TSTP Solution File: GRP124-6.004 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP124-6.004 : TPTP v3.4.2. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 12:25:36 EDT 2009
% Result : Unsatisfiable 7.1s
% Output : Refutation 7.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 23
% Syntax : Number of formulae : 135 ( 70 unt; 0 def)
% Number of atoms : 220 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 237 ( 152 ~; 85 |; 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 : 78 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(element_2,plain,
group_element(e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145295832,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
fof(element_3,plain,
group_element(e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145299640,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
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/GRP124-6.004.tptp',unknown),
[] ).
cnf(145370280,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/GRP124-6.004.tptp',unknown),
[] ).
cnf(145386976,plain,
( ~ product1(A,B,C)
| ~ product1(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product1_right_cancellation]),
[] ).
fof(e_2_is_not_e_3,plain,
~ equalish(e_2,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145327080,plain,
~ equalish(e_2,e_3),
inference(rewrite,[status(thm)],[e_2_is_not_e_3]),
[] ).
cnf(153897232,plain,
( ~ product1(A,e_2,B)
| ~ product1(A,e_3,B) ),
inference(resolution,[status(thm)],[145386976,145327080]),
[] ).
fof(product1_idempotence,plain,
! [A] : product1(A,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145399072,plain,
product1(A,A,A),
inference(rewrite,[status(thm)],[product1_idempotence]),
[] ).
cnf(153991008,plain,
~ product1(e_3,e_2,e_3),
inference(resolution,[status(thm)],[153897232,145399072]),
[] ).
cnf(175164664,plain,
( product1(e_3,e_2,e_1)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[145295832,145299640,145370280,153991008]),
[] ).
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/GRP124-6.004.tptp',unknown),
[] ).
cnf(145390608,plain,
( ~ product1(A,B,C)
| ~ product1(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product1_left_cancellation]),
[] ).
cnf(154571488,plain,
( ~ product1(B,A,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[145390608,145399072]),
[] ).
fof(e_4_is_not_e_1,plain,
~ equalish(e_4,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145345688,plain,
~ equalish(e_4,e_1),
inference(rewrite,[status(thm)],[e_4_is_not_e_1]),
[] ).
cnf(154681840,plain,
~ product1(e_1,e_4,e_4),
inference(resolution,[status(thm)],[154571488,145345688]),
[] ).
fof(element_1,plain,
group_element(e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145291784,plain,
group_element(e_1),
inference(rewrite,[status(thm)],[element_1]),
[] ).
fof(element_4,plain,
group_element(e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145303384,plain,
group_element(e_4),
inference(rewrite,[status(thm)],[element_4]),
[] ).
cnf(154354736,plain,
( ~ product1(A,B,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[145386976,145399072]),
[] ).
fof(e_1_is_not_e_4,plain,
~ equalish(e_1,e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145315648,plain,
~ equalish(e_1,e_4),
inference(rewrite,[status(thm)],[e_1_is_not_e_4]),
[] ).
cnf(154394904,plain,
~ product1(e_1,e_4,e_1),
inference(resolution,[status(thm)],[154354736,145315648]),
[] ).
fof(e_4_is_not_e_3,plain,
~ equalish(e_4,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145357072,plain,
~ equalish(e_4,e_3),
inference(rewrite,[status(thm)],[e_4_is_not_e_3]),
[] ).
cnf(154708592,plain,
~ product1(e_3,e_4,e_4),
inference(resolution,[status(thm)],[154571488,145357072]),
[] ).
fof(e_3_is_not_e_4,plain,
~ equalish(e_3,e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145341880,plain,
~ equalish(e_3,e_4),
inference(rewrite,[status(thm)],[e_3_is_not_e_4]),
[] ).
cnf(154447448,plain,
~ product1(e_3,e_4,e_3),
inference(resolution,[status(thm)],[154354736,145341880]),
[] ).
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/GRP124-6.004.tptp',unknown),
[] ).
cnf(145438552,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/GRP124-6.004.tptp',unknown),
[] ).
cnf(145417232,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/GRP124-6.004.tptp',unknown),
[] ).
cnf(145429456,plain,
product2(A,A,A),
inference(rewrite,[status(thm)],[product2_idempotence]),
[] ).
cnf(154774816,plain,
( ~ product2(A,A,B)
| equalish(A,B) ),
inference(resolution,[status(thm)],[145417232,145429456]),
[] ).
cnf(154913296,plain,
~ product2(e_4,e_4,e_3),
inference(resolution,[status(thm)],[154774816,145357072]),
[] ).
cnf(155645760,plain,
( ~ product1(e_3,e_4,A)
| ~ product1(A,e_3,e_4) ),
inference(resolution,[status(thm)],[145438552,154913296]),
[] ).
