TSTP Solution File: GRP121-1 by SPASS---3.9

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP121-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n014.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 : Sat Jul 16 11:45:25 EDT 2022

% Result   : Unsatisfiable 41.13s 41.39s
% Output   : Refutation 41.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   60
%            Number of leaves      :    3
% Syntax   : Number of clauses     :  268 ( 268 unt;   0 nHn; 268 RR)
%            Number of literals    :  268 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   15 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(multiply(u,multiply(multiply(u,multiply(multiply(u,u),multiply(v,w))),multiply(w,multiply(w,w)))),v),
    file('GRP121-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(multiply(identity,identity),identity),
    file('GRP121-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(multiply(a,identity),a),
    file('GRP121-1.p',unknown),
    [] ).

cnf(6,plain,
    equal(multiply(u,multiply(multiply(u,v),multiply(multiply(w,multiply(w,w)),multiply(multiply(w,multiply(w,w)),multiply(w,multiply(w,w)))))),multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),multiply(v,w)))),
    inference(spr,[status(thm),theory(equality)],[1]),
    [iquote('0:SpR:1.0,1.0')] ).

cnf(8,plain,
    equal(multiply(u,multiply(multiply(u,multiply(multiply(u,u),multiply(v,identity))),multiply(identity,identity))),v),
    inference(spr,[status(thm),theory(equality)],[2,1]),
    [iquote('0:SpR:2.0,1.0')] ).

cnf(9,plain,
    equal(multiply(u,multiply(multiply(u,multiply(multiply(u,u),identity)),multiply(identity,multiply(identity,identity)))),identity),
    inference(spr,[status(thm),theory(equality)],[2,1]),
    [iquote('0:SpR:2.0,1.0')] ).

cnf(11,plain,
    equal(multiply(u,multiply(multiply(u,multiply(multiply(u,u),multiply(v,identity))),identity)),v),
    inference(rew,[status(thm),theory(equality)],[2,8]),
    [iquote('0:Rew:2.0,8.0')] ).

cnf(12,plain,
    equal(multiply(u,multiply(multiply(u,multiply(multiply(u,u),identity)),identity)),identity),
    inference(rew,[status(thm),theory(equality)],[2,9]),
    [iquote('0:Rew:2.0,9.0,2.0,9.0')] ).

cnf(14,plain,
    equal(multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),identity)),multiply(u,multiply(multiply(u,identity),multiply(identity,multiply(identity,identity))))),
    inference(spr,[status(thm),theory(equality)],[12,1]),
    [iquote('0:SpR:12.0,1.0')] ).

cnf(18,plain,
    equal(multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),identity)),multiply(u,multiply(multiply(u,identity),identity))),
    inference(rew,[status(thm),theory(equality)],[2,14]),
    [iquote('0:Rew:2.0,14.0,2.0,14.0')] ).

cnf(22,plain,
    equal(multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),multiply(v,identity))),multiply(u,multiply(multiply(u,v),identity))),
    inference(spr,[status(thm),theory(equality)],[11]),
    [iquote('0:SpR:11.0,11.0')] ).

cnf(24,plain,
    equal(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(u,identity))),identity)),u),
    inference(spr,[status(thm),theory(equality)],[2,11]),
    [iquote('0:SpR:2.0,11.0')] ).

cnf(28,plain,
    equal(multiply(identity,multiply(multiply(identity,u),identity)),multiply(identity,multiply(identity,multiply(u,identity)))),
    inference(spr,[status(thm),theory(equality)],[24]),
    [iquote('0:SpR:24.0,24.0')] ).

cnf(34,plain,
    equal(multiply(identity,multiply(identity,multiply(multiply(identity,multiply(u,identity)),identity))),u),
    inference(rew,[status(thm),theory(equality)],[28,24]),
    [iquote('0:Rew:28.0,24.0')] ).

cnf(35,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(u,identity),identity)))),u),
    inference(rew,[status(thm),theory(equality)],[28,34]),
    [iquote('0:Rew:28.0,34.0')] ).

cnf(42,plain,
    equal(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(u,identity))),identity)),multiply(identity,multiply(identity,multiply(multiply(multiply(identity,u),identity),identity)))),
    inference(spr,[status(thm),theory(equality)],[28]),
    [iquote('0:SpR:28.0,28.0')] ).

cnf(61,plain,
    equal(multiply(identity,multiply(identity,multiply(multiply(multiply(identity,u),identity),identity))),u),
    inference(rew,[status(thm),theory(equality)],[35,42,28]),
    [iquote('0:Rew:35.0,42.0,28.0,42.0,28.0,42.0')] ).

cnf(65,plain,
    equal(multiply(identity,multiply(multiply(multiply(identity,u),identity),identity)),multiply(identity,multiply(identity,multiply(multiply(u,identity),identity)))),
    inference(spr,[status(thm),theory(equality)],[61]),
    [iquote('0:SpR:61.0,61.0')] ).

cnf(69,plain,
    equal(multiply(multiply(identity,multiply(multiply(identity,identity),multiply(u,v))),multiply(v,multiply(v,v))),multiply(identity,multiply(identity,multiply(multiply(u,identity),identity)))),
    inference(spr,[status(thm),theory(equality)],[1,61]),
    [iquote('0:SpR:1.0,61.0')] ).

cnf(73,plain,
    equal(multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(u,identity))),identity),identity))),multiply(multiply(identity,u),identity)),
    inference(spr,[status(thm),theory(equality)],[28,61]),
    [iquote('0:SpR:28.0,61.0')] ).

cnf(77,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity))))),multiply(multiply(identity,u),identity)),
    inference(rew,[status(thm),theory(equality)],[65,73]),
    [iquote('0:Rew:65.0,73.0,65.0,73.0')] ).

cnf(78,plain,
    equal(multiply(multiply(identity,u),identity),multiply(identity,multiply(u,identity))),
    inference(rew,[status(thm),theory(equality)],[35,77]),
    [iquote('0:Rew:35.0,77.0')] ).

cnf(88,plain,
    equal(multiply(multiply(identity,multiply(identity,multiply(u,v))),multiply(v,multiply(v,v))),multiply(identity,multiply(identity,multiply(multiply(u,identity),identity)))),
    inference(rew,[status(thm),theory(equality)],[2,69]),
    [iquote('0:Rew:2.0,69.0')] ).

cnf(100,plain,
    equal(multiply(u,multiply(multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),multiply(u,v))),multiply(multiply(multiply(v,multiply(v,v)),multiply(v,multiply(v,v))),multiply(multiply(multiply(v,multiply(v,v)),multiply(v,multiply(v,v))),multiply(multiply(v,multiply(v,v)),multiply(v,multiply(v,v))))))),multiply(v,multiply(v,v))),
    inference(spr,[status(thm),theory(equality)],[6,1]),
    [iquote('0:SpR:6.0,1.0')] ).

cnf(102,plain,
    equal(multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),multiply(multiply(multiply(u,u),multiply(v,multiply(w,multiply(w,w)))),w))),v),
    inference(spr,[status(thm),theory(equality)],[6,1]),
    [iquote('0:SpR:6.0,1.0')] ).

cnf(111,plain,
    equal(multiply(u,multiply(multiply(u,multiply(v,multiply(v,v))),multiply(multiply(multiply(multiply(v,multiply(v,v)),multiply(v,multiply(v,v))),multiply(multiply(multiply(v,multiply(v,v)),multiply(v,multiply(v,v))),multiply(multiply(v,multiply(v,v)),multiply(v,multiply(v,v))))),multiply(multiply(multiply(multiply(v,multiply(v,v)),multiply(v,multiply(v,v))),multiply(multiply(multiply(v,multiply(v,v)),multiply(v,multiply(v,v))),multiply(multiply(v,multiply(v,v)),multiply(v,multiply(v,v))))),multiply(multiply(multiply(v,multiply(v,v)),multiply(v,multiply(v,v))),multiply(multiply(multiply(v,multiply(v,v)),multiply(v,multiply(v,v))),multiply(multiply(v,multiply(v,v)),multiply(v,multiply(v,v))))))))),multiply(multiply(multiply(u,u),multiply(u,u)),multiply(multiply(multiply(multiply(u,u),multiply(u,u)),multiply(multiply(u,u),multiply(u,u))),multiply(multiply(u,u),v)))),
    inference(spr,[status(thm),theory(equality)],[6]),
    [iquote('0:SpR:6.0,6.0')] ).

cnf(112,plain,
    equal(multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(u,v),multiply(multiply(identity,multiply(identity,identity)),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),identity)),v),
    inference(spr,[status(thm),theory(equality)],[6,11]),
    [iquote('0:SpR:6.0,11.0')] ).

cnf(123,plain,
    equal(multiply(u,multiply(multiply(u,identity),multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(v,identity),identity))),multiply(multiply(identity,multiply(identity,multiply(multiply(v,identity),identity))),multiply(identity,multiply(identity,multiply(multiply(v,identity),identity))))),multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(v,identity),identity))),multiply(multiply(identity,multiply(identity,multiply(multiply(v,identity),identity))),multiply(identity,multiply(identity,multiply(multiply(v,identity),identity))))),multiply(multiply(identity,multiply(identity,multiply(multiply(v,identity),identity))),multiply(multiply(identity,multiply(identity,multiply(multiply(v,identity),identity))),multiply(identity,multiply(identity,multiply(multiply(v,identity),identity))))))))),multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),v))),
    inference(spr,[status(thm),theory(equality)],[35,6]),
    [iquote('0:SpR:35.0,6.0')] ).

cnf(125,plain,
    equal(multiply(u,multiply(multiply(u,v),multiply(multiply(multiply(multiply(v,multiply(multiply(v,v),multiply(w,identity))),identity),multiply(multiply(multiply(v,multiply(multiply(v,v),multiply(w,identity))),identity),multiply(multiply(v,multiply(multiply(v,v),multiply(w,identity))),identity))),multiply(multiply(multiply(multiply(v,multiply(multiply(v,v),multiply(w,identity))),identity),multiply(multiply(multiply(v,multiply(multiply(v,v),multiply(w,identity))),identity),multiply(multiply(v,multiply(multiply(v,v),multiply(w,identity))),identity))),multiply(multiply(multiply(v,multiply(multiply(v,v),multiply(w,identity))),identity),multiply(multiply(multiply(v,multiply(multiply(v,v),multiply(w,identity))),identity),multiply(multiply(v,multiply(multiply(v,v),multiply(w,identity))),identity))))))),multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),w))),
    inference(spr,[status(thm),theory(equality)],[11,6]),
    [iquote('0:SpR:11.0,6.0')] ).

cnf(129,plain,
    equal(multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(u,v),identity)),identity)),v),
    inference(rew,[status(thm),theory(equality)],[2,112]),
    [iquote('0:Rew:2.0,112.0,2.0,112.0,2.0,112.0,2.0,112.0')] ).

cnf(184,plain,
    equal(multiply(multiply(u,multiply(multiply(u,u),multiply(v,w))),multiply(w,multiply(w,w))),multiply(multiply(u,u),multiply(multiply(u,multiply(v,identity)),identity))),
    inference(spr,[status(thm),theory(equality)],[1,129]),
    [iquote('0:SpR:1.0,129.0')] ).

cnf(187,plain,
    equal(multiply(multiply(u,u),multiply(multiply(u,multiply(identity,identity)),identity)),multiply(multiply(u,multiply(multiply(u,u),identity)),identity)),
    inference(spr,[status(thm),theory(equality)],[12,129]),
    [iquote('0:SpR:12.0,129.0')] ).

cnf(188,plain,
    equal(multiply(multiply(u,multiply(multiply(u,u),multiply(v,identity))),identity),multiply(multiply(u,u),multiply(multiply(u,multiply(v,identity)),identity))),
    inference(spr,[status(thm),theory(equality)],[11,129]),
    [iquote('0:SpR:11.0,129.0')] ).

cnf(200,plain,
    equal(multiply(multiply(u,multiply(multiply(u,u),identity)),identity),multiply(multiply(u,u),multiply(multiply(u,identity),identity))),
    inference(rew,[status(thm),theory(equality)],[2,187]),
    [iquote('0:Rew:2.0,187.0')] ).

