TSTP Solution File: GRP134-1.003 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP134-1.003 : TPTP v3.4.2. Released v1.2.0.
% 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 12:28:53 EDT 2009

% Result   : Unsatisfiable 8.9s
% Output   : Refutation 8.9s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   76 (  21 unt;   0 def)
%            Number of atoms       :  167 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  187 (  96   ~;  91   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   76 (   0 sgn  18   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(product_total_function1,plain,
    ! [A,B] :
      ( ~ group_element(A)
      | ~ group_element(B)
      | product(A,B,e_1)
      | product(A,B,e_2)
      | product(A,B,e_3) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),
    [] ).

cnf(156264168,plain,
    ( ~ group_element(A)
    | ~ group_element(B)
    | product(A,B,e_1)
    | product(A,B,e_2)
    | product(A,B,e_3) ),
    inference(rewrite,[status(thm)],[product_total_function1]),
    [] ).

fof(element_2,plain,
    group_element(e_2),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),
    [] ).

cnf(156221552,plain,
    group_element(e_2),
    inference(rewrite,[status(thm)],[element_2]),
    [] ).

cnf(164203944,plain,
    ( ~ group_element(A)
    | product(A,e_2,e_1)
    | product(A,e_2,e_2)
    | product(A,e_2,e_3) ),
    inference(resolution,[status(thm)],[156264168,156221552]),
    [] ).

fof(element_1,plain,
    group_element(e_1),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),
    [] ).

cnf(156217600,plain,
    group_element(e_1),
    inference(rewrite,[status(thm)],[element_1]),
    [] ).

cnf(164250584,plain,
    ( product(e_1,e_2,e_1)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3) ),
    inference(resolution,[status(thm)],[164203944,156217600]),
    [] ).

fof(qg4,plain,
    ! [A,B,C,D] :
      ( ~ product(A,B,C)
      | ~ product(B,A,D)
      | product(C,D,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),
    [] ).

cnf(156292688,plain,
    ( ~ product(A,B,C)
    | ~ product(B,A,D)
    | product(C,D,B) ),
    inference(rewrite,[status(thm)],[qg4]),
    [] ).

fof(product_right_cancellation,plain,
    ! [A,B,C,D] :
      ( ~ product(A,B,C)
      | ~ product(A,D,C)
      | equalish(B,D) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),
    [] ).

cnf(156284680,plain,
    ( ~ product(A,B,C)
    | ~ product(A,D,C)
    | equalish(B,D) ),
    inference(rewrite,[status(thm)],[product_right_cancellation]),
    [] ).

fof(e_1_is_not_e_2,plain,
    ~ equalish(e_1,e_2),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),
    [] ).

cnf(156229848,plain,
    ~ equalish(e_1,e_2),
    inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
    [] ).

cnf(164291792,plain,
    ( ~ product(A,e_1,B)
    | ~ product(A,e_2,B) ),
    inference(resolution,[status(thm)],[156284680,156229848]),
    [] ).

cnf(164437560,plain,
    ( ~ product(A,B,C)
    | ~ product(B,A,e_2)
    | ~ product(C,e_1,B) ),
    inference(resolution,[status(thm)],[156292688,164291792]),
    [] ).

cnf(167310496,plain,
    ( product(e_1,e_2,e_1)
    | product(e_1,e_2,e_3)
    | ~ product(e_2,e_1,e_2) ),
    inference(resolution,[status(thm)],[164250584,164437560]),
    [] ).

fof(product_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/GRP134-1.003.tptp',unknown),
    [] ).

cnf(156280448,plain,
    ( ~ product(A,B,C)
    | ~ product(A,B,D)
    | equalish(C,D) ),
    inference(rewrite,[status(thm)],[product_total_function2]),
    [] ).

cnf(164267352,plain,
    ( ~ product(A,B,e_1)
    | ~ product(A,B,e_2) ),
    inference(resolution,[status(thm)],[156280448,156229848]),
    [] ).

cnf(164421832,plain,
    ( ~ product(A,e_2,B)
    | ~ product(e_2,A,C)
    | ~ product(B,C,e_1) ),
    inference(resolution,[status(thm)],[156292688,164267352]),
    [] ).

