%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG028-9 : 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 : n008.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 160.46s 21.71s
% Output : CNFRefutation 160.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 76
% Number of leaves : 12
% Syntax : Number of formulae : 156 ( 156 unt; 0 def)
% Number of atoms : 156 ( 155 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 54 ( 54 ~; 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 : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 278 ( 0 sgn 23 !; 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(associator,axiom,
! [VAR_0,VAR_1,VAR_2] : associator(VAR_0,VAR_1,VAR_2) = add(multiply(multiply(VAR_0,VAR_1),VAR_2),additive_inverse(multiply(VAR_0,multiply(VAR_1,VAR_2)))),
file('theBenchmark.p',associator) ).
cnf(c_15,plain,
associator(A,B,C) = add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))),
inference(clausify,[status(thm)],[associator]) ).
cnf(c_16,plain,
associator(A,B,C) = add(additive_inverse(multiply(A,multiply(B,C))),multiply(multiply(A,B),C)),
inference(paramod,[status(thm)],[c_10,c_15]) ).
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_left_moufang,axiom,
associator(x,multiply(y,x),z) != multiply(x,associator(x,y,z)),
file('theBenchmark.p',prove_left_moufang) ).
cnf(c_26,plain,
associator(x,multiply(y,x),z) != multiply(x,associator(x,y,z)),
inference(clausify,[status(thm)],[prove_left_moufang]) ).
cnf(c_11403,plain,
add(additive_inverse(multiply(x,multiply(multiply(y,x),z))),multiply(multiply(x,multiply(y,x)),z)) != multiply(x,associator(x,y,z)),
inference(paramod,[status(thm)],[c_16,c_26]) ).
cnf(c_11404,plain,
add(additive_inverse(multiply(x,multiply(multiply(y,x),z))),multiply(multiply(x,multiply(y,x)),z)) != multiply(x,add(additive_inverse(multiply(x,multiply(y,z))),multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_16,c_11403]) ).
cnf(c_11405,plain,
add(additive_inverse(multiply(x,multiply(multiply(y,x),z))),multiply(multiply(x,multiply(y,x)),z)) != add(multiply(x,additive_inverse(multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_8,c_11404]) ).
cnf(c_27,plain,
add(additive_inverse(multiply(x,multiply(multiply(y,x),z))),multiply(multiply(x,multiply(y,x)),z)) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_20,c_11405]) ).
cnf(c_11406,plain,
add(additive_identity,A) = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_6,c_12]) ).
cnf(c_11407,plain,
A = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_11406]) ).
cnf(c_31,plain,
add(A,add(additive_inverse(A),B)) = B,
inference(copy,[status(thm)],[c_11407]) ).
cnf(c_11408,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_11408]) ).
cnf(c_11409,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_11410,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_11409]) ).
cnf(c_11411,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_11410]) ).
cnf(c_11412,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_11411]) ).
cnf(c_11413,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_11412]) ).
cnf(c_11414,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_11413]) ).
cnf(c_11415,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_11414]) ).
cnf(c_11416,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_11415]) ).
cnf(c_11417,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_11416]) ).
cnf(c_11418,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_11417]) ).
cnf(c_11419,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_11418]) ).
cnf(c_11420,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_11419]) ).
cnf(c_11421,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_11420]) ).
cnf(c_11422,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_11421]) ).
cnf(c_11423,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_11422]) ).
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_11423]) ).
cnf(c_11424,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_11425,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_11424]) ).
cnf(c_11426,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_11425]) ).
cnf(c_11427,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_11426]) ).
cnf(c_11428,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_11427]) ).
cnf(c_11429,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_11428]) ).
cnf(c_11430,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_11429]) ).
cnf(c_11431,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_11430]) ).
cnf(c_11432,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_11431]) ).
cnf(c_11433,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_11432]) ).
cnf(c_11434,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_11433]) ).
cnf(c_11435,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_11434]) ).
cnf(c_11436,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_11435]) ).
cnf(c_11437,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_11436]) ).
cnf(c_11438,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_11437]) ).
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_11438]) ).
cnf(c_51,plain,
add(A,add(B,additive_inverse(A))) = B,
inference(paramod,[status(thm)],[c_10,c_31]) ).
cnf(c_54,plain,
add(additive_inverse(A),add(B,A)) = B,
inference(paramod,[status(thm)],[c_7,c_51]) ).
cnf(c_11439,plain,
add(A,B) = add(additive_inverse(C),add(add(A,C),B)),
inference(paramod,[status(thm)],[c_54,c_12]) ).
cnf(c_11440,plain,
add(A,B) = add(additive_inverse(C),add(A,add(C,B))),
inference(paramod,[status(thm)],[c_12,c_11439]) ).
