TSTP Solution File: BOO025-1 by EQP---0.9e
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : EQP---0.9e
% Problem : BOO025-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_eqp %s
% Computer : n024.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 : 600s
% DateTime : Thu Jul 14 23:37:09 EDT 2022
% Result : Unsatisfiable 0.76s 1.38s
% Output : Refutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 7
% Syntax : Number of clauses : 198 ( 198 unt; 0 nHn; 14 RR)
% Number of literals : 198 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 362 ( 97 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,plain,
equal(multiply(add(A,B),B),B),
file('BOO025-1.p',unknown),
[] ).
cnf(2,plain,
equal(multiply(A,add(B,C)),add(multiply(B,A),multiply(C,A))),
file('BOO025-1.p',unknown),
[] ).
cnf(3,plain,
equal(add(multiply(A,B),multiply(C,B)),multiply(B,add(A,C))),
inference(flip,[status(thm),theory(equality)],[2]),
[iquote('flip(2)')] ).
cnf(4,plain,
equal(add(A,inverse(A)),n1),
file('BOO025-1.p',unknown),
[] ).
cnf(5,plain,
equal(add(multiply(A,inverse(B)),add(multiply(A,C),multiply(inverse(B),C))),pixley(A,B,C)),
inference(flip,[status(thm),theory(equality)],[1]),
[iquote('flip(1)')] ).
cnf(6,plain,
equal(pixley(A,A,B),B),
file('BOO025-1.p',unknown),
[] ).
cnf(7,plain,
equal(pixley(A,B,B),A),
file('BOO025-1.p',unknown),
[] ).
cnf(8,plain,
equal(pixley(A,B,A),A),
file('BOO025-1.p',unknown),
[] ).
cnf(9,plain,
~ equal(multiply(b,inverse(b)),multiply(a,inverse(a))),
file('BOO025-1.p',unknown),
[] ).
cnf(10,plain,
equal(add(multiply(A,add(B,add(A,C))),multiply(C,add(B,add(A,C)))),add(A,C)),
inference(para,[status(thm),theory(equality)],[2,1]),
[iquote('para(2,1)')] ).
cnf(11,plain,
equal(multiply(n1,inverse(A)),inverse(A)),
inference(para,[status(thm),theory(equality)],[4,1]),
[iquote('para(4,1)')] ).
cnf(12,plain,
equal(multiply(multiply(A,add(B,C)),multiply(C,A)),multiply(C,A)),
inference(para,[status(thm),theory(equality)],[3,1]),
[iquote('para(3,1)')] ).
cnf(13,plain,
equal(add(A,multiply(B,A)),multiply(A,add(add(C,A),B))),
inference(para,[status(thm),theory(equality)],[1,3]),
[iquote('para(1,3)')] ).
cnf(14,plain,
equal(multiply(A,add(add(B,A),C)),add(A,multiply(C,A))),
inference(flip,[status(thm),theory(equality)],[13]),
[iquote('flip(13)')] ).
cnf(15,plain,
equal(add(multiply(A,B),B),multiply(B,add(A,add(C,B)))),
inference(para,[status(thm),theory(equality)],[1,3]),
[iquote('para(1,3)')] ).
cnf(16,plain,
equal(multiply(A,add(B,add(C,A))),add(multiply(B,A),A)),
inference(flip,[status(thm),theory(equality)],[15]),
[iquote('flip(15)')] ).
cnf(19,plain,
equal(add(add(multiply(A,B),multiply(C,B)),multiply(D,add(A,C))),multiply(add(A,C),add(B,D))),
inference(para,[status(thm),theory(equality)],[2,3]),
[iquote('para(2,3)')] ).
cnf(23,plain,
equal(multiply(A,n1),add(multiply(B,A),multiply(inverse(B),A))),
inference(para,[status(thm),theory(equality)],[4,2]),
[iquote('para(4,2)')] ).
cnf(24,plain,
equal(add(multiply(A,B),multiply(inverse(A),B)),multiply(B,n1)),
inference(flip,[status(thm),theory(equality)],[23]),
[iquote('flip(23)')] ).
cnf(32,plain,
equal(add(multiply(A,add(B,n1)),multiply(inverse(A),add(B,n1))),n1),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1,23]),1]),
[iquote('para(1,23),flip(1)')] ).
cnf(35,plain,
equal(add(multiply(A,inverse(B)),multiply(C,add(A,inverse(B)))),pixley(A,B,C)),
inference(para,[status(thm),theory(equality)],[3,5]),
[iquote('para(3,5)')] ).
cnf(36,plain,
equal(add(inverse(A),multiply(inverse(n1),inverse(A))),multiply(inverse(A),n1)),
inference(para,[status(thm),theory(equality)],[11,24]),
[iquote('para(11,24)')] ).
cnf(37,plain,
equal(multiply(inverse(A),n1),add(inverse(A),multiply(inverse(n1),inverse(A)))),
inference(flip,[status(thm),theory(equality)],[36]),
[iquote('flip(36)')] ).
cnf(38,plain,
equal(multiply(add(A,B),multiply(B,add(C,add(A,B)))),multiply(B,add(C,add(A,B)))),
inference(para,[status(thm),theory(equality)],[10,1]),
[iquote('para(10,1)')] ).
cnf(42,plain,
equal(add(multiply(A,add(B,add(A,C))),add(multiply(B,C),C)),add(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[2,10]),1]),
[iquote('para(2,10),demod([1])')] ).
cnf(43,plain,
equal(add(inverse(A),multiply(B,inverse(A))),multiply(inverse(A),add(n1,B))),
inference(para,[status(thm),theory(equality)],[11,3]),
[iquote('para(11,3)')] ).
cnf(45,plain,
equal(add(multiply(A,inverse(B)),inverse(B)),multiply(inverse(B),add(A,n1))),
inference(para,[status(thm),theory(equality)],[11,3]),
[iquote('para(11,3)')] ).
cnf(46,plain,
equal(multiply(inverse(A),add(B,n1)),add(multiply(B,inverse(A)),inverse(A))),
inference(flip,[status(thm),theory(equality)],[45]),
[iquote('flip(45)')] ).
cnf(47,plain,
equal(multiply(A,add(add(B,A),add(C,A))),add(A,A)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1,13]),1]),
[iquote('para(1,13),flip(1)')] ).
cnf(48,plain,
equal(add(multiply(A,inverse(B)),add(A,inverse(B))),pixley(A,B,add(C,add(A,inverse(B))))),
inference(para,[status(thm),theory(equality)],[10,5]),
[iquote('para(10,5)')] ).
cnf(49,plain,
equal(pixley(A,B,add(C,add(A,inverse(B)))),add(multiply(A,inverse(B)),add(A,inverse(B)))),
inference(flip,[status(thm),theory(equality)],[48]),
[iquote('flip(48)')] ).
