%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG029-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 91.88s 13.02s
% Output : CNFRefutation 91.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 61
% Number of leaves : 11
% Syntax : Number of formulae : 161 ( 161 unt; 0 def)
% Number of atoms : 161 ( 160 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 33 ( 33 ~; 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 : 351 ( 1 sgn 19 !; 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_multiplicative_zero,axiom,
! [VAR_0] : multiply(VAR_0,additive_identity) = additive_identity,
file('theBenchmark.p',right_multiplicative_zero) ).
cnf(c_4,plain,
multiply(A,additive_identity) = additive_identity,
inference(clausify,[status(thm)],[right_multiplicative_zero]) ).
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(prove_middle_law,axiom,
multiply(multiply(cx,cy),multiply(cz,cx)) != multiply(cx,multiply(multiply(cy,cz),cx)),
file('theBenchmark.p',prove_middle_law) ).
cnf(c_18,plain,
multiply(multiply(cx,cy),multiply(cz,cx)) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(clausify,[status(thm)],[prove_middle_law]) ).
cnf(c_19,plain,
multiply(cx,multiply(multiply(cy,cz),cx)) != multiply(multiply(cx,cy),multiply(cz,cx)),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_5637,plain,
multiply(A,additive_identity) = add(multiply(A,B),multiply(A,additive_inverse(B))),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_5638,plain,
additive_identity = add(multiply(A,B),multiply(A,additive_inverse(B))),
inference(paramod,[status(thm)],[c_4,c_5637]) ).
cnf(c_21,plain,
add(multiply(A,B),multiply(A,additive_inverse(B))) = additive_identity,
inference(copy,[status(thm)],[c_5638]) ).
cnf(c_5639,plain,
add(additive_identity,A) = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_6,c_12]) ).
cnf(c_5640,plain,
A = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_5639]) ).
cnf(c_25,plain,
add(A,add(additive_inverse(A),B)) = B,
inference(copy,[status(thm)],[c_5640]) ).
cnf(c_5641,plain,
add(add(A,B),C) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_10,c_12]) ).
cnf(c_27,plain,
add(A,add(B,C)) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_12,c_5641]) ).
cnf(c_5642,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_5643,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_5642]) ).
cnf(c_5644,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_5643]) ).
cnf(c_5645,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_5644]) ).
cnf(c_5646,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_5645]) ).
cnf(c_5647,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_5646]) ).
cnf(c_5648,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_5647]) ).
cnf(c_5649,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_5648]) ).
cnf(c_5650,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_5649]) ).
cnf(c_5651,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_5650]) ).
cnf(c_5652,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_5651]) ).
cnf(c_5653,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_5652]) ).
cnf(c_5654,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_5653]) ).
cnf(c_5655,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_5654]) ).
cnf(c_5656,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_5655]) ).
cnf(c_28,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_5656]) ).
cnf(c_5657,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_5658,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_5657]) ).
cnf(c_5659,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_5658]) ).
cnf(c_5660,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_5659]) ).
cnf(c_5661,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_5660]) ).
cnf(c_5662,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_5661]) ).
cnf(c_5663,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_5662]) ).
cnf(c_5664,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_5663]) ).
cnf(c_5665,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_5664]) ).
cnf(c_5666,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_5665]) ).
cnf(c_5667,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_27,c_5666]) ).
cnf(c_5668,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_5667]) ).
cnf(c_5669,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_5668]) ).
cnf(c_5670,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_5669]) ).
cnf(c_5671,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_5670]) ).
cnf(c_30,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_5671]) ).
cnf(c_48,plain,
add(A,add(B,additive_inverse(A))) = B,
inference(paramod,[status(thm)],[c_10,c_25]) ).
cnf(c_50,plain,
add(additive_inverse(A),add(B,A)) = B,
inference(paramod,[status(thm)],[c_7,c_48]) ).
cnf(c_5672,plain,
add(A,B) = add(additive_inverse(C),add(add(A,C),B)),
inference(paramod,[status(thm)],[c_50,c_12]) ).
cnf(c_5673,plain,
add(A,B) = add(additive_inverse(C),add(A,add(C,B))),
inference(paramod,[status(thm)],[c_12,c_5672]) ).
