TSTP Solution File: GRP120-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP120-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 12:56:06 EDT 2022
% Result : Unsatisfiable 9.77s 9.98s
% Output : Refutation 9.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 3
% Syntax : Number of clauses : 82 ( 82 unt; 0 nHn; 3 RR)
% Number of literals : 82 ( 81 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 123 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(identity,a) != a,
file('GRP120-1.p',unknown),
[] ).
cnf(3,axiom,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(B,C))),multiply(C,multiply(C,C)))) = B,
file('GRP120-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(identity,identity) = identity,
file('GRP120-1.p',unknown),
[] ).
cnf(8,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(A,B))),multiply(B,multiply(B,B)))) = A,
inference(para_into,[status(thm),theory(equality)],[3,6]),
[iquote('para_into,3.1.1.2.1.2.1,5.1.1')] ).
cnf(11,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),B)),multiply(multiply(multiply(C,multiply(multiply(C,C),multiply(B,D))),multiply(D,multiply(D,D))),multiply(multiply(multiply(C,multiply(multiply(C,C),multiply(B,D))),multiply(D,multiply(D,D))),multiply(multiply(C,multiply(multiply(C,C),multiply(B,D))),multiply(D,multiply(D,D))))))) = C,
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.2.1.2.2,3.1.1')] ).
cnf(13,plain,
multiply(A,multiply(multiply(A,B),multiply(multiply(C,multiply(C,C)),multiply(multiply(C,multiply(C,C)),multiply(C,multiply(C,C)))))) = multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(B,C))),
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.2.1.2,3.1.1')] ).
cnf(14,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(B,identity))),identity)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[3,6]),6]),
[iquote('para_into,3.1.1.2.2.2,5.1.1,demod,6')] ).
cnf(23,plain,
multiply(A,multiply(multiply(A,B),identity)) = multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(B,identity))),
inference(para_into,[status(thm),theory(equality)],[14,14]),
[iquote('para_into,14.1.1.2.1.2,14.1.1')] ).
cnf(24,plain,
multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(B,identity))) = multiply(A,multiply(multiply(A,B),identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[23])]),
[iquote('copy,23,flip.1')] ).
cnf(36,plain,
multiply(identity,multiply(multiply(identity,A),identity)) = multiply(identity,multiply(identity,multiply(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,14]),6,6,6]),
[iquote('para_into,7.1.1.2.1.2,14.1.1,demod,6,6,6')] ).
cnf(37,plain,
multiply(identity,multiply(multiply(identity,A),multiply(multiply(B,multiply(B,B)),multiply(multiply(B,multiply(B,B)),multiply(B,multiply(B,B)))))) = multiply(identity,multiply(identity,multiply(A,B))),
inference(para_into,[status(thm),theory(equality)],[8,8]),
[iquote('para_into,7.1.1.2.1.2,7.1.1')] ).
cnf(40,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),identity)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,6]),6,36,36]),
[iquote('para_into,7.1.1.2.2.2,5.1.1,demod,6,36,36')] ).
cnf(41,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),B)),multiply(multiply(multiply(identity,multiply(identity,multiply(B,C))),multiply(C,multiply(C,C))),multiply(multiply(multiply(identity,multiply(identity,multiply(B,C))),multiply(C,multiply(C,C))),multiply(multiply(identity,multiply(identity,multiply(B,C))),multiply(C,multiply(C,C))))))) = identity,
inference(para_from,[status(thm),theory(equality)],[8,3]),
[iquote('para_from,7.1.1,3.1.1.2.1.2.2')] ).
cnf(44,plain,
multiply(identity,multiply(A,multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(A,identity),identity),multiply(multiply(A,identity),identity))))) = identity,
inference(para_from,[status(thm),theory(equality)],[40,8]),
[iquote('para_from,39.1.1,7.1.1.2.1')] ).
cnf(51,plain,
multiply(identity,multiply(identity,multiply(multiply(multiply(identity,A),identity),identity))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[36,36]),36,36,40])]),
[iquote('para_into,35.1.1.2.1,35.1.1,demod,36,36,40,flip.1')] ).
cnf(60,plain,
multiply(identity,multiply(multiply(multiply(identity,A),identity),identity)) = multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[51,51])]),
[iquote('para_into,51.1.1.2.2.1.1,51.1.1,flip.1')] ).
