TSTP Solution File: SET012+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET012+4 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 02:37:00 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 46 ( 8 unt; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 154 ( 60 ~; 59 |; 28 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 93 ( 3 sgn 45 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpsSzz-t/sel_SET012+4.p_1',subset) ).
fof(2,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpsSzz-t/sel_SET012+4.p_1',equal_set) ).
fof(3,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/tmp/tmpsSzz-t/sel_SET012+4.p_1',difference) ).
fof(4,conjecture,
! [X1,X4] :
( subset(X1,X4)
=> equal_set(difference(X4,difference(X4,X1)),X1) ),
file('/tmp/tmpsSzz-t/sel_SET012+4.p_1',thI23) ).
fof(5,negated_conjecture,
~ ! [X1,X4] :
( subset(X1,X4)
=> equal_set(difference(X4,difference(X4,X1)),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)],[3,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,
! [X1,X2] :
( ( ~ equal_set(X1,X2)
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| equal_set(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(16,plain,
! [X3,X4] :
( ( ~ equal_set(X3,X4)
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,plain,
! [X3,X4] :
( ( subset(X3,X4)
| ~ equal_set(X3,X4) )
& ( subset(X4,X3)
| ~ equal_set(X3,X4) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(distribute,[status(thm)],[16]) ).
cnf(18,plain,
( equal_set(X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(21,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(22,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)],[21]) ).
fof(23,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)],[22]) ).
cnf(24,plain,
( member(X1,difference(X2,X3))
| member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(25,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(26,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(27,negated_conjecture,
? [X1,X4] :
( subset(X1,X4)
& ~ equal_set(difference(X4,difference(X4,X1)),X1) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(28,negated_conjecture,
? [X5,X6] :
( subset(X5,X6)
& ~ equal_set(difference(X6,difference(X6,X5)),X5) ),
inference(variable_rename,[status(thm)],[27]) ).
fof(29,negated_conjecture,
( subset(esk2_0,esk3_0)
& ~ equal_set(difference(esk3_0,difference(esk3_0,esk2_0)),esk2_0) ),
inference(skolemize,[status(esa)],[28]) ).
cnf(30,negated_conjecture,
~ equal_set(difference(esk3_0,difference(esk3_0,esk2_0)),esk2_0),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(31,negated_conjecture,
subset(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(32,negated_conjecture,
( ~ subset(esk2_0,difference(esk3_0,difference(esk3_0,esk2_0)))
| ~ subset(difference(esk3_0,difference(esk3_0,esk2_0)),esk2_0) ),
inference(spm,[status(thm)],[30,18,theory(equality)]) ).
cnf(36,plain,
( member(esk1_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[26,13,theory(equality)]) ).
cnf(37,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[14,31,theory(equality)]) ).
cnf(38,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[25,13,theory(equality)]) ).
cnf(39,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)],[12,24,theory(equality)]) ).
cnf(42,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)],[38,24,theory(equality)]) ).
cnf(44,negated_conjecture,
( member(esk1_2(esk2_0,X1),esk3_0)
| subset(esk2_0,X1) ),
inference(spm,[status(thm)],[37,13,theory(equality)]) ).
cnf(54,negated_conjecture,
( member(esk1_2(esk2_0,difference(esk3_0,X1)),X1)
| subset(esk2_0,difference(esk3_0,X1)) ),
inference(spm,[status(thm)],[39,44,theory(equality)]) ).
cnf(72,negated_conjecture,
( subset(esk2_0,difference(esk3_0,difference(X1,X2)))
| ~ member(esk1_2(esk2_0,difference(esk3_0,difference(X1,X2))),X2) ),
inference(spm,[status(thm)],[25,54,theory(equality)]) ).
cnf(77,plain,
( member(esk1_2(difference(X1,difference(X1,X2)),X3),X2)
| subset(difference(X1,difference(X1,X2)),X3) ),
inference(spm,[status(thm)],[42,36,theory(equality)]) ).
cnf(135,plain,
subset(difference(X1,difference(X1,X2)),X2),
inference(spm,[status(thm)],[12,77,theory(equality)]) ).
cnf(146,negated_conjecture,
( ~ subset(esk2_0,difference(esk3_0,difference(esk3_0,esk2_0)))
| $false ),
inference(rw,[status(thm)],[32,135,theory(equality)]) ).
cnf(147,negated_conjecture,
~ subset(esk2_0,difference(esk3_0,difference(esk3_0,esk2_0))),
inference(cn,[status(thm)],[146,theory(equality)]) ).
cnf(301,negated_conjecture,
subset(esk2_0,difference(esk3_0,difference(X1,esk2_0))),
inference(spm,[status(thm)],[72,13,theory(equality)]) ).
cnf(311,negated_conjecture,
$false,
inference(rw,[status(thm)],[147,301,theory(equality)]) ).
cnf(312,negated_conjecture,
$false,
inference(cn,[status(thm)],[311,theory(equality)]) ).
cnf(313,negated_conjecture,
$false,
312,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET012+4.p
% --creating new selector for [SET006+0.ax]
% -running prover on /tmp/tmpsSzz-t/sel_SET012+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET012+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET012+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET012+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
%
%------------------------------------------------------------------------------