%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : RNG023-7 : 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 @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May  6 15:20:18 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   10 (  10 unt;   0 def)
%            Number of atoms       :   10 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   12 (   0 sgn   6   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(right_additive_inverse,plain,
    ! [A] : $equal(add(A,additive_inverse(A)),additive_identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG023-7.tptp',unknown),
    [] ).

cnf(150505968,plain,
    $equal(add(A,additive_inverse(A)),additive_identity),
    inference(rewrite,[status(thm)],[right_additive_inverse]),
    [] ).

fof(prove_left_alternative,plain,
    ~ $equal(associator(x,x,y),additive_identity),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG023-7.tptp',unknown),
    [] ).

cnf(150682768,plain,
    ~ $equal(associator(x,x,y),additive_identity),
    inference(rewrite,[status(thm)],[prove_left_alternative]),
    [] ).

fof(associator,plain,
    ! [A,B,C] : $equal(add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))),associator(A,B,C)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG023-7.tptp',unknown),
    [] ).

cnf(150575000,plain,
    $equal(add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))),associator(A,B,C)),
    inference(rewrite,[status(thm)],[associator]),
    [] ).

cnf(158588344,plain,
    ~ $equal(add(multiply(multiply(x,x),y),additive_inverse(multiply(x,multiply(x,y)))),additive_identity),
    inference(paramodulation,[status(thm)],[150682768,150575000,theory(equality)]),
    [] ).

fof(left_alternative,plain,
    ! [A,B] : $equal(multiply(A,multiply(A,B)),multiply(multiply(A,A),B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG023-7.tptp',unknown),
    [] ).

cnf(150571096,plain,
    $equal(multiply(A,multiply(A,B)),multiply(multiply(A,A),B)),
    inference(rewrite,[status(thm)],[left_alternative]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[150505968,158588344,150571096,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(right_additive_inverse,plain,($equal(add(A,additive_inverse(A)),additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG023-7.tptp',unknown),[]).
% 
% cnf(150505968,plain,($equal(add(A,additive_inverse(A)),additive_identity)),inference(rewrite,[status(thm)],[right_additive_inverse]),[]).
% 
% fof(prove_left_alternative,plain,(~$equal(associator(x,x,y),additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG023-7.tptp',unknown),[]).
% 
% cnf(150682768,plain,(~$equal(associator(x,x,y),additive_identity)),inference(rewrite,[status(thm)],[prove_left_alternative]),[]).
% 
% fof(associator,plain,($equal(add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))),associator(A,B,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG023-7.tptp',unknown),[]).
% 
% cnf(150575000,plain,($equal(add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))),associator(A,B,C))),inference(rewrite,[status(thm)],[associator]),[]).
% 
% cnf(158588344,plain,(~$equal(add(multiply(multiply(x,x),y),additive_inverse(multiply(x,multiply(x,y)))),additive_identity)),inference(paramodulation,[status(thm)],[150682768,150575000,theory(equality)]),[]).
% 
% fof(left_alternative,plain,($equal(multiply(A,multiply(A,B)),multiply(multiply(A,A),B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG023-7.tptp',unknown),[]).
% 
% cnf(150571096,plain,($equal(multiply(A,multiply(A,B)),multiply(multiply(A,A),B))),inference(rewrite,[status(thm)],[left_alternative]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[150505968,158588344,150571096,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------