%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP121-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:27:24 AM UTC 2026
% Result : Unsatisfiable 2.45s 0.72s
% Output : CNFRefutation 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 107
% Number of leaves : 3
% Syntax : Number of formulae : 353 ( 353 unt; 0 def)
% Number of atoms : 353 ( 352 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 481 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,multiply(multiply(VAR_0,multiply(multiply(VAR_0,VAR_0),multiply(VAR_1,VAR_2))),multiply(VAR_2,multiply(VAR_2,VAR_2)))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(B,C))),multiply(C,multiply(C,C)))) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(single_axiom2,axiom,
multiply(identity,identity) = identity,
file('theBenchmark.p',single_axiom2) ).
cnf(c_2,plain,
multiply(identity,identity) = identity,
inference(clausify,[status(thm)],[single_axiom2]) ).
fof(prove_order3,axiom,
multiply(a,identity) != a,
file('theBenchmark.p',prove_order3) ).
cnf(c_3,plain,
multiply(a,identity) != a,
inference(clausify,[status(thm)],[prove_order3]) ).
cnf(c_4,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(A,B))),multiply(B,multiply(B,B)))) = A,
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_273,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(B,identity))),multiply(identity,identity))) = B,
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_6,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(B,identity))),identity)) = B,
inference(paramod,[status(thm)],[c_2,c_273]) ).
cnf(c_274,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(A,identity))),multiply(identity,identity))) = A,
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_7,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(A,identity))),identity)) = A,
inference(paramod,[status(thm)],[c_2,c_274]) ).
cnf(c_275,plain,
multiply(A,multiply(multiply(A,B),multiply(identity,multiply(identity,identity)))) = multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(B,identity))),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_276,plain,
multiply(A,multiply(multiply(A,B),multiply(identity,identity))) = multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(B,identity))),
inference(paramod,[status(thm)],[c_2,c_275]) ).
cnf(c_277,plain,
multiply(A,multiply(multiply(A,B),identity)) = multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(B,identity))),
inference(paramod,[status(thm)],[c_2,c_276]) ).
cnf(c_9,plain,
multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(B,identity))) = multiply(A,multiply(multiply(A,B),identity)),
inference(copy,[status(thm)],[c_277]) ).
cnf(c_278,plain,
multiply(identity,multiply(multiply(identity,A),multiply(identity,multiply(identity,identity)))) = multiply(identity,multiply(multiply(identity,identity),multiply(A,identity))),
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_279,plain,
multiply(identity,multiply(multiply(identity,A),multiply(identity,identity))) = multiply(identity,multiply(multiply(identity,identity),multiply(A,identity))),
inference(paramod,[status(thm)],[c_2,c_278]) ).
cnf(c_280,plain,
multiply(identity,multiply(multiply(identity,A),identity)) = multiply(identity,multiply(multiply(identity,identity),multiply(A,identity))),
inference(paramod,[status(thm)],[c_2,c_279]) ).
cnf(c_10,plain,
multiply(identity,multiply(multiply(identity,A),identity)) = multiply(identity,multiply(identity,multiply(A,identity))),
inference(paramod,[status(thm)],[c_2,c_280]) ).
cnf(c_281,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(A,identity)),identity))) = A,
inference(paramod,[status(thm)],[c_10,c_7]) ).
cnf(c_11,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),identity)))) = A,
inference(paramod,[status(thm)],[c_10,c_281]) ).
cnf(c_282,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(A,identity))),identity)) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,A),identity),identity))),
inference(paramod,[status(thm)],[c_10,c_10]) ).
cnf(c_283,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(A,identity)),identity))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,A),identity),identity))),
inference(paramod,[status(thm)],[c_10,c_282]) ).
cnf(c_284,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),identity)))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,A),identity),identity))),
inference(paramod,[status(thm)],[c_10,c_283]) ).
cnf(c_285,plain,
A = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,A),identity),identity))),
inference(paramod,[status(thm)],[c_11,c_284]) ).
cnf(c_13,plain,
multiply(identity,multiply(identity,multiply(multiply(multiply(identity,A),identity),identity))) = A,
inference(copy,[status(thm)],[c_285]) ).
cnf(c_286,plain,
multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))) = multiply(multiply(identity,multiply(multiply(identity,identity),multiply(A,B))),multiply(B,multiply(B,B))),
inference(paramod,[status(thm)],[c_1,c_13]) ).
cnf(c_287,plain,
multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))) = multiply(multiply(identity,multiply(identity,multiply(A,B))),multiply(B,multiply(B,B))),
inference(paramod,[status(thm)],[c_2,c_286]) ).
cnf(c_14,plain,
multiply(multiply(identity,multiply(identity,multiply(A,B))),multiply(B,multiply(B,B))) = multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))),
inference(copy,[status(thm)],[c_287]) ).
cnf(c_288,plain,
multiply(identity,multiply(A,multiply(identity,multiply(identity,identity)))) = multiply(multiply(identity,A),identity),
inference(paramod,[status(thm)],[c_13,c_4]) ).
cnf(c_289,plain,
multiply(identity,multiply(A,multiply(identity,identity))) = multiply(multiply(identity,A),identity),
inference(paramod,[status(thm)],[c_2,c_288]) ).
cnf(c_290,plain,
multiply(identity,multiply(A,identity)) = multiply(multiply(identity,A),identity),
inference(paramod,[status(thm)],[c_2,c_289]) ).
cnf(c_15,plain,
multiply(multiply(identity,A),identity) = multiply(identity,multiply(A,identity)),
inference(copy,[status(thm)],[c_290]) ).
cnf(c_291,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(identity,multiply(B,identity)))),multiply(identity,multiply(identity,identity)))) = multiply(identity,B),
inference(paramod,[status(thm)],[c_15,c_1]) ).
cnf(c_292,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(identity,multiply(B,identity)))),multiply(identity,identity))) = multiply(identity,B),
inference(paramod,[status(thm)],[c_2,c_291]) ).
cnf(c_16,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(identity,multiply(B,identity)))),identity)) = multiply(identity,B),
inference(paramod,[status(thm)],[c_2,c_292]) ).
cnf(c_293,plain,
multiply(multiply(A,A),multiply(multiply(A,multiply(multiply(A,B),identity)),multiply(identity,multiply(identity,identity)))) = B,
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_294,plain,
multiply(multiply(A,A),multiply(multiply(A,multiply(multiply(A,B),identity)),multiply(identity,identity))) = B,
inference(paramod,[status(thm)],[c_2,c_293]) ).
cnf(c_20,plain,
multiply(multiply(A,A),multiply(multiply(A,multiply(multiply(A,B),identity)),identity)) = B,
inference(paramod,[status(thm)],[c_2,c_294]) ).
cnf(c_295,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(A,multiply(A,A))) = multiply(identity,multiply(identity,multiply(identity,identity))),
inference(paramod,[status(thm)],[c_2,c_14]) ).
cnf(c_296,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(A,multiply(A,A))) = multiply(identity,multiply(identity,identity)),
inference(paramod,[status(thm)],[c_2,c_295]) ).
cnf(c_297,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(A,multiply(A,A))) = multiply(identity,identity),
inference(paramod,[status(thm)],[c_2,c_296]) ).
cnf(c_24,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(A,multiply(A,A))) = identity,
inference(paramod,[status(thm)],[c_2,c_297]) ).
cnf(c_298,plain,
multiply(A,multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(A,identity),identity),multiply(multiply(A,identity),identity)))) = multiply(identity,multiply(identity,multiply(multiply(identity,identity),identity))),
inference(paramod,[status(thm)],[c_11,c_14]) ).
cnf(c_299,plain,
multiply(A,multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(A,identity),identity),multiply(multiply(A,identity),identity)))) = multiply(identity,multiply(identity,multiply(identity,identity))),
inference(paramod,[status(thm)],[c_2,c_298]) ).
cnf(c_300,plain,
multiply(A,multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(A,identity),identity),multiply(multiply(A,identity),identity)))) = multiply(identity,multiply(identity,identity)),
inference(paramod,[status(thm)],[c_2,c_299]) ).
cnf(c_301,plain,
multiply(A,multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(A,identity),identity),multiply(multiply(A,identity),identity)))) = multiply(identity,identity),
inference(paramod,[status(thm)],[c_2,c_300]) ).
cnf(c_25,plain,
multiply(A,multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(A,identity),identity),multiply(multiply(A,identity),identity)))) = identity,
inference(paramod,[status(thm)],[c_2,c_301]) ).
cnf(c_302,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(identity,A),B))),multiply(B,multiply(B,B))) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(A,identity)),identity))),
inference(paramod,[status(thm)],[c_15,c_14]) ).
cnf(c_303,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(identity,A),B))),multiply(B,multiply(B,B))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),identity)))),
inference(paramod,[status(thm)],[c_15,c_302]) ).
cnf(c_26,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(identity,A),B))),multiply(B,multiply(B,B))) = A,
inference(paramod,[status(thm)],[c_11,c_303]) ).
cnf(c_304,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),B)),identity)) = multiply(identity,multiply(identity,multiply(multiply(identity,identity),multiply(B,identity)))),
inference(paramod,[status(thm)],[c_6,c_16]) ).