cnf(c_58,plain,
add(additive_inverse(A),add(B,add(A,C))) = add(B,C),
inference(copy,[status(thm)],[c_11440]) ).
cnf(c_59,plain,
add(additive_inverse(A),add(B,add(C,A))) = add(B,C),
inference(paramod,[status(thm)],[c_12,c_54]) ).
cnf(c_11441,plain,
add(additive_inverse(add(A,B)),A) = additive_inverse(B),
inference(paramod,[status(thm)],[c_54,c_54]) ).
cnf(c_62,plain,
add(A,additive_inverse(add(A,B))) = additive_inverse(B),
inference(paramod,[status(thm)],[c_10,c_11441]) ).
cnf(c_11442,plain,
add(additive_inverse(A),additive_inverse(B)) = additive_inverse(add(B,A)),
inference(paramod,[status(thm)],[c_54,c_62]) ).
cnf(c_73,plain,
additive_inverse(add(A,B)) = add(additive_inverse(B),additive_inverse(A)),
inference(copy,[status(thm)],[c_11442]) ).
cnf(c_11443,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_99,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_11443]) ).
cnf(c_105,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_11444,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_58]) ).
cnf(c_11445,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_105,c_11444]) ).
cnf(c_137,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_11445]) ).
cnf(c_11446,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_137,c_58]) ).
cnf(c_11447,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_11446]) ).
cnf(c_682,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_11447]) ).
cnf(c_11448,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_682,c_54]) ).
cnf(c_11449,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_11448]) ).
cnf(c_11450,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_11449]) ).
cnf(c_763,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_11450]) ).
cnf(c_11451,plain,
add(additive_inverse(multiply(x,multiply(multiply(y,x),z))),add(multiply(x,multiply(multiply(y,x),z)),add(multiply(multiply(y,x),multiply(x,z)),additive_inverse(multiply(multiply(multiply(y,x),x),z))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_763,c_27]) ).
cnf(c_11452,plain,
add(additive_inverse(multiply(x,multiply(multiply(y,x),z))),add(multiply(x,multiply(multiply(y,x),z)),add(multiply(multiply(y,x),multiply(x,z)),additive_inverse(multiply(multiply(y,multiply(x,x)),z))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_13,c_11451]) ).
cnf(c_11453,plain,
add(multiply(x,multiply(multiply(y,x),z)),add(additive_inverse(multiply(x,multiply(multiply(y,x),z))),add(multiply(multiply(y,x),multiply(x,z)),additive_inverse(multiply(multiply(y,multiply(x,x)),z))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_33,c_11452]) ).
cnf(c_1401,plain,
add(multiply(multiply(y,x),multiply(x,z)),additive_inverse(multiply(multiply(y,multiply(x,x)),z))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_31,c_11453]) ).
cnf(c_11454,plain,
add(add(multiply(y,multiply(x,multiply(x,z))),add(multiply(x,multiply(y,multiply(x,z))),additive_inverse(multiply(multiply(x,y),multiply(x,z))))),additive_inverse(multiply(multiply(y,multiply(x,x)),z))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_763,c_1401]) ).
cnf(c_11455,plain,
add(add(multiply(x,multiply(y,multiply(x,z))),add(multiply(y,multiply(x,multiply(x,z))),additive_inverse(multiply(multiply(x,y),multiply(x,z))))),additive_inverse(multiply(multiply(y,multiply(x,x)),z))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_33,c_11454]) ).
cnf(c_11456,plain,
add(multiply(x,multiply(y,multiply(x,z))),add(add(multiply(y,multiply(x,multiply(x,z))),additive_inverse(multiply(multiply(x,y),multiply(x,z)))),additive_inverse(multiply(multiply(y,multiply(x,x)),z)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_12,c_11455]) ).
cnf(c_2184,plain,
add(multiply(x,multiply(y,multiply(x,z))),add(multiply(y,multiply(x,multiply(x,z))),add(additive_inverse(multiply(multiply(x,y),multiply(x,z))),additive_inverse(multiply(multiply(y,multiply(x,x)),z))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_12,c_11456]) ).
cnf(c_11457,plain,
add(multiply(x,multiply(y,multiply(x,z))),add(multiply(y,multiply(x,multiply(x,z))),add(additive_inverse(multiply(multiply(x,y),multiply(x,z))),additive_inverse(add(multiply(y,multiply(multiply(x,x),z)),add(multiply(multiply(x,x),multiply(y,z)),additive_inverse(multiply(multiply(multiply(x,x),y),z)))))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_763,c_2184]) ).
cnf(c_11458,plain,
add(multiply(x,multiply(y,multiply(x,z))),add(multiply(y,multiply(x,multiply(x,z))),add(additive_inverse(multiply(multiply(x,y),multiply(x,z))),additive_inverse(add(multiply(y,multiply(x,multiply(x,z))),add(multiply(multiply(x,x),multiply(y,z)),additive_inverse(multiply(multiply(multiply(x,x),y),z)))))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_14,c_11457]) ).