cnf(62,plain,
multiply(multiply(identity,A),identity) = multiply(identity,multiply(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[51,36]),60,60,40])]),
[iquote('para_into,51.1.1.2.2.1.1,35.1.1,demod,60,60,40,flip.1')] ).
cnf(63,plain,
multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))) = multiply(multiply(identity,multiply(identity,multiply(A,B))),multiply(B,multiply(B,B))),
inference(para_into,[status(thm),theory(equality)],[51,8]),
[iquote('para_into,51.1.1.2.2.1.1,7.1.1')] ).
cnf(65,plain,
multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(A,B))),multiply(B,multiply(B,B))),identity)) = multiply(A,identity),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[62,8])]),
[iquote('para_into,61.1.1.1,7.1.1,flip.1')] ).
cnf(67,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(identity,multiply(B,identity)))),identity)) = multiply(identity,B),
inference(para_from,[status(thm),theory(equality)],[62,14]),
[iquote('para_from,61.1.1,14.1.1.2.1.2.2')] ).
cnf(115,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),B)),identity)) = multiply(identity,multiply(identity,multiply(identity,multiply(B,identity)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[67,14]),6]),
[iquote('para_into,67.1.1.2.1.2.2,14.1.1,demod,6')] ).
cnf(137,plain,
multiply(identity,multiply(multiply(multiply(identity,multiply(identity,A)),multiply(multiply(multiply(B,multiply(multiply(B,B),C)),multiply(multiply(multiply(A,multiply(multiply(A,A),multiply(C,D))),multiply(D,multiply(D,D))),multiply(multiply(multiply(A,multiply(multiply(A,A),multiply(C,D))),multiply(D,multiply(D,D))),multiply(multiply(A,multiply(multiply(A,A),multiply(C,D))),multiply(D,multiply(D,D)))))),multiply(multiply(multiply(B,multiply(multiply(B,B),C)),multiply(multiply(multiply(A,multiply(multiply(A,A),multiply(C,D))),multiply(D,multiply(D,D))),multiply(multiply(multiply(A,multiply(multiply(A,A),multiply(C,D))),multiply(D,multiply(D,D))),multiply(multiply(A,multiply(multiply(A,A),multiply(C,D))),multiply(D,multiply(D,D)))))),multiply(multiply(B,multiply(multiply(B,B),C)),multiply(multiply(multiply(A,multiply(multiply(A,A),multiply(C,D))),multiply(D,multiply(D,D))),multiply(multiply(multiply(A,multiply(multiply(A,A),multiply(C,D))),multiply(D,multiply(D,D))),multiply(multiply(A,multiply(multiply(A,A),multiply(C,D))),multiply(D,multiply(D,D))))))))),identity)) = multiply(B,identity),
inference(para_into,[status(thm),theory(equality)],[65,11]),
[iquote('para_into,65.1.1.2.1.1.2.2,11.1.1')] ).
cnf(152,plain,
multiply(identity,multiply(multiply(multiply(multiply(identity,multiply(identity,multiply(A,B))),multiply(B,multiply(B,B))),identity),identity)) = multiply(multiply(A,identity),identity),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[65,62])]),
[iquote('para_from,65.1.1,61.1.1.1,flip.1')] ).
cnf(190,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(A,multiply(B,multiply(B,B)))),B))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,8]),6,6,6,6])]),
[iquote('para_into,13.1.1,7.1.1,demod,6,6,6,6,flip.1')] ).
cnf(231,plain,
multiply(A,multiply(multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(A,B))),multiply(multiply(multiply(B,multiply(B,B)),multiply(B,multiply(B,B))),multiply(multiply(multiply(B,multiply(B,B)),multiply(B,multiply(B,B))),multiply(multiply(B,multiply(B,B)),multiply(B,multiply(B,B))))))) = multiply(B,multiply(B,B)),
inference(para_from,[status(thm),theory(equality)],[13,3]),
[iquote('para_from,13.1.1,3.1.1.2.1')] ).
cnf(249,plain,
multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(A,multiply(B,multiply(B,B)))),B),identity))) = multiply(A,identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[190,62]),62])]),
[iquote('para_from,190.1.1,61.1.1.1,demod,62,flip.1')] ).
cnf(253,plain,
multiply(multiply(identity,multiply(A,multiply(B,multiply(B,B)))),B) = multiply(identity,multiply(multiply(A,identity),identity)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[249,8]),6,6])]),
[iquote('para_from,249.1.1,7.1.1.2.1,demod,6,6,flip.1')] ).
