TSTP Solution File: GRP660+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP660+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 11:21:18 EST 2010
% Result : Theorem 1.41s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 6
% Syntax : Number of formulae : 94 ( 88 unt; 0 def)
% Number of atoms : 100 ( 97 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 4 |; 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 : 4 ( 4 usr; 0 con; 1-2 aty)
% Number of variables : 184 ( 0 sgn 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] : mult(mult(mult(X3,X2),X1),X3) = mult(X3,mult(X2,mult(X1,X3))),
file('/tmp/tmppMCQuq/sel_GRP660+1.p_1',f05) ).
fof(2,axiom,
! [X2,X3] : rd(mult(X3,X2),X2) = X3,
file('/tmp/tmppMCQuq/sel_GRP660+1.p_1',f04) ).
fof(3,axiom,
! [X2,X3] : mult(X3,ld(X3,X2)) = X2,
file('/tmp/tmppMCQuq/sel_GRP660+1.p_1',f01) ).
fof(4,conjecture,
? [X4] :
! [X5] :
( mult(X5,X4) = X5
& mult(X4,X5) = X5 ),
file('/tmp/tmppMCQuq/sel_GRP660+1.p_1',goals) ).
fof(5,axiom,
! [X2,X3] : mult(rd(X3,X2),X2) = X3,
file('/tmp/tmppMCQuq/sel_GRP660+1.p_1',f03) ).
fof(6,axiom,
! [X2,X3] : ld(X3,mult(X3,X2)) = X2,
file('/tmp/tmppMCQuq/sel_GRP660+1.p_1',f02) ).
fof(7,negated_conjecture,
~ ? [X4] :
! [X5] :
( mult(X5,X4) = X5
& mult(X4,X5) = X5 ),
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(X5,X4) != X5
| mult(X4,X5) != X5 ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(15,negated_conjecture,
! [X6] :
? [X7] :
( mult(X7,X6) != X7
| mult(X6,X7) != X7 ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,negated_conjecture,
! [X6] :
( mult(esk1_1(X6),X6) != esk1_1(X6)
| mult(X6,esk1_1(X6)) != esk1_1(X6) ),
inference(skolemize,[status(esa)],[15]) ).
cnf(17,negated_conjecture,
( mult(X1,esk1_1(X1)) != esk1_1(X1)
| mult(esk1_1(X1),X1) != esk1_1(X1) ),
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(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(87,plain,
rd(mult(X1,mult(X2,X3)),X1) = mult(mult(X1,X2),rd(X3,X1)),
inference(spm,[status(thm)],[28,19,theory(equality)]) ).
cnf(101,plain,
rd(mult(X1,X3),X1) = mult(mult(X1,X2),rd(ld(X2,X3),X1)),
inference(spm,[status(thm)],[87,13,theory(equality)]) ).
cnf(103,plain,
rd(mult(X1,X2),X1) = mult(mult(X1,rd(X2,X3)),rd(X3,X1)),
inference(spm,[status(thm)],[87,19,theory(equality)]) ).
cnf(122,plain,
ld(ld(X1,X2),ld(X1,mult(X3,X1))) = mult(ld(X2,X3),X1),
inference(spm,[status(thm)],[21,51,theory(equality)]) ).
cnf(145,plain,
rd(ld(X1,mult(X2,X1)),mult(X3,X1)) = ld(X1,rd(X2,X3)),
inference(spm,[status(thm)],[11,54,theory(equality)]) ).
cnf(242,plain,
mult(X2,rd(ld(ld(X1,X2),X3),X1)) = rd(mult(X1,X3),X1),
inference(spm,[status(thm)],[101,13,theory(equality)]) ).
cnf(280,plain,
rd(rd(mult(X1,X2),X1),rd(X3,X1)) = mult(X1,rd(X2,X3)),
inference(spm,[status(thm)],[11,103,theory(equality)]) ).
cnf(287,plain,
mult(mult(ld(X1,X2),rd(X3,X2)),X1) = rd(mult(ld(X1,X2),X3),ld(X1,X2)),
inference(spm,[status(thm)],[103,23,theory(equality)]) ).
cnf(315,plain,
ld(X2,ld(X1,mult(X3,X1))) = mult(ld(mult(X1,X2),X3),X1),
inference(spm,[status(thm)],[122,21,theory(equality)]) ).
cnf(316,plain,
ld(ld(X1,X2),X1) = mult(ld(X2,X1),X1),
inference(spm,[status(thm)],[122,21,theory(equality)]) ).
cnf(340,plain,
ld(X2,X1) = mult(ld(mult(X1,X2),X1),X1),
inference(spm,[status(thm)],[316,21,theory(equality)]) ).
cnf(341,plain,
ld(X2,rd(X1,X2)) = mult(ld(X1,rd(X1,X2)),rd(X1,X2)),
inference(spm,[status(thm)],[316,22,theory(equality)]) ).
cnf(342,plain,
rd(X1,mult(ld(X2,X1),X1)) = ld(X1,X2),
inference(spm,[status(thm)],[23,316,theory(equality)]) ).