cnf(c_58,plain,
add(additive_inverse(A),add(B,add(A,C))) = add(B,C),
inference(copy,[status(thm)],[c_5673]) ).
cnf(c_59,plain,
add(additive_inverse(A),add(B,add(C,A))) = add(B,C),
inference(paramod,[status(thm)],[c_12,c_50]) ).
cnf(c_5674,plain,
add(additive_inverse(multiply(A,additive_inverse(B))),additive_identity) = multiply(A,B),
inference(paramod,[status(thm)],[c_21,c_50]) ).
cnf(c_5675,plain,
add(additive_identity,additive_inverse(multiply(A,additive_inverse(B)))) = multiply(A,B),
inference(paramod,[status(thm)],[c_10,c_5674]) ).
cnf(c_60,plain,
additive_inverse(multiply(A,additive_inverse(B))) = multiply(A,B),
inference(paramod,[status(thm)],[c_1,c_5675]) ).
cnf(c_5676,plain,
add(additive_inverse(add(A,B)),A) = additive_inverse(B),
inference(paramod,[status(thm)],[c_50,c_50]) ).
cnf(c_64,plain,
add(A,additive_inverse(add(A,B))) = additive_inverse(B),
inference(paramod,[status(thm)],[c_10,c_5676]) ).
cnf(c_5677,plain,
additive_inverse(multiply(A,B)) = multiply(A,additive_inverse(B)),
inference(paramod,[status(thm)],[c_60,c_7]) ).
cnf(c_65,plain,
multiply(A,additive_inverse(B)) = additive_inverse(multiply(A,B)),
inference(copy,[status(thm)],[c_5677]) ).
cnf(c_5678,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_28,c_27]) ).
cnf(c_86,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_5678]) ).
cnf(c_5679,plain,
add(additive_inverse(A),additive_inverse(B)) = additive_inverse(add(B,A)),
inference(paramod,[status(thm)],[c_50,c_64]) ).
cnf(c_97,plain,
additive_inverse(add(A,B)) = add(additive_inverse(B),additive_inverse(A)),
inference(copy,[status(thm)],[c_5679]) ).
cnf(c_5680,plain,
add(additive_inverse(A),add(B,add(C,add(A,D)))) = add(add(B,C),D),
inference(paramod,[status(thm)],[c_12,c_58]) ).
cnf(c_101,plain,
add(additive_inverse(A),add(B,add(C,add(A,D)))) = add(B,add(C,D)),
inference(paramod,[status(thm)],[c_12,c_5680]) ).
cnf(c_5681,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_30,c_58]) ).
cnf(c_116,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_5681]) ).
cnf(c_123,plain,
add(additive_inverse(A),add(B,add(C,add(D,A)))) = add(B,add(C,D)),
inference(paramod,[status(thm)],[c_12,c_59]) ).
cnf(c_124,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_123,c_116]) ).
cnf(c_5682,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_86,c_50]) ).
cnf(c_5683,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_97,c_5682]) ).
cnf(c_5684,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_97,c_5683]) ).
cnf(c_5685,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_5684]) ).
cnf(c_5686,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_27,c_5685]) ).
cnf(c_5687,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_5686]) ).
cnf(c_5688,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_5687]) ).
cnf(c_5689,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_123,c_5688]) ).
cnf(c_5690,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_25,c_5689]) ).
cnf(c_283,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_5690]) ).
cnf(c_5691,plain,
multiply(cx,multiply(multiply(cy,cz),cx)) != add(additive_inverse(multiply(multiply(cx,multiply(cz,cx)),cy)),add(multiply(cx,multiply(cy,multiply(cz,cx))),multiply(cx,multiply(multiply(cz,cx),cy)))),
inference(paramod,[status(thm)],[c_283,c_19]) ).
cnf(c_5692,plain,
multiply(cx,multiply(multiply(cy,cz),cx)) != add(add(multiply(cx,multiply(cy,multiply(cz,cx))),multiply(cx,multiply(multiply(cz,cx),cy))),additive_inverse(multiply(multiply(cx,multiply(cz,cx)),cy))),
inference(paramod,[status(thm)],[c_10,c_5691]) ).
