TSTP Solution File: GRP583-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP583-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 12:57:18 EDT 2022
% Result : Unsatisfiable 1.65s 1.84s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of clauses : 95 ( 95 unt; 0 nHn; 8 RR)
% Number of literals : 95 ( 94 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 174 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('GRP583-1.p',unknown),
[] ).
cnf(3,axiom,
double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C,
file('GRP583-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP583-1.p',unknown),
[] ).
cnf(8,axiom,
inverse(A) = double_divide(A,identity),
file('GRP583-1.p',unknown),
[] ).
cnf(9,axiom,
identity = double_divide(A,inverse(A)),
file('GRP583-1.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(A,double_divide(identity,double_divide(B,double_divide(double_divide(identity,identity),A)))),double_divide(identity,identity)) = B,
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.1.2.1,10.1.1')] ).
cnf(15,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))),double_divide(identity,identity)) = B,
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.1.2.2.2,10.1.1')] ).
cnf(17,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A))))),double_divide(D,C))),double_divide(identity,identity)) = D,
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.1.2.2.2,3.1.1')] ).
cnf(19,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),double_divide(identity,identity)) = A,
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.1.2.2,10.1.1')] ).
cnf(21,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),A)),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(identity,C),double_divide(A,double_divide(C,B)))),
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.1.2.2,3.1.1')] ).
cnf(22,plain,
double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),C)),double_divide(identity,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[21])]),
[iquote('copy,21,flip.1')] ).
cnf(24,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)],[19,11]),11,11])]),
[iquote('para_into,19.1.1.1.2.1,10.1.1,demod,11,11,flip.1')] ).
cnf(25,plain,
double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))) = double_divide(double_divide(identity,double_divide(identity,C)),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[22]),24,24]),
[iquote('back_demod,22,demod,24,24')] ).
cnf(26,plain,
double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(B,double_divide(double_divide(identity,C),double_divide(A,double_divide(C,B)))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[21]),24,24]),
[iquote('back_demod,21,demod,24,24')] ).
cnf(28,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),24]),
[iquote('back_demod,19,demod,24')] ).
cnf(29,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A))))),double_divide(D,C))),identity) = D,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),24,24]),
[iquote('back_demod,17,demod,24,24')] ).
cnf(31,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))),identity) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[15]),24]),
[iquote('back_demod,15,demod,24')] ).
cnf(33,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))),identity) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[13]),24,24]),
[iquote('back_demod,13,demod,24,24')] ).
cnf(37,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),A) = identity,
inference(para_from,[status(thm),theory(equality)],[28,11]),
[iquote('para_from,27.1.1,10.1.1.2')] ).
cnf(41,plain,
double_divide(A,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),double_divide(B,identity))) = double_divide(double_divide(identity,double_divide(identity,B)),identity),
inference(para_into,[status(thm),theory(equality)],[25,37]),
[iquote('para_into,25.1.1.2.2.2,37.1.1')] ).
cnf(45,plain,
double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,24]),24])]),
[iquote('para_into,25.1.1.2.2.2,23.1.1,demod,24,flip.1')] ).
cnf(47,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,11]),45]),
[iquote('para_into,25.1.1.2.2.2,10.1.1,demod,45')] ).
cnf(48,plain,
double_divide(A,double_divide(double_divide(identity,B),identity)) = double_divide(identity,double_divide(identity,double_divide(B,A))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,37]),45,28]),
[iquote('para_into,25.1.1.2.2,37.1.1,demod,45,28')] ).
cnf(49,plain,
double_divide(double_divide(A,double_divide(B,C)),double_divide(double_divide(identity,double_divide(identity,B)),double_divide(identity,double_divide(identity,double_divide(A,identity))))) = double_divide(identity,double_divide(identity,double_divide(C,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,25]),45,45]),
[iquote('para_into,25.1.1.2.2,25.1.1,demod,45,45')] ).
