%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG029-7 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 08:26:26 AM UTC 2026
% Result : Unsatisfiable 105.05s 14.70s
% Output : CNFRefutation 105.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 11
% Syntax : Number of formulae : 174 ( 174 unt; 0 def)
% Number of atoms : 174 ( 173 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 34 ( 34 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 383 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_additive_identity,axiom,
! [VAR_0] : add(additive_identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_additive_identity) ).
cnf(c_1,plain,
add(additive_identity,A) = A,
inference(clausify,[status(thm)],[left_additive_identity]) ).
fof(right_additive_inverse,axiom,
! [VAR_0] : add(VAR_0,additive_inverse(VAR_0)) = additive_identity,
file('theBenchmark.p',right_additive_inverse) ).
cnf(c_6,plain,
add(A,additive_inverse(A)) = additive_identity,
inference(clausify,[status(thm)],[right_additive_inverse]) ).
fof(additive_inverse_additive_inverse,axiom,
! [VAR_0] : additive_inverse(additive_inverse(VAR_0)) = VAR_0,
file('theBenchmark.p',additive_inverse_additive_inverse) ).
cnf(c_7,plain,
additive_inverse(additive_inverse(A)) = A,
inference(clausify,[status(thm)],[additive_inverse_additive_inverse]) ).
fof(distribute1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,add(VAR_1,VAR_2)) = add(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',distribute1) ).
cnf(c_8,plain,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[distribute1]) ).
fof(distribute2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(add(VAR_0,VAR_1),VAR_2) = add(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',distribute2) ).
cnf(c_9,plain,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[distribute2]) ).
fof(commutativity_for_addition,axiom,
! [VAR_0,VAR_1] : add(VAR_0,VAR_1) = add(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_for_addition) ).
cnf(c_10,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutativity_for_addition]) ).
fof(associativity_for_addition,axiom,
! [VAR_0,VAR_1,VAR_2] : add(VAR_0,add(VAR_1,VAR_2)) = add(add(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_for_addition) ).
cnf(c_11,plain,
add(A,add(B,C)) = add(add(A,B),C),
inference(clausify,[status(thm)],[associativity_for_addition]) ).
cnf(c_12,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(copy,[status(thm)],[c_11]) ).
fof(right_alternative,axiom,
! [VAR_0,VAR_1] : multiply(multiply(VAR_0,VAR_1),VAR_1) = multiply(VAR_0,multiply(VAR_1,VAR_1)),
file('theBenchmark.p',right_alternative) ).
cnf(c_13,plain,
multiply(multiply(A,B),B) = multiply(A,multiply(B,B)),
inference(clausify,[status(thm)],[right_alternative]) ).
fof(left_alternative,axiom,
! [VAR_0,VAR_1] : multiply(multiply(VAR_0,VAR_0),VAR_1) = multiply(VAR_0,multiply(VAR_0,VAR_1)),
file('theBenchmark.p',left_alternative) ).
cnf(c_14,plain,
multiply(multiply(A,A),B) = multiply(A,multiply(A,B)),
inference(clausify,[status(thm)],[left_alternative]) ).
fof(inverse_product2,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,additive_inverse(VAR_1)) = additive_inverse(multiply(VAR_0,VAR_1)),
file('theBenchmark.p',inverse_product2) ).
cnf(c_20,plain,
multiply(A,additive_inverse(B)) = additive_inverse(multiply(A,B)),
inference(clausify,[status(thm)],[inverse_product2]) ).
fof(prove_middle_moufang,axiom,
multiply(multiply(x,y),multiply(z,x)) != multiply(multiply(x,multiply(y,z)),x),
file('theBenchmark.p',prove_middle_moufang) ).
cnf(c_26,plain,
multiply(multiply(x,y),multiply(z,x)) != multiply(multiply(x,multiply(y,z)),x),
inference(clausify,[status(thm)],[prove_middle_moufang]) ).
cnf(c_27,plain,
multiply(multiply(x,multiply(y,z)),x) != multiply(multiply(x,y),multiply(z,x)),
inference(copy,[status(thm)],[c_26]) ).
cnf(c_5473,plain,
add(additive_identity,A) = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_6,c_12]) ).
cnf(c_5474,plain,
A = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_5473]) ).
cnf(c_31,plain,
add(A,add(additive_inverse(A),B)) = B,
inference(copy,[status(thm)],[c_5474]) ).
cnf(c_5475,plain,
add(add(A,B),C) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_10,c_12]) ).
cnf(c_33,plain,
add(A,add(B,C)) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_12,c_5475]) ).
cnf(c_5476,plain,
multiply(A,multiply(add(B,C),add(B,C))) = add(multiply(multiply(A,add(B,C)),B),multiply(multiply(A,add(B,C)),C)),
inference(paramod,[status(thm)],[c_13,c_8]) ).
cnf(c_5477,plain,
multiply(A,add(multiply(add(B,C),B),multiply(add(B,C),C))) = add(multiply(multiply(A,add(B,C)),B),multiply(multiply(A,add(B,C)),C)),
inference(paramod,[status(thm)],[c_8,c_5476]) ).
cnf(c_5478,plain,
multiply(A,add(add(multiply(B,B),multiply(C,B)),multiply(add(B,C),C))) = add(multiply(multiply(A,add(B,C)),B),multiply(multiply(A,add(B,C)),C)),
inference(paramod,[status(thm)],[c_9,c_5477]) ).
cnf(c_5479,plain,
multiply(A,add(add(multiply(B,B),multiply(C,B)),add(multiply(B,C),multiply(C,C)))) = add(multiply(multiply(A,add(B,C)),B),multiply(multiply(A,add(B,C)),C)),
inference(paramod,[status(thm)],[c_9,c_5478]) ).
cnf(c_5480,plain,
multiply(A,add(multiply(B,B),add(multiply(C,B),add(multiply(B,C),multiply(C,C))))) = add(multiply(multiply(A,add(B,C)),B),multiply(multiply(A,add(B,C)),C)),
inference(paramod,[status(thm)],[c_12,c_5479]) ).
