%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG029-6 : 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 : n007.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 181.84s 24.75s
% Output : CNFRefutation 181.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 82
% Number of leaves : 11
% Syntax : Number of formulae : 173 ( 173 unt; 0 def)
% Number of atoms : 173 ( 172 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 51 ( 51 ~; 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 324 ( 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_moufang,axiom,
multiply(multiply(x,y),multiply(z,x)) != multiply(multiply(x,multiply(y,z)),x),
file('theBenchmark.p',prove_middle_moufang) ).
cnf(c_18,plain,
multiply(multiply(x,y),multiply(z,x)) != multiply(multiply(x,multiply(y,z)),x),
inference(clausify,[status(thm)],[prove_middle_moufang]) ).
cnf(c_19,plain,
multiply(multiply(x,multiply(y,z)),x) != multiply(multiply(x,y),multiply(z,x)),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_17512,plain,
multiply(A,additive_identity) = add(multiply(A,B),multiply(A,additive_inverse(B))),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_17513,plain,
additive_identity = add(multiply(A,B),multiply(A,additive_inverse(B))),
inference(paramod,[status(thm)],[c_4,c_17512]) ).
cnf(c_21,plain,
add(multiply(A,B),multiply(A,additive_inverse(B))) = additive_identity,
inference(copy,[status(thm)],[c_17513]) ).
cnf(c_17514,plain,
add(additive_identity,A) = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_6,c_12]) ).
cnf(c_17515,plain,
A = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_17514]) ).
cnf(c_25,plain,
add(A,add(additive_inverse(A),B)) = B,
inference(copy,[status(thm)],[c_17515]) ).
cnf(c_17516,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_17516]) ).
cnf(c_17517,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_17518,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_17517]) ).
cnf(c_17519,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_17518]) ).
cnf(c_17520,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_17519]) ).
cnf(c_17521,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_17520]) ).
cnf(c_17522,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_17521]) ).
cnf(c_17523,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_17522]) ).
cnf(c_17524,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_17523]) ).
cnf(c_17525,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_17524]) ).
cnf(c_17526,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_17525]) ).
cnf(c_17527,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_17526]) ).
cnf(c_17528,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_17527]) ).
cnf(c_17529,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_17528]) ).
cnf(c_17530,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_17529]) ).
cnf(c_17531,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_17530]) ).
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_17531]) ).
cnf(c_17532,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_17533,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_17532]) ).
cnf(c_17534,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_17533]) ).
cnf(c_17535,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_17534]) ).
cnf(c_17536,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_17535]) ).
cnf(c_17537,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_17536]) ).
cnf(c_17538,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_17537]) ).
cnf(c_17539,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_17538]) ).
cnf(c_17540,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_17539]) ).
cnf(c_17541,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_17540]) ).
cnf(c_17542,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_17541]) ).
cnf(c_17543,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_17542]) ).
cnf(c_17544,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_17543]) ).
cnf(c_17545,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_17544]) ).
cnf(c_17546,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_17545]) ).
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_17546]) ).
cnf(c_36,plain,
add(A,add(B,additive_inverse(A))) = B,
inference(paramod,[status(thm)],[c_10,c_25]) ).
cnf(c_38,plain,
add(additive_inverse(A),add(B,A)) = B,
inference(paramod,[status(thm)],[c_7,c_36]) ).
cnf(c_17547,plain,
add(A,B) = add(C,add(add(A,additive_inverse(C)),B)),
inference(paramod,[status(thm)],[c_36,c_12]) ).
cnf(c_17548,plain,
add(A,B) = add(C,add(A,add(additive_inverse(C),B))),
inference(paramod,[status(thm)],[c_12,c_17547]) ).
cnf(c_41,plain,
add(A,add(B,add(additive_inverse(A),C))) = add(B,C),
inference(copy,[status(thm)],[c_17548]) ).
cnf(c_17549,plain,
add(A,B) = add(additive_inverse(C),add(add(A,C),B)),
inference(paramod,[status(thm)],[c_38,c_12]) ).
cnf(c_17550,plain,
add(A,B) = add(additive_inverse(C),add(A,add(C,B))),
inference(paramod,[status(thm)],[c_12,c_17549]) ).
cnf(c_46,plain,
add(additive_inverse(A),add(B,add(A,C))) = add(B,C),
inference(copy,[status(thm)],[c_17550]) ).
