TSTP Solution File: GRP579-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP579-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 12:57:17 EDT 2022
% Result : Unsatisfiable 1.97s 2.18s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 5
% Syntax : Number of clauses : 83 ( 83 unt; 0 nHn; 9 RR)
% Number of literals : 83 ( 82 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 157 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('GRP579-1.p',unknown),
[] ).
cnf(3,axiom,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = C,
file('GRP579-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP579-1.p',unknown),
[] ).
cnf(8,axiom,
inverse(A) = double_divide(A,identity),
file('GRP579-1.p',unknown),
[] ).
cnf(9,axiom,
identity = double_divide(A,inverse(A)),
file('GRP579-1.p',unknown),
[] ).
cnf(11,plain,
double_divide(A,double_divide(A,identity)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9]),8])]),
[iquote('copy,9,demod,8,flip.1')] ).
cnf(12,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),6,6,6,6])]),
[iquote('back_demod,1,demod,6,6,6,6,flip.1')] ).
cnf(13,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,B),double_divide(A,identity))),double_divide(identity,identity)) = B,
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.1.2.1.1,10.1.1')] ).
cnf(17,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(B,A),identity),
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.1.2.1,10.1.1')] ).
cnf(20,plain,
double_divide(double_divide(double_divide(A,double_divide(identity,B)),C),double_divide(A,identity)) = double_divide(double_divide(B,C),double_divide(identity,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[3,3])]),
[iquote('para_into,3.1.1.1.2,3.1.1,flip.1')] ).
cnf(25,plain,
double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),double_divide(identity,identity)) = A,
inference(para_into,[status(thm),theory(equality)],[13,11]),
[iquote('para_into,13.1.1.1.2,10.1.1')] ).
cnf(33,plain,
double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(para_into,[status(thm),theory(equality)],[25,11]),
[iquote('para_into,25.1.1.1.1.1,10.1.1')] ).
cnf(37,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity))),double_divide(identity,identity)) = B,
inference(para_from,[status(thm),theory(equality)],[25,3]),
[iquote('para_from,25.1.1,3.1.1.1.2.1.1')] ).
cnf(40,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[33,3]),11]),
[iquote('para_from,33.1.1,3.1.1.1.2.1,demod,11')] ).
cnf(44,plain,
double_divide(identity,identity) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[40,13]),40,40]),
[iquote('para_from,39.1.1,13.1.1.1.2,demod,40,40')] ).
cnf(47,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity))),identity) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[37]),44,44]),
[iquote('back_demod,37,demod,44,44')] ).
cnf(58,plain,
double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),44]),
[iquote('back_demod,25,demod,44')] ).
cnf(62,plain,
double_divide(double_divide(double_divide(A,double_divide(identity,B)),C),double_divide(A,identity)) = double_divide(double_divide(B,C),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[20]),44]),
[iquote('back_demod,20,demod,44')] ).
cnf(66,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),identity) = double_divide(double_divide(B,A),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),44]),
[iquote('back_demod,17,demod,44')] ).
cnf(71,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),identity) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),44]),
[iquote('back_demod,3,demod,44')] ).
cnf(73,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),A)),identity) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[47]),58]),
[iquote('back_demod,47,demod,58')] ).
cnf(79,plain,
double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(A,identity),
inference(para_into,[status(thm),theory(equality)],[73,11]),
[iquote('para_into,73.1.1.1.2.1,10.1.1')] ).
cnf(81,plain,
double_divide(double_divide(identity,A),identity) = double_divide(double_divide(B,A),B),
inference(para_into,[status(thm),theory(equality)],[73,73]),
[iquote('para_into,73.1.1.1.2,73.1.1')] ).
cnf(83,plain,
double_divide(double_divide(A,identity),identity) = double_divide(double_divide(B,A),B),
inference(para_from,[status(thm),theory(equality)],[73,58]),
[iquote('para_from,73.1.1,57.1.1.1.1')] ).
cnf(84,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),A)),B) = identity,
inference(para_from,[status(thm),theory(equality)],[73,11]),
[iquote('para_from,73.1.1,10.1.1.2')] ).
cnf(86,plain,
double_divide(double_divide(A,B),A) = double_divide(double_divide(B,identity),identity),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[83])]),
[iquote('copy,83,flip.1')] ).
