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
%
%------------------------------------------------------------------------------