%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP099-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 12:56:03 EDT 2022
% Result : Unsatisfiable 2.82s 3.02s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of clauses : 85 ( 78 unt; 0 nHn; 9 RR)
% Number of literals : 106 ( 105 equ; 28 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 171 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
file('GRP099-1.p',unknown),
[] ).
cnf(2,plain,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(b4,a4) != multiply(a4,b4) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.4')] ).
cnf(3,axiom,
A = A,
file('GRP099-1.p',unknown),
[] ).
cnf(4,axiom,
double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B,
file('GRP099-1.p',unknown),
[] ).
cnf(7,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP099-1.p',unknown),
[] ).
cnf(9,axiom,
inverse(A) = double_divide(A,identity),
file('GRP099-1.p',unknown),
[] ).
cnf(10,axiom,
identity = double_divide(A,inverse(A)),
file('GRP099-1.p',unknown),
[] ).
cnf(12,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)],[10]),9])]),
[iquote('copy,10,demod,9,flip.1')] ).
cnf(13,plain,
( double_divide(identity,identity) != identity
| double_divide(double_divide(a2,identity),identity) != a2
| 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)
| double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity) ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),9,7,12,7,7,7,7,7,7,7])])]),
[iquote('back_demod,2,demod,9,7,12,7,7,7,7,7,7,7,flip.3,flip.4')] ).
cnf(19,plain,
double_divide(double_divide(A,identity),double_divide(identity,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,12]),12]),
[iquote('para_into,4.1.1.1.2.1,11.1.1,demod,12')] ).
cnf(20,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(A,double_divide(B,C)),double_divide(identity,C))),
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.1.2.1,4.1.1')] ).
cnf(23,plain,
double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))) = double_divide(double_divide(identity,double_divide(B,double_divide(identity,identity))),double_divide(identity,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[20])]),
[iquote('copy,20,flip.1')] ).
cnf(25,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(A,identity),
inference(para_from,[status(thm),theory(equality)],[19,4]),
[iquote('para_from,18.1.1,4.1.1.1.2.1')] ).
cnf(28,plain,
double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[23]),25]),
[iquote('back_demod,23,demod,25')] ).
cnf(32,plain,
double_divide(double_divide(identity,A),double_divide(identity,identity)) = double_divide(double_divide(A,identity),identity),
inference(para_into,[status(thm),theory(equality)],[25,19]),
[iquote('para_into,24.1.1.1.2,18.1.1')] ).
cnf(34,plain,
double_divide(identity,identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,12]),19])]),
[iquote('para_into,24.1.1.1.2,11.1.1,demod,19,flip.1')] ).
cnf(35,plain,
double_divide(double_divide(A,identity),identity) = double_divide(double_divide(identity,A),identity),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[32])]),34]),
[iquote('copy,32,flip.1,demod,34')] ).
cnf(44,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),34]),
[iquote('back_demod,18,demod,34')] ).
cnf(47,plain,
( identity != identity
| a2 != a2
| 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)
| double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[13]),34,44]),
[iquote('back_demod,13,demod,34,44')] ).
cnf(48,plain,
double_divide(double_divide(identity,A),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[35])]),44]),
[iquote('copy,35,flip.1,demod,44')] ).
cnf(50,plain,
double_divide(double_divide(A,identity),A) = identity,
inference(para_from,[status(thm),theory(equality)],[44,12]),
[iquote('para_from,43.1.1,11.1.1.2')] ).
cnf(52,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,A),identity)) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[28,44]),34]),
[iquote('para_into,28.1.1.2.1.2,43.1.1,demod,34')] ).
cnf(54,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[28,34]),34,44]),
[iquote('para_into,28.1.1.2.1.2,33.1.1,demod,34,44')] ).
cnf(63,plain,
double_divide(A,double_divide(double_divide(B,double_divide(A,double_divide(double_divide(C,double_divide(identity,D)),double_divide(identity,D)))),double_divide(C,identity))) = double_divide(B,identity),
inference(para_into,[status(thm),theory(equality)],[28,28]),
[iquote('para_into,28.1.1.2.2,28.1.1')] ).
