TSTP Solution File: GRP133-1.003 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP133-1.003 : 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 12:28:45 EDT 2009
% Result : Unsatisfiable 7.2s
% Output : Refutation 7.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of formulae : 123 ( 27 unt; 0 def)
% Number of atoms : 282 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 329 ( 170 ~; 159 |; 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 : 105 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(element_3,plain,
group_element(e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-1.003.tptp',unknown),
[] ).
cnf(169316144,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
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/GRP133-1.003.tptp',unknown),
[] ).
cnf(169371264,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product_total_function2]),
[] ).
fof(e_1_is_not_e_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-1.003.tptp',unknown),
[] ).
cnf(169320664,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(177358168,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolution,[status(thm)],[169371264,169320664]),
[] ).
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/GRP133-1.003.tptp',unknown),
[] ).
cnf(169354984,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_1,plain,
group_element(e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-1.003.tptp',unknown),
[] ).
cnf(169308416,plain,
group_element(e_1),
inference(rewrite,[status(thm)],[element_1]),
[] ).
cnf(177171592,plain,
( ~ group_element(A)
| product(e_1,A,e_1)
| product(e_1,A,e_2)
| product(e_1,A,e_3) ),
inference(resolution,[status(thm)],[169354984,169308416]),
[] ).
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/GRP133-1.003.tptp',unknown),
[] ).
cnf(169375496,plain,
( ~ product(A,B,C)
| ~ product(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product_right_cancellation]),
[] ).
fof(e_2_is_not_e_3,plain,
~ equalish(e_2,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-1.003.tptp',unknown),
[] ).
cnf(169331944,plain,
~ equalish(e_2,e_3),
inference(rewrite,[status(thm)],[e_2_is_not_e_3]),
[] ).
cnf(177472560,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_3,B) ),
inference(resolution,[status(thm)],[169375496,169331944]),
[] ).
cnf(179885656,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ product(e_1,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169316144,177171592,177472560]),
[] ).
cnf(177195904,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)],[169354984,169308416]),
[] ).
cnf(177382608,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolution,[status(thm)],[169375496,169320664]),
[] ).
cnf(179220128,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)],[177195904,177382608]),
[] ).
fof(qg3,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(B,A,D)
| product(C,D,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-1.003.tptp',unknown),
[] ).
cnf(169383504,plain,
( ~ product(A,B,C)
| ~ product(B,A,D)
| product(C,D,A) ),
inference(rewrite,[status(thm)],[qg3]),
[] ).
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/GRP133-1.003.tptp',unknown),
[] ).
cnf(169379128,plain,
( ~ product(A,B,C)
| ~ product(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product_left_cancellation]),
[] ).
cnf(177414976,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolution,[status(thm)],[169379128,169320664]),
[] ).
cnf(177539792,plain,
( ~ product(A,B,e_2)
| ~ product(B,A,C)
| ~ product(e_1,C,A) ),
inference(resolution,[status(thm)],[169383504,177414976]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-1.003.tptp',unknown),
[] ).
cnf(169324584,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(177489288,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolution,[status(thm)],[169379128,169324584]),
[] ).
cnf(177592952,plain,
( ~ product(A,B,e_3)
| ~ product(B,A,C)
| ~ product(e_1,C,A) ),
inference(resolution,[status(thm)],[169383504,177489288]),
[] ).
cnf(193010672,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,A)
| ~ product(e_1,A,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[177539792,179220128,177592952]),
[] ).
cnf(177495352,plain,
( ~ product(e_2,A,B)
| ~ product(e_3,A,B) ),
inference(resolution,[status(thm)],[169379128,169331944]),
[] ).
cnf(177605176,plain,
( ~ product(A,B,e_3)
| ~ product(B,A,C)
| ~ product(e_2,C,A) ),
inference(resolution,[status(thm)],[169383504,177495352]),
[] ).
cnf(193023936,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_2,e_3,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[179220128,193010672,179220128,177605176]),
[] ).
cnf(193460368,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,A,e_2)
| ~ product(A,e_1,e_3) ),
inference(resolution,[status(thm)],[193023936,169383504]),
[] ).
