TSTP Solution File: GRP502-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP502-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 12:57:08 EDT 2022
% Result : Unsatisfiable 2.13s 2.31s
% Output : Refutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 3
% Syntax : Number of clauses : 80 ( 80 unt; 0 nHn; 5 RR)
% Number of literals : 80 ( 79 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 293 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP502-1.p',unknown),
[] ).
cnf(2,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
double_divide(double_divide(A,inverse(double_divide(B,C))),double_divide(inverse(B),inverse(double_divide(D,double_divide(A,D))))) = C,
file('GRP502-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP502-1.p',unknown),
[] ).
cnf(8,plain,
inverse(double_divide(A,B)) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(9,plain,
double_divide(double_divide(A,multiply(B,C)),double_divide(inverse(C),multiply(double_divide(A,D),D))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),8,8]),
[iquote('back_demod,4,demod,8,8')] ).
cnf(11,plain,
double_divide(double_divide(A,multiply(B,double_divide(C,D))),double_divide(multiply(D,C),multiply(double_divide(A,E),E))) = B,
inference(para_into,[status(thm),theory(equality)],[9,8]),
[iquote('para_into,9.1.1.2.1,7.1.1')] ).
cnf(14,plain,
double_divide(double_divide(double_divide(A,multiply(B,C)),multiply(D,E)),double_divide(inverse(E),multiply(B,double_divide(inverse(C),multiply(double_divide(A,F),F))))) = D,
inference(para_into,[status(thm),theory(equality)],[9,9]),
[iquote('para_into,9.1.1.2.2.1,9.1.1')] ).
cnf(15,plain,
inverse(A) = multiply(double_divide(inverse(B),multiply(double_divide(C,D),D)),double_divide(C,multiply(A,B))),
inference(para_from,[status(thm),theory(equality)],[9,8]),
[iquote('para_from,9.1.1,7.1.1.1')] ).
cnf(16,plain,
multiply(double_divide(inverse(A),multiply(double_divide(B,C),C)),double_divide(B,multiply(D,A))) = inverse(D),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(18,plain,
multiply(double_divide(inverse(A),multiply(double_divide(B,C),C)),double_divide(B,multiply(double_divide(D,E),A))) = multiply(E,D),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,8])]),
[iquote('para_into,15.1.1,7.1.1,flip.1')] ).
cnf(22,plain,
multiply(multiply(double_divide(inverse(A),multiply(double_divide(B,C),C)),double_divide(B,multiply(b1,A))),b1) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[15,2]),
[iquote('para_from,15.1.1,2.1.1.1')] ).
cnf(26,plain,
multiply(double_divide(inverse(A),multiply(B,double_divide(inverse(C),multiply(double_divide(D,E),E)))),double_divide(double_divide(D,multiply(B,C)),multiply(F,A))) = inverse(F),
inference(para_into,[status(thm),theory(equality)],[16,9]),
[iquote('para_into,16.1.1.1.2.1,9.1.1')] ).
cnf(27,plain,
multiply(double_divide(multiply(multiply(A,B),C),multiply(double_divide(D,E),E)),double_divide(D,inverse(A))) = multiply(multiply(double_divide(C,F),F),inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,16]),8,8]),
[iquote('para_into,16.1.1.2.2,16.1.1,demod,8,8')] ).
cnf(32,plain,
double_divide(double_divide(A,inverse(B)),double_divide(multiply(multiply(B,C),D),multiply(double_divide(A,E),E))) = double_divide(inverse(C),multiply(double_divide(D,F),F)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[16,9]),8]),
[iquote('para_from,16.1.1,9.1.1.1.2,demod,8')] ).
cnf(38,plain,
double_divide(double_divide(double_divide(A,multiply(B,C)),multiply(D,double_divide(E,F))),double_divide(multiply(F,E),multiply(B,double_divide(inverse(C),multiply(double_divide(A,G),G))))) = D,
inference(para_into,[status(thm),theory(equality)],[11,9]),
[iquote('para_into,11.1.1.2.2.1,9.1.1')] ).