cnf(65,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[54])]),
[iquote('copy,54,flip.1')] ).
cnf(67,plain,
double_divide(double_divide(A,double_divide(identity,B)),double_divide(identity,B)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[48,28]),44])]),
[iquote('para_into,48.1.1.1,28.1.1,demod,44,flip.1')] ).
cnf(68,plain,
double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity))) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[63]),67]),
[iquote('back_demod,63,demod,67')] ).
cnf(78,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(identity,A))) = double_divide(B,identity),
inference(para_from,[status(thm),theory(equality)],[50,28]),
[iquote('para_from,50.1.1,28.1.1.2.1.2')] ).
cnf(87,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[65,48])]),
[iquote('para_into,65.1.1,48.1.1,flip.1')] ).
cnf(88,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[65,44])]),
[iquote('para_into,65.1.1,43.1.1,flip.1')] ).
cnf(99,plain,
double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(A,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[87,28]),87]),
[iquote('para_from,86.1.1,28.1.1.2.1.2,demod,87')] ).
cnf(101,plain,
double_divide(A,double_divide(double_divide(B,double_divide(A,double_divide(C,identity))),C)) = double_divide(B,identity),
inference(para_from,[status(thm),theory(equality)],[88,28]),
[iquote('para_from,88.1.1,28.1.1.2.2')] ).
cnf(104,plain,
double_divide(double_divide(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[52,52]),44,44,44]),
[iquote('para_into,52.1.1.2.1,52.1.1,demod,44,44,44')] ).
cnf(107,plain,
double_divide(double_divide(A,identity),double_divide(identity,double_divide(B,A))) = double_divide(B,identity),
inference(para_into,[status(thm),theory(equality)],[52,65]),
[iquote('para_into,52.1.1.2,65.1.1')] ).
cnf(111,plain,
double_divide(A,double_divide(B,A)) = B,
inference(para_into,[status(thm),theory(equality)],[104,104]),
[iquote('para_into,103.1.1.1,103.1.1')] ).
cnf(113,plain,
double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(double_divide(A,B),identity),
inference(para_into,[status(thm),theory(equality)],[104,52]),
[iquote('para_into,103.1.1.1,52.1.1')] ).
cnf(116,plain,
double_divide(double_divide(A,B),identity) = double_divide(double_divide(A,identity),double_divide(B,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[113])]),
[iquote('copy,113,flip.1')] ).
cnf(125,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)],[99,104])]),
[iquote('para_into,99.1.1.2.1,103.1.1,flip.1')] ).
cnf(135,plain,
double_divide(identity,double_divide(A,B)) = double_divide(double_divide(B,identity),double_divide(A,identity)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[116]),125]),
[iquote('back_demod,116,demod,125')] ).
cnf(146,plain,
( identity != identity
| a2 != a2
| 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))))
| double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4)) ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[47]),125,125,125,125,125,125])])]),
[iquote('back_demod,47,demod,125,125,125,125,125,125,flip.3,flip.4')] ).
cnf(154,plain,
double_divide(double_divide(A,B),B) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[99,104]),125,87])]),
[iquote('para_from,99.1.1,103.1.1.1,demod,125,87,flip.1')] ).
cnf(156,plain,
double_divide(A,double_divide(A,B)) = B,
inference(para_into,[status(thm),theory(equality)],[154,111]),
[iquote('para_into,153.1.1.1,111.1.1')] ).
cnf(157,plain,
double_divide(A,B) = double_divide(B,A),
inference(para_into,[status(thm),theory(equality)],[154,104]),
[iquote('para_into,153.1.1.1,103.1.1')] ).
cnf(158,plain,
double_divide(double_divide(A,B),double_divide(double_divide(C,A),double_divide(B,identity))) = double_divide(C,identity),
inference(para_into,[status(thm),theory(equality)],[68,154]),
[iquote('para_into,68.1.1.2.1.2,153.1.1')] ).