cnf(51,plain,
equal(multiply(multiply(A,add(B,add(C,A))),A),A),
inference(para,[status(thm),theory(equality)],[15,1]),
[iquote('para(15,1)')] ).
cnf(54,plain,
equal(add(inverse(A),add(multiply(n1,B),multiply(inverse(A),B))),pixley(n1,A,B)),
inference(para,[status(thm),theory(equality)],[11,5]),
[iquote('para(11,5)')] ).
cnf(64,plain,
equal(multiply(inverse(A),add(n1,n1)),add(inverse(A),inverse(A))),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[11,43]),1]),
[iquote('para(11,43),flip(1)')] ).
cnf(65,plain,
equal(multiply(A,multiply(B,add(add(C,B),D))),add(multiply(B,A),multiply(multiply(D,B),A))),
inference(para,[status(thm),theory(equality)],[13,2]),
[iquote('para(13,2)')] ).
cnf(81,plain,
equal(add(multiply(A,inverse(A)),multiply(B,n1)),B),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[4,35]),6]),
[iquote('para(4,35),demod([6])')] ).
cnf(87,plain,
equal(multiply(A,multiply(A,n1)),multiply(A,n1)),
inference(para,[status(thm),theory(equality)],[81,1]),
[iquote('para(81,1)')] ).
cnf(90,plain,
equal(add(inverse(n1),multiply(A,n1)),A),
inference(para,[status(thm),theory(equality)],[11,81]),
[iquote('para(11,81)')] ).
cnf(91,plain,
equal(add(inverse(n1),n1),add(A,n1)),
inference(para,[status(thm),theory(equality)],[1,90]),
[iquote('para(1,90)')] ).
cnf(98,plain,
equal(add(A,n1),add(B,n1)),
inference(para,[status(thm),theory(equality)],[91,91]),
[iquote('para(91,91)')] ).
cnf(118,plain,
equal(add(inverse(n1),n1),multiply(n1,add(A,add(B,n1)))),
inference(para,[status(thm),theory(equality)],[51,90]),
[iquote('para(51,90)')] ).
cnf(119,plain,
equal(multiply(n1,add(A,add(B,n1))),add(inverse(n1),n1)),
inference(flip,[status(thm),theory(equality)],[118]),
[iquote('flip(118)')] ).
cnf(120,plain,
equal(multiply(inverse(A),add(B,n1)),add(inverse(A),inverse(A))),
inference(para,[status(thm),theory(equality)],[98,64]),
[iquote('para(98,64)')] ).
cnf(122,plain,
equal(add(multiply(A,inverse(B)),inverse(B)),add(inverse(B),inverse(B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[46]),120]),1]),
[iquote('back_demod(46),demod([120]),flip(1)')] ).
cnf(124,plain,
equal(add(multiply(A,add(B,n1)),add(inverse(A),inverse(A))),n1),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[32]),120]),
[iquote('back_demod(32),demod([120])')] ).
cnf(136,plain,
equal(add(inverse(n1),add(multiply(A,B),multiply(inverse(A),B))),B),
inference(para,[status(thm),theory(equality)],[23,90]),
[iquote('para(23,90)')] ).
cnf(141,plain,
equal(add(A,n1),multiply(n1,add(B,add(C,n1)))),
inference(para,[status(thm),theory(equality)],[91,118]),
[iquote('para(91,118)')] ).
cnf(142,plain,
equal(multiply(n1,add(A,add(B,n1))),add(C,n1)),
inference(flip,[status(thm),theory(equality)],[141]),
[iquote('flip(141)')] ).
cnf(144,plain,
equal(multiply(A,add(B,n1)),add(multiply(C,A),multiply(n1,A))),
inference(para,[status(thm),theory(equality)],[98,2]),
[iquote('para(98,2)')] ).
cnf(145,plain,
equal(add(multiply(A,B),multiply(n1,B)),multiply(B,add(C,n1))),
inference(flip,[status(thm),theory(equality)],[144]),
[iquote('flip(144)')] ).
cnf(155,plain,
equal(multiply(A,add(B,n1)),add(A,multiply(n1,A))),
inference(para,[status(thm),theory(equality)],[98,14]),
[iquote('para(98,14)')] ).
cnf(156,plain,
equal(add(A,multiply(n1,A)),multiply(A,add(B,n1))),
inference(flip,[status(thm),theory(equality)],[155]),
[iquote('flip(155)')] ).
cnf(161,plain,
equal(add(add(A,add(B,n1)),multiply(n1,add(A,add(B,n1)))),add(B,n1)),
inference(para,[status(thm),theory(equality)],[155,1]),
[iquote('para(155,1)')] ).
cnf(174,plain,
equal(multiply(add(A,B),add(C,D)),add(add(multiply(A,C),multiply(B,C)),add(multiply(A,D),multiply(B,D)))),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[2,19]),1]),
[iquote('para(2,19),flip(1)')] ).
cnf(185,plain,
equal(multiply(multiply(n1,n1),add(A,n1)),add(multiply(n1,n1),multiply(n1,n1))),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[87,156]),1]),
[iquote('para(87,156),flip(1)')] ).
cnf(186,plain,
equal(add(add(multiply(A,B),multiply(inverse(A),B)),multiply(C,n1)),multiply(n1,add(B,C))),
inference(para,[status(thm),theory(equality)],[23,3]),
[iquote('para(23,3)')] ).
cnf(187,plain,
equal(multiply(n1,add(A,B)),add(add(multiply(C,A),multiply(inverse(C),A)),multiply(B,n1))),
inference(flip,[status(thm),theory(equality)],[186]),
[iquote('flip(186)')] ).
cnf(190,plain,
equal(add(multiply(A,inverse(B)),add(add(multiply(C,A),multiply(inverse(C),A)),multiply(inverse(B),n1))),pixley(A,B,n1)),
inference(para,[status(thm),theory(equality)],[23,5]),
[iquote('para(23,5)')] ).
cnf(198,plain,
equal(multiply(multiply(inverse(A),n1),n1),add(multiply(A,multiply(inverse(A),n1)),multiply(inverse(A),n1))),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[87,24]),1]),
[iquote('para(87,24),flip(1)')] ).
cnf(204,plain,
equal(multiply(A,B),add(multiply(inverse(n1),A),multiply(multiply(B,n1),A))),
inference(para,[status(thm),theory(equality)],[90,2]),
[iquote('para(90,2)')] ).
cnf(205,plain,
equal(add(multiply(inverse(n1),A),multiply(multiply(B,n1),A)),multiply(A,B)),
inference(flip,[status(thm),theory(equality)],[204]),
[iquote('flip(204)')] ).
cnf(210,plain,
equal(multiply(multiply(A,B),multiply(multiply(B,n1),A)),multiply(multiply(B,n1),A)),
inference(para,[status(thm),theory(equality)],[90,12]),
[iquote('para(90,12)')] ).