cnf(40,plain,
double_divide(double_divide(double_divide(A,multiply(B,double_divide(C,D))),multiply(E,F)),double_divide(inverse(F),multiply(B,double_divide(multiply(D,C),multiply(double_divide(A,G),G))))) = E,
inference(para_from,[status(thm),theory(equality)],[11,9]),
[iquote('para_from,11.1.1,9.1.1.2.2.1')] ).
cnf(46,plain,
multiply(double_divide(multiply(A,B),multiply(double_divide(C,D),D)),double_divide(C,multiply(double_divide(E,F),double_divide(B,A)))) = multiply(F,E),
inference(para_into,[status(thm),theory(equality)],[18,8]),
[iquote('para_into,18.1.1.1.1,7.1.1')] ).
cnf(187,plain,
multiply(multiply(double_divide(A,B),B),inverse(C)) = multiply(multiply(double_divide(A,D),D),inverse(C)),
inference(para_into,[status(thm),theory(equality)],[27,27]),
[iquote('para_into,27.1.1,27.1.1')] ).
cnf(231,plain,
multiply(double_divide(A,B),B) = multiply(double_divide(A,C),C),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[187,14]),14]),
[iquote('para_from,187.1.1,13.1.1.1.2,demod,14')] ).
cnf(243,plain,
multiply(A,double_divide(inverse(B),multiply(double_divide(C,D),D))) = multiply(double_divide(double_divide(C,multiply(A,B)),E),E),
inference(para_into,[status(thm),theory(equality)],[231,9]),
[iquote('para_into,231.1.1.1,9.1.1')] ).
cnf(247,plain,
multiply(double_divide(multiply(A,B),multiply(double_divide(C,D),D)),double_divide(C,multiply(double_divide(E,F),F))) = multiply(double_divide(B,A),E),
inference(para_from,[status(thm),theory(equality)],[231,46]),
[iquote('para_from,231.1.1,46.1.1.2.2')] ).
cnf(254,plain,
double_divide(double_divide(A,multiply(double_divide(B,C),C)),double_divide(multiply(D,E),multiply(double_divide(A,F),F))) = double_divide(B,double_divide(E,D)),
inference(para_from,[status(thm),theory(equality)],[231,11]),
[iquote('para_from,231.1.1,11.1.1.1.2')] ).
cnf(256,plain,
double_divide(double_divide(A,multiply(double_divide(B,C),C)),double_divide(inverse(D),multiply(double_divide(A,E),E))) = double_divide(B,D),
inference(para_from,[status(thm),theory(equality)],[231,9]),
[iquote('para_from,231.1.1,9.1.1.1.2')] ).
cnf(263,plain,
multiply(double_divide(double_divide(A,multiply(double_divide(inverse(B),multiply(double_divide(inverse(C),D),D)),C)),E),E) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[243,18])]),
[iquote('para_into,243.1.1,18.1.1,flip.1')] ).
cnf(272,plain,
double_divide(double_divide(A,multiply(double_divide(B,double_divide(inverse(C),multiply(double_divide(A,D),D))),C)),E) = double_divide(B,E),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[256,243]),256]),
[iquote('para_into,255.1.1.1.2,243.1.1,demod,256')] ).
cnf(303,plain,
multiply(double_divide(A,double_divide(B,A)),C) = multiply(double_divide(D,double_divide(B,D)),C),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[247,231]),247]),
[iquote('para_into,246.1.1.1.1,231.1.1,demod,247')] ).
cnf(304,plain,
multiply(double_divide(A,B),B) = multiply(double_divide(C,double_divide(D,C)),double_divide(D,A)),
inference(para_into,[status(thm),theory(equality)],[303,231]),
[iquote('para_into,303.1.1,231.1.1')] ).
cnf(305,plain,
multiply(double_divide(A,double_divide(B,A)),double_divide(B,C)) = multiply(double_divide(C,D),D),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[304])]),
[iquote('copy,304,flip.1')] ).
