%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : RNG005-2 : 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 @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 15:19:15 EDT 2009
% Result : Unsatisfiable 0.6s
% Output : Refutation 0.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 18 ( 12 unt; 0 def)
% Number of atoms : 33 ( 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 : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 30 ( 1 sgn 12 !; 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/RNG005-2.tptp',unknown),
[] ).
cnf(161100640,plain,
( ~ sum(A,B,C)
| sum(B,A,C) ),
inference(rewrite,[status(thm)],[commutativity_of_addition]),
[] ).
fof(prove_sum_is_additive_identity,plain,
~ sum(c,d,additive_identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG005-2.tptp',unknown),
[] ).
cnf(161174104,plain,
~ sum(c,d,additive_identity),
inference(rewrite,[status(thm)],[prove_sum_is_additive_identity]),
[] ).
cnf(173233104,plain,
~ sum(d,c,additive_identity),
inference(resolution,[status(thm)],[161100640,161174104]),
[] ).
fof(right_inverse,plain,
! [A] : sum(A,additive_inverse(A),additive_identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG005-2.tptp',unknown),
[] ).
cnf(161082368,plain,
sum(A,additive_inverse(A),additive_identity),
inference(rewrite,[status(thm)],[right_inverse]),
[] ).
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/RNG005-2.tptp',unknown),
[] ).
cnf(161138056,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(a_times_b,plain,
product(a,b,d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG005-2.tptp',unknown),
[] ).
cnf(161166240,plain,
product(a,b,d),
inference(rewrite,[status(thm)],[a_times_b]),
[] ).
cnf(169953032,plain,
( ~ product(A,b,B)
| ~ sum(a,A,C)
| ~ product(C,b,D)
| sum(d,B,D) ),
inference(resolution,[status(thm)],[161138056,161166240]),
[] ).
fof(multiplicative_identity1,plain,
! [A] : product(additive_identity,A,additive_identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG005-2.tptp',unknown),
[] ).
cnf(161158816,plain,
product(additive_identity,A,additive_identity),
inference(rewrite,[status(thm)],[multiplicative_identity1]),
[] ).
cnf(185052136,plain,
( ~ product(A,b,B)
| ~ sum(a,A,additive_identity)
| sum(d,B,additive_identity) ),
inference(resolution,[status(thm)],[169953032,161158816]),
[] ).
fof(a_inverse_times_b,plain,
product(additive_inverse(a),b,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG005-2.tptp',unknown),
[] ).
cnf(161170232,plain,
product(additive_inverse(a),b,c),
inference(rewrite,[status(thm)],[a_inverse_times_b]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[173233104,161082368,185052136,161170232]),
[] ).
%------------------------------------------------------------------------------
%----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/RNG005-2.tptp',unknown),[]).
%
% cnf(161100640,plain,(~sum(A,B,C)|sum(B,A,C)),inference(rewrite,[status(thm)],[commutativity_of_addition]),[]).
%
% fof(prove_sum_is_additive_identity,plain,(~sum(c,d,additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG005-2.tptp',unknown),[]).
%
% cnf(161174104,plain,(~sum(c,d,additive_identity)),inference(rewrite,[status(thm)],[prove_sum_is_additive_identity]),[]).
%
% cnf(173233104,plain,(~sum(d,c,additive_identity)),inference(resolution,[status(thm)],[161100640,161174104]),[]).
%
% fof(right_inverse,plain,(sum(A,additive_inverse(A),additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG005-2.tptp',unknown),[]).
%
% cnf(161082368,plain,(sum(A,additive_inverse(A),additive_identity)),inference(rewrite,[status(thm)],[right_inverse]),[]).
%
% 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/RNG005-2.tptp',unknown),[]).
%
% cnf(161138056,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(a_times_b,plain,(product(a,b,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG005-2.tptp',unknown),[]).
%
% cnf(161166240,plain,(product(a,b,d)),inference(rewrite,[status(thm)],[a_times_b]),[]).
%
% cnf(169953032,plain,(~product(A,b,B)|~sum(a,A,C)|~product(C,b,D)|sum(d,B,D)),inference(resolution,[status(thm)],[161138056,161166240]),[]).
%
% fof(multiplicative_identity1,plain,(product(additive_identity,A,additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG005-2.tptp',unknown),[]).
%
% cnf(161158816,plain,(product(additive_identity,A,additive_identity)),inference(rewrite,[status(thm)],[multiplicative_identity1]),[]).
%
% cnf(185052136,plain,(~product(A,b,B)|~sum(a,A,additive_identity)|sum(d,B,additive_identity)),inference(resolution,[status(thm)],[169953032,161158816]),[]).
%
% fof(a_inverse_times_b,plain,(product(additive_inverse(a),b,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG005-2.tptp',unknown),[]).
%
% cnf(161170232,plain,(product(additive_inverse(a),b,c)),inference(rewrite,[status(thm)],[a_inverse_times_b]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[173233104,161082368,185052136,161170232]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------