cnf(c_5693,plain,
multiply(cx,multiply(multiply(cy,cz),cx)) != add(multiply(cx,multiply(cy,multiply(cz,cx))),add(multiply(cx,multiply(multiply(cz,cx),cy)),additive_inverse(multiply(multiply(cx,multiply(cz,cx)),cy)))),
inference(paramod,[status(thm)],[c_12,c_5692]) ).
cnf(c_385,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(multiply(cx,multiply(multiply(cz,cx),cy)),additive_inverse(multiply(multiply(cx,multiply(cz,cx)),cy)))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(copy,[status(thm)],[c_5693]) ).
cnf(c_5694,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_124,c_58]) ).
cnf(c_5695,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_58,c_5694]) ).
cnf(c_907,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_5695]) ).
cnf(c_5696,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_907,c_50]) ).
cnf(c_5697,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_5696]) ).
cnf(c_5698,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_5697]) ).
cnf(c_1929,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_5698]) ).
cnf(c_5699,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_1929,c_283]) ).
cnf(c_5700,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_97,c_5699]) ).
cnf(c_5701,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_97,c_5700]) ).
cnf(c_5702,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_5701]) ).
cnf(c_5703,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_5702]) ).
cnf(c_5704,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_5703]) ).
cnf(c_5705,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_5704]) ).
cnf(c_5706,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_5705]) ).
cnf(c_2230,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_123,c_5706]) ).
cnf(c_5707,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(multiply(cx,multiply(multiply(cz,cx),cy)),additive_inverse(add(multiply(cx,multiply(multiply(cz,cx),cy)),add(multiply(multiply(cz,cx),multiply(cx,cy)),additive_inverse(multiply(multiply(multiply(cz,cx),cx),cy))))))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_1929,c_385]) ).
cnf(c_5708,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(multiply(cx,multiply(multiply(cz,cx),cy)),additive_inverse(add(multiply(cx,multiply(multiply(cz,cx),cy)),add(multiply(multiply(cz,cx),multiply(cx,cy)),additive_inverse(multiply(multiply(cz,multiply(cx,cx)),cy))))))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_13,c_5707]) ).
cnf(c_5709,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(multiply(cx,multiply(multiply(cz,cx),cy)),add(additive_inverse(add(multiply(multiply(cz,cx),multiply(cx,cy)),additive_inverse(multiply(multiply(cz,multiply(cx,cx)),cy)))),additive_inverse(multiply(cx,multiply(multiply(cz,cx),cy)))))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_97,c_5708]) ).
cnf(c_5710,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(multiply(cx,multiply(multiply(cz,cx),cy)),add(add(additive_inverse(additive_inverse(multiply(multiply(cz,multiply(cx,cx)),cy))),additive_inverse(multiply(multiply(cz,cx),multiply(cx,cy)))),additive_inverse(multiply(cx,multiply(multiply(cz,cx),cy)))))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_97,c_5709]) ).
cnf(c_5711,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(multiply(cx,multiply(multiply(cz,cx),cy)),add(add(multiply(multiply(cz,multiply(cx,cx)),cy),additive_inverse(multiply(multiply(cz,cx),multiply(cx,cy)))),additive_inverse(multiply(cx,multiply(multiply(cz,cx),cy)))))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_7,c_5710]) ).
cnf(c_5712,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(multiply(cx,multiply(multiply(cz,cx),cy)),add(add(additive_inverse(multiply(multiply(cz,cx),multiply(cx,cy))),multiply(multiply(cz,multiply(cx,cx)),cy)),additive_inverse(multiply(cx,multiply(multiply(cz,cx),cy)))))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_10,c_5711]) ).
cnf(c_5713,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(multiply(cx,multiply(multiply(cz,cx),cy)),add(additive_inverse(multiply(cx,multiply(multiply(cz,cx),cy))),add(additive_inverse(multiply(multiply(cz,cx),multiply(cx,cy))),multiply(multiply(cz,multiply(cx,cx)),cy))))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_10,c_5712]) ).
cnf(c_2250,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(additive_inverse(multiply(multiply(cz,cx),multiply(cx,cy))),multiply(multiply(cz,multiply(cx,cx)),cy))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_25,c_5713]) ).