cnf(317,plain,
double_divide(A,double_divide(B,A)) = double_divide(C,double_divide(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[303,14]),14]),
[iquote('para_from,303.1.1,13.1.1.1.2,demod,14')] ).
cnf(348,plain,
multiply(double_divide(double_divide(A,B),double_divide(C,double_divide(A,C))),double_divide(B,D)) = multiply(double_divide(D,E),E),
inference(para_into,[status(thm),theory(equality)],[305,317]),
[iquote('para_into,305.1.1.1.2,317.1.1')] ).
cnf(354,plain,
multiply(double_divide(A,multiply(double_divide(B,C),C)),D) = multiply(multiply(double_divide(A,E),E),multiply(B,D)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[305,27]),8,247,8]),
[iquote('para_from,305.1.1,27.1.1.1.1.1,demod,8,247,8')] ).
cnf(391,plain,
double_divide(A,double_divide(B,multiply(double_divide(C,D),D))) = double_divide(multiply(C,A),multiply(double_divide(B,E),E)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[32,305]),8,254,8]),
[iquote('para_into,32.1.1.2.1.1,305.1.1,demod,8,254,8')] ).
cnf(430,plain,
multiply(double_divide(double_divide(A,B),double_divide(C,double_divide(A,C))),double_divide(D,double_divide(E,D))) = multiply(double_divide(double_divide(E,B),F),F),
inference(para_into,[status(thm),theory(equality)],[348,317]),
[iquote('para_into,348.1.1.2,317.1.1')] ).
cnf(431,plain,
multiply(double_divide(double_divide(A,B),C),C) = multiply(double_divide(double_divide(D,B),double_divide(E,double_divide(D,E))),double_divide(F,double_divide(A,F))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[430])]),
[iquote('copy,430,flip.1')] ).
cnf(433,plain,
multiply(multiply(A,B),multiply(C,multiply(double_divide(C,D),D))) = multiply(A,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[354,263]),263])]),
[iquote('para_into,354.1.1,262.1.1,demod,263,flip.1')] ).
cnf(447,plain,
double_divide(multiply(A,double_divide(A,multiply(B,C))),multiply(double_divide(inverse(C),D),D)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[391,14]),272])]),
[iquote('para_into,391.1.1,13.1.1,demod,272,flip.1')] ).
cnf(449,plain,
double_divide(double_divide(inverse(A),multiply(B,double_divide(double_divide(C,multiply(D,A)),C))),D) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[447,38]),272]),
[iquote('para_from,446.1.1,38.1.1.2,demod,272')] ).
cnf(457,plain,
double_divide(A,double_divide(inverse(B),multiply(A,multiply(C,B)))) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[449,40]),447]),
[iquote('para_from,449.1.1,40.1.1.1,demod,447')] ).
cnf(459,plain,
double_divide(A,double_divide(multiply(B,C),multiply(A,multiply(D,double_divide(C,B))))) = D,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[449,38]),8,447]),
[iquote('para_from,449.1.1,38.1.1.1,demod,8,447')] ).
cnf(461,plain,
multiply(double_divide(inverse(A),multiply(B,multiply(C,A))),B) = inverse(C),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[449,26]),8,447]),
[iquote('para_from,449.1.1,26.1.1.2,demod,8,447')] ).
cnf(467,plain,
double_divide(multiply(A,B),double_divide(inverse(multiply(double_divide(C,D),D)),multiply(A,B))) = C,
inference(para_into,[status(thm),theory(equality)],[457,433]),
[iquote('para_into,457.1.1.2.2,432.1.1')] ).
cnf(516,plain,
double_divide(A,double_divide(inverse(multiply(double_divide(B,C),C)),A)) = B,
inference(para_into,[status(thm),theory(equality)],[467,317]),
[iquote('para_into,467.1.1,317.1.1')] ).
