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
%------------------------------------------------------------------------------