cnf(51,plain,
double_divide(double_divide(A,double_divide(identity,B)),double_divide(identity,double_divide(identity,double_divide(B,identity)))) = double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,25]),45,45]),
[iquote('para_into,25.1.1.2,25.1.1,demod,45,45')] ).
cnf(55,plain,
double_divide(A,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[41])]),45])]),
[iquote('copy,41,flip.1,demod,45,flip.1')] ).
cnf(63,plain,
double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))) = double_divide(identity,double_divide(identity,double_divide(C,identity))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),45])]),
[iquote('back_demod,26,demod,45,flip.1')] ).
cnf(64,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[31]),47,45]),
[iquote('back_demod,31,demod,47,45')] ).
cnf(67,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))) = double_divide(double_divide(A,double_divide(identity,B)),double_divide(identity,double_divide(identity,double_divide(B,identity)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[51])]),
[iquote('copy,51,flip.1')] ).
cnf(68,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),double_divide(B,A))),identity) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[29]),63]),
[iquote('back_demod,29,demod,63')] ).
cnf(83,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[33,37]),24,45]),
[iquote('para_into,33.1.1.1.2.2,37.1.1,demod,24,45')] ).
cnf(95,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[64]),83]),
[iquote('back_demod,64,demod,83')] ).
cnf(98,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))),B) = identity,
inference(para_from,[status(thm),theory(equality)],[33,11]),
[iquote('para_from,33.1.1,10.1.1.2')] ).
cnf(102,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),double_divide(identity,A)) = identity,
inference(para_from,[status(thm),theory(equality)],[45,37]),
[iquote('para_from,44.1.1,37.1.1.1.2')] ).
cnf(108,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),A) = identity,
inference(para_into,[status(thm),theory(equality)],[98,24]),
[iquote('para_into,98.1.1.1.2.2.2,23.1.1')] ).
cnf(127,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[108,33]),24,83])]),
[iquote('para_from,108.1.1,33.1.1.1.2.2,demod,24,83,flip.1')] ).
cnf(128,plain,
double_divide(double_divide(A,double_divide(identity,B)),double_divide(identity,double_divide(identity,double_divide(B,identity)))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[67]),127])]),
[iquote('back_demod,67,demod,127,flip.1')] ).
cnf(132,plain,
double_divide(A,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[55]),127]),
[iquote('back_demod,55,demod,127')] ).
cnf(140,plain,
double_divide(A,identity) = double_divide(identity,double_divide(identity,double_divide(identity,A))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[48,24]),24]),
[iquote('para_into,48.1.1.2.1,23.1.1,demod,24')] ).
cnf(143,plain,
double_divide(identity,double_divide(identity,double_divide(A,double_divide(identity,A)))) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[48,108]),83,127,95])]),
[iquote('para_into,48.1.1,108.1.1,demod,83,127,95,flip.1')] ).
cnf(149,plain,
double_divide(identity,double_divide(identity,double_divide(identity,A))) = double_divide(A,identity),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[140])]),
[iquote('copy,140,flip.1')] ).
cnf(170,plain,
double_divide(double_divide(A,identity),double_divide(identity,double_divide(identity,double_divide(B,double_divide(identity,A))))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(B,identity)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[47,48]),127]),
[iquote('para_into,46.1.1.2,48.1.1,demod,127')] ).
cnf(201,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[149,149])]),
[iquote('para_into,149.1.1.2,149.1.1,flip.1')] ).
cnf(202,plain,
double_divide(double_divide(A,double_divide(identity,A)),identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[149,143]),24])]),
[iquote('para_into,149.1.1.2,143.1.1,demod,24,flip.1')] ).
cnf(204,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),double_divide(B,A)),identity)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[68]),201]),
[iquote('back_demod,68,demod,201')] ).
cnf(207,plain,
double_divide(A,double_divide(identity,double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,A))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[48]),201]),
[iquote('back_demod,48,demod,201')] ).