cnf(201,plain,
    equal(multiply(u,multiply(multiply(u,u),multiply(multiply(u,identity),identity))),identity),
    inference(rew,[status(thm),theory(equality)],[200,12]),
    [iquote('0:Rew:200.0,12.0')] ).

cnf(206,plain,
    equal(multiply(u,multiply(multiply(u,u),multiply(multiply(u,multiply(v,identity)),identity))),v),
    inference(rew,[status(thm),theory(equality)],[188,11]),
    [iquote('0:Rew:188.0,11.0')] ).

cnf(207,plain,
    equal(multiply(u,multiply(multiply(u,v),multiply(multiply(multiply(multiply(v,v),multiply(multiply(v,multiply(w,identity)),identity)),multiply(multiply(multiply(v,v),multiply(multiply(v,multiply(w,identity)),identity)),multiply(multiply(v,v),multiply(multiply(v,multiply(w,identity)),identity)))),multiply(multiply(multiply(multiply(v,v),multiply(multiply(v,multiply(w,identity)),identity)),multiply(multiply(multiply(v,v),multiply(multiply(v,multiply(w,identity)),identity)),multiply(multiply(v,v),multiply(multiply(v,multiply(w,identity)),identity)))),multiply(multiply(multiply(v,v),multiply(multiply(v,multiply(w,identity)),identity)),multiply(multiply(multiply(v,v),multiply(multiply(v,multiply(w,identity)),identity)),multiply(multiply(v,v),multiply(multiply(v,multiply(w,identity)),identity)))))))),multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),w))),
    inference(rew,[status(thm),theory(equality)],[188,125]),
    [iquote('0:Rew:188.0,125.0')] ).

cnf(225,plain,
    equal(multiply(multiply(identity,u),multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(identity,multiply(u,identity)),identity))),identity),
    inference(spr,[status(thm),theory(equality)],[78,201]),
    [iquote('0:SpR:78.0,201.0')] ).

cnf(232,plain,
    equal(multiply(multiply(identity,u),multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(identity,multiply(multiply(u,identity),identity)))),identity),
    inference(rew,[status(thm),theory(equality)],[78,225]),
    [iquote('0:Rew:78.0,225.0')] ).

cnf(244,plain,
    equal(multiply(u,multiply(multiply(u,u),multiply(multiply(u,multiply(identity,multiply(v,identity))),identity))),multiply(identity,v)),
    inference(spr,[status(thm),theory(equality)],[78,206]),
    [iquote('0:SpR:78.0,206.0')] ).

cnf(298,plain,
    equal(multiply(multiply(u,u),multiply(multiply(u,u),multiply(multiply(u,identity),identity))),u),
    inference(spr,[status(thm),theory(equality)],[200,129]),
    [iquote('0:SpR:200.0,129.0')] ).

cnf(311,plain,
    equal(multiply(multiply(multiply(u,u),multiply(u,u)),multiply(multiply(multiply(u,u),identity),identity)),multiply(multiply(u,multiply(multiply(u,identity),identity)),identity)),
    inference(spr,[status(thm),theory(equality)],[18,200]),
    [iquote('0:SpR:18.0,200.0')] ).

cnf(323,plain,
    equal(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(identity,multiply(u,identity)),identity))),multiply(identity,u)),
    inference(spr,[status(thm),theory(equality)],[78,298]),
    [iquote('0:SpR:78.0,298.0')] ).

cnf(331,plain,
    equal(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(identity,multiply(multiply(u,identity),identity)))),multiply(identity,u)),
    inference(rew,[status(thm),theory(equality)],[78,323]),
    [iquote('0:Rew:78.0,323.0')] ).

cnf(341,plain,
    equal(multiply(u,multiply(multiply(u,u),multiply(multiply(u,multiply(identity,multiply(identity,multiply(v,identity)))),identity))),multiply(identity,multiply(identity,v))),
    inference(spr,[status(thm),theory(equality)],[78,244]),
    [iquote('0:SpR:78.0,244.0')] ).

cnf(385,plain,
    equal(multiply(multiply(identity,multiply(identity,u)),multiply(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(identity,u))),multiply(identity,multiply(multiply(identity,multiply(u,identity)),identity)))),identity),
    inference(spr,[status(thm),theory(equality)],[78,232]),
    [iquote('0:SpR:78.0,232.0')] ).

cnf(419,plain,
    equal(multiply(multiply(identity,multiply(identity,u)),multiply(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(identity,u))),multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))))),identity),
    inference(rew,[status(thm),theory(equality)],[78,385]),
    [iquote('0:Rew:78.0,385.0')] ).

cnf(546,plain,
    equal(multiply(identity,multiply(multiply(identity,identity),multiply(multiply(identity,multiply(u,multiply(v,multiply(v,v)))),v))),u),
    inference(spr,[status(thm),theory(equality)],[2,102]),
    [iquote('0:SpR:2.0,102.0')] ).

cnf(554,plain,
    equal(multiply(identity,multiply(identity,multiply(multiply(identity,multiply(u,multiply(v,multiply(v,v)))),v))),u),
    inference(rew,[status(thm),theory(equality)],[2,546]),
    [iquote('0:Rew:2.0,546.0')] ).

cnf(568,plain,
    equal(multiply(identity,multiply(multiply(identity,multiply(u,multiply(v,multiply(v,v)))),v)),multiply(multiply(identity,identity),multiply(multiply(identity,multiply(u,identity)),identity))),
    inference(spr,[status(thm),theory(equality)],[554,129]),
    [iquote('0:SpR:554.0,129.0')] ).

cnf(570,plain,
    equal(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(u,multiply(v,multiply(v,v)))),v)),identity)),multiply(u,identity)),
    inference(spr,[status(thm),theory(equality)],[554,78]),
    [iquote('0:SpR:554.0,78.0')] ).

cnf(580,plain,
    equal(multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(u,multiply(v,multiply(v,v)))),v),identity))),multiply(u,identity)),
    inference(rew,[status(thm),theory(equality)],[78,570]),
    [iquote('0:Rew:78.0,570.0')] ).

cnf(582,plain,
    equal(multiply(identity,multiply(multiply(identity,multiply(u,multiply(v,multiply(v,v)))),v)),multiply(identity,multiply(identity,multiply(multiply(u,identity),identity)))),
    inference(rew,[status(thm),theory(equality)],[2,568,78]),
    [iquote('0:Rew:2.0,568.0,78.0,568.0')] ).

cnf(593,plain,
    equal(multiply(u,multiply(multiply(u,identity),multiply(multiply(multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)),multiply(multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)),multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)))),multiply(multiply(multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)),multiply(multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)),multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)))),multiply(multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)),multiply(multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)),multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)))))))),multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),multiply(v,identity)))),
    inference(spr,[status(thm),theory(equality)],[580,6]),
    [iquote('0:SpR:580.0,6.0')] ).

cnf(595,plain,
    equal(multiply(identity,multiply(multiply(multiply(identity,multiply(u,multiply(v,multiply(v,v)))),v),identity)),multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(u,identity),identity)),identity))),
    inference(spr,[status(thm),theory(equality)],[580,129]),
    [iquote('0:SpR:580.0,129.0')] ).

cnf(612,plain,
    equal(multiply(identity,multiply(multiply(multiply(identity,multiply(u,multiply(v,multiply(v,v)))),v),identity)),multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity)))),
    inference(rew,[status(thm),theory(equality)],[2,595,78]),
    [iquote('0:Rew:2.0,595.0,78.0,595.0')] ).

cnf(621,plain,
    equal(multiply(u,multiply(multiply(u,identity),multiply(multiply(multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)),multiply(multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)),multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)))),multiply(multiply(multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)),multiply(multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)),multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)))),multiply(multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)),multiply(multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)),multiply(identity,multiply(multiply(multiply(identity,multiply(v,multiply(w,multiply(w,w)))),w),identity)))))))),multiply(u,multiply(multiply(u,v),identity))),
    inference(rew,[status(thm),theory(equality)],[22,593]),
    [iquote('0:Rew:22.0,593.0')] ).

cnf(622,plain,
    equal(multiply(u,multiply(multiply(u,identity),multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(v,identity),identity),identity))),multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(v,identity),identity),identity))),multiply(identity,multiply(identity,multiply(multiply(multiply(v,identity),identity),identity))))),multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(v,identity),identity),identity))),multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(v,identity),identity),identity))),multiply(identity,multiply(identity,multiply(multiply(multiply(v,identity),identity),identity))))),multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(v,identity),identity),identity))),multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(v,identity),identity),identity))),multiply(identity,multiply(identity,multiply(multiply(multiply(v,identity),identity),identity))))))))),multiply(u,multiply(multiply(u,v),identity))),
    inference(rew,[status(thm),theory(equality)],[612,621]),
    [iquote('0:Rew:612.0,621.0')] ).

cnf(654,plain,
    equal(multiply(u,multiply(multiply(multiply(u,identity),identity),multiply(multiply(multiply(u,identity),identity),multiply(multiply(u,identity),identity)))),multiply(identity,multiply(identity,multiply(multiply(identity,identity),identity)))),
    inference(spr,[status(thm),theory(equality)],[35,88]),
    [iquote('0:SpR:35.0,88.0')] ).

cnf(658,plain,
    equal(multiply(u,multiply(multiply(multiply(u,identity),identity),multiply(multiply(multiply(u,identity),identity),multiply(multiply(u,identity),identity)))),identity),
    inference(rew,[status(thm),theory(equality)],[2,654]),
    [iquote('0:Rew:2.0,654.0,2.0,654.0,2.0,654.0,2.0,654.0')] ).

cnf(686,plain,
    equal(multiply(multiply(multiply(u,identity),identity),multiply(multiply(multiply(u,identity),identity),multiply(multiply(u,identity),identity))),multiply(multiply(u,u),multiply(multiply(u,multiply(identity,identity)),identity))),
    inference(spr,[status(thm),theory(equality)],[658,129]),
    [iquote('0:SpR:658.0,129.0')] ).

cnf(715,plain,
    equal(multiply(multiply(multiply(u,identity),identity),multiply(multiply(multiply(u,identity),identity),multiply(multiply(u,identity),identity))),multiply(multiply(u,u),multiply(multiply(u,identity),identity))),
    inference(rew,[status(thm),theory(equality)],[2,686]),
    [iquote('0:Rew:2.0,686.0')] ).

cnf(833,plain,
    equal(multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),identity)),identity)),multiply(multiply(identity,multiply(u,multiply(v,multiply(v,v)))),v)),
    inference(spr,[status(thm),theory(equality)],[582,129]),
    [iquote('0:SpR:582.0,129.0')] ).

cnf(842,plain,
    equal(multiply(u,multiply(multiply(u,u),multiply(multiply(u,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(v,identity),identity))))),identity))),multiply(identity,multiply(identity,multiply(identity,multiply(v,multiply(identity,multiply(identity,identity))))))),
    inference(spr,[status(thm),theory(equality)],[582,341]),
    [iquote('0:SpR:582.0,341.0')] ).

cnf(844,plain,
    equal(multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(u,multiply(multiply(v,multiply(v,v)),multiply(multiply(v,multiply(v,v)),multiply(v,multiply(v,v)))))),identity),identity))),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),v))),
    inference(spr,[status(thm),theory(equality)],[582]),
    [iquote('0:SpR:582.0,582.0')] ).

cnf(857,plain,
    equal(multiply(multiply(identity,multiply(u,multiply(v,multiply(v,v)))),v),multiply(identity,multiply(multiply(u,identity),identity))),
    inference(rew,[status(thm),theory(equality)],[2,833,35,78]),
    [iquote('0:Rew:2.0,833.0,35.0,833.0,78.0,833.0,78.0,833.0')] ).

cnf(869,plain,
    equal(multiply(u,multiply(multiply(u,u),multiply(multiply(u,v),identity))),multiply(identity,multiply(identity,multiply(identity,multiply(v,identity))))),
    inference(rew,[status(thm),theory(equality)],[35,842,2]),
    [iquote('0:Rew:35.0,842.0,2.0,842.0,2.0,842.0')] ).