cnf(229,plain,
equal(add(multiply(inverse(n1),n1),add(multiply(A,multiply(inverse(A),n1)),multiply(inverse(A),n1))),inverse(A)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[204,11]),198]),
[iquote('para(204,11),demod([198])')] ).
cnf(233,plain,
equal(add(add(A,add(B,n1)),add(C,n1)),add(add(multiply(A,D),multiply(add(B,n1),D)),add(multiply(A,n1),n1))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[142,156]),174,1]),
[iquote('para(142,156),demod([174,1])')] ).
cnf(234,plain,
equal(add(add(multiply(A,B),multiply(add(C,n1),B)),add(multiply(A,n1),n1)),add(add(A,add(C,n1)),add(D,n1))),
inference(flip,[status(thm),theory(equality)],[233]),
[iquote('flip(233)')] ).
cnf(235,plain,
equal(add(add(multiply(A,B),multiply(n1,B)),add(multiply(A,n1),multiply(n1,n1))),add(add(A,n1),add(n1,multiply(n1,n1)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[155,156]),174]),1]),
[iquote('para(155,156),demod([174]),flip(1)')] ).
cnf(240,plain,
equal(add(multiply(A,multiply(B,n1)),multiply(B,n1)),multiply(multiply(B,n1),add(A,B))),
inference(para,[status(thm),theory(equality)],[87,3]),
[iquote('para(87,3)')] ).
cnf(241,plain,
equal(multiply(multiply(A,n1),add(B,A)),add(multiply(B,multiply(A,n1)),multiply(A,n1))),
inference(flip,[status(thm),theory(equality)],[240]),
[iquote('flip(240)')] ).
cnf(247,plain,
equal(add(inverse(n1),add(multiply(A,multiply(inverse(A),n1)),multiply(inverse(A),n1))),multiply(inverse(A),n1)),
inference(para,[status(thm),theory(equality)],[87,136]),
[iquote('para(87,136)')] ).
cnf(253,plain,
equal(add(multiply(A,multiply(n1,n1)),multiply(n1,n1)),add(multiply(n1,n1),multiply(n1,n1))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[87,145]),185]),
[iquote('para(87,145),demod([185])')] ).
cnf(259,plain,
equal(multiply(inverse(A),add(multiply(A,multiply(inverse(A),n1)),multiply(inverse(A),n1))),add(multiply(A,multiply(inverse(A),n1)),multiply(inverse(A),n1))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[11,210]),198,198]),
[iquote('para(11,210),demod([198,198])')] ).
cnf(312,plain,
equal(add(multiply(inverse(n1),n1),multiply(multiply(A,n1),multiply(inverse(n1),n1))),multiply(multiply(inverse(n1),n1),A)),
inference(para,[status(thm),theory(equality)],[87,205]),
[iquote('para(87,205)')] ).
cnf(313,plain,
equal(multiply(multiply(inverse(n1),n1),A),add(multiply(inverse(n1),n1),multiply(multiply(A,n1),multiply(inverse(n1),n1)))),
inference(flip,[status(thm),theory(equality)],[312]),
[iquote('flip(312)')] ).
cnf(321,plain,
equal(add(inverse(A),multiply(B,add(n1,inverse(A)))),pixley(n1,A,B)),
inference(para,[status(thm),theory(equality)],[11,35]),
[iquote('para(11,35)')] ).
cnf(406,plain,
equal(multiply(multiply(inverse(A),n1),inverse(A)),inverse(A)),
inference(para,[status(thm),theory(equality)],[124,51]),
[iquote('para(124,51)')] ).
cnf(416,plain,
equal(multiply(inverse(A),add(B,multiply(inverse(A),n1))),add(inverse(A),inverse(A))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[406,3]),122]),1]),
[iquote('para(406,3),demod([122]),flip(1)')] ).
cnf(417,plain,
equal(add(multiply(A,multiply(inverse(A),n1)),multiply(inverse(A),n1)),add(inverse(A),inverse(A))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[259]),416]),1]),
[iquote('back_demod(259),demod([416]),flip(1)')] ).
cnf(419,plain,
equal(add(inverse(n1),add(inverse(A),inverse(A))),multiply(inverse(A),n1)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[247]),417]),
[iquote('back_demod(247),demod([417])')] ).
cnf(420,plain,
equal(multiply(inverse(A),n1),add(inverse(n1),add(inverse(A),inverse(A)))),
inference(flip,[status(thm),theory(equality)],[419]),
[iquote('flip(419)')] ).
cnf(421,plain,
equal(add(multiply(inverse(n1),n1),add(inverse(A),inverse(A))),inverse(A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[229]),417]),
[iquote('back_demod(229),demod([417])')] ).
cnf(422,plain,
equal(multiply(multiply(inverse(A),n1),n1),add(inverse(A),inverse(A))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[198]),417]),
[iquote('back_demod(198),demod([417])')] ).
cnf(439,plain,
equal(add(multiply(A,inverse(A)),add(inverse(B),inverse(B))),multiply(inverse(B),n1)),
inference(para,[status(thm),theory(equality)],[422,81]),
[iquote('para(422,81)')] ).
cnf(440,plain,
equal(multiply(inverse(A),n1),add(multiply(B,inverse(B)),add(inverse(A),inverse(A)))),
inference(flip,[status(thm),theory(equality)],[439]),
[iquote('flip(439)')] ).
cnf(459,plain,
equal(multiply(add(inverse(n1),add(inverse(A),inverse(A))),inverse(A)),inverse(A)),
inference(para,[status(thm),theory(equality)],[420,406]),
[iquote('para(420,406)')] ).
cnf(462,plain,
equal(multiply(inverse(A),inverse(A)),add(inverse(A),inverse(A))),
inference(para,[status(thm),theory(equality)],[90,416]),
[iquote('para(90,416)')] ).
cnf(467,plain,
equal(add(inverse(n1),add(multiply(A,inverse(A)),add(inverse(B),inverse(B)))),inverse(B)),
inference(para,[status(thm),theory(equality)],[440,90]),
[iquote('para(440,90)')] ).
cnf(472,plain,
equal(multiply(inverse(A),add(multiply(B,inverse(B)),add(inverse(A),inverse(A)))),add(multiply(B,inverse(B)),add(inverse(A),inverse(A)))),
inference(para,[status(thm),theory(equality)],[467,1]),
[iquote('para(467,1)')] ).
cnf(474,plain,
equal(add(multiply(A,multiply(inverse(B),n1)),multiply(inverse(A),multiply(inverse(B),n1))),add(inverse(B),inverse(B))),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[422,23]),1]),
[iquote('para(422,23),flip(1)')] ).
cnf(482,plain,
equal(add(multiply(A,add(B,add(C,n1))),add(D,n1)),add(add(multiply(B,A),multiply(add(C,n1),A)),add(multiply(B,n1),n1))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[142,3]),174,1]),
[iquote('para(142,3),demod([174,1])')] ).