cnf(c_27,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),B)),identity)) = multiply(identity,multiply(identity,multiply(identity,multiply(B,identity)))),
inference(paramod,[status(thm)],[c_2,c_304]) ).
cnf(c_305,plain,
multiply(multiply(identity,multiply(identity,identity)),multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),identity),identity))),
inference(paramod,[status(thm)],[c_24,c_14]) ).
cnf(c_306,plain,
multiply(multiply(identity,identity),multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),identity),identity))),
inference(paramod,[status(thm)],[c_2,c_305]) ).
cnf(c_307,plain,
multiply(identity,multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),identity),identity))),
inference(paramod,[status(thm)],[c_2,c_306]) ).
cnf(c_308,plain,
multiply(identity,multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))))) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,A)),identity)),identity))),
inference(paramod,[status(thm)],[c_15,c_307]) ).
cnf(c_309,plain,
multiply(identity,multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))))) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(identity,A),identity))),identity))),
inference(paramod,[status(thm)],[c_15,c_308]) ).
cnf(c_310,plain,
multiply(identity,multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))))) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,identity)))),identity))),
inference(paramod,[status(thm)],[c_15,c_309]) ).
cnf(c_311,plain,
multiply(identity,multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(A,identity))),identity)))),
inference(paramod,[status(thm)],[c_15,c_310]) ).
cnf(c_312,plain,
multiply(identity,multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))))) = multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(A,identity)),identity))))),
inference(paramod,[status(thm)],[c_15,c_311]) ).
cnf(c_313,plain,
multiply(identity,multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))))) = multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),identity)))))),
inference(paramod,[status(thm)],[c_15,c_312]) ).
cnf(c_28,plain,
multiply(identity,multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))))) = multiply(identity,multiply(identity,A)),
inference(paramod,[status(thm)],[c_11,c_313]) ).
cnf(c_314,plain,
multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,identity)),identity)) = multiply(A,multiply(A,A)),
inference(paramod,[status(thm)],[c_24,c_20]) ).
cnf(c_315,plain,
multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),identity),identity)) = multiply(A,multiply(A,A)),
inference(paramod,[status(thm)],[c_2,c_314]) ).
cnf(c_316,plain,
multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,A)),identity)),identity)) = multiply(A,multiply(A,A)),
inference(paramod,[status(thm)],[c_15,c_315]) ).
cnf(c_317,plain,
multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),multiply(multiply(identity,multiply(identity,multiply(multiply(identity,A),identity))),identity)) = multiply(A,multiply(A,A)),
inference(paramod,[status(thm)],[c_15,c_316]) ).
cnf(c_318,plain,
multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,identity)))),identity)) = multiply(A,multiply(A,A)),
inference(paramod,[status(thm)],[c_15,c_317]) ).
cnf(c_319,plain,
multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(A,identity))),identity))) = multiply(A,multiply(A,A)),
inference(paramod,[status(thm)],[c_15,c_318]) ).
cnf(c_320,plain,
multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),multiply(identity,multiply(identity,multiply(multiply(identity,multiply(A,identity)),identity)))) = multiply(A,multiply(A,A)),
inference(paramod,[status(thm)],[c_15,c_319]) ).
cnf(c_321,plain,
multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))))) = multiply(A,multiply(A,A)),
inference(paramod,[status(thm)],[c_15,c_320]) ).
cnf(c_30,plain,
multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),A) = multiply(A,multiply(A,A)),
inference(paramod,[status(thm)],[c_11,c_321]) ).
cnf(c_322,plain,
multiply(multiply(A,A),multiply(multiply(A,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(B,identity)))),identity)),identity)) = multiply(multiply(A,multiply(multiply(A,A),B)),identity),
inference(paramod,[status(thm)],[c_27,c_20]) ).
cnf(c_323,plain,
multiply(multiply(A,A),multiply(multiply(A,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(B,identity))),identity))),identity)) = multiply(multiply(A,multiply(multiply(A,A),B)),identity),
inference(paramod,[status(thm)],[c_15,c_322]) ).
cnf(c_324,plain,
multiply(multiply(A,A),multiply(multiply(A,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(B,identity)),identity)))),identity)) = multiply(multiply(A,multiply(multiply(A,A),B)),identity),
inference(paramod,[status(thm)],[c_15,c_323]) ).
cnf(c_325,plain,
multiply(multiply(A,A),multiply(multiply(A,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(B,identity),identity))))),identity)) = multiply(multiply(A,multiply(multiply(A,A),B)),identity),
inference(paramod,[status(thm)],[c_15,c_324]) ).
cnf(c_326,plain,
multiply(multiply(A,A),multiply(multiply(A,B),identity)) = multiply(multiply(A,multiply(multiply(A,A),B)),identity),
inference(paramod,[status(thm)],[c_11,c_325]) ).
cnf(c_31,plain,
multiply(multiply(A,multiply(multiply(A,A),B)),identity) = multiply(multiply(A,A),multiply(multiply(A,B),identity)),
inference(copy,[status(thm)],[c_326]) ).
cnf(c_32,plain,
multiply(A,multiply(multiply(A,A),multiply(multiply(A,B),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(B,identity)))),
inference(paramod,[status(thm)],[c_31,c_27]) ).
cnf(c_35,plain,
multiply(multiply(A,A),multiply(multiply(A,A),multiply(multiply(A,identity),identity))) = A,
inference(paramod,[status(thm)],[c_31,c_20]) ).
cnf(c_327,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,B)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,B)))),multiply(multiply(A,B),multiply(multiply(A,B),multiply(A,B)))),multiply(B,multiply(B,B)))) = A,
inference(paramod,[status(thm)],[c_30,c_1]) ).
cnf(c_37,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,B)))),multiply(identity,multiply(B,multiply(B,B)))) = A,
inference(paramod,[status(thm)],[c_24,c_327]) ).
cnf(c_328,plain,
multiply(multiply(identity,multiply(identity,A)),multiply(identity,multiply(multiply(B,multiply(B,B)),multiply(multiply(B,multiply(B,B)),multiply(B,multiply(B,B)))))) = multiply(identity,multiply(multiply(identity,identity),multiply(A,B))),
inference(paramod,[status(thm)],[c_1,c_37]) ).
cnf(c_329,plain,
multiply(multiply(identity,multiply(identity,A)),multiply(identity,multiply(identity,B))) = multiply(identity,multiply(multiply(identity,identity),multiply(A,B))),
inference(paramod,[status(thm)],[c_28,c_328]) ).
cnf(c_38,plain,
multiply(multiply(identity,multiply(identity,A)),multiply(identity,multiply(identity,B))) = multiply(identity,multiply(identity,multiply(A,B))),
inference(paramod,[status(thm)],[c_2,c_329]) ).
cnf(c_39,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(identity,A),multiply(identity,A)))),A) = multiply(A,multiply(A,A)),
inference(paramod,[status(thm)],[c_38,c_30]) ).
cnf(c_330,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,A)),identity)),identity)) = multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A)))),
inference(paramod,[status(thm)],[c_28,c_20]) ).
cnf(c_331,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,A)),identity)),identity)) = multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A)))),
inference(paramod,[status(thm)],[c_2,c_330]) ).
cnf(c_332,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(identity,A),identity))),identity)) = multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A)))),
inference(paramod,[status(thm)],[c_15,c_331]) ).
cnf(c_333,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,identity)))),identity)) = multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A)))),
inference(paramod,[status(thm)],[c_15,c_332]) ).
cnf(c_334,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(A,identity))),identity))) = multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A)))),
inference(paramod,[status(thm)],[c_15,c_333]) ).
cnf(c_335,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(A,identity)),identity)))) = multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A)))),
inference(paramod,[status(thm)],[c_15,c_334]) ).
cnf(c_336,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))))) = multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A)))),
inference(paramod,[status(thm)],[c_15,c_335]) ).
cnf(c_337,plain,
multiply(identity,A) = multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A)))),
inference(paramod,[status(thm)],[c_11,c_336]) ).
cnf(c_40,plain,
multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A)))) = multiply(identity,A),
inference(copy,[status(thm)],[c_337]) ).
cnf(c_338,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,multiply(B,multiply(B,B)))))),multiply(identity,multiply(identity,B))) = A,
inference(paramod,[status(thm)],[c_28,c_37]) ).
cnf(c_41,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(A,multiply(B,multiply(B,B)))),B))) = A,
inference(paramod,[status(thm)],[c_38,c_338]) ).
cnf(c_339,plain,
multiply(A,multiply(identity,multiply(identity,B))) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(A,identity),identity)),B))),
inference(paramod,[status(thm)],[c_11,c_38]) ).
cnf(c_42,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(A,identity),identity)),B))) = multiply(A,multiply(identity,multiply(identity,B))),
inference(copy,[status(thm)],[c_339]) ).
cnf(c_43,plain,
multiply(multiply(identity,multiply(identity,A)),B) = multiply(identity,multiply(identity,multiply(A,multiply(identity,multiply(multiply(B,identity),identity))))),
inference(paramod,[status(thm)],[c_11,c_38]) ).