cnf(c_5481,plain,
add(multiply(A,multiply(B,B)),multiply(A,add(multiply(C,B),add(multiply(B,C),multiply(C,C))))) = add(multiply(multiply(A,add(B,C)),B),multiply(multiply(A,add(B,C)),C)),
inference(paramod,[status(thm)],[c_8,c_5480]) ).
cnf(c_5482,plain,
add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),multiply(A,add(multiply(B,C),multiply(C,C))))) = add(multiply(multiply(A,add(B,C)),B),multiply(multiply(A,add(B,C)),C)),
inference(paramod,[status(thm)],[c_8,c_5481]) ).
cnf(c_5483,plain,
add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C))))) = add(multiply(multiply(A,add(B,C)),B),multiply(multiply(A,add(B,C)),C)),
inference(paramod,[status(thm)],[c_8,c_5482]) ).
cnf(c_5484,plain,
add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C))))) = add(multiply(add(multiply(A,B),multiply(A,C)),B),multiply(multiply(A,add(B,C)),C)),
inference(paramod,[status(thm)],[c_8,c_5483]) ).
cnf(c_5485,plain,
add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C))))) = add(add(multiply(multiply(A,B),B),multiply(multiply(A,C),B)),multiply(multiply(A,add(B,C)),C)),
inference(paramod,[status(thm)],[c_9,c_5484]) ).
cnf(c_5486,plain,
add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C))))) = add(add(multiply(A,multiply(B,B)),multiply(multiply(A,C),B)),multiply(multiply(A,add(B,C)),C)),
inference(paramod,[status(thm)],[c_13,c_5485]) ).
cnf(c_5487,plain,
add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C))))) = add(add(multiply(A,multiply(B,B)),multiply(multiply(A,C),B)),multiply(add(multiply(A,B),multiply(A,C)),C)),
inference(paramod,[status(thm)],[c_8,c_5486]) ).
cnf(c_5488,plain,
add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C))))) = add(add(multiply(A,multiply(B,B)),multiply(multiply(A,C),B)),add(multiply(multiply(A,B),C),multiply(multiply(A,C),C))),
inference(paramod,[status(thm)],[c_9,c_5487]) ).
cnf(c_5489,plain,
add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C))))) = add(add(multiply(A,multiply(B,B)),multiply(multiply(A,C),B)),add(multiply(multiply(A,B),C),multiply(A,multiply(C,C)))),
inference(paramod,[status(thm)],[c_13,c_5488]) ).
cnf(c_5490,plain,
add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C))))) = add(multiply(A,multiply(B,B)),add(multiply(multiply(A,C),B),add(multiply(multiply(A,B),C),multiply(A,multiply(C,C))))),
inference(paramod,[status(thm)],[c_12,c_5489]) ).
cnf(c_34,plain,
add(multiply(A,multiply(B,B)),add(multiply(multiply(A,C),B),add(multiply(multiply(A,B),C),multiply(A,multiply(C,C))))) = add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C))))),
inference(copy,[status(thm)],[c_5490]) ).
cnf(c_5491,plain,
multiply(add(multiply(add(A,B),A),multiply(add(A,B),B)),C) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_8,c_14]) ).
cnf(c_5492,plain,
multiply(add(add(multiply(A,A),multiply(B,A)),multiply(add(A,B),B)),C) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_9,c_5491]) ).
cnf(c_5493,plain,
multiply(add(add(multiply(A,A),multiply(B,A)),add(multiply(A,B),multiply(B,B))),C) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_9,c_5492]) ).
cnf(c_5494,plain,
multiply(add(multiply(A,A),add(multiply(B,A),add(multiply(A,B),multiply(B,B)))),C) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_12,c_5493]) ).
cnf(c_5495,plain,
add(multiply(multiply(A,A),C),multiply(add(multiply(B,A),add(multiply(A,B),multiply(B,B))),C)) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_9,c_5494]) ).
cnf(c_5496,plain,
add(multiply(A,multiply(A,C)),multiply(add(multiply(B,A),add(multiply(A,B),multiply(B,B))),C)) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_14,c_5495]) ).
cnf(c_5497,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(B,A),C),multiply(add(multiply(A,B),multiply(B,B)),C))) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_9,c_5496]) ).
cnf(c_5498,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(B,A),C),add(multiply(multiply(A,B),C),multiply(multiply(B,B),C)))) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_9,c_5497]) ).
cnf(c_5499,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(B,A),C),add(multiply(multiply(A,B),C),multiply(B,multiply(B,C))))) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_14,c_5498]) ).
cnf(c_5500,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(B,A),C),add(multiply(B,multiply(B,C)),multiply(multiply(A,B),C)))) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_10,c_5499]) ).
cnf(c_5501,plain,
add(multiply(A,multiply(A,C)),add(multiply(B,multiply(B,C)),add(multiply(multiply(B,A),C),multiply(multiply(A,B),C)))) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_33,c_5500]) ).
cnf(c_5502,plain,
add(multiply(A,multiply(A,C)),add(multiply(B,multiply(B,C)),add(multiply(multiply(B,A),C),multiply(multiply(A,B),C)))) = multiply(add(A,B),add(multiply(A,C),multiply(B,C))),
inference(paramod,[status(thm)],[c_9,c_5501]) ).
cnf(c_5503,plain,
add(multiply(A,multiply(A,C)),add(multiply(B,multiply(B,C)),add(multiply(multiply(B,A),C),multiply(multiply(A,B),C)))) = add(multiply(add(A,B),multiply(A,C)),multiply(add(A,B),multiply(B,C))),
inference(paramod,[status(thm)],[c_8,c_5502]) ).
cnf(c_5504,plain,
add(multiply(A,multiply(A,C)),add(multiply(B,multiply(B,C)),add(multiply(multiply(B,A),C),multiply(multiply(A,B),C)))) = add(add(multiply(A,multiply(A,C)),multiply(B,multiply(A,C))),multiply(add(A,B),multiply(B,C))),
inference(paramod,[status(thm)],[c_9,c_5503]) ).
