TSTP Solution File: BOO026-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO026-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 23:49:28 EDT 2022
% Result : Unsatisfiable 6.42s 6.62s
% Output : Refutation 6.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 11
% Syntax : Number of clauses : 205 ( 205 unt; 0 nHn; 205 RR)
% Number of literals : 205 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(add(multiply(u,v),multiply(w,v)),multiply(v,add(u,w))),
file('BOO026-1.p',unknown),
[] ).
cnf(2,axiom,
equal(add(u,inverse(u)),n1),
file('BOO026-1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(add(u,v),add(w,v)),add(v,multiply(u,w))),
file('BOO026-1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(u,inverse(u)),n0),
file('BOO026-1.p',unknown),
[] ).
cnf(5,axiom,
equal(add(multiply(u,inverse(u)),add(multiply(u,v),multiply(inverse(u),v))),v),
file('BOO026-1.p',unknown),
[] ).
cnf(6,axiom,
equal(add(multiply(u,inverse(v)),add(multiply(u,v),multiply(inverse(v),v))),u),
file('BOO026-1.p',unknown),
[] ).
cnf(7,axiom,
equal(add(multiply(u,inverse(v)),add(multiply(u,u),multiply(inverse(v),u))),u),
file('BOO026-1.p',unknown),
[] ).
cnf(8,axiom,
equal(multiply(add(u,inverse(u)),multiply(add(u,v),add(inverse(u),v))),v),
file('BOO026-1.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(add(u,inverse(v)),multiply(add(u,v),add(inverse(v),v))),u),
file('BOO026-1.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(add(u,inverse(v)),multiply(add(u,u),add(inverse(v),u))),u),
file('BOO026-1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(multiply(add(a,b),b),b),
file('BOO026-1.p',unknown),
[] ).
cnf(12,plain,
equal(multiply(add(u,inverse(v)),add(u,multiply(u,inverse(v)))),u),
inference(rew,[status(thm),theory(equality)],[3,10]),
[iquote('0:Rew:3.0,10.0')] ).
cnf(13,plain,
equal(multiply(add(u,inverse(v)),add(v,multiply(u,inverse(v)))),u),
inference(rew,[status(thm),theory(equality)],[3,9]),
[iquote('0:Rew:3.0,9.0')] ).
cnf(14,plain,
equal(multiply(n1,add(u,n0)),u),
inference(rew,[status(thm),theory(equality)],[2,8,4,3]),
[iquote('0:Rew:2.0,8.0,4.0,8.0,3.0,8.0')] ).
cnf(15,plain,
equal(add(multiply(u,inverse(v)),multiply(u,add(u,inverse(v)))),u),
inference(rew,[status(thm),theory(equality)],[1,7]),
[iquote('0:Rew:1.0,7.0')] ).
cnf(16,plain,
equal(add(multiply(u,inverse(v)),multiply(v,add(u,inverse(v)))),u),
inference(rew,[status(thm),theory(equality)],[1,6]),
[iquote('0:Rew:1.0,6.0')] ).
cnf(17,plain,
equal(add(n0,multiply(u,n1)),u),
inference(rew,[status(thm),theory(equality)],[4,5,2,1]),
[iquote('0:Rew:4.0,5.0,2.0,5.0,1.0,5.0')] ).
cnf(46,plain,
equal(multiply(add(u,inverse(v)),n1),add(inverse(v),multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(47,plain,
equal(multiply(add(u,multiply(v,n1)),v),add(multiply(v,n1),multiply(u,n0))),
inference(spr,[status(thm),theory(equality)],[17,3]),
[iquote('0:SpR:17.0,3.0')] ).
cnf(50,plain,
equal(multiply(n1,add(u,inverse(v))),add(inverse(v),multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(51,plain,
equal(multiply(u,add(v,multiply(u,n1))),add(multiply(u,n1),multiply(n0,v))),
inference(spr,[status(thm),theory(equality)],[17,3]),
[iquote('0:SpR:17.0,3.0')] ).
cnf(52,plain,
equal(add(multiply(u,add(u,inverse(v))),multiply(multiply(u,inverse(v)),w)),multiply(u,add(w,multiply(u,add(u,inverse(v)))))),
inference(spr,[status(thm),theory(equality)],[15,3]),
[iquote('0:SpR:15.0,3.0')] ).
cnf(53,plain,
equal(add(multiply(u,add(v,inverse(u))),multiply(multiply(v,inverse(u)),w)),multiply(v,add(w,multiply(u,add(v,inverse(u)))))),
inference(spr,[status(thm),theory(equality)],[16,3]),
[iquote('0:SpR:16.0,3.0')] ).
cnf(60,plain,
equal(add(inverse(u),multiply(u,u)),multiply(n1,n1)),
inference(spr,[status(thm),theory(equality)],[2,46]),
[iquote('0:SpR:2.0,46.0')] ).
cnf(61,plain,
equal(multiply(add(u,inverse(inverse(u))),n1),add(inverse(inverse(u)),n0)),
inference(spr,[status(thm),theory(equality)],[4,46]),
[iquote('0:SpR:4.0,46.0')] ).
cnf(66,plain,
equal(multiply(multiply(n1,n1),add(u,multiply(v,v))),add(multiply(v,v),multiply(inverse(v),u))),
inference(spr,[status(thm),theory(equality)],[60,3]),
[iquote('0:SpR:60.0,3.0')] ).
cnf(70,plain,
equal(add(inverse(add(u,v)),add(v,multiply(u,u))),multiply(n1,n1)),
inference(spr,[status(thm),theory(equality)],[3,60]),
[iquote('0:SpR:3.0,60.0')] ).
cnf(72,plain,
equal(add(n0,add(inverse(inverse(u)),n0)),add(u,inverse(inverse(u)))),
inference(spr,[status(thm),theory(equality)],[61,17]),
[iquote('0:SpR:61.0,17.0')] ).
cnf(77,plain,
equal(multiply(add(n0,add(inverse(inverse(u)),n0)),add(u,multiply(u,inverse(inverse(u))))),u),
inference(spr,[status(thm),theory(equality)],[72,12]),
[iquote('0:SpR:72.0,12.0')] ).