cnf(255,plain,
multiply(A,multiply(multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(A,identity))),identity)) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[23,115]),6,6,6,6]),
[iquote('para_from,23.1.1,115.1.1.2.1,demod,6,6,6,6')] ).
cnf(257,plain,
multiply(multiply(A,A),multiply(multiply(A,multiply(multiply(A,B),identity)),identity)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[24,115]),40]),
[iquote('para_from,24.1.1,115.1.1.2.1,demod,40')] ).
cnf(260,plain,
multiply(multiply(A,multiply(multiply(A,A),B)),identity) = multiply(multiply(A,A),multiply(multiply(A,B),identity)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[257,115]),62,62,62,40])]),
[iquote('para_into,257.1.1.2.1.2.1,115.1.1,demod,62,62,62,40,flip.1')] ).
cnf(265,plain,
multiply(A,multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(A,A),multiply(A,identity)),identity))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[255]),260]),
[iquote('back_demod,255,demod,260')] ).
cnf(267,plain,
multiply(A,multiply(multiply(A,A),multiply(multiply(A,B),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(B,identity)))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[115]),260]),
[iquote('back_demod,115,demod,260')] ).
cnf(271,plain,
multiply(multiply(identity,A),multiply(multiply(multiply(identity,A),multiply(identity,A)),multiply(identity,multiply(multiply(A,identity),identity)))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[267,62]),62,6,6,6,6]),
[iquote('para_into,267.1.1.2.2.1,61.1.1,demod,62,6,6,6,6')] ).
cnf(273,plain,
multiply(A,multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(A,identity),identity),multiply(multiply(A,identity),identity)))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[44,271]),44,44,6,40]),
[iquote('para_from,43.1.1,271.1.1.1,demod,44,44,6,40')] ).
cnf(278,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(identity,A),B))),multiply(B,multiply(B,B))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[63,62]),62,40])]),
[iquote('para_into,63.1.1.2.2.1,61.1.1,demod,62,40,flip.1')] ).
cnf(279,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(A,multiply(A,A))) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[63,6]),6,6,6])]),
[iquote('para_into,63.1.1.2.2.1,5.1.1,demod,6,6,6,flip.1')] ).
cnf(281,plain,
multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),A) = multiply(A,multiply(A,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[279,257]),6,62,62,62,62,62,62,40]),
[iquote('para_from,279.1.1,257.1.1.2.1.2.1,demod,6,62,62,62,62,62,62,40')] ).
cnf(288,plain,
multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A)))) = multiply(identity,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[231,253]),6,6,6,6,62,62,62,62,62,62,40]),
[iquote('para_from,231.1.1,253.1.1.1,demod,6,6,6,6,62,62,62,62,62,62,40')] ).
cnf(293,plain,
multiply(identity,multiply(multiply(identity,A),multiply(identity,B))) = multiply(identity,multiply(identity,multiply(A,B))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[37]),288]),
[iquote('back_demod,37,demod,288')] ).
cnf(300,plain,
multiply(multiply(identity,A),multiply(identity,B)) = multiply(identity,multiply(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[293,278]),278])]),
[iquote('para_from,293.1.1,277.1.1.1.2.2.1,demod,278,flip.1')] ).
cnf(302,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),A) = multiply(A,multiply(A,A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[281]),300,300,300]),
[iquote('back_demod,281,demod,300,300,300')] ).
cnf(303,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))),B)) = multiply(A,multiply(identity,B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[300,40])]),
[iquote('para_into,299.1.1.1,39.1.1,flip.1')] ).
cnf(307,plain,
multiply(multiply(identity,A),B) = multiply(identity,multiply(A,multiply(identity,multiply(identity,multiply(multiply(B,identity),identity))))),
inference(para_into,[status(thm),theory(equality)],[300,40]),
[iquote('para_into,299.1.1.2,39.1.1')] ).
cnf(326,plain,
multiply(multiply(identity,multiply(A,multiply(identity,B))),multiply(B,multiply(B,B))) = multiply(identity,multiply(multiply(A,identity),identity)),
inference(para_from,[status(thm),theory(equality)],[303,278]),
[iquote('para_from,303.1.1,277.1.1.1.2')] ).
