TSTP Solution File: SET577+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET577+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 02:57:28 EST 2010
% Result : Theorem 0.56s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 64 ( 15 unt; 0 def)
% Number of atoms : 199 ( 24 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 215 ( 80 ~; 89 |; 38 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 123 ( 8 sgn 55 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/tmp/tmpk9TNEU/sel_SET577+3.p_1',commutativity_of_union) ).
fof(2,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpk9TNEU/sel_SET577+3.p_1',equal_defn) ).
fof(3,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/tmp/tmpk9TNEU/sel_SET577+3.p_1',union_defn) ).
fof(4,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpk9TNEU/sel_SET577+3.p_1',subset_defn) ).
fof(6,conjecture,
! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
| member(X4,X3) ) )
=> X1 = union(X2,X3) ),
file('/tmp/tmpk9TNEU/sel_SET577+3.p_1',prove_th18) ).
fof(8,negated_conjecture,
~ ! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
| member(X4,X3) ) )
=> X1 = union(X2,X3) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(9,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(10,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[9]) ).
fof(11,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(12,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[11]) ).
fof(13,plain,
! [X3,X4] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(distribute,[status(thm)],[12]) ).
cnf(14,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[13]) ).
fof(17,plain,
! [X1,X2,X3] :
( ( ~ 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)],[3]) ).
fof(18,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ( ~ member(X6,X4)
& ~ member(X6,X5) )
| member(X6,union(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[17]) ).
fof(19,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X4)
| member(X6,union(X4,X5)) )
& ( ~ member(X6,X5)
| member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[18]) ).
cnf(20,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(21,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(22,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[19]) ).
fof(23,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)],[4]) ).
fof(24,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)],[23]) ).
fof(25,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)],[24]) ).
fof(26,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)],[25]) ).
fof(27,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)],[26]) ).
cnf(28,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(29,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(30,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(40,negated_conjecture,
? [X1,X2,X3] :
( ! [X4] :
( ( ~ member(X4,X1)
| member(X4,X2)
| member(X4,X3) )
& ( ( ~ member(X4,X2)
& ~ member(X4,X3) )
| member(X4,X1) ) )
& X1 != union(X2,X3) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(41,negated_conjecture,
? [X5,X6,X7] :
( ! [X8] :
( ( ~ member(X8,X5)
| member(X8,X6)
| member(X8,X7) )
& ( ( ~ member(X8,X6)
& ~ member(X8,X7) )
| member(X8,X5) ) )
& X5 != union(X6,X7) ),
inference(variable_rename,[status(thm)],[40]) ).
fof(42,negated_conjecture,
( ! [X8] :
( ( ~ member(X8,esk3_0)
| member(X8,esk4_0)
| member(X8,esk5_0) )
& ( ( ~ member(X8,esk4_0)
& ~ member(X8,esk5_0) )
| member(X8,esk3_0) ) )
& esk3_0 != union(esk4_0,esk5_0) ),
inference(skolemize,[status(esa)],[41]) ).
fof(43,negated_conjecture,
! [X8] :
( ( ~ member(X8,esk3_0)
| member(X8,esk4_0)
| member(X8,esk5_0) )
& ( ( ~ member(X8,esk4_0)
& ~ member(X8,esk5_0) )
| member(X8,esk3_0) )
& esk3_0 != union(esk4_0,esk5_0) ),
inference(shift_quantors,[status(thm)],[42]) ).
fof(44,negated_conjecture,
! [X8] :
( ( ~ member(X8,esk3_0)
| member(X8,esk4_0)
| member(X8,esk5_0) )
& ( ~ member(X8,esk4_0)
| member(X8,esk3_0) )
& ( ~ member(X8,esk5_0)
| member(X8,esk3_0) )
& esk3_0 != union(esk4_0,esk5_0) ),
inference(distribute,[status(thm)],[43]) ).
cnf(45,negated_conjecture,
esk3_0 != union(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(46,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk5_0) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(47,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk4_0) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(48,negated_conjecture,
( member(X1,esk5_0)
| member(X1,esk4_0)
| ~ member(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(55,negated_conjecture,
( member(esk1_2(esk4_0,X1),esk3_0)
| subset(esk4_0,X1) ),
inference(spm,[status(thm)],[47,29,theory(equality)]) ).
cnf(56,negated_conjecture,
( member(esk1_2(esk5_0,X1),esk3_0)
| subset(esk5_0,X1) ),
inference(spm,[status(thm)],[46,29,theory(equality)]) ).
cnf(64,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[28,20,theory(equality)]) ).
