TSTP Solution File: GRP417-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP417-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 12:56:58 EDT 2022
% Result : Unsatisfiable 2.16s 2.32s
% Output : Refutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 2
% Syntax : Number of clauses : 80 ( 80 unt; 0 nHn; 2 RR)
% Number of literals : 80 ( 79 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 261 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('GRP417-1.p',unknown),
[] ).
cnf(4,axiom,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A)))))) = C,
file('GRP417-1.p',unknown),
[] ).
cnf(5,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(multiply(inverse(B),B)))),inverse(multiply(inverse(multiply(C,multiply(B,inverse(D)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(multiply(inverse(B),B)))))))))) = D,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,3.1.1.1.2.1.1.1.1,3.1.1')] ).
cnf(7,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,C))),inverse(multiply(inverse(A),A)))))) = multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(E,D)),multiply(E,inverse(C)))),inverse(multiply(inverse(D),D))))),
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,3.1.1.1.2.1.1.1.2.2,3.1.1')] ).
cnf(10,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A))))) = inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(E,D)),multiply(E,C))),inverse(multiply(inverse(D),D)))))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(17,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(inverse(C))))),inverse(multiply(inverse(A),A))))) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,4])]),
[iquote('para_into,7.1.1,3.1.1,flip.1')] ).
cnf(39,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),C)),inverse(multiply(inverse(A),A)))))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,inverse(inverse(C))))),inverse(multiply(inverse(B),B))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[17,7]),17]),
[iquote('para_from,16.1.1,7.1.1.1.2.1.1.1.2,demod,17')] ).
cnf(40,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(C))))),inverse(multiply(inverse(B),B))) = inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(B,D)),C)),inverse(multiply(inverse(D),D)))))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[39])]),
[iquote('copy,39,flip.1')] ).
cnf(59,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,inverse(C))))))),inverse(multiply(inverse(B),B))) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[39,4])]),
[iquote('para_into,39.1.1,3.1.1,flip.1')] ).
cnf(160,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(inverse(B),B))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,C))),inverse(multiply(inverse(B),B))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[59,7]),4]),
[iquote('para_into,58.1.1.1.1.2.2.1,7.1.1,demod,4')] ).
cnf(161,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(inverse(multiply(C,inverse(D))))))),A)),D)),inverse(multiply(inverse(A),A)))))) = multiply(inverse(C),C),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[59,7]),17]),
[iquote('para_from,58.1.1,7.1.1.1.2.1.1.1.2,demod,17')] ).
cnf(169,plain,
multiply(A,inverse(inverse(multiply(B,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(inverse(B),B)))))))) = C,
inference(para_from,[status(thm),theory(equality)],[40,17]),
[iquote('para_from,40.1.1,16.1.1.2.1')] ).
cnf(171,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),A)),D)),inverse(multiply(inverse(A),A))))))) = multiply(B,inverse(inverse(multiply(C,inverse(multiply(inverse(D),inverse(multiply(inverse(C),C)))))))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[169,169])]),
[iquote('para_into,168.1.1.2.1.1.2.1.1.1,168.1.1,flip.1')] ).
cnf(172,plain,
multiply(A,inverse(inverse(multiply(B,inverse(multiply(inverse(multiply(inverse(multiply(C,B)),multiply(C,D))),inverse(multiply(inverse(B),B)))))))) = multiply(A,D),
inference(para_into,[status(thm),theory(equality)],[169,160]),
[iquote('para_into,168.1.1.2.1.1.2.1,160.1.1')] ).
cnf(174,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),C)),inverse(multiply(inverse(A),A))))) = multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(B,D)),C)),inverse(multiply(inverse(D),D))))),
inference(para_from,[status(thm),theory(equality)],[169,17]),
[iquote('para_from,168.1.1,16.1.1.2.1.1.1.2')] ).
cnf(178,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,C))),inverse(multiply(inverse(A),A))))))) = C,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[172,169]),169])]),
[iquote('para_from,172.1.1,168.1.1.2.1.1.2.1.1.1,demod,169,flip.1')] ).
