TSTP Solution File: GRP124-7.004 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP124-7.004 : TPTP v3.4.2. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 12:25:39 EDT 2009
% Result : Unsatisfiable 7.2s
% Output : Refutation 7.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 21
% Syntax : Number of formulae : 75 ( 48 unt; 0 def)
% Number of atoms : 119 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 121 ( 77 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 56 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(element_1,plain,
group_element(e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172816480,plain,
group_element(e_1),
inference(rewrite,[status(thm)],[element_1]),
[] ).
fof(element_2,plain,
group_element(e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172820608,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
fof(product1_total_function1,plain,
! [A,B] :
( ~ group_element(A)
| ~ group_element(B)
| product1(A,B,e_1)
| product1(A,B,e_2)
| product1(A,B,e_3)
| product1(A,B,e_4) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172899184,plain,
( ~ group_element(A)
| ~ group_element(B)
| product1(A,B,e_1)
| product1(A,B,e_2)
| product1(A,B,e_3)
| product1(A,B,e_4) ),
inference(rewrite,[status(thm)],[product1_total_function1]),
[] ).
fof(product1_right_cancellation,plain,
! [A,B,C,D] :
( ~ product1(A,B,C)
| ~ product1(A,D,C)
| equalish(B,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172919296,plain,
( ~ product1(A,B,C)
| ~ product1(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product1_right_cancellation]),
[] ).
fof(product1_idempotence,plain,
! [A] : product1(A,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172927304,plain,
product1(A,A,A),
inference(rewrite,[status(thm)],[product1_idempotence]),
[] ).
cnf(182150536,plain,
( ~ product1(A,B,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[172919296,172927304]),
[] ).
fof(e_1_is_not_e_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172836600,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(182166488,plain,
~ product1(e_1,e_2,e_1),
inference(resolution,[status(thm)],[182150536,172836600]),
[] ).
cnf(186272688,plain,
( product1(e_1,e_2,e_2)
| product1(e_1,e_2,e_3)
| product1(e_1,e_2,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[172816480,172820608,172899184,182166488]),
[] ).
fof(product1_left_cancellation,plain,
! [A,B,C,D] :
( ~ product1(A,B,C)
| ~ product1(D,B,C)
| equalish(A,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172922928,plain,
( ~ product1(A,B,C)
| ~ product1(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product1_left_cancellation]),
[] ).
cnf(182388328,plain,
( ~ product1(B,A,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[172922928,172927304]),
[] ).
fof(e_2_is_not_e_1,plain,
~ equalish(e_2,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172749216,plain,
~ equalish(e_2,e_1),
inference(rewrite,[status(thm)],[e_2_is_not_e_1]),
[] ).
cnf(182430496,plain,
~ product1(e_1,e_2,e_2),
inference(resolution,[status(thm)],[182388328,172749216]),
[] ).
cnf(243462896,plain,
( product1(e_1,e_2,e_3)
| product1(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[186272688,182430496]),
[] ).
fof(e_3_is_not_e_1,plain,
~ equalish(e_3,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172863552,plain,
~ equalish(e_3,e_1),
inference(rewrite,[status(thm)],[e_3_is_not_e_1]),
[] ).
cnf(182469776,plain,
~ product1(e_1,e_3,e_3),
inference(resolution,[status(thm)],[182388328,172863552]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172840808,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(182174928,plain,
~ product1(e_1,e_3,e_1),
inference(resolution,[status(thm)],[182150536,172840808]),
[] ).
fof(element_3,plain,
group_element(e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172828424,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
fof(e_2_is_not_e_3,plain,
~ equalish(e_2,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172851960,plain,
~ equalish(e_2,e_3),
inference(rewrite,[status(thm)],[e_2_is_not_e_3]),
[] ).
cnf(182443840,plain,
~ product1(e_3,e_2,e_2),
inference(resolution,[status(thm)],[182388328,172851960]),
[] ).
fof(e_3_is_not_e_2,plain,
~ equalish(e_3,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172867216,plain,
~ equalish(e_3,e_2),
inference(rewrite,[status(thm)],[e_3_is_not_e_2]),
[] ).
cnf(182253320,plain,
~ product1(e_3,e_2,e_3),
inference(resolution,[status(thm)],[182150536,172867216]),
[] ).
fof(qg2a,plain,
! [A,B,C,D] :
( ~ product1(A,B,C)
| ~ product1(C,A,D)
| product2(D,B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172971424,plain,
( ~ product1(A,B,C)
| ~ product1(C,A,D)
| product2(D,B,A) ),
inference(rewrite,[status(thm)],[qg2a]),
[] ).
fof(product2_total_function2,plain,
! [A,B,C,D] :
( ~ product2(A,B,C)
| ~ product2(A,B,D)
| equalish(C,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172949776,plain,
( ~ product2(A,B,C)
| ~ product2(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product2_total_function2]),
[] ).