cnf(531,plain,
multiply(double_divide(inverse(multiply(double_divide(A,B),B)),C),C) = inverse(A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[516,8])]),
[iquote('para_from,516.1.1,7.1.1.1,flip.1')] ).
cnf(554,plain,
multiply(double_divide(inverse(A),multiply(B,inverse(C))),B) = multiply(A,inverse(multiply(double_divide(C,D),D))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[531,461]),8]),
[iquote('para_from,530.1.1,461.1.1.1.2.2,demod,8')] ).
cnf(559,plain,
double_divide(A,double_divide(inverse(inverse(B)),A)) = inverse(multiply(double_divide(B,C),C)),
inference(para_from,[status(thm),theory(equality)],[531,516]),
[iquote('para_from,530.1.1,516.1.1.2.1.1')] ).
cnf(563,plain,
multiply(A,inverse(multiply(double_divide(B,C),C))) = multiply(double_divide(inverse(A),multiply(D,inverse(B))),D),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[554])]),
[iquote('copy,554,flip.1')] ).
cnf(566,plain,
inverse(multiply(double_divide(A,B),B)) = double_divide(C,double_divide(inverse(inverse(A)),C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[559])]),
[iquote('copy,559,flip.1')] ).
cnf(585,plain,
inverse(multiply(double_divide(A,B),B)) = inverse(multiply(double_divide(A,C),C)),
inference(para_into,[status(thm),theory(equality)],[559,559]),
[iquote('para_into,559.1.1,559.1.1')] ).
cnf(622,plain,
double_divide(A,double_divide(double_divide(B,double_divide(inverse(inverse(C)),B)),A)) = C,
inference(para_from,[status(thm),theory(equality)],[566,516]),
[iquote('para_from,566.1.1,516.1.1.2.1')] ).
cnf(625,plain,
multiply(double_divide(double_divide(A,double_divide(inverse(inverse(B)),A)),C),C) = inverse(B),
inference(para_from,[status(thm),theory(equality)],[566,531]),
[iquote('para_from,566.1.1,530.1.1.1.1')] ).
cnf(634,plain,
double_divide(A,double_divide(double_divide(double_divide(B,inverse(inverse(C))),double_divide(D,double_divide(B,D))),A)) = C,
inference(para_into,[status(thm),theory(equality)],[622,317]),
[iquote('para_into,622.1.1.2.1.2,317.1.1')] ).
cnf(636,plain,
double_divide(double_divide(double_divide(A,double_divide(inverse(inverse(B)),A)),double_divide(C,double_divide(inverse(inverse(D)),C))),B) = D,
inference(para_into,[status(thm),theory(equality)],[622,622]),
[iquote('para_into,622.1.1.2,622.1.1')] ).
cnf(644,plain,
double_divide(multiply(A,multiply(double_divide(A,B),B)),inverse(C)) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[622,391]),625]),
[iquote('para_into,622.1.1,391.1.1,demod,625')] ).
cnf(652,plain,
inverse(multiply(A,double_divide(double_divide(B,double_divide(inverse(inverse(A)),B)),C))) = inverse(multiply(double_divide(C,D),D)),
inference(para_from,[status(thm),theory(equality)],[622,585]),
[iquote('para_from,622.1.1,585.1.1.1.1')] ).
cnf(661,plain,
inverse(multiply(double_divide(A,B),B)) = inverse(multiply(C,double_divide(double_divide(D,double_divide(inverse(inverse(C)),D)),A))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[652])]),
[iquote('copy,652,flip.1')] ).
cnf(677,plain,
double_divide(multiply(A,multiply(double_divide(A,B),B)),multiply(C,D)) = double_divide(D,C),
inference(para_into,[status(thm),theory(equality)],[644,8]),
[iquote('para_into,644.1.1.2,7.1.1')] ).
cnf(690,plain,
double_divide(double_divide(A,B),double_divide(inverse(A),multiply(C,inverse(C)))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[644,9]),677]),
[iquote('para_from,644.1.1,9.1.1.2.2.1,demod,677')] ).