cnf(c_47,plain,
add(additive_inverse(A),add(B,add(C,A))) = add(B,C),
inference(paramod,[status(thm)],[c_12,c_38]) ).
cnf(c_17551,plain,
add(additive_inverse(add(A,B)),A) = additive_inverse(B),
inference(paramod,[status(thm)],[c_38,c_38]) ).
cnf(c_50,plain,
add(A,additive_inverse(add(A,B))) = additive_inverse(B),
inference(paramod,[status(thm)],[c_10,c_17551]) ).
cnf(c_17552,plain,
add(additive_inverse(multiply(A,additive_inverse(B))),additive_identity) = multiply(A,B),
inference(paramod,[status(thm)],[c_21,c_38]) ).
cnf(c_17553,plain,
add(additive_identity,additive_inverse(multiply(A,additive_inverse(B)))) = multiply(A,B),
inference(paramod,[status(thm)],[c_10,c_17552]) ).
cnf(c_64,plain,
additive_inverse(multiply(A,additive_inverse(B))) = multiply(A,B),
inference(paramod,[status(thm)],[c_1,c_17553]) ).
cnf(c_17554,plain,
add(additive_inverse(A),additive_inverse(B)) = additive_inverse(add(B,A)),
inference(paramod,[status(thm)],[c_38,c_50]) ).
cnf(c_71,plain,
additive_inverse(add(A,B)) = add(additive_inverse(B),additive_inverse(A)),
inference(copy,[status(thm)],[c_17554]) ).
cnf(c_17555,plain,
additive_inverse(multiply(A,B)) = multiply(A,additive_inverse(B)),
inference(paramod,[status(thm)],[c_64,c_7]) ).
cnf(c_72,plain,
multiply(A,additive_inverse(B)) = additive_inverse(multiply(A,B)),
inference(copy,[status(thm)],[c_17555]) ).
cnf(c_17556,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_107,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_17556]) ).
cnf(c_115,plain,
add(additive_inverse(A),add(B,add(C,add(D,A)))) = add(B,add(C,D)),
inference(paramod,[status(thm)],[c_12,c_47]) ).
cnf(c_17557,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_46]) ).
cnf(c_17558,plain,
add(multiply(C,multiply(C,B)),add(multiply(A,multiply(C,B)),multiply(C,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_115,c_17557]) ).
cnf(c_138,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(copy,[status(thm)],[c_17558]) ).
cnf(c_17559,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_138,c_46]) ).
cnf(c_17560,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_46,c_17559]) ).
cnf(c_679,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_17560]) ).
cnf(c_17561,plain,
add(additive_identity,add(multiply(A,multiply(B,C)),multiply(B,multiply(A,C)))) = add(multiply(multiply(A,B),C),multiply(multiply(B,A),C)),
inference(paramod,[status(thm)],[c_679,c_1]) ).
cnf(c_17562,plain,
add(multiply(A,multiply(B,C)),multiply(B,multiply(A,C))) = add(multiply(multiply(A,B),C),multiply(multiply(B,A),C)),
inference(paramod,[status(thm)],[c_1,c_17561]) ).
cnf(c_750,plain,
add(multiply(multiply(A,B),C),multiply(multiply(B,A),C)) = add(multiply(A,multiply(B,C)),multiply(B,multiply(A,C))),
inference(copy,[status(thm)],[c_17562]) ).
cnf(c_17563,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_679,c_38]) ).
cnf(c_17564,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_17563]) ).
cnf(c_17565,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_17564]) ).
cnf(c_759,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_17565]) ).
cnf(c_831,plain,
add(multiply(A,multiply(B,B)),multiply(multiply(B,A),B)) = add(multiply(A,multiply(B,B)),multiply(B,multiply(A,B))),
inference(paramod,[status(thm)],[c_13,c_750]) ).
cnf(c_17566,plain,
add(additive_inverse(multiply(A,multiply(B,B))),add(C,add(multiply(A,multiply(B,B)),multiply(B,multiply(A,B))))) = add(C,multiply(multiply(B,A),B)),
inference(paramod,[status(thm)],[c_831,c_46]) ).
cnf(c_17567,plain,
add(C,multiply(B,multiply(A,B))) = add(C,multiply(multiply(B,A),B)),
inference(paramod,[status(thm)],[c_46,c_17566]) ).
cnf(c_917,plain,
add(A,multiply(multiply(B,C),B)) = add(A,multiply(B,multiply(C,B))),
inference(copy,[status(thm)],[c_17567]) ).