fof(product2_idempotence,plain,
! [A] : product2(A,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172962232,plain,
product2(A,A,A),
inference(rewrite,[status(thm)],[product2_idempotence]),
[] ).
cnf(182608632,plain,
( ~ product2(A,A,B)
| equalish(A,B) ),
inference(resolution,[status(thm)],[172949776,172962232]),
[] ).
cnf(182665952,plain,
~ product2(e_2,e_2,e_3),
inference(resolution,[status(thm)],[182608632,172851960]),
[] ).
cnf(183300320,plain,
( ~ product1(e_3,e_2,A)
| ~ product1(A,e_3,e_2) ),
inference(resolution,[status(thm)],[172971424,182665952]),
[] ).
cnf(186983288,plain,
( product1(e_3,e_2,e_4)
| ~ product1(e_1,e_3,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[182443840,182253320,172828424,172820608,172899184,183300320]),
[] ).
cnf(181563864,plain,
( ~ product1(e_1,A,B)
| ~ product1(e_3,A,B) ),
inference(resolution,[status(thm)],[172922928,172840808]),
[] ).
cnf(206155816,plain,
( ~ product1(e_1,e_3,e_2)
| ~ product1(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[186983288,181563864]),
[] ).
cnf(213178088,plain,
( ~ product1(e_1,e_2,e_4)
| product1(e_1,e_3,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[182469776,182174928,172816480,172828424,206155816,172899184]),
[] ).
cnf(181612672,plain,
( ~ product1(A,e_2,B)
| ~ product1(A,e_3,B) ),
inference(resolution,[status(thm)],[172919296,172851960]),
[] ).
cnf(213235400,plain,
~ product1(e_1,e_2,e_4),
inference(resolution,[status(thm)],[213178088,181612672]),
[] ).
cnf(243900936,plain,
product1(e_1,e_2,e_3),
inference(resolution,[status(thm)],[243462896,213235400]),
[] ).
fof(e_4_is_not_e_1,plain,
~ equalish(e_4,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172874592,plain,
~ equalish(e_4,e_1),
inference(rewrite,[status(thm)],[e_4_is_not_e_1]),
[] ).
cnf(182509872,plain,
~ product1(e_1,e_4,e_4),
inference(resolution,[status(thm)],[182388328,172874592]),
[] ).
fof(element_4,plain,
group_element(e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172832136,plain,
group_element(e_4),
inference(rewrite,[status(thm)],[element_4]),
[] ).
fof(e_1_is_not_e_4,plain,
~ equalish(e_1,e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172844536,plain,
~ equalish(e_1,e_4),
inference(rewrite,[status(thm)],[e_1_is_not_e_4]),
[] ).
cnf(182189064,plain,
~ product1(e_1,e_4,e_1),
inference(resolution,[status(thm)],[182150536,172844536]),
[] ).
fof(e_2_is_not_e_4,plain,
~ equalish(e_2,e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172859792,plain,
~ equalish(e_2,e_4),
inference(rewrite,[status(thm)],[e_2_is_not_e_4]),
[] ).
cnf(182457216,plain,
~ product1(e_4,e_2,e_2),
inference(resolution,[status(thm)],[182388328,172859792]),
[] ).
fof(e_4_is_not_e_2,plain,
~ equalish(e_4,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),
[] ).
cnf(172878240,plain,
~ equalish(e_4,e_2),
inference(rewrite,[status(thm)],[e_4_is_not_e_2]),
[] ).
cnf(182299912,plain,
~ product1(e_4,e_2,e_4),
inference(resolution,[status(thm)],[182150536,172878240]),
[] ).
cnf(182677848,plain,
~ product2(e_2,e_2,e_4),
inference(resolution,[status(thm)],[182608632,172859792]),
[] ).
cnf(183328632,plain,
( ~ product1(e_4,e_2,A)
| ~ product1(A,e_4,e_2) ),
inference(resolution,[status(thm)],[172971424,182677848]),
[] ).
cnf(186998112,plain,
( product1(e_4,e_2,e_3)
| ~ product1(e_1,e_4,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[182457216,182299912,172832136,172820608,172899184,183328632]),
[] ).
cnf(182355392,plain,
( ~ product1(e_1,A,B)
| ~ product1(e_4,A,B) ),
inference(resolution,[status(thm)],[172922928,172844536]),
[] ).
cnf(206598016,plain,
( ~ product1(e_1,e_4,e_2)
| ~ product1(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[186998112,182355392]),
[] ).
cnf(215400464,plain,
( ~ product1(e_1,e_2,e_3)
| product1(e_1,e_4,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[182509872,172832136,172816480,182189064,206598016,172899184]),
[] ).
