TSTP Solution File: GRP659+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP659+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 11:21:06 EST 2010
% Result : Theorem 0.55s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 6
% Syntax : Number of formulae : 91 ( 85 unt; 0 def)
% Number of atoms : 97 ( 94 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 : 171 ( 0 sgn 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] : mult(mult(X3,mult(X2,X1)),X2) = mult(mult(X3,X2),mult(X1,X2)),
file('/tmp/tmp82WwnO/sel_GRP659+1.p_1',f05) ).
fof(2,axiom,
! [X2,X3] : rd(mult(X3,X2),X2) = X3,
file('/tmp/tmp82WwnO/sel_GRP659+1.p_1',f04) ).
fof(3,axiom,
! [X2,X3] : mult(X3,ld(X3,X2)) = X2,
file('/tmp/tmp82WwnO/sel_GRP659+1.p_1',f01) ).
fof(4,conjecture,
? [X4] :
! [X5] :
( mult(X5,X4) = X5
& mult(X4,X5) = X5 ),
file('/tmp/tmp82WwnO/sel_GRP659+1.p_1',goals) ).
fof(5,axiom,
! [X2,X3] : mult(rd(X3,X2),X2) = X3,
file('/tmp/tmp82WwnO/sel_GRP659+1.p_1',f03) ).
fof(6,axiom,
! [X2,X3] : ld(X3,mult(X3,X2)) = X2,
file('/tmp/tmp82WwnO/sel_GRP659+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(X6,mult(X5,X4)),X5) = mult(mult(X6,X5),mult(X4,X5)),
inference(variable_rename,[status(thm)],[1]) ).
cnf(9,plain,
mult(mult(X1,mult(X2,X3)),X2) = mult(mult(X1,X2),mult(X3,X2)),
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(X1,X3),X2) = mult(mult(X1,X2),mult(ld(X2,X3),X2)),
inference(spm,[status(thm)],[9,13,theory(equality)]) ).
cnf(25,plain,
ld(mult(X1,mult(X2,X3)),mult(mult(X1,X2),mult(X3,X2))) = X2,
inference(spm,[status(thm)],[21,9,theory(equality)]) ).
cnf(27,plain,
mult(X1,X2) = mult(mult(rd(X1,mult(X2,X3)),X2),mult(X3,X2)),
inference(spm,[status(thm)],[9,19,theory(equality)]) ).
cnf(28,plain,
rd(mult(mult(X1,X2),mult(X3,X2)),X2) = mult(X1,mult(X2,X3)),
inference(spm,[status(thm)],[11,9,theory(equality)]) ).
cnf(42,plain,
mult(X1,mult(ld(X2,X3),X2)) = mult(mult(rd(X1,X2),X3),X2),
inference(spm,[status(thm)],[24,19,theory(equality)]) ).
cnf(53,plain,
mult(X1,X2) = mult(X1,mult(ld(X2,X2),X2)),
inference(spm,[status(thm)],[42,19,theory(equality)]) ).
cnf(65,plain,
ld(X1,mult(X1,X2)) = mult(ld(X2,X2),X2),
inference(spm,[status(thm)],[21,53,theory(equality)]) ).
cnf(76,plain,
X2 = mult(ld(X2,X2),X2),
inference(rw,[status(thm)],[65,21,theory(equality)]) ).
cnf(88,plain,
rd(X1,X1) = ld(X1,X1),
inference(spm,[status(thm)],[11,76,theory(equality)]) ).
cnf(89,plain,
mult(mult(X1,X2),ld(X2,X2)) = mult(mult(X1,ld(X2,X2)),mult(X2,ld(X2,X2))),
inference(spm,[status(thm)],[9,76,theory(equality)]) ).
cnf(91,plain,
mult(X1,mult(ld(X1,X2),X1)) = mult(mult(ld(X1,X1),X2),X1),
inference(spm,[status(thm)],[24,76,theory(equality)]) ).
cnf(93,plain,
mult(mult(X1,X2),ld(X2,X2)) = mult(mult(X1,ld(X2,X2)),X2),
inference(rw,[status(thm)],[89,13,theory(equality)]) ).
cnf(105,plain,
mult(X1,X1) = mult(mult(X1,X1),ld(X1,X1)),
inference(spm,[status(thm)],[93,13,theory(equality)]) ).
cnf(158,plain,
ld(mult(X1,mult(X2,X2)),mult(mult(X1,mult(X2,X2)),mult(ld(X2,X2),mult(X2,X2)))) = mult(X2,X2),
inference(spm,[status(thm)],[25,105,theory(equality)]) ).
cnf(167,plain,
mult(ld(X2,X2),mult(X2,X2)) = mult(X2,X2),
inference(rw,[status(thm)],[158,21,theory(equality)]) ).
cnf(270,plain,
rd(mult(X1,mult(X3,X2)),X2) = mult(rd(X1,X2),mult(X2,X3)),
inference(spm,[status(thm)],[28,19,theory(equality)]) ).
cnf(309,plain,
rd(mult(X1,X2),mult(X3,X2)) = mult(rd(X1,mult(X2,X3)),X2),
inference(spm,[status(thm)],[11,27,theory(equality)]) ).
