TSTP Solution File: GRP045-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP045-2 : 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 @ 2794MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 12:19:26 EDT 2009
% Result : Unsatisfiable 13.1s
% Output : Refutation 13.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 15 unt; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 32 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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; 0-2 aty)
% Number of variables : 59 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(associativity2,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),
[] ).
cnf(173790304,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
inference(rewrite,[status(thm)],[associativity2]),
[] ).
fof(product_with_a,plain,
product(c,a,result),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),
[] ).
cnf(173810424,plain,
product(c,a,result),
inference(rewrite,[status(thm)],[product_with_a]),
[] ).
cnf(188831144,plain,
( ~ product(c,A,B)
| ~ product(A,C,a)
| product(B,C,result) ),
inference(resolution,[status(thm)],[173790304,173810424]),
[] ).
fof(total_function1,plain,
! [A,B] : product(A,B,multiply(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),
[] ).
cnf(173771088,plain,
product(A,B,multiply(A,B)),
inference(rewrite,[status(thm)],[total_function1]),
[] ).
cnf(190044856,plain,
( ~ product(A,B,a)
| product(multiply(c,A),B,result) ),
inference(resolution,[status(thm)],[188831144,173771088]),
[] ).
fof(total_function2,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),
[] ).
cnf(173779144,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[total_function2]),
[] ).
fof(left_identity,plain,
! [A] : product(identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),
[] ).
cnf(173763128,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(181639608,plain,
( ~ product(identity,A,B)
| equalish(B,A) ),
inference(resolution,[status(thm)],[173779144,173763128]),
[] ).
fof(product_substitution3,plain,
! [A,B,C,D] :
( ~ equalish(A,B)
| ~ product(C,D,A)
| product(C,D,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),
[] ).
cnf(173801840,plain,
( ~ equalish(A,B)
| ~ product(C,D,A)
| product(C,D,B) ),
inference(rewrite,[status(thm)],[product_substitution3]),
[] ).
cnf(181644720,plain,
( ~ equalish(A,B)
| product(identity,A,B) ),
inference(resolution,[status(thm)],[173801840,173763128]),
[] ).
fof(a_equals_b,plain,
equalish(a,b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),
[] ).
cnf(173806424,plain,
equalish(a,b),
inference(rewrite,[status(thm)],[a_equals_b]),
[] ).
cnf(181655872,plain,
product(identity,a,b),
inference(resolution,[status(thm)],[181644720,173806424]),
[] ).
cnf(181879672,plain,
equalish(b,a),
inference(resolution,[status(thm)],[181639608,181655872]),
[] ).
cnf(182706848,plain,
product(identity,b,a),
inference(resolution,[status(thm)],[181879672,181644720]),
[] ).
cnf(253993136,plain,
product(multiply(c,identity),b,result),
inference(resolution,[status(thm)],[190044856,182706848]),
[] ).
fof(associativity1,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),
[] ).
cnf(173785944,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
inference(rewrite,[status(thm)],[associativity1]),
[] ).
fof(prove_product_with_b,plain,
~ product(c,b,result),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),
[] ).
cnf(173760616,plain,
~ product(c,b,result),
inference(rewrite,[status(thm)],[prove_product_with_b]),
[] ).
cnf(182056192,plain,
( ~ product(c,A,B)
| ~ product(A,C,b)
| ~ product(B,C,result) ),
inference(resolution,[status(thm)],[173785944,173760616]),
[] ).
cnf(182074960,plain,
( ~ product(c,identity,A)
| ~ product(A,b,result) ),
inference(resolution,[status(thm)],[182056192,173763128]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[253993136,182074960,173771088]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 12 seconds
% START OF PROOF SEQUENCE
% fof(associativity2,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),[]).
%
% cnf(173790304,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),inference(rewrite,[status(thm)],[associativity2]),[]).
%
% fof(product_with_a,plain,(product(c,a,result)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),[]).
%
% cnf(173810424,plain,(product(c,a,result)),inference(rewrite,[status(thm)],[product_with_a]),[]).
%
% cnf(188831144,plain,(~product(c,A,B)|~product(A,C,a)|product(B,C,result)),inference(resolution,[status(thm)],[173790304,173810424]),[]).
%
% fof(total_function1,plain,(product(A,B,multiply(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),[]).
%
% cnf(173771088,plain,(product(A,B,multiply(A,B))),inference(rewrite,[status(thm)],[total_function1]),[]).
%
% cnf(190044856,plain,(~product(A,B,a)|product(multiply(c,A),B,result)),inference(resolution,[status(thm)],[188831144,173771088]),[]).
%
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),[]).
%
% cnf(173779144,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[total_function2]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),[]).
%
% cnf(173763128,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(181639608,plain,(~product(identity,A,B)|equalish(B,A)),inference(resolution,[status(thm)],[173779144,173763128]),[]).
%
% fof(product_substitution3,plain,(~equalish(A,B)|~product(C,D,A)|product(C,D,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),[]).
%
% cnf(173801840,plain,(~equalish(A,B)|~product(C,D,A)|product(C,D,B)),inference(rewrite,[status(thm)],[product_substitution3]),[]).
%
% cnf(181644720,plain,(~equalish(A,B)|product(identity,A,B)),inference(resolution,[status(thm)],[173801840,173763128]),[]).
%
% fof(a_equals_b,plain,(equalish(a,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),[]).
%
% cnf(173806424,plain,(equalish(a,b)),inference(rewrite,[status(thm)],[a_equals_b]),[]).
%
% cnf(181655872,plain,(product(identity,a,b)),inference(resolution,[status(thm)],[181644720,173806424]),[]).
%
% cnf(181879672,plain,(equalish(b,a)),inference(resolution,[status(thm)],[181639608,181655872]),[]).
%
% cnf(182706848,plain,(product(identity,b,a)),inference(resolution,[status(thm)],[181879672,181644720]),[]).
%
% cnf(253993136,plain,(product(multiply(c,identity),b,result)),inference(resolution,[status(thm)],[190044856,182706848]),[]).
%
% fof(associativity1,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),[]).
%
% cnf(173785944,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),inference(rewrite,[status(thm)],[associativity1]),[]).
%
% fof(prove_product_with_b,plain,(~product(c,b,result)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP045-2.tptp',unknown),[]).
%
% cnf(173760616,plain,(~product(c,b,result)),inference(rewrite,[status(thm)],[prove_product_with_b]),[]).
%
% cnf(182056192,plain,(~product(c,A,B)|~product(A,C,b)|~product(B,C,result)),inference(resolution,[status(thm)],[173785944,173760616]),[]).
%
% cnf(182074960,plain,(~product(c,identity,A)|~product(A,b,result)),inference(resolution,[status(thm)],[182056192,173763128]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[253993136,182074960,173771088]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------