cnf(65,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[28,21,theory(equality)]) ).
cnf(70,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)],[22,29,theory(equality)]) ).
cnf(115,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[64,29,theory(equality)]) ).
cnf(116,negated_conjecture,
( subset(X1,union(X2,esk5_0))
| member(esk1_2(X1,union(X2,esk5_0)),esk4_0)
| ~ member(esk1_2(X1,union(X2,esk5_0)),esk3_0) ),
inference(spm,[status(thm)],[64,48,theory(equality)]) ).
cnf(119,negated_conjecture,
subset(esk4_0,union(X1,esk3_0)),
inference(spm,[status(thm)],[64,55,theory(equality)]) ).
cnf(120,negated_conjecture,
subset(esk5_0,union(X1,esk3_0)),
inference(spm,[status(thm)],[64,56,theory(equality)]) ).
cnf(124,negated_conjecture,
( member(X1,union(X2,esk3_0))
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[30,119,theory(equality)]) ).
cnf(128,negated_conjecture,
( member(X1,union(X2,esk3_0))
| ~ member(X1,esk5_0) ),
inference(spm,[status(thm)],[30,120,theory(equality)]) ).
cnf(129,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[115,10,theory(equality)]) ).
cnf(171,negated_conjecture,
( subset(X1,union(X2,esk3_0))
| ~ member(esk1_2(X1,union(X2,esk3_0)),esk4_0) ),
inference(spm,[status(thm)],[28,124,theory(equality)]) ).
cnf(180,negated_conjecture,
( subset(X1,union(X2,esk3_0))
| ~ member(esk1_2(X1,union(X2,esk3_0)),esk5_0) ),
inference(spm,[status(thm)],[28,128,theory(equality)]) ).
cnf(203,plain,
( member(esk1_2(union(X4,X4),X5),X4)
| subset(union(X4,X4),X5) ),
inference(ef,[status(thm)],[70,theory(equality)]) ).
cnf(322,plain,
subset(union(X1,X1),X1),
inference(spm,[status(thm)],[28,203,theory(equality)]) ).
cnf(332,plain,
( X1 = union(X1,X1)
| ~ subset(X1,union(X1,X1)) ),
inference(spm,[status(thm)],[14,322,theory(equality)]) ).
cnf(338,plain,
( X1 = union(X1,X1)
| $false ),
inference(rw,[status(thm)],[332,129,theory(equality)]) ).
cnf(339,plain,
X1 = union(X1,X1),
inference(cn,[status(thm)],[338,theory(equality)]) ).
cnf(362,negated_conjecture,
( subset(X1,esk3_0)
| ~ member(esk1_2(X1,esk3_0),esk4_0) ),
inference(spm,[status(thm)],[171,339,theory(equality)]) ).
cnf(364,negated_conjecture,
( subset(X1,esk3_0)
| ~ member(esk1_2(X1,esk3_0),esk5_0) ),
inference(spm,[status(thm)],[180,339,theory(equality)]) ).
cnf(393,negated_conjecture,
( subset(union(esk4_0,X1),esk3_0)
| member(esk1_2(union(esk4_0,X1),esk3_0),X1) ),
inference(spm,[status(thm)],[362,70,theory(equality)]) ).
cnf(434,negated_conjecture,
subset(union(esk4_0,esk5_0),esk3_0),
inference(spm,[status(thm)],[364,393,theory(equality)]) ).
cnf(472,negated_conjecture,
( esk3_0 = union(esk4_0,esk5_0)
| ~ subset(esk3_0,union(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[14,434,theory(equality)]) ).
cnf(474,negated_conjecture,
~ subset(esk3_0,union(esk4_0,esk5_0)),
inference(sr,[status(thm)],[472,45,theory(equality)]) ).
cnf(554,negated_conjecture,
( subset(X1,union(esk4_0,esk5_0))
| ~ member(esk1_2(X1,union(esk4_0,esk5_0)),esk3_0) ),
inference(spm,[status(thm)],[65,116,theory(equality)]) ).
cnf(14211,negated_conjecture,
subset(esk3_0,union(esk4_0,esk5_0)),
inference(spm,[status(thm)],[554,29,theory(equality)]) ).
cnf(14237,negated_conjecture,
$false,
inference(sr,[status(thm)],[14211,474,theory(equality)]) ).
cnf(14238,negated_conjecture,
$false,
14237,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET577+3.p
% --creating new selector for []
% -running prover on /tmp/tmpk9TNEU/sel_SET577+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET577+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET577+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET577+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
%
%------------------------------------------------------------------------------