cnf(175967688,plain,
( product1(e_3,e_4,e_1)
| ~ product1(e_2,e_3,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[154708592,154447448,145299640,145303384,145370280,155645760]),
[] ).
cnf(153904088,plain,
( ~ product1(e_2,A,B)
| ~ product1(e_3,A,B) ),
inference(resolution,[status(thm)],[145390608,145327080]),
[] ).
cnf(154018640,plain,
~ product1(e_2,e_3,e_3),
inference(resolution,[status(thm)],[153904088,145399072]),
[] ).
cnf(154091320,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[145295832,145299640,145370280,154018640]),
[] ).
cnf(153977736,plain,
~ product1(e_2,e_3,e_2),
inference(resolution,[status(thm)],[153897232,145399072]),
[] ).
cnf(154095840,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_4) ),
inference(resolution,[status(thm)],[154091320,153977736]),
[] ).
cnf(181245648,plain,
( product1(e_3,e_4,e_1)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[175967688,154095840]),
[] ).
fof(e_2_is_not_e_4,plain,
~ equalish(e_2,e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145288496,plain,
~ equalish(e_2,e_4),
inference(rewrite,[status(thm)],[e_2_is_not_e_4]),
[] ).
cnf(154543872,plain,
( ~ product1(e_2,A,B)
| ~ product1(e_4,A,B) ),
inference(resolution,[status(thm)],[145390608,145288496]),
[] ).
cnf(181618168,plain,
( product1(e_3,e_4,e_1)
| ~ product1(e_4,e_3,e_1) ),
inference(resolution,[status(thm)],[181245648,154543872]),
[] ).
fof(e_4_is_not_e_2,plain,
~ equalish(e_4,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145349336,plain,
~ equalish(e_4,e_2),
inference(rewrite,[status(thm)],[e_4_is_not_e_2]),
[] ).
cnf(154695216,plain,
~ product1(e_2,e_4,e_4),
inference(resolution,[status(thm)],[154571488,145349336]),
[] ).
cnf(154418312,plain,
~ product1(e_2,e_4,e_2),
inference(resolution,[status(thm)],[154354736,145288496]),
[] ).
cnf(154893288,plain,
~ product2(e_4,e_4,e_2),
inference(resolution,[status(thm)],[154774816,145349336]),
[] ).
cnf(155617512,plain,
( ~ product1(e_2,e_4,A)
| ~ product1(A,e_2,e_4) ),
inference(resolution,[status(thm)],[145438552,154893288]),
[] ).
cnf(175944880,plain,
( product1(e_2,e_4,e_3)
| ~ product1(e_1,e_2,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[154695216,154418312,145295832,145303384,145370280,155617512]),
[] ).
cnf(154494048,plain,
~ product1(e_4,e_3,e_4),
inference(resolution,[status(thm)],[154354736,145357072]),
[] ).
cnf(154668464,plain,
~ product1(e_4,e_3,e_3),
inference(resolution,[status(thm)],[154571488,145341880]),
[] ).
cnf(154869592,plain,
~ product2(e_3,e_3,e_4),
inference(resolution,[status(thm)],[154774816,145341880]),
[] ).
cnf(155578872,plain,
( ~ product1(e_4,e_3,A)
| ~ product1(A,e_4,e_3) ),
inference(resolution,[status(thm)],[145438552,154869592]),
[] ).
cnf(175924448,plain,
( product1(e_4,e_3,e_1)
| ~ product1(e_2,e_4,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[154494048,154668464,145299640,145303384,145370280,155578872]),
[] ).
cnf(180679408,plain,
( ~ product1(e_1,e_2,e_4)
| product1(e_4,e_3,e_1) ),
inference(resolution,[status(thm)],[175944880,175924448]),
[] ).
cnf(185998928,plain,
( product1(e_3,e_4,e_1)
| ~ product1(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[181618168,180679408]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145289272,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(154380736,plain,
~ product1(e_1,e_3,e_1),
inference(resolution,[status(thm)],[154354736,145289272]),
[] ).
fof(e_3_is_not_e_1,plain,
~ equalish(e_3,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145334664,plain,
~ equalish(e_3,e_1),
inference(rewrite,[status(thm)],[e_3_is_not_e_1]),
[] ).
cnf(154650200,plain,
~ product1(e_1,e_3,e_3),
inference(resolution,[status(thm)],[154571488,145334664]),
[] ).
cnf(154006176,plain,
~ product1(e_3,e_2,e_2),
inference(resolution,[status(thm)],[153904088,145399072]),
[] ).
