TSTP Solution File: GRP436-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP436-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 12:57:00 EDT 2022
% Result : Unsatisfiable 1.89s 2.07s
% Output : Refutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 2
% Syntax : Number of clauses : 81 ( 81 unt; 0 nHn; 3 RR)
% Number of literals : 81 ( 80 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 284 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP436-1.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(5,axiom,
multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A))))) = D,
file('GRP436-1.p',unknown),
[] ).
cnf(6,plain,
multiply(A,inverse(multiply(inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),E)))),multiply(F,multiply(multiply(inverse(F),inverse(D)),A))))) = E,
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,4.1.1.2.1.2.2.1.2.1,4.1.1')] ).
cnf(8,plain,
multiply(A,inverse(multiply(multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,D))),inverse(E))),multiply(E,multiply(C,A))))) = D,
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,4.1.1.2.1.2.2.1,4.1.1')] ).
cnf(16,plain,
multiply(A,inverse(multiply(multiply(B,multiply(C,inverse(D))),multiply(D,multiply(E,A))))) = multiply(F,multiply(multiply(inverse(F),inverse(multiply(C,E))),inverse(B))),
inference(para_into,[status(thm),theory(equality)],[8,5]),
[iquote('para_into,8.1.1.2.1.1.2.1,4.1.1')] ).
cnf(18,plain,
multiply(A,inverse(multiply(multiply(B,C),multiply(multiply(multiply(D,multiply(multiply(inverse(D),inverse(multiply(E,C))),inverse(F))),multiply(F,multiply(E,multiply(inverse(B),inverse(multiply(G,H)))))),multiply(G,A))))) = H,
inference(para_into,[status(thm),theory(equality)],[8,8]),
[iquote('para_into,8.1.1.2.1.1.2,8.1.1')] ).
cnf(37,plain,
multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))),inverse(multiply(multiply(E,multiply(F,inverse(G))),multiply(G,C)))) = multiply(H,multiply(multiply(inverse(H),inverse(multiply(F,D))),inverse(E))),
inference(para_into,[status(thm),theory(equality)],[16,5]),
[iquote('para_into,16.1.1.2.1.2.2,4.1.1')] ).
cnf(40,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))),inverse(B))) = D,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,8])]),
[iquote('para_into,16.1.1,8.1.1,flip.1')] ).
cnf(41,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,multiply(inverse(C),inverse(multiply(D,multiply(E,multiply(B,inverse(C))))))))),inverse(E))) = D,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,5])]),
[iquote('para_into,16.1.1,4.1.1,flip.1')] ).
cnf(62,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,E))),inverse(F))))),G))),inverse(B))) = inverse(multiply(multiply(F,multiply(D,inverse(H))),multiply(H,multiply(E,G)))),
inference(para_into,[status(thm),theory(equality)],[40,16]),
[iquote('para_into,39.1.1.2.1.2.1.1.2.1,16.1.1')] ).
cnf(70,plain,
inverse(multiply(multiply(A,multiply(B,inverse(C))),multiply(C,multiply(D,E)))) = multiply(F,multiply(multiply(inverse(F),inverse(multiply(multiply(inverse(G),inverse(multiply(H,multiply(multiply(inverse(H),inverse(multiply(B,D))),inverse(A))))),E))),inverse(G))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[62])]),
[iquote('copy,62,flip.1')] ).
cnf(139,plain,
multiply(A,multiply(multiply(inverse(A),inverse(B)),inverse(C))) = multiply(D,multiply(multiply(inverse(D),inverse(B)),inverse(C))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[6,40]),5]),
[iquote('para_from,6.1.1,39.1.1.2.1.2.1.1,demod,5')] ).
cnf(170,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(multiply(inverse(C),inverse(D)),inverse(E))))),F))),inverse(B))) = multiply(multiply(inverse(F),inverse(D)),inverse(E)),
inference(para_from,[status(thm),theory(equality)],[139,40]),
[iquote('para_from,139.1.1,39.1.1.2.1.2.1.1.2.1')] ).
cnf(186,plain,
inverse(multiply(multiply(A,multiply(B,inverse(C))),multiply(C,multiply(D,E)))) = multiply(multiply(inverse(E),inverse(multiply(B,D))),inverse(A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[70]),170]),
[iquote('back_demod,70,demod,170')] ).
