%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET931+1 : TPTP v5.0.0. Released v3.2.0.
% 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 03:48:24 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 44 ( 9 unt; 0 def)
% Number of atoms : 166 ( 137 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 207 ( 85 ~; 79 |; 39 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 4 sgn 24 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( subset(X1,unordered_pair(X2,X3))
<=> ~ ( X1 != empty_set
& X1 != singleton(X2)
& X1 != singleton(X3)
& X1 != unordered_pair(X2,X3) ) ),
file('/tmp/tmpmha-Xz/sel_SET931+1.p_1',l46_zfmisc_1) ).
fof(2,conjecture,
! [X1,X2,X3] :
( set_difference(X1,unordered_pair(X2,X3)) = empty_set
<=> ~ ( X1 != empty_set
& X1 != singleton(X2)
& X1 != singleton(X3)
& X1 != unordered_pair(X2,X3) ) ),
file('/tmp/tmpmha-Xz/sel_SET931+1.p_1',t75_zfmisc_1) ).
fof(5,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/tmp/tmpmha-Xz/sel_SET931+1.p_1',t37_xboole_1) ).
fof(9,negated_conjecture,
~ ! [X1,X2,X3] :
( set_difference(X1,unordered_pair(X2,X3)) = empty_set
<=> ~ ( X1 != empty_set
& X1 != singleton(X2)
& X1 != singleton(X3)
& X1 != unordered_pair(X2,X3) ) ),
inference(assume_negation,[status(cth)],[2]) ).
fof(11,plain,
! [X1,X2,X3] :
( ( ~ subset(X1,unordered_pair(X2,X3))
| X1 = empty_set
| X1 = singleton(X2)
| X1 = singleton(X3)
| X1 = unordered_pair(X2,X3) )
& ( ( X1 != empty_set
& X1 != singleton(X2)
& X1 != singleton(X3)
& X1 != unordered_pair(X2,X3) )
| subset(X1,unordered_pair(X2,X3)) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(12,plain,
! [X4,X5,X6] :
( ( ~ subset(X4,unordered_pair(X5,X6))
| X4 = empty_set
| X4 = singleton(X5)
| X4 = singleton(X6)
| X4 = unordered_pair(X5,X6) )
& ( ( X4 != empty_set
& X4 != singleton(X5)
& X4 != singleton(X6)
& X4 != unordered_pair(X5,X6) )
| subset(X4,unordered_pair(X5,X6)) ) ),
inference(variable_rename,[status(thm)],[11]) ).
fof(13,plain,
! [X4,X5,X6] :
( ( ~ subset(X4,unordered_pair(X5,X6))
| X4 = empty_set
| X4 = singleton(X5)
| X4 = singleton(X6)
| X4 = unordered_pair(X5,X6) )
& ( X4 != empty_set
| subset(X4,unordered_pair(X5,X6)) )
& ( X4 != singleton(X5)
| subset(X4,unordered_pair(X5,X6)) )
& ( X4 != singleton(X6)
| subset(X4,unordered_pair(X5,X6)) )
& ( X4 != unordered_pair(X5,X6)
| subset(X4,unordered_pair(X5,X6)) ) ),
inference(distribute,[status(thm)],[12]) ).
cnf(14,plain,
( subset(X1,unordered_pair(X2,X3))
| X1 != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[13]) ).
cnf(15,plain,
( subset(X1,unordered_pair(X2,X3))
| X1 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[13]) ).
cnf(16,plain,
( subset(X1,unordered_pair(X2,X3))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[13]) ).
cnf(17,plain,
( subset(X1,unordered_pair(X2,X3))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[13]) ).
cnf(18,plain,
( X1 = unordered_pair(X2,X3)
| X1 = singleton(X3)
| X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[13]) ).
fof(19,negated_conjecture,
? [X1,X2,X3] :
( ( set_difference(X1,unordered_pair(X2,X3)) != empty_set
| ( X1 != empty_set
& X1 != singleton(X2)
& X1 != singleton(X3)
& X1 != unordered_pair(X2,X3) ) )
& ( set_difference(X1,unordered_pair(X2,X3)) = empty_set
| X1 = empty_set
| X1 = singleton(X2)
| X1 = singleton(X3)
| X1 = unordered_pair(X2,X3) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(20,negated_conjecture,
? [X4,X5,X6] :
( ( set_difference(X4,unordered_pair(X5,X6)) != empty_set
| ( X4 != empty_set
& X4 != singleton(X5)
& X4 != singleton(X6)
& X4 != unordered_pair(X5,X6) ) )
& ( set_difference(X4,unordered_pair(X5,X6)) = empty_set
| X4 = empty_set
| X4 = singleton(X5)
| X4 = singleton(X6)
| X4 = unordered_pair(X5,X6) ) ),
inference(variable_rename,[status(thm)],[19]) ).
fof(21,negated_conjecture,
( ( set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set
| ( esk1_0 != empty_set
& esk1_0 != singleton(esk2_0)
& esk1_0 != singleton(esk3_0)
& esk1_0 != unordered_pair(esk2_0,esk3_0) ) )
& ( set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) = empty_set
| esk1_0 = empty_set
| esk1_0 = singleton(esk2_0)
| esk1_0 = singleton(esk3_0)
| esk1_0 = unordered_pair(esk2_0,esk3_0) ) ),
inference(skolemize,[status(esa)],[20]) ).
