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