cnf(86,plain,
equal(multiply(multiply(u,add(v,w)),add(x,multiply(w,u))),add(multiply(w,u),multiply(multiply(v,u),x))),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(88,plain,
equal(multiply(add(u,multiply(v,w)),multiply(w,add(x,v))),add(multiply(v,w),multiply(u,multiply(x,w)))),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(89,plain,
equal(multiply(inverse(u),add(v,u)),add(multiply(v,inverse(u)),n0)),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(90,plain,
equal(add(multiply(u,add(v,n0)),v),multiply(add(v,n0),add(u,n1))),
inference(spr,[status(thm),theory(equality)],[14,1]),
[iquote('0:SpR:14.0,1.0')] ).
cnf(96,plain,
equal(multiply(inverse(u),add(u,v)),add(n0,multiply(v,inverse(u)))),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(97,plain,
equal(add(u,multiply(v,add(u,n0))),multiply(add(u,n0),add(n1,v))),
inference(spr,[status(thm),theory(equality)],[14,1]),
[iquote('0:SpR:14.0,1.0')] ).
cnf(98,plain,
equal(multiply(add(u,multiply(u,inverse(v))),add(add(u,inverse(v)),w)),add(u,multiply(w,add(u,multiply(u,inverse(v)))))),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(100,plain,
equal(add(add(u,multiply(v,w)),multiply(x,add(w,u))),multiply(add(w,u),add(add(v,u),x))),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(103,plain,
equal(add(multiply(n1,inverse(u)),add(inverse(u),multiply(u,n1))),n1),
inference(spr,[status(thm),theory(equality)],[50,15]),
[iquote('0:SpR:50.0,15.0')] ).
cnf(110,plain,
equal(multiply(add(u,inverse(inverse(u))),multiply(n1,add(inverse(inverse(u)),inverse(u)))),u),
inference(spr,[status(thm),theory(equality)],[50,13]),
[iquote('0:SpR:50.0,13.0')] ).
cnf(116,plain,
equal(multiply(n1,add(inverse(u),inverse(u))),add(inverse(u),n0)),
inference(spr,[status(thm),theory(equality)],[4,50]),
[iquote('0:SpR:4.0,50.0')] ).
cnf(131,plain,
equal(add(multiply(inverse(n1),inverse(n1)),add(inverse(n1),n0)),inverse(n1)),
inference(spr,[status(thm),theory(equality)],[116,16]),
[iquote('0:SpR:116.0,16.0')] ).
cnf(156,plain,
equal(add(multiply(u,inverse(inverse(u))),n0),multiply(inverse(inverse(u)),n1)),
inference(spr,[status(thm),theory(equality)],[2,89]),
[iquote('0:SpR:2.0,89.0')] ).
cnf(181,plain,
equal(multiply(n1,multiply(inverse(inverse(u)),n1)),multiply(u,inverse(inverse(u)))),
inference(spr,[status(thm),theory(equality)],[156,14]),
[iquote('0:SpR:156.0,14.0')] ).
cnf(239,plain,
equal(add(n0,multiply(inverse(u),inverse(u))),multiply(inverse(u),n1)),
inference(spr,[status(thm),theory(equality)],[2,96]),
[iquote('0:SpR:2.0,96.0')] ).
cnf(241,plain,
equal(add(n0,multiply(multiply(u,n1),inverse(n0))),multiply(inverse(n0),u)),
inference(spr,[status(thm),theory(equality)],[17,96]),
[iquote('0:SpR:17.0,96.0')] ).
cnf(272,plain,
equal(multiply(add(multiply(u,n1),inverse(n0)),multiply(inverse(n0),u)),multiply(u,n1)),
inference(spr,[status(thm),theory(equality)],[241,13]),
[iquote('0:SpR:241.0,13.0')] ).
cnf(288,plain,
equal(add(inverse(add(u,multiply(v,u))),multiply(u,add(v,u))),multiply(n1,n1)),
inference(spr,[status(thm),theory(equality)],[1,70]),
[iquote('0:SpR:1.0,70.0')] ).
cnf(341,plain,
equal(multiply(u,u),add(multiply(u,n1),multiply(n0,n0))),
inference(spr,[status(thm),theory(equality)],[17,47]),
[iquote('0:SpR:17.0,47.0')] ).
cnf(364,plain,
equal(add(multiply(add(u,v),n1),multiply(n0,n0)),add(v,multiply(u,u))),
inference(spr,[status(thm),theory(equality)],[341,3]),
[iquote('0:SpR:341.0,3.0')] ).
cnf(416,plain,
equal(multiply(u,multiply(n1,add(v,u))),add(multiply(u,n1),multiply(n0,multiply(v,n1)))),
inference(spr,[status(thm),theory(equality)],[1,51]),
[iquote('0:SpR:1.0,51.0')] ).
cnf(489,plain,
equal(add(u,u),multiply(add(u,n0),add(n1,n1))),
inference(spr,[status(thm),theory(equality)],[14,90]),
[iquote('0:SpR:14.0,90.0')] ).
cnf(492,plain,
equal(add(add(n0,multiply(u,v)),v),multiply(add(v,n0),add(add(u,n0),n1))),
inference(spr,[status(thm),theory(equality)],[3,90]),
[iquote('0:SpR:3.0,90.0')] ).
cnf(509,plain,
equal(multiply(add(multiply(u,v),n0),add(n1,n1)),multiply(v,add(u,u))),
inference(spr,[status(thm),theory(equality)],[489,1]),
[iquote('0:SpR:489.0,1.0')] ).
cnf(577,plain,
equal(add(u,multiply(n0,add(u,n0))),add(n0,multiply(u,n1))),
inference(spr,[status(thm),theory(equality)],[97,3]),
[iquote('0:SpR:97.0,3.0')] ).
cnf(594,plain,
equal(add(u,multiply(n0,add(u,n0))),u),
inference(rew,[status(thm),theory(equality)],[17,577]),
[iquote('0:Rew:17.0,577.0')] ).
cnf(607,plain,
equal(multiply(u,add(v,multiply(n0,add(u,n0)))),add(multiply(n0,add(u,n0)),multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[594,3]),
[iquote('0:SpR:594.0,3.0')] ).
cnf(612,plain,
equal(multiply(add(u,multiply(n0,add(v,n0))),v),add(multiply(n0,add(v,n0)),multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[594,3]),
[iquote('0:SpR:594.0,3.0')] ).
cnf(742,plain,
equal(multiply(add(n1,n0),add(add(u,n0),v)),add(u,multiply(v,add(n1,n0)))),
inference(spr,[status(thm),theory(equality)],[17,100]),
[iquote('0:SpR:17.0,100.0')] ).
