TSTP Solution File: GRP711+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP711+1 : TPTP v5.0.0. Released v4.0.0.
% 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 : Sat Dec 25 11:24:06 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 36 unt; 0 def)
% Number of atoms : 80 ( 78 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 43 ( 13 ~; 15 |; 11 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 20 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : mult(i(X1),X1) = unit,
file('/tmp/tmpNFKeBI/sel_GRP711+1.p_1',f05) ).
fof(2,axiom,
! [X1] : mult(X1,i(X1)) = unit,
file('/tmp/tmpNFKeBI/sel_GRP711+1.p_1',f04) ).
fof(3,axiom,
! [X1] : mult(X1,unit) = X1,
file('/tmp/tmpNFKeBI/sel_GRP711+1.p_1',f01) ).
fof(4,conjecture,
! [X2,X3,X4] :
( ( mult(X2,X3) = mult(X2,X4)
=> X3 = X4 )
& ( mult(X3,X2) = mult(X4,X2)
=> X3 = X4 ) ),
file('/tmp/tmpNFKeBI/sel_GRP711+1.p_1',goals) ).
fof(5,axiom,
! [X5,X6,X1] : mult(X1,mult(X6,mult(X6,X5))) = mult(mult(mult(X1,X6),X6),X5),
file('/tmp/tmpNFKeBI/sel_GRP711+1.p_1',f03) ).
fof(6,axiom,
! [X1] : mult(unit,X1) = X1,
file('/tmp/tmpNFKeBI/sel_GRP711+1.p_1',f02) ).
fof(7,negated_conjecture,
~ ! [X2,X3,X4] :
( ( mult(X2,X3) = mult(X2,X4)
=> X3 = X4 )
& ( mult(X3,X2) = mult(X4,X2)
=> X3 = X4 ) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(8,plain,
! [X2] : mult(i(X2),X2) = unit,
inference(variable_rename,[status(thm)],[1]) ).
cnf(9,plain,
mult(i(X1),X1) = unit,
inference(split_conjunct,[status(thm)],[8]) ).
fof(10,plain,
! [X2] : mult(X2,i(X2)) = unit,
inference(variable_rename,[status(thm)],[2]) ).
cnf(11,plain,
mult(X1,i(X1)) = unit,
inference(split_conjunct,[status(thm)],[10]) ).
fof(12,plain,
! [X2] : mult(X2,unit) = X2,
inference(variable_rename,[status(thm)],[3]) ).
cnf(13,plain,
mult(X1,unit) = X1,
inference(split_conjunct,[status(thm)],[12]) ).
fof(14,negated_conjecture,
? [X2,X3,X4] :
( ( mult(X2,X3) = mult(X2,X4)
& X3 != X4 )
| ( mult(X3,X2) = mult(X4,X2)
& X3 != X4 ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(15,negated_conjecture,
? [X5,X6,X7] :
( ( mult(X5,X6) = mult(X5,X7)
& X6 != X7 )
| ( mult(X6,X5) = mult(X7,X5)
& X6 != X7 ) ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,negated_conjecture,
( ( mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0)
& esk2_0 != esk3_0 )
| ( mult(esk2_0,esk1_0) = mult(esk3_0,esk1_0)
& esk2_0 != esk3_0 ) ),
inference(skolemize,[status(esa)],[15]) ).
fof(17,negated_conjecture,
( ( mult(esk2_0,esk1_0) = mult(esk3_0,esk1_0)
| mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0) )
& ( esk2_0 != esk3_0
| mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0) )
& ( mult(esk2_0,esk1_0) = mult(esk3_0,esk1_0)
| esk2_0 != esk3_0 )
& ( esk2_0 != esk3_0
| esk2_0 != esk3_0 ) ),
inference(distribute,[status(thm)],[16]) ).
cnf(18,negated_conjecture,
( esk2_0 != esk3_0
| esk2_0 != esk3_0 ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(21,negated_conjecture,
( mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0)
| mult(esk2_0,esk1_0) = mult(esk3_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(22,plain,
! [X7,X8,X9] : mult(X9,mult(X8,mult(X8,X7))) = mult(mult(mult(X9,X8),X8),X7),
inference(variable_rename,[status(thm)],[5]) ).
cnf(23,plain,
mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3),
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,plain,
! [X2] : mult(unit,X2) = X2,
inference(variable_rename,[status(thm)],[6]) ).
cnf(25,plain,
mult(unit,X1) = X1,
inference(split_conjunct,[status(thm)],[24]) ).
cnf(28,plain,
mult(X1,mult(X2,mult(X2,unit))) = mult(mult(X1,X2),X2),
inference(spm,[status(thm)],[13,23,theory(equality)]) ).