cnf(c_5505,plain,
add(multiply(A,multiply(A,C)),add(multiply(B,multiply(B,C)),add(multiply(multiply(B,A),C),multiply(multiply(A,B),C)))) = add(add(multiply(A,multiply(A,C)),multiply(B,multiply(A,C))),add(multiply(A,multiply(B,C)),multiply(B,multiply(B,C)))),
inference(paramod,[status(thm)],[c_9,c_5504]) ).
cnf(c_36,plain,
add(multiply(A,multiply(A,B)),add(multiply(C,multiply(C,B)),add(multiply(multiply(C,A),B),multiply(multiply(A,C),B)))) = add(multiply(A,multiply(A,B)),add(multiply(C,multiply(A,B)),add(multiply(A,multiply(C,B)),multiply(C,multiply(C,B))))),
inference(paramod,[status(thm)],[c_12,c_5505]) ).
cnf(c_55,plain,
add(A,add(B,additive_inverse(A))) = B,
inference(paramod,[status(thm)],[c_10,c_31]) ).
cnf(c_58,plain,
add(additive_inverse(A),add(B,A)) = B,
inference(paramod,[status(thm)],[c_7,c_55]) ).
cnf(c_5506,plain,
add(A,B) = add(C,add(add(A,additive_inverse(C)),B)),
inference(paramod,[status(thm)],[c_55,c_12]) ).
cnf(c_5507,plain,
add(A,B) = add(C,add(A,add(additive_inverse(C),B))),
inference(paramod,[status(thm)],[c_12,c_5506]) ).
cnf(c_59,plain,
add(A,add(B,add(additive_inverse(A),C))) = add(B,C),
inference(copy,[status(thm)],[c_5507]) ).
cnf(c_5508,plain,
add(A,B) = add(additive_inverse(C),add(add(A,C),B)),
inference(paramod,[status(thm)],[c_58,c_12]) ).
cnf(c_5509,plain,
add(A,B) = add(additive_inverse(C),add(A,add(C,B))),
inference(paramod,[status(thm)],[c_12,c_5508]) ).
cnf(c_62,plain,
add(additive_inverse(A),add(B,add(A,C))) = add(B,C),
inference(copy,[status(thm)],[c_5509]) ).
cnf(c_63,plain,
add(additive_inverse(A),add(B,add(C,A))) = add(B,C),
inference(paramod,[status(thm)],[c_12,c_58]) ).
cnf(c_5510,plain,
add(additive_inverse(add(A,B)),A) = additive_inverse(B),
inference(paramod,[status(thm)],[c_58,c_58]) ).
cnf(c_66,plain,
add(A,additive_inverse(add(A,B))) = additive_inverse(B),
inference(paramod,[status(thm)],[c_10,c_5510]) ).
cnf(c_5511,plain,
add(additive_inverse(A),additive_inverse(B)) = additive_inverse(add(B,A)),
inference(paramod,[status(thm)],[c_58,c_66]) ).
cnf(c_72,plain,
additive_inverse(add(A,B)) = add(additive_inverse(B),additive_inverse(A)),
inference(copy,[status(thm)],[c_5511]) ).
cnf(c_5512,plain,
add(multiply(A,multiply(B,B)),add(multiply(A,multiply(A,B)),add(multiply(multiply(A,B),A),multiply(A,multiply(A,A))))) = add(multiply(A,multiply(B,B)),add(multiply(A,multiply(A,B)),add(multiply(A,multiply(B,A)),multiply(A,multiply(A,A))))),
inference(paramod,[status(thm)],[c_14,c_34]) ).
cnf(c_76,plain,
add(multiply(A,multiply(B,B)),add(multiply(A,multiply(A,B)),add(multiply(A,multiply(A,A)),multiply(multiply(A,B),A)))) = add(multiply(A,multiply(B,B)),add(multiply(A,multiply(A,B)),add(multiply(A,multiply(B,A)),multiply(A,multiply(A,A))))),
inference(paramod,[status(thm)],[c_10,c_5512]) ).
cnf(c_5513,plain,
add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C))))) = add(multiply(multiply(A,C),B),add(multiply(A,multiply(B,B)),add(multiply(multiply(A,B),C),multiply(A,multiply(C,C))))),
inference(paramod,[status(thm)],[c_34,c_33]) ).
cnf(c_83,plain,
add(multiply(multiply(A,B),C),add(multiply(A,multiply(C,C)),add(multiply(multiply(A,C),B),multiply(A,multiply(B,B))))) = add(multiply(A,multiply(C,C)),add(multiply(A,multiply(B,C)),add(multiply(A,multiply(C,B)),multiply(A,multiply(B,B))))),
inference(copy,[status(thm)],[c_5513]) ).
cnf(c_5514,plain,
add(additive_inverse(A),add(B,add(C,add(A,D)))) = add(add(B,C),D),
inference(paramod,[status(thm)],[c_12,c_62]) ).
cnf(c_95,plain,
add(additive_inverse(A),add(B,add(C,add(A,D)))) = add(B,add(C,D)),
inference(paramod,[status(thm)],[c_12,c_5514]) ).
cnf(c_5515,plain,
add(additive_inverse(multiply(A,multiply(A,B))),add(multiply(C,multiply(C,B)),add(multiply(A,multiply(C,B)),add(multiply(C,multiply(A,B)),multiply(A,multiply(A,B)))))) = add(multiply(C,multiply(C,B)),add(multiply(multiply(A,C),B),multiply(multiply(C,A),B))),
inference(paramod,[status(thm)],[c_36,c_62]) ).
cnf(c_99,plain,
add(multiply(A,multiply(A,B)),add(multiply(multiply(C,A),B),multiply(multiply(A,C),B))) = add(additive_inverse(multiply(C,multiply(C,B))),add(multiply(A,multiply(A,B)),add(multiply(C,multiply(A,B)),add(multiply(A,multiply(C,B)),multiply(C,multiply(C,B)))))),
inference(copy,[status(thm)],[c_5515]) ).