cnf(165818592,plain,
    ( product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3)
    | ~ product(e_2,e_1,e_2) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[156217600,156221552,156264168,164421832]),
    [] ).

cnf(174977016,plain,
    ( product(e_1,e_2,e_3)
    | ~ product(e_2,e_1,e_2) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[167310496,165818592,164267352]),
    [] ).

fof(e_1_is_not_e_3,plain,
    ~ equalish(e_1,e_3),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),
    [] ).

cnf(156233768,plain,
    ~ equalish(e_1,e_3),
    inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
    [] ).

cnf(164340632,plain,
    ( ~ product(A,B,e_1)
    | ~ product(A,B,e_3) ),
    inference(resolution,[status(thm)],[156280448,156233768]),
    [] ).

cnf(175242528,plain,
    ( ~ product(e_2,e_1,e_2)
    | ~ product(e_1,e_2,e_1) ),
    inference(resolution,[status(thm)],[174977016,164340632]),
    [] ).

cnf(164152824,plain,
    ( ~ group_element(A)
    | product(e_2,A,e_1)
    | product(e_2,A,e_2)
    | product(e_2,A,e_3) ),
    inference(resolution,[status(thm)],[156264168,156221552]),
    [] ).

cnf(164227040,plain,
    ( product(e_2,e_1,e_1)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3) ),
    inference(resolution,[status(thm)],[164152824,156217600]),
    [] ).

cnf(175937776,plain,
    ( ~ product(e_1,e_2,e_1)
    | product(e_2,e_1,e_1)
    | product(e_2,e_1,e_3) ),
    inference(resolution,[status(thm)],[175242528,164227040]),
    [] ).

fof(product_left_cancellation,plain,
    ! [A,B,C,D] :
      ( ~ product(A,B,C)
      | ~ product(D,B,C)
      | equalish(A,D) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),
    [] ).

cnf(156288312,plain,
    ( ~ product(A,B,C)
    | ~ product(D,B,C)
    | equalish(A,D) ),
    inference(rewrite,[status(thm)],[product_left_cancellation]),
    [] ).

cnf(164324160,plain,
    ( ~ product(e_1,A,B)
    | ~ product(e_2,A,B) ),
    inference(resolution,[status(thm)],[156288312,156229848]),
    [] ).

cnf(164443664,plain,
    ( ~ product(A,B,e_1)
    | ~ product(B,A,C)
    | ~ product(e_2,C,B) ),
    inference(resolution,[status(thm)],[156292688,164324160]),
    [] ).

cnf(165903312,plain,
    ( product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3)
    | ~ product(e_1,e_2,e_1) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[156217600,156221552,156264168,164443664]),
    [] ).

cnf(177609280,plain,
    ( product(e_2,e_1,e_3)
    | ~ product(e_1,e_2,e_1) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[175937776,165903312,164267352]),
    [] ).

cnf(164105088,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2)
    | product(e_1,e_1,e_3) ),
    inference(resolution,[status(thm)],[156264168,156217600]),
    [] ).

cnf(166073864,plain,
    ( product(e_1,e_1,e_2)
    | product(e_1,e_1,e_3)
    | ~ product(e_1,e_2,e_1) ),
    inference(resolution,[status(thm)],[164105088,164291792]),
    [] ).

cnf(164448976,plain,
    ( ~ product(A,B,e_2)
    | ~ product(B,A,C)
    | ~ product(e_1,C,B) ),
    inference(resolution,[status(thm)],[156292688,164324160]),
    [] ).

cnf(236186160,plain,
    ( product(e_1,e_1,e_3)
    | ~ product(e_1,e_2,e_1) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[166073864,166073864,164448976]),
    [] ).

cnf(236585120,plain,
    ~ product(e_1,e_2,e_1),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[177609280,236186160,164324160]),
    [] ).

cnf(238199304,plain,
    ( ~ product(A,e_1,e_1)
    | ~ product(e_1,A,e_2) ),
    inference(resolution,[status(thm)],[236585120,156292688]),
    [] ).

cnf(175234024,plain,
    ( ~ product(e_2,e_1,e_2)
    | ~ product(e_2,e_2,e_3) ),
    inference(resolution,[status(thm)],[174977016,164324160]),
    [] ).