cnf(886,plain,
    equal(multiply(u,multiply(multiply(v,multiply(v,v)),multiply(multiply(v,multiply(v,v)),multiply(v,multiply(v,v))))),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),v))),
    inference(rew,[status(thm),theory(equality)],[35,844,78]),
    [iquote('0:Rew:35.0,844.0,78.0,844.0,78.0,844.0')] ).

cnf(887,plain,
    equal(multiply(u,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(u,v),identity),identity))),w))),multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),multiply(v,w)))),
    inference(rew,[status(thm),theory(equality)],[886,6]),
    [iquote('0:Rew:886.0,6.0')] ).

cnf(889,plain,
    equal(multiply(u,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity))),multiply(identity,multiply(identity,multiply(multiply(multiply(v,identity),identity),identity)))))),multiply(u,multiply(multiply(u,v),identity))),
    inference(rew,[status(thm),theory(equality)],[886,622]),
    [iquote('0:Rew:886.0,622.0')] ).

cnf(903,plain,
    equal(multiply(u,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(u,multiply(v,multiply(v,v))),identity),identity))),multiply(multiply(v,multiply(v,v)),multiply(v,multiply(v,v)))))),multiply(multiply(multiply(u,u),multiply(u,u)),multiply(multiply(multiply(multiply(u,u),multiply(u,u)),multiply(multiply(u,u),multiply(u,u))),multiply(multiply(u,u),v)))),
    inference(rew,[status(thm),theory(equality)],[886,111]),
    [iquote('0:Rew:886.0,111.0')] ).

cnf(917,plain,
    equal(multiply(u,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity))),multiply(identity,multiply(identity,multiply(multiply(v,identity),identity)))))),multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),v))),
    inference(rew,[status(thm),theory(equality)],[886,123]),
    [iquote('0:Rew:886.0,123.0')] ).

cnf(918,plain,
    equal(multiply(u,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(u,v),identity),identity))),multiply(multiply(v,v),multiply(multiply(v,multiply(w,identity)),identity))))),multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),w))),
    inference(rew,[status(thm),theory(equality)],[886,207]),
    [iquote('0:Rew:886.0,207.0')] ).

cnf(964,plain,
    equal(multiply(u,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(u,multiply(v,multiply(v,v))),identity),identity))),multiply(multiply(v,multiply(v,v)),multiply(v,multiply(v,v)))))),multiply(multiply(u,u),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(u,u),multiply(u,u)),identity),identity))),v)))),
    inference(rew,[status(thm),theory(equality)],[887,903]),
    [iquote('0:Rew:887.0,903.0')] ).

cnf(1014,plain,
    equal(multiply(u,multiply(multiply(u,u),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(v,identity)))),identity))),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(u,u),multiply(multiply(u,v),identity)),identity))))),
    inference(spr,[status(thm),theory(equality)],[869]),
    [iquote('0:SpR:869.0,869.0')] ).

cnf(1016,plain,
    equal(multiply(u,multiply(multiply(u,multiply(multiply(u,u),v)),identity)),multiply(identity,multiply(identity,multiply(identity,multiply(v,identity))))),
    inference(spr,[status(thm),theory(equality)],[869,22]),
    [iquote('0:SpR:869.0,22.0')] ).

cnf(1029,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(identity,multiply(multiply(u,identity),identity))),identity)))),multiply(multiply(identity,u),multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(identity,identity)))),
    inference(spr,[status(thm),theory(equality)],[232,869]),
    [iquote('0:SpR:232.0,869.0')] ).

cnf(1057,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(u,u),multiply(multiply(u,v),identity)),identity)))),multiply(u,multiply(multiply(u,u),v))),
    inference(rew,[status(thm),theory(equality)],[35,1014,78]),
    [iquote('0:Rew:35.0,1014.0,78.0,1014.0,78.0,1014.0,78.0,1014.0')] ).

cnf(1059,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(identity,multiply(multiply(u,identity),identity))),identity)))),multiply(multiply(identity,u),multiply(multiply(multiply(identity,u),multiply(identity,u)),identity))),
    inference(rew,[status(thm),theory(equality)],[2,1029]),
    [iquote('0:Rew:2.0,1029.0')] ).

cnf(1170,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),v)),identity),identity)))),multiply(u,multiply(multiply(u,multiply(identity,multiply(identity,multiply(identity,multiply(v,identity))))),identity))),
    inference(spr,[status(thm),theory(equality)],[1016]),
    [iquote('0:SpR:1016.0,1016.0')] ).

cnf(1171,plain,
    equal(multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(v,identity)))),identity)),identity)),multiply(multiply(u,multiply(multiply(u,u),v)),identity)),
    inference(spr,[status(thm),theory(equality)],[1016,129]),
    [iquote('0:SpR:1016.0,129.0')] ).

cnf(1215,plain,
    equal(multiply(multiply(u,multiply(multiply(u,u),v)),identity),multiply(multiply(u,u),multiply(multiply(u,v),identity))),
    inference(rew,[status(thm),theory(equality)],[35,1171,78]),
    [iquote('0:Rew:35.0,1171.0,78.0,1171.0,78.0,1171.0,78.0,1171.0')] ).

cnf(1232,plain,
    equal(multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),v)),multiply(u,multiply(multiply(u,multiply(identity,multiply(identity,multiply(identity,multiply(v,identity))))),identity))),
    inference(rew,[status(thm),theory(equality)],[35,1170]),
    [iquote('0:Rew:35.0,1170.0')] ).

cnf(1268,plain,
    equal(multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(multiply(u,u),multiply(u,u)),multiply(v,identity))),identity)),multiply(multiply(u,multiply(u,multiply(multiply(u,v),identity))),identity)),
    inference(spr,[status(thm),theory(equality)],[22,1215]),
    [iquote('0:SpR:22.0,1215.0')] ).

cnf(1494,plain,
    equal(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(identity,u),multiply(identity,u))),multiply(multiply(identity,u),identity))),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(identity,multiply(multiply(u,identity),identity))),identity))))),
    inference(spr,[status(thm),theory(equality)],[331,869]),
    [iquote('0:SpR:331.0,869.0')] ).

cnf(1543,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(identity,multiply(multiply(u,identity),identity))),identity)))),multiply(multiply(identity,u),multiply(identity,multiply(multiply(u,identity),multiply(u,identity))))),
    inference(rew,[status(thm),theory(equality)],[35,1494,78,887]),
    [iquote('0:Rew:35.0,1494.0,78.0,1494.0,78.0,1494.0,78.0,1494.0,887.0,1494.0,78.0,1494.0')] ).

cnf(1544,plain,
    equal(multiply(multiply(identity,u),multiply(multiply(multiply(identity,u),multiply(identity,u)),identity)),multiply(multiply(identity,u),multiply(identity,multiply(multiply(u,identity),multiply(u,identity))))),
    inference(rew,[status(thm),theory(equality)],[1059,1543]),
    [iquote('0:Rew:1059.0,1543.0')] ).

cnf(1545,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(identity,multiply(multiply(u,identity),identity))),identity)))),multiply(multiply(identity,u),multiply(identity,multiply(multiply(u,identity),multiply(u,identity))))),
    inference(rew,[status(thm),theory(equality)],[1544,1059]),
    [iquote('0:Rew:1544.0,1059.0')] ).

cnf(1565,plain,
    equal(multiply(multiply(multiply(u,identity),identity),multiply(multiply(multiply(multiply(u,identity),identity),multiply(multiply(u,identity),identity)),multiply(multiply(multiply(u,u),multiply(multiply(u,identity),identity)),identity))),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(u,identity),identity),multiply(multiply(u,identity),identity)),identity))))),
    inference(spr,[status(thm),theory(equality)],[715,869]),
    [iquote('0:SpR:715.0,869.0')] ).

cnf(1567,plain,
    equal(multiply(multiply(identity,multiply(identity,multiply(multiply(u,u),multiply(multiply(u,identity),identity)))),multiply(multiply(multiply(multiply(u,identity),identity),multiply(multiply(u,identity),identity)),multiply(multiply(multiply(multiply(u,identity),identity),multiply(multiply(u,identity),identity)),multiply(multiply(multiply(u,identity),identity),multiply(multiply(u,identity),identity))))),multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(u,identity),identity),identity),identity)))),
    inference(spr,[status(thm),theory(equality)],[715,88]),
    [iquote('0:SpR:715.0,88.0')] ).

cnf(1570,plain,
    equal(multiply(multiply(identity,multiply(u,multiply(multiply(v,v),multiply(multiply(v,identity),identity)))),multiply(multiply(v,identity),identity)),multiply(identity,multiply(multiply(u,identity),identity))),
    inference(spr,[status(thm),theory(equality)],[715,857]),
    [iquote('0:SpR:715.0,857.0')] ).

cnf(1584,plain,
    equal(multiply(multiply(multiply(identity,multiply(u,identity)),identity),multiply(multiply(multiply(identity,multiply(u,identity)),identity),multiply(multiply(identity,multiply(u,identity)),identity))),multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(identity,multiply(u,identity)),identity))),
    inference(spr,[status(thm),theory(equality)],[78,715]),
    [iquote('0:SpR:78.0,715.0')] ).

cnf(1593,plain,
    equal(multiply(multiply(identity,multiply(multiply(u,identity),identity)),multiply(multiply(identity,multiply(multiply(u,identity),identity)),multiply(identity,multiply(multiply(u,identity),identity)))),multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(identity,multiply(multiply(u,identity),identity)))),
    inference(rew,[status(thm),theory(equality)],[78,1584]),
    [iquote('0:Rew:78.0,1584.0')] ).

cnf(1603,plain,
    equal(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(multiply(identity,u),multiply(multiply(multiply(identity,u),multiply(identity,multiply(multiply(u,identity),multiply(u,identity)))),identity)),identity)),multiply(multiply(multiply(identity,u),multiply(identity,u)),identity)),
    inference(spr,[status(thm),theory(equality)],[1544,129]),
    [iquote('0:SpR:1544.0,129.0')] ).

cnf(1604,plain,
    equal(multiply(multiply(identity,u),multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(multiply(identity,u),multiply(identity,multiply(multiply(u,identity),multiply(u,identity)))),identity))),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,u),multiply(identity,u)),identity),identity))))),
    inference(spr,[status(thm),theory(equality)],[1544,869]),
    [iquote('0:SpR:1544.0,869.0')] ).

cnf(1641,plain,
    equal(multiply(multiply(multiply(identity,u),multiply(identity,u)),identity),multiply(identity,multiply(multiply(u,identity),multiply(u,identity)))),
    inference(rew,[status(thm),theory(equality)],[129,1603]),
    [iquote('0:Rew:129.0,1603.0')] ).

cnf(1646,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),multiply(u,identity)),identity))))),multiply(multiply(identity,u),multiply(identity,u))),
    inference(rew,[status(thm),theory(equality)],[78,1604,869,35]),
    [iquote('0:Rew:78.0,1604.0,869.0,1604.0,35.0,1604.0')] ).

cnf(1685,plain,
    equal(multiply(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(identity,u),multiply(identity,u))),multiply(multiply(identity,multiply(multiply(u,identity),multiply(u,identity))),identity)),multiply(multiply(multiply(identity,u),multiply(multiply(multiply(identity,u),identity),identity)),identity)),
    inference(spr,[status(thm),theory(equality)],[1641,311]),
    [iquote('0:SpR:1641.0,311.0')] ).

cnf(1699,plain,
    equal(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(identity,u),multiply(identity,u))),multiply(multiply(identity,multiply(multiply(u,identity),multiply(u,identity))),identity))),multiply(identity,multiply(identity,multiply(identity,multiply(identity,identity))))),
    inference(spr,[status(thm),theory(equality)],[1641,869]),
    [iquote('0:SpR:1641.0,869.0')] ).

cnf(1710,plain,
    equal(multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),identity),multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),identity))),multiply(multiply(u,u),identity)),
    inference(spr,[status(thm),theory(equality)],[35,1641]),
    [iquote('0:SpR:35.0,1641.0')] ).

