TSTP Solution File: GRP667+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP667+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 11:22:20 EST 2010
% Result : Theorem 8.34s
% Output : CNFRefutation 8.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 11
% Syntax : Number of formulae : 91 ( 81 unt; 0 def)
% Number of atoms : 101 ( 96 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 175 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : mult(X1,unit) = X1,
file('/tmp/tmp5hONYU/sel_GRP667+1.p_1',f05) ).
fof(2,axiom,
! [X2,X1] : rd(mult(X1,X2),X2) = X1,
file('/tmp/tmp5hONYU/sel_GRP667+1.p_1',f04) ).
fof(3,axiom,
! [X3,X2,X1] : mult(mult(X1,X2),mult(mult(X3,X2),X3)) = mult(mult(X1,mult(mult(X2,X3),X2)),X3),
file('/tmp/tmp5hONYU/sel_GRP667+1.p_1',f07) ).
fof(4,axiom,
! [X1] : mult(unit,X1) = X1,
file('/tmp/tmp5hONYU/sel_GRP667+1.p_1',f06) ).
fof(5,axiom,
! [X2,X1] : mult(X1,ld(X1,X2)) = X2,
file('/tmp/tmp5hONYU/sel_GRP667+1.p_1',f01) ).
fof(6,conjecture,
mult(a,mult(b,mult(a,c))) = mult(mult(mult(a,b),a),c),
file('/tmp/tmp5hONYU/sel_GRP667+1.p_1',goals) ).
fof(7,axiom,
! [X2,X1] : mult(rd(X1,X2),X2) = X1,
file('/tmp/tmp5hONYU/sel_GRP667+1.p_1',f03) ).
fof(8,axiom,
! [X2,X1] : ld(X1,mult(X1,X2)) = X2,
file('/tmp/tmp5hONYU/sel_GRP667+1.p_1',f02) ).
fof(10,axiom,
! [X7,X8,X9] :
( mult(X7,mult(X8,mult(X9,X8))) = mult(mult(mult(X7,X8),X9),X8)
=> mult(X8,mult(X7,mult(X8,X9))) = mult(mult(mult(X8,X7),X8),X9) ),
file('/tmp/tmp5hONYU/sel_GRP667+1.p_1',f10) ).
fof(12,axiom,
! [X1] : mult(f(X1),f(X1)) = X1,
file('/tmp/tmp5hONYU/sel_GRP667+1.p_1',f09) ).
fof(13,axiom,
! [X2,X1] : mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
file('/tmp/tmp5hONYU/sel_GRP667+1.p_1',f08) ).
fof(14,negated_conjecture,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
inference(assume_negation,[status(cth)],[6]) ).
fof(15,negated_conjecture,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
inference(fof_simplification,[status(thm)],[14,theory(equality)]) ).
fof(16,plain,
! [X2] : mult(X2,unit) = X2,
inference(variable_rename,[status(thm)],[1]) ).
cnf(17,plain,
mult(X1,unit) = X1,
inference(split_conjunct,[status(thm)],[16]) ).
fof(18,plain,
! [X3,X4] : rd(mult(X4,X3),X3) = X4,
inference(variable_rename,[status(thm)],[2]) ).
cnf(19,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[18]) ).
fof(20,plain,
! [X4,X5,X6] : mult(mult(X6,X5),mult(mult(X4,X5),X4)) = mult(mult(X6,mult(mult(X5,X4),X5)),X4),
inference(variable_rename,[status(thm)],[3]) ).
cnf(21,plain,
mult(mult(X1,X2),mult(mult(X3,X2),X3)) = mult(mult(X1,mult(mult(X2,X3),X2)),X3),
inference(split_conjunct,[status(thm)],[20]) ).
fof(22,plain,
! [X2] : mult(unit,X2) = X2,
inference(variable_rename,[status(thm)],[4]) ).
cnf(23,plain,
mult(unit,X1) = X1,
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,plain,
! [X3,X4] : mult(X4,ld(X4,X3)) = X3,
inference(variable_rename,[status(thm)],[5]) ).
cnf(25,plain,
mult(X1,ld(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[24]) ).
cnf(26,negated_conjecture,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
inference(split_conjunct,[status(thm)],[15]) ).