cnf(94,plain,
double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(identity,A),
inference(para_from,[status(thm),theory(equality)],[79,58]),
[iquote('para_from,79.1.1,57.1.1.1.1')] ).
cnf(100,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[58]),94]),
[iquote('back_demod,57,demod,94')] ).
cnf(107,plain,
double_divide(double_divide(A,identity),A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[81,44]),44])]),
[iquote('para_into,81.1.1.1,43.1.1,demod,44,flip.1')] ).
cnf(110,plain,
double_divide(double_divide(A,double_divide(double_divide(B,C),B)),A) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[81,73])]),
[iquote('para_into,81.1.1,73.1.1,flip.1')] ).
cnf(137,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[86,107])]),
[iquote('para_into,86.1.1.1,107.1.1,flip.1')] ).
cnf(140,plain,
double_divide(double_divide(identity,double_divide(A,identity)),double_divide(B,A)) = double_divide(identity,double_divide(B,identity)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[86,86]),137,137]),
[iquote('para_into,86.1.1.1,86.1.1,demod,137,137')] ).
cnf(142,plain,
double_divide(double_divide(A,B),A) = double_divide(identity,double_divide(B,identity)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[86,84]),100,137]),
[iquote('para_into,86.1.1.1,84.1.1,demod,100,137')] ).
cnf(154,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[94]),137,142,137,100]),
[iquote('back_demod,93,demod,137,142,137,100')] ).
cnf(157,plain,
double_divide(identity,double_divide(A,identity)) = double_divide(double_divide(identity,double_divide(B,identity)),double_divide(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[140])]),
[iquote('copy,140,flip.1')] ).
cnf(161,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[110]),142,142,142,137,100]),
[iquote('back_demod,110,demod,142,142,142,137,100')] ).
cnf(162,plain,
double_divide(double_divide(identity,A),A) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[84]),142,161]),
[iquote('back_demod,84,demod,142,161')] ).
cnf(169,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[157])]),161,161]),
[iquote('copy,157,flip.1,demod,161,161')] ).
cnf(177,plain,
double_divide(double_divide(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[142]),169]),
[iquote('back_demod,141,demod,169')] ).
cnf(178,plain,
double_divide(double_divide(A,B),identity) = double_divide(double_divide(B,A),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[66]),169]),
[iquote('back_demod,66,demod,169')] ).
cnf(193,plain,
double_divide(double_divide(identity,A),double_divide(B,identity)) = double_divide(double_divide(B,A),identity),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[162,62]),100]),
[iquote('para_from,162.1.1,62.1.1.1.1,demod,100')] ).
cnf(194,plain,
double_divide(double_divide(A,B),identity) = double_divide(double_divide(identity,B),double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[193])]),
[iquote('copy,193,flip.1')] ).
cnf(197,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(para_into,[status(thm),theory(equality)],[169,11]),
[iquote('para_into,168.1.1.2,10.1.1')] ).
cnf(203,plain,
double_divide(double_divide(double_divide(A,B),C),double_divide(A,identity)) = double_divide(double_divide(double_divide(B,identity),C),identity),
inference(para_from,[status(thm),theory(equality)],[169,62]),
[iquote('para_from,168.1.1,62.1.1.1.1.2')] ).
cnf(204,plain,
double_divide(double_divide(double_divide(A,identity),B),identity) = double_divide(double_divide(double_divide(C,A),B),double_divide(C,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[203])]),
[iquote('copy,203,flip.1')] ).
cnf(208,plain,
double_divide(double_divide(A,B),double_divide(double_divide(double_divide(identity,C),A),identity)) = double_divide(double_divide(C,B),identity),
inference(para_from,[status(thm),theory(equality)],[177,62]),
[iquote('para_from,176.1.1,62.1.1.1.1')] ).
cnf(212,plain,
double_divide(double_divide(A,B),identity) = double_divide(double_divide(C,B),double_divide(double_divide(double_divide(identity,A),C),identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[208])]),
[iquote('copy,208,flip.1')] ).
cnf(265,plain,
double_divide(A,B) = double_divide(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[178,178]),197,177]),
[iquote('para_into,178.1.1.1,178.1.1,demod,197,177')] ).
cnf(273,plain,
double_divide(double_divide(A,B),identity) = double_divide(identity,double_divide(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[178,154])]),
[iquote('para_into,178.1.1,154.1.1,flip.1')] ).
