TSTP Solution File: GRP044-2 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP044-2 : 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 12:19:24 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 29 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_product_with_b,plain,
~ product(b,c,result),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP044-2.tptp',unknown),
[] ).
cnf(169435240,plain,
~ product(b,c,result),
inference(rewrite,[status(thm)],[prove_product_with_b]),
[] ).
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/GRP044-2.tptp',unknown),
[] ).
cnf(169464928,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
inference(rewrite,[status(thm)],[associativity2]),
[] ).
fof(product_substitution3,plain,
! [A,B,C,D] :
( ~ equalish(A,B)
| ~ product(C,D,A)
| product(C,D,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP044-2.tptp',unknown),
[] ).
cnf(169476464,plain,
( ~ equalish(A,B)
| ~ product(C,D,A)
| product(C,D,B) ),
inference(rewrite,[status(thm)],[product_substitution3]),
[] ).
fof(a_equals_b,plain,
equalish(a,b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP044-2.tptp',unknown),
[] ).
cnf(169481048,plain,
equalish(a,b),
inference(rewrite,[status(thm)],[a_equals_b]),
[] ).
cnf(177277848,plain,
( ~ product(A,B,a)
| product(A,B,b) ),
inference(resolution,[status(thm)],[169476464,169481048]),
[] ).
fof(left_identity,plain,
! [A] : product(identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP044-2.tptp',unknown),
[] ).
cnf(169437752,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(177325016,plain,
product(identity,a,b),
inference(resolution,[status(thm)],[177277848,169437752]),
[] ).
cnf(177661160,plain,
( ~ product(a,A,B)
| ~ product(identity,B,C)
| product(b,A,C) ),
inference(resolution,[status(thm)],[169464928,177325016]),
[] ).
cnf(177726608,plain,
( ~ product(a,A,B)
| product(b,A,B) ),
inference(resolution,[status(thm)],[177661160,169437752]),
[] ).
fof(product_with_a,plain,
product(a,c,result),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP044-2.tptp',unknown),
[] ).
cnf(169485048,plain,
product(a,c,result),
inference(rewrite,[status(thm)],[product_with_a]),
[] ).
cnf(177730864,plain,
product(b,c,result),
inference(resolution,[status(thm)],[177726608,169485048]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[169435240,177730864]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(prove_product_with_b,plain,(~product(b,c,result)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP044-2.tptp',unknown),[]).
%
% cnf(169435240,plain,(~product(b,c,result)),inference(rewrite,[status(thm)],[prove_product_with_b]),[]).
%
% 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/GRP044-2.tptp',unknown),[]).
%
% cnf(169464928,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),inference(rewrite,[status(thm)],[associativity2]),[]).
%
% fof(product_substitution3,plain,(~equalish(A,B)|~product(C,D,A)|product(C,D,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP044-2.tptp',unknown),[]).
%
% cnf(169476464,plain,(~equalish(A,B)|~product(C,D,A)|product(C,D,B)),inference(rewrite,[status(thm)],[product_substitution3]),[]).
%
% fof(a_equals_b,plain,(equalish(a,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP044-2.tptp',unknown),[]).
%
% cnf(169481048,plain,(equalish(a,b)),inference(rewrite,[status(thm)],[a_equals_b]),[]).
%
% cnf(177277848,plain,(~product(A,B,a)|product(A,B,b)),inference(resolution,[status(thm)],[169476464,169481048]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP044-2.tptp',unknown),[]).
%
% cnf(169437752,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(177325016,plain,(product(identity,a,b)),inference(resolution,[status(thm)],[177277848,169437752]),[]).
%
% cnf(177661160,plain,(~product(a,A,B)|~product(identity,B,C)|product(b,A,C)),inference(resolution,[status(thm)],[169464928,177325016]),[]).
%
% cnf(177726608,plain,(~product(a,A,B)|product(b,A,B)),inference(resolution,[status(thm)],[177661160,169437752]),[]).
%
% fof(product_with_a,plain,(product(a,c,result)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP044-2.tptp',unknown),[]).
%
% cnf(169485048,plain,(product(a,c,result)),inference(rewrite,[status(thm)],[product_with_a]),[]).
%
% cnf(177730864,plain,(product(b,c,result)),inference(resolution,[status(thm)],[177726608,169485048]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[169435240,177730864]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------