TSTP Solution File: SET159+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET159+4 : 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 02:52:45 EST 2010
% Result : Theorem 10.87s
% Output : CNFRefutation 10.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 52 ( 14 unt; 0 def)
% Number of atoms : 144 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 153 ( 61 ~; 65 |; 23 &)
% ( 3 <=>; 1 =>; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 137 ( 6 sgn 44 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpssmlgK/sel_SET159+4.p_1',subset) ).
fof(2,axiom,
! [X3,X1,X2] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/tmp/tmpssmlgK/sel_SET159+4.p_1',union) ).
fof(3,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpssmlgK/sel_SET159+4.p_1',equal_set) ).
fof(4,conjecture,
! [X1,X2,X4] : equal_set(union(union(X1,X2),X4),union(X1,union(X2,X4))),
file('/tmp/tmpssmlgK/sel_SET159+4.p_1',thI09) ).
fof(5,negated_conjecture,
~ ! [X1,X2,X4] : equal_set(union(union(X1,X2),X4),union(X1,union(X2,X4))),
inference(assume_negation,[status(cth)],[4]) ).
fof(6,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(7,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)],[6]) ).
fof(8,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)],[7]) ).
fof(9,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)],[8]) ).
fof(10,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)],[9]) ).
cnf(11,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[10]) ).
cnf(12,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[10]) ).
cnf(13,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[10]) ).
fof(14,plain,
! [X3,X1,X2] :
( ( ~ member(X3,union(X1,X2))
| member(X3,X1)
| member(X3,X2) )
& ( ( ~ member(X3,X1)
& ~ member(X3,X2) )
| member(X3,union(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(15,plain,
! [X4,X5,X6] :
( ( ~ member(X4,union(X5,X6))
| member(X4,X5)
| member(X4,X6) )
& ( ( ~ member(X4,X5)
& ~ member(X4,X6) )
| member(X4,union(X5,X6)) ) ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,plain,
! [X4,X5,X6] :
( ( ~ member(X4,union(X5,X6))
| member(X4,X5)
| member(X4,X6) )
& ( ~ member(X4,X5)
| member(X4,union(X5,X6)) )
& ( ~ member(X4,X6)
| member(X4,union(X5,X6)) ) ),
inference(distribute,[status(thm)],[15]) ).
cnf(17,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(18,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(19,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[16]) ).
fof(20,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)],[3]) ).
fof(21,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)],[20]) ).
fof(22,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)],[21]) ).
cnf(23,plain,
( equal_set(X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(26,negated_conjecture,
? [X1,X2,X4] : ~ equal_set(union(union(X1,X2),X4),union(X1,union(X2,X4))),
inference(fof_nnf,[status(thm)],[5]) ).
fof(27,negated_conjecture,
? [X5,X6,X7] : ~ equal_set(union(union(X5,X6),X7),union(X5,union(X6,X7))),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,negated_conjecture,
~ equal_set(union(union(esk2_0,esk3_0),esk4_0),union(esk2_0,union(esk3_0,esk4_0))),
inference(skolemize,[status(esa)],[27]) ).
cnf(29,negated_conjecture,
~ equal_set(union(union(esk2_0,esk3_0),esk4_0),union(esk2_0,union(esk3_0,esk4_0))),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(32,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[11,17,theory(equality)]) ).
cnf(33,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[11,18,theory(equality)]) ).
cnf(37,plain,
( member(esk1_2(union(X1,X2),X3),X2)
| member(esk1_2(union(X1,X2),X3),X1)
| subset(union(X1,X2),X3) ),
inference(spm,[status(thm)],[19,12,theory(equality)]) ).
cnf(38,negated_conjecture,
( ~ subset(union(esk2_0,union(esk3_0,esk4_0)),union(union(esk2_0,esk3_0),esk4_0))
| ~ subset(union(union(esk2_0,esk3_0),esk4_0),union(esk2_0,union(esk3_0,esk4_0))) ),
inference(spm,[status(thm)],[29,23,theory(equality)]) ).