cnf(251,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(A,multiply(D,inverse(B)))))),C))) = D,
inference(para_from,[status(thm),theory(equality)],[41,5]),
[iquote('para_from,41.1.1,4.1.1.2.1.2')] ).
cnf(259,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))) = multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(E,D))),E))),
inference(para_into,[status(thm),theory(equality)],[251,40]),
[iquote('para_into,251.1.1.2.1.1.2.1.2,39.1.1')] ).
cnf(262,plain,
multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))) = multiply(inverse(E),inverse(multiply(B,multiply(C,multiply(D,inverse(E)))))),
inference(para_from,[status(thm),theory(equality)],[251,5]),
[iquote('para_from,251.1.1,4.1.1.2.1.2.2.1')] ).
cnf(263,plain,
multiply(inverse(A),inverse(multiply(B,multiply(C,multiply(D,inverse(A)))))) = multiply(E,inverse(multiply(B,multiply(C,multiply(D,E))))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[262])]),
[iquote('copy,262,flip.1')] ).
cnf(269,plain,
multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))) = multiply(E,inverse(multiply(B,multiply(C,multiply(D,E))))),
inference(para_into,[status(thm),theory(equality)],[263,263]),
[iquote('para_into,263.1.1,263.1.1')] ).
cnf(271,plain,
multiply(inverse(A),inverse(multiply(multiply(B,inverse(multiply(C,multiply(A,multiply(D,B))))),C))) = D,
inference(para_from,[status(thm),theory(equality)],[269,251]),
[iquote('para_from,269.1.1,251.1.1.2.1.1')] ).
cnf(273,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,inverse(multiply(D,multiply(E,multiply(B,C)))))))),inverse(E))) = D,
inference(para_from,[status(thm),theory(equality)],[269,41]),
[iquote('para_from,269.1.1,41.1.1.2.1.2.1.2')] ).
cnf(291,plain,
inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = inverse(multiply(multiply(inverse(A),inverse(multiply(D,C))),D)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[259,18]),18]),
[iquote('para_from,259.1.1,17.1.1.2.1.2.1.2.2.2.2.1,demod,18')] ).
cnf(294,plain,
inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(D)),inverse(A)))))),B)) = inverse(D),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[291,6]),5])]),
[iquote('para_into,291.1.1.1.1,6.1.1,demod,5,flip.1')] ).
cnf(305,plain,
inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(D)),A))),inverse(C))))) = inverse(D),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[294,271]),186]),
[iquote('para_into,294.1.1.1.1,271.1.1,demod,186')] ).
cnf(307,plain,
inverse(multiply(multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(D)),A))))),B)) = inverse(D),
inference(para_into,[status(thm),theory(equality)],[294,269]),
[iquote('para_into,294.1.1.1.1,269.1.1')] ).
cnf(314,plain,
multiply(multiply(inverse(inverse(A)),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(inverse(A),inverse(D))))),C))),inverse(B)) = inverse(D),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[307,186]),186]),
[iquote('para_into,307.1.1.1.1.2,185.1.1,demod,186')] ).
cnf(324,plain,
multiply(multiply(inverse(inverse(A)),inverse(multiply(B,multiply(C,inverse(multiply(multiply(inverse(A),inverse(D)),multiply(E,multiply(B,C)))))))),inverse(E)) = inverse(D),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[305,269]),186]),
[iquote('para_into,305.1.1.1.2.2.1,269.1.1,demod,186')] ).
cnf(333,plain,
inverse(multiply(multiply(inverse(A),inverse(B)),multiply(C,multiply(inverse(C),inverse(D))))) = multiply(multiply(inverse(inverse(D)),inverse(inverse(B))),inverse(inverse(A))),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[324,314])]),
[iquote('para_from,324.1.1,314.1.1.1.2.1,flip.1')] ).
cnf(343,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),multiply(multiply(inverse(inverse(B)),inverse(inverse(C))),inverse(inverse(D)))),multiply(inverse(D),inverse(C))))) = inverse(A),
inference(para_from,[status(thm),theory(equality)],[333,271]),
[iquote('para_from,333.1.1,271.1.1.2.1.1.2')] ).
cnf(348,plain,
multiply(inverse(A),inverse(multiply(multiply(B,multiply(multiply(inverse(B),inverse(inverse(C))),inverse(inverse(D)))),multiply(inverse(D),inverse(C))))) = inverse(A),
inference(para_into,[status(thm),theory(equality)],[343,139]),
[iquote('para_into,343.1.1.2.1.1,139.1.1')] ).
