TSTP Solution File: GRP100-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP100-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 2.64s 2.88s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 6
% Syntax : Number of clauses : 82 ( 75 unt; 0 nHn; 9 RR)
% Number of literals : 103 ( 102 equ; 28 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 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 : 173 ( 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('GRP100-1.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('GRP100-1.p',unknown),
[] ).
cnf(4,axiom,
double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity))),double_divide(identity,identity)) = B,
file('GRP100-1.p',unknown),
[] ).
cnf(7,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP100-1.p',unknown),
[] ).
cnf(9,axiom,
inverse(A) = double_divide(A,identity),
file('GRP100-1.p',unknown),
[] ).
cnf(10,axiom,
identity = double_divide(A,inverse(A)),
file('GRP100-1.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(C,identity))),
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.1.2.1,4.1.1')] ).
cnf(21,plain,
double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity))) = 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(23,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(26,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)],[21]),23]),
[iquote('back_demod,21,demod,23')] ).
cnf(30,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)],[23,19]),
[iquote('para_into,22.1.1.1.2,18.1.1')] ).
cnf(32,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)],[23,12]),19])]),
[iquote('para_into,22.1.1.1.2,11.1.1,demod,19,flip.1')] ).
cnf(33,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)],[30])]),32]),
[iquote('copy,30,flip.1,demod,32')] ).
cnf(40,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),32]),
[iquote('back_demod,18,demod,32')] ).
cnf(43,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]),32,40]),
[iquote('back_demod,13,demod,32,40')] ).
cnf(45,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)],[33])]),40]),
[iquote('copy,33,flip.1,demod,40')] ).
cnf(48,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)],[26,40]),32]),
[iquote('para_into,26.1.1.2.1.2,39.1.1,demod,32')] ).
cnf(50,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[26,32]),32,40]),
[iquote('para_into,26.1.1.2.1.2,31.1.1,demod,32,40')] ).
cnf(55,plain,
double_divide(double_divide(A,double_divide(B,C)),double_divide(double_divide(A,identity),C)) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[26,26]),40]),
[iquote('para_into,26.1.1.2.1,26.1.1,demod,40')] ).
cnf(57,plain,
double_divide(A,double_divide(double_divide(B,double_divide(A,double_divide(C,identity))),C)) = double_divide(B,identity),
inference(para_into,[status(thm),theory(equality)],[26,40]),
[iquote('para_into,26.1.1.2.2,39.1.1')] ).
cnf(59,plain,
double_divide(A,double_divide(double_divide(B,double_divide(A,identity)),identity)) = double_divide(B,identity),
inference(para_into,[status(thm),theory(equality)],[26,32]),
[iquote('para_into,26.1.1.2.2,31.1.1')] ).
cnf(61,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[50])]),
[iquote('copy,50,flip.1')] ).
cnf(79,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[61,45])]),
[iquote('para_into,61.1.1,44.1.1,flip.1')] ).
cnf(84,plain,
double_divide(A,double_divide(double_divide(B,double_divide(identity,A)),identity)) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[61,26]),32]),
[iquote('para_from,61.1.1,26.1.1.2.1.2,demod,32')] ).
cnf(91,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)],[79,26]),45]),
[iquote('para_from,78.1.1,26.1.1.2.1.2,demod,45')] ).
cnf(93,plain,
double_divide(double_divide(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[48,48]),40,40,40]),
[iquote('para_into,48.1.1.2.1,48.1.1,demod,40,40,40')] ).
cnf(97,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)],[48,61]),
[iquote('para_into,48.1.1.2,61.1.1')] ).
cnf(102,plain,
double_divide(A,double_divide(B,A)) = B,
inference(para_into,[status(thm),theory(equality)],[93,93]),
[iquote('para_into,93.1.1.1,93.1.1')] ).
cnf(103,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)],[93,48]),
[iquote('para_into,93.1.1.1,48.1.1')] ).
cnf(106,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)],[103])]),
[iquote('copy,103,flip.1')] ).
cnf(115,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)],[91,93])]),
[iquote('para_into,91.1.1.2.1,93.1.1,flip.1')] ).
cnf(125,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)],[106]),115]),
[iquote('back_demod,106,demod,115')] ).