cnf(177658792,plain,
( product(B,B,A)
| ~ product(B,C,A)
| ~ product(C,B,A) ),
inference(resolution,[status(thm)],[169383504,169383504]),
[] ).
cnf(177826256,plain,
( ~ product(e_3,B,A)
| ~ product(B,e_3,A)
| ~ product(e_1,e_3,A) ),
inference(resolution,[status(thm)],[177658792,177489288]),
[] ).
cnf(227942128,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_3,e_1,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[179885656,193460368,179885656,177826256]),
[] ).
cnf(192974104,plain,
( product(e_1,e_1,e_3)
| ~ product(e_1,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[179220128,179220128,177539792]),
[] ).
cnf(177466512,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolution,[status(thm)],[169375496,169324584]),
[] ).
cnf(193115128,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[192974104,177466512]),
[] ).
cnf(194710008,plain,
( ~ product(e_1,e_2,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169316144,193115128,177171592]),
[] ).
cnf(177431448,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_3) ),
inference(resolution,[status(thm)],[169371264,169324584]),
[] ).
cnf(227699016,plain,
( product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[194710008,179885656,177431448]),
[] ).
cnf(177569256,plain,
( ~ product(A,B,C)
| ~ product(B,A,e_3)
| ~ product(C,e_1,A) ),
inference(resolution,[status(thm)],[169383504,177466512]),
[] ).
cnf(182932920,plain,
( ~ product(e_3,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[177195904,177569256,177195904]),
[] ).
cnf(179273984,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| ~ product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[177195904,177489288]),
[] ).
cnf(196376944,plain,
( product(e_1,e_1,e_2)
| ~ product(e_3,e_1,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[182932920,179273984,177431448]),
[] ).
cnf(196692568,plain,
( ~ product(e_3,e_1,e_1)
| ~ product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[196376944,177466512]),
[] ).
cnf(177563856,plain,
( ~ product(A,B,C)
| ~ product(B,A,e_1)
| ~ product(C,e_3,A) ),
inference(resolution,[status(thm)],[169383504,177466512]),
[] ).
cnf(179173328,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ product(e_3,e_1,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169308416,169316144,169354984,177563856]),
[] ).
cnf(201624728,plain,
( ~ product(e_3,e_1,e_1)
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[196692568,179173328]),
[] ).
cnf(201652336,plain,
( ~ product(e_3,e_1,e_1)
| ~ product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[201624728,177472560]),
[] ).
fof(element_2,plain,
group_element(e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-1.003.tptp',unknown),
[] ).
cnf(169312368,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
cnf(177294760,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)],[169354984,169312368]),
[] ).
cnf(177341400,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)],[177294760,169308416]),
[] ).
cnf(180304216,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_3)
| ~ product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[177341400,177382608]),
[] ).
cnf(192996472,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_3,e_1,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[179273984,177539792,179220128,177569256]),
[] ).
cnf(248067696,plain,
~ product(e_3,e_1,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[201652336,196376944,180304216,192996472]),
[] ).
cnf(177219568,plain,
( ~ group_element(A)
| product(A,e_1,e_1)
| product(A,e_1,e_2)
| product(A,e_1,e_3) ),
inference(resolution,[status(thm)],[169354984,169308416]),
[] ).
cnf(248382824,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169316144,248067696,177219568]),
[] ).
cnf(248907880,plain,
~ product(e_1,e_2,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[227942128,227699016,248382824,177539792]),
[] ).
cnf(249408456,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[248907880,177341400]),
[] ).
cnf(249556584,plain,
( product(e_1,e_2,e_2)
| ~ product(e_3,e_2,e_3) ),
inference(resolution,[status(thm)],[249408456,177489288]),
[] ).
cnf(248712424,plain,
( product(e_3,e_1,e_2)
| ~ product(e_3,e_2,e_3) ),
inference(resolution,[status(thm)],[248382824,177382608]),
[] ).
cnf(177267040,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[169354984,169312368]),
[] ).
cnf(182947096,plain,
( ~ product(e_3,e_1,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[177267040,177569256,177267040]),
[] ).
cnf(177705608,plain,
( ~ product(e_1,B,A)
| ~ product(B,e_1,A)
| ~ product(e_1,e_2,A) ),
inference(resolution,[status(thm)],[177658792,177382608]),
[] ).