cnf(351,plain,
multiply(A,multiply(inverse(A),inverse(B))) = multiply(C,multiply(inverse(C),inverse(B))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[348,139]),348]),
[iquote('para_from,347.1.1,139.1.1.2.1,demod,348')] ).
cnf(353,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[351,348]),348]),
[iquote('para_into,351.1.1.2,347.1.1,demod,348')] ).
cnf(430,plain,
multiply(A,multiply(B,inverse(B))) = multiply(C,multiply(inverse(C),inverse(inverse(A)))),
inference(para_from,[status(thm),theory(equality)],[353,351]),
[iquote('para_from,353.1.1,351.1.1.2')] ).
cnf(443,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,inverse(C)))),D))),inverse(B))) = inverse(D),
inference(para_from,[status(thm),theory(equality)],[353,40]),
[iquote('para_from,353.1.1,39.1.1.2.1.2.1.1.2.1')] ).
cnf(450,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(A,multiply(D,inverse(D)))))),C))) = B,
inference(para_from,[status(thm),theory(equality)],[353,271]),
[iquote('para_from,353.1.1,271.1.1.2.1.1.2.1.2.2')] ).
cnf(455,plain,
multiply(A,multiply(inverse(A),inverse(inverse(B)))) = multiply(B,multiply(C,inverse(C))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[430])]),
[iquote('copy,430,flip.1')] ).
cnf(627,plain,
multiply(multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(D)),A))))),B) = D,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[450,307]),450])]),
[iquote('para_into,449.1.1.2.1.1.1,307.1.1,demod,450,flip.1')] ).
cnf(633,plain,
multiply(multiply(inverse(A),inverse(multiply(B,C))),B) = multiply(multiply(inverse(A),inverse(multiply(D,C))),D),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[450,291]),450]),
[iquote('para_into,449.1.1.2.1.1.1,291.1.1,demod,450')] ).
cnf(642,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(multiply(C,inverse(C)),A))),D))) = D,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[450,37]),186,40])]),
[iquote('para_into,449.1.1.2.1.1,37.1.1,demod,186,40,flip.1')] ).
cnf(752,plain,
multiply(multiply(A,inverse(A)),B) = multiply(multiply(C,inverse(C)),B),
inference(para_from,[status(thm),theory(equality)],[642,627]),
[iquote('para_from,642.1.1,627.1.1.1.2.1')] ).
cnf(756,plain,
multiply(A,multiply(B,inverse(B))) = multiply(multiply(C,inverse(C)),multiply(inverse(multiply(D,inverse(D))),inverse(inverse(A)))),
inference(para_into,[status(thm),theory(equality)],[752,455]),
[iquote('para_into,752.1.1,455.1.1')] ).
cnf(787,plain,
multiply(multiply(inverse(A),inverse(multiply(B,inverse(B)))),C) = multiply(multiply(inverse(A),inverse(multiply(D,inverse(C)))),D),
inference(para_into,[status(thm),theory(equality)],[633,353]),
[iquote('para_into,633.1.1.1.2.1,353.1.1')] ).
cnf(788,plain,
multiply(multiply(inverse(A),inverse(multiply(B,inverse(C)))),B) = multiply(multiply(inverse(A),inverse(multiply(D,inverse(D)))),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[787])]),
[iquote('copy,787,flip.1')] ).
cnf(789,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),C))) = multiply(D,inverse(D)),
inference(para_from,[status(thm),theory(equality)],[633,642]),
[iquote('para_from,633.1.1,642.1.1.2.2')] ).
cnf(795,plain,
multiply(inverse(A),multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,inverse(C)))),A))) = multiply(D,inverse(D)),
inference(para_into,[status(thm),theory(equality)],[789,353]),
[iquote('para_into,789.1.1.2.2.1.2.1,353.1.1')] ).
cnf(798,plain,
multiply(A,inverse(A)) = multiply(inverse(B),multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,inverse(D)))),B))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[795])]),
[iquote('copy,795,flip.1')] ).
cnf(807,plain,
multiply(A,inverse(multiply(B,inverse(B)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[789,269]),5]),
[iquote('para_from,789.1.1,269.1.1.2.1,demod,5')] ).