cnf(357,plain,
rd(ld(X2,X1),X1) = ld(mult(X1,X2),X1),
inference(spm,[status(thm)],[11,340,theory(equality)]) ).
cnf(408,plain,
rd(X1,mult(X2,X1)) = ld(X1,rd(X1,X2)),
inference(spm,[status(thm)],[342,22,theory(equality)]) ).
cnf(425,plain,
rd(rd(X1,X2),rd(X1,mult(X2,X1))) = X1,
inference(spm,[status(thm)],[23,408,theory(equality)]) ).
cnf(742,plain,
ld(X1,ld(X2,X3)) = mult(ld(mult(X2,X1),rd(X3,X2)),X2),
inference(spm,[status(thm)],[315,19,theory(equality)]) ).
cnf(969,plain,
ld(X1,rd(X2,X2)) = ld(mult(mult(X2,X1),X1),mult(X2,X1)),
inference(spm,[status(thm)],[357,145,theory(equality)]) ).
cnf(1028,plain,
ld(X1,rd(mult(X2,X3),X2)) = rd(ld(ld(X2,X1),X3),X2),
inference(spm,[status(thm)],[21,242,theory(equality)]) ).
cnf(1102,plain,
rd(ld(rd(X1,mult(X2,X1)),X3),X1) = ld(rd(X1,X2),rd(mult(X1,X3),X1)),
inference(spm,[status(thm)],[1028,408,theory(equality)]) ).
cnf(1221,plain,
rd(rd(X2,X1),rd(X3,X1)) = mult(X1,rd(ld(X1,X2),X3)),
inference(spm,[status(thm)],[280,13,theory(equality)]) ).
cnf(1644,plain,
mult(rd(X1,mult(X2,X1)),rd(X1,X2)) = ld(X2,rd(X1,X2)),
inference(rw,[status(thm)],[341,408,theory(equality)]) ).
cnf(2073,plain,
mult(ld(X2,rd(X3,X1)),X1) = ld(ld(X1,X2),ld(X1,X3)),
inference(spm,[status(thm)],[742,13,theory(equality)]) ).
cnf(2455,plain,
ld(rd(mult(X1,X1),X1),mult(X1,rd(X1,X1))) = ld(rd(X1,X1),rd(X1,X1)),
inference(spm,[status(thm)],[969,103,theory(equality)]) ).
cnf(2493,plain,
rd(X1,X1) = ld(rd(X1,X1),rd(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2455,11,theory(equality)]),21,theory(equality)]) ).
cnf(2509,plain,
mult(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(spm,[status(thm)],[13,2493,theory(equality)]) ).
cnf(2510,plain,
rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(spm,[status(thm)],[23,2493,theory(equality)]) ).
cnf(2529,plain,
mult(X1,ld(mult(X1,X1),X1)) = rd(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2510,1221,theory(equality)]),357,theory(equality)]) ).
cnf(2562,plain,
mult(rd(X1,X1),mult(X1,rd(X1,X1))) = mult(mult(X1,rd(X1,X1)),rd(X1,X1)),
inference(spm,[status(thm)],[27,2509,theory(equality)]) ).
cnf(2597,plain,
mult(rd(X1,X1),mult(X1,rd(X1,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2562,103,theory(equality)]),11,theory(equality)]) ).
cnf(2625,plain,
ld(X1,rd(X1,X1)) = ld(mult(X1,X1),X1),
inference(spm,[status(thm)],[21,2529,theory(equality)]) ).
cnf(2670,plain,
rd(X1,mult(X1,X1)) = ld(mult(X1,X1),X1),
inference(rw,[status(thm)],[2625,408,theory(equality)]) ).
cnf(2695,plain,
rd(rd(X1,X1),ld(mult(X1,X1),X1)) = X1,
inference(spm,[status(thm)],[425,2670,theory(equality)]) ).
cnf(2704,plain,
mult(ld(mult(X1,X1),X1),rd(X1,X1)) = ld(X1,rd(X1,X1)),
inference(spm,[status(thm)],[1644,2670,theory(equality)]) ).
cnf(2718,plain,
mult(ld(mult(X1,X1),X1),rd(X1,X1)) = ld(mult(X1,X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2704,408,theory(equality)]),2670,theory(equality)]) ).
cnf(2775,plain,
ld(mult(mult(rd(X1,X1),rd(X1,X1)),X1),mult(rd(X1,X1),X1)) = rd(X1,X1),
inference(spm,[status(thm)],[26,2597,theory(equality)]) ).
cnf(2812,plain,
ld(X1,X1) = rd(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[2775,2509,theory(equality)]),19,theory(equality)]),19,theory(equality)]) ).
cnf(2849,plain,
ld(X1,ld(X1,X1)) = rd(X1,mult(X1,X1)),
inference(spm,[status(thm)],[408,2812,theory(equality)]) ).
cnf(2870,plain,
mult(ld(X1,X1),ld(X1,X1)) = rd(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2509,2812,theory(equality)]),2812,theory(equality)]) ).
cnf(2871,plain,
mult(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(rw,[status(thm)],[2870,2812,theory(equality)]) ).
cnf(2878,plain,
ld(X1,ld(X1,X1)) = ld(mult(X1,X1),X1),
inference(rw,[status(thm)],[2849,2670,theory(equality)]) ).