cnf(1157,plain,
equal(add(multiply(n0,n1),multiply(u,multiply(v,n1))),multiply(add(u,multiply(n0,n1)),v)),
inference(spr,[status(thm),theory(equality)],[14,88]),
[iquote('0:SpR:14.0,88.0')] ).
cnf(1200,plain,
equal(add(multiply(u,u),multiply(inverse(u),multiply(v,u))),multiply(multiply(n1,n1),multiply(u,add(v,u)))),
inference(spr,[status(thm),theory(equality)],[60,88]),
[iquote('0:SpR:60.0,88.0')] ).
cnf(1434,plain,
equal(add(multiply(n0,n1),multiply(multiply(u,n1),v)),multiply(u,add(v,multiply(n0,n1)))),
inference(spr,[status(thm),theory(equality)],[14,86]),
[iquote('0:SpR:14.0,86.0')] ).
cnf(1741,plain,
equal(add(multiply(add(u,v),n1),multiply(n0,n0)),add(v,add(multiply(u,n1),multiply(n0,n0)))),
inference(spr,[status(thm),theory(equality)],[341,364]),
[iquote('0:SpR:341.0,364.0')] ).
cnf(1974,plain,
equal(multiply(add(multiply(u,v),n0),add(n1,n1)),multiply(v,multiply(add(u,n0),add(n1,n1)))),
inference(spr,[status(thm),theory(equality)],[489,509]),
[iquote('0:SpR:489.0,509.0')] ).
cnf(2323,plain,
equal(multiply(u,add(add(u,inverse(v)),multiply(v,add(u,inverse(v))))),multiply(add(u,inverse(v)),add(v,multiply(u,inverse(v))))),
inference(spr,[status(thm),theory(equality)],[53,1]),
[iquote('0:SpR:53.0,1.0')] ).
cnf(2365,plain,
equal(multiply(u,add(add(u,inverse(v)),multiply(v,add(u,inverse(v))))),u),
inference(rew,[status(thm),theory(equality)],[13,2323]),
[iquote('0:Rew:13.0,2323.0')] ).
cnf(2403,plain,
equal(multiply(n1,add(add(n1,inverse(add(u,n0))),add(u,multiply(inverse(add(u,n0)),add(u,n0))))),n1),
inference(spr,[status(thm),theory(equality)],[97,2365]),
[iquote('0:SpR:97.0,2365.0')] ).
cnf(2523,plain,
equal(multiply(u,add(add(u,inverse(v)),multiply(u,add(u,inverse(v))))),multiply(add(u,inverse(v)),add(u,multiply(u,inverse(v))))),
inference(spr,[status(thm),theory(equality)],[52,1]),
[iquote('0:SpR:52.0,1.0')] ).
cnf(2569,plain,
equal(multiply(u,add(add(u,inverse(v)),multiply(u,add(u,inverse(v))))),u),
inference(rew,[status(thm),theory(equality)],[12,2523]),
[iquote('0:Rew:12.0,2523.0')] ).
cnf(3201,plain,
equal(add(u,multiply(multiply(u,inverse(v)),add(u,multiply(u,inverse(v))))),add(multiply(u,inverse(v)),multiply(u,add(u,inverse(v))))),
inference(spr,[status(thm),theory(equality)],[98,3]),
[iquote('0:SpR:98.0,3.0')] ).
cnf(3242,plain,
equal(add(u,multiply(multiply(u,inverse(v)),add(u,multiply(u,inverse(v))))),u),
inference(rew,[status(thm),theory(equality)],[15,3201]),
[iquote('0:Rew:15.0,3201.0')] ).
cnf(4336,plain,
equal(add(u,multiply(n0,add(n1,n0))),add(n0,multiply(n1,add(u,n0)))),
inference(spr,[status(thm),theory(equality)],[742,3]),
[iquote('0:SpR:742.0,3.0')] ).
cnf(4369,plain,
equal(add(u,multiply(n0,add(n1,n0))),add(n0,u)),
inference(rew,[status(thm),theory(equality)],[14,4336]),
[iquote('0:Rew:14.0,4336.0')] ).
cnf(4401,plain,
equal(add(n0,n1),n1),
inference(spr,[status(thm),theory(equality)],[4369,594]),
[iquote('0:SpR:4369.0,594.0')] ).
cnf(4408,plain,
equal(multiply(add(u,multiply(n0,add(n1,n0))),add(n0,v)),add(multiply(n0,add(n1,n0)),multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[4369,3]),
[iquote('0:SpR:4369.0,3.0')] ).
cnf(4416,plain,
equal(add(n0,inverse(add(n0,multiply(n1,n0)))),multiply(n1,n1)),
inference(spr,[status(thm),theory(equality)],[4369,288]),
[iquote('0:SpR:4369.0,288.0')] ).
cnf(4436,plain,
equal(add(multiply(n0,add(n1,n0)),multiply(u,v)),multiply(add(n0,u),add(n0,v))),
inference(rew,[status(thm),theory(equality)],[4369,4408]),
[iquote('0:Rew:4369.0,4408.0')] ).
cnf(4453,plain,
equal(multiply(n1,add(u,n1)),add(n1,multiply(n0,u))),
inference(spr,[status(thm),theory(equality)],[4401,3]),
[iquote('0:SpR:4401.0,3.0')] ).
cnf(4454,plain,
equal(add(n0,multiply(n1,inverse(n0))),multiply(inverse(n0),n1)),
inference(spr,[status(thm),theory(equality)],[4401,96]),
[iquote('0:SpR:4401.0,96.0')] ).
cnf(4458,plain,
equal(multiply(add(u,n1),n1),add(n1,multiply(u,n0))),
inference(spr,[status(thm),theory(equality)],[4401,3]),
[iquote('0:SpR:4401.0,3.0')] ).
cnf(4460,plain,
equal(add(multiply(n0,inverse(n1)),n0),multiply(inverse(n1),n1)),
inference(spr,[status(thm),theory(equality)],[4401,89]),
[iquote('0:SpR:4401.0,89.0')] ).
cnf(4495,plain,
equal(multiply(n1,multiply(inverse(n1),n1)),multiply(n0,inverse(n1))),
inference(spr,[status(thm),theory(equality)],[4460,14]),
[iquote('0:SpR:4460.0,14.0')] ).
cnf(4635,plain,
equal(add(n1,multiply(n0,n0)),multiply(n1,n1)),
inference(spr,[status(thm),theory(equality)],[4401,4453]),
[iquote('0:SpR:4401.0,4453.0')] ).
