TSTP Solution File: SET009+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET009+3 : 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 02:36:22 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 6 unt; 0 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 111 ( 43 ~; 41 |; 21 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 2 sgn 39 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(difference(X3,X2),difference(X3,X1)) ),
file('/tmp/tmpnJooE2/sel_SET009+3.p_1',prove_subset_difference) ).
fof(2,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/tmp/tmpnJooE2/sel_SET009+3.p_1',difference_defn) ).
fof(3,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpnJooE2/sel_SET009+3.p_1',subset_defn) ).
fof(5,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> subset(difference(X3,X2),difference(X3,X1)) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(6,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).
fof(7,negated_conjecture,
? [X1,X2,X3] :
( subset(X1,X2)
& ~ subset(difference(X3,X2),difference(X3,X1)) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(8,negated_conjecture,
? [X4,X5,X6] :
( subset(X4,X5)
& ~ subset(difference(X6,X5),difference(X6,X4)) ),
inference(variable_rename,[status(thm)],[7]) ).
fof(9,negated_conjecture,
( subset(esk1_0,esk2_0)
& ~ subset(difference(esk3_0,esk2_0),difference(esk3_0,esk1_0)) ),
inference(skolemize,[status(esa)],[8]) ).
cnf(10,negated_conjecture,
~ subset(difference(esk3_0,esk2_0),difference(esk3_0,esk1_0)),
inference(split_conjunct,[status(thm)],[9]) ).
cnf(11,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[9]) ).
fof(12,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)],[6]) ).
fof(13,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)],[12]) ).
fof(14,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)],[13]) ).
cnf(15,plain,
( member(X1,difference(X2,X3))
| member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(16,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(17,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[14]) ).
fof(18,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)],[3]) ).
fof(19,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)],[18]) ).
fof(20,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)],[19]) ).
fof(21,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)],[20]) ).
fof(22,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)],[21]) ).
cnf(23,plain,
( subset(X1,X2)
| ~ member(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(24,plain,
( subset(X1,X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(25,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(30,plain,
( member(esk4_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[17,24,theory(equality)]) ).
cnf(31,negated_conjecture,
( member(X1,esk2_0)
| ~ member(X1,esk1_0) ),
inference(spm,[status(thm)],[25,11,theory(equality)]) ).
cnf(33,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk4_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[16,24,theory(equality)]) ).
cnf(34,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)],[23,15,theory(equality)]) ).
cnf(42,negated_conjecture,
( subset(difference(X1,esk2_0),X2)
| ~ member(esk4_2(difference(X1,esk2_0),X2),esk1_0) ),
inference(spm,[status(thm)],[33,31,theory(equality)]) ).
cnf(60,plain,
( member(esk4_2(difference(X1,X2),difference(X1,X3)),X3)
| subset(difference(X1,X2),difference(X1,X3)) ),
inference(spm,[status(thm)],[34,30,theory(equality)]) ).
cnf(602,negated_conjecture,
subset(difference(X1,esk2_0),difference(X1,esk1_0)),
inference(spm,[status(thm)],[42,60,theory(equality)]) ).
cnf(615,negated_conjecture,
$false,
inference(rw,[status(thm)],[10,602,theory(equality)]) ).
cnf(616,negated_conjecture,
$false,
inference(cn,[status(thm)],[615,theory(equality)]) ).
cnf(617,negated_conjecture,
$false,
616,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET009+3.p
% --creating new selector for []
% -running prover on /tmp/tmpnJooE2/sel_SET009+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET009+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET009+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET009+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
%
%------------------------------------------------------------------------------