cnf(154825464,plain,
~ product2(e_2,e_2,e_3),
inference(resolution,[status(thm)],[154774816,145327080]),
[] ).
cnf(155487792,plain,
( ~ product1(e_3,e_2,A)
| ~ product1(A,e_3,e_2) ),
inference(resolution,[status(thm)],[145438552,154825464]),
[] ).
cnf(175869936,plain,
( product1(e_3,e_2,e_4)
| ~ product1(e_1,e_3,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[154006176,153991008,145299640,145295832,145370280,155487792]),
[] ).
cnf(153839528,plain,
( ~ product1(e_1,A,B)
| ~ product1(e_3,A,B) ),
inference(resolution,[status(thm)],[145390608,145289272]),
[] ).
cnf(178064192,plain,
( ~ product1(e_1,e_3,e_2)
| ~ product1(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[175869936,153839528]),
[] ).
cnf(174113472,plain,
( ~ product1(e_1,e_2,e_4)
| product1(e_1,e_3,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[145299640,145291784,154380736,154650200,178064192,145370280]),
[] ).
cnf(174192128,plain,
~ product1(e_1,e_2,e_4),
inference(forward_subsumption_resolution__resolution,[status(thm)],[185998928,174113472,155645760]),
[] ).
fof(e_2_is_not_e_1,plain,
~ equalish(e_2,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145323512,plain,
~ equalish(e_2,e_1),
inference(rewrite,[status(thm)],[e_2_is_not_e_1]),
[] ).
cnf(154618592,plain,
~ product1(e_1,e_2,e_2),
inference(resolution,[status(thm)],[154571488,145323512]),
[] ).
fof(e_1_is_not_e_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145307888,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(154366600,plain,
~ product1(e_1,e_2,e_1),
inference(resolution,[status(thm)],[154354736,145307888]),
[] ).
cnf(154632736,plain,
~ product1(e_4,e_2,e_2),
inference(resolution,[status(thm)],[154571488,145288496]),
[] ).
cnf(154479880,plain,
~ product1(e_4,e_2,e_4),
inference(resolution,[status(thm)],[154354736,145349336]),
[] ).
cnf(154834064,plain,
~ product2(e_2,e_2,e_4),
inference(resolution,[status(thm)],[154774816,145288496]),
[] ).
cnf(155512048,plain,
( ~ product1(e_4,e_2,A)
| ~ product1(A,e_4,e_2) ),
inference(resolution,[status(thm)],[145438552,154834064]),
[] ).
cnf(175880664,plain,
( product1(e_4,e_2,e_3)
| ~ product1(e_1,e_4,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[154632736,154479880,145303384,145295832,145370280,155512048]),
[] ).
cnf(154538552,plain,
( ~ product1(e_1,A,B)
| ~ product1(e_4,A,B) ),
inference(resolution,[status(thm)],[145390608,145315648]),
[] ).
cnf(178435936,plain,
( ~ product1(e_1,e_4,e_2)
| ~ product1(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[175880664,154538552]),
[] ).
cnf(194048600,plain,
~ product1(e_1,e_4,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174192128,154618592,154366600,145295832,145291784,178435936,145370280]),
[] ).
cnf(175915776,plain,
( product1(e_4,e_3,e_2)
| ~ product1(e_1,e_4,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[154668464,154494048,145303384,145299640,145370280,155578872]),
[] ).
cnf(179564184,plain,
( ~ product1(e_1,e_4,e_3)
| ~ product1(e_3,e_2,e_4) ),
inference(resolution,[status(thm)],[175915776,155487792]),
[] ).
cnf(205413960,plain,
~ product1(e_3,e_2,e_4),
inference(forward_subsumption_resolution__resolution,[status(thm)],[154681840,145291784,145303384,154394904,194048600,179564184,145370280]),
[] ).
cnf(223579704,plain,
( product1(e_3,e_2,e_1)
| product1(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[175164664,205413960]),
[] ).
cnf(154583400,plain,
~ product1(e_2,e_1,e_1),
inference(resolution,[status(thm)],[154571488,145307888]),
[] ).
cnf(154403376,plain,
~ product1(e_2,e_1,e_2),
inference(resolution,[status(thm)],[154354736,145323512]),
[] ).
cnf(154845864,plain,
~ product2(e_3,e_3,e_1),
inference(resolution,[status(thm)],[154774816,145334664]),
[] ).
cnf(155531432,plain,
( ~ product1(e_1,e_3,A)
| ~ product1(A,e_1,e_3) ),
inference(resolution,[status(thm)],[145438552,154845864]),
[] ).