cnf(165833832,plain,
    ( product(e_2,e_2,e_2)
    | product(e_2,e_2,e_3)
    | ~ product(e_1,e_1,e_1) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[156221552,156264168,164421832]),
    [] ).

cnf(176713120,plain,
    ( ~ product(e_1,e_1,e_1)
    | ~ product(e_2,e_1,e_2) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[175234024,165833832,164291792]),
    [] ).

cnf(177138320,plain,
    ( ~ product(e_2,e_1,e_2)
    | product(e_1,e_1,e_2)
    | product(e_1,e_1,e_3) ),
    inference(resolution,[status(thm)],[176713120,164105088]),
    [] ).

cnf(238194432,plain,
    ( product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3) ),
    inference(resolution,[status(thm)],[236585120,164250584]),
    [] ).

cnf(239495424,plain,
    ( product(e_1,e_2,e_2)
    | ~ product(e_1,e_1,e_3) ),
    inference(resolution,[status(thm)],[238194432,164291792]),
    [] ).

cnf(164567976,plain,
    ( product(B,B,A)
    | ~ product(C,B,A)
    | ~ product(B,C,A) ),
    inference(resolution,[status(thm)],[156292688,156292688]),
    [] ).

cnf(265646112,plain,
    ( product(e_1,e_1,e_2)
    | ~ product(e_2,e_1,e_2) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[177138320,239495424,164567976]),
    [] ).

cnf(301583608,plain,
    ~ product(e_2,e_1,e_2),
    inference(resolution,[status(thm)],[265646112,164324160]),
    [] ).

cnf(302102576,plain,
    ( product(e_2,e_1,e_1)
    | product(e_2,e_1,e_3) ),
    inference(resolution,[status(thm)],[301583608,164227040]),
    [] ).

cnf(302830072,plain,
    ( product(e_2,e_1,e_1)
    | ~ product(e_1,e_1,e_3) ),
    inference(resolution,[status(thm)],[302102576,164324160]),
    [] ).

cnf(164614792,plain,
    ( ~ product(B,e_1,A)
    | ~ product(e_1,B,A)
    | ~ product(e_1,e_2,A) ),
    inference(resolution,[status(thm)],[164567976,164291792]),
    [] ).

cnf(239923344,plain,
    ( product(e_1,e_2,e_2)
    | ~ product(e_2,e_1,e_3) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[238194432,238194432,164614792]),
    [] ).

fof(e_2_is_not_e_3,plain,
    ~ equalish(e_2,e_3),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),
    [] ).

cnf(156241128,plain,
    ~ equalish(e_2,e_3),
    inference(rewrite,[status(thm)],[e_2_is_not_e_3]),
    [] ).

cnf(164358800,plain,
    ( ~ product(A,B,e_2)
    | ~ product(A,B,e_3) ),
    inference(resolution,[status(thm)],[156280448,156241128]),
    [] ).

cnf(285730728,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_1,e_2,e_3) ),
    inference(resolution,[status(thm)],[239923344,164358800]),
    [] ).

cnf(239490984,plain,
    ( product(e_1,e_2,e_3)
    | ~ product(e_1,e_1,e_2) ),
    inference(resolution,[status(thm)],[238194432,164291792]),
    [] ).

cnf(164398472,plain,
    ( ~ product(e_1,A,B)
    | ~ product(e_3,A,B) ),
    inference(resolution,[status(thm)],[156288312,156233768]),
    [] ).

cnf(164502136,plain,
    ( ~ product(A,B,e_3)
    | ~ product(B,A,C)
    | ~ product(e_1,C,B) ),
    inference(resolution,[status(thm)],[156292688,164398472]),
    [] ).

cnf(303209528,plain,
    ~ product(e_1,e_1,e_2),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[285730728,239490984,302102576,164502136]),
    [] ).

cnf(303549840,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_3) ),
    inference(resolution,[status(thm)],[303209528,164105088]),
    [] ).

cnf(306210520,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_2,e_2) ),
    inference(resolution,[status(thm)],[303549840,239495424]),
    [] ).