cnf(483,plain,
equal(add(add(multiply(A,B),multiply(add(C,n1),B)),add(multiply(A,n1),n1)),add(multiply(B,add(A,add(C,n1))),add(D,n1))),
inference(flip,[status(thm),theory(equality)],[482]),
[iquote('flip(482)')] ).
cnf(490,plain,
equal(add(multiply(A,B),multiply(n1,B)),add(B,multiply(n1,B))),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[155,2]),1]),
[iquote('para(155,2),flip(1)')] ).
cnf(496,plain,
equal(add(multiply(A,multiply(n1,n1)),multiply(n1,n1)),add(n1,multiply(n1,n1))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[253]),490]),
[iquote('back_demod(253),demod([490])')] ).
cnf(497,plain,
equal(add(add(A,multiply(n1,A)),add(n1,multiply(n1,n1))),add(add(B,n1),add(n1,multiply(n1,n1)))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[235]),490,490]),
[iquote('back_demod(235),demod([490,490])')] ).
cnf(498,plain,
equal(add(add(A,n1),add(n1,multiply(n1,n1))),add(add(B,multiply(n1,B)),add(n1,multiply(n1,n1)))),
inference(flip,[status(thm),theory(equality)],[497]),
[iquote('flip(497)')] ).
cnf(517,plain,
equal(add(multiply(A,inverse(B)),add(inverse(B),inverse(B))),multiply(inverse(B),add(A,inverse(B)))),
inference(para,[status(thm),theory(equality)],[462,3]),
[iquote('para(462,3)')] ).
cnf(518,plain,
equal(multiply(inverse(A),add(B,inverse(A))),add(multiply(B,inverse(A)),add(inverse(A),inverse(A)))),
inference(flip,[status(thm),theory(equality)],[517]),
[iquote('flip(517)')] ).
cnf(525,plain,
equal(add(multiply(A,add(B,add(C,n1))),add(D,n1)),add(C,n1)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[142,490]),161]),
[iquote('para(142,490),demod([161])')] ).
cnf(526,plain,
equal(add(add(multiply(A,B),multiply(add(C,n1),B)),add(multiply(A,n1),n1)),add(C,n1)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[483]),525]),
[iquote('back_demod(483),demod([525])')] ).
cnf(527,plain,
equal(add(add(A,add(B,n1)),add(C,n1)),add(B,n1)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[234]),526]),1]),
[iquote('back_demod(234),demod([526]),flip(1)')] ).
cnf(530,plain,
equal(add(add(A,multiply(n1,A)),add(n1,multiply(n1,n1))),add(A,n1)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[527,1]),174,490,490]),
[iquote('para(527,1),demod([174,490,490])')] ).
cnf(531,plain,
equal(add(add(A,n1),add(n1,multiply(n1,n1))),add(B,n1)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[498]),530]),
[iquote('back_demod(498),demod([530])')] ).
cnf(532,plain,
equal(add(A,n1),add(add(B,n1),add(n1,multiply(n1,n1)))),
inference(flip,[status(thm),theory(equality)],[531]),
[iquote('flip(531)')] ).
cnf(539,plain,
equal(add(n1,multiply(n1,n1)),add(n1,n1)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[531,1]),174,490,87,496,530]),1]),
[iquote('para(531,1),demod([174,490,87,496,530]),flip(1)')] ).
cnf(540,plain,
equal(add(A,n1),add(add(B,n1),add(n1,n1))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[532]),539]),
[iquote('back_demod(532),demod([539])')] ).
cnf(570,plain,
equal(multiply(n1,add(A,n1)),add(n1,n1)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[539,156]),1]),
[iquote('para(539,156),flip(1)')] ).
cnf(590,plain,
equal(add(add(n1,n1),add(inverse(n1),inverse(n1))),n1),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[570,24]),120,1]),
[iquote('para(570,24),demod([120,1])')] ).
cnf(596,plain,
equal(add(add(A,n1),add(inverse(n1),inverse(n1))),n1),
inference(para,[status(thm),theory(equality)],[98,590]),
[iquote('para(98,590)')] ).
cnf(718,plain,
equal(add(add(A,n1),add(n1,n1)),multiply(n1,add(B,add(C,n1)))),
inference(para,[status(thm),theory(equality)],[540,118]),
[iquote('para(540,118)')] ).
cnf(722,plain,
equal(add(add(A,n1),add(B,n1)),multiply(n1,add(C,add(D,n1)))),
inference(para,[status(thm),theory(equality)],[98,718]),
[iquote('para(98,718)')] ).
cnf(723,plain,
equal(multiply(n1,add(A,add(B,n1))),add(add(C,n1),add(D,n1))),
inference(flip,[status(thm),theory(equality)],[722]),
[iquote('flip(722)')] ).
cnf(728,plain,
equal(multiply(inverse(A),pixley(B,A,add(C,add(B,inverse(A))))),add(inverse(A),inverse(A))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[48,16]),122]),
[iquote('para(48,16),demod([122])')] ).
cnf(744,plain,
equal(multiply(A,add(add(B,n1),add(n1,n1))),add(A,multiply(n1,A))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[540,2]),490]),
[iquote('para(540,2),demod([490])')] ).
cnf(750,plain,
equal(multiply(A,add(add(B,n1),add(C,n1))),add(A,multiply(n1,A))),
inference(para,[status(thm),theory(equality)],[98,744]),
[iquote('para(98,744)')] ).
cnf(751,plain,
equal(add(A,multiply(n1,A)),multiply(A,add(add(B,n1),add(C,n1)))),
inference(flip,[status(thm),theory(equality)],[750]),
[iquote('flip(750)')] ).
cnf(766,plain,
equal(add(inverse(A),multiply(B,add(multiply(inverse(A),add(C,add(D,inverse(A)))),inverse(A)))),pixley(multiply(inverse(A),add(C,add(D,inverse(A)))),A,B)),
inference(para,[status(thm),theory(equality)],[51,35]),
[iquote('para(51,35)')] ).
cnf(769,plain,
equal(multiply(multiply(A,add(B,A)),A),A),
inference(para,[status(thm),theory(equality)],[42,51]),
[iquote('para(42,51)')] ).
cnf(812,plain,
equal(add(inverse(A),add(multiply(n1,n1),add(multiply(B,inverse(A)),multiply(inverse(B),inverse(A))))),n1),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[23,54]),8]),
[iquote('para(23,54),demod([8])')] ).
cnf(835,plain,
equal(add(multiply(inverse(n1),multiply(A,add(B,A))),multiply(multiply(A,n1),multiply(A,add(B,A)))),A),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[769,204]),1]),
[iquote('para(769,204),flip(1)')] ).
cnf(890,plain,
equal(add(n1,multiply(add(inverse(n1),inverse(n1)),n1)),multiply(n1,n1)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[596,14]),1]),
[iquote('para(596,14),flip(1)')] ).
cnf(893,plain,
equal(multiply(inverse(n1),n1),add(inverse(n1),inverse(n1))),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[596,16]),122]),
[iquote('para(596,16),demod([122])')] ).
