TSTP Solution File: RNG040-1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : RNG040-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art01.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May  6 15:20:49 EDT 2009

% Result   : Unsatisfiable 0.9s
% Output   : Refutation 0.9s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   19 (  13 unt;   0 def)
%            Number of atoms       :   34 (   0 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   33 (  18   ~;  15   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   7 con; 0-0 aty)
%            Number of variables   :   26 (   0 sgn  10   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(commutativity_of_addition,plain,
    ! [A,B,C] :
      ( ~ sum(A,B,C)
      | sum(B,A,C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG040-1.tptp',unknown),
    [] ).

cnf(167419448,plain,
    ( ~ sum(A,B,C)
    | sum(B,A,C) ),
    inference(rewrite,[status(thm)],[commutativity_of_addition]),
    [] ).

fof(prove_equation,plain,
    ~ sum(l,n,additive_identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG040-1.tptp',unknown),
    [] ).

cnf(167529880,plain,
    ~ sum(l,n,additive_identity),
    inference(rewrite,[status(thm)],[prove_equation]),
    [] ).

cnf(187912912,plain,
    ~ sum(n,l,additive_identity),
    inference(resolution,[status(thm)],[167419448,167529880]),
    [] ).

fof(b_plus_c,plain,
    sum(b,c,d),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG040-1.tptp',unknown),
    [] ).

cnf(167513960,plain,
    sum(b,c,d),
    inference(rewrite,[status(thm)],[b_plus_c]),
    [] ).

cnf(187890536,plain,
    sum(c,b,d),
    inference(resolution,[status(thm)],[167419448,167513960]),
    [] ).

fof(distributivity3,plain,
    ! [A,B,C,D,E,F,G] :
      ( ~ product(A,B,C)
      | ~ product(D,B,E)
      | ~ sum(A,D,F)
      | ~ product(F,B,G)
      | sum(C,E,G) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG040-1.tptp',unknown),
    [] ).

cnf(167457472,plain,
    ( ~ product(A,B,C)
    | ~ product(D,B,E)
    | ~ sum(A,D,F)
    | ~ product(F,B,G)
    | sum(C,E,G) ),
    inference(rewrite,[status(thm)],[distributivity3]),
    [] ).

fof(d_plus_a,plain,
    product(d,a,additive_identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG040-1.tptp',unknown),
    [] ).

cnf(167517944,plain,
    product(d,a,additive_identity),
    inference(rewrite,[status(thm)],[d_plus_a]),
    [] ).

cnf(201966816,plain,
    ( ~ product(A,a,B)
    | ~ product(C,a,D)
    | ~ sum(A,C,d)
    | sum(B,D,additive_identity) ),
    inference(resolution,[status(thm)],[167457472,167517944]),
    [] ).

fof(c_plus_a,plain,
    product(c,a,n),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG040-1.tptp',unknown),
    [] ).

cnf(167525912,plain,
    product(c,a,n),
    inference(rewrite,[status(thm)],[c_plus_a]),
    [] ).

cnf(205835472,plain,
    ( ~ product(A,a,B)
    | ~ sum(c,A,d)
    | sum(n,B,additive_identity) ),
    inference(resolution,[status(thm)],[201966816,167525912]),
    [] ).

fof(b_plus_a,plain,
    product(b,a,l),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG040-1.tptp',unknown),
    [] ).

cnf(167521960,plain,
    product(b,a,l),
    inference(rewrite,[status(thm)],[b_plus_a]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[187912912,187890536,205835472,167521960]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(commutativity_of_addition,plain,(~sum(A,B,C)|sum(B,A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG040-1.tptp',unknown),[]).
% 
% cnf(167419448,plain,(~sum(A,B,C)|sum(B,A,C)),inference(rewrite,[status(thm)],[commutativity_of_addition]),[]).
% 
% fof(prove_equation,plain,(~sum(l,n,additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG040-1.tptp',unknown),[]).
% 
% cnf(167529880,plain,(~sum(l,n,additive_identity)),inference(rewrite,[status(thm)],[prove_equation]),[]).
% 
% cnf(187912912,plain,(~sum(n,l,additive_identity)),inference(resolution,[status(thm)],[167419448,167529880]),[]).
% 
% fof(b_plus_c,plain,(sum(b,c,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG040-1.tptp',unknown),[]).
% 
% cnf(167513960,plain,(sum(b,c,d)),inference(rewrite,[status(thm)],[b_plus_c]),[]).
% 
% cnf(187890536,plain,(sum(c,b,d)),inference(resolution,[status(thm)],[167419448,167513960]),[]).
% 
% fof(distributivity3,plain,(~product(A,B,C)|~product(D,B,E)|~sum(A,D,F)|~product(F,B,G)|sum(C,E,G)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG040-1.tptp',unknown),[]).
% 
% cnf(167457472,plain,(~product(A,B,C)|~product(D,B,E)|~sum(A,D,F)|~product(F,B,G)|sum(C,E,G)),inference(rewrite,[status(thm)],[distributivity3]),[]).
% 
% fof(d_plus_a,plain,(product(d,a,additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG040-1.tptp',unknown),[]).
% 
% cnf(167517944,plain,(product(d,a,additive_identity)),inference(rewrite,[status(thm)],[d_plus_a]),[]).
% 
% cnf(201966816,plain,(~product(A,a,B)|~product(C,a,D)|~sum(A,C,d)|sum(B,D,additive_identity)),inference(resolution,[status(thm)],[167457472,167517944]),[]).
% 
% fof(c_plus_a,plain,(product(c,a,n)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG040-1.tptp',unknown),[]).
% 
% cnf(167525912,plain,(product(c,a,n)),inference(rewrite,[status(thm)],[c_plus_a]),[]).
% 
% cnf(205835472,plain,(~product(A,a,B)|~sum(c,A,d)|sum(n,B,additive_identity)),inference(resolution,[status(thm)],[201966816,167525912]),[]).
% 
% fof(b_plus_a,plain,(product(b,a,l)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG040-1.tptp',unknown),[]).
% 
% cnf(167521960,plain,(product(b,a,l)),inference(rewrite,[status(thm)],[b_plus_a]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[187912912,187890536,205835472,167521960]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------