cnf(182135248,plain,
( ~ product1(A,e_2,B)
| ~ product1(A,e_4,B) ),
inference(resolution,[status(thm)],[172919296,172859792]),
[] ).
cnf(215494096,plain,
~ product1(e_1,e_2,e_3),
inference(resolution,[status(thm)],[215400464,182135248]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[243900936,215494096]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 7 seconds
% START OF PROOF SEQUENCE
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172816480,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
%
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172820608,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% fof(product1_total_function1,plain,(~group_element(A)|~group_element(B)|product1(A,B,e_1)|product1(A,B,e_2)|product1(A,B,e_3)|product1(A,B,e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172899184,plain,(~group_element(A)|~group_element(B)|product1(A,B,e_1)|product1(A,B,e_2)|product1(A,B,e_3)|product1(A,B,e_4)),inference(rewrite,[status(thm)],[product1_total_function1]),[]).
%
% fof(product1_right_cancellation,plain,(~product1(A,B,C)|~product1(A,D,C)|equalish(B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172919296,plain,(~product1(A,B,C)|~product1(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product1_right_cancellation]),[]).
%
% fof(product1_idempotence,plain,(product1(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172927304,plain,(product1(A,A,A)),inference(rewrite,[status(thm)],[product1_idempotence]),[]).
%
% cnf(182150536,plain,(~product1(A,B,A)|equalish(A,B)),inference(resolution,[status(thm)],[172919296,172927304]),[]).
%
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172836600,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(182166488,plain,(~product1(e_1,e_2,e_1)),inference(resolution,[status(thm)],[182150536,172836600]),[]).
%
% cnf(186272688,plain,(product1(e_1,e_2,e_2)|product1(e_1,e_2,e_3)|product1(e_1,e_2,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[172816480,172820608,172899184,182166488]),[]).
%
% fof(product1_left_cancellation,plain,(~product1(A,B,C)|~product1(D,B,C)|equalish(A,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172922928,plain,(~product1(A,B,C)|~product1(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product1_left_cancellation]),[]).
%
% cnf(182388328,plain,(~product1(B,A,A)|equalish(A,B)),inference(resolution,[status(thm)],[172922928,172927304]),[]).
%
% fof(e_2_is_not_e_1,plain,(~equalish(e_2,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172749216,plain,(~equalish(e_2,e_1)),inference(rewrite,[status(thm)],[e_2_is_not_e_1]),[]).
%
% cnf(182430496,plain,(~product1(e_1,e_2,e_2)),inference(resolution,[status(thm)],[182388328,172749216]),[]).
%
% cnf(243462896,plain,(product1(e_1,e_2,e_3)|product1(e_1,e_2,e_4)),inference(resolution,[status(thm)],[186272688,182430496]),[]).
%
% fof(e_3_is_not_e_1,plain,(~equalish(e_3,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172863552,plain,(~equalish(e_3,e_1)),inference(rewrite,[status(thm)],[e_3_is_not_e_1]),[]).
%
% cnf(182469776,plain,(~product1(e_1,e_3,e_3)),inference(resolution,[status(thm)],[182388328,172863552]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172840808,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(182174928,plain,(~product1(e_1,e_3,e_1)),inference(resolution,[status(thm)],[182150536,172840808]),[]).
%
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172828424,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% fof(e_2_is_not_e_3,plain,(~equalish(e_2,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172851960,plain,(~equalish(e_2,e_3)),inference(rewrite,[status(thm)],[e_2_is_not_e_3]),[]).
%
% cnf(182443840,plain,(~product1(e_3,e_2,e_2)),inference(resolution,[status(thm)],[182388328,172851960]),[]).
%
% fof(e_3_is_not_e_2,plain,(~equalish(e_3,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172867216,plain,(~equalish(e_3,e_2)),inference(rewrite,[status(thm)],[e_3_is_not_e_2]),[]).
%
% cnf(182253320,plain,(~product1(e_3,e_2,e_3)),inference(resolution,[status(thm)],[182150536,172867216]),[]).
%
% fof(qg2a,plain,(~product1(A,B,C)|~product1(C,A,D)|product2(D,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172971424,plain,(~product1(A,B,C)|~product1(C,A,D)|product2(D,B,A)),inference(rewrite,[status(thm)],[qg2a]),[]).
%
% fof(product2_total_function2,plain,(~product2(A,B,C)|~product2(A,B,D)|equalish(C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172949776,plain,(~product2(A,B,C)|~product2(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product2_total_function2]),[]).
%
% fof(product2_idempotence,plain,(product2(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172962232,plain,(product2(A,A,A)),inference(rewrite,[status(thm)],[product2_idempotence]),[]).