cnf(327,plain,
multiply(multiply(A,multiply(identity,multiply(B,multiply(B,B)))),B) = multiply(multiply(A,identity),identity),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[303,253]),62,62,62,62,40]),
[iquote('para_from,303.1.1,253.1.1.1,demod,62,62,62,62,40')] ).
cnf(333,plain,
multiply(multiply(multiply(A,multiply(identity,multiply(identity,multiply(identity,B)))),identity),identity) = multiply(multiply(multiply(A,identity),identity),B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[327,327]),300,300,288])]),
[iquote('para_into,327.1.1.1,327.1.1,demod,300,300,288,flip.1')] ).
cnf(341,plain,
multiply(identity,multiply(identity,multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,identity),identity))))) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[307,327]),6,6,300])]),
[iquote('para_into,307.1.1,327.1.1,demod,6,6,300,flip.1')] ).
cnf(353,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(B,multiply(B,B)))),B)) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[341,41]),300,300,341,300,300,341,300,300,300,300,300,300,288,40]),
[iquote('para_from,340.1.1,41.1.1.2.2.1.1,demod,300,300,341,300,300,341,300,300,300,300,300,300,288,40')] ).
cnf(355,plain,
multiply(identity,multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,identity),identity)))) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[341,278]),326,6,6,6])]),
[iquote('para_from,340.1.1,277.1.1.1.2.2.1,demod,326,6,6,6,flip.1')] ).
cnf(361,plain,
multiply(A,multiply(multiply(A,identity),multiply(multiply(multiply(A,A),identity),identity))) = identity,
inference(para_into,[status(thm),theory(equality)],[353,273]),
[iquote('para_into,353.1.1.2.1.2,273.1.1')] ).
cnf(365,plain,
multiply(multiply(A,identity),multiply(multiply(multiply(A,A),identity),identity)) = multiply(multiply(A,A),multiply(multiply(A,identity),identity)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[361,257]),6])]),
[iquote('para_from,361.1.1,257.1.1.2.1.2.1,demod,6,flip.1')] ).
cnf(367,plain,
multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,identity),identity))) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[355,278]),326,6,6,6])]),
[iquote('para_from,355.1.1,277.1.1.1.2.2.1,demod,326,6,6,6,flip.1')] ).
cnf(369,plain,
multiply(identity,multiply(A,multiply(multiply(multiply(A,multiply(A,A)),identity),identity))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[288,367]),300]),
[iquote('para_from,287.1.1,367.1.1.1,demod,300')] ).
cnf(372,plain,
multiply(multiply(A,multiply(identity,multiply(identity,B))),multiply(B,multiply(B,B))) = multiply(multiply(A,identity),identity),
inference(para_from,[status(thm),theory(equality)],[288,327]),
[iquote('para_from,287.1.1,327.1.1.1.2.2')] ).
cnf(379,plain,
multiply(A,multiply(multiply(multiply(A,multiply(A,A)),identity),identity)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[369,278]),372,6,6])]),
[iquote('para_from,369.1.1,277.1.1.1.2.2.1,demod,372,6,6,flip.1')] ).
cnf(382,plain,
multiply(multiply(A,multiply(A,A)),identity) = multiply(A,multiply(multiply(A,A),identity)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[379,267]),6,40])]),
[iquote('para_from,379.1.1,267.1.1.2.2.1,demod,6,40,flip.1')] ).
cnf(385,plain,
multiply(multiply(A,A),multiply(multiply(A,multiply(A,multiply(multiply(A,A),identity))),identity)) = multiply(A,A),
inference(para_from,[status(thm),theory(equality)],[382,257]),
[iquote('para_from,381.1.1,257.1.1.2.1.2')] ).
cnf(389,plain,
multiply(multiply(multiply(A,B),identity),identity) = multiply(multiply(multiply(A,identity),identity),multiply(multiply(B,identity),identity)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[333,63]),8]),
[iquote('para_into,333.1.1.1.1.2.2,63.1.1,demod,8')] ).
cnf(390,plain,
multiply(multiply(multiply(A,identity),identity),multiply(multiply(B,identity),identity)) = multiply(multiply(multiply(A,B),identity),identity),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[389])]),
[iquote('copy,389,flip.1')] ).
cnf(391,plain,
multiply(A,multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(A,A),identity),identity))) = identity,
inference(para_from,[status(thm),theory(equality)],[390,273]),
[iquote('para_from,390.1.1,273.1.1.2.2')] ).