cnf(4657,plain,
equal(multiply(multiply(n1,n1),multiply(n0,add(u,n0))),add(multiply(n0,n0),multiply(n1,multiply(u,n0)))),
inference(spr,[status(thm),theory(equality)],[4635,88]),
[iquote('0:SpR:4635.0,88.0')] ).
cnf(4707,plain,
equal(multiply(add(add(multiply(n1,n1),inverse(n0)),multiply(n0,n1)),inverse(n0)),add(multiply(n0,n1),multiply(n1,n1))),
inference(spr,[status(thm),theory(equality)],[272,1157]),
[iquote('0:SpR:272.0,1157.0')] ).
cnf(4712,plain,
equal(multiply(add(n1,multiply(n0,n1)),inverse(n1)),add(multiply(n0,n1),multiply(n0,inverse(n1)))),
inference(spr,[status(thm),theory(equality)],[4495,1157]),
[iquote('0:SpR:4495.0,1157.0')] ).
cnf(4715,plain,
equal(multiply(add(add(multiply(n1,n1),inverse(n0)),multiply(n0,n1)),inverse(n0)),multiply(n1,n1)),
inference(rew,[status(thm),theory(equality)],[4401,4707,1]),
[iquote('0:Rew:4401.0,4707.0,1.0,4707.0')] ).
cnf(4723,plain,
equal(add(n0,add(n1,multiply(u,n0))),add(u,n1)),
inference(spr,[status(thm),theory(equality)],[4458,17]),
[iquote('0:SpR:4458.0,17.0')] ).
cnf(4727,plain,
equal(multiply(add(u,n1),add(u,n1)),add(add(n1,multiply(u,n0)),multiply(n0,n0))),
inference(spr,[status(thm),theory(equality)],[4458,341]),
[iquote('0:SpR:4458.0,341.0')] ).
cnf(4752,plain,
equal(add(n1,multiply(u,u)),add(add(n1,multiply(u,n0)),multiply(n0,n0))),
inference(rew,[status(thm),theory(equality)],[3,4727]),
[iquote('0:Rew:3.0,4727.0')] ).
cnf(4781,plain,
equal(multiply(multiply(n1,n1),add(n0,multiply(n0,inverse(add(n0,multiply(n1,n0)))))),n0),
inference(spr,[status(thm),theory(equality)],[4416,12]),
[iquote('0:SpR:4416.0,12.0')] ).
cnf(4783,plain,
equal(add(multiply(n0,multiply(n1,n1)),multiply(multiply(n0,inverse(add(n0,multiply(n1,n0)))),u)),multiply(n0,add(u,multiply(n0,multiply(n1,n1))))),
inference(spr,[status(thm),theory(equality)],[4416,52]),
[iquote('0:SpR:4416.0,52.0')] ).
cnf(4789,plain,
equal(multiply(n0,add(multiply(n1,n1),multiply(n0,multiply(n1,n1)))),n0),
inference(spr,[status(thm),theory(equality)],[4416,2569]),
[iquote('0:SpR:4416.0,2569.0')] ).
cnf(4807,plain,
equal(multiply(n0,multiply(n1,multiply(n1,add(n1,n1)))),n0),
inference(rew,[status(thm),theory(equality)],[416,4789]),
[iquote('0:Rew:416.0,4789.0')] ).
cnf(4808,plain,
equal(multiply(n0,multiply(n1,add(n1,multiply(n0,n1)))),n0),
inference(rew,[status(thm),theory(equality)],[4453,4807]),
[iquote('0:Rew:4453.0,4807.0')] ).
cnf(4810,plain,
equal(multiply(multiply(n1,add(n1,multiply(n0,n1))),add(n0,u)),add(n0,multiply(u,multiply(n1,add(n1,multiply(n0,n1)))))),
inference(spr,[status(thm),theory(equality)],[4808,1]),
[iquote('0:SpR:4808.0,1.0')] ).
cnf(4832,plain,
equal(multiply(u,add(n1,multiply(n0,n1))),multiply(n1,add(n0,multiply(u,n1)))),
inference(spr,[status(thm),theory(equality)],[1434,1]),
[iquote('0:SpR:1434.0,1.0')] ).
cnf(4878,plain,
equal(multiply(u,add(n1,multiply(n0,n1))),multiply(n1,u)),
inference(rew,[status(thm),theory(equality)],[17,4832]),
[iquote('0:Rew:17.0,4832.0')] ).
cnf(4879,plain,
equal(multiply(n0,multiply(n1,n1)),n0),
inference(rew,[status(thm),theory(equality)],[4878,4808]),
[iquote('0:Rew:4878.0,4808.0')] ).
cnf(4885,plain,
equal(multiply(multiply(n1,n1),add(n0,u)),add(n0,multiply(u,multiply(n1,n1)))),
inference(rew,[status(thm),theory(equality)],[4878,4810]),
[iquote('0:Rew:4878.0,4810.0')] ).
cnf(4891,plain,
equal(add(n0,multiply(multiply(n0,inverse(add(n0,multiply(n1,n0)))),u)),multiply(n0,add(u,n0))),
inference(rew,[status(thm),theory(equality)],[4879,4783]),
[iquote('0:Rew:4879.0,4783.0')] ).
cnf(4896,plain,
equal(add(n0,multiply(multiply(n0,inverse(add(n0,multiply(n1,n0)))),multiply(n1,n1))),n0),
inference(rew,[status(thm),theory(equality)],[4885,4781]),
[iquote('0:Rew:4885.0,4781.0')] ).
cnf(4897,plain,
equal(multiply(n0,add(multiply(n1,n1),n0)),n0),
inference(rew,[status(thm),theory(equality)],[4891,4896]),
[iquote('0:Rew:4891.0,4896.0')] ).
cnf(4943,plain,
equal(multiply(add(multiply(n1,n1),n0),add(n0,n1)),add(n0,multiply(n1,n1))),
inference(spr,[status(thm),theory(equality)],[4897,90]),
[iquote('0:SpR:4897.0,90.0')] ).
cnf(4949,plain,
equal(multiply(add(multiply(n1,n1),n0),add(u,n0)),add(multiply(u,add(multiply(n1,n1),n0)),n0)),
inference(spr,[status(thm),theory(equality)],[4897,1]),
[iquote('0:SpR:4897.0,1.0')] ).
cnf(4956,plain,
equal(add(multiply(n1,n1),n0),multiply(n1,n1)),
inference(spr,[status(thm),theory(equality)],[4897,594]),
[iquote('0:SpR:4897.0,594.0')] ).