cnf(1720,plain,
    equal(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity))),multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity))))),multiply(multiply(u,u),identity)),
    inference(rew,[status(thm),theory(equality)],[78,1710]),
    [iquote('0:Rew:78.0,1710.0,78.0,1710.0')] ).

cnf(1728,plain,
    equal(multiply(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(identity,u),multiply(identity,u))),multiply(identity,multiply(multiply(multiply(u,identity),multiply(u,identity)),identity))),multiply(multiply(multiply(identity,u),multiply(identity,multiply(multiply(u,identity),identity))),identity)),
    inference(rew,[status(thm),theory(equality)],[78,1685]),
    [iquote('0:Rew:78.0,1685.0,78.0,1685.0,78.0,1685.0')] ).

cnf(1730,plain,
    equal(multiply(multiply(identity,u),multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity)))),identity),
    inference(rew,[status(thm),theory(equality)],[35,1699,78,887,2]),
    [iquote('0:Rew:35.0,1699.0,78.0,1699.0,78.0,1699.0,78.0,1699.0,887.0,1699.0,78.0,1699.0,2.0,1699.0,2.0,1699.0,2.0,1699.0,2.0,1699.0')] ).

cnf(1842,plain,
    equal(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(multiply(identity,u),multiply(identity,identity)),identity)),multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity)))),
    inference(spr,[status(thm),theory(equality)],[1730,129]),
    [iquote('0:SpR:1730.0,129.0')] ).

cnf(1862,plain,
    equal(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(multiply(identity,multiply(u,identity)),multiply(multiply(multiply(identity,multiply(u,identity)),multiply(identity,multiply(u,identity))),identity)))),identity),
    inference(spr,[status(thm),theory(equality)],[78,1730]),
    [iquote('0:SpR:78.0,1730.0')] ).

cnf(1878,plain,
    equal(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(multiply(identity,multiply(u,identity)),multiply(identity,multiply(multiply(multiply(u,identity),identity),multiply(multiply(u,identity),identity)))))),identity),
    inference(rew,[status(thm),theory(equality)],[1641,1862]),
    [iquote('0:Rew:1641.0,1862.0')] ).

cnf(1882,plain,
    equal(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(identity,multiply(multiply(u,identity),identity))),multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity)))),
    inference(rew,[status(thm),theory(equality)],[78,1842,2]),
    [iquote('0:Rew:78.0,1842.0,78.0,1842.0,2.0,1842.0')] ).

cnf(1892,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity))),identity)))),multiply(multiply(identity,u),multiply(identity,multiply(multiply(u,identity),multiply(u,identity))))),
    inference(rew,[status(thm),theory(equality)],[1882,1545]),
    [iquote('0:Rew:1882.0,1545.0')] ).

cnf(1894,plain,
    equal(multiply(multiply(identity,multiply(multiply(u,identity),identity)),multiply(multiply(identity,multiply(multiply(u,identity),identity)),multiply(identity,multiply(multiply(u,identity),identity)))),multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity)))),
    inference(rew,[status(thm),theory(equality)],[1882,1593]),
    [iquote('0:Rew:1882.0,1593.0')] ).

cnf(1895,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),multiply(u,identity)),multiply(multiply(multiply(u,identity),identity),identity)))))),multiply(multiply(identity,u),multiply(identity,multiply(multiply(u,identity),multiply(u,identity))))),
    inference(rew,[status(thm),theory(equality)],[1215,1892,78]),
    [iquote('0:Rew:1215.0,1892.0,78.0,1892.0')] ).

cnf(1922,plain,
    equal(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),multiply(u,identity)),identity)))),identity),multiply(multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),multiply(u,identity)),identity)))),identity),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),multiply(u,identity)),identity)))),identity)),identity)))),identity),
    inference(spr,[status(thm),theory(equality)],[1646,1730]),
    [iquote('0:SpR:1646.0,1730.0')] ).

cnf(1959,plain,
    equal(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),identity),identity)))),identity),
    inference(rew,[status(thm),theory(equality)],[18,1922,35,78]),
    [iquote('0:Rew:18.0,1922.0,35.0,1922.0,78.0,1922.0,78.0,1922.0,78.0,1922.0')] ).

cnf(1962,plain,
    equal(multiply(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(identity,u),multiply(identity,u))),multiply(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(identity,identity)),identity)),multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),identity),identity)))),
    inference(spr,[status(thm),theory(equality)],[1959,129]),
    [iquote('0:SpR:1959.0,129.0')] ).

cnf(2003,plain,
    equal(multiply(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(identity,u),multiply(identity,u))),multiply(identity,multiply(multiply(multiply(u,identity),multiply(u,identity)),identity))),multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),identity),identity)))),
    inference(rew,[status(thm),theory(equality)],[78,1962,1641,2]),
    [iquote('0:Rew:78.0,1962.0,1641.0,1962.0,2.0,1962.0')] ).

cnf(2004,plain,
    equal(multiply(multiply(multiply(identity,u),multiply(identity,multiply(multiply(u,identity),identity))),identity),multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),identity),identity)))),
    inference(rew,[status(thm),theory(equality)],[1728,2003]),
    [iquote('0:Rew:1728.0,2003.0')] ).

cnf(2060,plain,
    equal(multiply(identity,multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(identity,u),identity)),identity),multiply(multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(identity,u),identity)),identity),identity),identity))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(u,identity)))),multiply(identity,multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(identity,u),identity)),identity),identity))),identity)),
    inference(spr,[status(thm),theory(equality)],[869,2004]),
    [iquote('0:SpR:869.0,2004.0')] ).

cnf(2083,plain,
    equal(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(u,identity),identity),identity),identity))))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(u,identity)))),multiply(u,identity)),identity)),
    inference(rew,[status(thm),theory(equality)],[78,2060,35,2]),
    [iquote('0:Rew:78.0,2060.0,78.0,2060.0,35.0,2060.0,78.0,2060.0,78.0,2060.0,78.0,2060.0,78.0,2060.0,2.0,2060.0,78.0,2060.0')] ).

cnf(2107,plain,
    equal(multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),v)),identity)),identity)),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(u,w),identity),identity))),multiply(multiply(w,w),multiply(multiply(w,multiply(v,identity)),identity))))),
    inference(spr,[status(thm),theory(equality)],[918,129]),
    [iquote('0:SpR:918.0,129.0')] ).

cnf(2141,plain,
    equal(multiply(multiply(u,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(u,v),identity),identity))),multiply(multiply(v,v),multiply(multiply(v,multiply(w,identity)),identity))))),identity),multiply(multiply(multiply(u,u),multiply(u,u)),multiply(multiply(multiply(u,u),w),identity))),
    inference(spr,[status(thm),theory(equality)],[918,1215]),
    [iquote('0:SpR:918.0,1215.0')] ).

cnf(2222,plain,
    equal(multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(multiply(u,u),multiply(u,u)),multiply(multiply(multiply(u,u),v),identity))),identity)),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(u,w),identity),identity))),multiply(multiply(w,w),multiply(multiply(w,multiply(v,identity)),identity))))),
    inference(rew,[status(thm),theory(equality)],[1215,2107]),
    [iquote('0:Rew:1215.0,2107.0')] ).

cnf(2223,plain,
    equal(multiply(multiply(u,multiply(u,multiply(multiply(u,multiply(multiply(u,u),v)),identity))),identity),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(u,w),identity),identity))),multiply(multiply(w,w),multiply(multiply(w,multiply(v,identity)),identity))))),
    inference(rew,[status(thm),theory(equality)],[1268,2222]),
    [iquote('0:Rew:1268.0,2222.0')] ).

cnf(2224,plain,
    equal(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(u,v),identity),identity))),multiply(multiply(v,v),multiply(multiply(v,multiply(w,identity)),identity)))),multiply(multiply(u,multiply(identity,multiply(identity,multiply(identity,multiply(w,identity))))),identity)),
    inference(rew,[status(thm),theory(equality)],[869,2223,1215]),
    [iquote('0:Rew:869.0,2223.0,1215.0,2223.0')] ).

cnf(2227,plain,
    equal(multiply(multiply(u,multiply(multiply(u,multiply(identity,multiply(identity,multiply(identity,multiply(v,identity))))),identity)),identity),multiply(multiply(multiply(u,u),multiply(u,u)),multiply(multiply(multiply(u,u),v),identity))),
    inference(rew,[status(thm),theory(equality)],[2224,2141]),
    [iquote('0:Rew:2224.0,2141.0')] ).

cnf(2341,plain,
    equal(multiply(multiply(identity,u),multiply(multiply(u,identity),identity)),multiply(identity,multiply(multiply(multiply(u,u),identity),identity))),
    inference(spr,[status(thm),theory(equality)],[298,1570]),
    [iquote('0:SpR:298.0,1570.0')] ).

cnf(2374,plain,
    equal(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(multiply(identity,u),multiply(multiply(identity,multiply(multiply(multiply(u,u),identity),identity)),identity)),identity)),multiply(multiply(u,identity),identity)),
    inference(spr,[status(thm),theory(equality)],[2341,129]),
    [iquote('0:SpR:2341.0,129.0')] ).

cnf(2387,plain,
    equal(multiply(multiply(identity,multiply(identity,u)),multiply(multiply(identity,multiply(u,identity)),identity)),multiply(identity,multiply(multiply(multiply(multiply(identity,u),multiply(identity,u)),identity),identity))),
    inference(spr,[status(thm),theory(equality)],[78,2341]),
    [iquote('0:SpR:78.0,2341.0')] ).

cnf(2405,plain,
    equal(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(multiply(u,identity),identity))),multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),multiply(u,identity)),identity)))),
    inference(rew,[status(thm),theory(equality)],[78,2387,1641]),
    [iquote('0:Rew:78.0,2387.0,78.0,2387.0,1641.0,2387.0')] ).

cnf(2408,plain,
    equal(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(multiply(identity,u),multiply(identity,multiply(multiply(multiply(multiply(u,u),identity),identity),identity))),identity)),multiply(multiply(u,identity),identity)),
    inference(rew,[status(thm),theory(equality)],[78,2374]),
    [iquote('0:Rew:78.0,2374.0')] ).

cnf(3380,plain,
    equal(multiply(multiply(u,multiply(multiply(u,u),multiply(multiply(v,v),multiply(multiply(v,identity),identity)))),multiply(multiply(multiply(multiply(v,identity),identity),multiply(multiply(v,identity),identity)),multiply(multiply(multiply(multiply(v,identity),identity),multiply(multiply(v,identity),identity)),multiply(multiply(multiply(v,identity),identity),multiply(multiply(v,identity),identity))))),multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(multiply(v,identity),identity),identity)),identity))),
    inference(spr,[status(thm),theory(equality)],[715,184]),
    [iquote('0:SpR:715.0,184.0')] ).

cnf(3499,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(identity,u))),multiply(identity,multiply(identity,multiply(multiply(u,identity),identity)))),identity)))),multiply(multiply(identity,multiply(identity,u)),multiply(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(identity,u))),multiply(identity,identity)))),
    inference(spr,[status(thm),theory(equality)],[419,869]),
    [iquote('0:SpR:419.0,869.0')] ).

cnf(3503,plain,
    equal(multiply(identity,multiply(multiply(identity,multiply(multiply(u,identity),identity)),multiply(multiply(identity,multiply(multiply(u,identity),identity)),multiply(identity,multiply(multiply(u,identity),identity))))),multiply(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(identity,u))),multiply(multiply(multiply(identity,multiply(identity,u)),multiply(identity,identity)),identity))),
    inference(spr,[status(thm),theory(equality)],[419,184]),
    [iquote('0:SpR:419.0,184.0')] ).

cnf(3576,plain,
    equal(multiply(identity,multiply(multiply(identity,multiply(multiply(u,identity),identity)),multiply(multiply(identity,multiply(multiply(u,identity),identity)),multiply(identity,multiply(multiply(u,identity),identity))))),multiply(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(identity,u))),multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))))),
    inference(rew,[status(thm),theory(equality)],[78,3503,2]),
    [iquote('0:Rew:78.0,3503.0,78.0,3503.0,78.0,3503.0,78.0,3503.0,2.0,3503.0')] ).