cnf(3550,plain,
rd(ld(X1,X1),ld(mult(X1,X1),X1)) = X1,
inference(rw,[status(thm)],[2695,2812,theory(equality)]) ).
cnf(6102,plain,
mult(ld(mult(X1,X1),X1),ld(X1,X1)) = ld(mult(X1,X1),X1),
inference(rw,[status(thm)],[2718,2812,theory(equality)]) ).
cnf(26672,plain,
rd(ld(rd(ld(X1,X1),ld(mult(X1,X1),X1)),X2),ld(X1,X1)) = ld(rd(ld(X1,X1),ld(mult(X1,X1),X1)),rd(mult(ld(X1,X1),X2),ld(X1,X1))),
inference(spm,[status(thm)],[1102,6102,theory(equality)]) ).
cnf(26831,plain,
rd(ld(X1,X2),ld(X1,X1)) = ld(rd(ld(X1,X1),ld(mult(X1,X1),X1)),rd(mult(ld(X1,X1),X2),ld(X1,X1))),
inference(rw,[status(thm)],[26672,3550,theory(equality)]) ).
cnf(26832,plain,
rd(ld(X1,X2),ld(X1,X1)) = mult(ld(mult(X1,X1),X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[26831,3550,theory(equality)]),287,theory(equality)]),42,theory(equality)]),2878,theory(equality)]),21,theory(equality)]) ).
cnf(26898,plain,
rd(X2,ld(X1,X1)) = mult(ld(mult(X1,X1),X1),mult(X1,X2)),
inference(spm,[status(thm)],[26832,21,theory(equality)]) ).
cnf(27208,plain,
mult(ld(ld(X1,X1),ld(X1,X1)),mult(ld(X1,X1),X2)) = rd(X2,ld(ld(X1,X1),ld(X1,X1))),
inference(spm,[status(thm)],[26898,2871,theory(equality)]) ).
cnf(27369,plain,
mult(ld(X1,X1),mult(ld(X1,X1),X2)) = rd(X2,ld(ld(X1,X1),ld(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[27208,2073,theory(equality)]),408,theory(equality)]),2670,theory(equality)]),340,theory(equality)]) ).
cnf(27370,plain,
mult(ld(X1,X1),mult(ld(X1,X1),X2)) = rd(X2,ld(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[27369,2073,theory(equality)]),408,theory(equality)]),2670,theory(equality)]),340,theory(equality)]) ).
cnf(27708,plain,
ld(mult(mult(ld(X1,X1),ld(X1,X1)),X2),rd(mult(X2,ld(X1,X1)),ld(X1,X1))) = ld(X1,X1),
inference(spm,[status(thm)],[26,27370,theory(equality)]) ).
cnf(27883,plain,
ld(mult(ld(X1,X1),X2),X2) = ld(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[27708,2871,theory(equality)]),11,theory(equality)]) ).
cnf(28027,plain,
mult(mult(ld(X1,X1),X2),ld(X1,X1)) = X2,
inference(spm,[status(thm)],[13,27883,theory(equality)]) ).
cnf(28029,plain,
rd(X1,ld(X2,X2)) = mult(ld(X2,X2),X1),
inference(spm,[status(thm)],[23,27883,theory(equality)]) ).
cnf(28255,plain,
mult(ld(X2,X2),mult(X1,ld(X2,X2))) = X1,
inference(spm,[status(thm)],[11,28029,theory(equality)]) ).
cnf(29252,plain,
rd(X2,ld(X1,X1)) = mult(mult(ld(X1,X1),X2),rd(ld(X1,X1),ld(X1,X1))),
inference(spm,[status(thm)],[87,28255,theory(equality)]) ).
cnf(29410,plain,
mult(ld(X1,X1),X2) = mult(mult(ld(X1,X1),X2),rd(ld(X1,X1),ld(X1,X1))),
inference(rw,[status(thm)],[29252,28029,theory(equality)]) ).
cnf(29411,plain,
mult(ld(X1,X1),X2) = 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)],[29410,2812,theory(equality)]),2073,theory(equality)]),408,theory(equality)]),2670,theory(equality)]),340,theory(equality)]),28027,theory(equality)]) ).
cnf(29818,negated_conjecture,
mult(esk1_1(ld(X1,X1)),ld(X1,X1)) != esk1_1(ld(X1,X1)),
inference(spm,[status(thm)],[17,29411,theory(equality)]) ).
cnf(29819,plain,
mult(X2,ld(X1,X1)) = X2,
inference(rw,[status(thm)],[28255,29411,theory(equality)]) ).
cnf(31001,negated_conjecture,
$false,
inference(rw,[status(thm)],[29818,29819,theory(equality)]) ).
cnf(31002,negated_conjecture,
$false,
inference(cn,[status(thm)],[31001,theory(equality)]) ).
cnf(31003,negated_conjecture,
$false,
31002,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP660+1.p
% --creating new selector for []
% -running prover on /tmp/tmppMCQuq/sel_GRP660+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP660+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP660+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP660+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
%
%------------------------------------------------------------------------------