cnf(c_100,plain,
add(additive_inverse(A),add(B,add(C,add(D,A)))) = add(B,add(C,D)),
inference(paramod,[status(thm)],[c_12,c_63]) ).
cnf(c_101,plain,
add(multiply(A,multiply(A,B)),add(multiply(multiply(C,A),B),multiply(multiply(A,C),B))) = add(multiply(A,multiply(A,B)),add(multiply(C,multiply(A,B)),multiply(A,multiply(C,B)))),
inference(paramod,[status(thm)],[c_100,c_99]) ).
cnf(c_5516,plain,
add(additive_inverse(add(multiply(A,multiply(A,B)),add(multiply(A,multiply(A,A)),multiply(multiply(A,B),A)))),add(multiply(A,multiply(B,B)),add(multiply(A,multiply(A,B)),add(multiply(A,multiply(B,A)),multiply(A,multiply(A,A)))))) = multiply(A,multiply(B,B)),
inference(paramod,[status(thm)],[c_76,c_58]) ).
cnf(c_5517,plain,
add(add(additive_inverse(add(multiply(A,multiply(A,A)),multiply(multiply(A,B),A))),additive_inverse(multiply(A,multiply(A,B)))),add(multiply(A,multiply(B,B)),add(multiply(A,multiply(A,B)),add(multiply(A,multiply(B,A)),multiply(A,multiply(A,A)))))) = multiply(A,multiply(B,B)),
inference(paramod,[status(thm)],[c_72,c_5516]) ).
cnf(c_5518,plain,
add(add(add(additive_inverse(multiply(multiply(A,B),A)),additive_inverse(multiply(A,multiply(A,A)))),additive_inverse(multiply(A,multiply(A,B)))),add(multiply(A,multiply(B,B)),add(multiply(A,multiply(A,B)),add(multiply(A,multiply(B,A)),multiply(A,multiply(A,A)))))) = multiply(A,multiply(B,B)),
inference(paramod,[status(thm)],[c_72,c_5517]) ).
cnf(c_5519,plain,
add(add(add(additive_inverse(multiply(A,multiply(A,A))),additive_inverse(multiply(multiply(A,B),A))),additive_inverse(multiply(A,multiply(A,B)))),add(multiply(A,multiply(B,B)),add(multiply(A,multiply(A,B)),add(multiply(A,multiply(B,A)),multiply(A,multiply(A,A)))))) = multiply(A,multiply(B,B)),
inference(paramod,[status(thm)],[c_10,c_5518]) ).
cnf(c_5520,plain,
add(add(additive_inverse(multiply(A,multiply(A,B))),add(additive_inverse(multiply(A,multiply(A,A))),additive_inverse(multiply(multiply(A,B),A)))),add(multiply(A,multiply(B,B)),add(multiply(A,multiply(A,B)),add(multiply(A,multiply(B,A)),multiply(A,multiply(A,A)))))) = multiply(A,multiply(B,B)),
inference(paramod,[status(thm)],[c_10,c_5519]) ).
cnf(c_5521,plain,
add(add(multiply(A,multiply(B,B)),add(multiply(A,multiply(A,B)),add(multiply(A,multiply(B,A)),multiply(A,multiply(A,A))))),add(additive_inverse(multiply(A,multiply(A,B))),add(additive_inverse(multiply(A,multiply(A,A))),additive_inverse(multiply(multiply(A,B),A))))) = multiply(A,multiply(B,B)),
inference(paramod,[status(thm)],[c_10,c_5520]) ).
cnf(c_5522,plain,
add(multiply(A,multiply(B,B)),add(add(multiply(A,multiply(A,B)),add(multiply(A,multiply(B,A)),multiply(A,multiply(A,A)))),add(additive_inverse(multiply(A,multiply(A,B))),add(additive_inverse(multiply(A,multiply(A,A))),additive_inverse(multiply(multiply(A,B),A)))))) = multiply(A,multiply(B,B)),
inference(paramod,[status(thm)],[c_12,c_5521]) ).
cnf(c_5523,plain,
add(multiply(A,multiply(B,B)),add(multiply(A,multiply(A,B)),add(add(multiply(A,multiply(B,A)),multiply(A,multiply(A,A))),add(additive_inverse(multiply(A,multiply(A,B))),add(additive_inverse(multiply(A,multiply(A,A))),additive_inverse(multiply(multiply(A,B),A))))))) = multiply(A,multiply(B,B)),
inference(paramod,[status(thm)],[c_12,c_5522]) ).
cnf(c_5524,plain,
add(multiply(A,multiply(B,B)),add(multiply(A,multiply(A,B)),add(multiply(A,multiply(B,A)),add(multiply(A,multiply(A,A)),add(additive_inverse(multiply(A,multiply(A,B))),add(additive_inverse(multiply(A,multiply(A,A))),additive_inverse(multiply(multiply(A,B),A)))))))) = multiply(A,multiply(B,B)),
inference(paramod,[status(thm)],[c_12,c_5523]) ).
cnf(c_5525,plain,
add(multiply(A,multiply(B,B)),add(multiply(A,multiply(A,B)),add(multiply(A,multiply(B,A)),add(additive_inverse(multiply(A,multiply(A,B))),additive_inverse(multiply(multiply(A,B),A)))))) = multiply(A,multiply(B,B)),
inference(paramod,[status(thm)],[c_59,c_5524]) ).
cnf(c_176,plain,
add(multiply(A,multiply(B,B)),add(multiply(A,multiply(B,A)),additive_inverse(multiply(multiply(A,B),A)))) = multiply(A,multiply(B,B)),
inference(paramod,[status(thm)],[c_59,c_5525]) ).