cnf(175895032,plain,
( product1(e_1,e_3,e_4)
| ~ product1(e_2,e_1,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[154650200,154380736,145299640,145291784,145370280,155531432]),
[] ).
cnf(178844192,plain,
( ~ product1(e_2,e_1,e_3)
| ~ product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[175895032,155645760]),
[] ).
cnf(202098544,plain,
( ~ product1(e_3,e_4,e_1)
| product1(e_2,e_1,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[145295832,145291784,154583400,154403376,178844192,145370280]),
[] ).
cnf(154881456,plain,
~ product2(e_4,e_4,e_1),
inference(resolution,[status(thm)],[154774816,145345688]),
[] ).
cnf(155598256,plain,
( ~ product1(e_1,e_4,A)
| ~ product1(A,e_1,e_4) ),
inference(resolution,[status(thm)],[145438552,154881456]),
[] ).
cnf(175934624,plain,
( product1(e_1,e_4,e_3)
| ~ product1(e_2,e_1,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[154681840,154394904,145303384,145291784,145370280,155598256]),
[] ).
cnf(180323400,plain,
( ~ product1(e_2,e_1,e_4)
| product1(e_4,e_3,e_2) ),
inference(resolution,[status(thm)],[175934624,175915776]),
[] ).
cnf(202308280,plain,
( ~ product1(e_3,e_4,e_1)
| product1(e_4,e_3,e_2) ),
inference(resolution,[status(thm)],[202098544,180323400]),
[] ).
cnf(203470224,plain,
( ~ product1(e_3,e_4,e_1)
| ~ product1(e_3,e_2,e_4) ),
inference(resolution,[status(thm)],[202308280,155487792]),
[] ).
cnf(154432480,plain,
~ product1(e_3,e_1,e_3),
inference(resolution,[status(thm)],[154354736,145334664]),
[] ).
cnf(154596744,plain,
~ product1(e_3,e_1,e_1),
inference(resolution,[status(thm)],[154571488,145289272]),
[] ).
cnf(153706064,plain,
( ~ product1(A,e_1,B)
| ~ product1(A,e_2,B) ),
inference(resolution,[status(thm)],[145386976,145307888]),
[] ).
cnf(178057424,plain,
( ~ product1(e_1,e_3,e_2)
| ~ product1(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[175869936,153706064]),
[] ).
cnf(190132664,plain,
( ~ product1(e_1,e_3,e_2)
| product1(e_3,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[154432480,154596744,145299640,145291784,178057424,145370280]),
[] ).
cnf(154795672,plain,
~ product2(e_1,e_1,e_3),
inference(resolution,[status(thm)],[154774816,145289272]),
[] ).
cnf(155415968,plain,
( ~ product1(e_3,e_1,A)
| ~ product1(A,e_3,e_1) ),
inference(resolution,[status(thm)],[145438552,154795672]),
[] ).
cnf(181684424,plain,
( product1(e_3,e_4,e_1)
| ~ product1(e_3,e_1,e_2) ),
inference(resolution,[status(thm)],[181245648,155415968]),
[] ).
cnf(190692680,plain,
( ~ product1(e_1,e_3,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[190132664,181684424]),
[] ).
cnf(218520528,plain,
~ product1(e_1,e_3,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[175869936,203470224,190692680]),
[] ).
cnf(175955064,plain,
( product1(e_3,e_4,e_2)
| ~ product1(e_1,e_3,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[154708592,154447448,145299640,145303384,145370280,155645760]),
[] ).
cnf(180970328,plain,
( ~ product1(e_1,e_3,e_4)
| ~ product1(e_4,e_2,e_3) ),
inference(resolution,[status(thm)],[175955064,155512048]),
[] ).
cnf(208727248,plain,
( ~ product1(e_1,e_3,e_4)
| product1(e_4,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[154632736,154479880,145303384,145295832,180970328,145370280]),
[] ).
cnf(154551456,plain,
( ~ product1(e_3,A,B)
| ~ product1(e_4,A,B) ),
inference(resolution,[status(thm)],[145390608,145341880]),
[] ).
cnf(208884160,plain,
( ~ product1(e_1,e_3,e_4)
| ~ product1(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[208727248,154551456]),
[] ).
cnf(219233296,plain,
~ product1(e_3,e_2,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[218520528,154650200,145291784,145299640,154380736,208884160,145370280]),
[] ).
cnf(223524936,plain,
( product1(e_3,e_2,e_1)
| product1(e_3,e_2,e_4) ),
inference(resolution,[status(thm)],[175164664,154006176]),
[] ).
fof(product1_total_function2,plain,
! [A,B,C,D] :
( ~ product1(A,B,C)
| ~ product1(A,B,D)
| equalish(C,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),
[] ).
cnf(145382648,plain,
( ~ product1(A,B,C)
| ~ product1(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product1_total_function2]),
[] ).
cnf(154127184,plain,
( ~ product1(A,B,e_2)
| ~ product1(A,B,e_4) ),
inference(resolution,[status(thm)],[145382648,145288496]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[223579704,219233296,223524936,154127184]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 7 seconds
% START OF PROOF SEQUENCE
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145295832,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145299640,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% 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/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145370280,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/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145386976,plain,(~product1(A,B,C)|~product1(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product1_right_cancellation]),[]).