cnf(4965,plain,
equal(multiply(add(multiply(n1,n1),n0),n1),n1),
inference(rew,[status(thm),theory(equality)],[4401,4943,17]),
[iquote('0:Rew:4401.0,4943.0,17.0,4943.0')] ).
cnf(4966,plain,
equal(multiply(multiply(n1,n1),n1),n1),
inference(rew,[status(thm),theory(equality)],[4956,4965]),
[iquote('0:Rew:4956.0,4965.0')] ).
cnf(4985,plain,
equal(add(multiply(u,add(multiply(n1,n1),n0)),n0),add(n0,multiply(multiply(n1,n1),u))),
inference(rew,[status(thm),theory(equality)],[3,4949]),
[iquote('0:Rew:3.0,4949.0')] ).
cnf(4986,plain,
equal(add(multiply(u,multiply(n1,n1)),n0),add(n0,multiply(multiply(n1,n1),u))),
inference(rew,[status(thm),theory(equality)],[4956,4985]),
[iquote('0:Rew:4956.0,4985.0')] ).
cnf(5015,plain,
equal(multiply(n1,n1),add(n0,n1)),
inference(spr,[status(thm),theory(equality)],[4966,17]),
[iquote('0:SpR:4966.0,17.0')] ).
cnf(5018,plain,
equal(multiply(inverse(n0),multiply(n1,n1)),add(n0,multiply(n1,inverse(n0)))),
inference(spr,[status(thm),theory(equality)],[4966,241]),
[iquote('0:SpR:4966.0,241.0')] ).
cnf(5041,plain,
equal(multiply(n1,n1),n1),
inference(rew,[status(thm),theory(equality)],[4401,5015]),
[iquote('0:Rew:4401.0,5015.0')] ).
cnf(5042,plain,
equal(add(inverse(u),multiply(u,u)),n1),
inference(rew,[status(thm),theory(equality)],[5041,60]),
[iquote('0:Rew:5041.0,60.0')] ).
cnf(5072,plain,
equal(multiply(n0,n1),n0),
inference(rew,[status(thm),theory(equality)],[5041,4879]),
[iquote('0:Rew:5041.0,4879.0')] ).
cnf(5074,plain,
equal(add(multiply(u,u),multiply(inverse(u),v)),multiply(n1,add(v,multiply(u,u)))),
inference(rew,[status(thm),theory(equality)],[5041,66]),
[iquote('0:Rew:5041.0,66.0')] ).
cnf(5188,plain,
equal(add(multiply(u,n1),n0),add(n0,multiply(n1,u))),
inference(rew,[status(thm),theory(equality)],[5041,4986]),
[iquote('0:Rew:5041.0,4986.0')] ).
cnf(5310,plain,
equal(add(multiply(u,u),multiply(inverse(u),multiply(v,u))),multiply(n1,multiply(u,add(v,u)))),
inference(rew,[status(thm),theory(equality)],[5041,1200]),
[iquote('0:Rew:5041.0,1200.0')] ).
cnf(5594,plain,
equal(add(multiply(n0,n0),multiply(n1,multiply(u,n0))),multiply(n1,multiply(n0,add(u,n0)))),
inference(rew,[status(thm),theory(equality)],[5041,4657]),
[iquote('0:Rew:5041.0,4657.0')] ).
cnf(5600,plain,
equal(multiply(add(add(n1,inverse(n0)),multiply(n0,n1)),inverse(n0)),n1),
inference(rew,[status(thm),theory(equality)],[5041,4715]),
[iquote('0:Rew:5041.0,4715.0')] ).
cnf(5621,plain,
equal(multiply(n1,add(n0,u)),add(n0,multiply(u,n1))),
inference(rew,[status(thm),theory(equality)],[5041,4885]),
[iquote('0:Rew:5041.0,4885.0')] ).
cnf(5626,plain,
equal(add(n1,n0),n1),
inference(rew,[status(thm),theory(equality)],[5041,4956]),
[iquote('0:Rew:5041.0,4956.0')] ).
cnf(5644,plain,
equal(multiply(u,add(n1,n0)),multiply(n1,u)),
inference(rew,[status(thm),theory(equality)],[5072,4878]),
[iquote('0:Rew:5072.0,4878.0')] ).
cnf(5646,plain,
equal(multiply(add(n1,n0),inverse(n1)),add(n0,multiply(n0,inverse(n1)))),
inference(rew,[status(thm),theory(equality)],[5072,4712]),
[iquote('0:Rew:5072.0,4712.0')] ).
cnf(5726,plain,
equal(add(u,multiply(n0,n1)),add(n0,u)),
inference(rew,[status(thm),theory(equality)],[5626,4369]),
[iquote('0:Rew:5626.0,4369.0')] ).
cnf(5889,plain,
equal(multiply(add(n0,u),add(n0,v)),add(multiply(n0,n1),multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[5626,4436]),
[iquote('0:Rew:5626.0,4436.0')] ).
cnf(5987,plain,
equal(multiply(u,n1),multiply(n1,u)),
inference(rew,[status(thm),theory(equality)],[5626,5644]),
[iquote('0:Rew:5626.0,5644.0')] ).
cnf(5989,plain,
equal(multiply(n1,multiply(n1,inverse(n1))),multiply(n0,inverse(n1))),
inference(rew,[status(thm),theory(equality)],[5987,4495]),
[iquote('0:Rew:5987.0,4495.0')] ).
cnf(5992,plain,
equal(add(n0,multiply(n1,inverse(n0))),multiply(n1,inverse(n0))),
inference(rew,[status(thm),theory(equality)],[5987,4454]),
[iquote('0:Rew:5987.0,4454.0')] ).
cnf(5994,plain,
equal(add(n0,multiply(inverse(u),inverse(u))),multiply(n1,inverse(u))),
inference(rew,[status(thm),theory(equality)],[5987,239]),
[iquote('0:Rew:5987.0,239.0')] ).
cnf(5998,plain,
equal(multiply(n1,multiply(n1,inverse(inverse(u)))),multiply(u,inverse(inverse(u)))),
inference(rew,[status(thm),theory(equality)],[5987,181]),
[iquote('0:Rew:5987.0,181.0')] ).
cnf(6006,plain,
equal(multiply(n1,add(u,inverse(inverse(u)))),add(inverse(inverse(u)),n0)),
inference(rew,[status(thm),theory(equality)],[5987,61]),
[iquote('0:Rew:5987.0,61.0')] ).