cnf(160,plain,
double_divide(A,double_divide(double_divide(B,C),double_divide(identity,double_divide(A,C)))) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[68,111]),125]),
[iquote('para_into,68.1.1.2.1.2,111.1.1,demod,125')] ).
cnf(166,plain,
double_divide(A,double_divide(B,double_divide(C,identity))) = double_divide(identity,double_divide(double_divide(A,C),B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[68,154]),125]),
[iquote('para_into,68.1.1.2.1,153.1.1,demod,125')] ).
cnf(174,plain,
double_divide(identity,double_divide(A,B)) = double_divide(identity,double_divide(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[125,157]),125]),
[iquote('para_into,124.1.1.1,157.1.1,demod,125')] ).
cnf(183,plain,
double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[78,154]),154]),
[iquote('para_into,78.1.1.2.1,153.1.1,demod,154')] ).
cnf(189,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),B)) = B,
inference(para_into,[status(thm),theory(equality)],[183,157]),
[iquote('para_into,183.1.1.2,157.1.1')] ).
cnf(191,plain,
double_divide(double_divide(A,identity),B) = double_divide(B,double_divide(identity,A)),
inference(para_into,[status(thm),theory(equality)],[183,154]),
[iquote('para_into,183.1.1.2,153.1.1')] ).
cnf(192,plain,
double_divide(double_divide(A,identity),B) = double_divide(double_divide(identity,A),B),
inference(para_into,[status(thm),theory(equality)],[183,104]),
[iquote('para_into,183.1.1.2,103.1.1')] ).
cnf(193,plain,
double_divide(A,double_divide(identity,B)) = double_divide(double_divide(B,identity),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[191])]),
[iquote('copy,191,flip.1')] ).
cnf(194,plain,
double_divide(double_divide(identity,A),B) = double_divide(double_divide(A,identity),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[192])]),
[iquote('copy,192,flip.1')] ).
cnf(195,plain,
double_divide(A,double_divide(B,identity)) = double_divide(A,double_divide(identity,B)),
inference(para_from,[status(thm),theory(equality)],[183,104]),
[iquote('para_from,183.1.1,103.1.1.1')] ).
cnf(240,plain,
double_divide(double_divide(double_divide(identity,A),B),double_divide(A,identity)) = B,
inference(para_into,[status(thm),theory(equality)],[189,157]),
[iquote('para_into,189.1.1,157.1.1')] ).
cnf(247,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(identity,B)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[191,111])]),
[iquote('para_into,191.1.1,111.1.1,flip.1')] ).
cnf(277,plain,
double_divide(identity,double_divide(double_divide(A,identity),B)) = double_divide(identity,double_divide(double_divide(identity,A),B)),
inference(para_from,[status(thm),theory(equality)],[193,174]),
[iquote('para_from,193.1.1,174.1.1.2')] ).
cnf(284,plain,
double_divide(identity,double_divide(double_divide(identity,A),B)) = double_divide(identity,double_divide(double_divide(A,identity),B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[277])]),
[iquote('copy,277,flip.1')] ).
cnf(337,plain,
double_divide(double_divide(double_divide(identity,double_divide(A,B)),C),double_divide(identity,double_divide(B,A))) = C,
inference(para_into,[status(thm),theory(equality)],[240,125]),
[iquote('para_into,240.1.1.2,124.1.1')] ).
cnf(355,plain,
double_divide(A,double_divide(B,C)) = double_divide(identity,double_divide(double_divide(A,double_divide(C,identity)),B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[101,154]),125]),
[iquote('para_into,101.1.1.2.1,153.1.1,demod,125')] ).
cnf(356,plain,
double_divide(A,double_divide(B,C)) = double_divide(identity,double_divide(B,double_divide(A,double_divide(C,identity)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[101,104]),125]),
[iquote('para_into,101.1.1.2.1,103.1.1,demod,125')] ).
cnf(365,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(B,identity)),C)) = double_divide(A,double_divide(C,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[355])]),
[iquote('copy,355,flip.1')] ).