cnf(416,plain,
rd(mult(X1,X2),X3) = mult(rd(X1,X3),mult(X3,rd(X2,X3))),
inference(spm,[status(thm)],[270,19,theory(equality)]) ).
cnf(432,plain,
rd(mult(X1,X1),X1) = mult(rd(ld(X1,X1),X1),mult(X1,X1)),
inference(spm,[status(thm)],[270,167,theory(equality)]) ).
cnf(455,plain,
X1 = mult(rd(ld(X1,X1),X1),mult(X1,X1)),
inference(rw,[status(thm)],[432,11,theory(equality)]) ).
cnf(462,plain,
rd(X1,mult(X1,X1)) = rd(ld(X1,X1),X1),
inference(spm,[status(thm)],[11,455,theory(equality)]) ).
cnf(484,plain,
mult(rd(X1,mult(X1,X1)),X1) = ld(X1,X1),
inference(spm,[status(thm)],[19,462,theory(equality)]) ).
cnf(537,plain,
mult(rd(X1,mult(X2,X1)),X2) = ld(mult(X1,X2),mult(X1,X2)),
inference(spm,[status(thm)],[88,309,theory(equality)]) ).
cnf(576,plain,
ld(mult(X1,X1),mult(X1,X1)) = mult(rd(mult(X1,X1),mult(ld(X1,X1),mult(X1,X1))),ld(X1,X1)),
inference(spm,[status(thm)],[537,105,theory(equality)]) ).
cnf(598,plain,
ld(X1,X1) = mult(rd(mult(X1,X1),mult(ld(X1,X1),mult(X1,X1))),ld(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[576,537,theory(equality)]),484,theory(equality)]) ).
cnf(599,plain,
ld(X1,X1) = mult(ld(X1,X1),ld(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[598,167,theory(equality)]),88,theory(equality)]),537,theory(equality)]),484,theory(equality)]) ).
cnf(620,plain,
mult(ld(X1,X1),X1) = mult(X1,mult(ld(X1,ld(X1,X1)),X1)),
inference(spm,[status(thm)],[91,599,theory(equality)]) ).
cnf(640,plain,
X1 = mult(X1,mult(ld(X1,ld(X1,X1)),X1)),
inference(rw,[status(thm)],[620,76,theory(equality)]) ).
cnf(718,plain,
ld(X1,X1) = mult(ld(X1,ld(X1,X1)),X1),
inference(spm,[status(thm)],[21,640,theory(equality)]) ).
cnf(772,plain,
mult(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[640,718,theory(equality)]) ).
cnf(1694,plain,
mult(X1,mult(X2,rd(X3,X2))) = rd(mult(mult(X1,X2),X3),X2),
inference(spm,[status(thm)],[416,11,theory(equality)]) ).
cnf(1791,plain,
rd(mult(X1,X2),X2) = mult(X1,mult(X2,rd(ld(mult(X1,X2),mult(X1,X2)),X2))),
inference(spm,[status(thm)],[1694,772,theory(equality)]) ).
cnf(1823,plain,
X1 = mult(X1,mult(X2,rd(ld(mult(X1,X2),mult(X1,X2)),X2))),
inference(rw,[status(thm)],[1791,11,theory(equality)]) ).
cnf(1824,plain,
X1 = mult(X1,mult(X2,rd(X1,mult(X2,X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1823,537,theory(equality)]),11,theory(equality)]) ).
cnf(1831,plain,
ld(X1,X1) = mult(X2,rd(X1,mult(X2,X1))),
inference(spm,[status(thm)],[21,1824,theory(equality)]) ).
cnf(1908,plain,
mult(rd(X1,X2),rd(X2,X1)) = ld(X2,X2),
inference(spm,[status(thm)],[1831,19,theory(equality)]) ).
cnf(2134,plain,
mult(X2,rd(ld(X2,X1),X1)) = ld(ld(X2,X1),ld(X2,X1)),
inference(spm,[status(thm)],[1908,23,theory(equality)]) ).
cnf(2137,plain,
mult(ld(X2,X2),X2) = mult(X1,mult(ld(X2,rd(X2,X1)),X2)),
inference(spm,[status(thm)],[42,1908,theory(equality)]) ).
cnf(2189,plain,
X2 = mult(X1,mult(ld(X2,rd(X2,X1)),X2)),
inference(rw,[status(thm)],[2137,76,theory(equality)]) ).
cnf(2453,plain,
ld(X1,X2) = mult(ld(X2,rd(X2,X1)),X2),
inference(spm,[status(thm)],[21,2189,theory(equality)]) ).
cnf(2525,plain,
rd(ld(X2,X1),X1) = ld(X1,rd(X1,X2)),
inference(spm,[status(thm)],[11,2453,theory(equality)]) ).
cnf(2529,plain,
mult(ld(X1,X2),X1) = ld(ld(X2,X1),X1),
inference(spm,[status(thm)],[2453,23,theory(equality)]) ).
cnf(2566,plain,
mult(ld(X1,rd(X1,X2)),rd(X1,ld(X2,X1))) = ld(X1,X1),
inference(spm,[status(thm)],[1831,2453,theory(equality)]) ).