cnf(310,plain,
double_divide(double_divide(A,B),double_divide(identity,double_divide(A,double_divide(identity,C)))) = double_divide(identity,double_divide(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[212]),273,273])]),
[iquote('back_demod,212,demod,273,273,flip.1')] ).
cnf(319,plain,
double_divide(double_divide(double_divide(A,B),C),double_divide(A,identity)) = double_divide(identity,double_divide(C,double_divide(B,identity))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[204]),273])]),
[iquote('back_demod,204,demod,273,flip.1')] ).
cnf(324,plain,
double_divide(double_divide(identity,A),double_divide(B,identity)) = double_divide(identity,double_divide(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[194]),273])]),
[iquote('back_demod,194,demod,273,flip.1')] ).
cnf(336,plain,
double_divide(identity,double_divide(A,B)) = double_divide(identity,double_divide(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[178]),273,273]),
[iquote('back_demod,178,demod,273,273')] ).
cnf(343,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[71]),319,273]),
[iquote('back_demod,71,demod,319,273')] ).
cnf(345,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(a3,b3)),c3)) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),273,273,273,273])]),
[iquote('back_demod,12,demod,273,273,273,273,flip.1')] ).
cnf(353,plain,
double_divide(A,double_divide(A,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[265,177])]),
[iquote('para_into,265.1.1,176.1.1,flip.1')] ).
cnf(354,plain,
double_divide(double_divide(A,B),B) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[265,169])]),
[iquote('para_into,265.1.1,168.1.1,flip.1')] ).
cnf(406,plain,
double_divide(A,double_divide(B,identity)) = double_divide(identity,double_divide(double_divide(identity,A),B)),
inference(para_into,[status(thm),theory(equality)],[324,353]),
[iquote('para_into,324.1.1.1,352.1.1')] ).
cnf(416,plain,
double_divide(double_divide(identity,A),B) = double_divide(identity,double_divide(A,double_divide(identity,B))),
inference(para_into,[status(thm),theory(equality)],[324,177]),
[iquote('para_into,324.1.1.2,176.1.1')] ).
cnf(418,plain,
double_divide(A,double_divide(identity,B)) = double_divide(A,double_divide(B,identity)),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[406])]),416,353]),
[iquote('copy,406,flip.1,demod,416,353')] ).
cnf(429,plain,
double_divide(A,double_divide(B,identity)) = double_divide(A,double_divide(identity,B)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[406]),416,353]),
[iquote('back_demod,406,demod,416,353')] ).
cnf(434,plain,
double_divide(double_divide(a3,b3),double_divide(identity,c3)) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[345]),416,353]),
[iquote('back_demod,345,demod,416,353')] ).
cnf(435,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(identity,B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[343]),416,353]),
[iquote('back_demod,343,demod,416,353')] ).
cnf(446,plain,
double_divide(identity,double_divide(A,double_divide(identity,B))) = double_divide(B,double_divide(A,identity)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[418,265]),416]),
[iquote('para_into,418.1.1,265.1.1,demod,416')] ).
cnf(452,plain,
double_divide(identity,double_divide(double_divide(A,identity),B)) = double_divide(A,double_divide(identity,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[418,273]),273,416,353]),
[iquote('para_from,418.1.1,272.1.1.1,demod,273,416,353')] ).
cnf(466,plain,
double_divide(double_divide(double_divide(A,identity),B),double_divide(identity,A)) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[429,177])]),
[iquote('para_into,429.1.1,176.1.1,flip.1')] ).
cnf(471,plain,
double_divide(identity,double_divide(A,double_divide(identity,B))) = double_divide(B,double_divide(identity,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[429,336]),452]),
[iquote('para_from,429.1.1,336.1.1.2,demod,452')] ).
cnf(477,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,C))),double_divide(identity,double_divide(C,B))) = A,
inference(para_into,[status(thm),theory(equality)],[435,273]),
[iquote('para_into,435.1.1.1.2,272.1.1')] ).
cnf(523,plain,
double_divide(double_divide(A,identity),B) = double_divide(identity,double_divide(A,double_divide(identity,B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[466,169]),416])]),
[iquote('para_from,466.1.1,168.1.1.2,demod,416,flip.1')] ).
cnf(540,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))) = double_divide(identity,B),
inference(para_from,[status(thm),theory(equality)],[416,169]),
[iquote('para_from,415.1.1,168.1.1.2')] ).
