TSTP Solution File: GRP075-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP075-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 12:56:00 EDT 2022
% Result : Unsatisfiable 2.54s 2.78s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 6
% Syntax : Number of clauses : 87 ( 81 unt; 0 nHn; 8 RR)
% Number of literals : 99 ( 98 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 176 ( 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)) ),
file('GRP075-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP075-1.p',unknown),
[] ).
cnf(3,axiom,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) = C,
file('GRP075-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP075-1.p',unknown),
[] ).
cnf(8,axiom,
inverse(A) = double_divide(A,identity),
file('GRP075-1.p',unknown),
[] ).
cnf(9,axiom,
identity = double_divide(A,inverse(A)),
file('GRP075-1.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(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) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),8,6,11,6,6,6,6,6])]),
[iquote('back_demod,1,demod,8,6,11,6,6,6,6,6,flip.3')] ).
cnf(13,plain,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,identity),double_divide(A,identity))),B) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),11]),
[iquote('back_demod,3,demod,11')] ).
cnf(15,plain,
double_divide(double_divide(double_divide(A,B),double_divide(double_divide(C,identity),double_divide(A,identity))),double_divide(double_divide(D,double_divide(identity,identity)),double_divide(double_divide(B,identity),double_divide(D,identity)))) = C,
inference(para_into,[status(thm),theory(equality)],[13,13]),
[iquote('para_into,13.1.1.1.1.2,13.1.1')] ).
cnf(19,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,identity))),B) = A,
inference(para_into,[status(thm),theory(equality)],[13,11]),
[iquote('para_into,13.1.1.1.1,10.1.1')] ).
cnf(21,plain,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,double_divide(A,identity))),B) = double_divide(double_divide(D,double_divide(identity,identity)),double_divide(double_divide(C,identity),double_divide(D,identity))),
inference(para_into,[status(thm),theory(equality)],[13,13]),
[iquote('para_into,13.1.1.1.2.1,13.1.1')] ).
cnf(24,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),double_divide(B,identity)),identity),B) = A,
inference(para_into,[status(thm),theory(equality)],[13,11]),
[iquote('para_into,13.1.1.1.2,10.1.1')] ).
cnf(26,plain,
double_divide(double_divide(A,double_divide(identity,identity)),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(double_divide(double_divide(C,double_divide(D,identity)),double_divide(B,double_divide(C,identity))),D),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[21])]),
[iquote('copy,21,flip.1')] ).
cnf(30,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),B) = double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,identity))),
inference(para_into,[status(thm),theory(equality)],[19,19]),
[iquote('para_into,19.1.1.1.2.1,19.1.1')] ).
cnf(31,plain,
double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,identity))) = double_divide(double_divide(B,double_divide(identity,identity)),double_divide(double_divide(A,identity),double_divide(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,13]),30]),
[iquote('para_into,19.1.1.1.2.1,13.1.1,demod,30')] ).
cnf(32,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),double_divide(identity,double_divide(double_divide(B,identity),double_divide(identity,identity)))) = A,
inference(para_into,[status(thm),theory(equality)],[19,19]),
[iquote('para_into,19.1.1.1.2.2,19.1.1')] ).
cnf(36,plain,
double_divide(double_divide(identity,identity),double_divide(A,identity)) = A,
inference(para_into,[status(thm),theory(equality)],[19,11]),
[iquote('para_into,19.1.1.1.2,10.1.1')] ).
cnf(38,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),double_divide(identity,identity))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),30]),
[iquote('back_demod,19,demod,30')] ).
cnf(40,plain,
double_divide(double_divide(A,double_divide(identity,identity)),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(identity,double_divide(double_divide(B,identity),double_divide(identity,identity))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[31])]),
[iquote('copy,31,flip.1')] ).
cnf(41,plain,
double_divide(double_divide(A,double_divide(identity,identity)),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(double_divide(identity,identity),B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[36,13])]),
[iquote('para_into,36.1.1.2,13.1.1,flip.1')] ).
cnf(44,plain,
double_divide(identity,identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[36,11])]),
[iquote('para_into,36.1.1,10.1.1,flip.1')] ).
