TSTP Solution File: BOO005-1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : BOO005-1 : 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 11:25:45 EDT 2009

% Result   : Unsatisfiable 6.3s
% Output   : Refutation 6.3s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   21 (  14 unt;   0 def)
%            Number of atoms       :   37 (   0 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   34 (  18   ~;  16   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   42 (   4 sgn  16   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(distributivity5,plain,
    ! [A,B,C,D,E,F,G] :
      ( ~ sum(A,B,C)
      | ~ sum(A,D,E)
      | ~ product(B,D,F)
      | ~ sum(A,F,G)
      | product(C,E,G) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO005-1.tptp',unknown),
    [] ).

cnf(147463752,plain,
    ( ~ sum(A,B,C)
    | ~ sum(A,D,E)
    | ~ product(B,D,F)
    | ~ sum(A,F,G)
    | product(C,E,G) ),
    inference(rewrite,[status(thm)],[distributivity5]),
    [] ).

fof(additive_inverse2,plain,
    ! [A] : sum(A,inverse(A),multiplicative_identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO005-1.tptp',unknown),
    [] ).

cnf(147387736,plain,
    sum(A,inverse(A),multiplicative_identity),
    inference(rewrite,[status(thm)],[additive_inverse2]),
    [] ).

cnf(157174576,plain,
    ( ~ sum(A,B,C)
    | ~ product(inverse(A),B,inverse(A))
    | product(multiplicative_identity,C,multiplicative_identity) ),
    inference(resolution,[status(thm)],[147463752,147387736]),
    [] ).

fof(multiplicative_identity2,plain,
    ! [A] : product(A,multiplicative_identity,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO005-1.tptp',unknown),
    [] ).

cnf(147429584,plain,
    product(A,multiplicative_identity,A),
    inference(rewrite,[status(thm)],[multiplicative_identity2]),
    [] ).

cnf(174359160,plain,
    ( ~ sum(A,multiplicative_identity,B)
    | product(multiplicative_identity,B,multiplicative_identity) ),
    inference(resolution,[status(thm)],[157174576,147429584]),
    [] ).

fof(closure_of_addition,plain,
    ! [A,B] : sum(A,B,add(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO005-1.tptp',unknown),
    [] ).

cnf(147392208,plain,
    sum(A,B,add(A,B)),
    inference(rewrite,[status(thm)],[closure_of_addition]),
    [] ).

cnf(232035400,plain,
    product(multiplicative_identity,add(A,multiplicative_identity),multiplicative_identity),
    inference(resolution,[status(thm)],[174359160,147392208]),
    [] ).

fof(multiplication_is_well_defined,plain,
    ! [A,B,C,D] :
      ( ~ product(A,B,C)
      | ~ product(A,B,D)
      | $equal(D,C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO005-1.tptp',unknown),
    [] ).

cnf(147514088,plain,
    ( ~ product(A,B,C)
    | ~ product(A,B,D)
    | $equal(D,C) ),
    inference(rewrite,[status(thm)],[multiplication_is_well_defined]),
    [] ).

fof(multiplicative_identity1,plain,
    ! [A] : product(multiplicative_identity,A,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO005-1.tptp',unknown),
    [] ).

cnf(147425760,plain,
    product(multiplicative_identity,A,A),
    inference(rewrite,[status(thm)],[multiplicative_identity1]),
    [] ).

cnf(155714784,plain,
    ( ~ product(multiplicative_identity,A,B)
    | $equal(B,A) ),
    inference(resolution,[status(thm)],[147514088,147425760]),
    [] ).

cnf(278102784,plain,
    $equal(multiplicative_identity,add(A,multiplicative_identity)),
    inference(resolution,[status(thm)],[232035400,155714784]),
    [] ).

cnf(278724696,plain,
    sum(A,multiplicative_identity,multiplicative_identity),
    inference(paramodulation,[status(thm)],[278102784,147392208,theory(equality)]),
    [] ).

fof(prove_equations,plain,
    ~ sum(x,multiplicative_identity,multiplicative_identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO005-1.tptp',unknown),
    [] ).

cnf(147517864,plain,
    ~ sum(x,multiplicative_identity,multiplicative_identity),
    inference(rewrite,[status(thm)],[prove_equations]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[278724696,147517864]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 6 seconds
% START OF PROOF SEQUENCE
% fof(distributivity5,plain,(~sum(A,B,C)|~sum(A,D,E)|~product(B,D,F)|~sum(A,F,G)|product(C,E,G)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO005-1.tptp',unknown),[]).
% 
% cnf(147463752,plain,(~sum(A,B,C)|~sum(A,D,E)|~product(B,D,F)|~sum(A,F,G)|product(C,E,G)),inference(rewrite,[status(thm)],[distributivity5]),[]).
% 
% fof(additive_inverse2,plain,(sum(A,inverse(A),multiplicative_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO005-1.tptp',unknown),[]).
% 
% cnf(147387736,plain,(sum(A,inverse(A),multiplicative_identity)),inference(rewrite,[status(thm)],[additive_inverse2]),[]).
% 
% cnf(157174576,plain,(~sum(A,B,C)|~product(inverse(A),B,inverse(A))|product(multiplicative_identity,C,multiplicative_identity)),inference(resolution,[status(thm)],[147463752,147387736]),[]).
% 
% fof(multiplicative_identity2,plain,(product(A,multiplicative_identity,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO005-1.tptp',unknown),[]).
% 
% cnf(147429584,plain,(product(A,multiplicative_identity,A)),inference(rewrite,[status(thm)],[multiplicative_identity2]),[]).
% 
% cnf(174359160,plain,(~sum(A,multiplicative_identity,B)|product(multiplicative_identity,B,multiplicative_identity)),inference(resolution,[status(thm)],[157174576,147429584]),[]).
% 
% fof(closure_of_addition,plain,(sum(A,B,add(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO005-1.tptp',unknown),[]).
% 
% cnf(147392208,plain,(sum(A,B,add(A,B))),inference(rewrite,[status(thm)],[closure_of_addition]),[]).
% 
% cnf(232035400,plain,(product(multiplicative_identity,add(A,multiplicative_identity),multiplicative_identity)),inference(resolution,[status(thm)],[174359160,147392208]),[]).
% 
% fof(multiplication_is_well_defined,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO005-1.tptp',unknown),[]).
% 
% cnf(147514088,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[multiplication_is_well_defined]),[]).
% 
% fof(multiplicative_identity1,plain,(product(multiplicative_identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO005-1.tptp',unknown),[]).
% 
% cnf(147425760,plain,(product(multiplicative_identity,A,A)),inference(rewrite,[status(thm)],[multiplicative_identity1]),[]).
% 
% cnf(155714784,plain,(~product(multiplicative_identity,A,B)|$equal(B,A)),inference(resolution,[status(thm)],[147514088,147425760]),[]).
% 
% cnf(278102784,plain,($equal(multiplicative_identity,add(A,multiplicative_identity))),inference(resolution,[status(thm)],[232035400,155714784]),[]).
% 
% cnf(278724696,plain,(sum(A,multiplicative_identity,multiplicative_identity)),inference(paramodulation,[status(thm)],[278102784,147392208,theory(equality)]),[]).
% 
% fof(prove_equations,plain,(~sum(x,multiplicative_identity,multiplicative_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO005-1.tptp',unknown),[]).
% 
% cnf(147517864,plain,(~sum(x,multiplicative_identity,multiplicative_identity)),inference(rewrite,[status(thm)],[prove_equations]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[278724696,147517864]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------