cnf(185347840,plain,
( ~ product(e_1,e_2,A)
| ~ product(A,B,e_1)
| ~ product(B,A,e_1) ),
inference(resolution,[status(thm)],[177705608,169383504]),
[] ).
cnf(179546552,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_3)
| ~ product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[177267040,177414976]),
[] ).
cnf(177528376,plain,
( ~ product(A,B,C)
| ~ product(B,A,e_2)
| ~ product(C,e_1,A) ),
inference(resolution,[status(thm)],[169383504,177382608]),
[] ).
cnf(204424496,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_3,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[182947096,185347840,179546552,177528376]),
[] ).
cnf(252428160,plain,
~ product(e_3,e_2,e_3),
inference(forward_subsumption_resolution__resolution,[status(thm)],[249556584,248712424,204424496]),
[] ).
cnf(252592888,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169316144,252428160,177294760]),
[] ).
cnf(177818016,plain,
( ~ product(e_3,B,A)
| ~ product(B,e_3,A)
| ~ product(e_3,e_2,A) ),
inference(resolution,[status(thm)],[177658792,177472560]),
[] ).
cnf(253528552,plain,
( ~ product(e_2,e_3,e_1)
| ~ product(e_3,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[177358168,252592888,177818016]),
[] ).
cnf(177581536,plain,
( ~ product(A,B,C)
| ~ product(B,A,e_3)
| ~ product(C,e_2,A) ),
inference(resolution,[status(thm)],[169383504,177472560]),
[] ).
cnf(183564336,plain,
( ~ product(e_3,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[177267040,177581536,177267040]),
[] ).
cnf(179606128,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_3)
| ~ product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[177267040,177495352]),
[] ).
cnf(177449616,plain,
( ~ product(A,B,e_2)
| ~ product(A,B,e_3) ),
inference(resolution,[status(thm)],[169371264,169331944]),
[] ).
cnf(208107264,plain,
( product(e_2,e_2,e_1)
| ~ product(e_3,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[183564336,179606128,177449616]),
[] ).
cnf(253475376,plain,
( product(e_3,e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[252592888,208107264]),
[] ).
cnf(254137840,plain,
( product(e_2,e_2,e_1)
| ~ product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[253475376,177472560]),
[] ).
cnf(254271200,plain,
( product(e_2,e_2,e_1)
| ~ product(e_2,e_3,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[254137840,253475376,177658792]),
[] ).
cnf(177800304,plain,
( ~ product(e_2,B,A)
| ~ product(B,e_2,A)
| ~ product(e_2,e_3,A) ),
inference(resolution,[status(thm)],[177658792,177472560]),
[] ).
cnf(254404664,plain,
~ product(e_2,e_3,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[253528552,254271200,253475376,177800304]),
[] ).
cnf(184696536,plain,
( ~ product(e_2,e_3,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[177267040,177605176,177267040]),
[] ).
cnf(179575088,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_3)
| ~ product(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[177267040,177472560]),
[] ).
cnf(206847760,plain,
( product(e_2,e_2,e_1)
| ~ product(e_2,e_3,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[184696536,179575088,177449616]),
[] ).
cnf(207251536,plain,
( ~ product(e_2,e_3,e_2)
| ~ product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[206847760,177495352]),
[] ).
cnf(177692080,plain,
( ~ product(A,B,e_2)
| ~ product(B,A,e_2)
| ~ product(A,A,e_1) ),
inference(resolution,[status(thm)],[177658792,177358168]),
[] ).
cnf(253470960,plain,
~ product(e_2,e_3,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[207251536,206847760,252592888,177692080]),
[] ).
cnf(177243640,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)],[169354984,169312368]),
[] ).
cnf(253899168,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169316144,253470960,177243640]),
[] ).
cnf(255482216,plain,
~ product(e_1,e_3,e_3),
inference(forward_subsumption_resolution__resolution,[status(thm)],[254404664,253899168,177414976]),
[] ).
cnf(257054176,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169316144,255482216,177171592]),
[] ).
cnf(184105432,plain,
( ~ product(e_1,e_3,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[177267040,177592952,177267040]),
[] ).
cnf(179842920,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| ~ product(e_1,e_3,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[177267040,177267040,177563856]),
[] ).