cnf(3577,plain,
    equal(multiply(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(identity,u))),multiply(identity,multiply(identity,multiply(multiply(u,identity),identity)))),multiply(identity,multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity))))),
    inference(rew,[status(thm),theory(equality)],[1894,3576]),
    [iquote('0:Rew:1894.0,3576.0')] ).

cnf(3578,plain,
    equal(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity))))),identity),
    inference(rew,[status(thm),theory(equality)],[3577,419]),
    [iquote('0:Rew:3577.0,419.0')] ).

cnf(3584,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(identity,u))),multiply(identity,multiply(identity,multiply(multiply(u,identity),identity)))),identity)))),multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(multiply(identity,multiply(u,identity)),multiply(identity,multiply(u,identity)))))),
    inference(rew,[status(thm),theory(equality)],[78,3499,1641,2]),
    [iquote('0:Rew:78.0,3499.0,1641.0,3499.0,2.0,3499.0')] ).

cnf(3585,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity)))),identity)))),multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(multiply(identity,multiply(u,identity)),multiply(identity,multiply(u,identity)))))),
    inference(rew,[status(thm),theory(equality)],[3577,3584]),
    [iquote('0:Rew:3577.0,3584.0')] ).

cnf(3586,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),multiply(u,identity)),multiply(multiply(multiply(u,identity),identity),identity))))))),multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(multiply(identity,multiply(u,identity)),multiply(identity,multiply(u,identity)))))),
    inference(rew,[status(thm),theory(equality)],[1215,3585,78]),
    [iquote('0:Rew:1215.0,3585.0,78.0,3585.0,78.0,3585.0')] ).

cnf(3587,plain,
    equal(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(multiply(identity,multiply(u,identity)),multiply(identity,multiply(u,identity))))),multiply(identity,multiply(multiply(identity,u),multiply(identity,multiply(multiply(u,identity),multiply(u,identity)))))),
    inference(rew,[status(thm),theory(equality)],[1895,3586]),
    [iquote('0:Rew:1895.0,3586.0')] ).

cnf(3656,plain,
    equal(multiply(multiply(identity,multiply(identity,multiply(identity,u))),multiply(identity,multiply(identity,multiply(multiply(identity,multiply(u,identity)),multiply(multiply(multiply(identity,multiply(u,identity)),multiply(identity,multiply(u,identity))),identity))))),identity),
    inference(spr,[status(thm),theory(equality)],[78,3578]),
    [iquote('0:SpR:78.0,3578.0')] ).

cnf(3662,plain,
    equal(multiply(multiply(identity,u),multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),identity),multiply(multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),identity),multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),identity)),identity))))),identity),
    inference(spr,[status(thm),theory(equality)],[35,3578]),
    [iquote('0:SpR:35.0,3578.0')] ).

cnf(3678,plain,
    equal(multiply(multiply(identity,multiply(identity,multiply(identity,u))),multiply(identity,multiply(identity,multiply(multiply(identity,multiply(u,identity)),multiply(identity,multiply(multiply(multiply(u,identity),identity),multiply(multiply(u,identity),identity))))))),identity),
    inference(rew,[status(thm),theory(equality)],[1641,3656]),
    [iquote('0:Rew:1641.0,3656.0')] ).

cnf(3686,plain,
    equal(multiply(multiply(identity,u),multiply(identity,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity))),multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(multiply(u,identity),identity),identity),identity)),multiply(identity,multiply(multiply(multiply(multiply(u,identity),identity),identity),identity)))))))),identity),
    inference(rew,[status(thm),theory(equality)],[78,3662,1641]),
    [iquote('0:Rew:78.0,3662.0,1641.0,3662.0,78.0,3662.0,78.0,3662.0')] ).

cnf(3687,plain,
    equal(multiply(multiply(identity,u),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(u,identity),identity),identity)),multiply(identity,multiply(multiply(multiply(multiply(multiply(u,identity),identity),identity),identity),multiply(multiply(multiply(multiply(u,identity),identity),identity),identity)))))))),identity),
    inference(rew,[status(thm),theory(equality)],[3587,3686]),
    [iquote('0:Rew:3587.0,3686.0')] ).

cnf(3828,plain,
    equal(multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(u,multiply(u,u))),identity),identity))),multiply(multiply(u,multiply(u,u)),multiply(u,multiply(u,u))))),identity),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(u,multiply(u,u))),identity),identity))),multiply(multiply(u,multiply(u,u)),multiply(u,multiply(u,u))))),identity)),identity))),multiply(multiply(identity,multiply(multiply(identity,identity),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,identity),multiply(identity,identity)),identity),identity))),u)))),multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(u,multiply(u,u))),identity),identity))),multiply(multiply(u,multiply(u,u)),multiply(u,multiply(u,u))))),identity),identity)))),
    inference(spr,[status(thm),theory(equality)],[964,2405]),
    [iquote('0:SpR:964.0,2405.0')] ).

cnf(3915,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(multiply(u,multiply(u,u)),multiply(multiply(u,multiply(u,u)),multiply(u,multiply(u,u)))),identity),identity),multiply(multiply(multiply(multiply(u,multiply(u,u)),multiply(multiply(u,multiply(u,u)),multiply(u,multiply(u,u)))),identity),identity))))),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,u)))),multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(u,multiply(u,u)),multiply(multiply(u,multiply(u,u)),multiply(u,multiply(u,u)))),identity),identity))))),
    inference(rew,[status(thm),theory(equality)],[1641,3828,2,78,35]),
    [iquote('0:Rew:1641.0,3828.0,2.0,3828.0,2.0,3828.0,2.0,3828.0,2.0,3828.0,2.0,3828.0,2.0,3828.0,78.0,3828.0,78.0,3828.0,35.0,3828.0,78.0,3828.0,78.0,3828.0')] ).

cnf(4054,plain,
    equal(multiply(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(identity,u))),multiply(multiply(multiply(identity,multiply(identity,u)),multiply(identity,identity)),identity)),multiply(identity,multiply(multiply(identity,multiply(u,identity)),multiply(identity,multiply(multiply(multiply(u,identity),identity),multiply(multiply(u,identity),identity)))))),
    inference(spr,[status(thm),theory(equality)],[1878,129]),
    [iquote('0:SpR:1878.0,129.0')] ).

cnf(4089,plain,
    equal(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(u,identity))))),multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(identity,identity),multiply(multiply(identity,u),identity)),identity)),multiply(identity,multiply(multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(identity,u),identity)),identity),identity),multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(identity,u),identity)),identity),identity)))))),identity),
    inference(spr,[status(thm),theory(equality)],[869,1878]),
    [iquote('0:SpR:869.0,1878.0')] ).

cnf(4114,plain,
    equal(multiply(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(identity,u))),multiply(identity,multiply(identity,multiply(multiply(u,identity),identity)))),multiply(identity,multiply(multiply(identity,multiply(u,identity)),multiply(identity,multiply(multiply(multiply(u,identity),identity),multiply(multiply(u,identity),identity)))))),
    inference(rew,[status(thm),theory(equality)],[78,4054,2]),
    [iquote('0:Rew:78.0,4054.0,78.0,4054.0,78.0,4054.0,78.0,4054.0,2.0,4054.0')] ).

cnf(4115,plain,
    equal(multiply(identity,multiply(multiply(identity,multiply(u,identity)),multiply(identity,multiply(multiply(multiply(u,identity),identity),multiply(multiply(u,identity),identity))))),multiply(identity,multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity))))),
    inference(rew,[status(thm),theory(equality)],[3577,4114]),
    [iquote('0:Rew:3577.0,4114.0')] ).

cnf(4129,plain,
    equal(multiply(multiply(identity,u),multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(u,identity),identity),identity),multiply(multiply(multiply(multiply(multiply(u,identity),identity),identity),multiply(multiply(multiply(u,identity),identity),identity)),identity))))))),identity),
    inference(rew,[status(thm),theory(equality)],[4115,3687]),
    [iquote('0:Rew:4115.0,3687.0')] ).

cnf(4133,plain,
    equal(multiply(multiply(identity,multiply(identity,multiply(identity,u))),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity)))))),identity),
    inference(rew,[status(thm),theory(equality)],[4115,3678]),
    [iquote('0:Rew:4115.0,3678.0')] ).

cnf(4153,plain,
    equal(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(u,identity))))),multiply(identity,multiply(u,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity))),multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity)))))))),identity),
    inference(rew,[status(thm),theory(equality)],[35,4089,78,2]),
    [iquote('0:Rew:35.0,4089.0,78.0,4089.0,78.0,4089.0,78.0,4089.0,78.0,4089.0,2.0,4089.0,78.0,4089.0')] ).

cnf(4154,plain,
    equal(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(u,identity))))),multiply(identity,multiply(u,multiply(multiply(u,u),identity)))),identity),
    inference(rew,[status(thm),theory(equality)],[1720,4153]),
    [iquote('0:Rew:1720.0,4153.0')] ).

cnf(4201,plain,
    equal(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(u,u),identity))))),multiply(identity,multiply(u,multiply(multiply(u,identity),identity)))),identity),
    inference(spr,[status(thm),theory(equality)],[18,4154]),
    [iquote('0:SpR:18.0,4154.0')] ).

cnf(4812,plain,
    equal(multiply(multiply(multiply(identity,multiply(identity,multiply(identity,u))),multiply(identity,multiply(identity,multiply(identity,u)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,u))),multiply(identity,identity)),identity)),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity)))))),
    inference(spr,[status(thm),theory(equality)],[4133,129]),
    [iquote('0:SpR:4133.0,129.0')] ).

cnf(4883,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity))))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,u))),multiply(identity,multiply(identity,multiply(identity,u)))),u)),
    inference(rew,[status(thm),theory(equality)],[35,4812,78,2]),
    [iquote('0:Rew:35.0,4812.0,78.0,4812.0,78.0,4812.0,78.0,4812.0,78.0,4812.0,78.0,4812.0,78.0,4812.0,2.0,4812.0')] ).

cnf(4895,plain,
    equal(multiply(multiply(identity,u),multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(u,identity),identity)))),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))))),multiply(multiply(u,identity),identity)))),identity),
    inference(rew,[status(thm),theory(equality)],[4883,4129]),
    [iquote('0:Rew:4883.0,4129.0')] ).

cnf(4899,plain,
    equal(multiply(multiply(identity,u),multiply(identity,multiply(multiply(u,u),multiply(multiply(u,identity),identity)))),identity),
    inference(rew,[status(thm),theory(equality)],[35,4895]),
    [iquote('0:Rew:35.0,4895.0')] ).

cnf(4961,plain,
    equal(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(multiply(multiply(identity,u),multiply(identity,identity)),identity)),multiply(identity,multiply(multiply(u,u),multiply(multiply(u,identity),identity)))),
    inference(spr,[status(thm),theory(equality)],[4899,129]),
    [iquote('0:SpR:4899.0,129.0')] ).

cnf(4963,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(u,u),multiply(multiply(u,identity),identity))),identity)))),multiply(multiply(identity,u),multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(identity,identity)))),
    inference(spr,[status(thm),theory(equality)],[4899,869]),
    [iquote('0:SpR:4899.0,869.0')] ).

cnf(4988,plain,
    equal(multiply(u,multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),multiply(identity,multiply(identity,multiply(multiply(u,identity),identity)))),multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),identity),identity)))),identity),
    inference(spr,[status(thm),theory(equality)],[35,4899]),
    [iquote('0:SpR:35.0,4899.0')] ).

cnf(5006,plain,
    equal(multiply(multiply(multiply(identity,u),multiply(identity,u)),multiply(identity,multiply(multiply(u,identity),identity))),multiply(identity,multiply(multiply(u,u),multiply(multiply(u,identity),identity)))),
    inference(rew,[status(thm),theory(equality)],[78,4961,2]),
    [iquote('0:Rew:78.0,4961.0,78.0,4961.0,2.0,4961.0')] ).

cnf(5007,plain,
    equal(multiply(identity,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity))),multiply(identity,multiply(multiply(u,u),multiply(multiply(u,identity),identity)))),
    inference(rew,[status(thm),theory(equality)],[1882,5006]),
    [iquote('0:Rew:1882.0,5006.0')] ).

