf(40,negated_conjecture,
( member(X1,difference(esk4_0,esk2_0))
| subset(esk2_0,esk3_0)
| ~ member(X1,intersection(esk2_0,difference(esk4_0,esk3_0))) ),
inference(spm,[status(thm)],[14,30,theory(equality)]) ).
cnf(41,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[19,13,theory(equality)]) ).
cnf(50,negated_conjecture,
( subset(X1,esk4_0)
| ~ member(esk1_2(X1,esk4_0),esk2_0) ),
inference(spm,[status(thm)],[12,38,theory(equality)]) ).
cnf(58,plain,
( subset(intersection(X1,difference(X2,X3)),X4)
| ~ member(esk1_2(intersection(X1,difference(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[19,35,theory(equality)]) ).
cnf(61,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)],[41,18,theory(equality)]) ).
cnf(80,negated_conjecture,
subset(difference(esk2_0,X1),esk4_0),
inference(spm,[status(thm)],[50,36,theory(equality)]) ).
cnf(96,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,difference(esk2_0,X2)) ),
inference(spm,[status(thm)],[14,80,theory(equality)]) ).
cnf(134,negated_conjecture,
( member(X1,difference(esk4_0,esk2_0))
| subset(esk2_0,esk3_0)
| ~ member(X1,difference(esk4_0,esk3_0))
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[40,24,theory(equality)]) ).
cnf(273,negated_conjecture,
( member(esk1_2(difference(esk2_0,X1),X2),esk4_0)
| subset(difference(esk2_0,X1),X2) ),
inference(spm,[status(thm)],[96,13,theory(equality)]) ).
cnf(459,negated_conjecture,
( member(esk1_2(difference(esk2_0,difference(esk4_0,X1)),X2),X1)
| subset(difference(esk2_0,difference(esk4_0,X1)),X2) ),
inference(spm,[status(thm)],[61,273,theory(equality)]) ).
cnf(1101,negated_conjecture,
( subset(esk2_0,esk3_0)
| ~ member(X1,difference(esk4_0,esk3_0))
| ~ member(X1,esk2_0) ),
inference(csr,[status(thm)],[134,19]) ).
cnf(1318,negated_conjecture,
subset(difference(esk2_0,difference(esk4_0,X1)),X1),
inference(spm,[status(thm)],[12,459,theory(equality)]) ).
cnf(1349,negated_conjecture,
( member(X1,X2)
| ~ member(X1,difference(esk2_0,difference(esk4_0,X2))) ),
inference(spm,[status(thm)],[14,1318,theory(equality)]) ).
cnf(1422,negated_conjecture,
( member(X1,X2)
| member(X1,difference(esk4_0,X2))
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[1349,18,theory(equality)]) ).
cnf(3403,negated_conjecture,
( subset(esk2_0,esk3_0)
| member(X1,esk3_0)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[1101,1422,theory(equality)]) ).
cnf(3439,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk2_0) ),
inference(csr,[status(thm)],[3403,14]) ).
cnf(3440,negated_conjecture,
( subset(X1,esk3_0)
| ~ member(esk1_2(X1,esk3_0),esk2_0) ),
inference(spm,[status(thm)],[12,3439,theory(equality)]) ).
cnf(3472,negated_conjecture,
subset(esk2_0,esk3_0),
inference(spm,[status(thm)],[3440,13,theory(equality)]) ).
cnf(3475,negated_conjecture,
subset(intersection(esk2_0,X1),esk3_0),
inference(spm,[status(thm)],[3440,37,theory(equality)]) ).
cnf(3509,negated_conjecture,
( ~ subset(intersection(esk2_0,difference(esk4_0,esk3_0)),difference(esk4_0,esk2_0))
| $false ),
inference(rw,[status(thm)],[31,3472,theory(equality)]) ).
cnf(3510,negated_conjecture,
~ subset(intersection(esk2_0,difference(esk4_0,esk3_0)),difference(esk4_0,esk2_0)),
inference(cn,[status(thm)],[3509,theory(equality)]) ).
cnf(3514,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,intersection(esk2_0,X2)) ),
inference(spm,[status(thm)],[14,3475,theory(equality)]) ).
cnf(3811,negated_conjecture,
( member(esk1_2(intersection(esk2_0,X1),X2),esk3_0)
| subset(intersection(esk2_0,X1),X2) ),
inference(spm,[status(thm)],[3514,13,theory(equality)]) ).
cnf(4461,negated_conjecture,
subset(intersection(esk2_0,difference(X1,esk3_0)),X2),
inference(spm,[status(thm)],[58,3811,theory(equality)]) ).
cnf(4483,negated_conjecture,
$false,
inference(rw,[status(thm)],[3510,4461,theory(equality)]) ).
cnf(4484,negated_conjecture,
$false,
inference(cn,[status(thm)],[4483,theory(equality)]) ).
cnf(4485,negated_conjecture,
$false,
4484,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET699+4.p
% --creating new selector for [SET006+0.ax]
% -running prover on /tmp/tmpFZicfr/sel_SET699+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET699+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET699+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET699+4.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
%
%------------------------------------------------------------------------------