cnf(221616608,plain,
( product(e_2,e_2,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[184105432,179842920,177431448]),
[] ).
cnf(177522976,plain,
( ~ product(A,B,C)
| ~ product(B,A,e_1)
| ~ product(C,e_2,A) ),
inference(resolution,[status(thm)],[169383504,177382608]),
[] ).
cnf(179762360,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| ~ product(e_1,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[177267040,177267040,177522976]),
[] ).
cnf(204267240,plain,
( product(e_2,e_2,e_3)
| ~ product(e_1,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[179762360,179546552,177358168]),
[] ).
cnf(204649032,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[204267240,177472560]),
[] ).
cnf(250087528,plain,
( product(e_1,e_2,e_3)
| ~ product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[249408456,204649032]),
[] ).
cnf(254331200,plain,
( product(e_2,e_2,e_1)
| ~ product(e_2,e_3,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[250087528,253475376,177581536]),
[] ).
cnf(255586960,plain,
product(e_2,e_2,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[253475376,254331200,253899168,177658792]),
[] ).
cnf(177573720,plain,
( ~ product(A,B,C)
| ~ product(B,A,e_2)
| ~ product(C,e_3,A) ),
inference(resolution,[status(thm)],[169383504,177472560]),
[] ).
cnf(256663904,plain,
~ product(e_1,e_3,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[221616608,255586960,177573720]),
[] ).
cnf(267683088,plain,
product(e_1,e_3,e_1),
inference(resolution,[status(thm)],[257054176,256663904]),
[] ).
cnf(253173904,plain,
( product(e_3,e_2,e_1)
| ~ product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[252592888,177472560]),
[] ).
cnf(255471952,plain,
product(e_2,e_3,e_3),
inference(resolution,[status(thm)],[253899168,254404664]),
[] ).
cnf(256119400,plain,
~ product(e_3,e_3,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[253173904,255471952,177563856]),
[] ).
cnf(255497576,plain,
~ product(e_3,e_3,e_3),
inference(forward_subsumption_resolution__resolution,[status(thm)],[254404664,253899168,177495352]),
[] ).
cnf(177559296,plain,
( ~ product(e_3,A,B)
| ~ product(A,e_3,C)
| ~ product(B,C,e_2) ),
inference(resolution,[status(thm)],[169383504,177449616]),
[] ).
cnf(179111664,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| ~ product(e_1,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169316144,169354984,177559296]),
[] ).
cnf(257952376,plain,
~ product(e_1,e_1,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[256119400,255497576,179111664]),
[] ).
cnf(184090832,plain,
( ~ product(e_1,e_3,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[177195904,177592952,177195904]),
[] ).
cnf(179256800,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| ~ product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[177195904,177466512]),
[] ).
cnf(195453576,plain,
( product(e_1,e_1,e_2)
| ~ product(e_1,e_3,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[184090832,179256800,177431448]),
[] ).
cnf(261971624,plain,
~ product(e_1,e_3,e_1),
inference(resolution,[status(thm)],[257952376,195453576]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[267683088,261971624]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 7 seconds
% START OF PROOF SEQUENCE
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-1.003.tptp',unknown),[]).
%
% cnf(169316144,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% 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/GRP133-1.003.tptp',unknown),[]).
%
% cnf(169371264,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product_total_function2]),[]).
%
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-1.003.tptp',unknown),[]).
%
% cnf(169320664,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(177358168,plain,(~product(A,B,e_1)|~product(A,B,e_2)),inference(resolution,[status(thm)],[169371264,169320664]),[]).
%
% 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/GRP133-1.003.tptp',unknown),[]).
%
% cnf(169354984,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_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-1.003.tptp',unknown),[]).
%
% cnf(169308416,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
%
% cnf(177171592,plain,(~group_element(A)|product(e_1,A,e_1)|product(e_1,A,e_2)|product(e_1,A,e_3)),inference(resolution,[status(thm)],[169354984,169308416]),[]).
%
% 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/GRP133-1.003.tptp',unknown),[]).
%
% cnf(169375496,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product_right_cancellation]),[]).
%
% fof(e_2_is_not_e_3,plain,(~equalish(e_2,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-1.003.tptp',unknown),[]).
