%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP660+3 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 11:21:40 EST 2010
% Result : Theorem 2.20s
% Output : CNFRefutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 6
% Syntax : Number of formulae : 99 ( 92 unt; 0 def)
% Number of atoms : 106 ( 102 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 : 8 ( 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 : 183 ( 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/tmp8Vvj3C/sel_GRP660+3.p_1',f05) ).
fof(2,axiom,
! [X2,X3] : rd(mult(X3,X2),X2) = X3,
file('/tmp/tmp8Vvj3C/sel_GRP660+3.p_1',f04) ).
fof(3,axiom,
! [X2,X3] : mult(X3,ld(X3,X2)) = X2,
file('/tmp/tmp8Vvj3C/sel_GRP660+3.p_1',f01) ).
fof(4,conjecture,
! [X4,X5] :
( mult(X4,ld(X5,X5)) = X4
& mult(ld(X5,X5),X4) = X4 ),
file('/tmp/tmp8Vvj3C/sel_GRP660+3.p_1',goals) ).
fof(5,axiom,
! [X2,X3] : mult(rd(X3,X2),X2) = X3,
file('/tmp/tmp8Vvj3C/sel_GRP660+3.p_1',f03) ).
fof(6,axiom,
! [X2,X3] : ld(X3,mult(X3,X2)) = X2,
file('/tmp/tmp8Vvj3C/sel_GRP660+3.p_1',f02) ).
fof(7,negated_conjecture,
~ ! [X4,X5] :
( mult(X4,ld(X5,X5)) = X4
& mult(ld(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,ld(X5,X5)) != X4
| mult(ld(X5,X5),X4) != X4 ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(15,negated_conjecture,
? [X6,X7] :
( mult(X6,ld(X7,X7)) != X6
| mult(ld(X7,X7),X6) != X6 ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,negated_conjecture,
( mult(esk1_0,ld(esk2_0,esk2_0)) != esk1_0
| mult(ld(esk2_0,esk2_0),esk1_0) != esk1_0 ),
inference(skolemize,[status(esa)],[15]) ).
cnf(17,negated_conjecture,
( mult(ld(esk2_0,esk2_0),esk1_0) != esk1_0
| mult(esk1_0,ld(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,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[21,19,theory(equality)]) ).
cnf(23,plain,
rd(X2,ld(X1,X2)) = X1,
inference(spm,[status(thm)],[11,13,theory(equality)]) ).
cnf(24,plain,
mult(mult(X2,X3),X1) = mult(X1,mult(ld(X1,X2),mult(X3,X1))),
inference(spm,[status(thm)],[9,13,theory(equality)]) ).
cnf(26,plain,
ld(mult(mult(X1,X2),X3),mult(X1,mult(X2,mult(X3,X1)))) = X1,
inference(spm,[status(thm)],[21,9,theory(equality)]) ).
cnf(27,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(28,plain,
rd(mult(X1,mult(X2,mult(X3,X1))),X1) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[11,9,theory(equality)]) ).
cnf(39,plain,
mult(ld(X1,X2),mult(ld(ld(X1,X2),X3),X2)) = mult(mult(X3,X1),ld(X1,X2)),
inference(spm,[status(thm)],[24,13,theory(equality)]) ).
cnf(40,plain,
ld(X1,mult(mult(X2,X3),X1)) = mult(ld(X1,X2),mult(X3,X1)),
inference(spm,[status(thm)],[21,24,theory(equality)]) ).
cnf(42,plain,
mult(X1,mult(ld(X1,X2),X3)) = mult(mult(X2,rd(X3,X1)),X1),
inference(spm,[status(thm)],[24,19,theory(equality)]) ).
cnf(51,plain,
ld(X1,mult(X3,X1)) = mult(ld(X1,X2),mult(ld(X2,X3),X1)),
inference(spm,[status(thm)],[40,13,theory(equality)]) ).
cnf(54,plain,
ld(X1,mult(X2,X1)) = mult(ld(X1,rd(X2,X3)),mult(X3,X1)),
inference(spm,[status(thm)],[40,19,theory(equality)]) ).
cnf(67,plain,
ld(ld(X1,X2),ld(X1,mult(X3,X1))) = mult(ld(X2,X3),X1),
inference(spm,[status(thm)],[21,51,theory(equality)]) ).
cnf(68,plain,
mult(X2,mult(ld(mult(X1,X2),X3),X1)) = ld(X1,mult(X3,X1)),
inference(spm,[status(thm)],[51,21,theory(equality)]) ).
cnf(87,plain,
ld(X2,ld(X1,mult(X3,X1))) = mult(ld(mult(X1,X2),X3),X1),
inference(spm,[status(thm)],[67,21,theory(equality)]) ).