cnf(216,plain,
double_divide(identity,double_divide(A,double_divide(identity,A))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[202,108]),24,24]),
[iquote('para_from,202.1.1,108.1.1.1.2.2,demod,24,24')] ).
cnf(218,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity))))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(B,identity))))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[49,149]),24,24,201,201]),
[iquote('para_into,49.1.1.1.2,149.1.1,demod,24,24,201,201')] ).
cnf(228,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(identity,double_divide(B,identity)))),double_divide(double_divide(identity,double_divide(identity,double_divide(C,double_divide(D,B)))),double_divide(identity,double_divide(identity,double_divide(A,identity))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,D)),double_divide(identity,double_divide(identity,double_divide(C,identity)))),identity))),
inference(para_into,[status(thm),theory(equality)],[49,49]),
[iquote('para_into,49.1.1.1.2,49.1.1')] ).
cnf(242,plain,
double_divide(double_divide(double_divide(A,double_divide(identity,A)),double_divide(B,C)),double_divide(identity,double_divide(identity,double_divide(B,identity)))) = double_divide(identity,double_divide(identity,double_divide(C,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[49,202]),24,24,201,201]),
[iquote('para_into,49.1.1.2.2.2.2,202.1.1,demod,24,24,201,201')] ).
cnf(244,plain,
double_divide(double_divide(A,double_divide(B,C)),double_divide(double_divide(identity,double_divide(identity,B)),double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,A))))))) = double_divide(identity,double_divide(identity,double_divide(C,identity))),
inference(para_into,[status(thm),theory(equality)],[49,140]),
[iquote('para_into,49.1.1.2.2.2.2,140.1.1')] ).
cnf(252,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,double_divide(identity,double_divide(B,identity)))),identity))) = double_divide(double_divide(C,double_divide(identity,double_divide(identity,double_divide(D,identity)))),double_divide(double_divide(identity,double_divide(identity,double_divide(B,double_divide(A,D)))),double_divide(identity,double_divide(identity,double_divide(C,identity))))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[228])]),
[iquote('copy,228,flip.1')] ).
cnf(259,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[216,33]),83]),
[iquote('para_from,216.1.1,33.1.1.1.2,demod,83')] ).
cnf(262,plain,
double_divide(double_divide(double_divide(A,double_divide(identity,A)),double_divide(identity,double_divide(B,identity))),identity) = B,
inference(para_from,[status(thm),theory(equality)],[216,33]),
[iquote('para_from,216.1.1,33.1.1.1.2.2.2')] ).
cnf(268,plain,
double_divide(double_divide(A,double_divide(B,identity)),A) = double_divide(identity,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[218]),259,259]),
[iquote('back_demod,218,demod,259,259')] ).
cnf(270,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(B,A)),identity)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[204]),259]),
[iquote('back_demod,204,demod,259')] ).
cnf(272,plain,
double_divide(double_divide(A,identity),double_divide(identity,double_divide(identity,double_divide(B,double_divide(identity,A))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[170]),259]),
[iquote('back_demod,170,demod,259')] ).
cnf(276,plain,
double_divide(A,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[132]),259]),
[iquote('back_demod,132,demod,259')] ).
cnf(279,plain,
double_divide(double_divide(A,double_divide(identity,B)),double_divide(identity,double_divide(identity,double_divide(B,identity)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[128]),259]),
[iquote('back_demod,128,demod,259')] ).
cnf(288,plain,
double_divide(A,double_divide(identity,A)) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[102]),259]),
[iquote('back_demod,102,demod,259')] ).
cnf(290,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[95]),259]),
[iquote('back_demod,94,demod,259')] ).
cnf(294,plain,
double_divide(A,double_divide(A,double_divide(B,identity))) = double_divide(B,identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[276])]),290])]),
[iquote('copy,276,flip.1,demod,290,flip.1')] ).
cnf(299,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[262]),288,294]),
[iquote('back_demod,262,demod,288,294')] ).