cnf(728,plain,
double_divide(double_divide(inverse(A),multiply(B,inverse(B))),double_divide(inverse(inverse(C)),A)) = C,
inference(para_from,[status(thm),theory(equality)],[690,622]),
[iquote('para_from,690.1.1,622.1.1.2')] ).
cnf(731,plain,
inverse(multiply(A,double_divide(inverse(B),multiply(C,inverse(C))))) = double_divide(D,double_divide(inverse(multiply(A,B)),D)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[690,566]),8]),
[iquote('para_from,690.1.1,566.1.1.1.1,demod,8')] ).
cnf(739,plain,
double_divide(A,double_divide(inverse(multiply(B,double_divide(inverse(C),multiply(D,inverse(D))))),A)) = double_divide(C,B),
inference(para_from,[status(thm),theory(equality)],[690,516]),
[iquote('para_from,690.1.1,516.1.1.2.1.1.1')] ).
cnf(759,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(para_into,[status(thm),theory(equality)],[728,690]),
[iquote('para_into,728.1.1,690.1.1')] ).
cnf(760,plain,
multiply(double_divide(A,B),multiply(B,A)) = multiply(C,inverse(C)),
inference(para_into,[status(thm),theory(equality)],[759,8]),
[iquote('para_into,759.1.1.2,7.1.1')] ).
cnf(768,plain,
double_divide(inverse(A),A) = double_divide(inverse(B),B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[759,677]),677]),
[iquote('para_from,759.1.1,676.1.1.2,demod,677')] ).
cnf(788,plain,
double_divide(multiply(double_divide(A,B),B),double_divide(inverse(C),C)) = A,
inference(para_from,[status(thm),theory(equality)],[768,516]),
[iquote('para_from,768.1.1,516.1.1.2')] ).
cnf(840,plain,
double_divide(multiply(A,multiply(double_divide(B,C),C)),inverse(A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[788,391]),531]),
[iquote('para_into,788.1.1,391.1.1,demod,531')] ).
cnf(845,plain,
double_divide(multiply(A,inverse(A)),multiply(double_divide(B,C),C)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[840,760]),8]),
[iquote('para_into,840.1.1.1,760.1.1,demod,8')] ).
cnf(855,plain,
double_divide(double_divide(A,multiply(B,double_divide(inverse(C),C))),A) = B,
inference(para_from,[status(thm),theory(equality)],[845,459]),
[iquote('para_from,845.1.1,459.1.1.2')] ).
cnf(862,plain,
double_divide(multiply(A,inverse(A)),multiply(B,C)) = double_divide(C,B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[845,677]),433]),
[iquote('para_from,845.1.1,676.1.1.1.2.1,demod,433')] ).
cnf(875,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[845]),862]),
[iquote('back_demod,845,demod,862')] ).
cnf(901,plain,
inverse(multiply(A,double_divide(inverse(B),multiply(C,inverse(C))))) = double_divide(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[739]),875]),
[iquote('back_demod,739,demod,875')] ).
cnf(903,plain,
inverse(multiply(A,B)) = double_divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[731]),901,875])]),
[iquote('back_demod,731,demod,901,875,flip.1')] ).
cnf(917,plain,
double_divide(double_divide(inverse(inverse(A)),B),A) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[661]),903,875,875,903])]),
[iquote('back_demod,661,demod,903,875,875,903,flip.1')] ).
cnf(926,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[636]),875,875,917]),
[iquote('back_demod,636,demod,875,875,917')] ).
cnf(928,plain,
double_divide(double_divide(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[634]),926,875,875]),
[iquote('back_demod,634,demod,926,875,875')] ).
cnf(935,plain,
multiply(double_divide(double_divide(A,B),C),C) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[431]),875,928,875]),
[iquote('back_demod,431,demod,875,928,875')] ).
