TSTP Solution File: GRP029-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP029-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 12:18:41 EDT 2009
% Result : Unsatisfiable 13.2s
% Output : Refutation 13.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 14 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 26 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(associativity2,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP029-1.tptp',unknown),
[] ).
cnf(157199608,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
inference(rewrite,[status(thm)],[associativity2]),
[] ).
fof(left_inverse,plain,
! [A] : product(inverse(A),A,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP029-1.tptp',unknown),
[] ).
cnf(157206672,plain,
product(inverse(A),A,identity),
inference(rewrite,[status(thm)],[left_inverse]),
[] ).
cnf(165211768,plain,
( ~ product(A,B,A)
| product(identity,B,identity) ),
inference(resolution,[status(thm)],[157199608,157206672]),
[] ).
fof(associativity1,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP029-1.tptp',unknown),
[] ).
cnf(157195344,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
inference(rewrite,[status(thm)],[associativity1]),
[] ).
fof(total_function1,plain,
! [A,B] : product(A,B,multiply(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP029-1.tptp',unknown),
[] ).
cnf(157177096,plain,
product(A,B,multiply(A,B)),
inference(rewrite,[status(thm)],[total_function1]),
[] ).
cnf(165416608,plain,
( ~ product(A,B,C)
| ~ product(C,D,E)
| product(A,multiply(B,D),E) ),
inference(resolution,[status(thm)],[157195344,157177096]),
[] ).
cnf(165443512,plain,
( ~ product(identity,B,C)
| product(inverse(A),multiply(A,B),C) ),
inference(resolution,[status(thm)],[165416608,157206672]),
[] ).
fof(left_identity,plain,
! [A] : product(identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP029-1.tptp',unknown),
[] ).
cnf(157202872,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(165491488,plain,
product(inverse(A),multiply(A,B),B),
inference(resolution,[status(thm)],[165443512,157202872]),
[] ).
cnf(179863912,plain,
product(identity,multiply(A,inverse(A)),identity),
inference(resolution,[status(thm)],[165211768,165491488]),
[] ).
fof(total_function2,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(A,B,D)
| $equal(D,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP029-1.tptp',unknown),
[] ).
cnf(157188608,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| $equal(D,C) ),
inference(rewrite,[status(thm)],[total_function2]),
[] ).
cnf(164983864,plain,
( ~ product(identity,A,B)
| $equal(B,A) ),
inference(resolution,[status(thm)],[157188608,157202872]),
[] ).
cnf(217530960,plain,
$equal(identity,multiply(A,inverse(A))),
inference(resolution,[status(thm)],[179863912,164983864]),
[] ).
cnf(254229568,plain,
product(A,inverse(A),identity),
inference(paramodulation,[status(thm)],[217530960,157177096,theory(equality)]),
[] ).
cnf(165133648,plain,
( ~ product(A,inverse(C),B)
| ~ product(B,C,D)
| product(A,identity,D) ),
inference(resolution,[status(thm)],[157195344,157206672]),
[] ).
cnf(165157464,plain,
( ~ product(A,inverse(B),identity)
| product(A,identity,B) ),
inference(resolution,[status(thm)],[165133648,157202872]),
[] ).
cnf(257630648,plain,
product(A,identity,A),
inference(resolution,[status(thm)],[254229568,165157464]),
[] ).
fof(prove_there_is_a_right_identity,plain,
! [A] : ~ product(not_right_identity(A),A,not_right_identity(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP029-1.tptp',unknown),
[] ).
cnf(157210424,plain,
~ product(not_right_identity(A),A,not_right_identity(A)),
inference(rewrite,[status(thm)],[prove_there_is_a_right_identity]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[257630648,157210424]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 13 seconds
% START OF PROOF SEQUENCE
% fof(associativity2,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP029-1.tptp',unknown),[]).
%
% cnf(157199608,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),inference(rewrite,[status(thm)],[associativity2]),[]).
%
% fof(left_inverse,plain,(product(inverse(A),A,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP029-1.tptp',unknown),[]).
%
% cnf(157206672,plain,(product(inverse(A),A,identity)),inference(rewrite,[status(thm)],[left_inverse]),[]).
%
% cnf(165211768,plain,(~product(A,B,A)|product(identity,B,identity)),inference(resolution,[status(thm)],[157199608,157206672]),[]).
%
% fof(associativity1,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP029-1.tptp',unknown),[]).
%
% cnf(157195344,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),inference(rewrite,[status(thm)],[associativity1]),[]).
%
% fof(total_function1,plain,(product(A,B,multiply(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP029-1.tptp',unknown),[]).
%
% cnf(157177096,plain,(product(A,B,multiply(A,B))),inference(rewrite,[status(thm)],[total_function1]),[]).
%
% cnf(165416608,plain,(~product(A,B,C)|~product(C,D,E)|product(A,multiply(B,D),E)),inference(resolution,[status(thm)],[157195344,157177096]),[]).
%
% cnf(165443512,plain,(~product(identity,B,C)|product(inverse(A),multiply(A,B),C)),inference(resolution,[status(thm)],[165416608,157206672]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP029-1.tptp',unknown),[]).
%
% cnf(157202872,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(165491488,plain,(product(inverse(A),multiply(A,B),B)),inference(resolution,[status(thm)],[165443512,157202872]),[]).
%
% cnf(179863912,plain,(product(identity,multiply(A,inverse(A)),identity)),inference(resolution,[status(thm)],[165211768,165491488]),[]).
%
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP029-1.tptp',unknown),[]).
%
% cnf(157188608,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[total_function2]),[]).
%
% cnf(164983864,plain,(~product(identity,A,B)|$equal(B,A)),inference(resolution,[status(thm)],[157188608,157202872]),[]).
%
% cnf(217530960,plain,($equal(identity,multiply(A,inverse(A)))),inference(resolution,[status(thm)],[179863912,164983864]),[]).
%
% cnf(254229568,plain,(product(A,inverse(A),identity)),inference(paramodulation,[status(thm)],[217530960,157177096,theory(equality)]),[]).
%
% cnf(165133648,plain,(~product(A,inverse(C),B)|~product(B,C,D)|product(A,identity,D)),inference(resolution,[status(thm)],[157195344,157206672]),[]).
%
% cnf(165157464,plain,(~product(A,inverse(B),identity)|product(A,identity,B)),inference(resolution,[status(thm)],[165133648,157202872]),[]).
%
% cnf(257630648,plain,(product(A,identity,A)),inference(resolution,[status(thm)],[254229568,165157464]),[]).
%
% fof(prove_there_is_a_right_identity,plain,(~product(not_right_identity(A),A,not_right_identity(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP029-1.tptp',unknown),[]).
%
% cnf(157210424,plain,(~product(not_right_identity(A),A,not_right_identity(A))),inference(rewrite,[status(thm)],[prove_there_is_a_right_identity]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[257630648,157210424]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------