cnf(397,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,identity)))),multiply(A,A)) = multiply(A,multiply(A,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[365,333]),62,62,62,62,62,62,62,62,62,40,300,300,300,62,62,62,62,62,62,40,302]),
[iquote('para_into,365.1.1.2,333.1.1,demod,62,62,62,62,62,62,62,62,62,40,300,300,300,62,62,62,62,62,62,40,302')] ).
cnf(402,plain,
multiply(multiply(A,identity),identity) = multiply(A,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[397,152]),152,62,62,62,40]),
[iquote('para_from,397.1.1,151.1.1.2.1.1.1.2.2,demod,152,62,62,62,40')] ).
cnf(404,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(A,identity)))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[397,8]),8])]),
[iquote('para_from,397.1.1,7.1.1.2.1.2.2,demod,8,flip.1')] ).
cnf(407,plain,
multiply(A,multiply(multiply(A,identity),multiply(multiply(A,A),identity))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[391]),402,402]),
[iquote('back_demod,391,demod,402,402')] ).
cnf(416,plain,
multiply(multiply(A,multiply(identity,multiply(identity,B))),multiply(B,multiply(B,B))) = multiply(A,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[372]),402]),
[iquote('back_demod,371,demod,402')] ).
cnf(419,plain,
multiply(multiply(A,identity),multiply(multiply(A,A),identity)) = multiply(multiply(A,A),multiply(A,identity)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[365]),402,402]),
[iquote('back_demod,365,demod,402,402')] ).
cnf(439,plain,
multiply(multiply(A,multiply(identity,multiply(B,multiply(B,B)))),B) = multiply(A,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[327]),402]),
[iquote('back_demod,327,demod,402')] ).
cnf(467,plain,
multiply(multiply(A,A),multiply(A,identity)) = multiply(multiply(A,identity),multiply(multiply(A,A),identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[419])]),
[iquote('copy,419,flip.1')] ).
cnf(470,plain,
multiply(multiply(A,A),multiply(A,identity)) = multiply(A,multiply(multiply(A,A),identity)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[402,382]),260,402,382]),
[iquote('para_into,401.1.1.1,381.1.1,demod,260,402,382')] ).
cnf(474,plain,
multiply(multiply(A,identity),multiply(multiply(A,A),identity)) = multiply(A,multiply(multiply(A,A),identity)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[467]),470])]),
[iquote('back_demod,467,demod,470,flip.1')] ).
cnf(483,plain,
multiply(A,multiply(multiply(multiply(A,A),multiply(A,A)),multiply(A,multiply(multiply(A,A),identity)))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[265]),470,260,402,470]),
[iquote('back_demod,265,demod,470,260,402,470')] ).
cnf(486,plain,
multiply(A,multiply(A,multiply(multiply(A,A),identity))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[407]),474]),
[iquote('back_demod,407,demod,474')] ).
cnf(488,plain,
multiply(multiply(A,A),identity) = multiply(A,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[385]),486,6]),
[iquote('back_demod,385,demod,486,6')] ).
cnf(491,plain,
multiply(A,multiply(multiply(multiply(A,A),multiply(A,A)),multiply(A,multiply(A,A)))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[483]),488]),
[iquote('back_demod,483,demod,488')] ).
cnf(510,plain,
multiply(multiply(A,multiply(A,A)),identity) = multiply(A,multiply(A,A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[382]),488]),
[iquote('back_demod,381,demod,488')] ).
cnf(515,plain,
multiply(multiply(multiply(A,identity),multiply(A,identity)),multiply(multiply(A,identity),multiply(A,identity))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[402,257]),402,488]),
[iquote('para_from,401.1.1,257.1.1.2.1.2.1,demod,402,488')] ).
cnf(522,plain,
multiply(A,identity) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[137,300]),6,6,488,416,6,6,416,6,6,416,6,6,6,510,488,6,416,6,6,416,6,6,416,6,6,6,510,488,6,416,6,6,416,6,6,416,6,6,6,510,288,62,62,404])]),
[iquote('para_into,137.1.1.2.1.2.1.2.1.1.2,299.1.1,demod,6,6,488,416,6,6,416,6,6,416,6,6,6,510,488,6,416,6,6,416,6,6,416,6,6,6,510,488,6,416,6,6,416,6,6,416,6,6,6,510,288,62,62,404,flip.1')] ).