cnf(c_47,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,multiply(A,A))))),multiply(identity,A)) = identity,
inference(paramod,[status(thm)],[c_40,c_24]) ).
cnf(c_48,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(identity,A),multiply(B,multiply(B,B))))),multiply(identity,B)) = A,
inference(paramod,[status(thm)],[c_40,c_26]) ).
cnf(c_55,plain,
multiply(multiply(identity,A),multiply(identity,multiply(B,multiply(B,B)))) = multiply(identity,multiply(A,multiply(B,multiply(B,B)))),
inference(paramod,[status(thm)],[c_41,c_37]) ).
cnf(c_340,plain,
multiply(multiply(identity,A),multiply(identity,multiply(identity,B))) = multiply(identity,multiply(A,multiply(multiply(B,multiply(B,B)),multiply(multiply(B,multiply(B,B)),multiply(B,multiply(B,B)))))),
inference(paramod,[status(thm)],[c_40,c_55]) ).
cnf(c_57,plain,
multiply(multiply(identity,A),multiply(identity,multiply(identity,B))) = multiply(identity,multiply(A,multiply(identity,B))),
inference(paramod,[status(thm)],[c_40,c_340]) ).
cnf(c_58,plain,
multiply(identity,multiply(multiply(identity,A),multiply(identity,B))) = multiply(identity,multiply(identity,multiply(A,B))),
inference(paramod,[status(thm)],[c_57,c_38]) ).
cnf(c_60,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),A) = multiply(A,multiply(A,A)),
inference(paramod,[status(thm)],[c_58,c_39]) ).
cnf(c_341,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(A,identity),identity)),multiply(identity,multiply(multiply(B,identity),identity))))) = multiply(A,B),
inference(paramod,[status(thm)],[c_11,c_42]) ).
cnf(c_62,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(A,identity),identity),multiply(multiply(B,identity),identity))))) = multiply(A,B),
inference(paramod,[status(thm)],[c_58,c_341]) ).
cnf(c_342,plain,
multiply(multiply(A,multiply(identity,multiply(identity,B))),multiply(B,multiply(B,B))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(A,identity),identity)),identity),identity))),
inference(paramod,[status(thm)],[c_42,c_14]) ).
cnf(c_343,plain,
multiply(multiply(A,multiply(identity,multiply(identity,B))),multiply(B,multiply(B,B))) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(A,identity),identity),identity)),identity))),
inference(paramod,[status(thm)],[c_15,c_342]) ).
cnf(c_344,plain,
multiply(multiply(A,multiply(identity,multiply(identity,B))),multiply(B,multiply(B,B))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(A,identity),identity),identity),identity)))),
inference(paramod,[status(thm)],[c_15,c_343]) ).
cnf(c_63,plain,
multiply(multiply(A,multiply(identity,multiply(identity,B))),multiply(B,multiply(B,B))) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_11,c_344]) ).
cnf(c_345,plain,
multiply(multiply(identity,multiply(A,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(A,identity),identity)),multiply(identity,multiply(multiply(A,identity),identity))))))),multiply(identity,multiply(identity,multiply(multiply(A,identity),identity)))) = identity,
inference(paramod,[status(thm)],[c_42,c_47]) ).
cnf(c_346,plain,
multiply(multiply(identity,multiply(A,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(A,identity),identity),multiply(multiply(A,identity),identity))))))),multiply(identity,multiply(identity,multiply(multiply(A,identity),identity)))) = identity,
inference(paramod,[status(thm)],[c_58,c_345]) ).
cnf(c_347,plain,
multiply(multiply(identity,multiply(A,multiply(A,A))),multiply(identity,multiply(identity,multiply(multiply(A,identity),identity)))) = identity,
inference(paramod,[status(thm)],[c_62,c_346]) ).
cnf(c_64,plain,
multiply(identity,multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,identity),identity)))) = identity,
inference(paramod,[status(thm)],[c_57,c_347]) ).
cnf(c_348,plain,
multiply(multiply(identity,A),B) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))),multiply(identity,multiply(multiply(B,identity),identity))))),
inference(paramod,[status(thm)],[c_11,c_43]) ).
cnf(c_349,plain,
multiply(multiply(identity,A),B) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(A,identity),identity)),multiply(multiply(B,identity),identity))))),
inference(paramod,[status(thm)],[c_58,c_348]) ).
cnf(c_65,plain,
multiply(multiply(identity,A),B) = multiply(identity,multiply(A,multiply(identity,multiply(identity,multiply(multiply(B,identity),identity))))),
inference(paramod,[status(thm)],[c_42,c_349]) ).
cnf(c_350,plain,
multiply(multiply(identity,A),multiply(identity,B)) = multiply(multiply(identity,identity),multiply(A,B)),
inference(paramod,[status(thm)],[c_1,c_48]) ).
cnf(c_66,plain,
multiply(multiply(identity,A),multiply(identity,B)) = multiply(identity,multiply(A,B)),
inference(paramod,[status(thm)],[c_2,c_350]) ).
cnf(c_67,plain,
multiply(multiply(A,multiply(identity,multiply(identity,multiply(B,multiply(B,B))))),multiply(identity,B)) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_42,c_48]) ).
cnf(c_351,plain,
multiply(A,multiply(identity,B)) = multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,identity),multiply(A,C))),multiply(C,multiply(C,C))),B)),
inference(paramod,[status(thm)],[c_1,c_66]) ).
cnf(c_352,plain,
multiply(A,multiply(identity,B)) = multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(A,C))),multiply(C,multiply(C,C))),B)),
inference(paramod,[status(thm)],[c_2,c_351]) ).
cnf(c_69,plain,
multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(A,B))),multiply(B,multiply(B,B))),C)) = multiply(A,multiply(identity,C)),
inference(copy,[status(thm)],[c_352]) ).
cnf(c_353,plain,
multiply(A,multiply(identity,B)) = multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))),B)),
inference(paramod,[status(thm)],[c_11,c_66]) ).
cnf(c_71,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))),B)) = multiply(A,multiply(identity,B)),
inference(copy,[status(thm)],[c_353]) ).
cnf(c_74,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(A,identity),identity),B)))) = multiply(A,multiply(identity,multiply(identity,multiply(identity,B)))),
inference(paramod,[status(thm)],[c_66,c_42]) ).
cnf(c_75,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,A))),B) = multiply(identity,multiply(identity,multiply(identity,multiply(A,multiply(multiply(B,identity),identity))))),
inference(paramod,[status(thm)],[c_66,c_43]) ).
cnf(c_354,plain,
multiply(A,multiply(A,A)) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(A,A)),multiply(identity,multiply(multiply(A,identity),identity))))),
inference(paramod,[status(thm)],[c_60,c_43]) ).
cnf(c_355,plain,
multiply(A,multiply(A,A)) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,A),multiply(multiply(A,identity),identity))))),
inference(paramod,[status(thm)],[c_66,c_354]) ).
cnf(c_76,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,A),multiply(multiply(A,identity),identity))))) = multiply(A,multiply(A,A)),
inference(copy,[status(thm)],[c_355]) ).
cnf(c_356,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,multiply(identity,identity)),identity)) = multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,identity),identity))),
inference(paramod,[status(thm)],[c_64,c_20]) ).
cnf(c_357,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,identity)),identity)) = multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,identity),identity))),
inference(paramod,[status(thm)],[c_2,c_356]) ).
cnf(c_358,plain,
multiply(identity,multiply(multiply(identity,identity),identity)) = multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,identity),identity))),
inference(paramod,[status(thm)],[c_2,c_357]) ).
cnf(c_359,plain,
multiply(identity,multiply(identity,identity)) = multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,identity),identity))),
inference(paramod,[status(thm)],[c_2,c_358]) ).
cnf(c_360,plain,
multiply(identity,identity) = multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,identity),identity))),
inference(paramod,[status(thm)],[c_2,c_359]) ).
cnf(c_361,plain,
identity = multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,identity),identity))),
inference(paramod,[status(thm)],[c_2,c_360]) ).
cnf(c_81,plain,
multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,identity),identity))) = identity,
inference(copy,[status(thm)],[c_361]) ).
cnf(c_362,plain,
multiply(multiply(identity,multiply(identity,multiply(A,multiply(A,A)))),A) = multiply(identity,identity),
inference(paramod,[status(thm)],[c_64,c_43]) ).
cnf(c_83,plain,
multiply(multiply(identity,multiply(identity,multiply(A,multiply(A,A)))),A) = identity,
inference(paramod,[status(thm)],[c_2,c_362]) ).
cnf(c_84,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),identity)),multiply(B,multiply(B,B)))) = multiply(identity,multiply(identity,multiply(B,multiply(B,B)))),
inference(paramod,[status(thm)],[c_83,c_1]) ).
cnf(c_363,plain,
multiply(multiply(A,multiply(A,A)),multiply(multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))),multiply(identity,identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(A,identity),identity)),identity)))),
inference(paramod,[status(thm)],[c_81,c_32]) ).
cnf(c_364,plain,
multiply(multiply(A,multiply(A,A)),multiply(multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))),identity)) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(A,identity),identity)),identity)))),
inference(paramod,[status(thm)],[c_2,c_363]) ).