cnf(180,plain,
multiply(inverse(multiply(A,B)),inverse(inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,C))),E)),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))) = E,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[178,160]),171]),
[iquote('para_into,177.1.1.1.1.2.1.1.1.1.1,160.1.1,demod,171')] ).
cnf(184,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,C)))))),inverse(multiply(inverse(B),B)))) = C,
inference(para_into,[status(thm),theory(equality)],[178,39]),
[iquote('para_into,177.1.1.1,39.1.1')] ).
cnf(192,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = multiply(inverse(A),A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[161,160]),59]),
[iquote('para_into,161.1.1.1.2.1.1.1.1.1,160.1.1,demod,59')] ).
cnf(196,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,inverse(multiply(inverse(C),inverse(multiply(inverse(B),B))))))))) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[180,174]),171]),
[iquote('para_into,180.1.1.2.1.1,174.1.1,demod,171')] ).
cnf(201,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[196,160]),178]),
[iquote('para_into,196.1.1.2.2.1.1.2.1,160.1.1,demod,178')] ).
cnf(203,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(multiply(inverse(B),B)))) = multiply(inverse(C),C),
inference(para_into,[status(thm),theory(equality)],[196,192]),
[iquote('para_into,196.1.1.2.2.1,192.1.1')] ).
cnf(205,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(C,D)),multiply(C,inverse(inverse(E))))),inverse(multiply(inverse(D),D)))))) = multiply(inverse(multiply(D,B)),E),
inference(para_into,[status(thm),theory(equality)],[196,39]),
[iquote('para_into,196.1.1.2.2.1,39.1.1')] ).
cnf(225,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(D)))),inverse(multiply(inverse(C),C)))))),multiply(A,E)) = multiply(D,multiply(C,E)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[201,10]),178])]),
[iquote('para_into,201.1.1.1.1,10.1.1,demod,178,flip.1')] ).
cnf(248,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),inverse(inverse(multiply(multiply(D,C),E)))))),inverse(multiply(inverse(multiply(D,C)),multiply(D,C))))) = E,
inference(para_from,[status(thm),theory(equality)],[201,184]),
[iquote('para_from,201.1.1,184.1.1.1.1.1.1.1')] ).
cnf(250,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),inverse(inverse(multiply(multiply(D,C),inverse(E))))))),inverse(multiply(inverse(multiply(D,C)),multiply(D,C)))) = E,
inference(para_from,[status(thm),theory(equality)],[201,59]),
[iquote('para_from,201.1.1,58.1.1.1.1.1.1')] ).
cnf(264,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[203,59]),59]),
[iquote('para_into,203.1.1.1.1,58.1.1,demod,59')] ).
cnf(294,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),C)) = multiply(inverse(multiply(D,B)),multiply(D,A)),
inference(para_from,[status(thm),theory(equality)],[264,201]),
[iquote('para_from,264.1.1,201.1.1.2')] ).
cnf(301,plain,
inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(A)),inverse(A))))))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[264,5]),59,59,59]),
[iquote('para_from,264.1.1,5.1.1.1.2.1.1.1,demod,59,59,59')] ).
cnf(311,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(para_from,[status(thm),theory(equality)],[264,201]),
[iquote('para_from,264.1.1,201.1.1.1.1')] ).
cnf(320,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(inverse(C))))),inverse(multiply(inverse(D),D))))) = C,
inference(para_from,[status(thm),theory(equality)],[264,17]),
[iquote('para_from,264.1.1,16.1.1.2.1.2.1')] ).
cnf(323,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,C))),inverse(multiply(inverse(D),D))))))) = C,
inference(para_from,[status(thm),theory(equality)],[264,178]),
[iquote('para_from,264.1.1,177.1.1.1.1.2.1.2.1')] ).
cnf(337,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(C),B)),multiply(inverse(D),D)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[294])]),
[iquote('copy,294,flip.1')] ).
cnf(338,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(D),D)),multiply(inverse(B),C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[311])]),
[iquote('copy,311,flip.1')] ).