cnf(528,plain,
multiply(multiply(A,A),multiply(A,A)) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[515]),522,522,522,522]),
[iquote('back_demod,515,demod,522,522,522,522')] ).
cnf(545,plain,
multiply(multiply(A,multiply(identity,multiply(B,multiply(B,B)))),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[439]),522]),
[iquote('back_demod,439,demod,522')] ).
cnf(561,plain,
multiply(A,multiply(identity,multiply(A,multiply(A,A)))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[491]),528]),
[iquote('back_demod,491,demod,528')] ).
cnf(581,plain,
multiply(identity,A) = A,
inference(para_into,[status(thm),theory(equality)],[545,561]),
[iquote('para_into,545.1.1.1,561.1.1')] ).
cnf(583,plain,
$false,
inference(binary,[status(thm)],[581,1]),
[iquote('binary,581.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : GRP120-1 : TPTP v8.1.0. Released v1.2.0.
% 0.13/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 05:06:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.65/2.81 ----- Otter 3.3f, August 2004 -----
% 2.65/2.81 The process was started by sandbox2 on n029.cluster.edu,
% 2.65/2.81 Wed Jul 27 05:06:29 2022
% 2.65/2.81 The command was "./otter". The process ID is 32346.
% 2.65/2.81
% 2.65/2.81 set(prolog_style_variables).
% 2.65/2.81 set(auto).
% 2.65/2.81 dependent: set(auto1).
% 2.65/2.81 dependent: set(process_input).
% 2.65/2.81 dependent: clear(print_kept).
% 2.65/2.81 dependent: clear(print_new_demod).
% 2.65/2.81 dependent: clear(print_back_demod).
% 2.65/2.81 dependent: clear(print_back_sub).
% 2.65/2.81 dependent: set(control_memory).
% 2.65/2.81 dependent: assign(max_mem, 12000).
% 2.65/2.81 dependent: assign(pick_given_ratio, 4).
% 2.65/2.81 dependent: assign(stats_level, 1).
% 2.65/2.81 dependent: assign(max_seconds, 10800).
% 2.65/2.81 clear(print_given).
% 2.65/2.81
% 2.65/2.81 list(usable).
% 2.65/2.81 0 [] A=A.
% 2.65/2.81 0 [] multiply(Y,multiply(multiply(Y,multiply(multiply(Y,Y),multiply(X,Z))),multiply(Z,multiply(Z,Z))))=X.
% 2.65/2.81 0 [] multiply(identity,identity)=identity.
% 2.65/2.81 0 [] multiply(identity,a)!=a.
% 2.65/2.81 end_of_list.
% 2.65/2.81
% 2.65/2.81 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 2.65/2.81
% 2.65/2.81 All clauses are units, and equality is present; the
% 2.65/2.81 strategy will be Knuth-Bendix with positive clauses in sos.
% 2.65/2.81
% 2.65/2.81 dependent: set(knuth_bendix).
% 2.65/2.81 dependent: set(anl_eq).
% 2.65/2.81 dependent: set(para_from).
% 2.65/2.81 dependent: set(para_into).
% 2.65/2.81 dependent: clear(para_from_right).
% 2.65/2.81 dependent: clear(para_into_right).
% 2.65/2.81 dependent: set(para_from_vars).
% 2.65/2.81 dependent: set(eq_units_both_ways).
% 2.65/2.81 dependent: set(dynamic_demod_all).
% 2.65/2.81 dependent: set(dynamic_demod).
% 2.65/2.81 dependent: set(order_eq).
% 2.65/2.81 dependent: set(back_demod).
% 2.65/2.81 dependent: set(lrpo).
% 2.65/2.81
% 2.65/2.81 ------------> process usable:
% 2.65/2.81 ** KEPT (pick-wt=5): 1 [] multiply(identity,a)!=a.
% 2.65/2.81
% 2.65/2.81 ------------> process sos:
% 2.65/2.81 ** KEPT (pick-wt=3): 2 [] A=A.
% 2.65/2.81 ** KEPT (pick-wt=19): 3 [] multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(B,C))),multiply(C,multiply(C,C))))=B.
% 2.65/2.81 ---> New Demodulator: 4 [new_demod,3] multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(B,C))),multiply(C,multiply(C,C))))=B.
% 2.65/2.81 ** KEPT (pick-wt=5): 5 [] multiply(identity,identity)=identity.
