TSTP Solution File: BOO006-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : BOO006-1 : 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 11:25:53 EDT 2009
% Result : Unsatisfiable 34.7s
% Output : Refutation 34.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 15 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 39 ( 21 ~; 18 |; 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 : 48 ( 4 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/BOO/BOO006-1.tptp',unknown),
[] ).
cnf(163470056,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(multiplicative_inverse1,plain,
! [A] : product(inverse(A),A,additive_identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO006-1.tptp',unknown),
[] ).
cnf(163512792,plain,
product(inverse(A),A,additive_identity),
inference(rewrite,[status(thm)],[multiplicative_inverse1]),
[] ).
cnf(178199528,plain,
( ~ product(B,A,C)
| ~ sum(inverse(A),B,inverse(A))
| sum(additive_identity,C,additive_identity) ),
inference(resolution,[status(thm)],[163470056,163512792]),
[] ).
fof(additive_identity2,plain,
! [A] : sum(A,additive_identity,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO006-1.tptp',unknown),
[] ).
cnf(163409152,plain,
sum(A,additive_identity,A),
inference(rewrite,[status(thm)],[additive_identity2]),
[] ).
cnf(179677344,plain,
( ~ product(additive_identity,A,B)
| sum(additive_identity,B,additive_identity) ),
inference(resolution,[status(thm)],[178199528,163409152]),
[] ).
fof(closure_of_multiplication,plain,
! [A,B] : product(A,B,multiply(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO006-1.tptp',unknown),
[] ).
cnf(163416592,plain,
product(A,B,multiply(A,B)),
inference(rewrite,[status(thm)],[closure_of_multiplication]),
[] ).
cnf(196017424,plain,
sum(additive_identity,multiply(additive_identity,A),additive_identity),
inference(resolution,[status(thm)],[179677344,163416592]),
[] ).
fof(addition_is_well_defined,plain,
! [A,B,C,D] :
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| $equal(D,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO006-1.tptp',unknown),
[] ).
cnf(163524520,plain,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| $equal(D,C) ),
inference(rewrite,[status(thm)],[addition_is_well_defined]),
[] ).
fof(additive_identity1,plain,
! [A] : sum(additive_identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO006-1.tptp',unknown),
[] ).
cnf(163437704,plain,
sum(additive_identity,A,A),
inference(rewrite,[status(thm)],[additive_identity1]),
[] ).
cnf(171327504,plain,
( ~ sum(additive_identity,A,B)
| $equal(B,A) ),
inference(resolution,[status(thm)],[163524520,163437704]),
[] ).
cnf(366598240,plain,
$equal(additive_identity,multiply(additive_identity,A)),
inference(resolution,[status(thm)],[196017424,171327504]),
[] ).
cnf(369011352,plain,
product(additive_identity,A,additive_identity),
inference(paramodulation,[status(thm)],[366598240,163416592,theory(equality)]),
[] ).
fof(commutativity_of_multiplication,plain,
! [A,B,C] :
( ~ product(A,B,C)
| product(B,A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO006-1.tptp',unknown),
[] ).
cnf(163429680,plain,
( ~ product(A,B,C)
| product(B,A,C) ),
inference(rewrite,[status(thm)],[commutativity_of_multiplication]),
[] ).
fof(prove_equations,plain,
~ product(x,additive_identity,additive_identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO006-1.tptp',unknown),
[] ).
cnf(163537320,plain,
~ product(x,additive_identity,additive_identity),
inference(rewrite,[status(thm)],[prove_equations]),
[] ).
cnf(222978960,plain,
~ product(additive_identity,x,additive_identity),
inference(resolution,[status(thm)],[163429680,163537320]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[369011352,222978960]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 34 seconds
% START OF PROOF SEQUENCE
% fof(distributivity3,plain,(~product(A,B,C)|~product(D,B,E)|~sum(A,D,F)|~product(F,B,G)|sum(C,E,G)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO006-1.tptp',unknown),[]).
%
% cnf(163470056,plain,(~product(A,B,C)|~product(D,B,E)|~sum(A,D,F)|~product(F,B,G)|sum(C,E,G)),inference(rewrite,[status(thm)],[distributivity3]),[]).
%
% fof(multiplicative_inverse1,plain,(product(inverse(A),A,additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO006-1.tptp',unknown),[]).
%
% cnf(163512792,plain,(product(inverse(A),A,additive_identity)),inference(rewrite,[status(thm)],[multiplicative_inverse1]),[]).
%
% cnf(178199528,plain,(~product(B,A,C)|~sum(inverse(A),B,inverse(A))|sum(additive_identity,C,additive_identity)),inference(resolution,[status(thm)],[163470056,163512792]),[]).
%
% fof(additive_identity2,plain,(sum(A,additive_identity,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO006-1.tptp',unknown),[]).
%
% cnf(163409152,plain,(sum(A,additive_identity,A)),inference(rewrite,[status(thm)],[additive_identity2]),[]).
%
% cnf(179677344,plain,(~product(additive_identity,A,B)|sum(additive_identity,B,additive_identity)),inference(resolution,[status(thm)],[178199528,163409152]),[]).
%
% fof(closure_of_multiplication,plain,(product(A,B,multiply(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO006-1.tptp',unknown),[]).
%
% cnf(163416592,plain,(product(A,B,multiply(A,B))),inference(rewrite,[status(thm)],[closure_of_multiplication]),[]).
%
% cnf(196017424,plain,(sum(additive_identity,multiply(additive_identity,A),additive_identity)),inference(resolution,[status(thm)],[179677344,163416592]),[]).
%
% fof(addition_is_well_defined,plain,(~sum(A,B,C)|~sum(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO006-1.tptp',unknown),[]).
%
% cnf(163524520,plain,(~sum(A,B,C)|~sum(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[addition_is_well_defined]),[]).
%
% fof(additive_identity1,plain,(sum(additive_identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO006-1.tptp',unknown),[]).
%
% cnf(163437704,plain,(sum(additive_identity,A,A)),inference(rewrite,[status(thm)],[additive_identity1]),[]).
%
% cnf(171327504,plain,(~sum(additive_identity,A,B)|$equal(B,A)),inference(resolution,[status(thm)],[163524520,163437704]),[]).
%
% cnf(366598240,plain,($equal(additive_identity,multiply(additive_identity,A))),inference(resolution,[status(thm)],[196017424,171327504]),[]).
%
% cnf(369011352,plain,(product(additive_identity,A,additive_identity)),inference(paramodulation,[status(thm)],[366598240,163416592,theory(equality)]),[]).
%
% fof(commutativity_of_multiplication,plain,(~product(A,B,C)|product(B,A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO006-1.tptp',unknown),[]).
%
% cnf(163429680,plain,(~product(A,B,C)|product(B,A,C)),inference(rewrite,[status(thm)],[commutativity_of_multiplication]),[]).
%
% fof(prove_equations,plain,(~product(x,additive_identity,additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/BOO/BOO006-1.tptp',unknown),[]).
%
% cnf(163537320,plain,(~product(x,additive_identity,additive_identity)),inference(rewrite,[status(thm)],[prove_equations]),[]).
%
% cnf(222978960,plain,(~product(additive_identity,x,additive_identity)),inference(resolution,[status(thm)],[163429680,163537320]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[369011352,222978960]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------