cnf(46,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(identity,double_divide(double_divide(B,identity),identity)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[40]),44,44]),
[iquote('back_demod,40,demod,44,44')] ).
cnf(52,plain,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,double_divide(A,identity))),B) = double_divide(identity,double_divide(double_divide(C,identity),identity)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),44,46])]),
[iquote('back_demod,26,demod,44,46,flip.1')] ).
cnf(55,plain,
double_divide(double_divide(double_divide(A,B),double_divide(double_divide(C,identity),double_divide(A,identity))),double_divide(identity,double_divide(double_divide(B,identity),identity))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[15]),44,46]),
[iquote('back_demod,15,demod,44,46')] ).
cnf(58,plain,
double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(identity,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[41]),44,46,44]),
[iquote('back_demod,41,demod,44,46,44')] ).
cnf(60,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[38]),44,58]),
[iquote('back_demod,38,demod,44,58')] ).
cnf(61,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),double_divide(B,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[32]),44,60]),
[iquote('back_demod,32,demod,44,60')] ).
cnf(63,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),B) = double_divide(A,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[30]),44,60]),
[iquote('back_demod,29,demod,44,60')] ).
cnf(65,plain,
( 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) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),44]),
[iquote('back_demod,12,demod,44')] ).
cnf(67,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[13]),52,60]),
[iquote('back_demod,13,demod,52,60')] ).
cnf(68,plain,
double_divide(double_divide(double_divide(A,B),double_divide(double_divide(C,identity),double_divide(A,identity))),double_divide(identity,B)) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[55]),67]),
[iquote('back_demod,55,demod,67')] ).
cnf(72,plain,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,double_divide(A,identity))),B) = double_divide(identity,C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[52]),67]),
[iquote('back_demod,51,demod,67')] ).
cnf(80,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) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[65]),67]),
[iquote('back_demod,65,demod,67')] ).
cnf(85,plain,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),identity),B) = double_divide(A,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,24]),44,67]),
[iquote('para_into,24.1.1.1.1.1,24.1.1,demod,44,67')] ).
cnf(89,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(para_from,[status(thm),theory(equality)],[67,60]),
[iquote('para_from,66.1.1,59.1.1.2')] ).
cnf(90,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[89])]),
[iquote('copy,89,flip.1')] ).
cnf(93,plain,
double_divide(double_divide(identity,double_divide(A,B)),double_divide(B,identity)) = double_divide(A,identity),
inference(para_into,[status(thm),theory(equality)],[61,67]),
[iquote('para_into,61.1.1.1.2.1,66.1.1')] ).
cnf(95,plain,
double_divide(double_divide(identity,A),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[61,67]),44]),
[iquote('para_into,61.1.1.1.2,66.1.1,demod,44')] ).
cnf(98,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(para_from,[status(thm),theory(equality)],[90,60]),
[iquote('para_from,90.1.1,59.1.1.2')] ).
cnf(101,plain,
double_divide(double_divide(identity,double_divide(A,B)),double_divide(identity,B)) = double_divide(A,identity),
inference(para_into,[status(thm),theory(equality)],[63,95]),
[iquote('para_into,63.1.1.1.2.2,95.1.1')] ).
cnf(103,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,B))),B) = double_divide(A,identity),
inference(para_into,[status(thm),theory(equality)],[63,90]),
[iquote('para_into,63.1.1.1.2.2,90.1.1')] ).
cnf(105,plain,
double_divide(double_divide(double_divide(A,B),identity),double_divide(identity,B)) = double_divide(A,identity),
inference(para_into,[status(thm),theory(equality)],[85,95]),
[iquote('para_into,85.1.1.1.1.2,95.1.1')] ).
cnf(107,plain,
double_divide(double_divide(double_divide(A,double_divide(identity,B)),identity),B) = double_divide(A,identity),
inference(para_into,[status(thm),theory(equality)],[85,90]),
[iquote('para_into,85.1.1.1.1.2,90.1.1')] ).
cnf(111,plain,
double_divide(A,double_divide(identity,B)) = double_divide(A,double_divide(B,identity)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[101,85]),60,67]),
[iquote('para_into,101.1.1.1.2,85.1.1,demod,60,67')] ).
