%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP660+2 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 11:21:34 EST 2010
% Result : Theorem 2.27s
% Output : CNFRefutation 2.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 6
% Syntax : Number of formulae : 90 ( 83 unt; 0 def)
% Number of atoms : 97 ( 93 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 5 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 170 ( 0 sgn 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] : mult(mult(mult(X3,X2),X1),X3) = mult(X3,mult(X2,mult(X1,X3))),
file('/tmp/tmpeeLUb_/sel_GRP660+2.p_1',f05) ).
fof(2,axiom,
! [X2,X3] : rd(mult(X3,X2),X2) = X3,
file('/tmp/tmpeeLUb_/sel_GRP660+2.p_1',f04) ).
fof(3,axiom,
! [X2,X3] : mult(X3,ld(X3,X2)) = X2,
file('/tmp/tmpeeLUb_/sel_GRP660+2.p_1',f01) ).
fof(4,conjecture,
! [X4,X5] :
( mult(X4,rd(X5,X5)) = X4
& mult(rd(X5,X5),X4) = X4 ),
file('/tmp/tmpeeLUb_/sel_GRP660+2.p_1',goals) ).
fof(5,axiom,
! [X2,X3] : mult(rd(X3,X2),X2) = X3,
file('/tmp/tmpeeLUb_/sel_GRP660+2.p_1',f03) ).
fof(6,axiom,
! [X2,X3] : ld(X3,mult(X3,X2)) = X2,
file('/tmp/tmpeeLUb_/sel_GRP660+2.p_1',f02) ).
fof(7,negated_conjecture,
~ ! [X4,X5] :
( mult(X4,rd(X5,X5)) = X4
& mult(rd(X5,X5),X4) = X4 ),
inference(assume_negation,[status(cth)],[4]) ).
fof(8,plain,
! [X4,X5,X6] : mult(mult(mult(X6,X5),X4),X6) = mult(X6,mult(X5,mult(X4,X6))),
inference(variable_rename,[status(thm)],[1]) ).
cnf(9,plain,
mult(mult(mult(X1,X2),X3),X1) = mult(X1,mult(X2,mult(X3,X1))),
inference(split_conjunct,[status(thm)],[8]) ).
fof(10,plain,
! [X4,X5] : rd(mult(X5,X4),X4) = X5,
inference(variable_rename,[status(thm)],[2]) ).
cnf(11,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[10]) ).
fof(12,plain,
! [X4,X5] : mult(X5,ld(X5,X4)) = X4,
inference(variable_rename,[status(thm)],[3]) ).
cnf(13,plain,
mult(X1,ld(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[12]) ).
fof(14,negated_conjecture,
? [X4,X5] :
( mult(X4,rd(X5,X5)) != X4
| mult(rd(X5,X5),X4) != X4 ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(15,negated_conjecture,
? [X6,X7] :
( mult(X6,rd(X7,X7)) != X6
| mult(rd(X7,X7),X6) != X6 ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,negated_conjecture,
( mult(esk1_0,rd(esk2_0,esk2_0)) != esk1_0
| mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0 ),
inference(skolemize,[status(esa)],[15]) ).
cnf(17,negated_conjecture,
( mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0
| mult(esk1_0,rd(esk2_0,esk2_0)) != esk1_0 ),
inference(split_conjunct,[status(thm)],[16]) ).
fof(18,plain,
! [X4,X5] : mult(rd(X5,X4),X4) = X5,
inference(variable_rename,[status(thm)],[5]) ).
cnf(19,plain,
mult(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[18]) ).
fof(20,plain,
! [X4,X5] : ld(X5,mult(X5,X4)) = X4,
inference(variable_rename,[status(thm)],[6]) ).
cnf(21,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[20]) ).
cnf(22,plain,
rd(X2,ld(X1,X2)) = X1,
inference(spm,[status(thm)],[11,13,theory(equality)]) ).
cnf(23,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[21,19,theory(equality)]) ).
cnf(24,plain,
mult(mult(X1,X3),rd(X1,X2)) = mult(rd(X1,X2),mult(X2,mult(X3,rd(X1,X2)))),
inference(spm,[status(thm)],[9,19,theory(equality)]) ).
cnf(25,plain,
rd(mult(X1,mult(X2,mult(X3,X1))),X1) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[11,9,theory(equality)]) ).
cnf(26,plain,
mult(mult(X2,X3),X1) = mult(X1,mult(ld(X1,X2),mult(X3,X1))),
inference(spm,[status(thm)],[9,13,theory(equality)]) ).