cnf(c_5526,plain,
add(additive_inverse(multiply(A,multiply(B,B))),add(C,multiply(A,multiply(B,B)))) = add(C,add(multiply(A,multiply(B,A)),additive_inverse(multiply(multiply(A,B),A)))),
inference(paramod,[status(thm)],[c_176,c_62]) ).
cnf(c_5527,plain,
C = add(C,add(multiply(A,multiply(B,A)),additive_inverse(multiply(multiply(A,B),A)))),
inference(paramod,[status(thm)],[c_58,c_5526]) ).
cnf(c_220,plain,
add(A,add(multiply(B,multiply(C,B)),additive_inverse(multiply(multiply(B,C),B)))) = A,
inference(copy,[status(thm)],[c_5527]) ).
cnf(c_290,plain,
multiply(multiply(A,B),A) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_220,c_55]) ).
cnf(c_295,plain,
multiply(x,multiply(multiply(y,z),x)) != multiply(multiply(x,y),multiply(z,x)),
inference(paramod,[status(thm)],[c_290,c_27]) ).
cnf(c_5528,plain,
add(additive_inverse(add(multiply(A,multiply(B,B)),add(multiply(multiply(A,B),C),multiply(A,multiply(C,C))))),add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C)))))) = multiply(multiply(A,C),B),
inference(paramod,[status(thm)],[c_83,c_58]) ).
cnf(c_5529,plain,
add(add(additive_inverse(add(multiply(multiply(A,B),C),multiply(A,multiply(C,C)))),additive_inverse(multiply(A,multiply(B,B)))),add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C)))))) = multiply(multiply(A,C),B),
inference(paramod,[status(thm)],[c_72,c_5528]) ).
cnf(c_5530,plain,
add(add(add(additive_inverse(multiply(A,multiply(C,C))),additive_inverse(multiply(multiply(A,B),C))),additive_inverse(multiply(A,multiply(B,B)))),add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C)))))) = multiply(multiply(A,C),B),
inference(paramod,[status(thm)],[c_72,c_5529]) ).
cnf(c_5531,plain,
add(add(additive_inverse(multiply(A,multiply(B,B))),add(additive_inverse(multiply(A,multiply(C,C))),additive_inverse(multiply(multiply(A,B),C)))),add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C)))))) = multiply(multiply(A,C),B),
inference(paramod,[status(thm)],[c_10,c_5530]) ).
cnf(c_5532,plain,
add(multiply(A,multiply(B,B)),add(add(additive_inverse(multiply(A,multiply(B,B))),add(additive_inverse(multiply(A,multiply(C,C))),additive_inverse(multiply(multiply(A,B),C)))),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C)))))) = multiply(multiply(A,C),B),
inference(paramod,[status(thm)],[c_33,c_5531]) ).
cnf(c_5533,plain,
add(multiply(A,multiply(B,B)),add(additive_inverse(multiply(A,multiply(B,B))),add(add(additive_inverse(multiply(A,multiply(C,C))),additive_inverse(multiply(multiply(A,B),C))),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C))))))) = multiply(multiply(A,C),B),
inference(paramod,[status(thm)],[c_12,c_5532]) ).
cnf(c_5534,plain,
add(multiply(A,multiply(B,B)),add(additive_inverse(multiply(A,multiply(B,B))),add(additive_inverse(multiply(A,multiply(C,C))),add(additive_inverse(multiply(multiply(A,B),C)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C)))))))) = multiply(multiply(A,C),B),
inference(paramod,[status(thm)],[c_12,c_5533]) ).
cnf(c_5535,plain,
add(multiply(A,multiply(B,B)),add(additive_inverse(multiply(A,multiply(B,B))),add(additive_inverse(multiply(multiply(A,B),C)),add(multiply(A,multiply(C,B)),multiply(A,multiply(B,C)))))) = multiply(multiply(A,C),B),
inference(paramod,[status(thm)],[c_100,c_5534]) ).
cnf(c_5536,plain,
add(additive_inverse(multiply(multiply(A,B),C)),add(multiply(A,multiply(C,B)),multiply(A,multiply(B,C)))) = multiply(multiply(A,C),B),
inference(paramod,[status(thm)],[c_31,c_5535]) ).
cnf(c_333,plain,
multiply(multiply(A,B),C) = add(additive_inverse(multiply(multiply(A,C),B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,B)))),
inference(copy,[status(thm)],[c_5536]) ).
cnf(c_5537,plain,
multiply(x,multiply(multiply(y,z),x)) != add(additive_inverse(multiply(multiply(x,multiply(z,x)),y)),add(multiply(x,multiply(y,multiply(z,x))),multiply(x,multiply(multiply(z,x),y)))),
inference(paramod,[status(thm)],[c_333,c_295]) ).
cnf(c_5538,plain,
multiply(x,multiply(multiply(y,z),x)) != add(add(multiply(x,multiply(y,multiply(z,x))),multiply(x,multiply(multiply(z,x),y))),additive_inverse(multiply(multiply(x,multiply(z,x)),y))),
inference(paramod,[status(thm)],[c_10,c_5537]) ).
cnf(c_5539,plain,
multiply(x,multiply(multiply(y,z),x)) != add(multiply(x,multiply(y,multiply(z,x))),add(multiply(x,multiply(multiply(z,x),y)),additive_inverse(multiply(multiply(x,multiply(z,x)),y)))),
inference(paramod,[status(thm)],[c_12,c_5538]) ).
cnf(c_454,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(multiply(x,multiply(multiply(z,x),y)),additive_inverse(multiply(multiply(x,multiply(z,x)),y)))) != multiply(x,multiply(multiply(y,z),x)),
inference(copy,[status(thm)],[c_5539]) ).
cnf(c_5540,plain,
add(additive_inverse(multiply(A,multiply(A,B))),add(C,add(multiply(A,multiply(A,B)),add(multiply(D,multiply(A,B)),multiply(A,multiply(D,B)))))) = add(C,add(multiply(multiply(D,A),B),multiply(multiply(A,D),B))),
inference(paramod,[status(thm)],[c_101,c_62]) ).