cnf(c_17568,plain,
add(additive_identity,multiply(A,multiply(B,A))) = multiply(multiply(A,B),A),
inference(paramod,[status(thm)],[c_917,c_1]) ).
cnf(c_17569,plain,
multiply(A,multiply(B,A)) = multiply(multiply(A,B),A),
inference(paramod,[status(thm)],[c_1,c_17568]) ).
cnf(c_945,plain,
multiply(multiply(A,B),A) = multiply(A,multiply(B,A)),
inference(copy,[status(thm)],[c_17569]) ).
cnf(c_987,plain,
multiply(x,multiply(multiply(y,z),x)) != multiply(multiply(x,y),multiply(z,x)),
inference(paramod,[status(thm)],[c_945,c_19]) ).
cnf(c_17570,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_107,c_38]) ).
cnf(c_17571,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_71,c_17570]) ).
cnf(c_17572,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_71,c_17571]) ).
cnf(c_17573,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_17572]) ).
cnf(c_17574,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_17573]) ).
cnf(c_17575,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_17574]) ).
cnf(c_17576,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_17575]) ).
cnf(c_17577,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_115,c_17576]) ).
cnf(c_17578,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_17577]) ).
cnf(c_3098,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_17578]) ).
cnf(c_4576,plain,
add(multiply(multiply(A,B),C),multiply(multiply(A,C),B)) = add(multiply(A,multiply(C,B)),multiply(A,multiply(B,C))),
inference(paramod,[status(thm)],[c_3098,c_25]) ).
cnf(c_17579,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_3098,c_987]) ).
cnf(c_17580,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_17579]) ).
cnf(c_17581,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_17580]) ).
cnf(c_4646,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_17581]) ).
cnf(c_17582,plain,
multiply(multiply(A,B),C) = add(multiply(A,multiply(B,C)),add(multiply(B,multiply(A,C)),additive_inverse(add(additive_inverse(multiply(multiply(B,C),A)),add(multiply(B,multiply(A,C)),multiply(B,multiply(C,A))))))),
inference(paramod,[status(thm)],[c_3098,c_759]) ).
cnf(c_17583,plain,
multiply(multiply(A,B),C) = add(multiply(A,multiply(B,C)),add(multiply(B,multiply(A,C)),add(additive_inverse(add(multiply(B,multiply(A,C)),multiply(B,multiply(C,A)))),additive_inverse(additive_inverse(multiply(multiply(B,C),A)))))),
inference(paramod,[status(thm)],[c_71,c_17582]) ).
cnf(c_17584,plain,
multiply(multiply(A,B),C) = add(multiply(A,multiply(B,C)),add(multiply(B,multiply(A,C)),add(add(additive_inverse(multiply(B,multiply(C,A))),additive_inverse(multiply(B,multiply(A,C)))),additive_inverse(additive_inverse(multiply(multiply(B,C),A)))))),
inference(paramod,[status(thm)],[c_71,c_17583]) ).
cnf(c_17585,plain,
multiply(multiply(A,B),C) = add(multiply(A,multiply(B,C)),add(multiply(B,multiply(A,C)),add(add(additive_inverse(multiply(B,multiply(C,A))),additive_inverse(multiply(B,multiply(A,C)))),multiply(multiply(B,C),A)))),
inference(paramod,[status(thm)],[c_7,c_17584]) ).
cnf(c_17586,plain,
multiply(multiply(A,B),C) = add(multiply(A,multiply(B,C)),add(multiply(B,multiply(A,C)),add(additive_inverse(multiply(B,multiply(C,A))),add(additive_inverse(multiply(B,multiply(A,C))),multiply(multiply(B,C),A))))),
inference(paramod,[status(thm)],[c_12,c_17585]) ).
cnf(c_4701,plain,
multiply(multiply(A,B),C) = add(multiply(A,multiply(B,C)),add(additive_inverse(multiply(B,multiply(C,A))),multiply(multiply(B,C),A))),
inference(paramod,[status(thm)],[c_41,c_17586]) ).
cnf(c_17587,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_759,c_4646]) ).
cnf(c_17588,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_17587]) ).
cnf(c_17589,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_71,c_17588]) ).
cnf(c_17590,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_71,c_17589]) ).
cnf(c_17591,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_17590]) ).
cnf(c_17592,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_17591]) ).
cnf(c_17593,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_17592]) ).
cnf(c_6449,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_25,c_17593]) ).