cnf(2590,plain,
mult(ld(X1,rd(X1,X2)),X2) = ld(X1,X1),
inference(rw,[status(thm)],[2566,23,theory(equality)]) ).
cnf(2595,plain,
rd(X2,X1) = ld(X1,rd(X1,rd(X1,X2))),
inference(spm,[status(thm)],[2525,22,theory(equality)]) ).
cnf(2637,plain,
rd(X1,mult(ld(X1,X2),X1)) = ld(X2,X1),
inference(spm,[status(thm)],[23,2529,theory(equality)]) ).
cnf(2666,plain,
rd(ld(X1,X1),X2) = ld(X1,rd(X1,X2)),
inference(spm,[status(thm)],[11,2590,theory(equality)]) ).
cnf(2670,plain,
mult(ld(X1,X2),ld(X2,X1)) = ld(X1,X1),
inference(spm,[status(thm)],[2590,23,theory(equality)]) ).
cnf(2762,plain,
mult(X1,rd(X2,X1)) = rd(X1,rd(X1,X2)),
inference(spm,[status(thm)],[13,2595,theory(equality)]) ).
cnf(2876,plain,
rd(ld(X1,X2),ld(X2,rd(X2,X1))) = mult(ld(X1,X2),rd(X2,ld(X1,X2))),
inference(spm,[status(thm)],[2762,2525,theory(equality)]) ).
cnf(2897,plain,
rd(ld(X1,X2),ld(X2,rd(X2,X1))) = mult(ld(X1,X2),X1),
inference(rw,[status(thm)],[2876,23,theory(equality)]) ).
cnf(2903,plain,
rd(X1,mult(X2,X1)) = ld(mult(X1,X2),X1),
inference(spm,[status(thm)],[2637,21,theory(equality)]) ).
cnf(2993,plain,
rd(X1,ld(X2,X2)) = ld(mult(X1,ld(X2,rd(X2,X1))),X1),
inference(spm,[status(thm)],[2903,2590,theory(equality)]) ).
cnf(3037,plain,
ld(ld(X1,X2),ld(X1,X1)) = ld(X2,X1),
inference(spm,[status(thm)],[21,2670,theory(equality)]) ).
cnf(3274,plain,
rd(ld(X1,X1),X2) = ld(ld(X1,X1),rd(ld(X1,X1),X2)),
inference(spm,[status(thm)],[2666,3037,theory(equality)]) ).
cnf(3315,plain,
ld(X1,rd(X1,X2)) = ld(ld(X1,X1),rd(ld(X1,X1),X2)),
inference(rw,[status(thm)],[3274,2666,theory(equality)]) ).
cnf(3316,plain,
ld(X1,rd(X1,X2)) = ld(ld(X1,X1),ld(X1,rd(X1,X2))),
inference(rw,[status(thm)],[3315,2666,theory(equality)]) ).
cnf(3763,plain,
ld(ld(X2,X1),ld(X2,X1)) = mult(X2,ld(X1,rd(X1,X2))),
inference(rw,[status(thm)],[2134,2525,theory(equality)]) ).
cnf(9665,plain,
ld(ld(ld(X1,X2),ld(X1,X2)),ld(ld(X1,X2),mult(ld(X1,X2),X1))) = ld(ld(X1,X2),mult(ld(X1,X2),X1)),
inference(spm,[status(thm)],[3316,2897,theory(equality)]) ).
cnf(9726,plain,
rd(X1,ld(X2,X2)) = ld(ld(X1,X2),mult(ld(X1,X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[9665,3763,theory(equality)]),21,theory(equality)]),2993,theory(equality)]) ).
cnf(9727,plain,
rd(X1,ld(X2,X2)) = X1,
inference(rw,[status(thm)],[9726,21,theory(equality)]) ).
cnf(9729,plain,
mult(X1,ld(X2,X2)) = X1,
inference(spm,[status(thm)],[19,9727,theory(equality)]) ).
cnf(9852,plain,
ld(mult(X1,X2),mult(mult(X1,X2),mult(ld(X3,X3),X2))) = X2,
inference(spm,[status(thm)],[25,9729,theory(equality)]) ).
cnf(9955,plain,
mult(ld(X3,X3),X2) = X2,
inference(rw,[status(thm)],[9852,21,theory(equality)]) ).
cnf(10320,negated_conjecture,
mult(esk1_1(ld(X1,X1)),ld(X1,X1)) != esk1_1(ld(X1,X1)),
inference(spm,[status(thm)],[17,9955,theory(equality)]) ).
cnf(10461,negated_conjecture,
$false,
inference(rw,[status(thm)],[10320,9729,theory(equality)]) ).
cnf(10462,negated_conjecture,
$false,
inference(cn,[status(thm)],[10461,theory(equality)]) ).
cnf(10463,negated_conjecture,
$false,
10462,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP659+1.p
% --creating new selector for []
% -running prover on /tmp/tmp82WwnO/sel_GRP659+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP659+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP659+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP659+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
%
%------------------------------------------------------------------------------