%
% fof(e_2_is_not_e_3,plain,(~equalish(e_2,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145327080,plain,(~equalish(e_2,e_3)),inference(rewrite,[status(thm)],[e_2_is_not_e_3]),[]).
%
% cnf(153897232,plain,(~product1(A,e_2,B)|~product1(A,e_3,B)),inference(resolution,[status(thm)],[145386976,145327080]),[]).
%
% fof(product1_idempotence,plain,(product1(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145399072,plain,(product1(A,A,A)),inference(rewrite,[status(thm)],[product1_idempotence]),[]).
%
% cnf(153991008,plain,(~product1(e_3,e_2,e_3)),inference(resolution,[status(thm)],[153897232,145399072]),[]).
%
% cnf(175164664,plain,(product1(e_3,e_2,e_1)|product1(e_3,e_2,e_2)|product1(e_3,e_2,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[145295832,145299640,145370280,153991008]),[]).
%
% 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/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145390608,plain,(~product1(A,B,C)|~product1(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product1_left_cancellation]),[]).
%
% cnf(154571488,plain,(~product1(B,A,A)|equalish(A,B)),inference(resolution,[status(thm)],[145390608,145399072]),[]).
%
% fof(e_4_is_not_e_1,plain,(~equalish(e_4,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145345688,plain,(~equalish(e_4,e_1)),inference(rewrite,[status(thm)],[e_4_is_not_e_1]),[]).
%
% cnf(154681840,plain,(~product1(e_1,e_4,e_4)),inference(resolution,[status(thm)],[154571488,145345688]),[]).
%
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145291784,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
%
% fof(element_4,plain,(group_element(e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145303384,plain,(group_element(e_4)),inference(rewrite,[status(thm)],[element_4]),[]).
%
% cnf(154354736,plain,(~product1(A,B,A)|equalish(A,B)),inference(resolution,[status(thm)],[145386976,145399072]),[]).
%
% fof(e_1_is_not_e_4,plain,(~equalish(e_1,e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145315648,plain,(~equalish(e_1,e_4)),inference(rewrite,[status(thm)],[e_1_is_not_e_4]),[]).
%
% cnf(154394904,plain,(~product1(e_1,e_4,e_1)),inference(resolution,[status(thm)],[154354736,145315648]),[]).
%
% fof(e_4_is_not_e_3,plain,(~equalish(e_4,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145357072,plain,(~equalish(e_4,e_3)),inference(rewrite,[status(thm)],[e_4_is_not_e_3]),[]).
%
% cnf(154708592,plain,(~product1(e_3,e_4,e_4)),inference(resolution,[status(thm)],[154571488,145357072]),[]).
%
% fof(e_3_is_not_e_4,plain,(~equalish(e_3,e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145341880,plain,(~equalish(e_3,e_4)),inference(rewrite,[status(thm)],[e_3_is_not_e_4]),[]).
%
% cnf(154447448,plain,(~product1(e_3,e_4,e_3)),inference(resolution,[status(thm)],[154354736,145341880]),[]).
%
% fof(qg2a,plain,(~product1(A,B,C)|~product1(C,A,D)|product2(D,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145438552,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/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145417232,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/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145429456,plain,(product2(A,A,A)),inference(rewrite,[status(thm)],[product2_idempotence]),[]).
%
% cnf(154774816,plain,(~product2(A,A,B)|equalish(A,B)),inference(resolution,[status(thm)],[145417232,145429456]),[]).
%
% cnf(154913296,plain,(~product2(e_4,e_4,e_3)),inference(resolution,[status(thm)],[154774816,145357072]),[]).
%
% cnf(155645760,plain,(~product1(e_3,e_4,A)|~product1(A,e_3,e_4)),inference(resolution,[status(thm)],[145438552,154913296]),[]).
%
% cnf(175967688,plain,(product1(e_3,e_4,e_1)|~product1(e_2,e_3,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[154708592,154447448,145299640,145303384,145370280,155645760]),[]).
%
% cnf(153904088,plain,(~product1(e_2,A,B)|~product1(e_3,A,B)),inference(resolution,[status(thm)],[145390608,145327080]),[]).