cnf(c_3830,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_2230]) ).
cnf(c_3849,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_2230,c_58]) ).
cnf(c_5714,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_2230,c_2230]) ).
cnf(c_5715,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_5714]) ).
cnf(c_5716,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_5715]) ).
cnf(c_4102,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_101,c_5716]) ).
cnf(c_5717,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_3849,c_97]) ).
cnf(c_5718,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_97,c_5717]) ).
cnf(c_5719,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_5718]) ).
cnf(c_5720,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_5719]) ).
cnf(c_4607,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_5720]) ).
cnf(c_5721,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_4607]) ).
cnf(c_5722,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_5721]) ).
cnf(c_4842,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_5722]) ).
cnf(c_5723,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_3830,c_8]) ).
cnf(c_5724,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_65,c_5723]) ).
cnf(c_5118,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_5724]) ).
cnf(c_5725,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(additive_inverse(add(additive_inverse(multiply(cx,multiply(multiply(cx,cy),cz))),add(multiply(multiply(cx,multiply(cx,cy)),cz),multiply(cz,multiply(cx,multiply(cx,cy)))))),multiply(multiply(cz,multiply(cx,cx)),cy))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_4102,c_2250]) ).
cnf(c_5726,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(additive_inverse(add(additive_inverse(multiply(cx,multiply(multiply(cx,cy),cz))),add(multiply(cz,multiply(cx,multiply(cx,cy))),multiply(multiply(cx,multiply(cx,cy)),cz)))),multiply(multiply(cz,multiply(cx,cx)),cy))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_10,c_5725]) ).
cnf(c_5727,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(additive_inverse(add(multiply(cz,multiply(cx,multiply(cx,cy))),add(additive_inverse(multiply(cx,multiply(multiply(cx,cy),cz))),multiply(multiply(cx,multiply(cx,cy)),cz)))),multiply(multiply(cz,multiply(cx,cx)),cy))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_27,c_5726]) ).
cnf(c_5728,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(add(additive_inverse(add(additive_inverse(multiply(cx,multiply(multiply(cx,cy),cz))),multiply(multiply(cx,multiply(cx,cy)),cz))),additive_inverse(multiply(cz,multiply(cx,multiply(cx,cy))))),multiply(multiply(cz,multiply(cx,cx)),cy))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_97,c_5727]) ).
cnf(c_5729,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(add(add(additive_inverse(multiply(multiply(cx,multiply(cx,cy)),cz)),additive_inverse(additive_inverse(multiply(cx,multiply(multiply(cx,cy),cz))))),additive_inverse(multiply(cz,multiply(cx,multiply(cx,cy))))),multiply(multiply(cz,multiply(cx,cx)),cy))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_97,c_5728]) ).
cnf(c_5730,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(add(add(additive_inverse(multiply(multiply(cx,multiply(cx,cy)),cz)),multiply(cx,multiply(multiply(cx,cy),cz))),additive_inverse(multiply(cz,multiply(cx,multiply(cx,cy))))),multiply(multiply(cz,multiply(cx,cx)),cy))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_7,c_5729]) ).
cnf(c_5731,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(add(add(multiply(cx,multiply(multiply(cx,cy),cz)),additive_inverse(multiply(multiply(cx,multiply(cx,cy)),cz))),additive_inverse(multiply(cz,multiply(cx,multiply(cx,cy))))),multiply(multiply(cz,multiply(cx,cx)),cy))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_10,c_5730]) ).
cnf(c_5732,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(add(additive_inverse(multiply(cz,multiply(cx,multiply(cx,cy)))),add(multiply(cx,multiply(multiply(cx,cy),cz)),additive_inverse(multiply(multiply(cx,multiply(cx,cy)),cz)))),multiply(multiply(cz,multiply(cx,cx)),cy))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_10,c_5731]) ).
cnf(c_5733,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(additive_inverse(multiply(cz,multiply(cx,multiply(cx,cy)))),add(add(multiply(cx,multiply(multiply(cx,cy),cz)),additive_inverse(multiply(multiply(cx,multiply(cx,cy)),cz))),multiply(multiply(cz,multiply(cx,cx)),cy)))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_12,c_5732]) ).