cnf(946,plain,
multiply(double_divide(inverse(A),multiply(B,inverse(C))),B) = multiply(A,C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[563]),903,875])]),
[iquote('back_demod,563,demod,903,875,flip.1')] ).
cnf(980,plain,
multiply(A,double_divide(inverse(B),B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[855]),928]),
[iquote('back_demod,855,demod,928')] ).
cnf(1143,plain,
multiply(double_divide(inverse(A),multiply(b1,A)),b1) != multiply(inverse(a1),a1),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[980,22]),903,935]),
[iquote('para_from,980.1.1,22.1.1.1,demod,903,935')] ).
cnf(1144,plain,
$false,
inference(binary,[status(thm)],[1143,946]),
[iquote('binary,1143.1,946.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP502-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 05:05:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.13/2.31 ----- Otter 3.3f, August 2004 -----
% 2.13/2.31 The process was started by sandbox on n025.cluster.edu,
% 2.13/2.31 Wed Jul 27 05:05:45 2022
% 2.13/2.31 The command was "./otter". The process ID is 32628.
% 2.13/2.31
% 2.13/2.31 set(prolog_style_variables).
% 2.13/2.31 set(auto).
% 2.13/2.31 dependent: set(auto1).
% 2.13/2.31 dependent: set(process_input).
% 2.13/2.31 dependent: clear(print_kept).
% 2.13/2.31 dependent: clear(print_new_demod).
% 2.13/2.31 dependent: clear(print_back_demod).
% 2.13/2.31 dependent: clear(print_back_sub).
% 2.13/2.31 dependent: set(control_memory).
% 2.13/2.31 dependent: assign(max_mem, 12000).
% 2.13/2.31 dependent: assign(pick_given_ratio, 4).
% 2.13/2.31 dependent: assign(stats_level, 1).
% 2.13/2.31 dependent: assign(max_seconds, 10800).
% 2.13/2.31 clear(print_given).
% 2.13/2.31
% 2.13/2.31 list(usable).
% 2.13/2.31 0 [] A=A.
% 2.13/2.31 0 [] double_divide(double_divide(A,inverse(double_divide(B,C))),double_divide(inverse(B),inverse(double_divide(D,double_divide(A,D)))))=C.
% 2.13/2.31 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 2.13/2.31 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 2.13/2.31 end_of_list.
% 2.13/2.31
% 2.13/2.31 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 2.13/2.31
% 2.13/2.31 All clauses are units, and equality is present; the
% 2.13/2.31 strategy will be Knuth-Bendix with positive clauses in sos.
% 2.13/2.31
% 2.13/2.31 dependent: set(knuth_bendix).
% 2.13/2.31 dependent: set(anl_eq).
% 2.13/2.31 dependent: set(para_from).
% 2.13/2.31 dependent: set(para_into).
% 2.13/2.31 dependent: clear(para_from_right).
% 2.13/2.31 dependent: clear(para_into_right).
% 2.13/2.31 dependent: set(para_from_vars).
% 2.13/2.31 dependent: set(eq_units_both_ways).
% 2.13/2.31 dependent: set(dynamic_demod_all).
% 2.13/2.31 dependent: set(dynamic_demod).
% 2.13/2.31 dependent: set(order_eq).
% 2.13/2.31 dependent: set(back_demod).
% 2.13/2.31 dependent: set(lrpo).
% 2.13/2.31
% 2.13/2.31 ------------> process usable:
% 2.13/2.31 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 2.13/2.31
% 2.13/2.31 ------------> process sos:
% 2.13/2.31 ** KEPT (pick-wt=3): 3 [] A=A.
% 2.13/2.31 ** KEPT (pick-wt=18): 4 [] double_divide(double_divide(A,inverse(double_divide(B,C))),double_divide(inverse(B),inverse(double_divide(D,double_divide(A,D)))))=C.
% 2.13/2.31 ---> New Demodulator: 5 [new_demod,4] double_divide(double_divide(A,inverse(double_divide(B,C))),double_divide(inverse(B),inverse(double_divide(D,double_divide(A,D)))))=C.