cnf(301,plain,
double_divide(double_divide(identity,double_divide(A,B)),double_divide(A,identity)) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[242]),288,294,294]),
[iquote('back_demod,242,demod,288,294,294')] ).
cnf(303,plain,
double_divide(double_divide(A,double_divide(identity,B)),double_divide(B,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[279]),294]),
[iquote('back_demod,279,demod,294')] ).
cnf(308,plain,
double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[272]),290]),
[iquote('back_demod,272,demod,290')] ).
cnf(312,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[259]),294]),
[iquote('back_demod,258,demod,294')] ).
cnf(315,plain,
double_divide(double_divide(A,double_divide(identity,B)),double_divide(double_divide(C,double_divide(D,B)),double_divide(identity,A))) = double_divide(identity,double_divide(D,double_divide(identity,C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[252]),290,312,312,312,290,312])]),
[iquote('back_demod,252,demod,290,312,312,312,290,312,flip.1')] ).
cnf(323,plain,
double_divide(double_divide(A,double_divide(B,C)),double_divide(B,double_divide(identity,A))) = double_divide(identity,C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[244]),290,290,290,312]),
[iquote('back_demod,244,demod,290,290,290,312')] ).
cnf(337,plain,
double_divide(A,B) = double_divide(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[207]),312,290]),
[iquote('back_demod,207,demod,312,290')] ).
cnf(355,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[270]),312]),
[iquote('back_demod,270,demod,312')] ).
cnf(364,plain,
double_divide(double_divide(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[299,268]),355]),
[iquote('para_from,299.1.1,268.1.1.1.2,demod,355')] ).
cnf(366,plain,
double_divide(double_divide(a3,double_divide(double_divide(c3,b3),identity)),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(para_from,[status(thm),theory(equality)],[337,12]),
[iquote('para_from,337.1.1,12.1.1.1')] ).
cnf(369,plain,
double_divide(A,double_divide(A,B)) = B,
inference(para_into,[status(thm),theory(equality)],[355,337]),
[iquote('para_into,354.1.1.2,337.1.1')] ).
cnf(371,plain,
double_divide(double_divide(A,B),B) = A,
inference(para_into,[status(thm),theory(equality)],[355,337]),
[iquote('para_into,354.1.1,337.1.1')] ).
cnf(387,plain,
double_divide(A,double_divide(B,identity)) = double_divide(double_divide(identity,B),A),
inference(para_into,[status(thm),theory(equality)],[303,364]),
[iquote('para_into,303.1.1.1,364.1.1')] ).
cnf(398,plain,
double_divide(double_divide(identity,A),double_divide(B,identity)) = double_divide(double_divide(B,A),identity),
inference(para_into,[status(thm),theory(equality)],[301,369]),
[iquote('para_into,301.1.1.1.2,368.1.1')] ).
cnf(404,plain,
double_divide(double_divide(identity,A),B) = double_divide(double_divide(A,double_divide(identity,B)),identity),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[301,308]),371]),
[iquote('para_into,301.1.1.1.2,307.1.1,demod,371')] ).
cnf(412,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)],[398])]),
[iquote('copy,398,flip.1')] ).
cnf(416,plain,
double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(identity,double_divide(B,A)),
inference(para_from,[status(thm),theory(equality)],[301,371]),
[iquote('para_from,301.1.1,370.1.1.1')] ).
cnf(418,plain,
double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(identity,double_divide(A,B)),
inference(para_from,[status(thm),theory(equality)],[301,355]),
[iquote('para_from,301.1.1,354.1.1.2')] ).
cnf(419,plain,
double_divide(identity,double_divide(A,B)) = double_divide(identity,double_divide(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[416])]),418]),
[iquote('copy,416,flip.1,demod,418')] ).
cnf(472,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(para_into,[status(thm),theory(equality)],[315,387]),24,308]),
[iquote('para_into,315.1.1.2.1,387.1.1,demod,24,308')] ).
cnf(517,plain,
double_divide(double_divide(A,B),identity) = double_divide(identity,double_divide(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[412]),472,355]),
[iquote('back_demod,412,demod,472,355')] ).