cnf(c_365,plain,
multiply(multiply(A,multiply(A,A)),multiply(multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))),identity)) = multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(A,identity),identity),identity))))),
inference(paramod,[status(thm)],[c_15,c_364]) ).
cnf(c_85,plain,
multiply(multiply(A,multiply(A,A)),multiply(multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))),identity)) = multiply(identity,multiply(A,identity)),
inference(paramod,[status(thm)],[c_11,c_365]) ).
cnf(c_366,plain,
multiply(multiply(identity,A),multiply(identity,multiply(multiply(multiply(A,multiply(A,A)),identity),identity))) = identity,
inference(paramod,[status(thm)],[c_40,c_81]) ).
cnf(c_86,plain,
multiply(identity,multiply(A,multiply(multiply(multiply(A,multiply(A,A)),identity),identity))) = identity,
inference(paramod,[status(thm)],[c_66,c_366]) ).
cnf(c_367,plain,
multiply(multiply(identity,identity),multiply(multiply(identity,multiply(identity,identity)),identity)) = multiply(A,multiply(multiply(multiply(A,multiply(A,A)),identity),identity)),
inference(paramod,[status(thm)],[c_86,c_20]) ).
cnf(c_368,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,identity)),identity)) = multiply(A,multiply(multiply(multiply(A,multiply(A,A)),identity),identity)),
inference(paramod,[status(thm)],[c_2,c_367]) ).
cnf(c_369,plain,
multiply(identity,multiply(multiply(identity,identity),identity)) = multiply(A,multiply(multiply(multiply(A,multiply(A,A)),identity),identity)),
inference(paramod,[status(thm)],[c_2,c_368]) ).
cnf(c_370,plain,
multiply(identity,multiply(identity,identity)) = multiply(A,multiply(multiply(multiply(A,multiply(A,A)),identity),identity)),
inference(paramod,[status(thm)],[c_2,c_369]) ).
cnf(c_371,plain,
multiply(identity,identity) = multiply(A,multiply(multiply(multiply(A,multiply(A,A)),identity),identity)),
inference(paramod,[status(thm)],[c_2,c_370]) ).
cnf(c_372,plain,
identity = multiply(A,multiply(multiply(multiply(A,multiply(A,A)),identity),identity)),
inference(paramod,[status(thm)],[c_2,c_371]) ).
cnf(c_90,plain,
multiply(A,multiply(multiply(multiply(A,multiply(A,A)),identity),identity)) = identity,
inference(copy,[status(thm)],[c_372]) ).
cnf(c_373,plain,
multiply(multiply(A,A),multiply(multiply(A,multiply(identity,identity)),identity)) = multiply(multiply(multiply(A,multiply(A,A)),identity),identity),
inference(paramod,[status(thm)],[c_90,c_20]) ).
cnf(c_374,plain,
multiply(multiply(A,A),multiply(multiply(A,identity),identity)) = multiply(multiply(multiply(A,multiply(A,A)),identity),identity),
inference(paramod,[status(thm)],[c_2,c_373]) ).
cnf(c_92,plain,
multiply(multiply(multiply(A,multiply(A,A)),identity),identity) = multiply(multiply(A,A),multiply(multiply(A,identity),identity)),
inference(copy,[status(thm)],[c_374]) ).
cnf(c_375,plain,
multiply(multiply(A,multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,identity),multiply(B,C))),multiply(C,multiply(C,C))),multiply(multiply(multiply(identity,multiply(multiply(identity,identity),multiply(B,C))),multiply(C,multiply(C,C))),multiply(multiply(identity,multiply(multiply(identity,identity),multiply(B,C))),multiply(C,multiply(C,C)))))))),B) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_1,c_67]) ).
cnf(c_376,plain,
multiply(multiply(A,multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(B,C))),multiply(C,multiply(C,C))),multiply(multiply(multiply(identity,multiply(multiply(identity,identity),multiply(B,C))),multiply(C,multiply(C,C))),multiply(multiply(identity,multiply(multiply(identity,identity),multiply(B,C))),multiply(C,multiply(C,C)))))))),B) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_2,c_375]) ).
cnf(c_377,plain,
multiply(multiply(A,multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(B,C))),multiply(C,multiply(C,C))),multiply(multiply(multiply(identity,multiply(identity,multiply(B,C))),multiply(C,multiply(C,C))),multiply(multiply(identity,multiply(multiply(identity,identity),multiply(B,C))),multiply(C,multiply(C,C)))))))),B) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_2,c_376]) ).
cnf(c_378,plain,
multiply(multiply(A,multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(B,C))),multiply(C,multiply(C,C))),multiply(multiply(multiply(identity,multiply(identity,multiply(B,C))),multiply(C,multiply(C,C))),multiply(multiply(identity,multiply(identity,multiply(B,C))),multiply(C,multiply(C,C)))))))),B) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_2,c_377]) ).
cnf(c_379,plain,
multiply(multiply(A,multiply(identity,multiply(B,multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(B,C))),multiply(C,multiply(C,C))),multiply(multiply(identity,multiply(identity,multiply(B,C))),multiply(C,multiply(C,C)))))))),B) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_69,c_378]) ).
cnf(c_380,plain,
multiply(multiply(A,multiply(identity,multiply(B,multiply(B,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(B,C))),multiply(C,multiply(C,C)))))))),B) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_69,c_379]) ).
cnf(c_96,plain,
multiply(multiply(A,multiply(identity,multiply(B,multiply(B,B)))),B) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_4,c_380]) ).
cnf(c_381,plain,
multiply(multiply(A,multiply(B,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(B,identity),identity)),multiply(identity,multiply(multiply(B,identity),identity))))))),multiply(identity,multiply(identity,multiply(multiply(B,identity),identity)))) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_42,c_67]) ).
cnf(c_382,plain,
multiply(multiply(A,multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(B,identity),identity),multiply(multiply(B,identity),identity))))))),multiply(identity,multiply(identity,multiply(multiply(B,identity),identity)))) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_66,c_381]) ).
cnf(c_383,plain,
multiply(multiply(A,multiply(B,multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(B,identity),identity))))))),multiply(identity,multiply(identity,multiply(multiply(B,identity),identity)))) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_74,c_382]) ).
cnf(c_97,plain,
multiply(multiply(A,multiply(B,multiply(B,B))),multiply(identity,multiply(identity,multiply(multiply(B,identity),identity)))) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_11,c_383]) ).
cnf(c_384,plain,
multiply(multiply(multiply(A,identity),identity),B) = multiply(multiply(multiply(A,multiply(identity,multiply(identity,multiply(multiply(B,multiply(B,B)),multiply(multiply(B,multiply(B,B)),multiply(B,multiply(B,B))))))),identity),identity),
inference(paramod,[status(thm)],[c_67,c_96]) ).
cnf(c_385,plain,
multiply(multiply(multiply(A,identity),identity),B) = multiply(multiply(multiply(A,multiply(identity,multiply(identity,multiply(identity,B)))),identity),identity),
inference(paramod,[status(thm)],[c_40,c_384]) ).
cnf(c_99,plain,
multiply(multiply(multiply(A,multiply(identity,multiply(identity,multiply(identity,B)))),identity),identity) = multiply(multiply(multiply(A,identity),identity),B),
inference(copy,[status(thm)],[c_385]) ).
cnf(c_386,plain,
multiply(multiply(multiply(A,B),identity),identity) = multiply(multiply(multiply(A,identity),identity),multiply(multiply(B,identity),identity)),
inference(paramod,[status(thm)],[c_11,c_99]) ).
cnf(c_106,plain,
multiply(multiply(multiply(A,identity),identity),multiply(multiply(B,identity),identity)) = multiply(multiply(multiply(A,B),identity),identity),
inference(copy,[status(thm)],[c_386]) ).
cnf(c_387,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),identity),identity))))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),identity),identity))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_75,c_35]) ).
cnf(c_388,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,A)),identity)),identity))))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),identity),identity))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_15,c_387]) ).
cnf(c_389,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,multiply(multiply(identity,multiply(identity,multiply(multiply(identity,A),identity))),identity))))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),identity),identity))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_15,c_388]) ).
cnf(c_390,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,identity)))),identity))))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),identity),identity))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_15,c_389]) ).
cnf(c_391,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(A,identity))),identity)))))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),identity),identity))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_15,c_390]) ).
cnf(c_392,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(A,identity)),identity))))))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),identity),identity))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_15,c_391]) ).
cnf(c_393,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),identity)))))))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),identity),identity))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_15,c_392]) ).
cnf(c_394,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),multiply(identity,multiply(identity,multiply(identity,A)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),identity),identity))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_11,c_393]) ).
cnf(c_395,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,A)),multiply(identity,multiply(identity,A)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),identity),identity))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_66,c_394]) ).
cnf(c_396,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(multiply(identity,multiply(identity,multiply(multiply(identity,A),multiply(identity,A)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),identity),identity))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_66,c_395]) ).
cnf(c_397,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,A))),identity),identity))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_66,c_396]) ).
cnf(c_398,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,A)),identity)),identity))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_15,c_397]) ).
cnf(c_399,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(multiply(identity,multiply(identity,multiply(multiply(identity,A),identity))),identity))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_15,c_398]) ).