cnf(88,plain,
ld(ld(X1,X2),X1) = mult(ld(X2,X1),X1),
inference(spm,[status(thm)],[67,21,theory(equality)]) ).
cnf(104,plain,
ld(X2,X1) = mult(ld(mult(X1,X2),X1),X1),
inference(spm,[status(thm)],[88,21,theory(equality)]) ).
cnf(106,plain,
rd(X1,mult(ld(X2,X1),X1)) = ld(X1,X2),
inference(spm,[status(thm)],[23,88,theory(equality)]) ).
cnf(118,plain,
rd(ld(X2,X1),X1) = ld(mult(X1,X2),X1),
inference(spm,[status(thm)],[11,104,theory(equality)]) ).
cnf(120,plain,
mult(ld(mult(X1,mult(X2,mult(X3,X1))),mult(mult(X1,X2),X3)),mult(mult(X1,X2),X3)) = ld(X1,mult(mult(X1,X2),X3)),
inference(spm,[status(thm)],[104,9,theory(equality)]) ).
cnf(156,plain,
rd(X2,X1) = ld(mult(X1,rd(X1,X2)),X1),
inference(spm,[status(thm)],[118,22,theory(equality)]) ).
cnf(169,plain,
rd(X1,mult(X2,X1)) = ld(X1,rd(X1,X2)),
inference(spm,[status(thm)],[106,22,theory(equality)]) ).
cnf(207,plain,
rd(ld(X1,X2),X2) = ld(ld(X1,X2),rd(ld(X1,X2),X1)),
inference(spm,[status(thm)],[169,13,theory(equality)]) ).
cnf(217,plain,
ld(mult(X2,X1),X2) = ld(ld(X1,X2),rd(ld(X1,X2),X1)),
inference(rw,[status(thm)],[207,118,theory(equality)]) ).
cnf(237,plain,
mult(mult(X1,rd(X1,X2)),rd(X2,X1)) = X1,
inference(spm,[status(thm)],[13,156,theory(equality)]) ).
cnf(268,plain,
ld(X1,ld(X2,X3)) = mult(ld(mult(X2,X1),rd(X3,X2)),X2),
inference(spm,[status(thm)],[87,19,theory(equality)]) ).
cnf(568,plain,
rd(mult(X1,mult(X2,X3)),X1) = mult(mult(X1,X2),rd(X3,X1)),
inference(spm,[status(thm)],[28,19,theory(equality)]) ).
cnf(1109,plain,
mult(ld(ld(X1,X2),rd(X3,X1)),X2) = ld(ld(X1,X2),mult(X3,ld(X1,X2))),
inference(spm,[status(thm)],[54,13,theory(equality)]) ).
cnf(1112,plain,
rd(ld(X1,mult(X2,X1)),mult(X3,X1)) = ld(X1,rd(X2,X3)),
inference(spm,[status(thm)],[11,54,theory(equality)]) ).
cnf(1193,plain,
ld(ld(X1,X1),ld(mult(X1,X1),X1)) = ld(mult(X1,X1),X1),
inference(spm,[status(thm)],[217,118,theory(equality)]) ).
cnf(1332,plain,
mult(ld(X2,rd(X3,X1)),X1) = ld(ld(X1,X2),ld(X1,X3)),
inference(spm,[status(thm)],[268,13,theory(equality)]) ).
cnf(1648,plain,
mult(X1,mult(mult(X2,X1),ld(X1,X1))) = mult(mult(X1,ld(ld(X1,X1),X2)),X1),
inference(spm,[status(thm)],[24,39,theory(equality)]) ).
cnf(2413,plain,
ld(X1,rd(X2,X2)) = ld(mult(mult(X2,X1),X1),mult(X2,X1)),
inference(spm,[status(thm)],[118,1112,theory(equality)]) ).
cnf(2492,plain,
ld(X1,mult(X1,rd(X1,X1))) = ld(rd(X1,X1),rd(X1,X1)),
inference(spm,[status(thm)],[2413,237,theory(equality)]) ).
cnf(2532,plain,
rd(X1,X1) = ld(rd(X1,X1),rd(X1,X1)),
inference(rw,[status(thm)],[2492,21,theory(equality)]) ).
cnf(2541,plain,
mult(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(spm,[status(thm)],[13,2532,theory(equality)]) ).
cnf(2583,plain,
mult(rd(X1,X1),mult(X1,rd(X1,X1))) = mult(mult(X1,rd(X1,X1)),rd(X1,X1)),
inference(spm,[status(thm)],[27,2541,theory(equality)]) ).
cnf(2584,plain,
mult(rd(X1,X1),X1) = mult(X1,mult(ld(X1,rd(X1,X1)),X1)),
inference(spm,[status(thm)],[42,2541,theory(equality)]) ).