cnf(518,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(back_demod,[status(thm)],[404]),472,517,472,369]),
[iquote('back_demod,404,demod,472,517,472,369')] ).
cnf(543,plain,
double_divide(double_divide(b3,c3),double_divide(identity,a3)) != double_divide(double_divide(a3,b3),double_divide(identity,c3)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[366]),517,517,472,369,517,517,472,369]),
[iquote('back_demod,366,demod,517,517,472,369,517,517,472,369')] ).
cnf(576,plain,
double_divide(double_divide(A,B),double_divide(C,double_divide(identity,A))) = double_divide(identity,double_divide(B,C)),
inference(para_into,[status(thm),theory(equality)],[323,355]),
[iquote('para_into,323.1.1.1.2,354.1.1')] ).
cnf(759,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(C,B),double_divide(identity,A)),
inference(para_into,[status(thm),theory(equality)],[518,419]),
[iquote('para_into,518.1.1.2.2,419.1.1')] ).
cnf(1058,plain,
double_divide(double_divide(b3,c3),double_divide(a3,identity)) != double_divide(double_divide(a3,b3),double_divide(identity,c3)),
inference(para_into,[status(thm),theory(equality)],[543,337]),
[iquote('para_into,543.1.1.2,337.1.1')] ).
cnf(1097,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(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[576,364]),472]),
[iquote('para_into,576.1.1.2,364.1.1,demod,472')] ).
cnf(1157,plain,
double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) != double_divide(identity,double_divide(b3,double_divide(identity,double_divide(a3,c3)))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1058]),1097,355,1097,369]),
[iquote('back_demod,1058,demod,1097,355,1097,369')] ).
cnf(1208,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(identity,double_divide(B,double_divide(identity,double_divide(C,A)))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[759]),1097,369]),
[iquote('back_demod,759,demod,1097,369')] ).
cnf(1209,plain,
$false,
inference(binary,[status(thm)],[1208,1157]),
[iquote('binary,1208.1,1157.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP583-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.14/0.33 % Computer : n022.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Wed Jul 27 05:16:50 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.65/1.84 ----- Otter 3.3f, August 2004 -----
% 1.65/1.84 The process was started by sandbox2 on n022.cluster.edu,
% 1.65/1.84 Wed Jul 27 05:16:50 2022
% 1.65/1.84 The command was "./otter". The process ID is 18670.
% 1.65/1.84
% 1.65/1.84 set(prolog_style_variables).
% 1.65/1.84 set(auto).
% 1.65/1.84 dependent: set(auto1).
% 1.65/1.84 dependent: set(process_input).
% 1.65/1.84 dependent: clear(print_kept).
% 1.65/1.84 dependent: clear(print_new_demod).
% 1.65/1.84 dependent: clear(print_back_demod).
% 1.65/1.84 dependent: clear(print_back_sub).
% 1.65/1.84 dependent: set(control_memory).
% 1.65/1.84 dependent: assign(max_mem, 12000).
% 1.65/1.84 dependent: assign(pick_given_ratio, 4).
% 1.65/1.84 dependent: assign(stats_level, 1).
% 1.65/1.84 dependent: assign(max_seconds, 10800).
% 1.65/1.84 clear(print_given).
% 1.65/1.84
% 1.65/1.84 list(usable).
% 1.65/1.84 0 [] A=A.
% 1.65/1.84 0 [] double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity))=C.
% 1.65/1.84 0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.65/1.84 0 [] inverse(A)=double_divide(A,identity).
% 1.65/1.84 0 [] identity=double_divide(A,inverse(A)).
% 1.65/1.84 0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.65/1.84 end_of_list.
% 1.65/1.84
% 1.65/1.84 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.65/1.84
% 1.65/1.84 All clauses are units, and equality is present; the
% 1.65/1.84 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.65/1.84
% 1.65/1.84 dependent: set(knuth_bendix).