cnf(164404536,plain,
    ( ~ product(e_2,A,B)
    | ~ product(e_3,A,B) ),
    inference(resolution,[status(thm)],[156288312,156241128]),
    [] ).

cnf(164514360,plain,
    ( ~ product(A,B,e_3)
    | ~ product(B,A,C)
    | ~ product(e_2,C,B) ),
    inference(resolution,[status(thm)],[156292688,164404536]),
    [] ).

cnf(307062232,plain,
    ~ product(e_1,e_1,e_3),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[238199304,302830072,306210520,164514360]),
    [] ).

cnf(310428000,plain,
    product(e_1,e_1,e_1),
    inference(resolution,[status(thm)],[307062232,303549840]),
    [] ).

cnf(303231096,plain,
    ( product(e_2,e_1,e_1)
    | product(e_1,e_2,e_2) ),
    inference(resolution,[status(thm)],[302102576,239923344]),
    [] ).

cnf(306782256,plain,
    product(e_1,e_2,e_2),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[303231096,306210520,164324160]),
    [] ).

cnf(307607896,plain,
    ~ product(e_2,e_2,e_2),
    inference(resolution,[status(thm)],[306782256,164324160]),
    [] ).

cnf(311907888,plain,
    product(e_2,e_2,e_3),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[310428000,307607896,165833832]),
    [] ).

cnf(310831776,plain,
    ~ product(e_2,e_1,e_1),
    inference(resolution,[status(thm)],[310428000,164324160]),
    [] ).