cnf(c_400,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,identity)))),identity))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_15,c_399]) ).
cnf(c_401,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(A,identity))),identity)))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_15,c_400]) ).
cnf(c_402,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(identity,multiply(identity,multiply(multiply(identity,multiply(A,identity)),identity))))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_15,c_401]) ).
cnf(c_403,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),identity)))))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_15,c_402]) ).
cnf(c_404,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),A)) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_11,c_403]) ).
cnf(c_108,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(A,multiply(A,A))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_60,c_404]) ).
cnf(c_405,plain,
multiply(multiply(identity,multiply(multiply(A,B),identity)),identity) = multiply(identity,multiply(multiply(multiply(A,identity),identity),multiply(multiply(B,identity),identity))),
inference(paramod,[status(thm)],[c_106,c_15]) ).
cnf(c_406,plain,
multiply(identity,multiply(multiply(multiply(A,B),identity),identity)) = multiply(identity,multiply(multiply(multiply(A,identity),identity),multiply(multiply(B,identity),identity))),
inference(paramod,[status(thm)],[c_15,c_405]) ).
cnf(c_109,plain,
multiply(identity,multiply(multiply(multiply(A,identity),identity),multiply(multiply(B,identity),identity))) = multiply(identity,multiply(multiply(multiply(A,B),identity),identity)),
inference(copy,[status(thm)],[c_406]) ).
cnf(c_407,plain,
multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(B,identity),identity),identity)) = multiply(multiply(multiply(A,multiply(B,multiply(identity,multiply(identity,multiply(identity,identity))))),identity),identity),
inference(paramod,[status(thm)],[c_96,c_106]) ).
cnf(c_408,plain,
multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(B,identity),identity),identity)) = multiply(multiply(multiply(A,multiply(B,multiply(identity,multiply(identity,identity)))),identity),identity),
inference(paramod,[status(thm)],[c_2,c_407]) ).
cnf(c_409,plain,
multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(B,identity),identity),identity)) = multiply(multiply(multiply(A,multiply(B,multiply(identity,identity))),identity),identity),
inference(paramod,[status(thm)],[c_2,c_408]) ).
cnf(c_410,plain,
multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(B,identity),identity),identity)) = multiply(multiply(multiply(A,multiply(B,identity)),identity),identity),
inference(paramod,[status(thm)],[c_2,c_409]) ).
cnf(c_115,plain,
multiply(multiply(multiply(A,multiply(B,identity)),identity),identity) = multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(B,identity),identity),identity)),
inference(copy,[status(thm)],[c_410]) ).
cnf(c_411,plain,
multiply(identity,multiply(multiply(multiply(multiply(identity,multiply(identity,multiply(A,B))),identity),identity),multiply(multiply(multiply(B,multiply(B,B)),identity),identity))) = multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))),identity),identity)),
inference(paramod,[status(thm)],[c_14,c_109]) ).
cnf(c_412,plain,
multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,multiply(A,B)),identity)),identity),multiply(multiply(multiply(B,multiply(B,B)),identity),identity))) = multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))),identity),identity)),
inference(paramod,[status(thm)],[c_15,c_411]) ).
cnf(c_413,plain,
multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(A,B),identity))),identity),multiply(multiply(multiply(B,multiply(B,B)),identity),identity))) = multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))),identity),identity)),
inference(paramod,[status(thm)],[c_15,c_412]) ).
cnf(c_414,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(A,B),identity)),identity)),multiply(multiply(multiply(B,multiply(B,B)),identity),identity))) = multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))),identity),identity)),
inference(paramod,[status(thm)],[c_15,c_413]) ).
cnf(c_415,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(A,B),identity),identity))),multiply(multiply(multiply(B,multiply(B,B)),identity),identity))) = multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))),identity),identity)),
inference(paramod,[status(thm)],[c_15,c_414]) ).
cnf(c_416,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(A,B),identity),identity))),multiply(multiply(B,B),multiply(multiply(B,identity),identity)))) = multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))),identity),identity)),
inference(paramod,[status(thm)],[c_92,c_415]) ).
cnf(c_417,plain,
multiply(multiply(A,B),multiply(identity,multiply(multiply(B,B),multiply(multiply(B,identity),identity)))) = multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))),identity),identity)),
inference(paramod,[status(thm)],[c_71,c_416]) ).
cnf(c_418,plain,
multiply(multiply(A,B),multiply(identity,multiply(multiply(B,B),multiply(multiply(B,identity),identity)))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(A,identity),identity)),identity)),identity)),
inference(paramod,[status(thm)],[c_15,c_417]) ).
cnf(c_419,plain,
multiply(multiply(A,B),multiply(identity,multiply(multiply(B,B),multiply(multiply(B,identity),identity)))) = multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(A,identity),identity),identity))),identity)),
inference(paramod,[status(thm)],[c_15,c_418]) ).
cnf(c_420,plain,
multiply(multiply(A,B),multiply(identity,multiply(multiply(B,B),multiply(multiply(B,identity),identity)))) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(A,identity),identity),identity)),identity))),
inference(paramod,[status(thm)],[c_15,c_419]) ).
cnf(c_421,plain,
multiply(multiply(A,B),multiply(identity,multiply(multiply(B,B),multiply(multiply(B,identity),identity)))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(A,identity),identity),identity),identity)))),
inference(paramod,[status(thm)],[c_15,c_420]) ).
cnf(c_422,plain,
multiply(multiply(A,B),multiply(identity,multiply(multiply(B,B),multiply(multiply(B,identity),identity)))) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_11,c_421]) ).
cnf(c_116,plain,
multiply(multiply(A,identity),identity) = multiply(multiply(A,B),multiply(identity,multiply(multiply(B,B),multiply(multiply(B,identity),identity)))),
inference(copy,[status(thm)],[c_422]) ).
cnf(c_423,plain,
multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),identity),identity) = multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,A),multiply(multiply(A,identity),identity)))),
inference(paramod,[status(thm)],[c_60,c_116]) ).
cnf(c_424,plain,
multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(A,A))),identity)),identity) = multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,A),multiply(multiply(A,identity),identity)))),
inference(paramod,[status(thm)],[c_15,c_423]) ).
cnf(c_425,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(identity,multiply(A,A)),identity))),identity) = multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,A),multiply(multiply(A,identity),identity)))),
inference(paramod,[status(thm)],[c_15,c_424]) ).
cnf(c_426,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,A),identity)))),identity) = multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,A),multiply(multiply(A,identity),identity)))),
inference(paramod,[status(thm)],[c_15,c_425]) ).
cnf(c_427,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(A,A),identity))),identity)) = multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,A),multiply(multiply(A,identity),identity)))),
inference(paramod,[status(thm)],[c_15,c_426]) ).
cnf(c_428,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(A,A),identity)),identity))) = multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,A),multiply(multiply(A,identity),identity)))),
inference(paramod,[status(thm)],[c_15,c_427]) ).
cnf(c_429,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(A,A),identity),identity)))) = multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,A),multiply(multiply(A,identity),identity)))),
inference(paramod,[status(thm)],[c_15,c_428]) ).
cnf(c_430,plain,
multiply(A,A) = multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,A),multiply(multiply(A,identity),identity)))),
inference(paramod,[status(thm)],[c_11,c_429]) ).
cnf(c_119,plain,
multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,A),multiply(multiply(A,identity),identity)))) = multiply(A,A),
inference(copy,[status(thm)],[c_430]) ).
cnf(c_431,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),identity)),multiply(identity,B))) = multiply(identity,multiply(identity,multiply(multiply(B,multiply(B,B)),multiply(multiply(B,multiply(B,B)),multiply(B,multiply(B,B)))))),
inference(paramod,[status(thm)],[c_40,c_84]) ).
cnf(c_121,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),identity)),multiply(identity,B))) = multiply(identity,multiply(identity,multiply(identity,B))),
inference(paramod,[status(thm)],[c_40,c_431]) ).
cnf(c_432,plain,
multiply(multiply(identity,A),multiply(multiply(multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A)))),multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))))),identity)) = multiply(identity,multiply(multiply(A,multiply(A,A)),identity)),
inference(paramod,[status(thm)],[c_40,c_85]) ).
cnf(c_433,plain,
multiply(multiply(identity,A),multiply(multiply(multiply(identity,A),multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))))),identity)) = multiply(identity,multiply(multiply(A,multiply(A,A)),identity)),
inference(paramod,[status(thm)],[c_40,c_432]) ).
cnf(c_434,plain,
multiply(multiply(identity,A),multiply(multiply(multiply(identity,A),multiply(identity,A)),identity)) = multiply(identity,multiply(multiply(A,multiply(A,A)),identity)),
inference(paramod,[status(thm)],[c_40,c_433]) ).
cnf(c_435,plain,
multiply(multiply(identity,A),multiply(multiply(identity,multiply(A,A)),identity)) = multiply(identity,multiply(multiply(A,multiply(A,A)),identity)),
inference(paramod,[status(thm)],[c_66,c_434]) ).