cnf(30,plain,
mult(mult(X1,mult(X2,mult(X3,X1))),mult(X1,X2)) = mult(mult(X1,X2),mult(X3,mult(X1,mult(X1,X2)))),
inference(spm,[status(thm)],[9,9,theory(equality)]) ).
cnf(40,plain,
rd(mult(mult(X1,X3),rd(X1,X2)),mult(X2,mult(X3,rd(X1,X2)))) = rd(X1,X2),
inference(spm,[status(thm)],[11,24,theory(equality)]) ).
cnf(48,plain,
rd(mult(X1,mult(X2,X3)),X1) = mult(mult(X1,X2),rd(X3,X1)),
inference(spm,[status(thm)],[25,19,theory(equality)]) ).
cnf(62,plain,
rd(mult(X1,X2),X1) = mult(mult(X1,rd(X2,X3)),rd(X3,X1)),
inference(spm,[status(thm)],[48,19,theory(equality)]) ).
cnf(65,plain,
rd(mult(X1,X3),X1) = mult(mult(X1,X2),rd(ld(X2,X3),X1)),
inference(spm,[status(thm)],[48,13,theory(equality)]) ).
cnf(79,plain,
rd(rd(mult(X1,X2),X1),rd(X3,X1)) = mult(X1,rd(X2,X3)),
inference(spm,[status(thm)],[11,62,theory(equality)]) ).
cnf(81,plain,
mult(mult(X1,rd(X2,mult(X3,X1))),X3) = rd(mult(X1,X2),X1),
inference(spm,[status(thm)],[62,11,theory(equality)]) ).
cnf(99,plain,
rd(X1,rd(X2,X1)) = mult(X1,rd(X1,X2)),
inference(spm,[status(thm)],[79,11,theory(equality)]) ).
cnf(100,plain,
rd(rd(mult(X1,X2),X1),X3) = mult(X1,rd(X2,mult(X3,X1))),
inference(spm,[status(thm)],[79,11,theory(equality)]) ).
cnf(116,plain,
rd(X1,X2) = mult(X1,rd(X1,mult(X2,X1))),
inference(spm,[status(thm)],[99,11,theory(equality)]) ).
cnf(118,plain,
ld(mult(X1,rd(X1,X2)),X1) = rd(X2,X1),
inference(spm,[status(thm)],[23,99,theory(equality)]) ).
cnf(130,plain,
ld(X1,rd(X1,X2)) = rd(X1,mult(X2,X1)),
inference(spm,[status(thm)],[21,116,theory(equality)]) ).
cnf(131,plain,
mult(mult(rd(X1,X2),X3),X1) = mult(X1,mult(rd(X1,mult(X2,X1)),mult(X3,X1))),
inference(spm,[status(thm)],[9,116,theory(equality)]) ).
cnf(169,plain,
ld(mult(X1,X2),X1) = rd(ld(X2,X1),X1),
inference(spm,[status(thm)],[118,22,theory(equality)]) ).
cnf(179,plain,
mult(X1,mult(ld(X1,X2),X3)) = mult(mult(X2,rd(X3,X1)),X1),
inference(spm,[status(thm)],[26,19,theory(equality)]) ).
cnf(207,plain,
ld(X1,X2) = rd(X1,mult(ld(X2,X1),X1)),
inference(spm,[status(thm)],[130,22,theory(equality)]) ).
cnf(219,plain,
ld(X1,rd(X1,X2)) = rd(ld(X2,rd(X1,X2)),rd(X1,X2)),
inference(spm,[status(thm)],[169,19,theory(equality)]) ).
cnf(230,plain,
rd(X1,mult(X2,X1)) = rd(ld(X2,rd(X1,X2)),rd(X1,X2)),
inference(rw,[status(thm)],[219,130,theory(equality)]) ).
cnf(253,plain,
rd(rd(X2,X1),X3) = mult(X1,rd(ld(X1,X2),mult(X3,X1))),
inference(spm,[status(thm)],[100,13,theory(equality)]) ).
cnf(352,plain,
mult(ld(X1,X2),mult(ld(X2,X1),X1)) = X1,
inference(spm,[status(thm)],[19,207,theory(equality)]) ).
cnf(1027,plain,
mult(X1,rd(ld(X2,X3),rd(X1,X2))) = rd(mult(rd(X1,X2),X3),rd(X1,X2)),
inference(spm,[status(thm)],[65,19,theory(equality)]) ).