cnf(c_5541,plain,
add(C,add(multiply(D,multiply(A,B)),multiply(A,multiply(D,B)))) = add(C,add(multiply(multiply(D,A),B),multiply(multiply(A,D),B))),
inference(paramod,[status(thm)],[c_62,c_5540]) ).
cnf(c_791,plain,
add(A,add(multiply(multiply(B,C),D),multiply(multiply(C,B),D))) = add(A,add(multiply(B,multiply(C,D)),multiply(C,multiply(B,D)))),
inference(copy,[status(thm)],[c_5541]) ).
cnf(c_5542,plain,
add(additive_inverse(multiply(multiply(A,B),C)),add(multiply(B,multiply(A,C)),multiply(A,multiply(B,C)))) = multiply(multiply(B,A),C),
inference(paramod,[status(thm)],[c_791,c_58]) ).
cnf(c_5543,plain,
add(add(multiply(B,multiply(A,C)),multiply(A,multiply(B,C))),additive_inverse(multiply(multiply(A,B),C))) = multiply(multiply(B,A),C),
inference(paramod,[status(thm)],[c_10,c_5542]) ).
cnf(c_5544,plain,
add(multiply(B,multiply(A,C)),add(multiply(A,multiply(B,C)),additive_inverse(multiply(multiply(A,B),C)))) = multiply(multiply(B,A),C),
inference(paramod,[status(thm)],[c_12,c_5543]) ).
cnf(c_1898,plain,
multiply(multiply(A,B),C) = add(multiply(A,multiply(B,C)),add(multiply(B,multiply(A,C)),additive_inverse(multiply(multiply(B,A),C)))),
inference(copy,[status(thm)],[c_5544]) ).
cnf(c_5545,plain,
multiply(multiply(A,B),C) = add(additive_inverse(add(multiply(A,multiply(C,B)),add(multiply(C,multiply(A,B)),additive_inverse(multiply(multiply(C,A),B))))),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,B)))),
inference(paramod,[status(thm)],[c_1898,c_333]) ).
cnf(c_5546,plain,
multiply(multiply(A,B),C) = add(add(additive_inverse(add(multiply(C,multiply(A,B)),additive_inverse(multiply(multiply(C,A),B)))),additive_inverse(multiply(A,multiply(C,B)))),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,B)))),
inference(paramod,[status(thm)],[c_72,c_5545]) ).
cnf(c_5547,plain,
multiply(multiply(A,B),C) = add(add(add(additive_inverse(additive_inverse(multiply(multiply(C,A),B))),additive_inverse(multiply(C,multiply(A,B)))),additive_inverse(multiply(A,multiply(C,B)))),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,B)))),
inference(paramod,[status(thm)],[c_72,c_5546]) ).
cnf(c_5548,plain,
multiply(multiply(A,B),C) = add(add(add(multiply(multiply(C,A),B),additive_inverse(multiply(C,multiply(A,B)))),additive_inverse(multiply(A,multiply(C,B)))),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,B)))),
inference(paramod,[status(thm)],[c_7,c_5547]) ).
cnf(c_5549,plain,
multiply(multiply(A,B),C) = add(add(add(additive_inverse(multiply(C,multiply(A,B))),multiply(multiply(C,A),B)),additive_inverse(multiply(A,multiply(C,B)))),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,B)))),
inference(paramod,[status(thm)],[c_10,c_5548]) ).
cnf(c_5550,plain,
multiply(multiply(A,B),C) = add(add(additive_inverse(multiply(A,multiply(C,B))),add(additive_inverse(multiply(C,multiply(A,B))),multiply(multiply(C,A),B))),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,B)))),
inference(paramod,[status(thm)],[c_10,c_5549]) ).
cnf(c_5551,plain,
multiply(multiply(A,B),C) = add(additive_inverse(multiply(A,multiply(C,B))),add(add(additive_inverse(multiply(C,multiply(A,B))),multiply(multiply(C,A),B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,B))))),
inference(paramod,[status(thm)],[c_12,c_5550]) ).
cnf(c_5552,plain,
multiply(multiply(A,B),C) = add(additive_inverse(multiply(A,multiply(C,B))),add(additive_inverse(multiply(C,multiply(A,B))),add(multiply(multiply(C,A),B),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,B)))))),
inference(paramod,[status(thm)],[c_12,c_5551]) ).
cnf(c_2114,plain,
multiply(multiply(A,B),C) = add(additive_inverse(multiply(C,multiply(A,B))),add(multiply(multiply(C,A),B),multiply(A,multiply(B,C)))),
inference(paramod,[status(thm)],[c_100,c_5552]) ).
cnf(c_5553,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(multiply(x,multiply(multiply(z,x),y)),additive_inverse(add(multiply(x,multiply(multiply(z,x),y)),add(multiply(multiply(z,x),multiply(x,y)),additive_inverse(multiply(multiply(multiply(z,x),x),y))))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_1898,c_454]) ).
cnf(c_5554,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(multiply(x,multiply(multiply(z,x),y)),additive_inverse(add(multiply(x,multiply(multiply(z,x),y)),add(multiply(multiply(z,x),multiply(x,y)),additive_inverse(multiply(multiply(z,multiply(x,x)),y))))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_13,c_5553]) ).
cnf(c_5555,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(multiply(x,multiply(multiply(z,x),y)),add(additive_inverse(add(multiply(multiply(z,x),multiply(x,y)),additive_inverse(multiply(multiply(z,multiply(x,x)),y)))),additive_inverse(multiply(x,multiply(multiply(z,x),y)))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_72,c_5554]) ).
cnf(c_5556,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(multiply(x,multiply(multiply(z,x),y)),add(add(additive_inverse(additive_inverse(multiply(multiply(z,multiply(x,x)),y))),additive_inverse(multiply(multiply(z,x),multiply(x,y)))),additive_inverse(multiply(x,multiply(multiply(z,x),y)))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_72,c_5555]) ).