cnf(c_5734,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(additive_inverse(multiply(cz,multiply(cx,multiply(cx,cy)))),add(multiply(cx,multiply(multiply(cx,cy),cz)),add(additive_inverse(multiply(multiply(cx,multiply(cx,cy)),cz)),multiply(multiply(cz,multiply(cx,cx)),cy))))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_12,c_5733]) ).
cnf(c_5735,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(additive_inverse(multiply(cz,multiply(cx,multiply(cx,cy)))),add(multiply(cx,multiply(multiply(cx,cy),cz)),add(additive_inverse(multiply(cx,multiply(cx,multiply(cy,cz)))),multiply(cz,multiply(cx,multiply(cx,cy))))))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_4842,c_5734]) ).
cnf(c_5736,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(additive_inverse(multiply(cz,multiply(cx,multiply(cx,cy)))),add(add(additive_inverse(multiply(cx,multiply(cx,multiply(cy,cz)))),multiply(cz,multiply(cx,multiply(cx,cy)))),multiply(cx,multiply(multiply(cx,cy),cz))))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_10,c_5735]) ).
cnf(c_5737,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(additive_inverse(multiply(cz,multiply(cx,multiply(cx,cy)))),add(additive_inverse(multiply(cx,multiply(cx,multiply(cy,cz)))),add(multiply(cz,multiply(cx,multiply(cx,cy))),multiply(cx,multiply(multiply(cx,cy),cz)))))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_12,c_5736]) ).
cnf(c_5738,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(additive_inverse(multiply(cx,multiply(cx,multiply(cy,cz)))),add(additive_inverse(multiply(cz,multiply(cx,multiply(cx,cy)))),add(multiply(cz,multiply(cx,multiply(cx,cy))),multiply(cx,multiply(multiply(cx,cy),cz)))))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_27,c_5737]) ).
cnf(c_5739,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(additive_inverse(multiply(cx,multiply(cx,multiply(cy,cz)))),add(multiply(cz,multiply(cx,multiply(cx,cy))),add(additive_inverse(multiply(cz,multiply(cx,multiply(cx,cy)))),multiply(cx,multiply(multiply(cx,cy),cz)))))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_27,c_5738]) ).
cnf(c_5740,plain,
add(multiply(cx,multiply(cy,multiply(cz,cx))),add(additive_inverse(multiply(cx,multiply(cx,multiply(cy,cz)))),multiply(cx,multiply(multiply(cx,cy),cz)))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_25,c_5739]) ).
cnf(c_5741,plain,
add(additive_inverse(multiply(cx,multiply(cx,multiply(cy,cz)))),add(multiply(cx,multiply(cy,multiply(cz,cx))),multiply(cx,multiply(multiply(cx,cy),cz)))) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(paramod,[status(thm)],[c_27,c_5740]) ).
cnf(c_5635,plain,
multiply(cx,multiply(multiply(cy,cz),cx)) != add(additive_inverse(multiply(cx,multiply(cx,multiply(cy,cz)))),add(multiply(cx,multiply(cy,multiply(cz,cx))),multiply(cx,multiply(multiply(cx,cy),cz)))),
inference(copy,[status(thm)],[c_5741]) ).
cnf(c_5636,plain,
$false,
inference(resolve,[status(thm)],[c_5635,c_5118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG029-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sat Sep 26 05:48:34 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.30 % Process 4030150 was started by sandbox2 on n012,
% 0.04/0.30 % Sat Sep 26 05:48:34 2026
% 0.04/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.04/0.30
% 0.04/0.30 % From the command line: assign(max_seconds, 300).
% 91.88/13.02
% 91.88/13.02 % SZS status Unsatisfiable for theBenchmark
% 91.88/13.02
% 91.88/13.02 % Proof 1 at 4.26 (+ 0.32) seconds.
% 91.88/13.02 % Length of proof is 45.
% 91.88/13.02 % Level of proof is 15.
% 91.88/13.02 % Maximum clause weight is 86.000.
% 91.88/13.02 % Given clauses 193.
% 91.88/13.02
% 91.88/13.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------