%
% cnf(169331944,plain,(~equalish(e_2,e_3)),inference(rewrite,[status(thm)],[e_2_is_not_e_3]),[]).
%
% cnf(177472560,plain,(~product(A,e_2,B)|~product(A,e_3,B)),inference(resolution,[status(thm)],[169375496,169331944]),[]).
%
% cnf(179885656,plain,(product(e_1,e_3,e_2)|product(e_1,e_3,e_3)|~product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169316144,177171592,177472560]),[]).
%
% cnf(177195904,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)],[169354984,169308416]),[]).
%
% cnf(177382608,plain,(~product(A,e_1,B)|~product(A,e_2,B)),inference(resolution,[status(thm)],[169375496,169320664]),[]).
%
% cnf(179220128,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)],[177195904,177382608]),[]).
%
% fof(qg3,plain,(~product(A,B,C)|~product(B,A,D)|product(C,D,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-1.003.tptp',unknown),[]).
%
% cnf(169383504,plain,(~product(A,B,C)|~product(B,A,D)|product(C,D,A)),inference(rewrite,[status(thm)],[qg3]),[]).
%
% 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/GRP133-1.003.tptp',unknown),[]).
%
% cnf(169379128,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product_left_cancellation]),[]).
%
% cnf(177414976,plain,(~product(e_1,A,B)|~product(e_2,A,B)),inference(resolution,[status(thm)],[169379128,169320664]),[]).
%
% cnf(177539792,plain,(~product(A,B,e_2)|~product(B,A,C)|~product(e_1,C,A)),inference(resolution,[status(thm)],[169383504,177414976]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-1.003.tptp',unknown),[]).
%
% cnf(169324584,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(177489288,plain,(~product(e_1,A,B)|~product(e_3,A,B)),inference(resolution,[status(thm)],[169379128,169324584]),[]).
%
% cnf(177592952,plain,(~product(A,B,e_3)|~product(B,A,C)|~product(e_1,C,A)),inference(resolution,[status(thm)],[169383504,177489288]),[]).
%
% cnf(193010672,plain,(~product(e_1,e_2,e_1)|~product(e_1,e_1,A)|~product(e_1,A,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177539792,179220128,177592952]),[]).
%
% cnf(177495352,plain,(~product(e_2,A,B)|~product(e_3,A,B)),inference(resolution,[status(thm)],[169379128,169331944]),[]).
%
% cnf(177605176,plain,(~product(A,B,e_3)|~product(B,A,C)|~product(e_2,C,A)),inference(resolution,[status(thm)],[169383504,177495352]),[]).
%
% cnf(193023936,plain,(~product(e_1,e_2,e_1)|~product(e_2,e_3,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[179220128,193010672,179220128,177605176]),[]).
%
% cnf(193460368,plain,(~product(e_1,e_2,e_1)|~product(e_1,A,e_2)|~product(A,e_1,e_3)),inference(resolution,[status(thm)],[193023936,169383504]),[]).
%
% cnf(177658792,plain,(product(B,B,A)|~product(B,C,A)|~product(C,B,A)),inference(resolution,[status(thm)],[169383504,169383504]),[]).
%
% cnf(177826256,plain,(~product(e_3,B,A)|~product(B,e_3,A)|~product(e_1,e_3,A)),inference(resolution,[status(thm)],[177658792,177489288]),[]).
%
% cnf(227942128,plain,(~product(e_1,e_2,e_1)|~product(e_3,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[179885656,193460368,179885656,177826256]),[]).
%
% cnf(192974104,plain,(product(e_1,e_1,e_3)|~product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[179220128,179220128,177539792]),[]).
%
% cnf(177466512,plain,(~product(A,e_1,B)|~product(A,e_3,B)),inference(resolution,[status(thm)],[169375496,169324584]),[]).
%
% cnf(193115128,plain,(~product(e_1,e_2,e_1)|~product(e_1,e_3,e_3)),inference(resolution,[status(thm)],[192974104,177466512]),[]).
%
% cnf(194710008,plain,(~product(e_1,e_2,e_1)|product(e_1,e_3,e_1)|product(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169316144,193115128,177171592]),[]).