fof(22,negated_conjecture,
( ( esk1_0 != empty_set
| set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set )
& ( esk1_0 != singleton(esk2_0)
| set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set )
& ( esk1_0 != singleton(esk3_0)
| set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set )
& ( esk1_0 != unordered_pair(esk2_0,esk3_0)
| set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set )
& ( set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) = empty_set
| esk1_0 = empty_set
| esk1_0 = singleton(esk2_0)
| esk1_0 = singleton(esk3_0)
| esk1_0 = unordered_pair(esk2_0,esk3_0) ) ),
inference(distribute,[status(thm)],[21]) ).
cnf(23,negated_conjecture,
( esk1_0 = unordered_pair(esk2_0,esk3_0)
| esk1_0 = singleton(esk3_0)
| esk1_0 = singleton(esk2_0)
| esk1_0 = empty_set
| set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) = empty_set ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(24,negated_conjecture,
( set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set
| esk1_0 != unordered_pair(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(25,negated_conjecture,
( set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set
| esk1_0 != singleton(esk3_0) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(26,negated_conjecture,
( set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set
| esk1_0 != singleton(esk2_0) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(27,negated_conjecture,
( set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set
| esk1_0 != empty_set ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(33,plain,
! [X1,X2] :
( ( set_difference(X1,X2) != empty_set
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| set_difference(X1,X2) = empty_set ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(34,plain,
! [X3,X4] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| set_difference(X3,X4) = empty_set ) ),
inference(variable_rename,[status(thm)],[33]) ).
cnf(35,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(36,plain,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(48,negated_conjecture,
( empty_set != esk1_0
| ~ subset(esk1_0,unordered_pair(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[27,35,theory(equality)]) ).
cnf(49,negated_conjecture,
( singleton(esk2_0) != esk1_0
| ~ subset(esk1_0,unordered_pair(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[26,35,theory(equality)]) ).
cnf(50,negated_conjecture,
( singleton(esk3_0) != esk1_0
| ~ subset(esk1_0,unordered_pair(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[25,35,theory(equality)]) ).
cnf(51,negated_conjecture,
( unordered_pair(esk2_0,esk3_0) != esk1_0
| ~ subset(esk1_0,unordered_pair(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[24,35,theory(equality)]) ).
cnf(67,negated_conjecture,
empty_set != esk1_0,
inference(csr,[status(thm)],[48,17]) ).
cnf(68,negated_conjecture,
( set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) = empty_set
| unordered_pair(esk2_0,esk3_0) = esk1_0
| singleton(esk3_0) = esk1_0
| singleton(esk2_0) = esk1_0 ),
inference(sr,[status(thm)],[23,67,theory(equality)]) ).
cnf(69,negated_conjecture,
singleton(esk2_0) != esk1_0,
inference(csr,[status(thm)],[49,16]) ).
cnf(70,negated_conjecture,
singleton(esk3_0) != esk1_0,
inference(csr,[status(thm)],[50,15]) ).
cnf(71,negated_conjecture,
unordered_pair(esk2_0,esk3_0) != esk1_0,
inference(csr,[status(thm)],[51,14]) ).
cnf(72,negated_conjecture,
( set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) = empty_set
| singleton(esk3_0) = esk1_0
| singleton(esk2_0) = esk1_0 ),
inference(sr,[status(thm)],[68,71,theory(equality)]) ).
cnf(73,negated_conjecture,
( set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) = empty_set
| singleton(esk2_0) = esk1_0 ),
inference(sr,[status(thm)],[72,70,theory(equality)]) ).
cnf(74,negated_conjecture,
set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) = empty_set,
inference(sr,[status(thm)],[73,69,theory(equality)]) ).
cnf(75,negated_conjecture,
subset(esk1_0,unordered_pair(esk2_0,esk3_0)),
inference(spm,[status(thm)],[36,74,theory(equality)]) ).
cnf(84,negated_conjecture,
( unordered_pair(esk2_0,esk3_0) = esk1_0
| singleton(esk2_0) = esk1_0
| singleton(esk3_0) = esk1_0
| empty_set = esk1_0 ),
inference(spm,[status(thm)],[18,75,theory(equality)]) ).
cnf(85,negated_conjecture,
( singleton(esk2_0) = esk1_0
| singleton(esk3_0) = esk1_0
| empty_set = esk1_0 ),
inference(sr,[status(thm)],[84,71,theory(equality)]) ).
cnf(86,negated_conjecture,
( singleton(esk3_0) = esk1_0
| empty_set = esk1_0 ),
inference(sr,[status(thm)],[85,69,theory(equality)]) ).
cnf(87,negated_conjecture,
empty_set = esk1_0,
inference(sr,[status(thm)],[86,70,theory(equality)]) ).
cnf(88,negated_conjecture,
$false,
inference(sr,[status(thm)],[87,67,theory(equality)]) ).
cnf(89,negated_conjecture,
$false,
88,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET931+1.p
% --creating new selector for []
% -running prover on /tmp/tmpmha-Xz/sel_SET931+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET931+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET931+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET931+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
%
%------------------------------------------------------------------------------