cnf(5041,plain,
    equal(multiply(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(identity,u))),multiply(identity,multiply(identity,multiply(multiply(u,identity),identity)))),multiply(identity,multiply(identity,multiply(multiply(u,u),multiply(multiply(u,identity),identity))))),
    inference(rew,[status(thm),theory(equality)],[5007,3577]),
    [iquote('0:Rew:5007.0,3577.0')] ).

cnf(5060,plain,
    equal(multiply(multiply(identity,u),multiply(identity,multiply(multiply(u,identity),multiply(u,identity)))),multiply(identity,multiply(u,multiply(multiply(u,u),identity)))),
    inference(rew,[status(thm),theory(equality)],[1057,4963,78,1641,2]),
    [iquote('0:Rew:1057.0,4963.0,78.0,4963.0,1641.0,4963.0,2.0,4963.0')] ).

cnf(5075,plain,
    equal(multiply(multiply(identity,multiply(identity,u)),multiply(identity,multiply(multiply(identity,multiply(u,identity)),multiply(identity,multiply(u,identity))))),multiply(identity,multiply(identity,multiply(u,multiply(multiply(u,u),identity))))),
    inference(rew,[status(thm),theory(equality)],[5060,3587]),
    [iquote('0:Rew:5060.0,3587.0')] ).

cnf(5084,plain,
    equal(multiply(u,multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),multiply(identity,multiply(identity,multiply(multiply(u,identity),identity)))),multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(u,identity),identity),identity),identity)))))),identity),
    inference(rew,[status(thm),theory(equality)],[78,4988]),
    [iquote('0:Rew:78.0,4988.0,78.0,4988.0,78.0,4988.0,78.0,4988.0')] ).

cnf(5085,plain,
    equal(multiply(u,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(u,identity),identity),multiply(multiply(u,identity),identity)),multiply(multiply(multiply(multiply(u,identity),identity),identity),identity)))))),identity),
    inference(rew,[status(thm),theory(equality)],[5041,5084]),
    [iquote('0:Rew:5041.0,5084.0')] ).

cnf(5714,plain,
    equal(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),multiply(identity,multiply(identity,multiply(multiply(u,identity),identity)))),identity))),multiply(u,multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),identity),multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),identity))))),
    inference(spr,[status(thm),theory(equality)],[35,5060]),
    [iquote('0:SpR:35.0,5060.0')] ).

cnf(5738,plain,
    equal(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(u,identity),identity),identity)),multiply(identity,multiply(multiply(multiply(u,identity),identity),identity)))))),multiply(u,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity))),multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity))))))),
    inference(rew,[status(thm),theory(equality)],[78,5714,1641]),
    [iquote('0:Rew:78.0,5714.0,1641.0,5714.0,78.0,5714.0,78.0,5714.0')] ).

cnf(5739,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),multiply(u,identity)),multiply(multiply(multiply(u,identity),identity),identity))))),multiply(u,multiply(multiply(u,u),identity))),
    inference(rew,[status(thm),theory(equality)],[5007,5738,5075,1720]),
    [iquote('0:Rew:5007.0,5738.0,5075.0,5738.0,1720.0,5738.0')] ).

cnf(5742,plain,
    equal(multiply(u,multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity))),identity),
    inference(rew,[status(thm),theory(equality)],[5739,5085]),
    [iquote('0:Rew:5739.0,5085.0')] ).

cnf(6057,plain,
    equal(multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity)),multiply(multiply(u,u),multiply(multiply(u,multiply(identity,identity)),identity))),
    inference(spr,[status(thm),theory(equality)],[5742,129]),
    [iquote('0:SpR:5742.0,129.0')] ).

cnf(6135,plain,
    equal(multiply(multiply(u,identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity)),multiply(multiply(u,u),multiply(multiply(u,identity),identity))),
    inference(rew,[status(thm),theory(equality)],[2,6057]),
    [iquote('0:Rew:2.0,6057.0')] ).

cnf(6211,plain,
    equal(multiply(multiply(identity,multiply(identity,multiply(multiply(u,u),multiply(multiply(u,identity),identity)))),multiply(multiply(multiply(multiply(u,identity),multiply(u,identity)),identity),multiply(multiply(multiply(multiply(u,identity),multiply(u,identity)),identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity)))),multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity)))),
    inference(spr,[status(thm),theory(equality)],[6135,88]),
    [iquote('0:SpR:6135.0,88.0')] ).

cnf(6221,plain,
    equal(multiply(multiply(u,multiply(multiply(u,u),multiply(multiply(v,v),multiply(multiply(v,identity),identity)))),multiply(multiply(multiply(multiply(v,identity),multiply(v,identity)),identity),multiply(multiply(multiply(multiply(v,identity),multiply(v,identity)),identity),multiply(multiply(multiply(v,identity),multiply(v,identity)),identity)))),multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(v,identity),identity)),identity))),
    inference(spr,[status(thm),theory(equality)],[6135,184]),
    [iquote('0:SpR:6135.0,184.0')] ).

cnf(6601,plain,
    equal(multiply(multiply(u,multiply(u,u)),multiply(multiply(u,multiply(u,u)),multiply(u,multiply(u,u)))),multiply(identity,multiply(multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(identity,u))),identity),identity))),
    inference(spr,[status(thm),theory(equality)],[100,857]),
    [iquote('0:SpR:100.0,857.0')] ).

cnf(6689,plain,
    equal(multiply(multiply(u,multiply(u,u)),multiply(multiply(u,multiply(u,u)),multiply(u,multiply(u,u)))),multiply(identity,u)),
    inference(rew,[status(thm),theory(equality)],[35,6601,78,2]),
    [iquote('0:Rew:35.0,6601.0,78.0,6601.0,78.0,6601.0,78.0,6601.0,78.0,6601.0,78.0,6601.0,78.0,6601.0,2.0,6601.0,2.0,6601.0')] ).

cnf(6699,plain,
    equal(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,u)))),multiply(identity,multiply(identity,multiply(multiply(multiply(identity,u),identity),identity)))),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,u),identity),identity),multiply(multiply(multiply(identity,u),identity),identity)))))),
    inference(rew,[status(thm),theory(equality)],[6689,3915]),
    [iquote('0:Rew:6689.0,3915.0')] ).

cnf(6710,plain,
    equal(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),v)),multiply(u,multiply(identity,v))),
    inference(rew,[status(thm),theory(equality)],[6689,886]),
    [iquote('0:Rew:6689.0,886.0')] ).

cnf(6716,plain,
    equal(multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),multiply(v,w))),multiply(u,multiply(multiply(u,v),multiply(identity,w)))),
    inference(rew,[status(thm),theory(equality)],[6710,887]),
    [iquote('0:Rew:6710.0,887.0')] ).

cnf(6925,plain,
    equal(multiply(multiply(u,v),multiply(identity,multiply(multiply(v,v),multiply(multiply(v,multiply(w,identity)),identity)))),multiply(multiply(u,multiply(identity,multiply(identity,multiply(identity,multiply(w,identity))))),identity)),
    inference(rew,[status(thm),theory(equality)],[6710,2224]),
    [iquote('0:Rew:6710.0,2224.0')] ).

cnf(6928,plain,
    equal(multiply(u,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(u,identity),identity),identity),identity))))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(u,identity)))),multiply(u,identity)),identity)),
    inference(rew,[status(thm),theory(equality)],[6710,2083]),
    [iquote('0:Rew:6710.0,2083.0')] ).

cnf(7084,plain,
    equal(multiply(u,multiply(multiply(u,identity),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(v,identity),identity)))))),multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),v))),
    inference(rew,[status(thm),theory(equality)],[6710,917]),
    [iquote('0:Rew:6710.0,917.0')] ).

cnf(7086,plain,
    equal(multiply(multiply(u,identity),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity))))),multiply(multiply(u,u),identity)),
    inference(rew,[status(thm),theory(equality)],[6710,1720]),
    [iquote('0:Rew:6710.0,1720.0')] ).

cnf(7087,plain,
    equal(multiply(u,multiply(multiply(u,identity),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(v,identity),identity),identity)))))),multiply(u,multiply(multiply(u,v),identity))),
    inference(rew,[status(thm),theory(equality)],[6710,889]),
    [iquote('0:Rew:6710.0,889.0')] ).

cnf(7093,plain,
    equal(multiply(multiply(u,identity),multiply(u,identity)),multiply(multiply(u,u),identity)),
    inference(rew,[status(thm),theory(equality)],[35,7086]),
    [iquote('0:Rew:35.0,7086.0')] ).

cnf(7096,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(u,u),identity),identity))))),multiply(multiply(identity,u),multiply(identity,u))),
    inference(rew,[status(thm),theory(equality)],[7093,1646]),
    [iquote('0:Rew:7093.0,1646.0')] ).

cnf(7100,plain,
    equal(multiply(multiply(multiply(u,identity),identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity)),multiply(multiply(u,u),multiply(multiply(u,identity),identity))),
    inference(rew,[status(thm),theory(equality)],[7093,715]),
    [iquote('0:Rew:7093.0,715.0')] ).

cnf(7103,plain,
    equal(multiply(multiply(u,multiply(multiply(u,u),multiply(multiply(v,v),multiply(multiply(v,identity),identity)))),multiply(multiply(multiply(multiply(v,identity),multiply(v,identity)),identity),multiply(multiply(multiply(multiply(v,identity),multiply(v,identity)),multiply(multiply(v,identity),multiply(v,identity))),identity))),multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(v,identity),identity)),identity))),
    inference(rew,[status(thm),theory(equality)],[7093,6221]),
    [iquote('0:Rew:7093.0,6221.0')] ).

cnf(7157,plain,
    equal(multiply(multiply(identity,multiply(identity,multiply(multiply(u,u),multiply(multiply(u,identity),identity)))),multiply(multiply(multiply(multiply(u,u),identity),identity),multiply(multiply(multiply(multiply(u,u),identity),identity),multiply(multiply(multiply(u,u),identity),identity)))),multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity)))),
    inference(rew,[status(thm),theory(equality)],[7093,6211]),
    [iquote('0:Rew:7093.0,6211.0')] ).

cnf(7192,plain,
    equal(multiply(multiply(u,multiply(multiply(u,u),multiply(multiply(v,v),multiply(multiply(v,identity),identity)))),multiply(multiply(multiply(multiply(v,identity),multiply(v,identity)),identity),multiply(multiply(multiply(multiply(v,identity),multiply(v,identity)),identity),multiply(multiply(multiply(v,identity),multiply(v,identity)),identity)))),multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(multiply(v,identity),identity),identity)),identity))),
    inference(rew,[status(thm),theory(equality)],[7093,3380]),
    [iquote('0:Rew:7093.0,3380.0')] ).

cnf(7194,plain,
    equal(multiply(multiply(multiply(u,identity),identity),multiply(multiply(multiply(multiply(u,identity),multiply(u,identity)),identity),multiply(multiply(multiply(u,u),multiply(multiply(u,identity),identity)),identity))),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(u,identity),multiply(u,identity)),identity),identity))))),
    inference(rew,[status(thm),theory(equality)],[7093,1565]),
    [iquote('0:Rew:7093.0,1565.0')] ).

cnf(7197,plain,
    equal(multiply(multiply(identity,multiply(identity,multiply(multiply(u,u),multiply(multiply(u,identity),identity)))),multiply(multiply(multiply(multiply(u,identity),multiply(u,identity)),identity),multiply(multiply(multiply(multiply(u,identity),multiply(u,identity)),identity),multiply(multiply(multiply(u,identity),multiply(u,identity)),identity)))),multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(u,identity),identity),identity),identity)))),
    inference(rew,[status(thm),theory(equality)],[7093,1567]),
    [iquote('0:Rew:7093.0,1567.0')] ).

cnf(7204,plain,
    equal(multiply(multiply(identity,u),multiply(identity,u)),multiply(identity,multiply(u,u))),
    inference(rew,[status(thm),theory(equality)],[35,7096]),
    [iquote('0:Rew:35.0,7096.0')] ).