cnf(2612,plain,
mult(rd(X1,X1),mult(X1,rd(X1,X1))) = X1,
inference(rw,[status(thm)],[2583,237,theory(equality)]) ).
cnf(2613,plain,
X1 = mult(X1,mult(ld(X1,rd(X1,X1)),X1)),
inference(rw,[status(thm)],[2584,19,theory(equality)]) ).
cnf(2802,plain,
ld(X1,X1) = mult(ld(X1,rd(X1,X1)),X1),
inference(spm,[status(thm)],[21,2613,theory(equality)]) ).
cnf(2859,plain,
rd(ld(X1,X1),X1) = ld(X1,rd(X1,X1)),
inference(spm,[status(thm)],[11,2802,theory(equality)]) ).
cnf(2905,plain,
ld(mult(X1,X1),X1) = ld(X1,rd(X1,X1)),
inference(rw,[status(thm)],[2859,118,theory(equality)]) ).
cnf(2950,plain,
ld(ld(X1,X1),ld(X1,rd(X1,X1))) = ld(mult(X1,X1),X1),
inference(rw,[status(thm)],[1193,2905,theory(equality)]) ).
cnf(2951,plain,
ld(ld(X1,X1),ld(X1,rd(X1,X1))) = ld(X1,rd(X1,X1)),
inference(rw,[status(thm)],[2950,2905,theory(equality)]) ).
cnf(2952,plain,
mult(ld(X1,rd(rd(X1,X1),X1)),X1) = ld(X1,rd(X1,X1)),
inference(rw,[status(thm)],[2951,1332,theory(equality)]) ).
cnf(4127,plain,
ld(mult(mult(rd(X1,X1),rd(X1,X1)),X1),mult(rd(X1,X1),X1)) = rd(X1,X1),
inference(spm,[status(thm)],[26,2612,theory(equality)]) ).
cnf(4166,plain,
ld(X1,X1) = rd(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[4127,2541,theory(equality)]),19,theory(equality)]),19,theory(equality)]) ).
cnf(4342,plain,
mult(ld(X1,X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[2612,4166,theory(equality)]),4166,theory(equality)]),13,theory(equality)]) ).
cnf(4351,plain,
mult(ld(X1,ld(X1,ld(X1,X1))),X1) = ld(X1,rd(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[2952,4166,theory(equality)]),118,theory(equality)]),2905,theory(equality)]),4166,theory(equality)]) ).
cnf(4352,plain,
mult(ld(X1,ld(X1,ld(X1,X1))),X1) = ld(X1,ld(X1,X1)),
inference(rw,[status(thm)],[4351,4166,theory(equality)]) ).
cnf(4357,plain,
mult(ld(X1,ld(X1,X1)),X1) = ld(X1,X1),
inference(rw,[status(thm)],[2802,4166,theory(equality)]) ).
cnf(4367,plain,
ld(mult(mult(X1,X2),X2),mult(X1,X2)) = ld(X2,ld(X1,X1)),
inference(rw,[status(thm)],[2413,4166,theory(equality)]) ).
cnf(4385,plain,
mult(X1,mult(ld(X1,X2),ld(X1,X1))) = ld(ld(X1,X1),mult(X2,ld(X1,X1))),
inference(spm,[status(thm)],[68,4342,theory(equality)]) ).
cnf(4906,plain,
mult(ld(X1,X1),ld(X1,ld(X1,X1))) = ld(X1,mult(ld(X1,ld(X1,X1)),X1)),
inference(spm,[status(thm)],[51,4352,theory(equality)]) ).
cnf(4953,plain,
mult(ld(X1,X1),ld(X1,ld(X1,X1))) = ld(X1,ld(X1,X1)),
inference(rw,[status(thm)],[4906,4357,theory(equality)]) ).
cnf(4969,plain,
mult(mult(mult(X1,X2),X2),ld(X2,ld(X1,X1))) = mult(X1,X2),
inference(spm,[status(thm)],[13,4367,theory(equality)]) ).
cnf(6717,plain,
mult(ld(X1,ld(X1,X1)),mult(ld(ld(X1,ld(X1,X1)),X2),ld(X1,X1))) = ld(ld(X1,X1),mult(X2,ld(X1,X1))),
inference(spm,[status(thm)],[68,4953,theory(equality)]) ).
cnf(6765,plain,
mult(mult(X2,X1),ld(X1,ld(X1,X1))) = ld(ld(X1,X1),mult(X2,ld(X1,X1))),
inference(rw,[status(thm)],[6717,39,theory(equality)]) ).