%
% cnf(177431448,plain,(~product(A,B,e_1)|~product(A,B,e_3)),inference(resolution,[status(thm)],[169371264,169324584]),[]).
%
% cnf(227699016,plain,(product(e_1,e_3,e_2)|~product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[194710008,179885656,177431448]),[]).
%
% cnf(177569256,plain,(~product(A,B,C)|~product(B,A,e_3)|~product(C,e_1,A)),inference(resolution,[status(thm)],[169383504,177466512]),[]).
%
% cnf(182932920,plain,(~product(e_3,e_1,e_1)|product(e_1,e_1,e_1)|product(e_1,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177195904,177569256,177195904]),[]).
%
% cnf(179273984,plain,(product(e_1,e_1,e_2)|product(e_1,e_1,e_3)|~product(e_3,e_1,e_1)),inference(resolution,[status(thm)],[177195904,177489288]),[]).
%
% cnf(196376944,plain,(product(e_1,e_1,e_2)|~product(e_3,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[182932920,179273984,177431448]),[]).
%
% cnf(196692568,plain,(~product(e_3,e_1,e_1)|~product(e_1,e_3,e_2)),inference(resolution,[status(thm)],[196376944,177466512]),[]).
%
% cnf(177563856,plain,(~product(A,B,C)|~product(B,A,e_1)|~product(C,e_3,A)),inference(resolution,[status(thm)],[169383504,177466512]),[]).
%
% cnf(179173328,plain,(product(e_1,e_3,e_2)|product(e_1,e_3,e_3)|~product(e_3,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169308416,169316144,169354984,177563856]),[]).
%
% cnf(201624728,plain,(~product(e_3,e_1,e_1)|product(e_1,e_3,e_3)),inference(resolution,[status(thm)],[196692568,179173328]),[]).
%
% cnf(201652336,plain,(~product(e_3,e_1,e_1)|~product(e_1,e_2,e_3)),inference(resolution,[status(thm)],[201624728,177472560]),[]).
%
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-1.003.tptp',unknown),[]).
%
% cnf(169312368,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% cnf(177294760,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)],[169354984,169312368]),[]).
%
% cnf(177341400,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)],[177294760,169308416]),[]).
%
% cnf(180304216,plain,(product(e_1,e_2,e_1)|product(e_1,e_2,e_3)|~product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[177341400,177382608]),[]).
%
% cnf(192996472,plain,(~product(e_1,e_2,e_1)|~product(e_3,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[179273984,177539792,179220128,177569256]),[]).
%
% cnf(248067696,plain,(~product(e_3,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[201652336,196376944,180304216,192996472]),[]).
%
% cnf(177219568,plain,(~group_element(A)|product(A,e_1,e_1)|product(A,e_1,e_2)|product(A,e_1,e_3)),inference(resolution,[status(thm)],[169354984,169308416]),[]).
%
% cnf(248382824,plain,(product(e_3,e_1,e_2)|product(e_3,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169316144,248067696,177219568]),[]).
%
% cnf(248907880,plain,(~product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[227942128,227699016,248382824,177539792]),[]).
%
% cnf(249408456,plain,(product(e_1,e_2,e_2)|product(e_1,e_2,e_3)),inference(resolution,[status(thm)],[248907880,177341400]),[]).
%
% cnf(249556584,plain,(product(e_1,e_2,e_2)|~product(e_3,e_2,e_3)),inference(resolution,[status(thm)],[249408456,177489288]),[]).
%
% cnf(248712424,plain,(product(e_3,e_1,e_2)|~product(e_3,e_2,e_3)),inference(resolution,[status(thm)],[248382824,177382608]),[]).
%
% cnf(177267040,plain,(product(e_2,e_2,e_1)|product(e_2,e_2,e_2)|product(e_2,e_2,e_3)),inference(resolution,[status(thm)],[169354984,169312368]),[]).
%
% cnf(182947096,plain,(~product(e_3,e_1,e_2)|product(e_2,e_2,e_1)|product(e_2,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177267040,177569256,177267040]),[]).
%
% cnf(177705608,plain,(~product(e_1,B,A)|~product(B,e_1,A)|~product(e_1,e_2,A)),inference(resolution,[status(thm)],[177658792,177382608]),[]).