cnf(c_436,plain,
multiply(multiply(identity,A),multiply(identity,multiply(multiply(A,A),identity))) = multiply(identity,multiply(multiply(A,multiply(A,A)),identity)),
inference(paramod,[status(thm)],[c_15,c_435]) ).
cnf(c_437,plain,
multiply(identity,multiply(A,multiply(multiply(A,A),identity))) = multiply(identity,multiply(multiply(A,multiply(A,A)),identity)),
inference(paramod,[status(thm)],[c_66,c_436]) ).
cnf(c_123,plain,
multiply(identity,multiply(multiply(A,multiply(A,A)),identity)) = multiply(identity,multiply(A,multiply(multiply(A,A),identity))),
inference(copy,[status(thm)],[c_437]) ).
cnf(c_438,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(identity,multiply(A,multiply(multiply(A,A),identity))),B))),multiply(B,multiply(B,B))) = multiply(multiply(A,multiply(A,A)),identity),
inference(paramod,[status(thm)],[c_123,c_26]) ).
cnf(c_439,plain,
multiply(A,multiply(multiply(A,A),identity)) = multiply(multiply(A,multiply(A,A)),identity),
inference(paramod,[status(thm)],[c_26,c_438]) ).
cnf(c_124,plain,
multiply(multiply(A,multiply(A,A)),identity) = multiply(A,multiply(multiply(A,A),identity)),
inference(copy,[status(thm)],[c_439]) ).
cnf(c_125,plain,
multiply(multiply(A,A),multiply(multiply(A,multiply(A,multiply(multiply(A,A),identity))),identity)) = multiply(A,A),
inference(paramod,[status(thm)],[c_124,c_20]) ).
cnf(c_126,plain,
multiply(A,multiply(multiply(A,A),multiply(A,multiply(multiply(A,A),identity)))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,A),identity)))),
inference(paramod,[status(thm)],[c_124,c_32]) ).
cnf(c_440,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),identity)),B)) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(B,C))),multiply(C,multiply(C,C)))))),
inference(paramod,[status(thm)],[c_1,c_121]) ).
cnf(c_441,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),identity)),B)) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(B,C))),multiply(C,multiply(C,C)))))),
inference(paramod,[status(thm)],[c_2,c_440]) ).
cnf(c_127,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,A),identity)),B)) = multiply(identity,multiply(identity,B)),
inference(paramod,[status(thm)],[c_4,c_441]) ).
cnf(c_442,plain,
multiply(A,multiply(multiply(A,identity),identity)) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(A,A),identity),multiply(multiply(A,A),identity)),multiply(multiply(multiply(multiply(A,A),identity),identity),identity))))),
inference(paramod,[status(thm)],[c_116,c_121]) ).
cnf(c_443,plain,
multiply(A,multiply(multiply(A,identity),identity)) = multiply(multiply(multiply(A,A),identity),multiply(multiply(multiply(A,A),identity),multiply(multiply(A,A),identity))),
inference(paramod,[status(thm)],[c_76,c_442]) ).
cnf(c_129,plain,
multiply(multiply(multiply(A,A),identity),multiply(multiply(multiply(A,A),identity),multiply(multiply(A,A),identity))) = multiply(A,multiply(multiply(A,identity),identity)),
inference(copy,[status(thm)],[c_443]) ).
cnf(c_133,plain,
multiply(multiply(A,multiply(A,A)),multiply(multiply(identity,multiply(A,identity)),B)) = multiply(identity,multiply(identity,B)),
inference(paramod,[status(thm)],[c_85,c_127]) ).
cnf(c_444,plain,
multiply(multiply(A,multiply(A,A)),identity) = multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,multiply(A,identity)),identity),identity),multiply(multiply(multiply(multiply(identity,multiply(A,identity)),identity),identity),multiply(multiply(multiply(identity,multiply(A,identity)),identity),identity))))),
inference(paramod,[status(thm)],[c_25,c_133]) ).
cnf(c_445,plain,
multiply(A,multiply(multiply(A,A),identity)) = multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,multiply(A,identity)),identity),identity),multiply(multiply(multiply(multiply(identity,multiply(A,identity)),identity),identity),multiply(multiply(multiply(identity,multiply(A,identity)),identity),identity))))),
inference(paramod,[status(thm)],[c_124,c_444]) ).
cnf(c_446,plain,
multiply(A,multiply(multiply(A,A),identity)) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(A,identity),identity)),identity),multiply(multiply(multiply(multiply(identity,multiply(A,identity)),identity),identity),multiply(multiply(multiply(identity,multiply(A,identity)),identity),identity))))),
inference(paramod,[status(thm)],[c_15,c_445]) ).
cnf(c_447,plain,
multiply(A,multiply(multiply(A,A),identity)) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(A,identity),identity),identity)),multiply(multiply(multiply(multiply(identity,multiply(A,identity)),identity),identity),multiply(multiply(multiply(identity,multiply(A,identity)),identity),identity))))),
inference(paramod,[status(thm)],[c_15,c_446]) ).
cnf(c_448,plain,
multiply(A,multiply(multiply(A,A),identity)) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(A,identity),identity),identity)),multiply(multiply(multiply(identity,multiply(multiply(A,identity),identity)),identity),multiply(multiply(multiply(identity,multiply(A,identity)),identity),identity))))),
inference(paramod,[status(thm)],[c_15,c_447]) ).
cnf(c_449,plain,
multiply(A,multiply(multiply(A,A),identity)) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(A,identity),identity),identity)),multiply(multiply(identity,multiply(multiply(multiply(A,identity),identity),identity)),multiply(multiply(multiply(identity,multiply(A,identity)),identity),identity))))),
inference(paramod,[status(thm)],[c_15,c_448]) ).
cnf(c_450,plain,
multiply(A,multiply(multiply(A,A),identity)) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(A,identity),identity),identity)),multiply(multiply(identity,multiply(multiply(multiply(A,identity),identity),identity)),multiply(multiply(identity,multiply(multiply(A,identity),identity)),identity))))),
inference(paramod,[status(thm)],[c_15,c_449]) ).
cnf(c_451,plain,
multiply(A,multiply(multiply(A,A),identity)) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(A,identity),identity),identity)),multiply(multiply(identity,multiply(multiply(multiply(A,identity),identity),identity)),multiply(identity,multiply(multiply(multiply(A,identity),identity),identity)))))),
inference(paramod,[status(thm)],[c_15,c_450]) ).
cnf(c_452,plain,
multiply(A,multiply(multiply(A,A),identity)) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(A,identity),identity),identity)),multiply(identity,multiply(multiply(multiply(multiply(A,identity),identity),identity),multiply(multiply(multiply(A,identity),identity),identity)))))),
inference(paramod,[status(thm)],[c_66,c_451]) ).
cnf(c_453,plain,
multiply(A,multiply(multiply(A,A),identity)) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(A,identity),identity),identity),multiply(multiply(multiply(multiply(A,identity),identity),identity),multiply(multiply(multiply(A,identity),identity),identity)))))),
inference(paramod,[status(thm)],[c_66,c_452]) ).
cnf(c_454,plain,
multiply(A,multiply(multiply(A,A),identity)) = multiply(multiply(A,identity),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(A,identity),identity),identity),multiply(multiply(multiply(A,identity),identity),identity)))))),
inference(paramod,[status(thm)],[c_74,c_453]) ).
cnf(c_455,plain,
multiply(A,multiply(multiply(A,A),identity)) = multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(A,identity),identity),identity)))))),
inference(paramod,[status(thm)],[c_74,c_454]) ).
cnf(c_456,plain,
multiply(A,multiply(multiply(A,A),identity)) = multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity))),
inference(paramod,[status(thm)],[c_11,c_455]) ).
cnf(c_135,plain,
multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity))) = multiply(A,multiply(multiply(A,A),identity)),
inference(copy,[status(thm)],[c_456]) ).
cnf(c_457,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(identity,multiply(A,identity)),multiply(identity,multiply(A,identity))))),multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(A,identity)),identity),identity)))) = multiply(multiply(multiply(A,multiply(A,A)),identity),identity),
inference(paramod,[status(thm)],[c_133,c_97]) ).
cnf(c_458,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),multiply(A,identity))))),multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(A,identity)),identity),identity)))) = multiply(multiply(multiply(A,multiply(A,A)),identity),identity),
inference(paramod,[status(thm)],[c_66,c_457]) ).
cnf(c_459,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),multiply(A,identity))))),multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(A,identity),identity)),identity)))) = multiply(multiply(multiply(A,multiply(A,A)),identity),identity),
inference(paramod,[status(thm)],[c_15,c_458]) ).
cnf(c_460,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),multiply(A,identity))))),multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(A,identity),identity),identity))))) = multiply(multiply(multiply(A,multiply(A,A)),identity),identity),
inference(paramod,[status(thm)],[c_15,c_459]) ).
cnf(c_461,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),multiply(A,identity))))),multiply(A,identity)) = multiply(multiply(multiply(A,multiply(A,A)),identity),identity),
inference(paramod,[status(thm)],[c_11,c_460]) ).
cnf(c_462,plain,
multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity))) = multiply(multiply(multiply(A,multiply(A,A)),identity),identity),
inference(paramod,[status(thm)],[c_60,c_461]) ).