cnf(40,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),X4) ),
inference(spm,[status(thm)],[32,17,theory(equality)]) ).
cnf(41,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),X3) ),
inference(spm,[status(thm)],[32,18,theory(equality)]) ).
cnf(44,plain,
( subset(X1,union(union(X2,X3),X4))
| ~ member(esk1_2(X1,union(union(X2,X3),X4)),X3) ),
inference(spm,[status(thm)],[33,17,theory(equality)]) ).
cnf(45,plain,
( subset(X1,union(union(X2,X3),X4))
| ~ member(esk1_2(X1,union(union(X2,X3),X4)),X2) ),
inference(spm,[status(thm)],[33,18,theory(equality)]) ).
cnf(55,plain,
( subset(union(X1,X2),union(X3,X2))
| member(esk1_2(union(X1,X2),union(X3,X2)),X1) ),
inference(spm,[status(thm)],[32,37,theory(equality)]) ).
cnf(56,plain,
( subset(union(X1,X2),union(X1,X3))
| member(esk1_2(union(X1,X2),union(X1,X3)),X2) ),
inference(spm,[status(thm)],[33,37,theory(equality)]) ).
cnf(81,plain,
( subset(union(X1,X2),union(X3,union(X4,X2)))
| member(esk1_2(union(X1,X2),union(X3,union(X4,X2))),X1) ),
inference(spm,[status(thm)],[40,37,theory(equality)]) ).
cnf(150,plain,
( subset(union(X1,X2),union(union(X1,X3),X4))
| member(esk1_2(union(X1,X2),union(union(X1,X3),X4)),X2) ),
inference(spm,[status(thm)],[45,37,theory(equality)]) ).
cnf(403,plain,
subset(union(X1,X2),union(union(X3,X1),X2)),
inference(spm,[status(thm)],[44,55,theory(equality)]) ).
cnf(411,plain,
( member(X1,union(union(X2,X3),X4))
| ~ member(X1,union(X3,X4)) ),
inference(spm,[status(thm)],[13,403,theory(equality)]) ).
cnf(423,plain,
subset(union(X1,X2),union(X1,union(X2,X3))),
inference(spm,[status(thm)],[41,56,theory(equality)]) ).
cnf(433,plain,
( member(X1,union(X2,union(X3,X4)))
| ~ member(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[13,423,theory(equality)]) ).
cnf(791,plain,
( subset(X1,union(union(X2,X3),X4))
| ~ member(esk1_2(X1,union(union(X2,X3),X4)),union(X3,X4)) ),
inference(spm,[status(thm)],[11,411,theory(equality)]) ).
cnf(883,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),union(X2,X3)) ),
inference(spm,[status(thm)],[11,433,theory(equality)]) ).
cnf(80963,plain,
subset(union(X1,union(X2,X3)),union(union(X1,X2),X3)),
inference(spm,[status(thm)],[791,150,theory(equality)]) ).
cnf(81652,negated_conjecture,
( $false
| ~ subset(union(union(esk2_0,esk3_0),esk4_0),union(esk2_0,union(esk3_0,esk4_0))) ),
inference(rw,[status(thm)],[38,80963,theory(equality)]) ).
cnf(81653,negated_conjecture,
~ subset(union(union(esk2_0,esk3_0),esk4_0),union(esk2_0,union(esk3_0,esk4_0))),
inference(cn,[status(thm)],[81652,theory(equality)]) ).
cnf(103787,plain,
subset(union(union(X1,X2),X3),union(X1,union(X2,X3))),
inference(spm,[status(thm)],[883,81,theory(equality)]) ).
cnf(104511,negated_conjecture,
$false,
inference(rw,[status(thm)],[81653,103787,theory(equality)]) ).
cnf(104512,negated_conjecture,
$false,
inference(cn,[status(thm)],[104511,theory(equality)]) ).
cnf(104513,negated_conjecture,
$false,
104512,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET159+4.p
% --creating new selector for [SET006+0.ax]
% -running prover on /tmp/tmpssmlgK/sel_SET159+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET159+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET159+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET159+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
%
%------------------------------------------------------------------------------