TSTP Solution File: RNG038-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : RNG038-2 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.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 15:20:43 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 12 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 49 ( 27 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 2 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(some_property,plain,
! [A,B] :
( ~ equalish(A,additive_identity)
| product(A,h(A,B),B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG038-2.tptp',unknown),
[] ).
cnf(164496600,plain,
( ~ equalish(A,additive_identity)
| product(A,h(A,B),B) ),
inference(rewrite,[status(thm)],[some_property]),
[] ).
fof(addition_is_well_defined,plain,
! [A,B,C,D] :
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| equalish(C,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG038-2.tptp',unknown),
[] ).
cnf(164474768,plain,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[addition_is_well_defined]),
[] ).
fof(additive_identity2,plain,
! [A] : sum(A,additive_identity,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG038-2.tptp',unknown),
[] ).
cnf(164394096,plain,
sum(A,additive_identity,A),
inference(rewrite,[status(thm)],[additive_identity2]),
[] ).
cnf(175008040,plain,
equalish(A,A),
inference(resolution,[status(thm)],[164474768,164394096]),
[] ).
cnf(175180376,plain,
product(additive_identity,h(additive_identity,A),A),
inference(resolution,[status(thm)],[164496600,175008040]),
[] ).
fof(multiplicative_identity1,plain,
! [A] : product(additive_identity,A,additive_identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG038-2.tptp',unknown),
[] ).
cnf(164483320,plain,
product(additive_identity,A,additive_identity),
inference(rewrite,[status(thm)],[multiplicative_identity1]),
[] ).
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/RNG038-2.tptp',unknown),
[] ).
cnf(164466712,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]),
[] ).
cnf(175418712,plain,
( ~ product(A,B,C)
| ~ sum(A,additive_identity,D)
| ~ product(D,B,E)
| sum(C,additive_identity,E) ),
inference(resolution,[status(thm)],[164466712,164483320]),
[] ).
cnf(174994312,plain,
( ~ sum(A,additive_identity,B)
| equalish(A,B) ),
inference(resolution,[status(thm)],[164474768,164394096]),
[] ).
fof(a_not_additive_identity,plain,
~ equalish(a,additive_identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG038-2.tptp',unknown),
[] ).
cnf(164504504,plain,
~ equalish(a,additive_identity),
inference(rewrite,[status(thm)],[a_not_additive_identity]),
[] ).
cnf(175678880,plain,
~ sum(a,additive_identity,additive_identity),
inference(resolution,[status(thm)],[174994312,164504504]),
[] ).
cnf(176482696,plain,
( ~ product(A,B,a)
| ~ sum(A,additive_identity,C)
| ~ product(C,B,additive_identity) ),
inference(resolution,[status(thm)],[175418712,175678880]),
[] ).
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/RNG038-2.tptp',unknown),
[] ).
cnf(164429368,plain,
( ~ sum(A,B,C)
| sum(B,A,C) ),
inference(rewrite,[status(thm)],[commutativity_of_addition]),
[] ).
cnf(174933136,plain,
sum(additive_identity,A,A),
inference(resolution,[status(thm)],[164429368,164394096]),
[] ).
cnf(176487368,plain,
~ product(additive_identity,A,a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[164483320,176482696,174933136]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[175180376,176487368]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(some_property,plain,(~equalish(A,additive_identity)|product(A,h(A,B),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG038-2.tptp',unknown),[]).
%
% cnf(164496600,plain,(~equalish(A,additive_identity)|product(A,h(A,B),B)),inference(rewrite,[status(thm)],[some_property]),[]).
%
% fof(addition_is_well_defined,plain,(~sum(A,B,C)|~sum(A,B,D)|equalish(C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG038-2.tptp',unknown),[]).
%
% cnf(164474768,plain,(~sum(A,B,C)|~sum(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[addition_is_well_defined]),[]).
%
% fof(additive_identity2,plain,(sum(A,additive_identity,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG038-2.tptp',unknown),[]).
%
% cnf(164394096,plain,(sum(A,additive_identity,A)),inference(rewrite,[status(thm)],[additive_identity2]),[]).
%
% cnf(175008040,plain,(equalish(A,A)),inference(resolution,[status(thm)],[164474768,164394096]),[]).
%
% cnf(175180376,plain,(product(additive_identity,h(additive_identity,A),A)),inference(resolution,[status(thm)],[164496600,175008040]),[]).
%
% fof(multiplicative_identity1,plain,(product(additive_identity,A,additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG038-2.tptp',unknown),[]).
%
% cnf(164483320,plain,(product(additive_identity,A,additive_identity)),inference(rewrite,[status(thm)],[multiplicative_identity1]),[]).
%
% 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/RNG038-2.tptp',unknown),[]).
%
% cnf(164466712,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]),[]).
%
% cnf(175418712,plain,(~product(A,B,C)|~sum(A,additive_identity,D)|~product(D,B,E)|sum(C,additive_identity,E)),inference(resolution,[status(thm)],[164466712,164483320]),[]).
%
% cnf(174994312,plain,(~sum(A,additive_identity,B)|equalish(A,B)),inference(resolution,[status(thm)],[164474768,164394096]),[]).
%
% fof(a_not_additive_identity,plain,(~equalish(a,additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG038-2.tptp',unknown),[]).
%
% cnf(164504504,plain,(~equalish(a,additive_identity)),inference(rewrite,[status(thm)],[a_not_additive_identity]),[]).
%
% cnf(175678880,plain,(~sum(a,additive_identity,additive_identity)),inference(resolution,[status(thm)],[174994312,164504504]),[]).
%
% cnf(176482696,plain,(~product(A,B,a)|~sum(A,additive_identity,C)|~product(C,B,additive_identity)),inference(resolution,[status(thm)],[175418712,175678880]),[]).
%
% fof(commutativity_of_addition,plain,(~sum(A,B,C)|sum(B,A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG038-2.tptp',unknown),[]).
%
% cnf(164429368,plain,(~sum(A,B,C)|sum(B,A,C)),inference(rewrite,[status(thm)],[commutativity_of_addition]),[]).
%
% cnf(174933136,plain,(sum(additive_identity,A,A)),inference(resolution,[status(thm)],[164429368,164394096]),[]).
%
% cnf(176487368,plain,(~product(additive_identity,A,a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[164483320,176482696,174933136]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[175180376,176487368]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------