fof(27,plain,
! [X3,X4] : mult(rd(X4,X3),X3) = X4,
inference(variable_rename,[status(thm)],[7]) ).
cnf(28,plain,
mult(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X3,X4] : ld(X4,mult(X4,X3)) = X3,
inference(variable_rename,[status(thm)],[8]) ).
cnf(30,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[29]) ).
fof(34,plain,
! [X7,X8,X9] :
( mult(X7,mult(X8,mult(X9,X8))) != mult(mult(mult(X7,X8),X9),X8)
| mult(X8,mult(X7,mult(X8,X9))) = mult(mult(mult(X8,X7),X8),X9) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(35,plain,
! [X10,X11,X12] :
( mult(X10,mult(X11,mult(X12,X11))) != mult(mult(mult(X10,X11),X12),X11)
| mult(X11,mult(X10,mult(X11,X12))) = mult(mult(mult(X11,X10),X11),X12) ),
inference(variable_rename,[status(thm)],[34]) ).
cnf(36,plain,
( mult(X1,mult(X2,mult(X1,X3))) = mult(mult(mult(X1,X2),X1),X3)
| mult(X2,mult(X1,mult(X3,X1))) != mult(mult(mult(X2,X1),X3),X1) ),
inference(split_conjunct,[status(thm)],[35]) ).
fof(40,plain,
! [X2] : mult(f(X2),f(X2)) = X2,
inference(variable_rename,[status(thm)],[12]) ).
cnf(41,plain,
mult(f(X1),f(X1)) = X1,
inference(split_conjunct,[status(thm)],[40]) ).
fof(42,plain,
! [X3,X4] : mult(mult(X4,X3),X4) = mult(X4,mult(X3,X4)),
inference(variable_rename,[status(thm)],[13]) ).
cnf(43,plain,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
inference(split_conjunct,[status(thm)],[42]) ).
cnf(45,plain,
ld(X1,X1) = unit,
inference(spm,[status(thm)],[30,17,theory(equality)]) ).
cnf(48,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[30,28,theory(equality)]) ).
cnf(57,plain,
mult(X2,X1) = mult(X1,mult(ld(X1,X2),X1)),
inference(spm,[status(thm)],[43,25,theory(equality)]) ).
cnf(59,plain,
mult(X1,rd(X1,X2)) = mult(rd(X1,X2),mult(X2,rd(X1,X2))),
inference(spm,[status(thm)],[43,28,theory(equality)]) ).
cnf(60,plain,
rd(mult(X1,mult(X2,X1)),X1) = mult(X1,X2),
inference(spm,[status(thm)],[19,43,theory(equality)]) ).
cnf(69,negated_conjecture,
mult(mult(a,mult(b,a)),c) != mult(a,mult(b,mult(a,c))),
inference(rw,[status(thm)],[26,43,theory(equality)]) ).
cnf(70,plain,
mult(mult(X1,mult(X2,mult(X3,X2))),X3) = mult(mult(X1,X2),mult(mult(X3,X2),X3)),
inference(rw,[status(thm)],[21,43,theory(equality)]) ).
cnf(71,plain,
mult(mult(X1,mult(X2,mult(X3,X2))),X3) = mult(mult(X1,X2),mult(X3,mult(X2,X3))),
inference(rw,[status(thm)],[70,43,theory(equality)]) ).
cnf(72,plain,
mult(mult(X1,X2),mult(unit,mult(X2,unit))) = mult(X1,mult(X2,mult(unit,X2))),
inference(spm,[status(thm)],[17,71,theory(equality)]) ).
cnf(76,plain,
mult(mult(X1,mult(X2,X1)),X2) = mult(mult(unit,X1),mult(X2,mult(X1,X2))),
inference(spm,[status(thm)],[71,23,theory(equality)]) ).
cnf(81,plain,
rd(mult(mult(X1,X2),mult(X3,mult(X2,X3))),X3) = mult(X1,mult(X2,mult(X3,X2))),
inference(spm,[status(thm)],[19,71,theory(equality)]) ).
cnf(89,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,mult(unit,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[72,17,theory(equality)]),23,theory(equality)]) ).
cnf(90,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[89,23,theory(equality)]) ).
cnf(97,plain,
mult(mult(X1,mult(X2,X1)),X2) = mult(X1,mult(X2,mult(X1,X2))),
inference(rw,[status(thm)],[76,23,theory(equality)]) ).