cnf(1030,plain,
ld(mult(X1,X2),rd(mult(X1,X3),X1)) = rd(ld(X2,X3),X1),
inference(spm,[status(thm)],[21,65,theory(equality)]) ).
cnf(1162,plain,
rd(rd(X1,mult(X1,X1)),rd(X1,X1)) = rd(X1,mult(X1,X1)),
inference(spm,[status(thm)],[230,130,theory(equality)]) ).
cnf(1351,plain,
ld(rd(X1,mult(X1,X1)),rd(X1,mult(X1,X1))) = rd(X1,X1),
inference(spm,[status(thm)],[23,1162,theory(equality)]) ).
cnf(1370,plain,
mult(X1,rd(ld(X1,X2),X3)) = rd(rd(X2,X1),rd(X3,X1)),
inference(spm,[status(thm)],[253,19,theory(equality)]) ).
cnf(1435,plain,
rd(X1,rd(X3,X2)) = mult(X2,rd(ld(X2,mult(X1,X2)),X3)),
inference(spm,[status(thm)],[1370,11,theory(equality)]) ).
cnf(2402,plain,
rd(ld(X2,X2),X1) = rd(mult(X1,X2),mult(X1,mult(X1,X2))),
inference(spm,[status(thm)],[130,1030,theory(equality)]) ).
cnf(2478,plain,
rd(mult(ld(X1,X1),X1),X1) = rd(ld(X1,X1),ld(X1,X1)),
inference(spm,[status(thm)],[2402,352,theory(equality)]) ).
cnf(2517,plain,
ld(X1,X1) = rd(ld(X1,X1),ld(X1,X1)),
inference(rw,[status(thm)],[2478,11,theory(equality)]) ).
cnf(2524,plain,
mult(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(spm,[status(thm)],[19,2517,theory(equality)]) ).
cnf(2525,plain,
ld(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(spm,[status(thm)],[23,2517,theory(equality)]) ).
cnf(2980,plain,
mult(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(spm,[status(thm)],[2524,1351,theory(equality)]) ).
cnf(3036,plain,
rd(mult(mult(X1,rd(X1,X1)),rd(X1,X1)),mult(X1,rd(X1,X1))) = rd(X1,X1),
inference(spm,[status(thm)],[40,2980,theory(equality)]) ).
cnf(3073,plain,
rd(X1,mult(X1,rd(X1,X1))) = rd(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3036,62,theory(equality)]),11,theory(equality)]) ).
cnf(3082,plain,
ld(rd(X1,X1),X1) = mult(X1,rd(X1,X1)),
inference(spm,[status(thm)],[23,3073,theory(equality)]) ).
cnf(3115,plain,
X1 = mult(X1,rd(X1,X1)),
inference(rw,[status(thm)],[3082,23,theory(equality)]) ).
cnf(3145,plain,
ld(X1,X1) = rd(X1,X1),
inference(spm,[status(thm)],[21,3115,theory(equality)]) ).
cnf(3157,plain,
mult(mult(rd(X1,X1),rd(X2,X1)),X1) = rd(mult(rd(X1,X1),X2),rd(X1,X1)),
inference(spm,[status(thm)],[81,3115,theory(equality)]) ).
cnf(3203,plain,
mult(X1,mult(rd(X1,mult(X1,X1)),X2)) = rd(mult(rd(X1,X1),X2),rd(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3157,179,theory(equality)]),130,theory(equality)]) ).
cnf(3232,plain,
rd(rd(X1,X1),rd(X1,X1)) = ld(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[2525,3145,theory(equality)]),3145,theory(equality)]),3145,theory(equality)]) ).
cnf(3233,plain,
rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(rw,[status(thm)],[3232,3145,theory(equality)]) ).
cnf(3234,plain,
mult(X1,rd(rd(X1,X1),X1)) = rd(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3233,1370,theory(equality)]),3145,theory(equality)]) ).
cnf(3254,plain,
ld(X1,rd(X1,X1)) = rd(rd(X1,X1),X1),
inference(spm,[status(thm)],[21,3234,theory(equality)]) ).
cnf(3303,plain,
rd(X1,mult(X1,X1)) = rd(rd(X1,X1),X1),
inference(rw,[status(thm)],[3254,130,theory(equality)]) ).