%
% cnf(185347840,plain,(~product(e_1,e_2,A)|~product(A,B,e_1)|~product(B,A,e_1)),inference(resolution,[status(thm)],[177705608,169383504]),[]).
%
% cnf(179546552,plain,(product(e_2,e_2,e_1)|product(e_2,e_2,e_3)|~product(e_1,e_2,e_2)),inference(resolution,[status(thm)],[177267040,177414976]),[]).
%
% cnf(177528376,plain,(~product(A,B,C)|~product(B,A,e_2)|~product(C,e_1,A)),inference(resolution,[status(thm)],[169383504,177382608]),[]).
%
% cnf(204424496,plain,(~product(e_1,e_2,e_2)|~product(e_3,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[182947096,185347840,179546552,177528376]),[]).
%
% cnf(252428160,plain,(~product(e_3,e_2,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[249556584,248712424,204424496]),[]).
%
% cnf(252592888,plain,(product(e_3,e_2,e_1)|product(e_3,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169316144,252428160,177294760]),[]).
%
% cnf(177818016,plain,(~product(e_3,B,A)|~product(B,e_3,A)|~product(e_3,e_2,A)),inference(resolution,[status(thm)],[177658792,177472560]),[]).
%
% cnf(253528552,plain,(~product(e_2,e_3,e_1)|~product(e_3,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177358168,252592888,177818016]),[]).
%
% cnf(177581536,plain,(~product(A,B,C)|~product(B,A,e_3)|~product(C,e_2,A)),inference(resolution,[status(thm)],[169383504,177472560]),[]).
%
% cnf(183564336,plain,(~product(e_3,e_2,e_2)|product(e_2,e_2,e_1)|product(e_2,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177267040,177581536,177267040]),[]).
%
% cnf(179606128,plain,(product(e_2,e_2,e_1)|product(e_2,e_2,e_3)|~product(e_3,e_2,e_2)),inference(resolution,[status(thm)],[177267040,177495352]),[]).
%
% cnf(177449616,plain,(~product(A,B,e_2)|~product(A,B,e_3)),inference(resolution,[status(thm)],[169371264,169331944]),[]).
%
% cnf(208107264,plain,(product(e_2,e_2,e_1)|~product(e_3,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[183564336,179606128,177449616]),[]).
%
% cnf(253475376,plain,(product(e_3,e_2,e_1)|product(e_2,e_2,e_1)),inference(resolution,[status(thm)],[252592888,208107264]),[]).
%
% cnf(254137840,plain,(product(e_2,e_2,e_1)|~product(e_3,e_3,e_1)),inference(resolution,[status(thm)],[253475376,177472560]),[]).
%
% cnf(254271200,plain,(product(e_2,e_2,e_1)|~product(e_2,e_3,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[254137840,253475376,177658792]),[]).
%
% cnf(177800304,plain,(~product(e_2,B,A)|~product(B,e_2,A)|~product(e_2,e_3,A)),inference(resolution,[status(thm)],[177658792,177472560]),[]).
%
% cnf(254404664,plain,(~product(e_2,e_3,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[253528552,254271200,253475376,177800304]),[]).
%
% cnf(184696536,plain,(~product(e_2,e_3,e_2)|product(e_2,e_2,e_1)|product(e_2,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177267040,177605176,177267040]),[]).
%
% cnf(179575088,plain,(product(e_2,e_2,e_1)|product(e_2,e_2,e_3)|~product(e_2,e_3,e_2)),inference(resolution,[status(thm)],[177267040,177472560]),[]).
%
% cnf(206847760,plain,(product(e_2,e_2,e_1)|~product(e_2,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[184696536,179575088,177449616]),[]).
%
% cnf(207251536,plain,(~product(e_2,e_3,e_2)|~product(e_3,e_2,e_1)),inference(resolution,[status(thm)],[206847760,177495352]),[]).
%
% cnf(177692080,plain,(~product(A,B,e_2)|~product(B,A,e_2)|~product(A,A,e_1)),inference(resolution,[status(thm)],[177658792,177358168]),[]).
%
% cnf(253470960,plain,(~product(e_2,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[207251536,206847760,252592888,177692080]),[]).
%
% cnf(177243640,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)],[169354984,169312368]),[]).