cnf(589,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(C,B),double_divide(A,identity)),
inference(para_into,[status(thm),theory(equality)],[446,336]),
[iquote('para_into,446.1.1.2.2,336.1.1')] ).
cnf(592,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(identity,double_divide(C,double_divide(identity,double_divide(B,A)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[589])]),
[iquote('copy,589,flip.1')] ).
cnf(716,plain,
double_divide(double_divide(A,double_divide(identity,B)),C) = double_divide(identity,double_divide(double_divide(B,double_divide(identity,A)),double_divide(identity,C))),
inference(para_from,[status(thm),theory(equality)],[471,416]),
[iquote('para_from,471.1.1,415.1.1.1')] ).
cnf(725,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(identity,B)),double_divide(identity,C))) = double_divide(double_divide(B,double_divide(identity,A)),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[716])]),
[iquote('copy,716,flip.1')] ).
cnf(826,plain,
double_divide(double_divide(A,double_divide(identity,B)),double_divide(identity,C)) = double_divide(identity,double_divide(A,double_divide(B,double_divide(identity,C)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[310,540]),416,353,416,353])]),
[iquote('para_into,310.1.1.1,540.1.1,demod,416,353,416,353,flip.1')] ).
cnf(874,plain,
double_divide(double_divide(A,double_divide(identity,B)),C) = double_divide(B,double_divide(A,double_divide(identity,C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[725]),826,353])]),
[iquote('back_demod,725,demod,826,353,flip.1')] ).
cnf(896,plain,
double_divide(double_divide(A,B),double_divide(C,double_divide(B,A))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[477]),874,353]),
[iquote('back_demod,477,demod,874,353')] ).
cnf(1001,plain,
double_divide(double_divide(A,B),C) = double_divide(C,double_divide(B,A)),
inference(para_into,[status(thm),theory(equality)],[896,354]),
[iquote('para_into,896.1.1.2,354.1.1')] ).
cnf(1007,plain,
double_divide(A,double_divide(B,C)) = double_divide(double_divide(C,B),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1001])]),
[iquote('copy,1001,flip.1')] ).
cnf(1049,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(identity,double_divide(B,double_divide(identity,double_divide(A,C)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[319,353]),273]),
[iquote('para_into,318.1.1.1.1,352.1.1,demod,273')] ).
cnf(1066,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(identity,double_divide(C,double_divide(identity,double_divide(A,B)))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[592]),1049]),
[iquote('back_demod,592,demod,1049')] ).
cnf(1109,plain,
double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(a3,b3)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[434,1007]),523])]),
[iquote('para_into,434.1.1,1007.1.1,demod,523,flip.1')] ).
cnf(1110,plain,
$false,
inference(binary,[status(thm)],[1109,1066]),
[iquote('binary,1109.1,1066.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP579-1 : TPTP v8.1.0. Released v2.6.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 05:54:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.97/2.18 ----- Otter 3.3f, August 2004 -----
% 1.97/2.18 The process was started by sandbox on n023.cluster.edu,
% 1.97/2.18 Wed Jul 27 05:54:48 2022
% 1.97/2.18 The command was "./otter". The process ID is 6389.
% 1.97/2.18
% 1.97/2.18 set(prolog_style_variables).
% 1.97/2.18 set(auto).
% 1.97/2.18 dependent: set(auto1).
% 1.97/2.18 dependent: set(process_input).
% 1.97/2.18 dependent: clear(print_kept).
% 1.97/2.18 dependent: clear(print_new_demod).
% 1.97/2.18 dependent: clear(print_back_demod).
% 1.97/2.18 dependent: clear(print_back_sub).
% 1.97/2.18 dependent: set(control_memory).
% 1.97/2.18 dependent: assign(max_mem, 12000).
% 1.97/2.18 dependent: assign(pick_given_ratio, 4).
% 1.97/2.18 dependent: assign(stats_level, 1).
% 1.97/2.18 dependent: assign(max_seconds, 10800).
% 1.97/2.18 clear(print_given).
% 1.97/2.18
% 1.97/2.18 list(usable).
% 1.97/2.18 0 [] A=A.
% 1.97/2.18 0 [] double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 1.97/2.18 0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.97/2.18 0 [] inverse(A)=double_divide(A,identity).