cnf(366,plain,
double_divide(identity,double_divide(A,double_divide(B,double_divide(C,identity)))) = double_divide(B,double_divide(A,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[356])]),
[iquote('copy,356,flip.1')] ).
cnf(380,plain,
double_divide(identity,double_divide(double_divide(A,identity),B)) = double_divide(A,double_divide(identity,B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[107,247]),104,125])]),
[iquote('para_into,107.1.1.2.2,247.1.1,demod,104,125,flip.1')] ).
cnf(398,plain,
double_divide(identity,double_divide(double_divide(identity,A),B)) = double_divide(A,double_divide(identity,B)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[284]),380]),
[iquote('back_demod,284,demod,380')] ).
cnf(416,plain,
( identity != identity
| a2 != a2
| double_divide(double_divide(a3,b3),double_divide(identity,c3)) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3))))
| double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4)) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[146]),398]),
[iquote('back_demod,146,demod,398')] ).
cnf(422,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)],[135,195]),154]),
[iquote('para_into,135.1.1.2,195.1.1,demod,154')] ).
cnf(424,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_into,[status(thm),theory(equality)],[135,191]),154])]),
[iquote('para_into,135.1.1.2,191.1.1,demod,154,flip.1')] ).
cnf(426,plain,
double_divide(A,double_divide(B,identity)) = double_divide(identity,double_divide(B,double_divide(identity,A))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[422])]),
[iquote('copy,422,flip.1')] ).
cnf(456,plain,
double_divide(double_divide(identity,A),B) = double_divide(identity,double_divide(A,double_divide(identity,B))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[194]),424]),
[iquote('back_demod,194,demod,424')] ).
cnf(471,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,B),double_divide(identity,C)),double_divide(B,A))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[337]),456,456,156]),
[iquote('back_demod,337,demod,456,456,156')] ).
cnf(505,plain,
double_divide(double_divide(A,B),double_divide(C,double_divide(B,identity))) = double_divide(identity,double_divide(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[158,154]),125]),
[iquote('para_into,158.1.1.2.1,153.1.1,demod,125')] ).
cnf(544,plain,
double_divide(A,double_divide(B,double_divide(identity,double_divide(A,C)))) = double_divide(identity,double_divide(C,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[160,154]),125]),
[iquote('para_into,160.1.1.2.1,153.1.1,demod,125')] ).
cnf(701,plain,
double_divide(identity,double_divide(double_divide(A,B),C)) = double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,C)))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[166,426])]),
[iquote('para_into,166.1.1.2,426.1.1,flip.1')] ).
cnf(724,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)],[471]),701,456,156,156]),
[iquote('back_demod,471,demod,701,456,156,156')] ).
cnf(729,plain,
double_divide(A,double_divide(B,C)) = double_divide(A,double_divide(C,B)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[365]),701,424,156,156]),
[iquote('back_demod,365,demod,701,424,156,156')] ).
cnf(753,plain,
double_divide(double_divide(A,B),C) = double_divide(C,double_divide(B,A)),
inference(para_into,[status(thm),theory(equality)],[724,154]),
[iquote('para_into,724.1.1.2,153.1.1')] ).
cnf(757,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)],[753])]),
[iquote('copy,753,flip.1')] ).
cnf(1220,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(A,double_divide(C,identity))))) = double_divide(B,C),
inference(para_from,[status(thm),theory(equality)],[356,156]),
[iquote('para_from,356.1.1,155.1.1.2')] ).
cnf(1238,plain,
( identity != identity
| a2 != a2
| 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))))
| double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(a4,b4)) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[416,757]),424])]),
[iquote('para_into,416.3.1,757.1.1,demod,424,flip.3')] ).
cnf(1282,plain,
double_divide(double_divide(A,B),C) = double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,C))))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[505,104]),424]),
[iquote('para_into,505.1.1.2,103.1.1,demod,424')] ).
cnf(1376,plain,
double_divide(A,double_divide(B,double_divide(C,double_divide(A,D)))) = double_divide(C,double_divide(D,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[544,366]),1282,1282,156,156,156,156]),
[iquote('para_into,544.1.1.2.2,366.1.1,demod,1282,1282,156,156,156,156')] ).