cnf(38,plain,
mult(X1,mult(X2,X2)) = mult(mult(X1,X2),X2),
inference(rw,[status(thm)],[28,13,theory(equality)]) ).
cnf(57,plain,
mult(unit,X1) = mult(i(X1),mult(X1,X1)),
inference(spm,[status(thm)],[38,9,theory(equality)]) ).
cnf(59,negated_conjecture,
( mult(mult(esk3_0,esk1_0),esk1_0) = mult(esk2_0,mult(esk1_0,esk1_0))
| mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[38,21,theory(equality)]) ).
cnf(60,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(rw,[status(thm)],[23,38,theory(equality)]) ).
cnf(67,plain,
X1 = mult(i(X1),mult(X1,X1)),
inference(rw,[status(thm)],[57,25,theory(equality)]) ).
cnf(68,negated_conjecture,
( mult(esk3_0,mult(esk1_0,esk1_0)) = mult(esk2_0,mult(esk1_0,esk1_0))
| mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[59,38,theory(equality)]) ).
cnf(86,plain,
mult(X1,mult(X2,mult(X2,i(mult(X1,mult(X2,X2)))))) = unit,
inference(spm,[status(thm)],[11,60,theory(equality)]) ).
cnf(87,plain,
mult(unit,X2) = mult(i(mult(X1,X1)),mult(X1,mult(X1,X2))),
inference(spm,[status(thm)],[60,9,theory(equality)]) ).
cnf(92,plain,
mult(X1,X2) = mult(i(X1),mult(X1,mult(X1,X2))),
inference(spm,[status(thm)],[60,67,theory(equality)]) ).
cnf(103,plain,
X2 = mult(i(mult(X1,X1)),mult(X1,mult(X1,X2))),
inference(rw,[status(thm)],[87,25,theory(equality)]) ).
cnf(164,plain,
mult(i(mult(X1,X1)),mult(X1,unit)) = i(X1),
inference(spm,[status(thm)],[103,11,theory(equality)]) ).
cnf(186,plain,
mult(i(mult(X1,X1)),X1) = i(X1),
inference(rw,[status(thm)],[164,13,theory(equality)]) ).
cnf(338,plain,
mult(i(i(X1)),mult(i(X1),X1)) = X1,
inference(spm,[status(thm)],[92,67,theory(equality)]) ).
cnf(361,plain,
mult(i(i(X1)),unit) = X1,
inference(rw,[status(thm)],[338,9,theory(equality)]) ).
cnf(370,plain,
X1 = i(i(X1)),
inference(spm,[status(thm)],[13,361,theory(equality)]) ).
cnf(507,plain,
mult(i(mult(X1,X1)),mult(X1,unit)) = mult(X2,mult(X2,i(mult(X1,mult(X2,X2))))),
inference(spm,[status(thm)],[103,86,theory(equality)]) ).
cnf(542,plain,
i(X1) = mult(X2,mult(X2,i(mult(X1,mult(X2,X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[507,13,theory(equality)]),186,theory(equality)]) ).
cnf(630,negated_conjecture,
( mult(esk1_0,mult(esk1_0,i(mult(esk3_0,mult(esk1_0,esk1_0))))) = i(esk2_0)
| mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[542,68,theory(equality)]) ).
cnf(656,negated_conjecture,
( i(esk3_0) = i(esk2_0)
| mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[630,542,theory(equality)]) ).
cnf(658,negated_conjecture,
( mult(i(mult(esk1_0,esk1_0)),mult(esk1_0,mult(esk1_0,esk3_0))) = esk2_0
| i(esk2_0) = i(esk3_0) ),
inference(spm,[status(thm)],[103,656,theory(equality)]) ).
cnf(662,negated_conjecture,
( esk3_0 = esk2_0
| i(esk2_0) = i(esk3_0) ),
inference(rw,[status(thm)],[658,103,theory(equality)]) ).
cnf(663,negated_conjecture,
i(esk2_0) = i(esk3_0),
inference(sr,[status(thm)],[662,18,theory(equality)]) ).
cnf(670,negated_conjecture,
i(i(esk3_0)) = esk2_0,
inference(spm,[status(thm)],[370,663,theory(equality)]) ).
cnf(675,negated_conjecture,
esk3_0 = esk2_0,
inference(rw,[status(thm)],[670,370,theory(equality)]) ).
cnf(676,negated_conjecture,
$false,
inference(sr,[status(thm)],[675,18,theory(equality)]) ).
cnf(677,negated_conjecture,
$false,
676,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP711+1.p
% --creating new selector for []
% -running prover on /tmp/tmpNFKeBI/sel_GRP711+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP711+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP711+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP711+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
%
%------------------------------------------------------------------------------