% 1.97/2.18 0 [] identity=double_divide(A,inverse(A)).
% 1.97/2.18 0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.97/2.18 end_of_list.
% 1.97/2.18
% 1.97/2.18 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.97/2.18
% 1.97/2.18 All clauses are units, and equality is present; the
% 1.97/2.18 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.97/2.18
% 1.97/2.18 dependent: set(knuth_bendix).
% 1.97/2.18 dependent: set(anl_eq).
% 1.97/2.18 dependent: set(para_from).
% 1.97/2.18 dependent: set(para_into).
% 1.97/2.18 dependent: clear(para_from_right).
% 1.97/2.18 dependent: clear(para_into_right).
% 1.97/2.18 dependent: set(para_from_vars).
% 1.97/2.18 dependent: set(eq_units_both_ways).
% 1.97/2.18 dependent: set(dynamic_demod_all).
% 1.97/2.18 dependent: set(dynamic_demod).
% 1.97/2.18 dependent: set(order_eq).
% 1.97/2.18 dependent: set(back_demod).
% 1.97/2.18 dependent: set(lrpo).
% 1.97/2.18
% 1.97/2.18 ------------> process usable:
% 1.97/2.18 ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.97/2.18
% 1.97/2.18 ------------> process sos:
% 1.97/2.18 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.97/2.18 ** KEPT (pick-wt=17): 3 [] double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 1.97/2.18 ---> New Demodulator: 4 [new_demod,3] double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 1.97/2.18 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.97/2.18 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.97/2.18 ** KEPT (pick-wt=6): 7 [] inverse(A)=double_divide(A,identity).
% 1.97/2.18 ---> New Demodulator: 8 [new_demod,7] inverse(A)=double_divide(A,identity).
% 1.97/2.18 ** KEPT (pick-wt=7): 10 [copy,9,demod,8,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.97/2.18 ---> New Demodulator: 11 [new_demod,10] double_divide(A,double_divide(A,identity))=identity.
% 1.97/2.18 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.97/2.18 >>>> Starting back demodulation with 4.
% 1.97/2.18 >>>> Starting back demodulation with 6.
% 1.97/2.18 >> back demodulating 1 with 6.
% 1.97/2.18 >>>> Starting back demodulation with 8.
% 1.97/2.18 >>>> Starting back demodulation with 11.
% 1.97/2.18
% 1.97/2.18 ======= end of input processing =======
% 1.97/2.18
% 1.97/2.18 =========== start of search ===========
% 1.97/2.18
% 1.97/2.18 -------- PROOF --------
% 1.97/2.18
% 1.97/2.18 ----> UNIT CONFLICT at 0.07 sec ----> 1110 [binary,1109.1,1066.1] $F.
% 1.97/2.18
% 1.97/2.18 Length of proof is 77. Level of proof is 28.
% 1.97/2.18
% 1.97/2.18 ---------------- PROOF ----------------
% 1.97/2.18 % SZS status Unsatisfiable
% 1.97/2.18 % SZS output start Refutation
% See solution above
% 1.97/2.18 ------------ end of proof -------------
% 1.97/2.18
% 1.97/2.18
% 1.97/2.18 Search stopped by max_proofs option.
% 1.97/2.18
% 1.97/2.18
% 1.97/2.18 Search stopped by max_proofs option.
% 1.97/2.18
% 1.97/2.18 ============ end of search ============
% 1.97/2.18
% 1.97/2.18 -------------- statistics -------------
% 1.97/2.18 clauses given 76
% 1.97/2.18 clauses generated 2944
% 1.97/2.18 clauses kept 672
% 1.97/2.18 clauses forward subsumed 2975
% 1.97/2.18 clauses back subsumed 18
% 1.97/2.18 Kbytes malloced 2929
% 1.97/2.18
% 1.97/2.18 ----------- times (seconds) -----------
% 1.97/2.18 user CPU time 0.07 (0 hr, 0 min, 0 sec)
% 1.97/2.18 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.97/2.18 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.97/2.18
% 1.97/2.18 That finishes the proof of the theorem.
% 1.97/2.18
% 1.97/2.18 Process 6389 finished Wed Jul 27 05:54:50 2022
% 1.97/2.18 Otter interrupted
% 1.97/2.18 PROOF FOUND
%------------------------------------------------------------------------------