% 1.65/1.84 dependent: set(anl_eq).
% 1.65/1.84 dependent: set(para_from).
% 1.65/1.84 dependent: set(para_into).
% 1.65/1.84 dependent: clear(para_from_right).
% 1.65/1.84 dependent: clear(para_into_right).
% 1.65/1.84 dependent: set(para_from_vars).
% 1.65/1.84 dependent: set(eq_units_both_ways).
% 1.65/1.84 dependent: set(dynamic_demod_all).
% 1.65/1.84 dependent: set(dynamic_demod).
% 1.65/1.84 dependent: set(order_eq).
% 1.65/1.84 dependent: set(back_demod).
% 1.65/1.84 dependent: set(lrpo).
% 1.65/1.84
% 1.65/1.84 ------------> process usable:
% 1.65/1.84 ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.65/1.84
% 1.65/1.84 ------------> process sos:
% 1.65/1.84 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.65/1.84 ** KEPT (pick-wt=17): 3 [] double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity))=C.
% 1.65/1.84 ---> New Demodulator: 4 [new_demod,3] double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity))=C.
% 1.65/1.84 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.65/1.84 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.65/1.84 ** KEPT (pick-wt=6): 7 [] inverse(A)=double_divide(A,identity).
% 1.65/1.84 ---> New Demodulator: 8 [new_demod,7] inverse(A)=double_divide(A,identity).
% 1.65/1.84 ** KEPT (pick-wt=7): 10 [copy,9,demod,8,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.65/1.84 ---> New Demodulator: 11 [new_demod,10] double_divide(A,double_divide(A,identity))=identity.
% 1.65/1.84 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.65/1.84 >>>> Starting back demodulation with 4.
% 1.65/1.84 >>>> Starting back demodulation with 6.
% 1.65/1.84 >> back demodulating 1 with 6.
% 1.65/1.84 >>>> Starting back demodulation with 8.
% 1.65/1.84 >>>> Starting back demodulation with 11.
% 1.65/1.84
% 1.65/1.84 ======= end of input processing =======
% 1.65/1.84
% 1.65/1.84 =========== start of search ===========
% 1.65/1.84
% 1.65/1.84 -------- PROOF --------
% 1.65/1.84
% 1.65/1.84 ----> UNIT CONFLICT at 0.08 sec ----> 1209 [binary,1208.1,1157.1] $F.
% 1.65/1.84
% 1.65/1.84 Length of proof is 89. Level of proof is 23.
% 1.65/1.84
% 1.65/1.84 ---------------- PROOF ----------------
% 1.65/1.84 % SZS status Unsatisfiable
% 1.65/1.84 % SZS output start Refutation
% See solution above
% 1.65/1.84 ------------ end of proof -------------
% 1.65/1.84
% 1.65/1.84
% 1.65/1.84 Search stopped by max_proofs option.
% 1.65/1.84
% 1.65/1.84
% 1.65/1.84 Search stopped by max_proofs option.
% 1.65/1.84
% 1.65/1.84 ============ end of search ============
% 1.65/1.84
% 1.65/1.84 -------------- statistics -------------
% 1.65/1.84 clauses given 74
% 1.65/1.84 clauses generated 2448
% 1.65/1.84 clauses kept 830
% 1.65/1.84 clauses forward subsumed 2528
% 1.65/1.84 clauses back subsumed 10
% 1.65/1.84 Kbytes malloced 2929
% 1.65/1.84
% 1.65/1.84 ----------- times (seconds) -----------
% 1.65/1.84 user CPU time 0.08 (0 hr, 0 min, 0 sec)
% 1.65/1.84 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.84 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.65/1.84
% 1.65/1.84 That finishes the proof of the theorem.
% 1.65/1.84
% 1.65/1.84 Process 18670 finished Wed Jul 27 05:16:52 2022
% 1.65/1.84 Otter interrupted
% 1.65/1.84 PROOF FOUND
%------------------------------------------------------------------------------