cnf(24289,plain,
ld(ld(X1,X1),mult(ld(X1,X1),mult(mult(X2,ld(X1,X1)),ld(ld(X1,X1),ld(X1,X1))))) = mult(X1,mult(ld(X1,mult(ld(X1,X1),ld(ld(ld(X1,X1),ld(X1,X1)),X2))),ld(X1,X1))),
inference(spm,[status(thm)],[4385,1648,theory(equality)]) ).
cnf(24387,plain,
mult(mult(X2,ld(X1,X1)),ld(X1,X1)) = mult(X1,mult(ld(X1,mult(ld(X1,X1),ld(ld(ld(X1,X1),ld(X1,X1)),X2))),ld(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[24289,1332,theory(equality)]),4166,theory(equality)]),4357,theory(equality)]),21,theory(equality)]) ).
cnf(24388,plain,
mult(mult(X2,ld(X1,X1)),ld(X1,X1)) = mult(X1,mult(ld(X1,X2),ld(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[24387,1332,theory(equality)]),4166,theory(equality)]),4357,theory(equality)]),13,theory(equality)]) ).
cnf(27659,plain,
mult(X1,mult(ld(X1,X2),ld(X1,X1))) = mult(mult(X2,X1),ld(X1,ld(X1,X1))),
inference(rw,[status(thm)],[6765,4385,theory(equality)]) ).
cnf(40149,plain,
mult(ld(ld(X1,X1),rd(X2,X1)),X1) = mult(X1,mult(ld(X1,X2),ld(X1,X1))),
inference(rw,[status(thm)],[4385,1109,theory(equality)]) ).
cnf(42026,plain,
rd(mult(X1,mult(ld(X1,X2),ld(X1,X1))),X1) = ld(ld(X1,X1),rd(X2,X1)),
inference(spm,[status(thm)],[11,40149,theory(equality)]) ).
cnf(42215,plain,
mult(X2,ld(X1,ld(X1,X1))) = ld(ld(X1,X1),rd(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[42026,568,theory(equality)]),13,theory(equality)]),118,theory(equality)]),2905,theory(equality)]),4166,theory(equality)]) ).
cnf(43211,plain,
ld(ld(X1,X1),X2) = mult(mult(X2,X1),ld(X1,ld(X1,X1))),
inference(spm,[status(thm)],[42215,11,theory(equality)]) ).
cnf(43347,plain,
ld(ld(X1,X1),X2) = mult(X1,mult(ld(X1,X2),ld(X1,X1))),
inference(rw,[status(thm)],[43211,27659,theory(equality)]) ).
cnf(43588,plain,
mult(ld(mult(ld(X1,X1),ld(ld(X1,X1),X2)),mult(mult(ld(X1,X1),X1),ld(X1,X2))),mult(mult(ld(X1,X1),X1),ld(X1,X2))) = ld(ld(X1,X1),mult(mult(ld(X1,X1),X1),ld(X1,X2))),
inference(spm,[status(thm)],[120,43347,theory(equality)]) ).
cnf(43792,plain,
X2 = ld(ld(X1,X1),mult(mult(ld(X1,X1),X1),ld(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[43588,13,theory(equality)]),4342,theory(equality)]),13,theory(equality)]),4342,theory(equality)]),13,theory(equality)]),4342,theory(equality)]) ).
cnf(43793,plain,
X2 = ld(ld(X1,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[43792,4342,theory(equality)]),13,theory(equality)]) ).
cnf(43880,plain,
mult(ld(X1,X1),X2) = X2,
inference(spm,[status(thm)],[13,43793,theory(equality)]) ).
cnf(43962,plain,
mult(mult(mult(X1,ld(X2,X2)),ld(X2,X2)),ld(X1,X1)) = mult(X1,ld(X2,X2)),
inference(spm,[status(thm)],[4969,43793,theory(equality)]) ).
cnf(44185,plain,
X1 = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[43962,24388,theory(equality)]),43347,theory(equality)]),43793,theory(equality)]),13,theory(equality)]) ).
cnf(44636,negated_conjecture,
( mult(esk1_0,ld(esk2_0,esk2_0)) != esk1_0
| $false ),
inference(rw,[status(thm)],[17,43880,theory(equality)]) ).
cnf(44637,negated_conjecture,
mult(esk1_0,ld(esk2_0,esk2_0)) != esk1_0,
inference(cn,[status(thm)],[44636,theory(equality)]) ).
cnf(46179,negated_conjecture,
$false,
inference(rw,[status(thm)],[44637,44185,theory(equality)]) ).
cnf(46180,negated_conjecture,
$false,
inference(cn,[status(thm)],[46179,theory(equality)]) ).
cnf(46181,negated_conjecture,
$false,
46180,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP660+3.p
% --creating new selector for []
% -running prover on /tmp/tmp8Vvj3C/sel_GRP660+3.p_1 with time limit 29
% -prover status Theorem
% Problem GRP660+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP660+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP660+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
%
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