cnf(350,plain,
multiply(A,multiply(inverse(B),B)) = multiply(A,multiply(inverse(C),C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[294,10]),323,225]),
[iquote('para_into,294.1.1.1.1,10.1.1,demod,323,225')] ).
cnf(359,plain,
multiply(A,multiply(inverse(multiply(inverse(B),B)),multiply(inverse(C),C))) = multiply(A,multiply(inverse(D),D)),
inference(para_into,[status(thm),theory(equality)],[350,350]),
[iquote('para_into,350.1.1.2,350.1.1')] ).
cnf(360,plain,
multiply(inverse(A),A) = multiply(inverse(multiply(inverse(B),B)),multiply(inverse(C),C)),
inference(para_into,[status(thm),theory(equality)],[350,264]),
[iquote('para_into,350.1.1,264.1.1')] ).
cnf(363,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),B)) = multiply(inverse(C),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[360])]),
[iquote('copy,360,flip.1')] ).
cnf(395,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(multiply(inverse(B),B)),C)) = multiply(inverse(multiply(D,multiply(inverse(E),E))),multiply(D,C)),
inference(para_from,[status(thm),theory(equality)],[363,201]),
[iquote('para_from,363.1.1,201.1.1.1.1')] ).
cnf(398,plain,
multiply(inverse(multiply(A,multiply(inverse(B),B))),multiply(A,C)) = multiply(inverse(multiply(inverse(D),D)),multiply(inverse(multiply(inverse(E),E)),C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[395])]),
[iquote('copy,395,flip.1')] ).
cnf(399,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),multiply(inverse(C),C))) = multiply(inverse(multiply(D,B)),multiply(D,multiply(inverse(E),E))),
inference(para_into,[status(thm),theory(equality)],[311,350]),
[iquote('para_into,311.1.1.2,350.1.1')] ).
cnf(401,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(inverse(multiply(E,multiply(inverse(D),C))),multiply(E,multiply(inverse(F),F))),
inference(para_into,[status(thm),theory(equality)],[311,294]),
[iquote('para_into,311.1.1.2,294.1.1')] ).
cnf(403,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(inverse(C),C))) = multiply(inverse(multiply(inverse(D),D)),multiply(inverse(B),multiply(inverse(E),E))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[399])]),
[iquote('copy,399,flip.1')] ).
cnf(413,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(multiply(inverse(B),B)),C)) = multiply(inverse(multiply(inverse(C),multiply(inverse(D),D))),multiply(inverse(E),E)),
inference(para_into,[status(thm),theory(equality)],[337,363]),
[iquote('para_into,337.1.1.1.1,363.1.1')] ).
cnf(476,plain,
inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(C),C)))))) = A,
inference(para_into,[status(thm),theory(equality)],[301,264]),
[iquote('para_into,301.1.1.1.2.1.2.1,264.1.1')] ).
cnf(482,plain,
inverse(multiply(inverse(A),multiply(inverse(B),B))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[476,476]),476]),
[iquote('para_into,475.1.1.1.2.1.2,475.1.1,demod,476')] ).
cnf(508,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(multiply(inverse(B),B)),C)) = multiply(C,multiply(inverse(D),D)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[413]),482]),
[iquote('back_demod,413,demod,482')] ).
cnf(542,plain,
multiply(A,multiply(inverse(A),B)) = multiply(B,multiply(inverse(C),C)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[476,337]),476]),
[iquote('para_from,475.1.1,337.1.1.1,demod,476')] ).
cnf(554,plain,
multiply(A,multiply(inverse(B),B)) = multiply(C,multiply(inverse(C),A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[542])]),
[iquote('copy,542,flip.1')] ).
cnf(576,plain,
inverse(multiply(inverse(A),A)) = multiply(inverse(B),B),
inference(para_into,[status(thm),theory(equality)],[482,363]),
[iquote('para_into,481.1.1.1,363.1.1')] ).
cnf(577,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),C))) = multiply(inverse(C),B),
inference(para_into,[status(thm),theory(equality)],[482,338]),
[iquote('para_into,481.1.1.1,338.1.1')] ).
cnf(580,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = multiply(inverse(C),B),
inference(para_into,[status(thm),theory(equality)],[482,294]),
[iquote('para_into,481.1.1.1,294.1.1')] ).