cnf(c_17594,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(add(multiply(z,multiply(x,multiply(x,y))),add(multiply(x,multiply(z,multiply(x,y))),additive_inverse(multiply(multiply(x,z),multiply(x,y)))))),multiply(multiply(z,multiply(x,x)),y))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_759,c_6449]) ).
cnf(c_17595,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(add(multiply(x,multiply(z,multiply(x,y))),add(multiply(z,multiply(x,multiply(x,y))),additive_inverse(multiply(multiply(x,z),multiply(x,y)))))),multiply(multiply(z,multiply(x,x)),y))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_27,c_17594]) ).
cnf(c_17596,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(add(additive_inverse(add(multiply(z,multiply(x,multiply(x,y))),additive_inverse(multiply(multiply(x,z),multiply(x,y))))),additive_inverse(multiply(x,multiply(z,multiply(x,y))))),multiply(multiply(z,multiply(x,x)),y))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_71,c_17595]) ).
cnf(c_17597,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(add(add(additive_inverse(additive_inverse(multiply(multiply(x,z),multiply(x,y)))),additive_inverse(multiply(z,multiply(x,multiply(x,y))))),additive_inverse(multiply(x,multiply(z,multiply(x,y))))),multiply(multiply(z,multiply(x,x)),y))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_71,c_17596]) ).
cnf(c_17598,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(add(add(multiply(multiply(x,z),multiply(x,y)),additive_inverse(multiply(z,multiply(x,multiply(x,y))))),additive_inverse(multiply(x,multiply(z,multiply(x,y))))),multiply(multiply(z,multiply(x,x)),y))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_7,c_17597]) ).
cnf(c_17599,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(add(add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),multiply(multiply(x,z),multiply(x,y))),additive_inverse(multiply(x,multiply(z,multiply(x,y))))),multiply(multiply(z,multiply(x,x)),y))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_10,c_17598]) ).
cnf(c_17600,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),multiply(multiply(x,z),multiply(x,y)))),multiply(multiply(z,multiply(x,x)),y))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_10,c_17599]) ).
cnf(c_17601,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),add(add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),multiply(multiply(x,z),multiply(x,y))),multiply(multiply(z,multiply(x,x)),y)))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_12,c_17600]) ).
cnf(c_6980,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),add(multiply(multiply(x,z),multiply(x,y)),multiply(multiply(z,multiply(x,x)),y))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_12,c_17601]) ).
cnf(c_17602,plain,
add(multiply(A,multiply(B,C)),multiply(A,multiply(C,B))) = add(multiply(multiply(A,B),C),multiply(multiply(A,C),B)),
inference(paramod,[status(thm)],[c_4576,c_10]) ).
cnf(c_7797,plain,
add(multiply(multiply(A,B),C),multiply(multiply(A,C),B)) = add(multiply(A,multiply(B,C)),multiply(A,multiply(C,B))),
inference(copy,[status(thm)],[c_17602]) ).
cnf(c_17603,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),add(multiply(multiply(x,z),multiply(x,y)),add(multiply(z,multiply(multiply(x,x),y)),add(additive_inverse(multiply(multiply(x,x),multiply(y,z))),multiply(multiply(multiply(x,x),y),z))))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_4701,c_6980]) ).
cnf(c_17604,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),add(multiply(multiply(x,z),multiply(x,y)),add(multiply(z,multiply(x,multiply(x,y))),add(additive_inverse(multiply(multiply(x,x),multiply(y,z))),multiply(multiply(multiply(x,x),y),z))))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_14,c_17603]) ).
cnf(c_17605,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),add(multiply(multiply(x,z),multiply(x,y)),add(multiply(z,multiply(x,multiply(x,y))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(multiply(multiply(x,x),y),z))))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_14,c_17604]) ).
cnf(c_17606,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),add(multiply(multiply(x,z),multiply(x,y)),add(multiply(z,multiply(x,multiply(x,y))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(multiply(x,multiply(x,y)),z))))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_14,c_17605]) ).
cnf(c_17607,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),add(multiply(multiply(x,z),multiply(x,y)),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(z,multiply(x,multiply(x,y))),multiply(multiply(x,multiply(x,y)),z))))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_27,c_17606]) ).
cnf(c_17608,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(multiply(x,z),multiply(x,y)),add(multiply(z,multiply(x,multiply(x,y))),multiply(multiply(x,multiply(x,y)),z))))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_27,c_17607]) ).