cnf(130,plain,
double_divide(A,double_divide(identity,double_divide(double_divide(identity,A),B))) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[84]),115]),
[iquote('back_demod,84,demod,115')] ).
cnf(134,plain,
double_divide(A,double_divide(identity,double_divide(double_divide(A,identity),B))) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[59]),115]),
[iquote('back_demod,59,demod,115')] ).
cnf(136,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)],[43]),115,115,115,115,115,115])])]),
[iquote('back_demod,43,demod,115,115,115,115,115,115,flip.3,flip.4')] ).
cnf(144,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)],[91,93]),115,79])]),
[iquote('para_from,91.1.1,93.1.1.1,demod,115,79,flip.1')] ).
cnf(146,plain,
double_divide(A,double_divide(A,B)) = B,
inference(para_into,[status(thm),theory(equality)],[144,102]),
[iquote('para_into,143.1.1.1,101.1.1')] ).
cnf(147,plain,
double_divide(A,B) = double_divide(B,A),
inference(para_into,[status(thm),theory(equality)],[144,93]),
[iquote('para_into,143.1.1.1,93.1.1')] ).
cnf(165,plain,
double_divide(double_divide(A,double_divide(B,double_divide(C,double_divide(A,identity)))),C) = double_divide(B,identity),
inference(para_into,[status(thm),theory(equality)],[55,102]),
[iquote('para_into,55.1.1.2,101.1.1')] ).
cnf(185,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)],[57,144]),115]),
[iquote('para_into,57.1.1.2.1,143.1.1,demod,115')] ).
cnf(186,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)],[57,93]),115]),
[iquote('para_into,57.1.1.2.1,93.1.1,demod,115')] ).
cnf(192,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)],[186])]),
[iquote('copy,186,flip.1')] ).
cnf(196,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(A,identity)))) = double_divide(B,identity),
inference(para_into,[status(thm),theory(equality)],[97,144]),
[iquote('para_into,97.1.1.1,143.1.1')] ).
cnf(200,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))) = double_divide(B,identity),
inference(para_into,[status(thm),theory(equality)],[97,93]),
[iquote('para_into,97.1.1.1,93.1.1')] ).
cnf(229,plain,
double_divide(double_divide(identity,double_divide(A,B)),double_divide(A,identity)) = double_divide(identity,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[125,102]),115])]),
[iquote('para_into,125.1.1.2,101.1.1,demod,115,flip.1')] ).
cnf(234,plain,
double_divide(identity,double_divide(double_divide(identity,A),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)],[130,102]),115])]),
[iquote('para_into,130.1.1.2.2,101.1.1,demod,115,flip.1')] ).
cnf(238,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)],[136]),234]),
[iquote('back_demod,136,demod,234')] ).
cnf(250,plain,
double_divide(A,double_divide(identity,B)) = double_divide(identity,double_divide(B,double_divide(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[134,146]),115]),
[iquote('para_into,134.1.1.2.2,145.1.1,demod,115')] ).
cnf(284,plain,
double_divide(A,double_divide(B,identity)) = double_divide(identity,double_divide(B,double_divide(A,identity))),
inference(para_from,[status(thm),theory(equality)],[196,146]),
[iquote('para_from,196.1.1,145.1.1.2')] ).
cnf(286,plain,
double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(B,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[284])]),
[iquote('copy,284,flip.1')] ).
cnf(288,plain,
double_divide(A,double_divide(B,identity)) = double_divide(identity,double_divide(B,double_divide(identity,A))),
inference(para_from,[status(thm),theory(equality)],[200,146]),
[iquote('para_from,200.1.1,145.1.1.2')] ).
cnf(290,plain,
double_divide(double_divide(A,identity),B) = double_divide(identity,double_divide(A,double_divide(identity,B))),
inference(para_from,[status(thm),theory(equality)],[200,93]),
[iquote('para_from,200.1.1,93.1.1.1')] ).
cnf(306,plain,
double_divide(A,double_divide(B,identity)) = double_divide(A,double_divide(identity,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[229,200]),102,146]),
[iquote('para_into,229.1.1.1.2,200.1.1,demod,102,146')] ).
cnf(312,plain,
double_divide(A,double_divide(identity,B)) = double_divide(A,double_divide(B,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[306])]),
[iquote('copy,306,flip.1')] ).
