TSTP Solution File: SET602+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET602+4 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 03:00:30 EST 2010
% Result : Theorem 0.16s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 16 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 131 ( 56 ~; 45 |; 25 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 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 : 70 ( 5 sgn 46 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpz-hnrR/sel_SET602+4.p_1',subset) ).
fof(2,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpz-hnrR/sel_SET602+4.p_1',equal_set) ).
fof(3,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/tmp/tmpz-hnrR/sel_SET602+4.p_1',difference) ).
fof(4,axiom,
! [X3] : ~ member(X3,empty_set),
file('/tmp/tmpz-hnrR/sel_SET602+4.p_1',empty_set) ).
fof(5,conjecture,
! [X4] : equal_set(difference(X4,X4),empty_set),
file('/tmp/tmpz-hnrR/sel_SET602+4.p_1',thI29) ).
fof(6,negated_conjecture,
~ ! [X4] : equal_set(difference(X4,X4),empty_set),
inference(assume_negation,[status(cth)],[5]) ).
fof(7,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[3,theory(equality)]) ).
fof(8,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[4,theory(equality)]) ).
fof(9,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(10,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)],[9]) ).
fof(11,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)],[10]) ).
fof(12,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)],[11]) ).
fof(13,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)],[12]) ).
cnf(15,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[13]) ).
fof(17,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(18,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)],[17]) ).
fof(19,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)],[18]) ).
cnf(20,plain,
( equal_set(X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[19]) ).
fof(23,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)],[7]) ).
fof(24,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)],[23]) ).
fof(25,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)],[24]) ).
cnf(27,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(28,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(29,plain,
! [X4] : ~ member(X4,empty_set),
inference(variable_rename,[status(thm)],[8]) ).
cnf(30,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,negated_conjecture,
? [X4] : ~ equal_set(difference(X4,X4),empty_set),
inference(fof_nnf,[status(thm)],[6]) ).
fof(32,negated_conjecture,
? [X5] : ~ equal_set(difference(X5,X5),empty_set),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,negated_conjecture,
~ equal_set(difference(esk2_0,esk2_0),empty_set),
inference(skolemize,[status(esa)],[32]) ).
cnf(34,negated_conjecture,
~ equal_set(difference(esk2_0,esk2_0),empty_set),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(35,negated_conjecture,
( ~ subset(empty_set,difference(esk2_0,esk2_0))
| ~ subset(difference(esk2_0,esk2_0),empty_set) ),
inference(spm,[status(thm)],[34,20,theory(equality)]) ).
cnf(38,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[30,15,theory(equality)]) ).
cnf(39,plain,
( member(esk1_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[28,15,theory(equality)]) ).
cnf(41,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[27,15,theory(equality)]) ).
cnf(53,negated_conjecture,
( $false
| ~ subset(difference(esk2_0,esk2_0),empty_set) ),
inference(rw,[status(thm)],[35,38,theory(equality)]) ).
cnf(54,negated_conjecture,
~ subset(difference(esk2_0,esk2_0),empty_set),
inference(cn,[status(thm)],[53,theory(equality)]) ).
cnf(79,plain,
subset(difference(X1,X1),X2),
inference(spm,[status(thm)],[41,39,theory(equality)]) ).
cnf(82,negated_conjecture,
$false,
inference(rw,[status(thm)],[54,79,theory(equality)]) ).
cnf(83,negated_conjecture,
$false,
inference(cn,[status(thm)],[82,theory(equality)]) ).
cnf(84,negated_conjecture,
$false,
83,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET602+4.p
% --creating new selector for [SET006+0.ax]
% -running prover on /tmp/tmpz-hnrR/sel_SET602+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET602+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET602+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET602+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
%
%------------------------------------------------------------------------------