cnf(2306,plain,
double_divide(A,double_divide(B,double_divide(C,double_divide(D,E)))) = double_divide(C,double_divide(D,double_divide(A,double_divide(E,B)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1376,1220]),1282,1282,156,1282,1282,156,156,156,156,156,156]),
[iquote('para_into,1376.1.1.2.2.2,1220.1.1,demod,1282,1282,156,1282,1282,156,156,156,156,156,156')] ).
cnf(2335,plain,
double_divide(A,double_divide(B,double_divide(C,double_divide(D,E)))) = double_divide(C,double_divide(E,double_divide(A,double_divide(B,D)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[2306])]),
[iquote('copy,2306,flip.1')] ).
cnf(4553,plain,
$false,
inference(hyper,[status(thm)],[1238,3,3,2335,729]),
[iquote('hyper,1238,3,3,2335,729')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP099-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 05:06:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.82/3.02 ----- Otter 3.3f, August 2004 -----
% 2.82/3.02 The process was started by sandbox on n003.cluster.edu,
% 2.82/3.02 Wed Jul 27 05:06:41 2022
% 2.82/3.02 The command was "./otter". The process ID is 19879.
% 2.82/3.02
% 2.82/3.02 set(prolog_style_variables).
% 2.82/3.02 set(auto).
% 2.82/3.02 dependent: set(auto1).
% 2.82/3.02 dependent: set(process_input).
% 2.82/3.02 dependent: clear(print_kept).
% 2.82/3.02 dependent: clear(print_new_demod).
% 2.82/3.02 dependent: clear(print_back_demod).
% 2.82/3.02 dependent: clear(print_back_sub).
% 2.82/3.02 dependent: set(control_memory).
% 2.82/3.02 dependent: assign(max_mem, 12000).
% 2.82/3.02 dependent: assign(pick_given_ratio, 4).
% 2.82/3.02 dependent: assign(stats_level, 1).
% 2.82/3.02 dependent: assign(max_seconds, 10800).
% 2.82/3.02 clear(print_given).
% 2.82/3.02
% 2.82/3.02 list(usable).
% 2.82/3.02 0 [] A=A.
% 2.82/3.02 0 [] double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),double_divide(identity,Z))),double_divide(identity,identity))=Y.
% 2.82/3.02 0 [] multiply(X,Y)=double_divide(double_divide(Y,X),identity).
% 2.82/3.02 0 [] inverse(X)=double_divide(X,identity).
% 2.82/3.02 0 [] identity=double_divide(X,inverse(X)).
% 2.82/3.02 0 [] multiply(inverse(a1),a1)!=identity|multiply(identity,a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3))|multiply(a4,b4)!=multiply(b4,a4).
% 2.82/3.02 end_of_list.
% 2.82/3.02
% 2.82/3.02 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 2.82/3.02
% 2.82/3.02 This is a Horn set with equality. The strategy will be
% 2.82/3.02 Knuth-Bendix and hyper_res, with positive clauses in
% 2.82/3.02 sos and nonpositive clauses in usable.
% 2.82/3.02
% 2.82/3.02 dependent: set(knuth_bendix).
% 2.82/3.02 dependent: set(anl_eq).
% 2.82/3.02 dependent: set(para_from).
% 2.82/3.02 dependent: set(para_into).
% 2.82/3.02 dependent: clear(para_from_right).
% 2.82/3.02 dependent: clear(para_into_right).
% 2.82/3.02 dependent: set(para_from_vars).
% 2.82/3.02 dependent: set(eq_units_both_ways).
% 2.82/3.02 dependent: set(dynamic_demod_all).
% 2.82/3.02 dependent: set(dynamic_demod).
% 2.82/3.02 dependent: set(order_eq).
% 2.82/3.02 dependent: set(back_demod).
% 2.82/3.02 dependent: set(lrpo).
% 2.82/3.02 dependent: set(hyper_res).