cnf(317255752,plain,
    product(e_2,e_1,e_3),
    inference(resolution,[status(thm)],[310831776,302102576]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[311907888,317255752,164291792]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 8 seconds
% START OF PROOF SEQUENCE
% fof(product_total_function1,plain,(~group_element(A)|~group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),[]).
% 
% cnf(156264168,plain,(~group_element(A)|~group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3)),inference(rewrite,[status(thm)],[product_total_function1]),[]).
% 
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),[]).
% 
% cnf(156221552,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
% 
% cnf(164203944,plain,(~group_element(A)|product(A,e_2,e_1)|product(A,e_2,e_2)|product(A,e_2,e_3)),inference(resolution,[status(thm)],[156264168,156221552]),[]).
% 
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),[]).
% 
% cnf(156217600,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
% 
% cnf(164250584,plain,(product(e_1,e_2,e_1)|product(e_1,e_2,e_2)|product(e_1,e_2,e_3)),inference(resolution,[status(thm)],[164203944,156217600]),[]).
% 
% fof(qg4,plain,(~product(A,B,C)|~product(B,A,D)|product(C,D,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),[]).
% 
% cnf(156292688,plain,(~product(A,B,C)|~product(B,A,D)|product(C,D,B)),inference(rewrite,[status(thm)],[qg4]),[]).
% 
% fof(product_right_cancellation,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),[]).
% 
% cnf(156284680,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product_right_cancellation]),[]).
% 
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),[]).
% 
% cnf(156229848,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
% 
% cnf(164291792,plain,(~product(A,e_1,B)|~product(A,e_2,B)),inference(resolution,[status(thm)],[156284680,156229848]),[]).
% 
% cnf(164437560,plain,(~product(A,B,C)|~product(B,A,e_2)|~product(C,e_1,B)),inference(resolution,[status(thm)],[156292688,164291792]),[]).
% 
% cnf(167310496,plain,(product(e_1,e_2,e_1)|product(e_1,e_2,e_3)|~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[164250584,164437560]),[]).
% 
% fof(product_total_function2,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),[]).
% 
% cnf(156280448,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product_total_function2]),[]).
% 
% cnf(164267352,plain,(~product(A,B,e_1)|~product(A,B,e_2)),inference(resolution,[status(thm)],[156280448,156229848]),[]).
% 
% cnf(164421832,plain,(~product(A,e_2,B)|~product(e_2,A,C)|~product(B,C,e_1)),inference(resolution,[status(thm)],[156292688,164267352]),[]).
% 
% cnf(165818592,plain,(product(e_1,e_2,e_2)|product(e_1,e_2,e_3)|~product(e_2,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156217600,156221552,156264168,164421832]),[]).
% 
% cnf(174977016,plain,(product(e_1,e_2,e_3)|~product(e_2,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[167310496,165818592,164267352]),[]).
% 
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),[]).
% 
% cnf(156233768,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
% 
% cnf(164340632,plain,(~product(A,B,e_1)|~product(A,B,e_3)),inference(resolution,[status(thm)],[156280448,156233768]),[]).
% 
% cnf(175242528,plain,(~product(e_2,e_1,e_2)|~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[174977016,164340632]),[]).
% 
% cnf(164152824,plain,(~group_element(A)|product(e_2,A,e_1)|product(e_2,A,e_2)|product(e_2,A,e_3)),inference(resolution,[status(thm)],[156264168,156221552]),[]).
% 
% cnf(164227040,plain,(product(e_2,e_1,e_1)|product(e_2,e_1,e_2)|product(e_2,e_1,e_3)),inference(resolution,[status(thm)],[164152824,156217600]),[]).
% 
% cnf(175937776,plain,(~product(e_1,e_2,e_1)|product(e_2,e_1,e_1)|product(e_2,e_1,e_3)),inference(resolution,[status(thm)],[175242528,164227040]),[]).
% 
% fof(product_left_cancellation,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),[]).
% 
% cnf(156288312,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product_left_cancellation]),[]).
% 
% cnf(164324160,plain,(~product(e_1,A,B)|~product(e_2,A,B)),inference(resolution,[status(thm)],[156288312,156229848]),[]).
% 
% cnf(164443664,plain,(~product(A,B,e_1)|~product(B,A,C)|~product(e_2,C,B)),inference(resolution,[status(thm)],[156292688,164324160]),[]).
% 
% cnf(165903312,plain,(product(e_2,e_1,e_2)|product(e_2,e_1,e_3)|~product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156217600,156221552,156264168,164443664]),[]).
% 
% cnf(177609280,plain,(product(e_2,e_1,e_3)|~product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[175937776,165903312,164267352]),[]).
% 
% cnf(164105088,plain,(product(e_1,e_1,e_1)|product(e_1,e_1,e_2)|product(e_1,e_1,e_3)),inference(resolution,[status(thm)],[156264168,156217600]),[]).
% 
% cnf(166073864,plain,(product(e_1,e_1,e_2)|product(e_1,e_1,e_3)|~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[164105088,164291792]),[]).
% 
