TSTP Solution File: GRP017-1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP017-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art09.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 12:18:00 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   19 (  12 unt;   0 def)
%            Number of atoms       :   33 (   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 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   32 (   0 sgn  12   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/GRP017-1.tptp',unknown),
    [] ).

cnf(155511584,plain,
    ( ~ product(A,B,C)
    | ~ product(B,D,E)
    | ~ product(C,D,F)
    | product(A,E,F) ),
    inference(rewrite,[status(thm)],[associativity1]),
    [] ).

fof(left_identity,plain,
    ! [A] : product(identity,A,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),
    [] ).

cnf(155478368,plain,
    product(identity,A,A),
    inference(rewrite,[status(thm)],[left_identity]),
    [] ).

cnf(163388928,plain,
    ( ~ product(A,B,identity)
    | ~ product(B,C,D)
    | product(A,D,C) ),
    inference(resolution,[status(thm)],[155511584,155478368]),
    [] ).

fof(b_times_a_is_identity,plain,
    product(b,a,identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),
    [] ).

cnf(155475880,plain,
    product(b,a,identity),
    inference(rewrite,[status(thm)],[b_times_a_is_identity]),
    [] ).

cnf(163469136,plain,
    ( ~ product(a,A,B)
    | product(b,B,A) ),
    inference(resolution,[status(thm)],[163388928,155475880]),
    [] ).

fof(a_times_c_is_identity,plain,
    product(a,c,identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),
    [] ).

cnf(155530704,plain,
    product(a,c,identity),
    inference(rewrite,[status(thm)],[a_times_c_is_identity]),
    [] ).

cnf(163594256,plain,
    product(b,identity,c),
    inference(resolution,[status(thm)],[163469136,155530704]),
    [] ).

fof(prove_b_equals_c,plain,
    ~ $equal(c,b),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),
    [] ).

cnf(155538888,plain,
    ~ $equal(c,b),
    inference(rewrite,[status(thm)],[prove_b_equals_c]),
    [] ).

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/GRP017-1.tptp',unknown),
    [] ).

cnf(155504816,plain,
    ( ~ product(A,B,C)
    | ~ product(A,B,D)
    | $equal(D,C) ),
    inference(rewrite,[status(thm)],[total_function2]),
    [] ).

fof(right_identity,plain,
    ! [A] : product(A,identity,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),
    [] ).

cnf(155482472,plain,
    product(A,identity,A),
    inference(rewrite,[status(thm)],[right_identity]),
    [] ).

cnf(164280072,plain,
    ( ~ product(A,identity,B)
    | $equal(B,A) ),
    inference(resolution,[status(thm)],[155504816,155482472]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[163594256,155538888,164280072]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% 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/GRP017-1.tptp',unknown),[]).
% 
% cnf(155511584,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),inference(rewrite,[status(thm)],[associativity1]),[]).
% 
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),[]).
% 
% cnf(155478368,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
% 
% cnf(163388928,plain,(~product(A,B,identity)|~product(B,C,D)|product(A,D,C)),inference(resolution,[status(thm)],[155511584,155478368]),[]).
% 
% fof(b_times_a_is_identity,plain,(product(b,a,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),[]).
% 
% cnf(155475880,plain,(product(b,a,identity)),inference(rewrite,[status(thm)],[b_times_a_is_identity]),[]).
% 
% cnf(163469136,plain,(~product(a,A,B)|product(b,B,A)),inference(resolution,[status(thm)],[163388928,155475880]),[]).
% 
% fof(a_times_c_is_identity,plain,(product(a,c,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),[]).
% 
% cnf(155530704,plain,(product(a,c,identity)),inference(rewrite,[status(thm)],[a_times_c_is_identity]),[]).
% 
% cnf(163594256,plain,(product(b,identity,c)),inference(resolution,[status(thm)],[163469136,155530704]),[]).
% 
% fof(prove_b_equals_c,plain,(~$equal(c,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),[]).
% 
% cnf(155538888,plain,(~$equal(c,b)),inference(rewrite,[status(thm)],[prove_b_equals_c]),[]).
% 
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),[]).
% 
% cnf(155504816,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[total_function2]),[]).
% 
% fof(right_identity,plain,(product(A,identity,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP017-1.tptp',unknown),[]).
% 
% cnf(155482472,plain,(product(A,identity,A)),inference(rewrite,[status(thm)],[right_identity]),[]).
% 
% cnf(164280072,plain,(~product(A,identity,B)|$equal(B,A)),inference(resolution,[status(thm)],[155504816,155482472]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[163594256,155538888,164280072]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------