% 2.65/2.81 ---> New Demodulator: 6 [new_demod,5] multiply(identity,identity)=identity.
% 2.65/2.81 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 2.65/2.81 >>>> Starting back demodulation with 4.
% 2.65/2.81 >>>> Starting back demodulation with 6.
% 2.65/2.81
% 2.65/2.81 ======= end of input processing =======
% 2.65/2.81
% 2.65/2.81 =========== start of search ===========
% 2.65/2.81
% 2.65/2.81
% 2.65/2.81 Resetting weight limit to 23.
% 2.65/2.81
% 2.65/2.81
% 2.65/2.81 Resetting weight limit to 23.
% 2.65/2.81
% 2.65/2.81 sos_size=113
% 2.65/2.81 WARNING, demod_limit (given clause 91): 0 [para_into,85.1.1.2.2.1.1,75.1.1,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,70,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,70,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] 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% 9.77/9.98 WARNING, demod_limit stopped the demodulation of a clause.
% 9.77/9.98 This warning will not be repeated.
% 9.77/9.98
% 9.77/9.98
% 9.77/9.98
% 9.77/9.98 Resetting weight limit to 21.
% 9.77/9.98
% 9.77/9.98 iply(E,multiply(E,E))),multiply(multiply(multiply(C,multiply(multiply(C,C),multiply(identity,E))),multiply(E,multiply(E,E))),multiply(multiply(C,multiply(multiply(C,C),multiply(identity,E))),multiply(E,multiply(E,E))))),multiply(multiply(multiply(C,multiply(multiply(C,C),multiply(identity,E))),multiply(E,multiply(E,E))),multiply(multiply(multiply(C,multiply(multiply(C,C),multiply(identity,E))),multiply(E,multiply(E,E))),multiply(multiply(C,multiply(multiply(C,C),multiply(identity,E))),multiply(E,multiply(E,E)))))),multiply(D,F))),multiply(F,multiply(F,F)))))))))))))=identity.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98 WARNING, demod_limit.
% 9.77/9.98
% 9.77/9.98 Resetting weight limit to 21.
% 9.77/9.98
% 9.77/9.98 sos_size=41
% 9.77/9.98
% 9.77/9.98
% 9.77/9.98 Resetting weight limit to 9.
% 9.77/9.98
% 9.77/9.98
% 9.77/9.98 Resetting weight limit to 9.
% 9.77/9.98
% 9.77/9.98 sos_size=26
% 9.77/9.98
% 9.77/9.98 -------- PROOF --------
% 9.77/9.98
% 9.77/9.98 ----> UNIT CONFLICT at 8.04 sec ----> 583 [binary,581.1,1.1] $F.
% 9.77/9.98
% 9.77/9.98 Length of proof is 78. Level of proof is 29.
% 9.77/9.98
% 9.77/9.98 ---------------- PROOF ----------------
% 9.77/9.98 % SZS status Unsatisfiable
% 9.77/9.98 % SZS output start Refutation
% See solution above
% 9.77/9.98 ------------ end of proof -------------
% 9.77/9.98
% 9.77/9.98
% 9.77/9.98 Search stopped by max_proofs option.
% 9.77/9.98
% 9.77/9.98
% 9.77/9.98 Search stopped by max_proofs option.
% 9.77/9.98
% 9.77/9.98 ============ end of search ============
% 9.77/9.98
% 9.77/9.98 -------------- statistics -------------
% 9.77/9.98 clauses given 149
% 9.77/9.98 clauses generated 33360
% 9.77/9.98 clauses kept 327
% 9.77/9.98 clauses forward subsumed 5576
% 9.77/9.98 clauses back subsumed 0
% 9.77/9.98 Kbytes malloced 8789
% 9.77/9.98
% 9.77/9.98 ----------- times (seconds) -----------
% 9.77/9.98 user CPU time 8.04 (0 hr, 0 min, 8 sec)
% 9.77/9.98 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 9.77/9.98 wall-clock time 10 (0 hr, 0 min, 10 sec)
% 9.77/9.98
% 9.77/9.98 That finishes the proof of the theorem.
% 9.77/9.98
% 9.77/9.98 Process 32346 finished Wed Jul 27 05:06:39 2022
% 9.77/9.98 Otter interrupted
% 9.77/9.98 PROOF FOUND
%------------------------------------------------------------------------------