%
% cnf(182608632,plain,(~product2(A,A,B)|equalish(A,B)),inference(resolution,[status(thm)],[172949776,172962232]),[]).
%
% cnf(182665952,plain,(~product2(e_2,e_2,e_3)),inference(resolution,[status(thm)],[182608632,172851960]),[]).
%
% cnf(183300320,plain,(~product1(e_3,e_2,A)|~product1(A,e_3,e_2)),inference(resolution,[status(thm)],[172971424,182665952]),[]).
%
% cnf(186983288,plain,(product1(e_3,e_2,e_4)|~product1(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[182443840,182253320,172828424,172820608,172899184,183300320]),[]).
%
% cnf(181563864,plain,(~product1(e_1,A,B)|~product1(e_3,A,B)),inference(resolution,[status(thm)],[172922928,172840808]),[]).
%
% cnf(206155816,plain,(~product1(e_1,e_3,e_2)|~product1(e_1,e_2,e_4)),inference(resolution,[status(thm)],[186983288,181563864]),[]).
%
% cnf(213178088,plain,(~product1(e_1,e_2,e_4)|product1(e_1,e_3,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[182469776,182174928,172816480,172828424,206155816,172899184]),[]).
%
% cnf(181612672,plain,(~product1(A,e_2,B)|~product1(A,e_3,B)),inference(resolution,[status(thm)],[172919296,172851960]),[]).
%
% cnf(213235400,plain,(~product1(e_1,e_2,e_4)),inference(resolution,[status(thm)],[213178088,181612672]),[]).
%
% cnf(243900936,plain,(product1(e_1,e_2,e_3)),inference(resolution,[status(thm)],[243462896,213235400]),[]).
%
% fof(e_4_is_not_e_1,plain,(~equalish(e_4,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172874592,plain,(~equalish(e_4,e_1)),inference(rewrite,[status(thm)],[e_4_is_not_e_1]),[]).
%
% cnf(182509872,plain,(~product1(e_1,e_4,e_4)),inference(resolution,[status(thm)],[182388328,172874592]),[]).
%
% fof(element_4,plain,(group_element(e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172832136,plain,(group_element(e_4)),inference(rewrite,[status(thm)],[element_4]),[]).
%
% fof(e_1_is_not_e_4,plain,(~equalish(e_1,e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172844536,plain,(~equalish(e_1,e_4)),inference(rewrite,[status(thm)],[e_1_is_not_e_4]),[]).
%
% cnf(182189064,plain,(~product1(e_1,e_4,e_1)),inference(resolution,[status(thm)],[182150536,172844536]),[]).
%
% fof(e_2_is_not_e_4,plain,(~equalish(e_2,e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172859792,plain,(~equalish(e_2,e_4)),inference(rewrite,[status(thm)],[e_2_is_not_e_4]),[]).
%
% cnf(182457216,plain,(~product1(e_4,e_2,e_2)),inference(resolution,[status(thm)],[182388328,172859792]),[]).
%
% fof(e_4_is_not_e_2,plain,(~equalish(e_4,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-7.004.tptp',unknown),[]).
%
% cnf(172878240,plain,(~equalish(e_4,e_2)),inference(rewrite,[status(thm)],[e_4_is_not_e_2]),[]).
%
% cnf(182299912,plain,(~product1(e_4,e_2,e_4)),inference(resolution,[status(thm)],[182150536,172878240]),[]).
%
% cnf(182677848,plain,(~product2(e_2,e_2,e_4)),inference(resolution,[status(thm)],[182608632,172859792]),[]).
%
% cnf(183328632,plain,(~product1(e_4,e_2,A)|~product1(A,e_4,e_2)),inference(resolution,[status(thm)],[172971424,182677848]),[]).
%
% cnf(186998112,plain,(product1(e_4,e_2,e_3)|~product1(e_1,e_4,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[182457216,182299912,172832136,172820608,172899184,183328632]),[]).
%
% cnf(182355392,plain,(~product1(e_1,A,B)|~product1(e_4,A,B)),inference(resolution,[status(thm)],[172922928,172844536]),[]).
%
% cnf(206598016,plain,(~product1(e_1,e_4,e_2)|~product1(e_1,e_2,e_3)),inference(resolution,[status(thm)],[186998112,182355392]),[]).
%
% cnf(215400464,plain,(~product1(e_1,e_2,e_3)|product1(e_1,e_4,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[182509872,172832136,172816480,182189064,206598016,172899184]),[]).
%
% cnf(182135248,plain,(~product1(A,e_2,B)|~product1(A,e_4,B)),inference(resolution,[status(thm)],[172919296,172859792]),[]).
%
% cnf(215494096,plain,(~product1(e_1,e_2,e_3)),inference(resolution,[status(thm)],[215400464,182135248]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[243900936,215494096]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------