TSTP Solution File: GRP710+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP710+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 11:24:02 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 46 unt; 0 def)
% Number of atoms : 82 ( 65 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 45 ( 27 ~; 14 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 106 ( 10 sgn 32 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : mult(i(X1),X1) = unit,
file('/tmp/tmpkPckyf/sel_GRP710+1.p_1',f05) ).
fof(2,axiom,
! [X1] : mult(X1,i(X1)) = unit,
file('/tmp/tmpkPckyf/sel_GRP710+1.p_1',f04) ).
fof(3,axiom,
! [X1] : mult(X1,unit) = X1,
file('/tmp/tmpkPckyf/sel_GRP710+1.p_1',f01) ).
fof(4,conjecture,
( ! [X2,X3] :
? [X4] : mult(X2,X4) = X3
& ! [X5,X6] :
? [X7] : mult(X7,X6) = X5 ),
file('/tmp/tmpkPckyf/sel_GRP710+1.p_1',goals) ).
fof(5,axiom,
! [X8,X9,X1] : mult(X1,mult(X9,mult(X9,X8))) = mult(mult(mult(X1,X9),X9),X8),
file('/tmp/tmpkPckyf/sel_GRP710+1.p_1',f03) ).
fof(6,axiom,
! [X1] : mult(unit,X1) = X1,
file('/tmp/tmpkPckyf/sel_GRP710+1.p_1',f02) ).
fof(7,negated_conjecture,
~ ( ! [X2,X3] :
? [X4] : mult(X2,X4) = X3
& ! [X5,X6] :
? [X7] : mult(X7,X6) = X5 ),
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,X4) != X3
| ? [X5,X6] :
! [X7] : mult(X7,X6) != X5 ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(15,negated_conjecture,
( ? [X8,X9] :
! [X10] : mult(X8,X10) != X9
| ? [X11,X12] :
! [X13] : mult(X13,X12) != X11 ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,negated_conjecture,
( ! [X10] : mult(esk1_0,X10) != esk2_0
| ! [X13] : mult(X13,esk4_0) != esk3_0 ),
inference(skolemize,[status(esa)],[15]) ).
fof(17,negated_conjecture,
! [X10,X13] :
( mult(X13,esk4_0) != esk3_0
| mult(esk1_0,X10) != esk2_0 ),
inference(shift_quantors,[status(thm)],[16]) ).
cnf(18,negated_conjecture,
( mult(esk1_0,X1) != esk2_0
| mult(X2,esk4_0) != esk3_0 ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(19,plain,
! [X10,X11,X12] : mult(X12,mult(X11,mult(X11,X10))) = mult(mult(mult(X12,X11),X11),X10),
inference(variable_rename,[status(thm)],[5]) ).
cnf(20,plain,
mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3),
inference(split_conjunct,[status(thm)],[19]) ).
fof(21,plain,
! [X2] : mult(unit,X2) = X2,
inference(variable_rename,[status(thm)],[6]) ).
cnf(22,plain,
mult(unit,X1) = X1,
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,plain,
( ~ epred1_0
<=> ! [X2] : mult(X2,esk4_0) != esk3_0 ),
introduced(definition),
[split] ).
cnf(24,plain,
( epred1_0
| mult(X2,esk4_0) != esk3_0 ),
inference(split_equiv,[status(thm)],[23]) ).
fof(25,plain,
( ~ epred2_0
<=> ! [X1] : mult(esk1_0,X1) != esk2_0 ),
introduced(definition),
[split] ).
cnf(26,plain,
( epred2_0
| mult(esk1_0,X1) != esk2_0 ),
inference(split_equiv,[status(thm)],[25]) ).
cnf(27,negated_conjecture,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[18,23,theory(equality)]),25,theory(equality)]),
[split] ).
cnf(30,plain,
mult(X1,mult(X2,mult(X2,unit))) = mult(mult(X1,X2),X2),
inference(spm,[status(thm)],[13,20,theory(equality)]) ).
cnf(39,plain,
mult(X1,mult(X2,X2)) = mult(mult(X1,X2),X2),
inference(rw,[status(thm)],[30,13,theory(equality)]) ).
cnf(59,plain,
mult(unit,i(X1)) = mult(X1,mult(i(X1),i(X1))),
inference(spm,[status(thm)],[39,11,theory(equality)]) ).
cnf(60,plain,
mult(unit,X1) = mult(i(X1),mult(X1,X1)),
inference(spm,[status(thm)],[39,9,theory(equality)]) ).
cnf(63,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(rw,[status(thm)],[20,39,theory(equality)]) ).
cnf(69,plain,
i(X1) = mult(X1,mult(i(X1),i(X1))),
inference(rw,[status(thm)],[59,22,theory(equality)]) ).
cnf(70,plain,
X1 = mult(i(X1),mult(X1,X1)),
inference(rw,[status(thm)],[60,22,theory(equality)]) ).
cnf(90,plain,
mult(mult(X1,X1),X2) = mult(unit,mult(X1,mult(X1,X2))),
inference(spm,[status(thm)],[63,22,theory(equality)]) ).