cnf(6008,plain,
equal(multiply(n1,n0),n0),
inference(rew,[status(thm),theory(equality)],[5987,5072]),
[iquote('0:Rew:5987.0,5072.0')] ).
cnf(6459,plain,
equal(add(multiply(n1,add(u,v)),multiply(n0,n0)),add(v,add(multiply(u,n1),multiply(n0,n0)))),
inference(rew,[status(thm),theory(equality)],[5987,1741]),
[iquote('0:Rew:5987.0,1741.0')] ).
cnf(6463,plain,
equal(add(n0,multiply(multiply(n0,inverse(add(n0,n0))),u)),multiply(n0,add(u,n0))),
inference(rew,[status(thm),theory(equality)],[6008,4891]),
[iquote('0:Rew:6008.0,4891.0')] ).
cnf(6467,plain,
equal(add(u,n0),add(n0,u)),
inference(rew,[status(thm),theory(equality)],[6008,5726,5987]),
[iquote('0:Rew:6008.0,5726.0,5987.0,5726.0')] ).
cnf(6473,plain,
equal(add(multiply(inverse(n1),inverse(n1)),add(n0,inverse(n1))),inverse(n1)),
inference(rew,[status(thm),theory(equality)],[6467,131]),
[iquote('0:Rew:6467.0,131.0')] ).
cnf(6475,plain,
equal(multiply(n1,add(inverse(u),inverse(u))),add(n0,inverse(u))),
inference(rew,[status(thm),theory(equality)],[6467,116]),
[iquote('0:Rew:6467.0,116.0')] ).
cnf(6477,plain,
equal(add(n0,add(n0,inverse(inverse(u)))),add(u,inverse(inverse(u)))),
inference(rew,[status(thm),theory(equality)],[6467,72]),
[iquote('0:Rew:6467.0,72.0')] ).
cnf(6646,plain,
equal(multiply(add(n0,multiply(u,v)),add(n1,n1)),multiply(v,multiply(add(u,n0),add(n1,n1)))),
inference(rew,[status(thm),theory(equality)],[6467,1974]),
[iquote('0:Rew:6467.0,1974.0')] ).
cnf(6740,plain,
equal(multiply(add(n0,add(n0,inverse(inverse(u)))),add(u,multiply(u,inverse(inverse(u))))),u),
inference(rew,[status(thm),theory(equality)],[6467,77]),
[iquote('0:Rew:6467.0,77.0')] ).
cnf(6797,plain,
equal(add(n0,multiply(u,n1)),add(n0,multiply(n1,u))),
inference(rew,[status(thm),theory(equality)],[6467,5188]),
[iquote('0:Rew:6467.0,5188.0')] ).
cnf(6798,plain,
equal(add(n0,multiply(n1,u)),u),
inference(rew,[status(thm),theory(equality)],[17,6797]),
[iquote('0:Rew:17.0,6797.0')] ).
cnf(6799,plain,
equal(multiply(n1,add(n0,u)),u),
inference(rew,[status(thm),theory(equality)],[17,5621]),
[iquote('0:Rew:17.0,5621.0')] ).
cnf(6806,plain,
equal(multiply(n0,inverse(n1)),multiply(n1,n0)),
inference(rew,[status(thm),theory(equality)],[4,5989]),
[iquote('0:Rew:4.0,5989.0')] ).
cnf(6807,plain,
equal(multiply(n0,inverse(n1)),n0),
inference(rew,[status(thm),theory(equality)],[6008,6806]),
[iquote('0:Rew:6008.0,6806.0')] ).
cnf(6810,plain,
equal(multiply(n1,inverse(n0)),inverse(n0)),
inference(rew,[status(thm),theory(equality)],[6798,5992]),
[iquote('0:Rew:6798.0,5992.0')] ).
cnf(6831,plain,
equal(add(n0,inverse(n0)),inverse(n0)),
inference(rew,[status(thm),theory(equality)],[6810,5018,5987,5041]),
[iquote('0:Rew:6810.0,5018.0,5987.0,5018.0,5041.0,5018.0,6810.0,5018.0')] ).
cnf(6832,plain,
equal(inverse(n0),n1),
inference(rew,[status(thm),theory(equality)],[2,6831]),
[iquote('0:Rew:2.0,6831.0')] ).
cnf(6903,plain,
equal(add(n1,n1),n1),
inference(rew,[status(thm),theory(equality)],[6799,5600,5987,6467,6008,6832]),
[iquote('0:Rew:6799.0,5600.0,5987.0,5600.0,6467.0,5600.0,6008.0,5600.0,5987.0,5600.0,6832.0,5600.0')] ).
cnf(6904,plain,
equal(add(u,u),multiply(add(u,n0),n1)),
inference(rew,[status(thm),theory(equality)],[6903,489]),
[iquote('0:Rew:6903.0,489.0')] ).
cnf(6946,plain,
equal(add(u,u),multiply(n1,add(u,n0))),
inference(rew,[status(thm),theory(equality)],[5987,6904]),
[iquote('0:Rew:5987.0,6904.0')] ).
cnf(6947,plain,
equal(add(u,u),u),
inference(rew,[status(thm),theory(equality)],[14,6946]),
[iquote('0:Rew:14.0,6946.0')] ).
cnf(6948,plain,
equal(multiply(n1,inverse(u)),add(n0,inverse(u))),
inference(rew,[status(thm),theory(equality)],[6947,6475]),
[iquote('0:Rew:6947.0,6475.0')] ).
cnf(6949,plain,
equal(add(add(n0,inverse(u)),add(inverse(u),multiply(u,n1))),n1),
inference(rew,[status(thm),theory(equality)],[6948,103]),
[iquote('0:Rew:6948.0,103.0')] ).
cnf(6957,plain,
equal(add(n0,multiply(inverse(u),inverse(u))),add(n0,inverse(u))),
inference(rew,[status(thm),theory(equality)],[6948,5994]),
[iquote('0:Rew:6948.0,5994.0')] ).
cnf(6960,plain,
equal(add(n0,inverse(n1)),n0),
inference(rew,[status(thm),theory(equality)],[6948,5646,5626,6947,6807]),
[iquote('0:Rew:6948.0,5646.0,5626.0,5646.0,6947.0,5646.0,6807.0,5646.0')] ).
cnf(6974,plain,
equal(multiply(u,inverse(inverse(u))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[6799,5998,6948]),
[iquote('0:Rew:6799.0,5998.0,6948.0,5998.0')] ).
