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