% 2.13/2.31 ** KEPT (pick-wt=8): 7 [copy,6,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 2.13/2.31 ---> New Demodulator: 8 [new_demod,7] inverse(double_divide(A,B))=multiply(B,A).
% 2.13/2.31 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 2.13/2.31 >>>> Starting back demodulation with 5.
% 2.13/2.31 >>>> Starting back demodulation with 8.
% 2.13/2.31 >> back demodulating 4 with 8.
% 2.13/2.31 >>>> Starting back demodulation with 10.
% 2.13/2.31
% 2.13/2.31 ======= end of input processing =======
% 2.13/2.31
% 2.13/2.31 =========== start of search ===========
% 2.13/2.31
% 2.13/2.31
% 2.13/2.31 Resetting weight limit to 26.
% 2.13/2.31
% 2.13/2.31
% 2.13/2.31 Resetting weight limit to 26.
% 2.13/2.31
% 2.13/2.31 sos_size=175
% 2.13/2.31
% 2.13/2.31
% 2.13/2.31 Resetting weight limit to 23.
% 2.13/2.31
% 2.13/2.31
% 2.13/2.31 Resetting weight limit to 23.
% 2.13/2.31
% 2.13/2.31 sos_size=198
% 2.13/2.31
% 2.13/2.31
% 2.13/2.31 Resetting weight limit to 19.
% 2.13/2.31
% 2.13/2.31
% 2.13/2.31 Resetting weight limit to 19.
% 2.13/2.31
% 2.13/2.31 sos_size=306
% 2.13/2.31
% 2.13/2.31
% 2.13/2.31 Resetting weight limit to 16.
% 2.13/2.31
% 2.13/2.31
% 2.13/2.31 Resetting weight limit to 16.
% 2.13/2.31
% 2.13/2.31 sos_size=480
% 2.13/2.31
% 2.13/2.31
% 2.13/2.31 Resetting weight limit to 14.
% 2.13/2.31
% 2.13/2.31
% 2.13/2.31 Resetting weight limit to 14.
% 2.13/2.31
% 2.13/2.31 sos_size=533
% 2.13/2.31
% 2.13/2.31 -------- PROOF --------
% 2.13/2.31
% 2.13/2.31 ----> UNIT CONFLICT at 0.21 sec ----> 1144 [binary,1143.1,946.1] $F.
% 2.13/2.31
% 2.13/2.31 Length of proof is 76. Level of proof is 39.
% 2.13/2.31
% 2.13/2.31 ---------------- PROOF ----------------
% 2.13/2.31 % SZS status Unsatisfiable
% 2.13/2.31 % SZS output start Refutation
% See solution above
% 2.13/2.31 ------------ end of proof -------------
% 2.13/2.31
% 2.13/2.31
% 2.13/2.31 Search stopped by max_proofs option.
% 2.13/2.31
% 2.13/2.31
% 2.13/2.31 Search stopped by max_proofs option.
% 2.13/2.31
% 2.13/2.31 ============ end of search ============
% 2.13/2.31
% 2.13/2.31 -------------- statistics -------------
% 2.13/2.31 clauses given 137
% 2.13/2.31 clauses generated 18051
% 2.13/2.31 clauses kept 881
% 2.13/2.31 clauses forward subsumed 3855
% 2.13/2.31 clauses back subsumed 12
% 2.13/2.31 Kbytes malloced 9765
% 2.13/2.31
% 2.13/2.31 ----------- times (seconds) -----------
% 2.13/2.31 user CPU time 0.21 (0 hr, 0 min, 0 sec)
% 2.13/2.31 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.13/2.31 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.13/2.31
% 2.13/2.31 That finishes the proof of the theorem.
% 2.13/2.31
% 2.13/2.31 Process 32628 finished Wed Jul 27 05:05:47 2022
% 2.13/2.31 Otter interrupted
% 2.13/2.31 PROOF FOUND
%------------------------------------------------------------------------------