cnf(c_463,plain,
multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity))) = multiply(multiply(A,multiply(multiply(A,A),identity)),identity),
inference(paramod,[status(thm)],[c_124,c_462]) ).
cnf(c_138,plain,
multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity))) = multiply(multiply(A,A),multiply(multiply(A,identity),identity)),
inference(paramod,[status(thm)],[c_31,c_463]) ).
cnf(c_464,plain,
multiply(multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity))),identity) = multiply(multiply(A,A),multiply(multiply(A,identity),identity)),
inference(paramod,[status(thm)],[c_135,c_31]) ).
cnf(c_146,plain,
multiply(multiply(A,identity),multiply(multiply(multiply(A,identity),multiply(A,identity)),identity)) = multiply(multiply(A,A),multiply(multiply(A,identity),identity)),
inference(paramod,[status(thm)],[c_124,c_464]) ).
cnf(c_465,plain,
multiply(multiply(A,A),multiply(multiply(multiply(A,A),identity),multiply(multiply(multiply(A,A),identity),multiply(multiply(A,A),identity)))) = multiply(A,multiply(multiply(A,multiply(multiply(A,A),identity)),identity)),
inference(paramod,[status(thm)],[c_138,c_9]) ).
cnf(c_466,plain,
multiply(multiply(A,A),multiply(A,multiply(multiply(A,identity),identity))) = multiply(A,multiply(multiply(A,multiply(multiply(A,A),identity)),identity)),
inference(paramod,[status(thm)],[c_129,c_465]) ).
cnf(c_467,plain,
multiply(multiply(A,A),multiply(A,multiply(multiply(A,identity),identity))) = multiply(A,multiply(multiply(A,A),multiply(multiply(A,identity),identity))),
inference(paramod,[status(thm)],[c_31,c_466]) ).
cnf(c_468,plain,
multiply(multiply(A,A),multiply(A,multiply(multiply(A,identity),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(identity,identity)))),
inference(paramod,[status(thm)],[c_32,c_467]) ).
cnf(c_469,plain,
multiply(multiply(A,A),multiply(A,multiply(multiply(A,identity),identity))) = multiply(identity,multiply(identity,multiply(identity,identity))),
inference(paramod,[status(thm)],[c_2,c_468]) ).
cnf(c_470,plain,
multiply(multiply(A,A),multiply(A,multiply(multiply(A,identity),identity))) = multiply(identity,multiply(identity,identity)),
inference(paramod,[status(thm)],[c_2,c_469]) ).
cnf(c_471,plain,
multiply(multiply(A,A),multiply(A,multiply(multiply(A,identity),identity))) = multiply(identity,identity),
inference(paramod,[status(thm)],[c_2,c_470]) ).
cnf(c_155,plain,
multiply(multiply(A,A),multiply(A,multiply(multiply(A,identity),identity))) = identity,
inference(paramod,[status(thm)],[c_2,c_471]) ).
cnf(c_472,plain,
multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(A,A),multiply(multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity))),identity)),identity)) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_138,c_20]) ).
cnf(c_473,plain,
multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(A,A),multiply(multiply(A,identity),multiply(multiply(multiply(A,identity),multiply(A,identity)),identity))),identity)) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_124,c_472]) ).
cnf(c_474,plain,
multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(A,A),multiply(multiply(A,A),multiply(multiply(A,identity),identity))),identity)) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_146,c_473]) ).
cnf(c_156,plain,
multiply(multiply(multiply(A,A),multiply(A,A)),multiply(A,identity)) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_35,c_474]) ).
cnf(c_475,plain,
multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity))),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(A,identity),identity),identity)))),
inference(paramod,[status(thm)],[c_138,c_32]) ).
cnf(c_476,plain,
multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(A,identity),multiply(multiply(multiply(A,identity),multiply(A,identity)),identity)))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(A,identity),identity),identity)))),
inference(paramod,[status(thm)],[c_124,c_475]) ).
cnf(c_477,plain,
multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(A,A),multiply(multiply(A,identity),identity)))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(A,identity),identity),identity)))),
inference(paramod,[status(thm)],[c_146,c_476]) ).
cnf(c_161,plain,
multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(A,A),multiply(multiply(A,identity),identity)))) = multiply(A,identity),
inference(paramod,[status(thm)],[c_11,c_477]) ).
cnf(c_478,plain,
multiply(A,multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity)))) = multiply(identity,multiply(identity,multiply(identity,multiply(identity,identity)))),
inference(paramod,[status(thm)],[c_138,c_32]) ).
cnf(c_479,plain,
multiply(A,multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity)))) = multiply(identity,multiply(identity,multiply(identity,identity))),
inference(paramod,[status(thm)],[c_2,c_478]) ).
cnf(c_480,plain,
multiply(A,multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity)))) = multiply(identity,multiply(identity,identity)),
inference(paramod,[status(thm)],[c_2,c_479]) ).
cnf(c_481,plain,
multiply(A,multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity)))) = multiply(identity,identity),
inference(paramod,[status(thm)],[c_2,c_480]) ).
cnf(c_162,plain,
multiply(A,multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity)))) = identity,
inference(paramod,[status(thm)],[c_2,c_481]) ).
cnf(c_482,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(A,identity),multiply(A,identity)),multiply(multiply(multiply(A,identity),identity),identity))))) = multiply(A,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(A,identity),identity),multiply(multiply(A,identity),identity)))))),
inference(paramod,[status(thm)],[c_138,c_74]) ).
cnf(c_483,plain,
multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity))) = multiply(A,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(A,identity),identity),multiply(multiply(A,identity),identity)))))),
inference(paramod,[status(thm)],[c_76,c_482]) ).
cnf(c_484,plain,
multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity))) = multiply(A,multiply(A,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),identity)))))),
inference(paramod,[status(thm)],[c_74,c_483]) ).
cnf(c_167,plain,
multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity))) = multiply(A,multiply(A,A)),
inference(paramod,[status(thm)],[c_11,c_484]) ).
cnf(c_485,plain,
multiply(multiply(multiply(multiply(A,identity),identity),identity),multiply(multiply(multiply(multiply(A,identity),multiply(A,identity)),identity),identity)) = multiply(multiply(multiply(multiply(A,A),multiply(multiply(A,identity),identity)),identity),identity),
inference(paramod,[status(thm)],[c_138,c_106]) ).
cnf(c_486,plain,
multiply(multiply(multiply(multiply(A,identity),identity),identity),multiply(multiply(multiply(multiply(A,identity),identity),identity),multiply(multiply(multiply(A,identity),identity),identity))) = multiply(multiply(multiply(multiply(A,A),multiply(multiply(A,identity),identity)),identity),identity),
inference(paramod,[status(thm)],[c_115,c_485]) ).
cnf(c_487,plain,
multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(A,identity),identity),multiply(multiply(A,identity),identity))) = multiply(multiply(multiply(multiply(A,A),multiply(multiply(A,identity),identity)),identity),identity),
inference(paramod,[status(thm)],[c_167,c_486]) ).
cnf(c_488,plain,
multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity))) = multiply(multiply(multiply(multiply(A,A),multiply(multiply(A,identity),identity)),identity),identity),
inference(paramod,[status(thm)],[c_167,c_487]) ).
cnf(c_489,plain,
multiply(A,multiply(A,A)) = multiply(multiply(multiply(multiply(A,A),multiply(multiply(A,identity),identity)),identity),identity),
inference(paramod,[status(thm)],[c_167,c_488]) ).
cnf(c_490,plain,
multiply(A,multiply(A,A)) = multiply(multiply(multiply(multiply(A,A),identity),identity),multiply(multiply(multiply(multiply(A,identity),identity),identity),identity)),
inference(paramod,[status(thm)],[c_115,c_489]) ).
cnf(c_169,plain,
multiply(multiply(multiply(multiply(A,A),identity),identity),multiply(multiply(multiply(multiply(A,identity),identity),identity),identity)) = multiply(A,multiply(A,A)),
inference(copy,[status(thm)],[c_490]) ).
cnf(c_491,plain,
multiply(multiply(multiply(multiply(A,A),identity),identity),multiply(multiply(multiply(multiply(A,identity),identity),identity),identity)) = multiply(multiply(multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity))),identity),identity),
inference(paramod,[status(thm)],[c_138,c_106]) ).
cnf(c_492,plain,
multiply(A,multiply(A,A)) = multiply(multiply(multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity))),identity),identity),
inference(paramod,[status(thm)],[c_169,c_491]) ).
cnf(c_493,plain,
multiply(A,multiply(A,A)) = multiply(multiply(multiply(A,multiply(A,A)),identity),identity),
inference(paramod,[status(thm)],[c_167,c_492]) ).
cnf(c_494,plain,
multiply(A,multiply(A,A)) = multiply(multiply(A,multiply(multiply(A,A),identity)),identity),
inference(paramod,[status(thm)],[c_124,c_493]) ).
cnf(c_495,plain,
multiply(A,multiply(A,A)) = multiply(multiply(A,A),multiply(multiply(A,identity),identity)),
inference(paramod,[status(thm)],[c_31,c_494]) ).