cnf(146,plain,
( mult(mult(X1,mult(X2,X1)),X3) = mult(X1,mult(X2,mult(X1,X3)))
| mult(mult(mult(X2,X1),X3),X1) != mult(X2,mult(X1,mult(X3,X1))) ),
inference(rw,[status(thm)],[36,43,theory(equality)]) ).
cnf(150,plain,
( mult(mult(X1,X1),X2) = mult(X1,mult(unit,mult(X1,X2)))
| mult(mult(X1,X2),X1) != mult(unit,mult(X1,mult(X2,X1))) ),
inference(spm,[status(thm)],[146,23,theory(equality)]) ).
cnf(176,plain,
( mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2))
| mult(mult(X1,X2),X1) != mult(unit,mult(X1,mult(X2,X1))) ),
inference(rw,[status(thm)],[150,23,theory(equality)]) ).
cnf(177,plain,
( mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2))
| mult(X1,mult(X2,X1)) != mult(unit,mult(X1,mult(X2,X1))) ),
inference(rw,[status(thm)],[176,43,theory(equality)]) ).
cnf(178,plain,
( mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2))
| $false ),
inference(rw,[status(thm)],[177,23,theory(equality)]) ).
cnf(179,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(cn,[status(thm)],[178,theory(equality)]) ).
cnf(186,plain,
mult(X1,X2) = mult(f(X1),mult(f(X1),X2)),
inference(spm,[status(thm)],[179,41,theory(equality)]) ).
cnf(380,plain,
ld(X1,mult(X2,X1)) = mult(ld(X1,X2),X1),
inference(spm,[status(thm)],[30,57,theory(equality)]) ).
cnf(385,plain,
mult(mult(X1,mult(X3,X2)),ld(X2,X3)) = mult(mult(X1,X2),mult(ld(X2,X3),mult(X2,ld(X2,X3)))),
inference(spm,[status(thm)],[71,57,theory(equality)]) ).
cnf(407,plain,
mult(mult(X1,mult(X3,X2)),ld(X2,X3)) = mult(mult(X1,X2),mult(ld(X2,X3),X3)),
inference(rw,[status(thm)],[385,25,theory(equality)]) ).
cnf(420,plain,
rd(mult(X1,X2),X1) = mult(X1,rd(X2,X1)),
inference(spm,[status(thm)],[60,28,theory(equality)]) ).
cnf(640,plain,
rd(mult(X1,mult(X2,mult(X1,X2))),X2) = mult(X1,mult(X2,X1)),
inference(spm,[status(thm)],[19,97,theory(equality)]) ).
cnf(819,plain,
ld(X1,X1) = mult(ld(X1,unit),X1),
inference(spm,[status(thm)],[380,23,theory(equality)]) ).
cnf(846,plain,
unit = mult(ld(X1,unit),X1),
inference(rw,[status(thm)],[819,45,theory(equality)]) ).
cnf(3630,plain,
rd(mult(unit,mult(X2,mult(X1,X2))),X2) = mult(ld(X1,unit),mult(X1,mult(X2,X1))),
inference(spm,[status(thm)],[81,846,theory(equality)]) ).
cnf(3710,plain,
mult(X2,X1) = mult(ld(X1,unit),mult(X1,mult(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[3630,23,theory(equality)]),420,theory(equality)]),19,theory(equality)]) ).
cnf(8087,plain,
mult(ld(X1,unit),mult(X1,X2)) = X2,
inference(spm,[status(thm)],[3710,28,theory(equality)]) ).
cnf(8619,plain,
mult(ld(X1,unit),X2) = ld(X1,X2),
inference(spm,[status(thm)],[8087,25,theory(equality)]) ).
cnf(8622,plain,
rd(X2,mult(X1,X2)) = ld(X1,unit),
inference(spm,[status(thm)],[19,8087,theory(equality)]) ).
cnf(8949,plain,
mult(ld(X1,X2),X2) = mult(ld(X1,unit),mult(X2,X2)),
inference(spm,[status(thm)],[90,8619,theory(equality)]) ).
cnf(9083,plain,
mult(ld(X1,X2),X2) = ld(X1,mult(X2,X2)),
inference(rw,[status(thm)],[8949,8619,theory(equality)]) ).