cnf(7321,plain,
    equal(multiply(multiply(identity,multiply(u,u)),multiply(multiply(multiply(identity,u),multiply(identity,multiply(multiply(multiply(multiply(u,u),identity),identity),identity))),identity)),multiply(multiply(u,identity),identity)),
    inference(rew,[status(thm),theory(equality)],[7204,2408]),
    [iquote('0:Rew:7204.0,2408.0')] ).

cnf(7355,plain,
    equal(multiply(multiply(multiply(u,identity),identity),multiply(multiply(multiply(u,u),identity),identity)),multiply(multiply(u,u),multiply(multiply(u,identity),identity))),
    inference(rew,[status(thm),theory(equality)],[7093,7100]),
    [iquote('0:Rew:7093.0,7100.0')] ).

cnf(7356,plain,
    equal(multiply(u,multiply(multiply(u,identity),multiply(v,identity))),multiply(u,multiply(multiply(u,v),identity))),
    inference(rew,[status(thm),theory(equality)],[35,7087]),
    [iquote('0:Rew:35.0,7087.0')] ).

cnf(7377,plain,
    equal(multiply(multiply(u,u),multiply(multiply(multiply(u,u),multiply(u,u)),v)),multiply(u,multiply(multiply(u,identity),v))),
    inference(rew,[status(thm),theory(equality)],[35,7084]),
    [iquote('0:Rew:35.0,7084.0')] ).

cnf(7378,plain,
    equal(multiply(u,multiply(multiply(u,identity),multiply(v,w))),multiply(u,multiply(multiply(u,v),multiply(identity,w)))),
    inference(rew,[status(thm),theory(equality)],[7377,6716]),
    [iquote('0:Rew:7377.0,6716.0')] ).

cnf(7381,plain,
    equal(multiply(u,multiply(multiply(u,multiply(identity,multiply(identity,multiply(identity,multiply(v,identity))))),identity)),multiply(u,multiply(multiply(u,identity),v))),
    inference(rew,[status(thm),theory(equality)],[7377,1232]),
    [iquote('0:Rew:7377.0,1232.0')] ).

cnf(7393,plain,
    equal(multiply(multiply(multiply(u,u),multiply(u,u)),multiply(multiply(multiply(u,u),v),identity)),multiply(multiply(u,multiply(multiply(u,identity),v)),identity)),
    inference(rew,[status(thm),theory(equality)],[7381,2227]),
    [iquote('0:Rew:7381.0,2227.0')] ).

cnf(7436,plain,
    equal(multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(u,identity)))),multiply(u,identity)),identity),multiply(u,multiply(multiply(u,identity),identity))),
    inference(rew,[status(thm),theory(equality)],[35,6928]),
    [iquote('0:Rew:35.0,6928.0')] ).

cnf(7618,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(u,identity),identity)),multiply(identity,multiply(multiply(u,identity),identity)))))),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,u)))),u)),
    inference(rew,[status(thm),theory(equality)],[35,6699,78]),
    [iquote('0:Rew:35.0,6699.0,78.0,6699.0,78.0,6699.0')] ).

cnf(7619,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(u,u),identity),identity))))),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,u)))),u)),
    inference(rew,[status(thm),theory(equality)],[7093,7618,7204]),
    [iquote('0:Rew:7093.0,7618.0,7093.0,7618.0,7204.0,7618.0')] ).

cnf(7620,plain,
    equal(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,u)))),u),multiply(identity,multiply(u,u))),
    inference(rew,[status(thm),theory(equality)],[35,7619]),
    [iquote('0:Rew:35.0,7619.0')] ).

cnf(7673,plain,
    equal(multiply(multiply(multiply(u,identity),identity),multiply(multiply(multiply(multiply(u,identity),multiply(u,identity)),identity),multiply(multiply(multiply(u,u),multiply(multiply(u,identity),identity)),identity))),multiply(multiply(u,identity),multiply(u,identity))),
    inference(rew,[status(thm),theory(equality)],[35,7194]),
    [iquote('0:Rew:35.0,7194.0')] ).

cnf(7674,plain,
    equal(multiply(multiply(multiply(u,identity),identity),multiply(multiply(multiply(multiply(u,u),identity),identity),multiply(multiply(multiply(u,u),multiply(multiply(u,identity),identity)),identity))),multiply(multiply(u,u),identity)),
    inference(rew,[status(thm),theory(equality)],[7093,7673]),
    [iquote('0:Rew:7093.0,7673.0')] ).

cnf(7746,plain,
    equal(multiply(multiply(identity,multiply(identity,multiply(multiply(u,u),multiply(multiply(u,identity),identity)))),multiply(multiply(u,multiply(multiply(u,identity),identity)),identity)),multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity)))),
    inference(rew,[status(thm),theory(equality)],[7393,7157,7355,7093]),
    [iquote('0:Rew:7393.0,7157.0,7355.0,7157.0,7093.0,7157.0,7093.0,7157.0')] ).

cnf(7842,plain,
    equal(multiply(multiply(u,multiply(multiply(u,u),multiply(multiply(v,v),multiply(multiply(v,identity),identity)))),multiply(multiply(v,multiply(multiply(v,identity),identity)),identity)),multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(v,identity),identity)),identity))),
    inference(rew,[status(thm),theory(equality)],[7393,7103,7355,7093]),
    [iquote('0:Rew:7393.0,7103.0,7355.0,7103.0,7093.0,7103.0,7093.0,7103.0')] ).

cnf(7847,plain,
    equal(multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(u,identity),identity),identity),identity))),multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity)))),
    inference(rew,[status(thm),theory(equality)],[7746,7197,7393,7355,7093]),
    [iquote('0:Rew:7746.0,7197.0,7393.0,7197.0,7355.0,7197.0,7093.0,7197.0,7093.0,7197.0,7093.0,7197.0')] ).

cnf(7916,plain,
    equal(multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(multiply(v,identity),identity),identity)),identity)),multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(v,identity),identity)),identity))),
    inference(rew,[status(thm),theory(equality)],[7842,7192,7393,7355,7093]),
    [iquote('0:Rew:7842.0,7192.0,7393.0,7192.0,7355.0,7192.0,7093.0,7192.0,7093.0,7192.0,7093.0,7192.0')] ).

cnf(8499,plain,
    equal(multiply(multiply(multiply(u,identity),multiply(multiply(multiply(u,u),identity),v)),identity),multiply(multiply(multiply(u,u),identity),multiply(multiply(multiply(u,identity),v),identity))),
    inference(spr,[status(thm),theory(equality)],[7093,1215]),
    [iquote('0:SpR:7093.0,1215.0')] ).

cnf(8724,plain,
    equal(multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(u,multiply(multiply(u,v),identity)),identity)),identity)),multiply(multiply(u,identity),multiply(v,identity))),
    inference(spr,[status(thm),theory(equality)],[7356,129]),
    [iquote('0:SpR:7356.0,129.0')] ).

cnf(8774,plain,
    equal(multiply(multiply(u,identity),multiply(v,identity)),multiply(multiply(u,v),identity)),
    inference(rew,[status(thm),theory(equality)],[129,8724]),
    [iquote('0:Rew:129.0,8724.0')] ).

cnf(8788,plain,
    equal(multiply(multiply(multiply(u,identity),multiply(multiply(multiply(u,u),identity),v)),identity),multiply(multiply(multiply(u,u),multiply(multiply(u,identity),v)),identity)),
    inference(rew,[status(thm),theory(equality)],[8774,8499]),
    [iquote('0:Rew:8774.0,8499.0')] ).

cnf(8836,plain,
    equal(multiply(multiply(multiply(u,identity),identity),multiply(multiply(multiply(multiply(u,u),identity),multiply(multiply(u,u),multiply(multiply(u,identity),identity))),identity)),multiply(multiply(u,u),identity)),
    inference(rew,[status(thm),theory(equality)],[8774,7674]),
    [iquote('0:Rew:8774.0,7674.0')] ).

cnf(8855,plain,
    equal(multiply(multiply(multiply(u,identity),multiply(multiply(u,u),identity)),identity),multiply(multiply(u,u),multiply(multiply(u,identity),identity))),
    inference(rew,[status(thm),theory(equality)],[8774,7355]),
    [iquote('0:Rew:8774.0,7355.0')] ).

cnf(8897,plain,
    equal(multiply(multiply(multiply(u,multiply(u,u)),identity),identity),multiply(multiply(u,u),multiply(multiply(u,identity),identity))),
    inference(rew,[status(thm),theory(equality)],[8774,8855]),
    [iquote('0:Rew:8774.0,8855.0')] ).

cnf(8913,plain,
    equal(multiply(multiply(multiply(u,u),multiply(multiply(u,identity),multiply(multiply(u,u),multiply(multiply(u,identity),identity)))),identity),multiply(multiply(u,u),identity)),
    inference(rew,[status(thm),theory(equality)],[8788,8836,8774]),
    [iquote('0:Rew:8788.0,8836.0,8774.0,8836.0')] ).

cnf(9041,plain,
    equal(multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(u,multiply(multiply(u,identity),multiply(v,w))),identity)),identity)),multiply(multiply(u,v),multiply(identity,w))),
    inference(spr,[status(thm),theory(equality)],[7378,129]),
    [iquote('0:SpR:7378.0,129.0')] ).

cnf(9149,plain,
    equal(multiply(multiply(u,identity),multiply(v,w)),multiply(multiply(u,v),multiply(identity,w))),
    inference(rew,[status(thm),theory(equality)],[129,9041]),
    [iquote('0:Rew:129.0,9041.0')] ).

cnf(9151,plain,
    equal(multiply(multiply(identity,identity),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(u,u),identity)))),multiply(u,multiply(multiply(u,identity),identity)))),identity),
    inference(rew,[status(thm),theory(equality)],[9149,4201]),
    [iquote('0:Rew:9149.0,4201.0')] ).

cnf(9387,plain,
    equal(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(u,u),identity)))),multiply(u,multiply(multiply(u,identity),identity)))),identity),
    inference(rew,[status(thm),theory(equality)],[2,9151]),
    [iquote('0:Rew:2.0,9151.0')] ).

cnf(10013,plain,
    equal(multiply(multiply(u,identity),multiply(multiply(v,v),multiply(multiply(v,w),identity))),multiply(multiply(u,multiply(v,multiply(multiply(v,v),w))),identity)),
    inference(spr,[status(thm),theory(equality)],[1215,8774]),
    [iquote('0:SpR:1215.0,8774.0')] ).

cnf(10121,plain,
    equal(multiply(multiply(multiply(u,u),multiply(multiply(u,multiply(u,multiply(multiply(u,u),identity))),identity)),identity),multiply(multiply(u,u),identity)),
    inference(rew,[status(thm),theory(equality)],[10013,8913]),
    [iquote('0:Rew:10013.0,8913.0')] ).

cnf(10253,plain,
    equal(multiply(multiply(u,v),multiply(identity,multiply(multiply(v,v),multiply(multiply(v,w),identity)))),multiply(multiply(u,identity),multiply(identity,multiply(identity,multiply(identity,multiply(w,identity)))))),
    inference(spr,[status(thm),theory(equality)],[869,9149]),
    [iquote('0:SpR:869.0,9149.0')] ).

cnf(10258,plain,
    equal(multiply(multiply(identity,u),multiply(identity,v)),multiply(identity,multiply(u,v))),
    inference(spr,[status(thm),theory(equality)],[2,9149]),
    [iquote('0:SpR:2.0,9149.0')] ).

cnf(10291,plain,
    equal(multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,u)))),identity),multiply(u,v)),multiply(multiply(identity,multiply(u,u)),multiply(identity,v))),
    inference(spr,[status(thm),theory(equality)],[7620,9149]),
    [iquote('0:SpR:7620.0,9149.0')] ).

cnf(10326,plain,
    equal(multiply(multiply(identity,multiply(u,u)),multiply(multiply(identity,multiply(u,multiply(multiply(multiply(multiply(u,u),identity),identity),identity))),identity)),multiply(multiply(u,identity),identity)),
    inference(rew,[status(thm),theory(equality)],[10258,7321]),
    [iquote('0:Rew:10258.0,7321.0')] ).