cnf(c_170,plain,
multiply(multiply(A,A),multiply(multiply(A,identity),identity)) = multiply(A,multiply(A,A)),
inference(copy,[status(thm)],[c_495]) ).
cnf(c_496,plain,
multiply(multiply(A,identity),identity) = multiply(multiply(A,B),multiply(identity,multiply(multiply(B,identity),multiply(multiply(B,identity),multiply(B,identity))))),
inference(paramod,[status(thm)],[c_138,c_116]) ).
cnf(c_172,plain,
multiply(multiply(A,identity),identity) = multiply(multiply(A,B),multiply(identity,multiply(B,multiply(B,B)))),
inference(paramod,[status(thm)],[c_167,c_496]) ).
cnf(c_497,plain,
multiply(multiply(multiply(A,A),multiply(multiply(A,identity),identity)),multiply(identity,multiply(multiply(multiply(A,identity),multiply(A,identity)),multiply(multiply(multiply(A,identity),identity),identity)))) = multiply(multiply(A,identity),multiply(A,identity)),
inference(paramod,[status(thm)],[c_138,c_119]) ).
cnf(c_498,plain,
multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(multiply(A,identity),multiply(A,identity)),multiply(multiply(multiply(A,identity),identity),identity)))) = multiply(multiply(A,identity),multiply(A,identity)),
inference(paramod,[status(thm)],[c_170,c_497]) ).
cnf(c_499,plain,
multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity))))) = multiply(multiply(A,identity),multiply(A,identity)),
inference(paramod,[status(thm)],[c_170,c_498]) ).
cnf(c_174,plain,
multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(A,multiply(A,A)))) = multiply(multiply(A,identity),multiply(A,identity)),
inference(paramod,[status(thm)],[c_167,c_499]) ).
cnf(c_500,plain,
multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,identity))))) = multiply(A,A),
inference(paramod,[status(thm)],[c_138,c_119]) ).
cnf(c_501,plain,
multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(A,multiply(A,A)))) = multiply(A,A),
inference(paramod,[status(thm)],[c_167,c_500]) ).
cnf(c_175,plain,
multiply(multiply(A,identity),multiply(A,identity)) = multiply(A,A),
inference(paramod,[status(thm)],[c_174,c_501]) ).
cnf(c_502,plain,
multiply(multiply(A,A),multiply(multiply(A,identity),identity)) = multiply(A,multiply(multiply(A,A),identity)),
inference(paramod,[status(thm)],[c_138,c_135]) ).
cnf(c_503,plain,
multiply(A,multiply(A,A)) = multiply(A,multiply(multiply(A,A),identity)),
inference(paramod,[status(thm)],[c_170,c_502]) ).
cnf(c_178,plain,
multiply(A,multiply(multiply(A,A),identity)) = multiply(A,multiply(A,A)),
inference(copy,[status(thm)],[c_503]) ).
cnf(c_186,plain,
multiply(A,multiply(multiply(A,identity),multiply(A,A))) = identity,
inference(paramod,[status(thm)],[c_175,c_162]) ).
cnf(c_504,plain,
multiply(multiply(A,identity),multiply(A,A)) = multiply(multiply(A,A),multiply(multiply(A,identity),identity)),
inference(paramod,[status(thm)],[c_175,c_138]) ).
cnf(c_190,plain,
multiply(multiply(A,identity),multiply(A,A)) = multiply(A,multiply(A,A)),
inference(paramod,[status(thm)],[c_170,c_504]) ).
cnf(c_195,plain,
multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(A,multiply(A,A)))) = multiply(A,identity),
inference(paramod,[status(thm)],[c_170,c_161]) ).
cnf(c_202,plain,
multiply(multiply(A,A),multiply(A,multiply(A,A))) = A,
inference(paramod,[status(thm)],[c_170,c_35]) ).
cnf(c_505,plain,
multiply(A,multiply(multiply(A,A),multiply(A,multiply(A,A)))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,A),identity)))),
inference(paramod,[status(thm)],[c_178,c_126]) ).
cnf(c_506,plain,
multiply(A,A) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,A),identity)))),
inference(paramod,[status(thm)],[c_202,c_505]) ).
cnf(c_212,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,A),identity)))) = multiply(A,A),
inference(copy,[status(thm)],[c_506]) ).
cnf(c_213,plain,
multiply(multiply(A,A),multiply(multiply(A,multiply(A,multiply(A,A))),identity)) = multiply(A,A),
inference(paramod,[status(thm)],[c_178,c_125]) ).
cnf(c_217,plain,
multiply(A,multiply(A,multiply(A,A))) = identity,
inference(paramod,[status(thm)],[c_190,c_186]) ).
cnf(c_507,plain,
multiply(multiply(A,A),multiply(identity,identity)) = multiply(A,A),
inference(paramod,[status(thm)],[c_217,c_213]) ).
cnf(c_218,plain,
multiply(multiply(A,A),identity) = multiply(A,A),
inference(paramod,[status(thm)],[c_2,c_507]) ).
cnf(c_219,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))) = multiply(A,A),
inference(paramod,[status(thm)],[c_218,c_212]) ).
cnf(c_508,plain,
multiply(multiply(A,A),multiply(A,multiply(A,A))) = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_219,c_108]) ).
cnf(c_509,plain,
A = multiply(identity,multiply(identity,multiply(identity,A))),
inference(paramod,[status(thm)],[c_202,c_508]) ).
cnf(c_220,plain,
multiply(identity,multiply(identity,multiply(identity,A))) = A,
inference(copy,[status(thm)],[c_509]) ).
cnf(c_510,plain,
multiply(A,B) = multiply(identity,multiply(identity,multiply(identity,multiply(A,multiply(multiply(B,identity),identity))))),
inference(paramod,[status(thm)],[c_220,c_75]) ).
cnf(c_511,plain,
multiply(A,B) = multiply(A,multiply(multiply(B,identity),identity)),
inference(paramod,[status(thm)],[c_220,c_510]) ).
cnf(c_224,plain,
multiply(A,multiply(multiply(B,identity),identity)) = multiply(A,B),
inference(copy,[status(thm)],[c_511]) ).
cnf(c_233,plain,
multiply(multiply(A,A),multiply(A,A)) = identity,
inference(paramod,[status(thm)],[c_224,c_155]) ).
cnf(c_245,plain,
multiply(multiply(identity,A),B) = multiply(identity,multiply(A,multiply(identity,multiply(identity,B)))),
inference(paramod,[status(thm)],[c_224,c_65]) ).
cnf(c_247,plain,
multiply(multiply(A,A),multiply(identity,multiply(A,multiply(A,A)))) = multiply(A,identity),
inference(paramod,[status(thm)],[c_233,c_195]) ).
cnf(c_512,plain,
multiply(identity,multiply(A,identity)) = multiply(multiply(A,identity),identity),
inference(paramod,[status(thm)],[c_233,c_156]) ).
cnf(c_248,plain,
multiply(multiply(A,identity),identity) = multiply(identity,multiply(A,identity)),
inference(copy,[status(thm)],[c_512]) ).
cnf(c_513,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,multiply(identity,multiply(identity,B)))))),multiply(B,multiply(B,B))) = A,
inference(paramod,[status(thm)],[c_245,c_26]) ).
cnf(c_514,plain,
multiply(multiply(A,multiply(identity,multiply(identity,B))),multiply(B,multiply(B,B))) = A,
inference(paramod,[status(thm)],[c_220,c_513]) ).
cnf(c_515,plain,
multiply(multiply(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_63,c_514]) ).
cnf(c_260,plain,
multiply(identity,multiply(A,identity)) = A,
inference(paramod,[status(thm)],[c_248,c_515]) ).
cnf(c_516,plain,
multiply(identity,multiply(A,identity)) = multiply(multiply(A,B),multiply(identity,multiply(B,multiply(B,B)))),
inference(paramod,[status(thm)],[c_248,c_172]) ).
cnf(c_517,plain,
A = multiply(multiply(A,B),multiply(identity,multiply(B,multiply(B,B)))),
inference(paramod,[status(thm)],[c_260,c_516]) ).
cnf(c_264,plain,
multiply(multiply(A,B),multiply(identity,multiply(B,multiply(B,B)))) = A,
inference(copy,[status(thm)],[c_517]) ).
cnf(c_518,plain,
A = multiply(A,identity),
inference(paramod,[status(thm)],[c_264,c_247]) ).
cnf(c_271,plain,
multiply(A,identity) = A,
inference(copy,[status(thm)],[c_518]) ).
cnf(c_272,plain,
$false,
inference(resolve,[status(thm)],[c_271,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP121-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:25:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 372523 was started by sandbox2 on n003,
% 0.10/0.37 % Fri Sep 25 14:25:09 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 2.45/0.72
% 2.45/0.72 % SZS status Unsatisfiable for theBenchmark
% 2.45/0.72
% 2.45/0.72 % Proof 1 at 0.26 (+ 0.07) seconds.
% 2.45/0.72 % Length of proof is 104.
% 2.45/0.72 % Level of proof is 38.
% 2.45/0.72 % Maximum clause weight is 100.000.
% 2.45/0.72 % Given clauses 89.
% 2.45/0.72
% 2.45/0.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------