cnf(112,plain,
double_divide(A,double_divide(B,identity)) = double_divide(A,double_divide(identity,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[111])]),
[iquote('copy,111,flip.1')] ).
cnf(116,plain,
double_divide(double_divide(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[68,98]),44,67,98]),
[iquote('para_into,68.1.1.1.1,97.1.1,demod,44,67,98')] ).
cnf(141,plain,
double_divide(A,double_divide(B,A)) = B,
inference(para_into,[status(thm),theory(equality)],[116,116]),
[iquote('para_into,115.1.1.1,115.1.1')] ).
cnf(143,plain,
double_divide(double_divide(A,identity),double_divide(identity,double_divide(A,B))) = double_divide(identity,B),
inference(para_into,[status(thm),theory(equality)],[116,101]),
[iquote('para_into,115.1.1.1,101.1.1')] ).
cnf(149,plain,
double_divide(double_divide(identity,A),double_divide(identity,B)) = double_divide(double_divide(B,A),identity),
inference(para_from,[status(thm),theory(equality)],[116,101]),
[iquote('para_from,115.1.1,101.1.1.1.2')] ).
cnf(151,plain,
double_divide(double_divide(A,identity),B) = double_divide(double_divide(double_divide(B,identity),A),identity),
inference(para_from,[status(thm),theory(equality)],[116,85]),
[iquote('para_from,115.1.1,85.1.1.1.1')] ).
cnf(153,plain,
double_divide(double_divide(double_divide(A,identity),B),identity) = double_divide(double_divide(identity,B),A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[116,63])]),
[iquote('para_from,115.1.1,63.1.1.1.2,flip.1')] ).
cnf(156,plain,
double_divide(double_divide(identity,A),B) = double_divide(double_divide(A,identity),B),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[151])]),153]),
[iquote('copy,151,flip.1,demod,153')] ).
cnf(157,plain,
double_divide(double_divide(A,identity),B) = double_divide(double_divide(identity,A),B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[151]),153]),
[iquote('back_demod,151,demod,153')] ).
cnf(158,plain,
( identity != identity
| a2 != a2
| double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != double_divide(double_divide(identity,a3),double_divide(c3,b3)) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[80]),153])]),
[iquote('back_demod,80,demod,153,flip.3')] ).
cnf(162,plain,
double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(identity,double_divide(B,A)),
inference(para_into,[status(thm),theory(equality)],[141,93]),
[iquote('para_into,141.1.1.2,93.1.1')] ).
cnf(164,plain,
double_divide(double_divide(A,double_divide(B,identity)),identity) = double_divide(B,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[141,85])]),
[iquote('para_into,141.1.1.2,85.1.1,flip.1')] ).
cnf(167,plain,
double_divide(identity,double_divide(A,B)) = double_divide(double_divide(B,identity),double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[162])]),
[iquote('copy,162,flip.1')] ).
cnf(168,plain,
( identity != identity
| a2 != a2
| double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(double_divide(b3,a3),double_divide(c3,identity)) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[158]),164])]),
[iquote('back_demod,158,demod,164,flip.3')] ).
cnf(174,plain,
double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,A))) = B,
inference(para_from,[status(thm),theory(equality)],[112,141]),
[iquote('para_from,112.1.1,141.1.1.2')] ).
cnf(206,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(B,double_divide(A,C))),C) = double_divide(identity,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[72,93]),116]),
[iquote('para_into,72.1.1.1.1,93.1.1,demod,116')] ).
cnf(222,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)],[103,141]),
[iquote('para_from,103.1.1,141.1.1.2')] ).
cnf(226,plain,
double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(double_divide(B,A),identity),
inference(para_from,[status(thm),theory(equality)],[105,174]),
[iquote('para_from,105.1.1,174.1.1.2')] ).
cnf(227,plain,
double_divide(double_divide(A,B),identity) = double_divide(double_divide(B,identity),double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[226])]),
[iquote('copy,226,flip.1')] ).