%
% cnf(154018640,plain,(~product1(e_2,e_3,e_3)),inference(resolution,[status(thm)],[153904088,145399072]),[]).
%
% cnf(154091320,plain,(product1(e_2,e_3,e_1)|product1(e_2,e_3,e_2)|product1(e_2,e_3,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[145295832,145299640,145370280,154018640]),[]).
%
% cnf(153977736,plain,(~product1(e_2,e_3,e_2)),inference(resolution,[status(thm)],[153897232,145399072]),[]).
%
% cnf(154095840,plain,(product1(e_2,e_3,e_1)|product1(e_2,e_3,e_4)),inference(resolution,[status(thm)],[154091320,153977736]),[]).
%
% cnf(181245648,plain,(product1(e_3,e_4,e_1)|product1(e_2,e_3,e_1)),inference(resolution,[status(thm)],[175967688,154095840]),[]).
%
% fof(e_2_is_not_e_4,plain,(~equalish(e_2,e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145288496,plain,(~equalish(e_2,e_4)),inference(rewrite,[status(thm)],[e_2_is_not_e_4]),[]).
%
% cnf(154543872,plain,(~product1(e_2,A,B)|~product1(e_4,A,B)),inference(resolution,[status(thm)],[145390608,145288496]),[]).
%
% cnf(181618168,plain,(product1(e_3,e_4,e_1)|~product1(e_4,e_3,e_1)),inference(resolution,[status(thm)],[181245648,154543872]),[]).
%
% fof(e_4_is_not_e_2,plain,(~equalish(e_4,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145349336,plain,(~equalish(e_4,e_2)),inference(rewrite,[status(thm)],[e_4_is_not_e_2]),[]).
%
% cnf(154695216,plain,(~product1(e_2,e_4,e_4)),inference(resolution,[status(thm)],[154571488,145349336]),[]).
%
% cnf(154418312,plain,(~product1(e_2,e_4,e_2)),inference(resolution,[status(thm)],[154354736,145288496]),[]).
%
% cnf(154893288,plain,(~product2(e_4,e_4,e_2)),inference(resolution,[status(thm)],[154774816,145349336]),[]).
%
% cnf(155617512,plain,(~product1(e_2,e_4,A)|~product1(A,e_2,e_4)),inference(resolution,[status(thm)],[145438552,154893288]),[]).
%
% cnf(175944880,plain,(product1(e_2,e_4,e_3)|~product1(e_1,e_2,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[154695216,154418312,145295832,145303384,145370280,155617512]),[]).
%
% cnf(154494048,plain,(~product1(e_4,e_3,e_4)),inference(resolution,[status(thm)],[154354736,145357072]),[]).
%
% cnf(154668464,plain,(~product1(e_4,e_3,e_3)),inference(resolution,[status(thm)],[154571488,145341880]),[]).
%
% cnf(154869592,plain,(~product2(e_3,e_3,e_4)),inference(resolution,[status(thm)],[154774816,145341880]),[]).
%
% cnf(155578872,plain,(~product1(e_4,e_3,A)|~product1(A,e_4,e_3)),inference(resolution,[status(thm)],[145438552,154869592]),[]).
%
% cnf(175924448,plain,(product1(e_4,e_3,e_1)|~product1(e_2,e_4,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[154494048,154668464,145299640,145303384,145370280,155578872]),[]).
%
% cnf(180679408,plain,(~product1(e_1,e_2,e_4)|product1(e_4,e_3,e_1)),inference(resolution,[status(thm)],[175944880,175924448]),[]).
%
% cnf(185998928,plain,(product1(e_3,e_4,e_1)|~product1(e_1,e_2,e_4)),inference(resolution,[status(thm)],[181618168,180679408]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145289272,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(154380736,plain,(~product1(e_1,e_3,e_1)),inference(resolution,[status(thm)],[154354736,145289272]),[]).
%
% fof(e_3_is_not_e_1,plain,(~equalish(e_3,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145334664,plain,(~equalish(e_3,e_1)),inference(rewrite,[status(thm)],[e_3_is_not_e_1]),[]).
%
% cnf(154650200,plain,(~product1(e_1,e_3,e_3)),inference(resolution,[status(thm)],[154571488,145334664]),[]).
%
% cnf(154006176,plain,(~product1(e_3,e_2,e_2)),inference(resolution,[status(thm)],[153904088,145399072]),[]).
%
% cnf(154825464,plain,(~product2(e_2,e_2,e_3)),inference(resolution,[status(thm)],[154774816,145327080]),[]).