cnf(6983,plain,
equal(multiply(n1,add(u,inverse(inverse(u)))),add(n0,inverse(inverse(u)))),
inference(rew,[status(thm),theory(equality)],[6467,6006]),
[iquote('0:Rew:6467.0,6006.0')] ).
cnf(6986,plain,
equal(inverse(n1),n0),
inference(rew,[status(thm),theory(equality)],[6960,6473,6957,6467]),
[iquote('0:Rew:6960.0,6473.0,6957.0,6473.0,6467.0,6473.0,6960.0,6473.0')] ).
cnf(7022,plain,
equal(multiply(n0,n0),n0),
inference(rew,[status(thm),theory(equality)],[6986,6807]),
[iquote('0:Rew:6986.0,6807.0')] ).
cnf(7030,plain,
equal(multiply(u,u),add(multiply(u,n1),n0)),
inference(rew,[status(thm),theory(equality)],[7022,341]),
[iquote('0:Rew:7022.0,341.0')] ).
cnf(7070,plain,
equal(add(n1,multiply(u,u)),add(add(n1,multiply(u,n0)),n0)),
inference(rew,[status(thm),theory(equality)],[7022,4752]),
[iquote('0:Rew:7022.0,4752.0')] ).
cnf(7077,plain,
equal(multiply(u,u),add(n0,multiply(u,n1))),
inference(rew,[status(thm),theory(equality)],[6467,7030]),
[iquote('0:Rew:6467.0,7030.0')] ).
cnf(7078,plain,
equal(multiply(u,u),u),
inference(rew,[status(thm),theory(equality)],[17,7077]),
[iquote('0:Rew:17.0,7077.0')] ).
cnf(7082,plain,
equal(add(inverse(u),u),n1),
inference(rew,[status(thm),theory(equality)],[7078,5042]),
[iquote('0:Rew:7078.0,5042.0')] ).
cnf(7083,plain,
equal(multiply(add(u,inverse(inverse(u))),multiply(n1,n1)),u),
inference(rew,[status(thm),theory(equality)],[7082,110]),
[iquote('0:Rew:7082.0,110.0')] ).
cnf(7105,plain,
equal(add(n0,inverse(inverse(u))),u),
inference(rew,[status(thm),theory(equality)],[6983,7083,5987,7078]),
[iquote('0:Rew:6983.0,7083.0,5987.0,7083.0,7078.0,7083.0')] ).
cnf(7107,plain,
equal(add(u,inverse(inverse(u))),add(n0,u)),
inference(rew,[status(thm),theory(equality)],[7105,6477]),
[iquote('0:Rew:7105.0,6477.0')] ).
cnf(7116,plain,
equal(add(n0,add(n1,multiply(u,n0))),add(n1,u)),
inference(rew,[status(thm),theory(equality)],[7078,7070,6467]),
[iquote('0:Rew:7078.0,7070.0,6467.0,7070.0')] ).
cnf(7117,plain,
equal(add(u,n1),add(n1,u)),
inference(rew,[status(thm),theory(equality)],[4723,7116]),
[iquote('0:Rew:4723.0,7116.0')] ).
cnf(7119,plain,
equal(add(add(n0,multiply(u,v)),v),multiply(add(v,n0),add(n1,add(u,n0)))),
inference(rew,[status(thm),theory(equality)],[7117,492]),
[iquote('0:Rew:7117.0,492.0')] ).
cnf(7179,plain,
equal(multiply(add(n0,u),add(n0,v)),add(n0,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[6008,5889,5987]),
[iquote('0:Rew:6008.0,5889.0,5987.0,5889.0')] ).
cnf(7203,plain,
equal(add(u,multiply(inverse(u),v)),multiply(n1,add(v,u))),
inference(rew,[status(thm),theory(equality)],[7078,5074]),
[iquote('0:Rew:7078.0,5074.0')] ).
cnf(7290,plain,
equal(multiply(n0,add(u,n0)),add(n0,multiply(n0,u))),
inference(rew,[status(thm),theory(equality)],[6008,6463,5987,6832,6947]),
[iquote('0:Rew:6008.0,6463.0,5987.0,6463.0,6832.0,6463.0,6947.0,6463.0')] ).
cnf(7293,plain,
equal(multiply(add(u,add(n0,multiply(n0,v))),v),add(add(n0,multiply(n0,v)),multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[7290,612]),
[iquote('0:Rew:7290.0,612.0')] ).
cnf(7300,plain,
equal(multiply(u,add(v,add(n0,multiply(n0,u)))),add(add(n0,multiply(n0,u)),multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[7290,607]),
[iquote('0:Rew:7290.0,607.0')] ).
cnf(7346,plain,
equal(multiply(u,n0),multiply(n0,u)),
inference(rew,[status(thm),theory(equality)],[6798,5594,7078,6799,7290]),
[iquote('0:Rew:6798.0,5594.0,7078.0,5594.0,6799.0,5594.0,7290.0,5594.0')] ).
cnf(7390,plain,
equal(add(n0,u),u),
inference(rew,[status(thm),theory(equality)],[7078,6740,7179,7105,7107,6974]),
[iquote('0:Rew:7078.0,6740.0,7179.0,6740.0,7105.0,6740.0,7107.0,6740.0,6974.0,6740.0')] ).
cnf(7396,plain,
equal(multiply(u,n1),u),
inference(rew,[status(thm),theory(equality)],[7390,17]),
[iquote('0:Rew:7390.0,17.0')] ).
cnf(7410,plain,
equal(add(inverse(u),add(inverse(u),multiply(u,n1))),n1),
inference(rew,[status(thm),theory(equality)],[7390,6949]),
[iquote('0:Rew:7390.0,6949.0')] ).
cnf(7426,plain,
equal(multiply(n1,u),u),
inference(rew,[status(thm),theory(equality)],[7390,6798]),
[iquote('0:Rew:7390.0,6798.0')] ).
cnf(7429,plain,
equal(add(u,n0),u),
inference(rew,[status(thm),theory(equality)],[7390,6467]),
[iquote('0:Rew:7390.0,6467.0')] ).
cnf(7483,plain,
equal(multiply(add(u,v),v),add(v,multiply(u,n0))),
inference(rew,[status(thm),theory(equality)],[7396,47]),
[iquote('0:Rew:7396.0,47.0')] ).
cnf(7485,plain,
equal(multiply(u,add(v,u)),add(u,multiply(n0,v))),
inference(rew,[status(thm),theory(equality)],[7396,51]),
[iquote('0:Rew:7396.0,51.0')] ).