cnf(584,plain,
multiply(inverse(A),A) = inverse(multiply(inverse(B),B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[576])]),
[iquote('copy,576,flip.1')] ).
cnf(602,plain,
multiply(A,inverse(multiply(multiply(inverse(inverse(inverse(B))),A),inverse(multiply(inverse(C),C))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[320]),580]),
[iquote('back_demod,320,demod,580')] ).
cnf(627,plain,
multiply(inverse(multiply(multiply(inverse(A),B),multiply(inverse(multiply(C,B)),inverse(inverse(multiply(multiply(C,A),inverse(D))))))),multiply(inverse(A),A)) = D,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[250]),580,580]),
[iquote('back_demod,250,demod,580,580')] ).
cnf(630,plain,
multiply(multiply(inverse(A),B),multiply(inverse(multiply(C,B)),inverse(inverse(multiply(multiply(C,A),D))))) = D,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[248]),580,580,482]),
[iquote('back_demod,248,demod,580,580,482')] ).
cnf(637,plain,
multiply(inverse(multiply(A,inverse(multiply(multiply(inverse(inverse(B)),C),inverse(multiply(inverse(C),C)))))),multiply(A,D)) = multiply(B,multiply(C,D)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[225]),580]),
[iquote('back_demod,224,demod,580')] ).
cnf(641,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(multiply(inverse(inverse(inverse(C))),D),inverse(multiply(inverse(D),D)))))) = multiply(inverse(multiply(D,B)),C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[205]),580]),
[iquote('back_demod,205,demod,580')] ).
cnf(650,plain,
multiply(inverse(inverse(A)),multiply(inverse(B),B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[627]),630]),
[iquote('back_demod,627,demod,630')] ).
cnf(769,plain,
inverse(inverse(multiply(inverse(A),A))) = multiply(inverse(B),B),
inference(para_from,[status(thm),theory(equality)],[584,482]),
[iquote('para_from,584.1.1,481.1.1.1')] ).
cnf(770,plain,
multiply(A,inverse(multiply(inverse(B),B))) = multiply(A,multiply(inverse(C),C)),
inference(para_from,[status(thm),theory(equality)],[584,359]),
[iquote('para_from,584.1.1,359.1.1.2')] ).
cnf(773,plain,
inverse(multiply(inverse(A),inverse(multiply(inverse(B),B)))) = A,
inference(para_from,[status(thm),theory(equality)],[584,482]),
[iquote('para_from,584.1.1,481.1.1.1.2')] ).
cnf(776,plain,
multiply(inverse(A),A) = inverse(inverse(multiply(inverse(B),B))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[769])]),
[iquote('copy,769,flip.1')] ).
cnf(777,plain,
multiply(A,multiply(inverse(B),B)) = multiply(A,inverse(multiply(inverse(C),C))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[770])]),
[iquote('copy,770,flip.1')] ).
cnf(783,plain,
multiply(inverse(inverse(A)),multiply(multiply(inverse(B),B),multiply(inverse(C),C))) = A,
inference(para_into,[status(thm),theory(equality)],[650,576]),
[iquote('para_into,650.1.1.2.1,576.1.1')] ).
cnf(790,plain,
multiply(inverse(inverse(A)),inverse(multiply(inverse(B),B))) = A,
inference(para_into,[status(thm),theory(equality)],[650,584]),
[iquote('para_into,650.1.1.2,584.1.1')] ).
cnf(809,plain,
multiply(inverse(inverse(A)),inverse(inverse(multiply(inverse(B),B)))) = A,
inference(para_from,[status(thm),theory(equality)],[776,650]),
[iquote('para_from,776.1.1,650.1.1.2')] ).
cnf(843,plain,
multiply(A,inverse(multiply(inverse(B),B))) = multiply(C,multiply(inverse(C),A)),
inference(para_into,[status(thm),theory(equality)],[554,809]),
[iquote('para_into,554.1.1.2,809.1.1')] ).