cnf(229,plain,
double_divide(double_divide(A,double_divide(identity,B)),identity) = double_divide(B,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[107,141])]),
[iquote('para_from,107.1.1,141.1.1.2,flip.1')] ).
cnf(306,plain,
double_divide(A,double_divide(identity,B)) = double_divide(identity,double_divide(B,double_divide(identity,A))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[143,174]),67]),
[iquote('para_into,143.1.1.2.2,174.1.1,demod,67')] ).
cnf(309,plain,
double_divide(identity,double_divide(A,double_divide(identity,B))) = double_divide(B,double_divide(identity,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[306])]),
[iquote('copy,306,flip.1')] ).
cnf(483,plain,
double_divide(double_divide(A,double_divide(B,identity)),C) = double_divide(double_divide(identity,double_divide(B,double_divide(A,identity))),C),
inference(para_from,[status(thm),theory(equality)],[164,157]),
[iquote('para_from,163.1.1,157.1.1.1')] ).
cnf(499,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),C) = double_divide(double_divide(B,double_divide(A,identity)),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[483])]),
[iquote('copy,483,flip.1')] ).
cnf(539,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(B,identity)),double_divide(identity,C)) = double_divide(double_divide(C,double_divide(B,A)),identity),
inference(para_from,[status(thm),theory(equality)],[167,149]),
[iquote('para_from,167.1.1,149.1.1.1')] ).
cnf(561,plain,
double_divide(double_divide(A,double_divide(B,C)),identity) = double_divide(double_divide(double_divide(C,identity),double_divide(B,identity)),double_divide(identity,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[539])]),
[iquote('copy,539,flip.1')] ).
cnf(590,plain,
double_divide(A,B) = double_divide(identity,double_divide(double_divide(B,identity),double_divide(identity,A))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[222,157]),116]),
[iquote('para_into,222.1.1.2,157.1.1,demod,116')] ).
cnf(595,plain,
double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,B))) = double_divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[590])]),
[iquote('copy,590,flip.1')] ).
cnf(729,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(B,identity)),C) = double_divide(double_divide(identity,double_divide(B,A)),C),
inference(para_from,[status(thm),theory(equality)],[227,157]),
[iquote('para_from,227.1.1,157.1.1.1')] ).
cnf(745,plain,
double_divide(double_divide(identity,double_divide(A,B)),C) = double_divide(double_divide(double_divide(B,identity),double_divide(A,identity)),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[729])]),
[iquote('copy,729,flip.1')] ).
cnf(881,plain,
double_divide(double_divide(A,double_divide(identity,B)),C) = double_divide(double_divide(A,double_divide(B,identity)),C),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[309,156]),229]),
[iquote('para_from,309.1.1,156.1.1.1,demod,229')] ).
cnf(902,plain,
double_divide(double_divide(A,double_divide(B,identity)),C) = double_divide(double_divide(A,double_divide(identity,B)),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[881])]),
[iquote('copy,881,flip.1')] ).
cnf(1711,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(B,identity)),C) = double_divide(B,double_divide(identity,double_divide(A,C))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[206,103]),98]),
[iquote('para_into,206.1.1.1.2,103.1.1,demod,98')] ).
cnf(1772,plain,
double_divide(double_divide(identity,double_divide(A,B)),C) = double_divide(A,double_divide(identity,double_divide(B,C))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[745]),1711]),
[iquote('back_demod,745,demod,1711')] ).
cnf(1782,plain,
double_divide(double_divide(A,double_divide(B,C)),identity) = double_divide(B,double_divide(identity,double_divide(C,double_divide(identity,A)))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[561]),1711]),
[iquote('back_demod,561,demod,1711')] ).
cnf(1829,plain,
double_divide(double_divide(A,double_divide(B,identity)),C) = double_divide(B,double_divide(identity,double_divide(double_divide(A,identity),C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[499]),1772])]),
[iquote('back_demod,499,demod,1772,flip.1')] ).
cnf(1931,plain,
double_divide(double_divide(A,double_divide(identity,B)),C) = double_divide(B,double_divide(identity,double_divide(double_divide(A,identity),C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[902]),1829])]),
[iquote('back_demod,902,demod,1829,flip.1')] ).