cnf(92,plain,
mult(unit,X2) = mult(i(mult(X1,X1)),mult(X1,mult(X1,X2))),
inference(spm,[status(thm)],[63,9,theory(equality)]) ).
cnf(93,plain,
mult(mult(X1,mult(X2,mult(X2,X3))),X3) = mult(mult(X1,mult(X2,X2)),mult(X3,X3)),
inference(spm,[status(thm)],[39,63,theory(equality)]) ).
cnf(97,plain,
mult(X1,X2) = mult(i(X1),mult(X1,mult(X1,X2))),
inference(spm,[status(thm)],[63,70,theory(equality)]) ).
cnf(102,negated_conjecture,
( epred1_0
| mult(X1,mult(X2,mult(X2,esk4_0))) != esk3_0 ),
inference(spm,[status(thm)],[24,63,theory(equality)]) ).
cnf(108,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(rw,[status(thm)],[90,22,theory(equality)]) ).
cnf(109,plain,
X2 = mult(i(mult(X1,X1)),mult(X1,mult(X1,X2))),
inference(rw,[status(thm)],[92,22,theory(equality)]) ).
cnf(110,plain,
mult(mult(X1,mult(X2,mult(X2,X3))),X3) = mult(X1,mult(X2,mult(X2,mult(X3,X3)))),
inference(rw,[status(thm)],[93,63,theory(equality)]) ).
cnf(123,negated_conjecture,
( epred1_0
| mult(X1,mult(i(esk4_0),unit)) != esk3_0 ),
inference(spm,[status(thm)],[102,9,theory(equality)]) ).
cnf(132,negated_conjecture,
( epred1_0
| mult(X1,i(esk4_0)) != esk3_0 ),
inference(rw,[status(thm)],[123,13,theory(equality)]) ).
cnf(138,plain,
mult(X1,mult(X1,i(mult(X1,X1)))) = unit,
inference(spm,[status(thm)],[11,108,theory(equality)]) ).
cnf(197,plain,
mult(i(i(X1)),mult(i(X1),X1)) = X1,
inference(spm,[status(thm)],[97,70,theory(equality)]) ).
cnf(204,plain,
mult(i(X1),unit) = mult(X1,i(mult(X1,X1))),
inference(spm,[status(thm)],[97,138,theory(equality)]) ).
cnf(215,plain,
i(i(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[197,9,theory(equality)]),13,theory(equality)]) ).
cnf(224,plain,
i(X1) = mult(X1,i(mult(X1,X1))),
inference(rw,[status(thm)],[204,13,theory(equality)]) ).
cnf(404,plain,
mult(i(mult(X1,X1)),mult(X1,i(X1))) = mult(i(X1),i(X1)),
inference(spm,[status(thm)],[109,69,theory(equality)]) ).
cnf(411,plain,
mult(i(i(mult(X1,X1))),mult(i(mult(X1,X1)),X2)) = X2,
inference(spm,[status(thm)],[97,109,theory(equality)]) ).
cnf(429,plain,
i(mult(X1,X1)) = mult(i(X1),i(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[404,11,theory(equality)]),13,theory(equality)]) ).
cnf(436,plain,
mult(X1,mult(X1,mult(i(mult(X1,X1)),X2))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[411,215,theory(equality)]),108,theory(equality)]) ).
cnf(549,negated_conjecture,
( epred2_0
| X1 != esk2_0 ),
inference(spm,[status(thm)],[26,436,theory(equality)]) ).
cnf(574,negated_conjecture,
epred2_0,
inference(er,[status(thm)],[549,theory(equality)]) ).
cnf(576,negated_conjecture,
( $false
| ~ epred1_0 ),
inference(rw,[status(thm)],[27,574,theory(equality)]) ).
cnf(577,negated_conjecture,
~ epred1_0,
inference(cn,[status(thm)],[576,theory(equality)]) ).
cnf(1127,plain,
mult(mult(X1,mult(X2,unit)),i(X2)) = mult(X1,mult(X2,mult(X2,mult(i(X2),i(X2))))),
inference(spm,[status(thm)],[110,11,theory(equality)]) ).
cnf(1193,plain,
mult(mult(X1,X2),i(X2)) = mult(X1,mult(X2,mult(X2,mult(i(X2),i(X2))))),
inference(rw,[status(thm)],[1127,13,theory(equality)]) ).
cnf(1194,plain,
mult(mult(X1,X2),i(X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1193,429,theory(equality)]),224,theory(equality)]),11,theory(equality)]),13,theory(equality)]) ).
cnf(1304,negated_conjecture,
( epred1_0
| X1 != esk3_0 ),
inference(spm,[status(thm)],[132,1194,theory(equality)]) ).
cnf(1326,negated_conjecture,
X1 != esk3_0,
inference(sr,[status(thm)],[1304,577,theory(equality)]) ).
cnf(1707,negated_conjecture,
$false,
inference(er,[status(thm)],[1326,theory(equality)]) ).
cnf(1708,negated_conjecture,
$false,
1707,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP710+1.p
% --creating new selector for []
% -running prover on /tmp/tmpkPckyf/sel_GRP710+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP710+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP710+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP710+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
%
%------------------------------------------------------------------------------