%
% cnf(155487792,plain,(~product1(e_3,e_2,A)|~product1(A,e_3,e_2)),inference(resolution,[status(thm)],[145438552,154825464]),[]).
%
% cnf(175869936,plain,(product1(e_3,e_2,e_4)|~product1(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[154006176,153991008,145299640,145295832,145370280,155487792]),[]).
%
% cnf(153839528,plain,(~product1(e_1,A,B)|~product1(e_3,A,B)),inference(resolution,[status(thm)],[145390608,145289272]),[]).
%
% cnf(178064192,plain,(~product1(e_1,e_3,e_2)|~product1(e_1,e_2,e_4)),inference(resolution,[status(thm)],[175869936,153839528]),[]).
%
% cnf(174113472,plain,(~product1(e_1,e_2,e_4)|product1(e_1,e_3,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[145299640,145291784,154380736,154650200,178064192,145370280]),[]).
%
% cnf(174192128,plain,(~product1(e_1,e_2,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[185998928,174113472,155645760]),[]).
%
% fof(e_2_is_not_e_1,plain,(~equalish(e_2,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145323512,plain,(~equalish(e_2,e_1)),inference(rewrite,[status(thm)],[e_2_is_not_e_1]),[]).
%
% cnf(154618592,plain,(~product1(e_1,e_2,e_2)),inference(resolution,[status(thm)],[154571488,145323512]),[]).
%
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145307888,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(154366600,plain,(~product1(e_1,e_2,e_1)),inference(resolution,[status(thm)],[154354736,145307888]),[]).
%
% cnf(154632736,plain,(~product1(e_4,e_2,e_2)),inference(resolution,[status(thm)],[154571488,145288496]),[]).
%
% cnf(154479880,plain,(~product1(e_4,e_2,e_4)),inference(resolution,[status(thm)],[154354736,145349336]),[]).
%
% cnf(154834064,plain,(~product2(e_2,e_2,e_4)),inference(resolution,[status(thm)],[154774816,145288496]),[]).
%
% cnf(155512048,plain,(~product1(e_4,e_2,A)|~product1(A,e_4,e_2)),inference(resolution,[status(thm)],[145438552,154834064]),[]).
%
% cnf(175880664,plain,(product1(e_4,e_2,e_3)|~product1(e_1,e_4,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[154632736,154479880,145303384,145295832,145370280,155512048]),[]).
%
% cnf(154538552,plain,(~product1(e_1,A,B)|~product1(e_4,A,B)),inference(resolution,[status(thm)],[145390608,145315648]),[]).
%
% cnf(178435936,plain,(~product1(e_1,e_4,e_2)|~product1(e_1,e_2,e_3)),inference(resolution,[status(thm)],[175880664,154538552]),[]).
%
% cnf(194048600,plain,(~product1(e_1,e_4,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174192128,154618592,154366600,145295832,145291784,178435936,145370280]),[]).
%
% cnf(175915776,plain,(product1(e_4,e_3,e_2)|~product1(e_1,e_4,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[154668464,154494048,145303384,145299640,145370280,155578872]),[]).
%
% cnf(179564184,plain,(~product1(e_1,e_4,e_3)|~product1(e_3,e_2,e_4)),inference(resolution,[status(thm)],[175915776,155487792]),[]).
%
% cnf(205413960,plain,(~product1(e_3,e_2,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[154681840,145291784,145303384,154394904,194048600,179564184,145370280]),[]).
%
% cnf(223579704,plain,(product1(e_3,e_2,e_1)|product1(e_3,e_2,e_2)),inference(resolution,[status(thm)],[175164664,205413960]),[]).
%
% cnf(154583400,plain,(~product1(e_2,e_1,e_1)),inference(resolution,[status(thm)],[154571488,145307888]),[]).
%
% cnf(154403376,plain,(~product1(e_2,e_1,e_2)),inference(resolution,[status(thm)],[154354736,145323512]),[]).
%
% cnf(154845864,plain,(~product2(e_3,e_3,e_1)),inference(resolution,[status(thm)],[154774816,145334664]),[]).
%
% cnf(155531432,plain,(~product1(e_1,e_3,A)|~product1(A,e_1,e_3)),inference(resolution,[status(thm)],[145438552,154845864]),[]).
%
% cnf(175895032,plain,(product1(e_1,e_3,e_4)|~product1(e_2,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[154650200,154380736,145299640,145291784,145370280,155531432]),[]).
%
% cnf(178844192,plain,(~product1(e_2,e_1,e_3)|~product1(e_3,e_4,e_1)),inference(resolution,[status(thm)],[175895032,155645760]),[]).