cnf(845,plain,
multiply(A,multiply(inverse(A),inverse(inverse(B)))) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[554,650])]),
[iquote('para_into,554.1.1,650.1.1,flip.1')] ).
cnf(862,plain,
multiply(inverse(multiply(inverse(A),A)),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[602,843]),845,773]),
[iquote('para_into,602.1.1.2.1.1,843.1.1,demod,845,773')] ).
cnf(870,plain,
multiply(multiply(inverse(A),A),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[602,777]),790,773]),
[iquote('para_into,602.1.1.2.1.1,777.1.1,demod,790,773')] ).
cnf(874,plain,
inverse(multiply(inverse(A),B)) = multiply(inverse(B),A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[577]),862]),
[iquote('back_demod,577,demod,862')] ).
cnf(876,plain,
multiply(A,multiply(inverse(B),B)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[508]),874,874,870,870])]),
[iquote('back_demod,508,demod,874,874,870,870,flip.1')] ).
cnf(880,plain,
multiply(inverse(multiply(A,B)),A) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[403]),876,874,876,870]),
[iquote('back_demod,403,demod,876,874,876,870')] ).
cnf(882,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(B),C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[401]),874,870,876,880,874]),
[iquote('back_demod,401,demod,874,870,876,880,874')] ).
cnf(886,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[398]),876,874,874,870,870]),
[iquote('back_demod,398,demod,876,874,874,870,870')] ).
cnf(888,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[783]),876,876]),
[iquote('back_demod,783,demod,876,876')] ).
cnf(902,plain,
multiply(inverse(multiply(A,B)),C) = multiply(inverse(B),multiply(inverse(A),C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[641]),888,874,876,874,882])]),
[iquote('back_demod,641,demod,888,874,876,874,882,flip.1')] ).
cnf(903,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[637]),888,874,876,902,888,886]),
[iquote('back_demod,637,demod,888,874,876,902,888,886')] ).
cnf(905,plain,
$false,
inference(binary,[status(thm)],[903,1]),
[iquote('binary,903.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP417-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Jul 27 04:59:35 EDT 2022
% 0.14/0.35 % CPUTime :
% 2.16/2.32 ----- Otter 3.3f, August 2004 -----
% 2.16/2.32 The process was started by sandbox on n022.cluster.edu,
% 2.16/2.32 Wed Jul 27 04:59:35 2022
% 2.16/2.32 The command was "./otter". The process ID is 14913.
% 2.16/2.32
% 2.16/2.32 set(prolog_style_variables).
% 2.16/2.32 set(auto).
% 2.16/2.32 dependent: set(auto1).
% 2.16/2.32 dependent: set(process_input).
% 2.16/2.32 dependent: clear(print_kept).
% 2.16/2.32 dependent: clear(print_new_demod).
% 2.16/2.32 dependent: clear(print_back_demod).
% 2.16/2.32 dependent: clear(print_back_sub).
% 2.16/2.32 dependent: set(control_memory).
% 2.16/2.32 dependent: assign(max_mem, 12000).
% 2.16/2.32 dependent: assign(pick_given_ratio, 4).
% 2.16/2.32 dependent: assign(stats_level, 1).
% 2.16/2.32 dependent: assign(max_seconds, 10800).
% 2.16/2.32 clear(print_given).
% 2.16/2.32
% 2.16/2.32 list(usable).
% 2.16/2.32 0 [] A=A.
% 2.16/2.32 0 [] inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A))))))=C.
% 2.16/2.32 0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 2.16/2.32 end_of_list.
% 2.16/2.32
% 2.16/2.32 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 2.16/2.32
% 2.16/2.32 All clauses are units, and equality is present; the
% 2.16/2.32 strategy will be Knuth-Bendix with positive clauses in sos.
% 2.16/2.32
% 2.16/2.32 dependent: set(knuth_bendix).
% 2.16/2.32 dependent: set(anl_eq).
% 2.16/2.32 dependent: set(para_from).
% 2.16/2.32 dependent: set(para_into).
% 2.16/2.32 dependent: clear(para_from_right).
% 2.16/2.32 dependent: clear(para_into_right).