%
% cnf(253899168,plain,(product(e_2,e_3,e_1)|product(e_2,e_3,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169316144,253470960,177243640]),[]).
%
% cnf(255482216,plain,(~product(e_1,e_3,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[254404664,253899168,177414976]),[]).
%
% cnf(257054176,plain,(product(e_1,e_3,e_1)|product(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169316144,255482216,177171592]),[]).
%
% cnf(184105432,plain,(~product(e_1,e_3,e_2)|product(e_2,e_2,e_1)|product(e_2,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177267040,177592952,177267040]),[]).
%
% cnf(179842920,plain,(product(e_2,e_2,e_2)|product(e_2,e_2,e_3)|~product(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177267040,177267040,177563856]),[]).
%
% cnf(221616608,plain,(product(e_2,e_2,e_2)|~product(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[184105432,179842920,177431448]),[]).
%
% cnf(177522976,plain,(~product(A,B,C)|~product(B,A,e_1)|~product(C,e_2,A)),inference(resolution,[status(thm)],[169383504,177382608]),[]).
%
% cnf(179762360,plain,(product(e_2,e_2,e_2)|product(e_2,e_2,e_3)|~product(e_1,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177267040,177267040,177522976]),[]).
%
% cnf(204267240,plain,(product(e_2,e_2,e_3)|~product(e_1,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[179762360,179546552,177358168]),[]).
%
% cnf(204649032,plain,(~product(e_1,e_2,e_2)|~product(e_2,e_3,e_3)),inference(resolution,[status(thm)],[204267240,177472560]),[]).
%
% cnf(250087528,plain,(product(e_1,e_2,e_3)|~product(e_2,e_3,e_3)),inference(resolution,[status(thm)],[249408456,204649032]),[]).
%
% cnf(254331200,plain,(product(e_2,e_2,e_1)|~product(e_2,e_3,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[250087528,253475376,177581536]),[]).
%
% cnf(255586960,plain,(product(e_2,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[253475376,254331200,253899168,177658792]),[]).
%
% cnf(177573720,plain,(~product(A,B,C)|~product(B,A,e_2)|~product(C,e_3,A)),inference(resolution,[status(thm)],[169383504,177472560]),[]).
%
% cnf(256663904,plain,(~product(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[221616608,255586960,177573720]),[]).
%
% cnf(267683088,plain,(product(e_1,e_3,e_1)),inference(resolution,[status(thm)],[257054176,256663904]),[]).
%
% cnf(253173904,plain,(product(e_3,e_2,e_1)|~product(e_3,e_3,e_2)),inference(resolution,[status(thm)],[252592888,177472560]),[]).
%
% cnf(255471952,plain,(product(e_2,e_3,e_3)),inference(resolution,[status(thm)],[253899168,254404664]),[]).
%
% cnf(256119400,plain,(~product(e_3,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[253173904,255471952,177563856]),[]).
%
% cnf(255497576,plain,(~product(e_3,e_3,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[254404664,253899168,177495352]),[]).
%
% cnf(177559296,plain,(~product(e_3,A,B)|~product(A,e_3,C)|~product(B,C,e_2)),inference(resolution,[status(thm)],[169383504,177449616]),[]).
%
% cnf(179111664,plain,(product(e_3,e_3,e_2)|product(e_3,e_3,e_3)|~product(e_1,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169316144,169354984,177559296]),[]).
%
% cnf(257952376,plain,(~product(e_1,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[256119400,255497576,179111664]),[]).
%
% cnf(184090832,plain,(~product(e_1,e_3,e_1)|product(e_1,e_1,e_1)|product(e_1,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177195904,177592952,177195904]),[]).
%
% cnf(179256800,plain,(product(e_1,e_1,e_2)|product(e_1,e_1,e_3)|~product(e_1,e_3,e_1)),inference(resolution,[status(thm)],[177195904,177466512]),[]).
%
% cnf(195453576,plain,(product(e_1,e_1,e_2)|~product(e_1,e_3,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[184090832,179256800,177431448]),[]).
%
% cnf(261971624,plain,(~product(e_1,e_3,e_1)),inference(resolution,[status(thm)],[257952376,195453576]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[267683088,261971624]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------