%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP549-1 : TPTP v3.4.2. Released v2.6.0.
% 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 13:07:54 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   13 (  13 unt;   0 def)
%            Number of atoms       :   13 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    6 (   6   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :    8 (   0 sgn   4   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(identity,plain,
    ! [A] : $equal(divide(A,A),identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP549-1.tptp',unknown),
    [] ).

cnf(145135400,plain,
    $equal(divide(A,A),identity),
    inference(rewrite,[status(thm)],[identity]),
    [] ).

fof(prove_these_axioms_1,plain,
    ~ $equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP549-1.tptp',unknown),
    [] ).

cnf(145144016,plain,
    ~ $equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
    inference(rewrite,[status(thm)],[prove_these_axioms_1]),
    [] ).

fof(multiply,plain,
    ! [A,B] : $equal(divide(A,divide(identity,B)),multiply(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP549-1.tptp',unknown),
    [] ).

cnf(145127656,plain,
    $equal(divide(A,divide(identity,B)),multiply(A,B)),
    inference(rewrite,[status(thm)],[multiply]),
    [] ).

cnf(152980920,plain,
    ~ $equal(multiply(inverse(b1),b1),divide(inverse(a1),divide(identity,a1))),
    inference(paramodulation,[status(thm)],[145144016,145127656,theory(equality)]),
    [] ).

fof(inverse,plain,
    ! [A] : $equal(divide(identity,A),inverse(A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP549-1.tptp',unknown),
    [] ).

cnf(145131520,plain,
    $equal(divide(identity,A),inverse(A)),
    inference(rewrite,[status(thm)],[inverse]),
    [] ).

cnf(153171464,plain,
    ~ $equal(multiply(inverse(b1),b1),divide(inverse(a1),inverse(a1))),
    inference(paramodulation,[status(thm)],[152980920,145131520,theory(equality)]),
    [] ).

cnf(153254552,plain,
    ~ $equal(multiply(inverse(b1),b1),identity),
    inference(paramodulation,[status(thm)],[153171464,145135400,theory(equality)]),
    [] ).

cnf(153353584,plain,
    ~ $equal(divide(inverse(b1),divide(identity,b1)),identity),
    inference(paramodulation,[status(thm)],[153254552,145127656,theory(equality)]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[145135400,153353584,145131520,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(identity,plain,($equal(divide(A,A),identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP549-1.tptp',unknown),[]).
% 
% cnf(145135400,plain,($equal(divide(A,A),identity)),inference(rewrite,[status(thm)],[identity]),[]).
% 
% fof(prove_these_axioms_1,plain,(~$equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP549-1.tptp',unknown),[]).
% 
% cnf(145144016,plain,(~$equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))),inference(rewrite,[status(thm)],[prove_these_axioms_1]),[]).
% 
% fof(multiply,plain,($equal(divide(A,divide(identity,B)),multiply(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP549-1.tptp',unknown),[]).
% 
% cnf(145127656,plain,($equal(divide(A,divide(identity,B)),multiply(A,B))),inference(rewrite,[status(thm)],[multiply]),[]).
% 
% cnf(152980920,plain,(~$equal(multiply(inverse(b1),b1),divide(inverse(a1),divide(identity,a1)))),inference(paramodulation,[status(thm)],[145144016,145127656,theory(equality)]),[]).
% 
% fof(inverse,plain,($equal(divide(identity,A),inverse(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP549-1.tptp',unknown),[]).
% 
% cnf(145131520,plain,($equal(divide(identity,A),inverse(A))),inference(rewrite,[status(thm)],[inverse]),[]).
% 
% cnf(153171464,plain,(~$equal(multiply(inverse(b1),b1),divide(inverse(a1),inverse(a1)))),inference(paramodulation,[status(thm)],[152980920,145131520,theory(equality)]),[]).
% 
% cnf(153254552,plain,(~$equal(multiply(inverse(b1),b1),identity)),inference(paramodulation,[status(thm)],[153171464,145135400,theory(equality)]),[]).
% 
% cnf(153353584,plain,(~$equal(divide(inverse(b1),divide(identity,b1)),identity)),inference(paramodulation,[status(thm)],[153254552,145127656,theory(equality)]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[145135400,153353584,145131520,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------