%
% cnf(202098544,plain,(~product1(e_3,e_4,e_1)|product1(e_2,e_1,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[145295832,145291784,154583400,154403376,178844192,145370280]),[]).
%
% cnf(154881456,plain,(~product2(e_4,e_4,e_1)),inference(resolution,[status(thm)],[154774816,145345688]),[]).
%
% cnf(155598256,plain,(~product1(e_1,e_4,A)|~product1(A,e_1,e_4)),inference(resolution,[status(thm)],[145438552,154881456]),[]).
%
% cnf(175934624,plain,(product1(e_1,e_4,e_3)|~product1(e_2,e_1,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[154681840,154394904,145303384,145291784,145370280,155598256]),[]).
%
% cnf(180323400,plain,(~product1(e_2,e_1,e_4)|product1(e_4,e_3,e_2)),inference(resolution,[status(thm)],[175934624,175915776]),[]).
%
% cnf(202308280,plain,(~product1(e_3,e_4,e_1)|product1(e_4,e_3,e_2)),inference(resolution,[status(thm)],[202098544,180323400]),[]).
%
% cnf(203470224,plain,(~product1(e_3,e_4,e_1)|~product1(e_3,e_2,e_4)),inference(resolution,[status(thm)],[202308280,155487792]),[]).
%
% cnf(154432480,plain,(~product1(e_3,e_1,e_3)),inference(resolution,[status(thm)],[154354736,145334664]),[]).
%
% cnf(154596744,plain,(~product1(e_3,e_1,e_1)),inference(resolution,[status(thm)],[154571488,145289272]),[]).
%
% cnf(153706064,plain,(~product1(A,e_1,B)|~product1(A,e_2,B)),inference(resolution,[status(thm)],[145386976,145307888]),[]).
%
% cnf(178057424,plain,(~product1(e_1,e_3,e_2)|~product1(e_3,e_1,e_4)),inference(resolution,[status(thm)],[175869936,153706064]),[]).
%
% cnf(190132664,plain,(~product1(e_1,e_3,e_2)|product1(e_3,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[154432480,154596744,145299640,145291784,178057424,145370280]),[]).
%
% cnf(154795672,plain,(~product2(e_1,e_1,e_3)),inference(resolution,[status(thm)],[154774816,145289272]),[]).
%
% cnf(155415968,plain,(~product1(e_3,e_1,A)|~product1(A,e_3,e_1)),inference(resolution,[status(thm)],[145438552,154795672]),[]).
%
% cnf(181684424,plain,(product1(e_3,e_4,e_1)|~product1(e_3,e_1,e_2)),inference(resolution,[status(thm)],[181245648,155415968]),[]).
%
% cnf(190692680,plain,(~product1(e_1,e_3,e_2)|product1(e_3,e_4,e_1)),inference(resolution,[status(thm)],[190132664,181684424]),[]).
%
% cnf(218520528,plain,(~product1(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[175869936,203470224,190692680]),[]).
%
% cnf(175955064,plain,(product1(e_3,e_4,e_2)|~product1(e_1,e_3,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[154708592,154447448,145299640,145303384,145370280,155645760]),[]).
%
% cnf(180970328,plain,(~product1(e_1,e_3,e_4)|~product1(e_4,e_2,e_3)),inference(resolution,[status(thm)],[175955064,155512048]),[]).
%
% cnf(208727248,plain,(~product1(e_1,e_3,e_4)|product1(e_4,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[154632736,154479880,145303384,145295832,180970328,145370280]),[]).
%
% cnf(154551456,plain,(~product1(e_3,A,B)|~product1(e_4,A,B)),inference(resolution,[status(thm)],[145390608,145341880]),[]).
%
% cnf(208884160,plain,(~product1(e_1,e_3,e_4)|~product1(e_3,e_2,e_1)),inference(resolution,[status(thm)],[208727248,154551456]),[]).
%
% cnf(219233296,plain,(~product1(e_3,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[218520528,154650200,145291784,145299640,154380736,208884160,145370280]),[]).
%
% cnf(223524936,plain,(product1(e_3,e_2,e_1)|product1(e_3,e_2,e_4)),inference(resolution,[status(thm)],[175164664,154006176]),[]).
%
% fof(product1_total_function2,plain,(~product1(A,B,C)|~product1(A,B,D)|equalish(C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-6.004.tptp',unknown),[]).
%
% cnf(145382648,plain,(~product1(A,B,C)|~product1(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product1_total_function2]),[]).
%
% cnf(154127184,plain,(~product1(A,B,e_2)|~product1(A,B,e_4)),inference(resolution,[status(thm)],[145382648,145288496]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[223579704,219233296,223524936,154127184]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------