cnf(894,plain,
equal(add(add(inverse(n1),inverse(n1)),add(inverse(A),inverse(A))),inverse(A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[421]),893]),
[iquote('back_demod(421),demod([893])')] ).
cnf(895,plain,
equal(multiply(add(inverse(n1),inverse(n1)),A),add(add(inverse(n1),inverse(n1)),multiply(multiply(A,n1),add(inverse(n1),inverse(n1))))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[313]),893,893,893]),
[iquote('back_demod(313),demod([893,893,893])')] ).
cnf(896,plain,
equal(add(add(inverse(n1),inverse(n1)),multiply(multiply(A,n1),add(inverse(n1),inverse(n1)))),multiply(add(inverse(n1),inverse(n1)),A)),
inference(flip,[status(thm),theory(equality)],[895]),
[iquote('flip(895)')] ).
cnf(899,plain,
equal(add(inverse(n1),add(inverse(n1),inverse(n1))),inverse(n1)),
inference(para,[status(thm),theory(equality)],[893,90]),
[iquote('para(893,90)')] ).
cnf(911,plain,
equal(add(add(inverse(n1),inverse(n1)),multiply(inverse(inverse(n1)),n1)),multiply(n1,n1)),
inference(para,[status(thm),theory(equality)],[893,24]),
[iquote('para(893,24)')] ).
cnf(921,plain,
equal(add(add(inverse(n1),inverse(n1)),multiply(A,n1)),multiply(n1,add(inverse(n1),A))),
inference(para,[status(thm),theory(equality)],[893,3]),
[iquote('para(893,3)')] ).
cnf(922,plain,
equal(multiply(n1,add(inverse(n1),A)),add(add(inverse(n1),inverse(n1)),multiply(A,n1))),
inference(flip,[status(thm),theory(equality)],[921]),
[iquote('flip(921)')] ).
cnf(929,plain,
equal(add(inverse(n1),inverse(n1)),inverse(n1)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[893,37]),462,899]),
[iquote('para(893,37),demod([462,899])')] ).
cnf(934,plain,
equal(multiply(n1,add(inverse(n1),A)),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[922]),929,90]),
[iquote('back_demod(922),demod([929,90])')] ).
cnf(937,plain,
equal(inverse(inverse(n1)),multiply(n1,n1)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[911]),929,90]),
[iquote('back_demod(911),demod([929,90])')] ).
cnf(940,plain,
equal(add(inverse(n1),multiply(multiply(A,n1),inverse(n1))),multiply(inverse(n1),A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[896]),929,929,929]),
[iquote('back_demod(896),demod([929,929,929])')] ).
cnf(941,plain,
equal(multiply(inverse(n1),A),add(inverse(n1),multiply(multiply(A,n1),inverse(n1)))),
inference(flip,[status(thm),theory(equality)],[940]),
[iquote('flip(940)')] ).
cnf(942,plain,
equal(add(inverse(n1),add(inverse(A),inverse(A))),inverse(A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[894]),929]),
[iquote('back_demod(894),demod([929])')] ).
cnf(943,plain,
equal(add(inverse(A),inverse(A)),inverse(A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[459]),942,462]),
[iquote('back_demod(459),demod([942,462])')] ).
cnf(945,plain,
equal(multiply(inverse(n1),n1),inverse(n1)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[893]),943]),
[iquote('back_demod(893),demod([943])')] ).
cnf(946,plain,
equal(multiply(n1,n1),n1),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[890]),943,945,4]),1]),
[iquote('back_demod(890),demod([943,945,4]),flip(1)')] ).
cnf(947,plain,
equal(inverse(inverse(n1)),n1),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[937]),946]),
[iquote('back_demod(937),demod([946])')] ).
cnf(950,plain,
equal(add(inverse(A),add(n1,add(multiply(B,inverse(A)),multiply(inverse(B),inverse(A))))),n1),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[812]),946]),
[iquote('back_demod(812),demod([946])')] ).
cnf(982,plain,
equal(multiply(inverse(A),pixley(B,A,add(C,add(B,inverse(A))))),inverse(A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[728]),943]),
[iquote('back_demod(728),demod([943])')] ).
cnf(990,plain,
equal(multiply(inverse(A),add(B,inverse(A))),inverse(A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[518]),943,122,943]),
[iquote('back_demod(518),demod([943,122,943])')] ).
cnf(995,plain,
equal(add(multiply(A,multiply(inverse(B),n1)),multiply(inverse(A),multiply(inverse(B),n1))),inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[474]),943]),
[iquote('back_demod(474),demod([943])')] ).
cnf(996,plain,
equal(add(multiply(A,inverse(A)),inverse(B)),inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[472]),943,990,943]),1]),
[iquote('back_demod(472),demod([943,990,943]),flip(1)')] ).
cnf(1000,plain,
equal(multiply(inverse(A),n1),inverse(A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[440]),943,996]),
[iquote('back_demod(440),demod([943,996])')] ).
cnf(1002,plain,
equal(add(multiply(A,inverse(B)),multiply(inverse(A),inverse(B))),inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[995]),1000,1000]),
[iquote('back_demod(995),demod([1000,1000])')] ).
cnf(1005,plain,
equal(add(inverse(A),add(n1,inverse(A))),n1),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[950]),1002]),
[iquote('back_demod(950),demod([1002])')] ).
cnf(1035,plain,
equal(add(multiply(A,inverse(B)),add(add(multiply(C,A),multiply(inverse(C),A)),inverse(B))),pixley(A,B,n1)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[190]),1000]),
[iquote('back_demod(190),demod([1000])')] ).
cnf(1052,plain,
equal(add(inverse(n1),n1),n1),
inference(para,[status(thm),theory(equality)],[947,4]),
[iquote('para(947,4)')] ).
cnf(1053,plain,
equal(multiply(n1,add(A,add(B,n1))),n1),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[119]),1052]),
[iquote('back_demod(119),demod([1052])')] ).
cnf(1054,plain,
equal(add(add(A,n1),add(B,n1)),n1),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[723]),1053]),1]),
[iquote('back_demod(723),demod([1053]),flip(1)')] ).
cnf(1060,plain,
equal(add(A,multiply(n1,A)),multiply(A,n1)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[751]),1054]),
[iquote('back_demod(751),demod([1054])')] ).
cnf(1061,plain,
equal(multiply(A,n1),add(A,multiply(n1,A))),
inference(flip,[status(thm),theory(equality)],[1060]),
[iquote('flip(1060)')] ).
cnf(1086,plain,
equal(multiply(n1,A),multiply(A,n1)),
inference(para,[status(thm),theory(equality)],[90,934]),
[iquote('para(90,934)')] ).
cnf(1087,plain,
equal(multiply(A,n1),multiply(n1,A)),
inference(flip,[status(thm),theory(equality)],[1086]),
[iquote('flip(1086)')] ).