% 2.16/2.32 dependent: set(para_from_vars).
% 2.16/2.32 dependent: set(eq_units_both_ways).
% 2.16/2.32 dependent: set(dynamic_demod_all).
% 2.16/2.32 dependent: set(dynamic_demod).
% 2.16/2.32 dependent: set(order_eq).
% 2.16/2.32 dependent: set(back_demod).
% 2.16/2.32 dependent: set(lrpo).
% 2.16/2.32
% 2.16/2.32 ------------> process usable:
% 2.16/2.32 ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 2.16/2.32
% 2.16/2.32 ------------> process sos:
% 2.16/2.32 ** KEPT (pick-wt=3): 2 [] A=A.
% 2.16/2.32 ** KEPT (pick-wt=22): 3 [] inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A))))))=C.
% 2.16/2.32 ---> New Demodulator: 4 [new_demod,3] inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A))))))=C.
% 2.16/2.32 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 2.16/2.32 >>>> Starting back demodulation with 4.
% 2.16/2.32
% 2.16/2.32 ======= end of input processing =======
% 2.16/2.32
% 2.16/2.32 =========== start of search ===========
% 2.16/2.32
% 2.16/2.32
% 2.16/2.32 Resetting weight limit to 39.
% 2.16/2.32
% 2.16/2.32
% 2.16/2.32 Resetting weight limit to 39.
% 2.16/2.32
% 2.16/2.32 sos_size=97
% 2.16/2.32
% 2.16/2.32
% 2.16/2.32 Resetting weight limit to 29.
% 2.16/2.32
% 2.16/2.32
% 2.16/2.32 Resetting weight limit to 29.
% 2.16/2.32
% 2.16/2.32 sos_size=148
% 2.16/2.32
% 2.16/2.32
% 2.16/2.32 Resetting weight limit to 15.
% 2.16/2.32
% 2.16/2.32
% 2.16/2.32 Resetting weight limit to 15.
% 2.16/2.32
% 2.16/2.32 sos_size=299
% 2.16/2.32
% 2.16/2.32
% 2.16/2.32 Resetting weight limit to 14.
% 2.16/2.32
% 2.16/2.32
% 2.16/2.32 Resetting weight limit to 14.
% 2.16/2.32
% 2.16/2.32 sos_size=252
% 2.16/2.32
% 2.16/2.32 -------- PROOF --------
% 2.16/2.32
% 2.16/2.32 ----> UNIT CONFLICT at 0.39 sec ----> 905 [binary,903.1,1.1] $F.
% 2.16/2.32
% 2.16/2.32 Length of proof is 77. Level of proof is 28.
% 2.16/2.32
% 2.16/2.32 ---------------- PROOF ----------------
% 2.16/2.32 % SZS status Unsatisfiable
% 2.16/2.32 % SZS output start Refutation
% See solution above
% 2.16/2.32 ------------ end of proof -------------
% 2.16/2.32
% 2.16/2.32
% 2.16/2.32 Search stopped by max_proofs option.
% 2.16/2.32
% 2.16/2.32
% 2.16/2.32 Search stopped by max_proofs option.
% 2.16/2.32
% 2.16/2.32 ============ end of search ============
% 2.16/2.32
% 2.16/2.32 -------------- statistics -------------
% 2.16/2.32 clauses given 139
% 2.16/2.32 clauses generated 22008
% 2.16/2.32 clauses kept 694
% 2.16/2.32 clauses forward subsumed 3734
% 2.16/2.32 clauses back subsumed 19
% 2.16/2.32 Kbytes malloced 7812
% 2.16/2.32
% 2.16/2.32 ----------- times (seconds) -----------
% 2.16/2.32 user CPU time 0.39 (0 hr, 0 min, 0 sec)
% 2.16/2.32 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.16/2.32 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.16/2.32
% 2.16/2.32 That finishes the proof of the theorem.
% 2.16/2.32
% 2.16/2.32 Process 14913 finished Wed Jul 27 04:59:37 2022
% 2.16/2.32 Otter interrupted
% 2.16/2.32 PROOF FOUND
%------------------------------------------------------------------------------