%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET579+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 02:57:37 EST 2010
% Result : Theorem 0.19s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 48 ( 7 unt; 0 def)
% Number of atoms : 178 ( 19 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 213 ( 83 ~; 76 |; 43 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 99 ( 2 sgn 58 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpLfmWib/sel_SET579+3.p_1',equal_defn) ).
fof(2,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/tmp/tmpLfmWib/sel_SET579+3.p_1',difference_defn) ).
fof(3,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpLfmWib/sel_SET579+3.p_1',subset_defn) ).
fof(5,conjecture,
! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
& ~ member(X4,X3) ) )
=> X1 = difference(X2,X3) ),
file('/tmp/tmpLfmWib/sel_SET579+3.p_1',prove_th20) ).
fof(6,negated_conjecture,
~ ! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
& ~ member(X4,X3) ) )
=> X1 = difference(X2,X3) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(7,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).
fof(8,negated_conjecture,
~ ! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
& ~ member(X4,X3) ) )
=> X1 = difference(X2,X3) ),
inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).
fof(9,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(10,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[9]) ).
fof(11,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)],[10]) ).
cnf(12,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[11]) ).
fof(15,plain,
! [X1,X2,X3] :
( ( ~ member(X3,difference(X1,X2))
| ( member(X3,X1)
& ~ member(X3,X2) ) )
& ( ~ member(X3,X1)
| member(X3,X2)
| member(X3,difference(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(16,plain,
! [X4,X5,X6] :
( ( ~ member(X6,difference(X4,X5))
| ( member(X6,X4)
& ~ member(X6,X5) ) )
& ( ~ member(X6,X4)
| member(X6,X5)
| member(X6,difference(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,plain,
! [X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X5)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X4)
| member(X6,X5)
| member(X6,difference(X4,X5)) ) ),
inference(distribute,[status(thm)],[16]) ).
cnf(18,plain,
( member(X1,difference(X2,X3))
| member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(19,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(20,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(21,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)],[3]) ).
fof(22,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)],[21]) ).
fof(23,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)],[22]) ).
fof(24,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)],[23]) ).
fof(25,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)],[24]) ).
cnf(26,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(27,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(31,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 != difference(X2,X3) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(32,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 != difference(X6,X7) ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,negated_conjecture,
( ! [X8] :
( ( ~ member(X8,esk2_0)
| ( member(X8,esk3_0)
& ~ member(X8,esk4_0) ) )
& ( ~ member(X8,esk3_0)
| member(X8,esk4_0)
| member(X8,esk2_0) ) )
& esk2_0 != difference(esk3_0,esk4_0) ),
inference(skolemize,[status(esa)],[32]) ).
fof(34,negated_conjecture,
! [X8] :
( ( ~ member(X8,esk2_0)
| ( member(X8,esk3_0)
& ~ member(X8,esk4_0) ) )
& ( ~ member(X8,esk3_0)
| member(X8,esk4_0)
| member(X8,esk2_0) )
& esk2_0 != difference(esk3_0,esk4_0) ),
inference(shift_quantors,[status(thm)],[33]) ).
fof(35,negated_conjecture,
! [X8] :
( ( member(X8,esk3_0)
| ~ member(X8,esk2_0) )
& ( ~ member(X8,esk4_0)
| ~ member(X8,esk2_0) )
& ( ~ member(X8,esk3_0)
| member(X8,esk4_0)
| member(X8,esk2_0) )
& esk2_0 != difference(esk3_0,esk4_0) ),
inference(distribute,[status(thm)],[34]) ).
cnf(36,negated_conjecture,
esk2_0 != difference(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(37,negated_conjecture,
( member(X1,esk2_0)
| member(X1,esk4_0)
| ~ member(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(38,negated_conjecture,
( ~ member(X1,esk2_0)
| ~ member(X1,esk4_0) ),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(39,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(49,plain,
( member(esk1_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[20,27,theory(equality)]) ).
cnf(50,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[19,27,theory(equality)]) ).
cnf(53,plain,
( subset(X1,difference(X2,X3))
| member(esk1_2(X1,difference(X2,X3)),X3)
| ~ member(esk1_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[26,18,theory(equality)]) ).
cnf(65,negated_conjecture,
( subset(difference(X1,esk4_0),X2)
| member(esk1_2(difference(X1,esk4_0),X2),esk2_0)
| ~ member(esk1_2(difference(X1,esk4_0),X2),esk3_0) ),
inference(spm,[status(thm)],[50,37,theory(equality)]) ).
cnf(146,negated_conjecture,
( member(esk1_2(X1,difference(esk3_0,X2)),X2)
| subset(X1,difference(esk3_0,X2))
| ~ member(esk1_2(X1,difference(esk3_0,X2)),esk2_0) ),
inference(spm,[status(thm)],[53,39,theory(equality)]) ).
cnf(511,negated_conjecture,
( member(esk1_2(difference(esk3_0,esk4_0),X1),esk2_0)
| subset(difference(esk3_0,esk4_0),X1) ),
inference(spm,[status(thm)],[65,49,theory(equality)]) ).
cnf(818,negated_conjecture,
subset(difference(esk3_0,esk4_0),esk2_0),
inference(spm,[status(thm)],[26,511,theory(equality)]) ).
cnf(822,negated_conjecture,
( esk2_0 = difference(esk3_0,esk4_0)
| ~ subset(esk2_0,difference(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[12,818,theory(equality)]) ).
cnf(824,negated_conjecture,
~ subset(esk2_0,difference(esk3_0,esk4_0)),
inference(sr,[status(thm)],[822,36,theory(equality)]) ).
cnf(898,negated_conjecture,
( member(esk1_2(esk2_0,difference(esk3_0,X1)),X1)
| subset(esk2_0,difference(esk3_0,X1)) ),
inference(spm,[status(thm)],[146,27,theory(equality)]) ).
cnf(907,negated_conjecture,
( subset(esk2_0,difference(esk3_0,esk4_0))
| ~ member(esk1_2(esk2_0,difference(esk3_0,esk4_0)),esk2_0) ),
inference(spm,[status(thm)],[38,898,theory(equality)]) ).
cnf(918,negated_conjecture,
~ member(esk1_2(esk2_0,difference(esk3_0,esk4_0)),esk2_0),
inference(sr,[status(thm)],[907,824,theory(equality)]) ).
cnf(945,negated_conjecture,
subset(esk2_0,difference(esk3_0,esk4_0)),
inference(spm,[status(thm)],[918,27,theory(equality)]) ).
cnf(946,negated_conjecture,
$false,
inference(sr,[status(thm)],[945,824,theory(equality)]) ).
cnf(947,negated_conjecture,
$false,
946,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET579+3.p
% --creating new selector for []
% -running prover on /tmp/tmpLfmWib/sel_SET579+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET579+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET579+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET579+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
%
%------------------------------------------------------------------------------