% cnf(164448976,plain,(~product(A,B,e_2)|~product(B,A,C)|~product(e_1,C,B)),inference(resolution,[status(thm)],[156292688,164324160]),[]).
% 
% cnf(236186160,plain,(product(e_1,e_1,e_3)|~product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[166073864,166073864,164448976]),[]).
% 
% cnf(236585120,plain,(~product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177609280,236186160,164324160]),[]).
% 
% cnf(238199304,plain,(~product(A,e_1,e_1)|~product(e_1,A,e_2)),inference(resolution,[status(thm)],[236585120,156292688]),[]).
% 
% cnf(175234024,plain,(~product(e_2,e_1,e_2)|~product(e_2,e_2,e_3)),inference(resolution,[status(thm)],[174977016,164324160]),[]).
% 
% cnf(165833832,plain,(product(e_2,e_2,e_2)|product(e_2,e_2,e_3)|~product(e_1,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156221552,156264168,164421832]),[]).
% 
% cnf(176713120,plain,(~product(e_1,e_1,e_1)|~product(e_2,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[175234024,165833832,164291792]),[]).
% 
% cnf(177138320,plain,(~product(e_2,e_1,e_2)|product(e_1,e_1,e_2)|product(e_1,e_1,e_3)),inference(resolution,[status(thm)],[176713120,164105088]),[]).
% 
% cnf(238194432,plain,(product(e_1,e_2,e_2)|product(e_1,e_2,e_3)),inference(resolution,[status(thm)],[236585120,164250584]),[]).
% 
% cnf(239495424,plain,(product(e_1,e_2,e_2)|~product(e_1,e_1,e_3)),inference(resolution,[status(thm)],[238194432,164291792]),[]).
% 
% cnf(164567976,plain,(product(B,B,A)|~product(C,B,A)|~product(B,C,A)),inference(resolution,[status(thm)],[156292688,156292688]),[]).
% 
% cnf(265646112,plain,(product(e_1,e_1,e_2)|~product(e_2,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177138320,239495424,164567976]),[]).
% 
% cnf(301583608,plain,(~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[265646112,164324160]),[]).
% 
% cnf(302102576,plain,(product(e_2,e_1,e_1)|product(e_2,e_1,e_3)),inference(resolution,[status(thm)],[301583608,164227040]),[]).
% 
% cnf(302830072,plain,(product(e_2,e_1,e_1)|~product(e_1,e_1,e_3)),inference(resolution,[status(thm)],[302102576,164324160]),[]).
% 
% cnf(164614792,plain,(~product(B,e_1,A)|~product(e_1,B,A)|~product(e_1,e_2,A)),inference(resolution,[status(thm)],[164567976,164291792]),[]).
% 
% cnf(239923344,plain,(product(e_1,e_2,e_2)|~product(e_2,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[238194432,238194432,164614792]),[]).
% 
% fof(e_2_is_not_e_3,plain,(~equalish(e_2,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-1.003.tptp',unknown),[]).
% 
% cnf(156241128,plain,(~equalish(e_2,e_3)),inference(rewrite,[status(thm)],[e_2_is_not_e_3]),[]).
% 
% cnf(164358800,plain,(~product(A,B,e_2)|~product(A,B,e_3)),inference(resolution,[status(thm)],[156280448,156241128]),[]).
% 
% cnf(285730728,plain,(~product(e_2,e_1,e_3)|~product(e_1,e_2,e_3)),inference(resolution,[status(thm)],[239923344,164358800]),[]).
% 
% cnf(239490984,plain,(product(e_1,e_2,e_3)|~product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[238194432,164291792]),[]).
% 
% cnf(164398472,plain,(~product(e_1,A,B)|~product(e_3,A,B)),inference(resolution,[status(thm)],[156288312,156233768]),[]).
% 
% cnf(164502136,plain,(~product(A,B,e_3)|~product(B,A,C)|~product(e_1,C,B)),inference(resolution,[status(thm)],[156292688,164398472]),[]).
% 
% cnf(303209528,plain,(~product(e_1,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[285730728,239490984,302102576,164502136]),[]).
% 
% cnf(303549840,plain,(product(e_1,e_1,e_1)|product(e_1,e_1,e_3)),inference(resolution,[status(thm)],[303209528,164105088]),[]).
% 
% cnf(306210520,plain,(product(e_1,e_1,e_1)|product(e_1,e_2,e_2)),inference(resolution,[status(thm)],[303549840,239495424]),[]).
% 
% cnf(164404536,plain,(~product(e_2,A,B)|~product(e_3,A,B)),inference(resolution,[status(thm)],[156288312,156241128]),[]).
% 
% cnf(164514360,plain,(~product(A,B,e_3)|~product(B,A,C)|~product(e_2,C,B)),inference(resolution,[status(thm)],[156292688,164404536]),[]).
% 
% cnf(307062232,plain,(~product(e_1,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[238199304,302830072,306210520,164514360]),[]).
% 
% cnf(310428000,plain,(product(e_1,e_1,e_1)),inference(resolution,[status(thm)],[307062232,303549840]),[]).
% 
% cnf(303231096,plain,(product(e_2,e_1,e_1)|product(e_1,e_2,e_2)),inference(resolution,[status(thm)],[302102576,239923344]),[]).
% 
% cnf(306782256,plain,(product(e_1,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[303231096,306210520,164324160]),[]).
% 
% cnf(307607896,plain,(~product(e_2,e_2,e_2)),inference(resolution,[status(thm)],[306782256,164324160]),[]).
% 
% cnf(311907888,plain,(product(e_2,e_2,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[310428000,307607896,165833832]),[]).
% 
% cnf(310831776,plain,(~product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[310428000,164324160]),[]).
% 
% cnf(317255752,plain,(product(e_2,e_1,e_3)),inference(resolution,[status(thm)],[310831776,302102576]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[311907888,317255752,164291792]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------