cnf(1096,plain,
equal(multiply(add(inverse(n1),A),n1),A),
inference(para,[status(thm),theory(equality)],[1086,934]),
[iquote('para(1086,934)')] ).
cnf(1124,plain,
equal(add(A,multiply(n1,A)),multiply(n1,A)),
inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1087,1061]),1]),
[iquote('para(1087,1061),flip(1)')] ).
cnf(1126,plain,
equal(add(multiply(A,B),multiply(n1,B)),multiply(n1,B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[490]),1124]),
[iquote('back_demod(490),demod([1124])')] ).
cnf(1159,plain,
equal(add(add(inverse(n1),A),A),A),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[934,1124]),934]),
[iquote('para(934,1124),demod([934])')] ).
cnf(1160,plain,
equal(multiply(A,A),A),
inference(para,[status(thm),theory(equality)],[1159,1]),
[iquote('para(1159,1)')] ).
cnf(1171,plain,
equal(add(multiply(A,inverse(A)),multiply(n1,B)),B),
inference(para,[status(thm),theory(equality)],[1087,81]),
[iquote('para(1087,81)')] ).
cnf(1200,plain,
equal(add(multiply(A,inverse(A)),B),add(inverse(n1),B)),
inference(para,[status(thm),theory(equality)],[1096,81]),
[iquote('para(1096,81)')] ).
cnf(1201,plain,
equal(add(inverse(n1),A),add(multiply(B,inverse(B)),A)),
inference(flip,[status(thm),theory(equality)],[1200]),
[iquote('flip(1200)')] ).
cnf(1232,plain,
equal(add(multiply(A,B),multiply(B,n1)),multiply(n1,B)),
inference(para,[status(thm),theory(equality)],[1086,1126]),
[iquote('para(1086,1126)')] ).
cnf(1233,plain,
equal(multiply(n1,A),add(multiply(B,A),multiply(A,n1))),
inference(flip,[status(thm),theory(equality)],[1232]),
[iquote('flip(1232)')] ).
cnf(1260,plain,
equal(add(multiply(A,B),multiply(B,n1)),multiply(B,n1)),
inference(para,[status(thm),theory(equality)],[1233,1086]),
[iquote('para(1233,1086)')] ).
cnf(1291,plain,
equal(add(multiply(A,add(B,A)),multiply(A,add(B,A))),add(A,A)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[65,38]),1,47]),
[iquote('para(65,38),demod([1,47])')] ).
cnf(1307,plain,
equal(add(multiply(A,B),B),multiply(B,add(A,B))),
inference(para,[status(thm),theory(equality)],[1160,3]),
[iquote('para(1160,3)')] ).
cnf(1308,plain,
equal(multiply(A,add(B,A)),add(multiply(B,A),A)),
inference(flip,[status(thm),theory(equality)],[1307]),
[iquote('flip(1307)')] ).
cnf(1390,plain,
equal(add(A,A),A),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[934,1126]),934,934]),
[iquote('para(934,1126),demod([934,934])')] ).
cnf(1402,plain,
equal(multiply(A,add(B,A)),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1291]),1390,1390]),
[iquote('back_demod(1291),demod([1390,1390])')] ).
cnf(1404,plain,
equal(add(multiply(A,B),B),B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1308]),1402]),1]),
[iquote('back_demod(1308),demod([1402]),flip(1)')] ).
cnf(1494,plain,
equal(multiply(multiply(A,n1),add(B,A)),multiply(A,n1)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[241]),1404]),
[iquote('back_demod(241),demod([1404])')] ).
cnf(1531,plain,
equal(multiply(A,add(B,add(C,A))),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[16]),1404]),
[iquote('back_demod(16),demod([1404])')] ).
cnf(1548,plain,
equal(add(inverse(A),multiply(B,inverse(A))),pixley(inverse(A),A,B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[766]),1531,1390,1531]),
[iquote('back_demod(766),demod([1531,1390,1531])')] ).
cnf(1566,plain,
equal(multiply(inverse(n1),A),pixley(inverse(n1),n1,multiply(A,n1))),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[941]),1548]),
[iquote('back_demod(941),demod([1548])')] ).
cnf(1567,plain,
equal(pixley(inverse(n1),n1,multiply(A,n1)),multiply(inverse(n1),A)),
inference(flip,[status(thm),theory(equality)],[1566]),
[iquote('flip(1566)')] ).
cnf(1637,plain,
equal(add(multiply(inverse(n1),A),multiply(multiply(A,n1),A)),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[835]),1402,1402]),
[iquote('back_demod(835),demod([1402,1402])')] ).
cnf(1664,plain,
equal(add(A,add(B,A)),add(B,A)),
inference(para,[status(thm),theory(equality)],[1402,1404]),
[iquote('para(1402,1404)')] ).
cnf(1667,plain,
equal(add(n1,inverse(A)),n1),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1005]),1664]),
[iquote('back_demod(1005),demod([1664])')] ).
cnf(1668,plain,
equal(add(inverse(A),multiply(B,n1)),pixley(n1,A,B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[321]),1667]),
[iquote('back_demod(321),demod([1667])')] ).
cnf(1708,plain,
equal(multiply(multiply(A,n1),A),multiply(A,n1)),
inference(para,[status(thm),theory(equality)],[1390,1494]),
[iquote('para(1390,1494)')] ).
cnf(1709,plain,
equal(multiply(A,n1),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1637]),1708,1260]),
[iquote('back_demod(1637),demod([1708,1260])')] ).
cnf(1728,plain,
equal(add(inverse(A),B),pixley(n1,A,B)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1668]),1709]),
[iquote('back_demod(1668),demod([1709])')] ).
cnf(1758,plain,
equal(add(multiply(A,inverse(A)),B),B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1201]),1728,6]),1]),
[iquote('back_demod(1201),demod([1728,6]),flip(1)')] ).
cnf(1759,plain,
equal(multiply(n1,A),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1171]),1758]),
[iquote('back_demod(1171),demod([1758])')] ).
cnf(1793,plain,
equal(add(add(multiply(A,B),multiply(inverse(A),B)),C),add(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[187]),1759,1709]),1]),
[iquote('back_demod(187),demod([1759,1709]),flip(1)')] ).
cnf(1798,plain,
equal(add(multiply(A,inverse(B)),add(A,inverse(B))),pixley(A,B,n1)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1035]),1793]),
[iquote('back_demod(1035),demod([1793])')] ).
cnf(1800,plain,
equal(pixley(A,B,add(C,add(A,inverse(B)))),pixley(A,B,n1)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[49]),1798]),
[iquote('back_demod(49),demod([1798])')] ).
cnf(1802,plain,
equal(multiply(inverse(A),pixley(B,A,n1)),inverse(A)),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[982]),1800]),
[iquote('back_demod(982),demod([1800])')] ).