cnf(816,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(inverse(B),C))),inverse(B))) = inverse(C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[443]),807]),
[iquote('back_demod,443,demod,807')] ).
cnf(817,plain,
multiply(A,inverse(A)) = multiply(inverse(B),multiply(C,multiply(inverse(C),B))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[798]),807]),
[iquote('back_demod,798,demod,807')] ).
cnf(818,plain,
multiply(inverse(A),multiply(B,multiply(inverse(B),A))) = multiply(C,inverse(C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[795]),807]),
[iquote('back_demod,795,demod,807')] ).
cnf(820,plain,
multiply(multiply(inverse(A),inverse(multiply(B,inverse(C)))),B) = multiply(inverse(A),C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[788]),807]),
[iquote('back_demod,788,demod,807')] ).
cnf(856,plain,
multiply(multiply(inverse(multiply(A,inverse(A))),inverse(multiply(B,multiply(C,multiply(inverse(C),inverse(D)))))),B) = D,
inference(para_from,[status(thm),theory(equality)],[807,627]),
[iquote('para_from,806.1.1,627.1.1.1.2.1.2.2')] ).
cnf(877,plain,
multiply(inverse(A),multiply(B,multiply(inverse(B),A))) = multiply(inverse(C),multiply(D,multiply(inverse(D),C))),
inference(para_into,[status(thm),theory(equality)],[817,817]),
[iquote('para_into,817.1.1,817.1.1')] ).
cnf(924,plain,
multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,multiply(inverse(C),D))))),B) = multiply(inverse(A),inverse(D)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[818,633]),807])]),
[iquote('para_from,818.1.1,633.1.1.1.2.1,demod,807,flip.1')] ).
cnf(937,plain,
multiply(inverse(multiply(A,inverse(A))),inverse(inverse(B))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[856]),924]),
[iquote('back_demod,856,demod,924')] ).
cnf(942,plain,
multiply(A,multiply(B,inverse(B))) = multiply(multiply(C,inverse(C)),A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[756]),937]),
[iquote('back_demod,756,demod,937')] ).
cnf(955,plain,
multiply(A,multiply(inverse(A),B)) = inverse(inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[937,40]),807,820]),
[iquote('para_from,936.1.1,39.1.1.2.1.2.1.1.2.1,demod,807,820')] ).
cnf(962,plain,
inverse(inverse(A)) = multiply(B,multiply(inverse(B),A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[955])]),
[iquote('copy,955,flip.1')] ).
cnf(971,plain,
multiply(multiply(A,inverse(A)),B) = inverse(inverse(inverse(inverse(B)))),
inference(para_into,[status(thm),theory(equality)],[955,937]),
[iquote('para_into,955.1.1.2,936.1.1')] ).
cnf(974,plain,
multiply(A,inverse(A)) = inverse(inverse(inverse(multiply(B,inverse(B))))),
inference(para_into,[status(thm),theory(equality)],[955,807]),
[iquote('para_into,955.1.1.2,806.1.1')] ).
cnf(983,plain,
multiply(A,multiply(B,inverse(B))) = inverse(inverse(inverse(inverse(A)))),
inference(para_into,[status(thm),theory(equality)],[955,353]),
[iquote('para_into,955.1.1.2,353.1.1')] ).
cnf(993,plain,
inverse(inverse(inverse(inverse(A)))) = multiply(multiply(B,inverse(B)),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[971])]),
[iquote('copy,971,flip.1')] ).
cnf(996,plain,
inverse(inverse(inverse(multiply(A,inverse(A))))) = multiply(B,inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[974])]),
[iquote('copy,974,flip.1')] ).
cnf(1001,plain,
inverse(inverse(inverse(inverse(A)))) = multiply(A,multiply(B,inverse(B))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[983])]),
[iquote('copy,983,flip.1')] ).
cnf(1021,plain,
inverse(multiply(A,inverse(multiply(B,inverse(inverse(A)))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[955,273]),816]),
[iquote('para_from,955.1.1,273.1.1.2.1.2.1.2.2.1.2,demod,816')] ).
cnf(1091,plain,
inverse(inverse(inverse(inverse(inverse(inverse(multiply(A,inverse(inverse(multiply(B,inverse(B))))))))))) = A,
inference(para_from,[status(thm),theory(equality)],[971,1021]),
[iquote('para_from,971.1.1,1021.1.1.1')] ).