cnf(9279,plain,
mult(X1,mult(ld(X1,X2),X2)) = mult(X2,X2),
inference(spm,[status(thm)],[25,9083,theory(equality)]) ).
cnf(9281,plain,
ld(X1,X2) = mult(ld(X1,f(X2)),f(X2)),
inference(spm,[status(thm)],[9083,41,theory(equality)]) ).
cnf(9348,plain,
mult(rd(X1,X2),mult(X2,X1)) = mult(X1,X1),
inference(spm,[status(thm)],[9279,48,theory(equality)]) ).
cnf(10177,plain,
rd(mult(X1,X1),mult(X2,X1)) = rd(X1,X2),
inference(spm,[status(thm)],[19,9348,theory(equality)]) ).
cnf(18117,plain,
rd(mult(rd(X1,X2),mult(X2,X1)),X2) = mult(rd(X1,X2),mult(X2,rd(X1,X2))),
inference(spm,[status(thm)],[640,28,theory(equality)]) ).
cnf(18228,plain,
rd(mult(X1,X1),X2) = mult(rd(X1,X2),mult(X2,rd(X1,X2))),
inference(rw,[status(thm)],[18117,9348,theory(equality)]) ).
cnf(18229,plain,
rd(mult(X1,X1),X2) = mult(X1,rd(X1,X2)),
inference(rw,[status(thm)],[18228,59,theory(equality)]) ).
cnf(18954,plain,
mult(X1,ld(X2,unit)) = rd(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[10177,18229,theory(equality)]),8622,theory(equality)]) ).
cnf(19003,plain,
ld(X1,rd(X1,X2)) = ld(X2,unit),
inference(spm,[status(thm)],[30,18954,theory(equality)]) ).
cnf(21446,plain,
ld(mult(X1,X2),X1) = ld(X2,unit),
inference(spm,[status(thm)],[19003,19,theory(equality)]) ).
cnf(164851,plain,
mult(mult(X1,mult(X2,X3)),ld(mult(f(X2),X3),f(X2))) = mult(mult(X1,mult(f(X2),X3)),mult(ld(mult(f(X2),X3),f(X2)),f(X2))),
inference(spm,[status(thm)],[407,186,theory(equality)]) ).
cnf(165441,plain,
rd(mult(X1,mult(X2,X3)),X3) = mult(mult(X1,mult(f(X2),X3)),mult(ld(mult(f(X2),X3),f(X2)),f(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[164851,21446,theory(equality)]),18954,theory(equality)]) ).
cnf(165442,plain,
rd(mult(X1,mult(X2,X3)),X3) = mult(mult(X1,X3),ld(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[165441,21446,theory(equality)]),8619,theory(equality)]),407,theory(equality)]),9281,theory(equality)]) ).
cnf(166846,plain,
mult(mult(mult(X1,X3),ld(X3,X2)),X3) = mult(X1,mult(X2,X3)),
inference(spm,[status(thm)],[28,165442,theory(equality)]) ).
cnf(167507,plain,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(mult(X2,X3),X2)),
inference(spm,[status(thm)],[166846,30,theory(equality)]) ).
cnf(168027,plain,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(X2,mult(X3,X2))),
inference(rw,[status(thm)],[167507,43,theory(equality)]) ).
cnf(168857,plain,
( mult(mult(X1,mult(X2,X1)),X3) = mult(X1,mult(X2,mult(X1,X3)))
| $false ),
inference(rw,[status(thm)],[146,168027,theory(equality)]) ).
cnf(168858,plain,
mult(mult(X1,mult(X2,X1)),X3) = mult(X1,mult(X2,mult(X1,X3))),
inference(cn,[status(thm)],[168857,theory(equality)]) ).
cnf(169935,negated_conjecture,
$false,
inference(rw,[status(thm)],[69,168858,theory(equality)]) ).
cnf(169936,negated_conjecture,
$false,
inference(cn,[status(thm)],[169935,theory(equality)]) ).
cnf(169937,negated_conjecture,
$false,
169936,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP667+1.p
% --creating new selector for []
% -running prover on /tmp/tmp5hONYU/sel_GRP667+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP667+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP667+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP667+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
%
%------------------------------------------------------------------------------