cnf(7556,plain,
equal(add(add(n1,inverse(add(u,n0))),add(u,multiply(inverse(add(u,n0)),add(u,n0)))),n1),
inference(rew,[status(thm),theory(equality)],[7426,2403]),
[iquote('0:Rew:7426.0,2403.0')] ).
cnf(7562,plain,
equal(add(u,multiply(inverse(u),v)),add(v,u)),
inference(rew,[status(thm),theory(equality)],[7426,7203]),
[iquote('0:Rew:7426.0,7203.0')] ).
cnf(7662,plain,
equal(add(n1,inverse(u)),n1),
inference(rew,[status(thm),theory(equality)],[7117,7410,7082,7396]),
[iquote('0:Rew:7117.0,7410.0,7082.0,7410.0,7396.0,7410.0')] ).
cnf(7670,plain,
~ equal(add(b,multiply(a,n0)),b),
inference(rew,[status(thm),theory(equality)],[7483,11]),
[iquote('0:Rew:7483.0,11.0')] ).
cnf(7678,plain,
~ equal(add(b,multiply(n0,a)),b),
inference(rew,[status(thm),theory(equality)],[7346,7670]),
[iquote('0:Rew:7346.0,7670.0')] ).
cnf(7679,plain,
equal(add(u,add(multiply(u,inverse(v)),multiply(n0,u))),u),
inference(rew,[status(thm),theory(equality)],[7485,3242]),
[iquote('0:Rew:7485.0,3242.0')] ).
cnf(7769,plain,
equal(add(multiply(u,v),v),multiply(v,add(n1,u))),
inference(rew,[status(thm),theory(equality)],[7390,7119,7429]),
[iquote('0:Rew:7390.0,7119.0,7429.0,7119.0,7429.0,7119.0')] ).
cnf(7787,plain,
equal(add(multiply(u,v),v),add(v,multiply(n0,u))),
inference(rew,[status(thm),theory(equality)],[7562,5310,7078,7426,7485]),
[iquote('0:Rew:7562.0,5310.0,7078.0,5310.0,7426.0,5310.0,7485.0,5310.0')] ).
cnf(7790,plain,
equal(multiply(u,add(n1,v)),add(u,multiply(n0,v))),
inference(rew,[status(thm),theory(equality)],[7787,7769]),
[iquote('0:Rew:7787.0,7769.0')] ).
cnf(7957,plain,
equal(add(u,v),add(v,u)),
inference(rew,[status(thm),theory(equality)],[7429,6459,7426,7396,7078]),
[iquote('0:Rew:7429.0,6459.0,7426.0,6459.0,7429.0,6459.0,7396.0,6459.0,7078.0,6459.0')] ).
cnf(7979,plain,
equal(add(u,add(multiply(n0,u),multiply(u,inverse(v)))),u),
inference(rew,[status(thm),theory(equality)],[7957,7679]),
[iquote('0:Rew:7957.0,7679.0')] ).
cnf(7986,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[7396,6646,7390,7429,6947]),
[iquote('0:Rew:7396.0,6646.0,7390.0,6646.0,7396.0,6646.0,7429.0,6646.0,6947.0,6646.0')] ).
cnf(8047,plain,
equal(multiply(u,add(v,multiply(n0,u))),add(multiply(n0,u),multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[7986,7293,7390]),
[iquote('0:Rew:7986.0,7293.0,7390.0,7293.0')] ).
cnf(8048,plain,
equal(multiply(u,add(v,multiply(n0,u))),multiply(u,add(n0,v))),
inference(rew,[status(thm),theory(equality)],[1,8047]),
[iquote('0:Rew:1.0,8047.0')] ).
cnf(8049,plain,
equal(multiply(u,add(v,multiply(n0,u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[7390,8048]),
[iquote('0:Rew:7390.0,8048.0')] ).
cnf(8050,plain,
equal(add(multiply(n0,u),multiply(u,v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[8049,7300,7390]),
[iquote('0:Rew:8049.0,7300.0,7390.0,7300.0')] ).
cnf(8051,plain,
equal(add(u,multiply(u,inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[8050,7979]),
[iquote('0:Rew:8050.0,7979.0')] ).
cnf(8100,plain,
equal(add(n1,u),n1),
inference(rew,[status(thm),theory(equality)],[7662,7556,8051,7986,7429]),
[iquote('0:Rew:7662.0,7556.0,8051.0,7556.0,7986.0,7556.0,7429.0,7556.0')] ).
cnf(8107,plain,
equal(add(u,multiply(n0,v)),multiply(u,n1)),
inference(rew,[status(thm),theory(equality)],[8100,7790]),
[iquote('0:Rew:8100.0,7790.0')] ).
cnf(8117,plain,
equal(add(u,multiply(n0,v)),u),
inference(rew,[status(thm),theory(equality)],[7396,8107]),
[iquote('0:Rew:7396.0,8107.0')] ).
cnf(8118,plain,
$false,
inference(unc,[status(thm)],[8117,7678]),
[iquote('0:UnC:8117.0,7678.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.08 % Problem : BOO026-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.09 % Command : run_spass %d %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Wed Jun 1 20:10:59 EDT 2022
% 0.08/0.28 % CPUTime :
% 6.42/6.62
% 6.42/6.62 SPASS V 3.9
% 6.42/6.62 SPASS beiseite: Proof found.
% 6.42/6.62 % SZS status Theorem
% 6.42/6.62 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.42/6.62 SPASS derived 6267 clauses, backtracked 0 clauses, performed 0 splits and kept 3107 clauses.
% 6.42/6.62 SPASS allocated 83690 KBytes.
% 6.42/6.62 SPASS spent 0:00:06.32 on the problem.
% 6.42/6.62 0:00:00.03 for the input.
% 6.42/6.62 0:00:00.00 for the FLOTTER CNF translation.
% 6.42/6.62 0:00:00.05 for inferences.
% 6.42/6.62 0:00:00.00 for the backtracking.
% 6.42/6.62 0:00:06.23 for the reduction.
% 6.42/6.62
% 6.42/6.62
% 6.42/6.62 Here is a proof with depth 8, length 205 :
% 6.42/6.62 % SZS output start Refutation
% See solution above
% 6.44/6.72 Formulae used in the proof : multiply_add_property additive_inverse add_multiply_property multiplicative_inverse pixley1 pixley2 pixley3 pixley1_dual pixley2_dual pixley3_dual prove_multiply_add
% 6.44/6.72
%------------------------------------------------------------------------------