cnf(1134,plain,
inverse(inverse(multiply(A,multiply(inverse(A),B)))) = multiply(multiply(C,inverse(C)),B),
inference(para_into,[status(thm),theory(equality)],[993,962]),
[iquote('para_into,993.1.1.1.1,962.1.1')] ).
cnf(1138,plain,
multiply(multiply(A,inverse(A)),B) = inverse(inverse(multiply(C,multiply(inverse(C),B)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1134])]),
[iquote('copy,1134,flip.1')] ).
cnf(1153,plain,
inverse(multiply(inverse(multiply(A,inverse(A))),inverse(multiply(B,multiply(C,inverse(C)))))) = B,
inference(para_from,[status(thm),theory(equality)],[996,1021]),
[iquote('para_from,996.1.1,1021.1.1.1.2.1.2')] ).
cnf(1155,plain,
inverse(inverse(multiply(A,inverse(A)))) = multiply(B,inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[996,993]),807]),
[iquote('para_from,996.1.1,993.1.1.1.1,demod,807')] ).
cnf(1185,plain,
inverse(multiply(inverse(multiply(A,inverse(A))),inverse(B))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1155,1021]),807]),
[iquote('para_from,1155.1.1,1021.1.1.1.2.1.2.1,demod,807')] ).
cnf(1188,plain,
multiply(A,inverse(multiply(inverse(multiply(B,inverse(B))),multiply(C,inverse(C))))) = A,
inference(para_from,[status(thm),theory(equality)],[1155,807]),
[iquote('para_from,1155.1.1,806.1.1.2.1.2')] ).
cnf(1198,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1153]),1185]),
[iquote('back_demod,1153,demod,1185')] ).
cnf(1203,plain,
multiply(A,inverse(inverse(multiply(B,inverse(B))))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1188]),1198]),
[iquote('back_demod,1188,demod,1198')] ).
cnf(1221,plain,
inverse(inverse(inverse(inverse(A)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1001]),1198]),
[iquote('back_demod,1001,demod,1198')] ).
cnf(1231,plain,
multiply(multiply(A,inverse(A)),B) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[942]),1198])]),
[iquote('back_demod,942,demod,1198,flip.1')] ).
cnf(1287,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1091]),1203,1221]),
[iquote('back_demod,1091,demod,1203,1221')] ).
cnf(1300,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1138]),1231,1287])]),
[iquote('back_demod,1138,demod,1231,1287,flip.1')] ).
cnf(1322,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[877]),1300,1300]),
[iquote('back_demod,877,demod,1300,1300')] ).
cnf(1323,plain,
$false,
inference(binary,[status(thm)],[1322,2]),
[iquote('binary,1322.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP436-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.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 05:19:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.89/2.07 ----- Otter 3.3f, August 2004 -----
% 1.89/2.07 The process was started by sandbox on n019.cluster.edu,
% 1.89/2.07 Wed Jul 27 05:19:07 2022
% 1.89/2.07 The command was "./otter". The process ID is 2022.
% 1.89/2.07
% 1.89/2.07 set(prolog_style_variables).
% 1.89/2.07 set(auto).
% 1.89/2.07 dependent: set(auto1).
% 1.89/2.07 dependent: set(process_input).
% 1.89/2.07 dependent: clear(print_kept).
% 1.89/2.07 dependent: clear(print_new_demod).
% 1.89/2.07 dependent: clear(print_back_demod).
% 1.89/2.07 dependent: clear(print_back_sub).
% 1.89/2.07 dependent: set(control_memory).
% 1.89/2.07 dependent: assign(max_mem, 12000).
% 1.89/2.07 dependent: assign(pick_given_ratio, 4).
% 1.89/2.07 dependent: assign(stats_level, 1).
% 1.89/2.07 dependent: assign(max_seconds, 10800).
% 1.89/2.07 clear(print_given).
% 1.89/2.07
% 1.89/2.07 list(usable).
% 1.89/2.07 0 [] A=A.
% 1.89/2.07 0 [] multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A)))))=D.
% 1.89/2.07 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.89/2.07 end_of_list.
% 1.89/2.07
% 1.89/2.07 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.89/2.07
% 1.89/2.07 All clauses are units, and equality is present; the
% 1.89/2.07 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.89/2.07
% 1.89/2.07 dependent: set(knuth_bendix).