cnf(350,plain,
double_divide(double_divide(double_divide(identity,A),B),double_divide(A,identity)) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[312,93])]),
[iquote('para_into,312.1.1,93.1.1,flip.1')] ).
cnf(374,plain,
double_divide(double_divide(identity,A),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)],[350,102]),290])]),
[iquote('para_from,350.1.1,101.1.1.2,demod,290,flip.1')] ).
cnf(409,plain,
double_divide(double_divide(A,B),C) = double_divide(identity,double_divide(B,double_divide(C,double_divide(A,identity)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[165,93]),115]),
[iquote('para_into,165.1.1.1.2,93.1.1,demod,115')] ).
cnf(416,plain,
double_divide(identity,double_divide(A,double_divide(B,double_divide(C,identity)))) = double_divide(double_divide(C,A),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[409])]),
[iquote('copy,409,flip.1')] ).
cnf(643,plain,
double_divide(double_divide(A,double_divide(B,identity)),C) = double_divide(identity,double_divide(double_divide(B,double_divide(A,identity)),double_divide(identity,C))),
inference(para_into,[status(thm),theory(equality)],[374,286]),
[iquote('para_into,373.1.1.1,286.1.1')] ).
cnf(647,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(B,identity)),double_divide(identity,C))) = double_divide(double_divide(B,double_divide(A,identity)),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[643])]),
[iquote('copy,643,flip.1')] ).
cnf(710,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(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[185,288]),144])]),
[iquote('para_into,185.1.1.2,288.1.1,demod,144,flip.1')] ).
cnf(714,plain,
double_divide(A,double_divide(B,double_divide(C,D))) = double_divide(A,double_divide(identity,double_divide(C,double_divide(identity,double_divide(D,double_divide(identity,B)))))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[185,185]),710,290,146,146,115,710,374,146,710]),
[iquote('para_into,185.1.1.2,185.1.1,demod,710,290,146,146,115,710,374,146,710')] ).
cnf(719,plain,
double_divide(double_divide(A,B),C) = double_divide(C,double_divide(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[185,147]),710,290,146,146]),
[iquote('para_into,185.1.1,147.1.1,demod,710,290,146,146')] ).
cnf(720,plain,
double_divide(double_divide(double_divide(A,B),C),double_divide(B,A)) = C,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[185,93]),710,290,146,146])]),
[iquote('para_into,185.1.1,93.1.1,demod,710,290,146,146,flip.1')] ).
cnf(738,plain,
double_divide(double_divide(A,double_divide(B,identity)),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)],[647]),710,146,290,146])]),
[iquote('back_demod,647,demod,710,146,290,146,flip.1')] ).
cnf(778,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)],[719])]),
[iquote('copy,719,flip.1')] ).
cnf(815,plain,
double_divide(A,double_divide(B,C)) = double_divide(A,double_divide(C,B)),
inference(para_into,[status(thm),theory(equality)],[719,147]),
[iquote('para_into,719.1.1,147.1.1')] ).
cnf(837,plain,
double_divide(double_divide(A,B),C) = double_divide(double_divide(B,A),C),
inference(para_from,[status(thm),theory(equality)],[720,102]),
[iquote('para_from,720.1.1,101.1.1.2')] ).
cnf(965,plain,
double_divide(double_divide(double_divide(A,B),C),D) = double_divide(double_divide(C,double_divide(B,A)),D),
inference(para_into,[status(thm),theory(equality)],[837,837]),
[iquote('para_into,837.1.1.1,837.1.1')] ).
cnf(970,plain,
double_divide(double_divide(double_divide(A,B),C),D) = double_divide(A,double_divide(identity,double_divide(B,double_divide(C,double_divide(identity,D))))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[837,186]),374,710,146,738])]),
[iquote('para_into,837.1.1.1,186.1.1,demod,374,710,146,738,flip.1')] ).
cnf(973,plain,
double_divide(double_divide(A,double_divide(B,C)),D) = double_divide(C,double_divide(identity,double_divide(B,double_divide(A,double_divide(identity,D))))),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[965])]),970]),
[iquote('copy,965,flip.1,demod,970')] ).
