TSTP Solution File: SET867+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET867+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 03:42:10 EST 2010
% Result : Theorem 0.29s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 6 unt; 0 def)
% Number of atoms : 119 ( 38 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 153 ( 57 ~; 62 |; 30 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 58 ( 1 sgn 40 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/tmp/tmpxLXc3S/sel_SET867+1.p_1',d4_tarski) ).
fof(2,conjecture,
union(empty_set) = empty_set,
file('/tmp/tmpxLXc3S/sel_SET867+1.p_1',t2_zfmisc_1) ).
fof(6,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/tmp/tmpxLXc3S/sel_SET867+1.p_1',d1_xboole_0) ).
fof(8,negated_conjecture,
union(empty_set) != empty_set,
inference(assume_negation,[status(cth)],[2]) ).
fof(9,negated_conjecture,
union(empty_set) != empty_set,
inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).
fof(12,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).
fof(13,plain,
! [X1,X2] :
( ( X2 != union(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X3,X4)
& in(X4,X1) ) )
& ( ! [X4] :
( ~ in(X3,X4)
| ~ in(X4,X1) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X3,X4)
| ~ in(X4,X1) ) )
& ( in(X3,X2)
| ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) )
| X2 = union(X1) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(14,plain,
! [X5,X6] :
( ( X6 != union(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ? [X8] :
( in(X7,X8)
& in(X8,X5) ) )
& ( ! [X9] :
( ~ in(X7,X9)
| ~ in(X9,X5) )
| in(X7,X6) ) ) )
& ( ? [X10] :
( ( ~ in(X10,X6)
| ! [X11] :
( ~ in(X10,X11)
| ~ in(X11,X5) ) )
& ( in(X10,X6)
| ? [X12] :
( in(X10,X12)
& in(X12,X5) ) ) )
| X6 = union(X5) ) ),
inference(variable_rename,[status(thm)],[13]) ).
fof(15,plain,
! [X5,X6] :
( ( X6 != union(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ( in(X7,esk1_3(X5,X6,X7))
& in(esk1_3(X5,X6,X7),X5) ) )
& ( ! [X9] :
( ~ in(X7,X9)
| ~ in(X9,X5) )
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk2_2(X5,X6),X6)
| ! [X11] :
( ~ in(esk2_2(X5,X6),X11)
| ~ in(X11,X5) ) )
& ( in(esk2_2(X5,X6),X6)
| ( in(esk2_2(X5,X6),esk3_2(X5,X6))
& in(esk3_2(X5,X6),X5) ) ) )
| X6 = union(X5) ) ),
inference(skolemize,[status(esa)],[14]) ).
fof(16,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ~ in(esk2_2(X5,X6),X11)
| ~ in(X11,X5)
| ~ in(esk2_2(X5,X6),X6) )
& ( in(esk2_2(X5,X6),X6)
| ( in(esk2_2(X5,X6),esk3_2(X5,X6))
& in(esk3_2(X5,X6),X5) ) ) )
| X6 = union(X5) )
& ( ( ( ~ in(X7,X9)
| ~ in(X9,X5)
| in(X7,X6) )
& ( ~ in(X7,X6)
| ( in(X7,esk1_3(X5,X6,X7))
& in(esk1_3(X5,X6,X7),X5) ) ) )
| X6 != union(X5) ) ),
inference(shift_quantors,[status(thm)],[15]) ).
fof(17,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(esk2_2(X5,X6),X11)
| ~ in(X11,X5)
| ~ in(esk2_2(X5,X6),X6)
| X6 = union(X5) )
& ( in(esk2_2(X5,X6),esk3_2(X5,X6))
| in(esk2_2(X5,X6),X6)
| X6 = union(X5) )
& ( in(esk3_2(X5,X6),X5)
| in(esk2_2(X5,X6),X6)
| X6 = union(X5) )
& ( ~ in(X7,X9)
| ~ in(X9,X5)
| in(X7,X6)
| X6 != union(X5) )
& ( in(X7,esk1_3(X5,X6,X7))
| ~ in(X7,X6)
| X6 != union(X5) )
& ( in(esk1_3(X5,X6,X7),X5)
| ~ in(X7,X6)
| X6 != union(X5) ) ),
inference(distribute,[status(thm)],[16]) ).
cnf(21,plain,
( X1 = union(X2)
| in(esk2_2(X2,X1),X1)
| in(esk3_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(24,negated_conjecture,
union(empty_set) != empty_set,
inference(split_conjunct,[status(thm)],[9]) ).
fof(34,plain,
! [X1] :
( ( X1 != empty_set
| ! [X2] : ~ in(X2,X1) )
& ( ? [X2] : in(X2,X1)
| X1 = empty_set ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(35,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( ? [X5] : in(X5,X3)
| X3 = empty_set ) ),
inference(variable_rename,[status(thm)],[34]) ).
fof(36,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( in(esk6_1(X3),X3)
| X3 = empty_set ) ),
inference(skolemize,[status(esa)],[35]) ).
fof(37,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| X3 != empty_set )
& ( in(esk6_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[36]) ).
cnf(39,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(50,plain,
( union(X1) = X2
| in(esk2_2(X1,X2),X2)
| empty_set != X1 ),
inference(spm,[status(thm)],[39,21,theory(equality)]) ).
cnf(62,plain,
( union(X2) = X1
| empty_set != X1
| empty_set != X2 ),
inference(spm,[status(thm)],[39,50,theory(equality)]) ).
cnf(66,plain,
( union(X1) = empty_set
| empty_set != X1 ),
inference(er,[status(thm)],[62,theory(equality)]) ).
cnf(67,negated_conjecture,
$false,
inference(spm,[status(thm)],[24,66,theory(equality)]) ).
cnf(68,negated_conjecture,
$false,
67,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET867+1.p
% --creating new selector for []
% -running prover on /tmp/tmpxLXc3S/sel_SET867+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET867+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET867+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET867+1.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
%
%------------------------------------------------------------------------------