cnf(1974,plain,
double_divide(double_divide(identity,A),double_divide(B,C)) = double_divide(double_divide(C,A),double_divide(identity,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[595,149]),1931,67,1782,98]),
[iquote('para_from,595.1.1,149.1.1.2,demod,1931,67,1782,98')] ).
cnf(1977,plain,
double_divide(double_divide(A,B),double_divide(identity,C)) = double_divide(double_divide(identity,B),double_divide(C,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1974])]),
[iquote('copy,1974,flip.1')] ).
cnf(3775,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(double_divide(identity,B),double_divide(C,A)),
inference(para_into,[status(thm),theory(equality)],[1977,89]),
[iquote('para_into,1977.1.1.2,89.1.1')] ).
cnf(3797,plain,
double_divide(double_divide(identity,A),double_divide(B,C)) = double_divide(double_divide(C,A),double_divide(B,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3775])]),
[iquote('copy,3775,flip.1')] ).
cnf(4384,plain,
$false,
inference(hyper,[status(thm)],[3797,168,2,2]),
[iquote('hyper,3797,168,2,2')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP075-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n020.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 05:20:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.54/2.78 ----- Otter 3.3f, August 2004 -----
% 2.54/2.78 The process was started by sandbox2 on n020.cluster.edu,
% 2.54/2.78 Wed Jul 27 05:20:23 2022
% 2.54/2.78 The command was "./otter". The process ID is 16532.
% 2.54/2.78
% 2.54/2.78 set(prolog_style_variables).
% 2.54/2.78 set(auto).
% 2.54/2.78 dependent: set(auto1).
% 2.54/2.78 dependent: set(process_input).
% 2.54/2.78 dependent: clear(print_kept).
% 2.54/2.78 dependent: clear(print_new_demod).
% 2.54/2.78 dependent: clear(print_back_demod).
% 2.54/2.78 dependent: clear(print_back_sub).
% 2.54/2.78 dependent: set(control_memory).
% 2.54/2.78 dependent: assign(max_mem, 12000).
% 2.54/2.78 dependent: assign(pick_given_ratio, 4).
% 2.54/2.78 dependent: assign(stats_level, 1).
% 2.54/2.78 dependent: assign(max_seconds, 10800).
% 2.54/2.78 clear(print_given).
% 2.54/2.78
% 2.54/2.78 list(usable).
% 2.54/2.78 0 [] A=A.
% 2.54/2.78 0 [] double_divide(double_divide(double_divide(X,double_divide(Y,identity)),double_divide(double_divide(Z,double_divide(U,double_divide(U,identity))),double_divide(X,identity))),Y)=Z.
% 2.54/2.78 0 [] multiply(X,Y)=double_divide(double_divide(Y,X),identity).
% 2.54/2.78 0 [] inverse(X)=double_divide(X,identity).
% 2.54/2.78 0 [] identity=double_divide(X,inverse(X)).
% 2.54/2.78 0 [] multiply(inverse(a1),a1)!=identity|multiply(identity,a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 2.54/2.78 end_of_list.
% 2.54/2.78
% 2.54/2.78 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 2.54/2.78
% 2.54/2.78 This is a Horn set with equality. The strategy will be
% 2.54/2.78 Knuth-Bendix and hyper_res, with positive clauses in
% 2.54/2.78 sos and nonpositive clauses in usable.
% 2.54/2.78
% 2.54/2.78 dependent: set(knuth_bendix).
% 2.54/2.78 dependent: set(anl_eq).
% 2.54/2.78 dependent: set(para_from).
% 2.54/2.78 dependent: set(para_into).
% 2.54/2.78 dependent: clear(para_from_right).
% 2.54/2.78 dependent: clear(para_into_right).
% 2.54/2.78 dependent: set(para_from_vars).
% 2.54/2.78 dependent: set(eq_units_both_ways).
% 2.54/2.78 dependent: set(dynamic_demod_all).
% 2.54/2.78 dependent: set(dynamic_demod).
% 2.54/2.78 dependent: set(order_eq).