cnf(1823,plain,
equal(multiply(inverse(n1),A),pixley(inverse(n1),n1,A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1567]),1709]),1]),
[iquote('back_demod(1567),demod([1709]),flip(1)')] ).
cnf(1896,plain,
equal(add(multiply(A,B),multiply(inverse(A),B)),B),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[24]),1709]),
[iquote('back_demod(24),demod([1709])')] ).
cnf(1945,plain,
equal(add(A,pixley(inverse(n1),n1,A)),A),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1759,1896]),1823]),
[iquote('para(1759,1896),demod([1823])')] ).
cnf(2012,plain,
equal(pixley(inverse(n1),n1,A),inverse(n1)),
inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[7,1802]),1823]),
[iquote('para(7,1802),demod([1823])')] ).
cnf(2015,plain,
equal(add(A,inverse(n1)),A),
inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1945]),2012]),
[iquote('back_demod(1945),demod([2012])')] ).
cnf(2049,plain,
equal(multiply(A,inverse(A)),inverse(n1)),
inference(para,[status(thm),theory(equality)],[2015,1758]),
[iquote('para(2015,1758)')] ).
cnf(2050,plain,
equal(inverse(n1),multiply(A,inverse(A))),
inference(flip,[status(thm),theory(equality)],[2049]),
[iquote('flip(2049)')] ).
cnf(2067,plain,
equal(add(A,multiply(B,inverse(B))),A),
inference(para,[status(thm),theory(equality)],[2050,2015]),
[iquote('para(2050,2015)')] ).
cnf(2282,plain,
equal(multiply(A,inverse(A)),multiply(B,inverse(B))),
inference(para,[status(thm),theory(equality)],[2067,1758]),
[iquote('para(2067,1758)')] ).
cnf(2283,plain,
$false,
inference(conflict,[status(thm)],[2282,9]),
[iquote('conflict(2282,9)')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : BOO025-1 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : tptp2X_and_run_eqp %s
% 0.15/0.35 % Computer : n024.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Wed Jun 1 16:38:51 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.76/1.38 ----- EQP 0.9e, May 2009 -----
% 0.76/1.38 The job began on n024.cluster.edu, Wed Jun 1 16:38:51 2022
% 0.76/1.38 The command was "./eqp09e".
% 0.76/1.38
% 0.76/1.38 set(prolog_style_variables).
% 0.76/1.38 set(lrpo).
% 0.76/1.38 set(basic_paramod).
% 0.76/1.38 set(functional_subsume).
% 0.76/1.38 set(ordered_paramod).
% 0.76/1.38 set(prime_paramod).
% 0.76/1.38 set(para_pairs).
% 0.76/1.38 assign(pick_given_ratio,4).
% 0.76/1.38 clear(print_kept).
% 0.76/1.38 clear(print_new_demod).
% 0.76/1.38 clear(print_back_demod).
% 0.76/1.38 clear(print_given).
% 0.76/1.38 assign(max_mem,64000).
% 0.76/1.38 end_of_commands.
% 0.76/1.38
% 0.76/1.38 Usable:
% 0.76/1.38 end_of_list.
% 0.76/1.38
% 0.76/1.38 Sos:
% 0.76/1.38 0 (wt=-1) [] multiply(add(A,B),B) = B.
% 0.76/1.38 0 (wt=-1) [] multiply(A,add(B,C)) = add(multiply(B,A),multiply(C,A)).
% 0.76/1.38 0 (wt=-1) [] add(A,inverse(A)) = n1.
% 0.76/1.38 0 (wt=-1) [] pixley(A,B,C) = add(multiply(A,inverse(B)),add(multiply(A,C),multiply(inverse(B),C))).
% 0.76/1.38 0 (wt=-1) [] pixley(A,A,B) = B.
% 0.76/1.38 0 (wt=-1) [] pixley(A,B,B) = A.
% 0.76/1.38 0 (wt=-1) [] pixley(A,B,A) = A.
% 0.76/1.38 0 (wt=-1) [] -(multiply(b,inverse(b)) = multiply(a,inverse(a))).
% 0.76/1.38 end_of_list.
% 0.76/1.38
% 0.76/1.38 Demodulators:
% 0.76/1.38 end_of_list.
% 0.76/1.38
% 0.76/1.38 Passive:
% 0.76/1.38 end_of_list.
% 0.76/1.38
% 0.76/1.38 Starting to process input.
% 0.76/1.38
% 0.76/1.38 ** KEPT: 1 (wt=7) [] multiply(add(A,B),B) = B.
% 0.76/1.38 1 is a new demodulator.
% 0.76/1.38
% 0.76/1.38 ** KEPT: 2 (wt=13) [] multiply(A,add(B,C)) = add(multiply(B,A),multiply(C,A)).
% 0.76/1.38
% 0.76/1.38 ** KEPT: 3 (wt=13) [flip(2)] add(multiply(A,B),multiply(C,B)) = multiply(B,add(A,C)).
% 0.76/1.38 clause forward subsumed: 0 (wt=13) [flip(3)] multiply(B,add(A,C)) = add(multiply(A,B),multiply(C,B)).
% 0.76/1.38
% 0.76/1.38 ** KEPT: 4 (wt=6) [] add(A,inverse(A)) = n1.
% 0.76/1.38 4 is a new demodulator.
% 0.76/1.38
% 0.76/1.38 ** KEPT: 5 (wt=18) [flip(1)] add(multiply(A,inverse(B)),add(multiply(A,C),multiply(inverse(B),C))) = pixley(A,B,C).
% 0.76/1.38 5 is a new demodulator.
% 0.76/1.38
% 0.76/1.38 ** KEPT: 6 (wt=6) [] pixley(A,A,B) = B.
% 0.76/1.38 6 is a new demodulator.
% 0.76/1.38
% 0.76/1.38 ** KEPT: 7 (wt=6) [] pixley(A,B,B) = A.
% 0.76/1.38 7 is a new demodulator.
% 0.76/1.38
% 0.76/1.38 ** KEPT: 8 (wt=6) [] pixley(A,B,A) = A.
% 0.76/1.38 8 is a new demodulator.
% 0.76/1.38
% 0.76/1.38 ** KEPT: 9 (wt=9) [] -(multiply(b,inverse(b)) = multiply(a,inverse(a))).
% 0.76/1.38 ---------------- PROOF FOUND ----------------
% 0.76/1.38 % SZS status Unsatisfiable
% 0.76/1.38
% 0.76/1.38
% 0.76/1.38 After processing input:
% 0.76/1.38
% 0.76/1.38 Usable:
% 0.76/1.38 end_of_list.
% 0.76/1.38
% 0.76/1.38 Sos:
% 0.76/1.38 4 (wt=6) [] add(A,inverse(A)) = n1.
% 0.76/1.38 6 (wt=6) [] pixley(A,A,B) = B.
% 0.76/1.38 7 (wt=6) [] pixley(A,B,B) = A.
% 0.76/1.38 8 (wt=6) [] pixley(A,B,A) = A.