cnf(1047,plain,
double_divide(A,double_divide(B,double_divide(C,D))) = double_divide(D,double_divide(B,double_divide(C,A))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[192,250]),973,102,290,146,146]),
[iquote('para_from,192.1.1,250.1.1.2,demod,973,102,290,146,146')] ).
cnf(1223,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)],[238,778]),290])]),
[iquote('para_into,238.3.1,778.1.1,demod,290,flip.3')] ).
cnf(1378,plain,
double_divide(double_divide(A,B),C) = double_divide(identity,double_divide(B,double_divide(identity,double_divide(A,double_divide(identity,C))))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[416,778]),374])]),
[iquote('para_into,416.1.1.2.2,778.1.1,demod,374,flip.1')] ).
cnf(2334,plain,
double_divide(A,double_divide(B,double_divide(C,double_divide(D,A)))) = double_divide(C,double_divide(D,B)),
inference(para_from,[status(thm),theory(equality)],[1047,146]),
[iquote('para_from,1047.1.1,145.1.1.2')] ).
cnf(3270,plain,
double_divide(A,double_divide(B,double_divide(C,double_divide(D,E)))) = double_divide(A,double_divide(D,double_divide(C,double_divide(E,B)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[714,2334]),1378,146,1378,146,1378,146,146,146,146,146]),
[iquote('para_into,714.1.1.2.2,2334.1.1,demod,1378,146,1378,146,1378,146,146,146,146,146')] ).
cnf(3298,plain,
double_divide(A,double_divide(B,double_divide(C,double_divide(D,E)))) = double_divide(A,double_divide(E,double_divide(C,double_divide(B,D)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3270])]),
[iquote('copy,3270,flip.1')] ).
cnf(4446,plain,
$false,
inference(hyper,[status(thm)],[1223,3,3,3298,815]),
[iquote('hyper,1223,3,3,3298,815')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP100-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n017.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 04:54:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.64/2.88 ----- Otter 3.3f, August 2004 -----
% 2.64/2.88 The process was started by sandbox on n017.cluster.edu,
% 2.64/2.88 Wed Jul 27 04:54:48 2022
% 2.64/2.88 The command was "./otter". The process ID is 20443.
% 2.64/2.88
% 2.64/2.88 set(prolog_style_variables).
% 2.64/2.88 set(auto).
% 2.64/2.88 dependent: set(auto1).
% 2.64/2.88 dependent: set(process_input).
% 2.64/2.88 dependent: clear(print_kept).
% 2.64/2.88 dependent: clear(print_new_demod).
% 2.64/2.88 dependent: clear(print_back_demod).
% 2.64/2.88 dependent: clear(print_back_sub).
% 2.64/2.88 dependent: set(control_memory).
% 2.64/2.88 dependent: assign(max_mem, 12000).
% 2.64/2.88 dependent: assign(pick_given_ratio, 4).
% 2.64/2.88 dependent: assign(stats_level, 1).
% 2.64/2.88 dependent: assign(max_seconds, 10800).
% 2.64/2.88 clear(print_given).
% 2.64/2.88
% 2.64/2.88 list(usable).
% 2.64/2.88 0 [] A=A.
% 2.64/2.88 0 [] double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),double_divide(Z,identity))),double_divide(identity,identity))=Y.
% 2.64/2.88 0 [] multiply(X,Y)=double_divide(double_divide(Y,X),identity).
% 2.64/2.88 0 [] inverse(X)=double_divide(X,identity).
% 2.64/2.88 0 [] identity=double_divide(X,inverse(X)).
% 2.64/2.88 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).
% 2.64/2.88 end_of_list.
% 2.64/2.88
% 2.64/2.88 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 2.64/2.88
% 2.64/2.88 This is a Horn set with equality. The strategy will be
% 2.64/2.88 Knuth-Bendix and hyper_res, with positive clauses in
% 2.64/2.88 sos and nonpositive clauses in usable.
% 2.64/2.88
% 2.64/2.88 dependent: set(knuth_bendix).
% 2.64/2.88 dependent: set(anl_eq).
% 2.64/2.88 dependent: set(para_from).
% 2.64/2.88 dependent: set(para_into).
% 2.64/2.88 dependent: clear(para_from_right).
% 2.64/2.88 dependent: clear(para_into_right).
% 2.64/2.88 dependent: set(para_from_vars).