cnf(10365,plain,
    equal(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(u,identity))))),multiply(u,v)),multiply(identity,multiply(multiply(u,u),v))),
    inference(rew,[status(thm),theory(equality)],[78,10291,2,9149]),
    [iquote('0:Rew:78.0,10291.0,78.0,10291.0,78.0,10291.0,78.0,10291.0,2.0,10291.0,9149.0,10291.0')] ).

cnf(10405,plain,
    equal(multiply(identity,multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(multiply(multiply(u,u),identity),identity),identity)),identity))),multiply(multiply(u,identity),identity)),
    inference(rew,[status(thm),theory(equality)],[2,10326,9149,78]),
    [iquote('0:Rew:2.0,10326.0,9149.0,10326.0,78.0,10326.0')] ).

cnf(10406,plain,
    equal(multiply(identity,multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(multiply(u,u),identity),identity)),identity))),multiply(multiply(u,identity),identity)),
    inference(rew,[status(thm),theory(equality)],[7916,10405]),
    [iquote('0:Rew:7916.0,10405.0')] ).

cnf(10422,plain,
    equal(multiply(multiply(u,identity),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(v,identity),identity))))),multiply(multiply(u,multiply(identity,multiply(identity,multiply(identity,multiply(v,identity))))),identity)),
    inference(rew,[status(thm),theory(equality)],[10253,6925]),
    [iquote('0:Rew:10253.0,6925.0')] ).

cnf(10434,plain,
    equal(multiply(multiply(u,multiply(identity,multiply(identity,multiply(identity,multiply(v,identity))))),identity),multiply(multiply(u,identity),v)),
    inference(rew,[status(thm),theory(equality)],[35,10422]),
    [iquote('0:Rew:35.0,10422.0')] ).

cnf(11153,plain,
    equal(multiply(multiply(identity,multiply(u,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))),multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))))))),multiply(identity,multiply(identity,multiply(multiply(u,identity),identity)))),multiply(identity,multiply(multiply(identity,identity),identity))),
    inference(spr,[status(thm),theory(equality)],[6710,857]),
    [iquote('0:SpR:6710.0,857.0')] ).

cnf(11260,plain,
    equal(multiply(identity,multiply(multiply(u,identity),multiply(multiply(u,u),multiply(multiply(u,identity),identity)))),identity),
    inference(rew,[status(thm),theory(equality)],[2,11153,9149,35,8774]),
    [iquote('0:Rew:2.0,11153.0,9149.0,11153.0,9149.0,11153.0,35.0,11153.0,2.0,11153.0,8774.0,11153.0,8774.0,11153.0,9149.0,11153.0,9149.0,11153.0,2.0,11153.0,2.0,11153.0,2.0,11153.0')] ).

cnf(11261,plain,
    equal(multiply(identity,multiply(multiply(u,multiply(u,multiply(multiply(u,u),identity))),identity)),identity),
    inference(rew,[status(thm),theory(equality)],[10013,11260]),
    [iquote('0:Rew:10013.0,11260.0')] ).

cnf(11293,plain,
    equal(multiply(multiply(u,multiply(u,multiply(multiply(u,u),identity))),identity),multiply(multiply(identity,identity),multiply(multiply(identity,multiply(identity,identity)),identity))),
    inference(spr,[status(thm),theory(equality)],[11261,129]),
    [iquote('0:SpR:11261.0,129.0')] ).

cnf(11353,plain,
    equal(multiply(multiply(u,multiply(u,multiply(multiply(u,u),identity))),identity),identity),
    inference(rew,[status(thm),theory(equality)],[2,11293]),
    [iquote('0:Rew:2.0,11293.0,2.0,11293.0,2.0,11293.0,2.0,11293.0')] ).

cnf(11357,plain,
    equal(multiply(multiply(multiply(u,u),identity),identity),multiply(multiply(u,u),identity)),
    inference(rew,[status(thm),theory(equality)],[11353,10121]),
    [iquote('0:Rew:11353.0,10121.0')] ).

cnf(11419,plain,
    equal(multiply(identity,multiply(multiply(u,u),multiply(multiply(u,multiply(multiply(u,u),identity)),identity))),multiply(multiply(u,identity),identity)),
    inference(rew,[status(thm),theory(equality)],[11357,10406]),
    [iquote('0:Rew:11357.0,10406.0')] ).

cnf(11426,plain,
    equal(multiply(multiply(u,identity),identity),multiply(identity,u)),
    inference(rew,[status(thm),theory(equality)],[298,11419,1215]),
    [iquote('0:Rew:298.0,11419.0,1215.0,11419.0')] ).

cnf(11428,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(identity,u)))),u),
    inference(rew,[status(thm),theory(equality)],[11426,35]),
    [iquote('0:Rew:11426.0,35.0')] ).

cnf(11432,plain,
    equal(multiply(multiply(u,u),multiply(multiply(u,u),multiply(identity,u))),u),
    inference(rew,[status(thm),theory(equality)],[11426,298]),
    [iquote('0:Rew:11426.0,298.0')] ).

cnf(11450,plain,
    equal(multiply(multiply(u,u),multiply(multiply(u,identity),identity)),multiply(identity,multiply(u,multiply(u,u)))),
    inference(rew,[status(thm),theory(equality)],[11426,8897]),
    [iquote('0:Rew:11426.0,8897.0')] ).

cnf(11471,plain,
    equal(multiply(identity,multiply(identity,multiply(multiply(multiply(u,identity),identity),identity))),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(u,identity),identity))))),
    inference(rew,[status(thm),theory(equality)],[11426,7847]),
    [iquote('0:Rew:11426.0,7847.0')] ).

cnf(11480,plain,
    equal(multiply(multiply(u,u),identity),multiply(identity,multiply(u,u))),
    inference(rew,[status(thm),theory(equality)],[11426,11357]),
    [iquote('0:Rew:11426.0,11357.0')] ).

cnf(11576,plain,
    equal(multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(u,identity)))),multiply(u,identity)),identity),multiply(u,multiply(identity,u))),
    inference(rew,[status(thm),theory(equality)],[11426,7436]),
    [iquote('0:Rew:11426.0,7436.0')] ).

cnf(11593,plain,
    equal(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(u,u),identity)))),multiply(u,multiply(identity,u)))),identity),
    inference(rew,[status(thm),theory(equality)],[11426,9387]),
    [iquote('0:Rew:11426.0,9387.0')] ).

cnf(11664,plain,
    equal(multiply(identity,multiply(u,u)),multiply(u,u)),
    inference(rew,[status(thm),theory(equality)],[11428,7620]),
    [iquote('0:Rew:11428.0,7620.0')] ).

cnf(11676,plain,
    equal(multiply(multiply(u,identity),multiply(u,v)),multiply(identity,multiply(multiply(u,u),v))),
    inference(rew,[status(thm),theory(equality)],[11428,10365]),
    [iquote('0:Rew:11428.0,10365.0')] ).

cnf(11718,plain,
    equal(multiply(multiply(u,u),identity),multiply(u,u)),
    inference(rew,[status(thm),theory(equality)],[11664,11480]),
    [iquote('0:Rew:11664.0,11480.0')] ).

cnf(11801,plain,
    equal(multiply(multiply(u,u),multiply(identity,u)),multiply(identity,multiply(u,multiply(u,u)))),
    inference(rew,[status(thm),theory(equality)],[11426,11450]),
    [iquote('0:Rew:11426.0,11450.0')] ).

cnf(11802,plain,
    equal(multiply(multiply(u,u),multiply(identity,multiply(u,multiply(u,u)))),u),
    inference(rew,[status(thm),theory(equality)],[11801,11432]),
    [iquote('0:Rew:11801.0,11432.0')] ).

cnf(11812,plain,
    equal(multiply(identity,multiply(multiply(u,u),multiply(u,multiply(identity,u)))),identity),
    inference(rew,[status(thm),theory(equality)],[11664,11593,11718]),
    [iquote('0:Rew:11664.0,11593.0,11664.0,11593.0,11664.0,11593.0,11718.0,11593.0')] ).

cnf(11823,plain,
    equal(multiply(identity,multiply(identity,multiply(multiply(identity,u),identity))),u),
    inference(rew,[status(thm),theory(equality)],[11428,11471,11426]),
    [iquote('0:Rew:11428.0,11471.0,11426.0,11471.0')] ).

cnf(11824,plain,
    equal(multiply(identity,multiply(identity,multiply(identity,multiply(u,identity)))),u),
    inference(rew,[status(thm),theory(equality)],[78,11823]),
    [iquote('0:Rew:78.0,11823.0')] ).

cnf(11829,plain,
    equal(multiply(multiply(u,multiply(u,identity)),identity),multiply(u,multiply(identity,u))),
    inference(rew,[status(thm),theory(equality)],[11824,11576]),
    [iquote('0:Rew:11824.0,11576.0')] ).

cnf(11842,plain,
    equal(multiply(multiply(u,v),identity),multiply(multiply(u,identity),v)),
    inference(rew,[status(thm),theory(equality)],[11824,10434]),
    [iquote('0:Rew:11824.0,10434.0')] ).

cnf(11943,plain,
    equal(multiply(u,multiply(identity,u)),multiply(u,u)),
    inference(rew,[status(thm),theory(equality)],[11664,11829,11718,11676,11842]),
    [iquote('0:Rew:11664.0,11829.0,11718.0,11829.0,11676.0,11829.0,11842.0,11829.0')] ).

cnf(11944,plain,
    equal(multiply(identity,multiply(multiply(u,u),multiply(u,u))),identity),
    inference(rew,[status(thm),theory(equality)],[11943,11812]),
    [iquote('0:Rew:11943.0,11812.0')] ).

cnf(11945,plain,
    equal(multiply(multiply(u,u),multiply(u,u)),identity),
    inference(rew,[status(thm),theory(equality)],[11664,11944]),
    [iquote('0:Rew:11664.0,11944.0')] ).

cnf(11951,plain,
    equal(multiply(multiply(u,u),multiply(identity,v)),multiply(u,multiply(multiply(u,identity),v))),
    inference(rew,[status(thm),theory(equality)],[11945,7377]),
    [iquote('0:Rew:11945.0,7377.0')] ).

cnf(11961,plain,
    equal(multiply(u,multiply(multiply(u,identity),multiply(u,multiply(u,u)))),u),
    inference(rew,[status(thm),theory(equality)],[11951,11802]),
    [iquote('0:Rew:11951.0,11802.0')] ).

cnf(11963,plain,
    equal(multiply(u,multiply(identity,identity)),u),
    inference(rew,[status(thm),theory(equality)],[11945,11961,11676]),
    [iquote('0:Rew:11945.0,11961.0,11676.0,11961.0')] ).

cnf(11964,plain,
    equal(multiply(u,identity),u),
    inference(rew,[status(thm),theory(equality)],[2,11963]),
    [iquote('0:Rew:2.0,11963.0')] ).

cnf(11965,plain,
    $false,
    inference(unc,[status(thm)],[11964,3]),
    [iquote('0:UnC:11964.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP121-1 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n014.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Tue Jun 14 09:32:51 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 41.13/41.39  
% 41.13/41.39  SPASS V 3.9 
% 41.13/41.39  SPASS beiseite: Proof found.
% 41.13/41.39  % SZS status Theorem
% 41.13/41.39  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 41.13/41.39  SPASS derived 6376 clauses, backtracked 0 clauses, performed 0 splits and kept 2593 clauses.
% 41.13/41.39  SPASS allocated 127429 KBytes.
% 41.13/41.39  SPASS spent	0:0:41.02 on the problem.
% 41.13/41.39  		0:00:00.03 for the input.
% 41.13/41.39  		0:00:00.00 for the FLOTTER CNF translation.
% 41.13/41.39  		0:00:00.11 for inferences.
% 41.13/41.39  		0:00:00.00 for the backtracking.
% 41.13/41.39  		0:0:40.85 for the reduction.
% 41.13/41.39  
% 41.13/41.39  
% 41.13/41.39  Here is a proof with depth 14, length 268 :
% 41.13/41.39  % SZS output start Refutation
% See solution above
% 41.51/41.76  Formulae used in the proof : single_axiom single_axiom2 prove_order3
% 41.51/41.76  
%------------------------------------------------------------------------------