% 1.89/2.07 dependent: set(anl_eq).
% 1.89/2.07 dependent: set(para_from).
% 1.89/2.07 dependent: set(para_into).
% 1.89/2.07 dependent: clear(para_from_right).
% 1.89/2.07 dependent: clear(para_into_right).
% 1.89/2.07 dependent: set(para_from_vars).
% 1.89/2.07 dependent: set(eq_units_both_ways).
% 1.89/2.07 dependent: set(dynamic_demod_all).
% 1.89/2.07 dependent: set(dynamic_demod).
% 1.89/2.07 dependent: set(order_eq).
% 1.89/2.07 dependent: set(back_demod).
% 1.89/2.07 dependent: set(lrpo).
% 1.89/2.07
% 1.89/2.07 ------------> process usable:
% 1.89/2.07 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.89/2.07
% 1.89/2.07 ------------> process sos:
% 1.89/2.07 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.89/2.07 ** KEPT (pick-wt=18): 4 [] multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A)))))=D.
% 1.89/2.07 ---> New Demodulator: 5 [new_demod,4] multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A)))))=D.
% 1.89/2.07 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.89/2.07 >>>> Starting back demodulation with 5.
% 1.89/2.07
% 1.89/2.07 ======= end of input processing =======
% 1.89/2.07
% 1.89/2.07 =========== start of search ===========
% 1.89/2.07
% 1.89/2.07
% 1.89/2.07 Resetting weight limit to 31.
% 1.89/2.07
% 1.89/2.07
% 1.89/2.07 Resetting weight limit to 31.
% 1.89/2.07
% 1.89/2.07 sos_size=100
% 1.89/2.07
% 1.89/2.07
% 1.89/2.07 Resetting weight limit to 29.
% 1.89/2.07
% 1.89/2.07
% 1.89/2.07 Resetting weight limit to 29.
% 1.89/2.07
% 1.89/2.07 sos_size=124
% 1.89/2.07
% 1.89/2.07
% 1.89/2.07 Resetting weight limit to 22.
% 1.89/2.07
% 1.89/2.07
% 1.89/2.07 Resetting weight limit to 22.
% 1.89/2.07
% 1.89/2.07 sos_size=342
% 1.89/2.07
% 1.89/2.07
% 1.89/2.07 Resetting weight limit to 16.
% 1.89/2.07
% 1.89/2.07
% 1.89/2.07 Resetting weight limit to 16.
% 1.89/2.07
% 1.89/2.07 sos_size=526
% 1.89/2.07
% 1.89/2.07 -------- PROOF --------
% 1.89/2.07
% 1.89/2.07 ----> UNIT CONFLICT at 0.20 sec ----> 1323 [binary,1322.1,2.1] $F.
% 1.89/2.07
% 1.89/2.07 Length of proof is 78. Level of proof is 32.
% 1.89/2.07
% 1.89/2.07 ---------------- PROOF ----------------
% 1.89/2.07 % SZS status Unsatisfiable
% 1.89/2.07 % SZS output start Refutation
% See solution above
% 1.89/2.07 ------------ end of proof -------------
% 1.89/2.07
% 1.89/2.07
% 1.89/2.07 Search stopped by max_proofs option.
% 1.89/2.07
% 1.89/2.07
% 1.89/2.07 Search stopped by max_proofs option.
% 1.89/2.07
% 1.89/2.07 ============ end of search ============
% 1.89/2.07
% 1.89/2.07 -------------- statistics -------------
% 1.89/2.07 clauses given 77
% 1.89/2.07 clauses generated 8918
% 1.89/2.07 clauses kept 930
% 1.89/2.07 clauses forward subsumed 2281
% 1.89/2.07 clauses back subsumed 11
% 1.89/2.07 Kbytes malloced 10742
% 1.89/2.07
% 1.89/2.07 ----------- times (seconds) -----------
% 1.89/2.07 user CPU time 0.21 (0 hr, 0 min, 0 sec)
% 1.89/2.07 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.89/2.07 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.89/2.07
% 1.89/2.07 That finishes the proof of the theorem.
% 1.89/2.07
% 1.89/2.07 Process 2022 finished Wed Jul 27 05:19:08 2022
% 1.89/2.07 Otter interrupted
% 1.89/2.07 PROOF FOUND
%------------------------------------------------------------------------------