cnf(c_5557,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(multiply(x,multiply(multiply(z,x),y)),add(add(multiply(multiply(z,multiply(x,x)),y),additive_inverse(multiply(multiply(z,x),multiply(x,y)))),additive_inverse(multiply(x,multiply(multiply(z,x),y)))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_7,c_5556]) ).
cnf(c_5558,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(multiply(x,multiply(multiply(z,x),y)),add(add(additive_inverse(multiply(multiply(z,x),multiply(x,y))),multiply(multiply(z,multiply(x,x)),y)),additive_inverse(multiply(x,multiply(multiply(z,x),y)))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_10,c_5557]) ).
cnf(c_5559,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(multiply(x,multiply(multiply(z,x),y)),add(additive_inverse(multiply(x,multiply(multiply(z,x),y))),add(additive_inverse(multiply(multiply(z,x),multiply(x,y))),multiply(multiply(z,multiply(x,x)),y))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_10,c_5558]) ).
cnf(c_2136,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(multiply(z,x),multiply(x,y))),multiply(multiply(z,multiply(x,x)),y))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_31,c_5559]) ).
cnf(c_3767,plain,
multiply(multiply(A,B),C) = add(additive_inverse(multiply(C,multiply(A,B))),add(multiply(A,multiply(B,C)),multiply(multiply(C,A),B))),
inference(paramod,[status(thm)],[c_10,c_2114]) ).
cnf(c_3786,plain,
add(additive_inverse(multiply(multiply(A,B),C)),multiply(multiply(B,C),A)) = add(additive_inverse(multiply(A,multiply(B,C))),multiply(B,multiply(C,A))),
inference(paramod,[status(thm)],[c_2114,c_62]) ).
cnf(c_5560,plain,
multiply(multiply(A,B),C) = add(additive_inverse(multiply(C,multiply(A,B))),add(add(additive_inverse(multiply(B,multiply(C,A))),add(multiply(multiply(B,C),A),multiply(C,multiply(A,B)))),multiply(A,multiply(B,C)))),
inference(paramod,[status(thm)],[c_2114,c_2114]) ).
cnf(c_5561,plain,
multiply(multiply(A,B),C) = add(additive_inverse(multiply(C,multiply(A,B))),add(additive_inverse(multiply(B,multiply(C,A))),add(add(multiply(multiply(B,C),A),multiply(C,multiply(A,B))),multiply(A,multiply(B,C))))),
inference(paramod,[status(thm)],[c_12,c_5560]) ).
cnf(c_5562,plain,
multiply(multiply(A,B),C) = add(additive_inverse(multiply(C,multiply(A,B))),add(additive_inverse(multiply(B,multiply(C,A))),add(multiply(multiply(B,C),A),add(multiply(C,multiply(A,B)),multiply(A,multiply(B,C)))))),
inference(paramod,[status(thm)],[c_12,c_5561]) ).
cnf(c_4038,plain,
multiply(multiply(A,B),C) = add(additive_inverse(multiply(B,multiply(C,A))),add(multiply(multiply(B,C),A),multiply(A,multiply(B,C)))),
inference(paramod,[status(thm)],[c_95,c_5562]) ).
cnf(c_5563,plain,
additive_inverse(add(additive_inverse(multiply(A,multiply(B,C))),multiply(B,multiply(C,A)))) = add(additive_inverse(multiply(multiply(B,C),A)),additive_inverse(additive_inverse(multiply(multiply(A,B),C)))),
inference(paramod,[status(thm)],[c_3786,c_72]) ).
cnf(c_5564,plain,
add(additive_inverse(multiply(B,multiply(C,A))),additive_inverse(additive_inverse(multiply(A,multiply(B,C))))) = add(additive_inverse(multiply(multiply(B,C),A)),additive_inverse(additive_inverse(multiply(multiply(A,B),C)))),
inference(paramod,[status(thm)],[c_72,c_5563]) ).
cnf(c_5565,plain,
add(additive_inverse(multiply(B,multiply(C,A))),multiply(A,multiply(B,C))) = add(additive_inverse(multiply(multiply(B,C),A)),additive_inverse(additive_inverse(multiply(multiply(A,B),C)))),
inference(paramod,[status(thm)],[c_7,c_5564]) ).
cnf(c_5566,plain,
add(additive_inverse(multiply(B,multiply(C,A))),multiply(A,multiply(B,C))) = add(additive_inverse(multiply(multiply(B,C),A)),multiply(multiply(A,B),C)),
inference(paramod,[status(thm)],[c_7,c_5565]) ).
cnf(c_4511,plain,
add(additive_inverse(multiply(multiply(A,B),C)),multiply(multiply(C,A),B)) = add(additive_inverse(multiply(A,multiply(B,C))),multiply(C,multiply(A,B))),
inference(copy,[status(thm)],[c_5566]) ).
cnf(c_5567,plain,
add(additive_inverse(multiply(multiply(A,multiply(A,B)),C)),multiply(multiply(C,multiply(A,A)),B)) = add(additive_inverse(multiply(multiply(A,A),multiply(B,C))),multiply(C,multiply(multiply(A,A),B))),
inference(paramod,[status(thm)],[c_14,c_4511]) ).
cnf(c_5568,plain,
add(additive_inverse(multiply(multiply(A,multiply(A,B)),C)),multiply(multiply(C,multiply(A,A)),B)) = add(additive_inverse(multiply(A,multiply(A,multiply(B,C)))),multiply(C,multiply(multiply(A,A),B))),
inference(paramod,[status(thm)],[c_14,c_5567]) ).
cnf(c_4832,plain,
add(additive_inverse(multiply(multiply(A,multiply(A,B)),C)),multiply(multiply(C,multiply(A,A)),B)) = add(additive_inverse(multiply(A,multiply(A,multiply(B,C)))),multiply(C,multiply(A,multiply(A,B)))),
inference(paramod,[status(thm)],[c_14,c_5568]) ).