% 2.54/2.78 dependent: set(back_demod).
% 2.54/2.78 dependent: set(lrpo).
% 2.54/2.78 dependent: set(hyper_res).
% 2.54/2.78 dependent: clear(order_hyper).
% 2.54/2.78
% 2.54/2.78 ------------> process usable:
% 2.54/2.78 ** KEPT (pick-wt=22): 1 [] multiply(inverse(a1),a1)!=identity|multiply(identity,a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 2.54/2.78
% 2.54/2.78 ------------> process sos:
% 2.54/2.78 ** KEPT (pick-wt=3): 2 [] A=A.
% 2.54/2.78 ** KEPT (pick-wt=21): 3 [] double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B)=C.
% 2.54/2.78 ---> New Demodulator: 4 [new_demod,3] double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B)=C.
% 2.54/2.78 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 2.54/2.78 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 2.54/2.78 ** KEPT (pick-wt=6): 7 [] inverse(A)=double_divide(A,identity).
% 2.54/2.78 ---> New Demodulator: 8 [new_demod,7] inverse(A)=double_divide(A,identity).
% 2.54/2.78 ** KEPT (pick-wt=7): 10 [copy,9,demod,8,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 2.54/2.78 ---> New Demodulator: 11 [new_demod,10] double_divide(A,double_divide(A,identity))=identity.
% 2.54/2.78 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 2.54/2.78 >>>> Starting back demodulation with 4.
% 2.54/2.78 >>>> Starting back demodulation with 6.
% 2.54/2.78 >> back demodulating 1 with 6.
% 2.54/2.78 >>>> Starting back demodulation with 8.
% 2.54/2.78 >>>> Starting back demodulation with 11.
% 2.54/2.78 >> back demodulating 3 with 11.
% 2.54/2.78 >>>> Starting back demodulation with 14.
% 2.54/2.78
% 2.54/2.78 ======= end of input processing =======
% 2.54/2.78
% 2.54/2.78 =========== start of search ===========
% 2.54/2.78
% 2.54/2.78
% 2.54/2.78 Resetting weight limit to 17.
% 2.54/2.78
% 2.54/2.78
% 2.54/2.78 Resetting weight limit to 17.
% 2.54/2.78
% 2.54/2.78 sos_size=1776
% 2.54/2.78
% 2.54/2.78 -------- PROOF --------
% 2.54/2.78
% 2.54/2.78 -----> EMPTY CLAUSE at 0.70 sec ----> 4384 [hyper,3797,168,2,2] $F.
% 2.54/2.78
% 2.54/2.78 Length of proof is 80. Level of proof is 27.
% 2.54/2.78
% 2.54/2.78 ---------------- PROOF ----------------
% 2.54/2.78 % SZS status Unsatisfiable
% 2.54/2.78 % SZS output start Refutation
% See solution above
% 2.54/2.78 ------------ end of proof -------------
% 2.54/2.78
% 2.54/2.78
% 2.54/2.78 Search stopped by max_proofs option.
% 2.54/2.78
% 2.54/2.78
% 2.54/2.78 Search stopped by max_proofs option.
% 2.54/2.78
% 2.54/2.78 ============ end of search ============
% 2.54/2.78
% 2.54/2.78 -------------- statistics -------------
% 2.54/2.78 clauses given 249
% 2.54/2.78 clauses generated 78759
% 2.54/2.78 clauses kept 3306
% 2.54/2.78 clauses forward subsumed 63407
% 2.54/2.78 clauses back subsumed 130
% 2.54/2.78 Kbytes malloced 4882
% 2.54/2.78
% 2.54/2.78 ----------- times (seconds) -----------
% 2.54/2.78 user CPU time 0.70 (0 hr, 0 min, 0 sec)
% 2.54/2.78 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.54/2.78 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.54/2.78
% 2.54/2.78 That finishes the proof of the theorem.
% 2.54/2.78
% 2.54/2.78 Process 16532 finished Wed Jul 27 05:20:26 2022
% 2.54/2.78 Otter interrupted
% 2.54/2.78 PROOF FOUND
%------------------------------------------------------------------------------