cnf(c_17609,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),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))),add(multiply(multiply(x,z),multiply(x,y)),multiply(multiply(x,multiply(x,y)),z))))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_27,c_17608]) ).
cnf(c_17610,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),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))),add(multiply(x,multiply(z,multiply(x,y))),multiply(x,multiply(multiply(x,y),z)))))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_7797,c_17609]) ).
cnf(c_17611,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(z,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_27,c_17610]) ).
cnf(c_17612,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(z,multiply(x,multiply(x,y)))),add(multiply(x,multiply(z,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_27,c_17611]) ).
cnf(c_17613,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(z,multiply(x,y))),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_27,c_17612]) ).
cnf(c_17614,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(z,multiply(x,y))),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_27,c_17613]) ).
cnf(c_17615,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(z,multiply(x,y))),multiply(x,multiply(multiply(x,y),z)))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_25,c_17614]) ).
cnf(c_17616,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),add(multiply(x,multiply(z,multiply(x,y))),multiply(x,multiply(multiply(x,y),z)))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_27,c_17615]) ).
cnf(c_17617,plain,
add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(z,multiply(x,y))),add(additive_inverse(multiply(x,multiply(z,multiply(x,y)))),multiply(x,multiply(multiply(x,y),z)))))) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_27,c_17616]) ).
cnf(c_17618,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_25,c_17617]) ).
cnf(c_17619,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_27,c_17618]) ).
cnf(c_16784,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_17619]) ).
cnf(c_17620,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,add(multiply(x,multiply(y,z)),add(additive_inverse(multiply(y,multiply(z,x))),multiply(multiply(y,z),x)))))),
inference(paramod,[status(thm)],[c_4701,c_16784]) ).
cnf(c_17621,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))),add(multiply(x,multiply(x,multiply(y,z))),multiply(x,add(additive_inverse(multiply(y,multiply(z,x))),multiply(multiply(y,z),x)))))),
inference(paramod,[status(thm)],[c_8,c_17620]) ).
cnf(c_17622,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))),add(multiply(x,multiply(x,multiply(y,z))),add(multiply(x,additive_inverse(multiply(y,multiply(z,x)))),multiply(x,multiply(multiply(y,z),x)))))),
inference(paramod,[status(thm)],[c_8,c_17621]) ).
cnf(c_17623,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))),add(multiply(x,multiply(x,multiply(y,z))),add(additive_inverse(multiply(x,multiply(y,multiply(z,x)))),multiply(x,multiply(multiply(y,z),x)))))),
inference(paramod,[status(thm)],[c_72,c_17622]) ).
cnf(c_17624,plain,
multiply(x,multiply(multiply(y,z),x)) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(x,multiply(y,z))),add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,multiply(y,multiply(z,x)))),multiply(x,multiply(multiply(y,z),x)))))),
inference(paramod,[status(thm)],[c_27,c_17623]) ).
cnf(c_17625,plain,
multiply(x,multiply(multiply(y,z),x)) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(x,multiply(y,z))),multiply(x,multiply(multiply(y,z),x)))),
inference(paramod,[status(thm)],[c_25,c_17624]) ).
cnf(c_17626,plain,
multiply(x,multiply(multiply(y,z),x)) != add(multiply(x,multiply(x,multiply(y,z))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(y,z),x)))),
inference(paramod,[status(thm)],[c_27,c_17625]) ).
cnf(c_17627,plain,
multiply(x,multiply(multiply(y,z),x)) != multiply(x,multiply(multiply(y,z),x)),
inference(paramod,[status(thm)],[c_25,c_17626]) ).
cnf(c_17511,plain,
$false,
inference(copy,[status(thm)],[c_17627]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG029-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.33 % Computer : n007.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Sat Sep 26 05:47:08 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 2931532 was started by sandbox2 on n007,
% 0.08/0.34 % Sat Sep 26 05:47:08 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.34
% 0.08/0.34 % From the command line: assign(max_seconds, 300).
% 181.84/24.75
% 181.84/24.75 % SZS status Unsatisfiable for theBenchmark
% 181.84/24.75
% 181.84/24.75 % Proof 1 at 23.10 (+ 0.93) seconds.
% 181.84/24.75 % Length of proof is 46.
% 181.84/24.75 % Level of proof is 18.
% 181.84/24.75 % Maximum clause weight is 49.000.
% 181.84/24.75 % Given clauses 289.
% 181.84/24.75
% 181.84/24.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------