cnf(c_5569,plain,
multiply(A,multiply(multiply(B,C),D)) = add(multiply(A,additive_inverse(multiply(D,multiply(B,C)))),multiply(A,add(multiply(B,multiply(C,D)),multiply(multiply(D,B),C)))),
inference(paramod,[status(thm)],[c_3767,c_8]) ).
cnf(c_5570,plain,
multiply(A,multiply(multiply(B,C),D)) = add(additive_inverse(multiply(A,multiply(D,multiply(B,C)))),multiply(A,add(multiply(B,multiply(C,D)),multiply(multiply(D,B),C)))),
inference(paramod,[status(thm)],[c_20,c_5569]) ).
cnf(c_4981,plain,
multiply(A,multiply(multiply(B,C),D)) = add(additive_inverse(multiply(A,multiply(D,multiply(B,C)))),add(multiply(A,multiply(B,multiply(C,D))),multiply(A,multiply(multiply(D,B),C)))),
inference(paramod,[status(thm)],[c_8,c_5570]) ).
cnf(c_5571,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(add(additive_inverse(multiply(x,multiply(multiply(x,y),z))),add(multiply(multiply(x,multiply(x,y)),z),multiply(z,multiply(x,multiply(x,y)))))),multiply(multiply(z,multiply(x,x)),y))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_4038,c_2136]) ).
cnf(c_5572,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(add(additive_inverse(multiply(x,multiply(multiply(x,y),z))),add(multiply(z,multiply(x,multiply(x,y))),multiply(multiply(x,multiply(x,y)),z)))),multiply(multiply(z,multiply(x,x)),y))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_10,c_5571]) ).
cnf(c_5573,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(add(multiply(z,multiply(x,multiply(x,y))),add(additive_inverse(multiply(x,multiply(multiply(x,y),z))),multiply(multiply(x,multiply(x,y)),z)))),multiply(multiply(z,multiply(x,x)),y))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_33,c_5572]) ).
cnf(c_5574,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(add(additive_inverse(add(additive_inverse(multiply(x,multiply(multiply(x,y),z))),multiply(multiply(x,multiply(x,y)),z))),additive_inverse(multiply(z,multiply(x,multiply(x,y))))),multiply(multiply(z,multiply(x,x)),y))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_72,c_5573]) ).
cnf(c_5575,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(add(add(additive_inverse(multiply(multiply(x,multiply(x,y)),z)),additive_inverse(additive_inverse(multiply(x,multiply(multiply(x,y),z))))),additive_inverse(multiply(z,multiply(x,multiply(x,y))))),multiply(multiply(z,multiply(x,x)),y))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_72,c_5574]) ).
cnf(c_5576,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(add(add(additive_inverse(multiply(multiply(x,multiply(x,y)),z)),multiply(x,multiply(multiply(x,y),z))),additive_inverse(multiply(z,multiply(x,multiply(x,y))))),multiply(multiply(z,multiply(x,x)),y))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_7,c_5575]) ).
cnf(c_5577,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(add(add(multiply(x,multiply(multiply(x,y),z)),additive_inverse(multiply(multiply(x,multiply(x,y)),z))),additive_inverse(multiply(z,multiply(x,multiply(x,y))))),multiply(multiply(z,multiply(x,x)),y))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_10,c_5576]) ).
cnf(c_5578,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),add(multiply(x,multiply(multiply(x,y),z)),additive_inverse(multiply(multiply(x,multiply(x,y)),z)))),multiply(multiply(z,multiply(x,x)),y))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_10,c_5577]) ).
cnf(c_5579,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),add(add(multiply(x,multiply(multiply(x,y),z)),additive_inverse(multiply(multiply(x,multiply(x,y)),z))),multiply(multiply(z,multiply(x,x)),y)))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_12,c_5578]) ).
cnf(c_5580,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),add(multiply(x,multiply(multiply(x,y),z)),add(additive_inverse(multiply(multiply(x,multiply(x,y)),z)),multiply(multiply(z,multiply(x,x)),y))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_12,c_5579]) ).
cnf(c_5581,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),add(multiply(x,multiply(multiply(x,y),z)),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(z,multiply(x,multiply(x,y))))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_4832,c_5580]) ).
cnf(c_5582,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),add(add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(z,multiply(x,multiply(x,y)))),multiply(x,multiply(multiply(x,y),z))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_10,c_5581]) ).
cnf(c_5583,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(z,multiply(x,multiply(x,y))),multiply(x,multiply(multiply(x,y),z)))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_12,c_5582]) ).
cnf(c_5584,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),add(multiply(z,multiply(x,multiply(x,y))),multiply(x,multiply(multiply(x,y),z)))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_33,c_5583]) ).
cnf(c_5585,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(z,multiply(x,multiply(x,y))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),multiply(x,multiply(multiply(x,y),z)))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_33,c_5584]) ).
cnf(c_5586,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z)))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_31,c_5585]) ).
cnf(c_5587,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(y,multiply(z,x))),multiply(x,multiply(multiply(x,y),z)))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_33,c_5586]) ).
cnf(c_5471,plain,
multiply(x,multiply(multiply(y,z),x)) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(y,multiply(z,x))),multiply(x,multiply(multiply(x,y),z)))),
inference(copy,[status(thm)],[c_5587]) ).
cnf(c_5472,plain,
$false,
inference(resolve,[status(thm)],[c_5471,c_4981]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG029-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n026.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 05:51:55 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 225230 was started by sandbox on n026,
% 0.19/0.44 % Sat Sep 26 05:51:55 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 105.05/14.70
% 105.05/14.70 % SZS status Unsatisfiable for theBenchmark
% 105.05/14.70
% 105.05/14.70 % Proof 1 at 5.71 (+ 0.42) seconds.
% 105.05/14.70 % Length of proof is 48.
% 105.05/14.70 % Level of proof is 15.
% 105.05/14.70 % Maximum clause weight is 86.000.
% 105.05/14.70 % Given clauses 191.
% 105.05/14.70
% 105.05/14.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------