% 0.76/1.38 1 (wt=7) [] multiply(add(A,B),B) = B.
% 0.76/1.38 9 (wt=9) [] -(multiply(b,inverse(b)) = multiply(a,inverse(a))).
% 0.76/1.38 2 (wt=13) [] multiply(A,add(B,C)) = add(multiply(B,A),multiply(C,A)).
% 0.76/1.38 3 (wt=13) [flip(2)] add(multiply(A,B),multiply(C,B)) = multiply(B,add(A,C)).
% 0.76/1.38 5 (wt=18) [flip(1)] add(multiply(A,inverse(B)),add(multiply(A,C),multiply(inverse(B),C))) = pixley(A,B,C).
% 0.76/1.38 end_of_list.
% 0.76/1.38
% 0.76/1.38 Demodulators:
% 0.76/1.38 1 (wt=7) [] multiply(add(A,B),B) = B.
% 0.76/1.38 4 (wt=6) [] add(A,inverse(A)) = n1.
% 0.76/1.38 5 (wt=18) [flip(1)] add(multiply(A,inverse(B)),add(multiply(A,C),multiply(inverse(B),C))) = pixley(A,B,C).
% 0.76/1.38 6 (wt=6) [] pixley(A,A,B) = B.
% 0.76/1.38 7 (wt=6) [] pixley(A,B,B) = A.
% 0.76/1.38 8 (wt=6) [] pixley(A,B,A) = A.
% 0.76/1.38 end_of_list.
% 0.76/1.38
% 0.76/1.38 Passive:
% 0.76/1.38 end_of_list.
% 0.76/1.38
% 0.76/1.38 UNIT CONFLICT from 2282 and 9 at 0.17 seconds.
% 0.76/1.38
% 0.76/1.38 ---------------- PROOF ----------------
% 0.76/1.38 % SZS output start Refutation
% See solution above
% 0.76/1.38 ------------ end of proof -------------
% 0.76/1.38
% 0.76/1.38
% 0.76/1.38 ------------- memory usage ------------
% 0.76/1.38 Memory dynamically allocated (tp_alloc): 4882.
% 0.76/1.38 type (bytes each) gets frees in use avail bytes
% 0.76/1.38 sym_ent ( 96) 58 0 58 0 5.4 K
% 0.76/1.38 term ( 16) 172854 105149 67705 50 1314.4 K
% 0.76/1.38 gen_ptr ( 8) 367609 61647 305962 197 2391.9 K
% 0.76/1.38 context ( 808) 150210 150208 2 5 5.5 K
% 0.76/1.38 trail ( 12) 38165 38165 0 7 0.1 K
% 0.76/1.38 bt_node ( 68) 48342 48339 3 18 1.4 K
% 0.76/1.38 ac_position (285432) 0 0 0 0 0.0 K
% 0.76/1.38 ac_match_pos (14044) 0 0 0 0 0.0 K
% 0.76/1.38 ac_match_free_vars_pos (4020)
% 0.76/1.38 0 0 0 0 0.0 K
% 0.76/1.38 discrim ( 12) 60478 29692 30786 0 360.8 K
% 0.76/1.38 flat ( 40) 426000 426000 0 125 4.9 K
% 0.76/1.38 discrim_pos ( 12) 5751 5751 0 1 0.0 K
% 0.76/1.38 fpa_head ( 12) 13422 0 13422 0 157.3 K
% 0.76/1.38 fpa_tree ( 28) 8395 8395 0 29 0.8 K
% 0.76/1.38 fpa_pos ( 36) 3474 3474 0 1 0.0 K
% 0.76/1.38 literal ( 12) 8416 6134 2282 1 26.8 K
% 0.76/1.38 clause ( 24) 8416 6134 2282 1 53.5 K
% 0.76/1.38 list ( 12) 1251 1195 56 9 0.8 K
% 0.76/1.38 list_pos ( 20) 10912 6319 4593 0 89.7 K
% 0.76/1.38 pair_index ( 40) 2 0 2 0 0.1 K
% 0.76/1.38
% 0.76/1.38 -------------- statistics -------------
% 0.76/1.38 Clauses input 8
% 0.76/1.38 Usable input 0
% 0.76/1.38 Sos input 8
% 0.76/1.38 Demodulators input 0
% 0.76/1.38 Passive input 0
% 0.76/1.38
% 0.76/1.38 Processed BS (before search) 10
% 0.76/1.38 Forward subsumed BS 1
% 0.76/1.38 Kept BS 9
% 0.76/1.38 New demodulators BS 6
% 0.76/1.38 Back demodulated BS 0
% 0.76/1.38
% 0.76/1.38 Clauses or pairs given 7867
% 0.76/1.38 Clauses generated 4894
% 0.76/1.38 Forward subsumed 2621
% 0.76/1.38 Deleted by weight 0
% 0.76/1.38 Deleted by variable count 0
% 0.76/1.38 Kept 2273
% 0.76/1.38 New demodulators 1186
% 0.76/1.38 Back demodulated 1316
% 0.76/1.38 Ordered paramod prunes 0
% 0.76/1.38 Basic paramod prunes 25471
% 0.76/1.38 Prime paramod prunes 174
% 0.76/1.38 Semantic prunes 0
% 0.76/1.38
% 0.76/1.38 Rewrite attmepts 76851
% 0.76/1.38 Rewrites 4557
% 0.76/1.38
% 0.76/1.38 FPA overloads 0
% 0.76/1.38 FPA underloads 0
% 0.76/1.38
% 0.76/1.38 Usable size 0
% 0.76/1.38 Sos size 965
% 0.76/1.38 Demodulators size 382
% 0.76/1.38 Passive size 0
% 0.76/1.38 Disabled size 1316
% 0.76/1.38
% 0.76/1.38 Proofs found 1
% 0.76/1.38
% 0.76/1.38 ----------- times (seconds) ----------- Wed Jun 1 16:38:52 2022
% 0.76/1.38
% 0.76/1.38 user CPU time 0.17 (0 hr, 0 min, 0 sec)
% 0.76/1.38 system CPU time 0.11 (0 hr, 0 min, 0 sec)
% 0.76/1.38 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 0.76/1.38 input time 0.00
% 0.76/1.38 paramodulation time 0.02
% 0.76/1.38 demodulation time 0.02
% 0.76/1.38 orient time 0.02
% 0.76/1.38 weigh time 0.00
% 0.76/1.38 forward subsume time 0.01
% 0.76/1.38 back demod find time 0.01
% 0.76/1.38 conflict time 0.00
% 0.76/1.38 LRPO time 0.01
% 0.76/1.38 store clause time 0.04
% 0.76/1.38 disable clause time 0.01
% 0.76/1.38 prime paramod time 0.01
% 0.76/1.38 semantics time 0.00
% 0.76/1.38
% 0.76/1.38 EQP interrupted
%------------------------------------------------------------------------------