% 2.64/2.88 dependent: set(eq_units_both_ways).
% 2.64/2.88 dependent: set(dynamic_demod_all).
% 2.64/2.88 dependent: set(dynamic_demod).
% 2.64/2.88 dependent: set(order_eq).
% 2.64/2.88 dependent: set(back_demod).
% 2.64/2.88 dependent: set(lrpo).
% 2.64/2.88 dependent: set(hyper_res).
% 2.64/2.88 dependent: clear(order_hyper).
% 2.64/2.88
% 2.64/2.88 ------------> process usable:
% 2.64/2.88 ** 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).
% 2.64/2.88
% 2.64/2.88 ------------> process sos:
% 2.64/2.88 ** KEPT (pick-wt=3): 3 [] A=A.
% 2.64/2.88 ** KEPT (pick-wt=17): 4 [] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity))),double_divide(identity,identity))=B.
% 2.64/2.88 ---> New Demodulator: 5 [new_demod,4] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity))),double_divide(identity,identity))=B.
% 2.64/2.88 ** KEPT (pick-wt=9): 6 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 2.64/2.88 ---> New Demodulator: 7 [new_demod,6] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 2.64/2.88 ** KEPT (pick-wt=6): 8 [] inverse(A)=double_divide(A,identity).
% 2.64/2.88 ---> New Demodulator: 9 [new_demod,8] inverse(A)=double_divide(A,identity).
% 2.64/2.88 ** KEPT (pick-wt=7): 11 [copy,10,demod,9,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 2.64/2.88 ---> New Demodulator: 12 [new_demod,11] double_divide(A,double_divide(A,identity))=identity.
% 2.64/2.88 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 2.64/2.88 >>>> Starting back demodulation with 5.
% 2.64/2.88 >>>> Starting back demodulation with 7.
% 2.64/2.88 >> back demodulating 2 with 7.
% 2.64/2.88 >>>> Starting back demodulation with 9.
% 2.64/2.88 >>>> Starting back demodulation with 12.
% 2.64/2.88
% 2.64/2.88 ======= end of input processing =======
% 2.64/2.88
% 2.64/2.88 =========== start of search ===========
% 2.64/2.88
% 2.64/2.88
% 2.64/2.88 Resetting weight limit to 19.
% 2.64/2.88
% 2.64/2.88
% 2.64/2.88 Resetting weight limit to 19.
% 2.64/2.88
% 2.64/2.88 sos_size=1973
% 2.64/2.88
% 2.64/2.88 -------- PROOF --------
% 2.64/2.88
% 2.64/2.88 -----> EMPTY CLAUSE at 1.02 sec ----> 4446 [hyper,1223,3,3,3298,815] $F.
% 2.64/2.88
% 2.64/2.88 Length of proof is 75. Level of proof is 25.
% 2.64/2.88
% 2.64/2.88 ---------------- PROOF ----------------
% 2.64/2.88 % SZS status Unsatisfiable
% 2.64/2.88 % SZS output start Refutation
% See solution above
% 2.64/2.89 ------------ end of proof -------------
% 2.64/2.89
% 2.64/2.89
% 2.64/2.89 Search stopped by max_proofs option.
% 2.64/2.89
% 2.64/2.89
% 2.64/2.89 Search stopped by max_proofs option.
% 2.64/2.89
% 2.64/2.89 ============ end of search ============
% 2.64/2.89
% 2.64/2.89 -------------- statistics -------------
% 2.64/2.89 clauses given 261
% 2.64/2.89 clauses generated 83914
% 2.64/2.89 clauses kept 3776
% 2.64/2.89 clauses forward subsumed 57797
% 2.64/2.89 clauses back subsumed 802
% 2.64/2.89 Kbytes malloced 4882
% 2.64/2.89
% 2.64/2.89 ----------- times (seconds) -----------
% 2.64/2.89 user CPU time 1.02 (0 hr, 0 min, 1 sec)
% 2.64/2.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.64/2.89 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.64/2.89
% 2.64/2.89 That finishes the proof of the theorem.
% 2.64/2.89
% 2.64/2.89 Process 20443 finished Wed Jul 27 04:54:50 2022
% 2.64/2.89 Otter interrupted
% 2.64/2.89 PROOF FOUND
%------------------------------------------------------------------------------