% 2.82/3.02 dependent: clear(order_hyper).
% 2.82/3.02
% 2.82/3.02 ------------> process usable:
% 2.82/3.02 ** KEPT (pick-wt=29): 2 [copy,1,flip.4] multiply(inverse(a1),a1)!=identity|multiply(identity,a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3))|multiply(b4,a4)!=multiply(a4,b4).
% 2.82/3.02
% 2.82/3.02 ------------> process sos:
% 2.82/3.02 ** KEPT (pick-wt=3): 3 [] A=A.
% 2.82/3.02 ** KEPT (pick-wt=17): 4 [] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity))=B.
% 2.82/3.02 ---> New Demodulator: 5 [new_demod,4] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity))=B.
% 2.82/3.02 ** KEPT (pick-wt=9): 6 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 2.82/3.02 ---> New Demodulator: 7 [new_demod,6] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 2.82/3.02 ** KEPT (pick-wt=6): 8 [] inverse(A)=double_divide(A,identity).
% 2.82/3.02 ---> New Demodulator: 9 [new_demod,8] inverse(A)=double_divide(A,identity).
% 2.82/3.02 ** KEPT (pick-wt=7): 11 [copy,10,demod,9,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 2.82/3.02 ---> New Demodulator: 12 [new_demod,11] double_divide(A,double_divide(A,identity))=identity.
% 2.82/3.02 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 2.82/3.02 >>>> Starting back demodulation with 5.
% 2.82/3.02 >>>> Starting back demodulation with 7.
% 2.82/3.02 >> back demodulating 2 with 7.
% 2.82/3.02 >>>> Starting back demodulation with 9.
% 2.82/3.02 >>>> Starting back demodulation with 12.
% 2.82/3.02
% 2.82/3.02 ======= end of input processing =======
% 2.82/3.02
% 2.82/3.02 =========== start of search ===========
% 2.82/3.02
% 2.82/3.02
% 2.82/3.02 Resetting weight limit to 19.
% 2.82/3.02
% 2.82/3.02
% 2.82/3.02 Resetting weight limit to 19.
% 2.82/3.02
% 2.82/3.02 sos_size=2334
% 2.82/3.02
% 2.82/3.02 -------- PROOF --------
% 2.82/3.02
% 2.82/3.02 -----> EMPTY CLAUSE at 1.15 sec ----> 4553 [hyper,1238,3,3,2335,729] $F.
% 2.82/3.02
% 2.82/3.02 Length of proof is 78. Level of proof is 20.
% 2.82/3.02
% 2.82/3.02 ---------------- PROOF ----------------
% 2.82/3.02 % SZS status Unsatisfiable
% 2.82/3.02 % SZS output start Refutation
% See solution above
% 2.82/3.02 ------------ end of proof -------------
% 2.82/3.02
% 2.82/3.02
% 2.82/3.02 Search stopped by max_proofs option.
% 2.82/3.02
% 2.82/3.02
% 2.82/3.02 Search stopped by max_proofs option.
% 2.82/3.02
% 2.82/3.02 ============ end of search ============
% 2.82/3.02
% 2.82/3.02 -------------- statistics -------------
% 2.82/3.02 clauses given 286
% 2.82/3.02 clauses generated 108170
% 2.82/3.02 clauses kept 3911
% 2.82/3.02 clauses forward subsumed 64531
% 2.82/3.02 clauses back subsumed 647
% 2.82/3.02 Kbytes malloced 4882
% 2.82/3.02
% 2.82/3.02 ----------- times (seconds) -----------
% 2.82/3.02 user CPU time 1.15 (0 hr, 0 min, 1 sec)
% 2.82/3.02 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.82/3.02 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.82/3.02
% 2.82/3.02 That finishes the proof of the theorem.
% 2.82/3.02
% 2.82/3.02 Process 19879 finished Wed Jul 27 05:06:44 2022
% 2.82/3.02 Otter interrupted
% 2.82/3.02 PROOF FOUND
%------------------------------------------------------------------------------