cnf(41598,plain,
mult(X1,rd(ld(X1,X2),rd(X1,X1))) = mult(X1,mult(rd(X1,mult(X1,X1)),X2)),
inference(rw,[status(thm)],[3203,1027,theory(equality)]) ).
cnf(42596,plain,
mult(X1,mult(rd(X1,mult(X1,X1)),mult(X2,X1))) = rd(X2,rd(rd(X1,X1),X1)),
inference(spm,[status(thm)],[1435,41598,theory(equality)]) ).
cnf(42774,plain,
mult(mult(rd(X1,X1),X2),X1) = rd(X2,rd(rd(X1,X1),X1)),
inference(rw,[status(thm)],[42596,131,theory(equality)]) ).
cnf(42775,plain,
mult(mult(rd(X1,X1),X2),X1) = rd(X2,rd(X1,mult(X1,X1))),
inference(rw,[status(thm)],[42774,3303,theory(equality)]) ).
cnf(43491,plain,
rd(X1,rd(rd(X2,X2),rd(X2,X2))) = mult(mult(rd(rd(X2,X2),rd(X2,X2)),X1),rd(X2,X2)),
inference(spm,[status(thm)],[42775,2980,theory(equality)]) ).
cnf(43673,plain,
rd(X1,rd(X2,X2)) = mult(mult(rd(rd(X2,X2),rd(X2,X2)),X1),rd(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[43491,1370,theory(equality)]),3145,theory(equality)]),3303,theory(equality)]),116,theory(equality)]) ).
cnf(43674,plain,
rd(X1,rd(X2,X2)) = mult(mult(rd(X2,X2),X1),rd(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[43673,1370,theory(equality)]),3145,theory(equality)]),3303,theory(equality)]),116,theory(equality)]) ).
cnf(43820,plain,
mult(rd(X2,rd(X1,X1)),rd(X1,X1)) = mult(rd(X1,X1),mult(X2,mult(rd(X1,X1),rd(X1,X1)))),
inference(spm,[status(thm)],[9,43674,theory(equality)]) ).
cnf(44014,plain,
X2 = mult(rd(X1,X1),mult(X2,mult(rd(X1,X1),rd(X1,X1)))),
inference(rw,[status(thm)],[43820,19,theory(equality)]) ).
cnf(44015,plain,
X2 = mult(rd(X1,X1),mult(X2,rd(X1,X1))),
inference(rw,[status(thm)],[44014,2980,theory(equality)]) ).
cnf(44175,plain,
mult(mult(rd(X1,X1),X2),mult(rd(X1,X1),rd(X1,X1))) = mult(mult(rd(X1,X1),rd(X1,X1)),mult(X2,mult(rd(X1,X1),mult(rd(X1,X1),rd(X1,X1))))),
inference(spm,[status(thm)],[30,44015,theory(equality)]) ).
cnf(44368,plain,
rd(X2,rd(X1,X1)) = mult(mult(rd(X1,X1),rd(X1,X1)),mult(X2,mult(rd(X1,X1),mult(rd(X1,X1),rd(X1,X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[44175,2980,theory(equality)]),43674,theory(equality)]) ).
cnf(44369,plain,
rd(X2,rd(X1,X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[44368,2980,theory(equality)]),2980,theory(equality)]),2980,theory(equality)]),44015,theory(equality)]) ).
cnf(44519,plain,
mult(X1,rd(X2,X2)) = X1,
inference(spm,[status(thm)],[19,44369,theory(equality)]) ).
cnf(45193,plain,
mult(rd(X1,X1),X2) = X2,
inference(rw,[status(thm)],[44015,44519,theory(equality)]) ).
cnf(45209,negated_conjecture,
( $false
| mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0 ),
inference(rw,[status(thm)],[17,44519,theory(equality)]) ).
cnf(45210,negated_conjecture,
mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0,
inference(cn,[status(thm)],[45209,theory(equality)]) ).
cnf(46758,negated_conjecture,
$false,
inference(rw,[status(thm)],[45210,45193,theory(equality)]) ).
cnf(46759,negated_conjecture,
$false,
inference(cn,[status(thm)],[46758,theory(equality)]) ).
cnf(46760,negated_conjecture,
$false,
46759,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP660+2.p
% --creating new selector for []
% -running prover on /tmp/tmpeeLUb_/sel_GRP660+2.p_1 with time limit 29
% -prover status Theorem
% Problem GRP660+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP660+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP660+2.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
%
%------------------------------------------------------------------------------