cnf(c_11459,plain,
add(multiply(x,multiply(y,multiply(x,z))),add(multiply(y,multiply(x,multiply(x,z))),add(additive_inverse(multiply(multiply(x,y),multiply(x,z))),additive_inverse(add(multiply(y,multiply(x,multiply(x,z))),add(multiply(x,multiply(x,multiply(y,z))),additive_inverse(multiply(multiply(multiply(x,x),y),z)))))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_14,c_11458]) ).
cnf(c_11460,plain,
add(multiply(x,multiply(y,multiply(x,z))),add(multiply(y,multiply(x,multiply(x,z))),add(additive_inverse(multiply(multiply(x,y),multiply(x,z))),additive_inverse(add(multiply(y,multiply(x,multiply(x,z))),add(multiply(x,multiply(x,multiply(y,z))),additive_inverse(multiply(multiply(x,multiply(x,y)),z)))))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_14,c_11459]) ).
cnf(c_11461,plain,
add(multiply(x,multiply(y,multiply(x,z))),add(multiply(y,multiply(x,multiply(x,z))),add(additive_inverse(multiply(multiply(x,y),multiply(x,z))),additive_inverse(add(multiply(x,multiply(x,multiply(y,z))),add(multiply(y,multiply(x,multiply(x,z))),additive_inverse(multiply(multiply(x,multiply(x,y)),z)))))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_33,c_11460]) ).
cnf(c_11462,plain,
add(multiply(x,multiply(y,multiply(x,z))),add(multiply(y,multiply(x,multiply(x,z))),add(additive_inverse(multiply(multiply(x,y),multiply(x,z))),add(additive_inverse(add(multiply(y,multiply(x,multiply(x,z))),additive_inverse(multiply(multiply(x,multiply(x,y)),z)))),additive_inverse(multiply(x,multiply(x,multiply(y,z)))))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_73,c_11461]) ).
cnf(c_11463,plain,
add(multiply(x,multiply(y,multiply(x,z))),add(multiply(y,multiply(x,multiply(x,z))),add(additive_inverse(multiply(multiply(x,y),multiply(x,z))),add(add(additive_inverse(additive_inverse(multiply(multiply(x,multiply(x,y)),z))),additive_inverse(multiply(y,multiply(x,multiply(x,z))))),additive_inverse(multiply(x,multiply(x,multiply(y,z)))))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_73,c_11462]) ).
cnf(c_11464,plain,
add(multiply(x,multiply(y,multiply(x,z))),add(multiply(y,multiply(x,multiply(x,z))),add(additive_inverse(multiply(multiply(x,y),multiply(x,z))),add(add(multiply(multiply(x,multiply(x,y)),z),additive_inverse(multiply(y,multiply(x,multiply(x,z))))),additive_inverse(multiply(x,multiply(x,multiply(y,z)))))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_7,c_11463]) ).
cnf(c_11465,plain,
add(multiply(x,multiply(y,multiply(x,z))),add(multiply(y,multiply(x,multiply(x,z))),add(additive_inverse(multiply(multiply(x,y),multiply(x,z))),add(add(additive_inverse(multiply(y,multiply(x,multiply(x,z)))),multiply(multiply(x,multiply(x,y)),z)),additive_inverse(multiply(x,multiply(x,multiply(y,z)))))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_10,c_11464]) ).
cnf(c_11466,plain,
add(multiply(x,multiply(y,multiply(x,z))),add(multiply(y,multiply(x,multiply(x,z))),add(additive_inverse(multiply(multiply(x,y),multiply(x,z))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(y,multiply(x,multiply(x,z)))),multiply(multiply(x,multiply(x,y)),z)))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_10,c_11465]) ).
cnf(c_11467,plain,
add(multiply(x,multiply(y,multiply(x,z))),add(multiply(y,multiply(x,multiply(x,z))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(multiply(x,y),multiply(x,z))),add(additive_inverse(multiply(y,multiply(x,multiply(x,z)))),multiply(multiply(x,multiply(x,y)),z)))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_33,c_11466]) ).
cnf(c_11468,plain,
add(multiply(x,multiply(y,multiply(x,z))),add(multiply(y,multiply(x,multiply(x,z))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(y,multiply(x,multiply(x,z)))),add(additive_inverse(multiply(multiply(x,y),multiply(x,z))),multiply(multiply(x,multiply(x,y)),z)))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_33,c_11467]) ).
cnf(c_11469,plain,
add(multiply(x,multiply(y,multiply(x,z))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(y,multiply(x,multiply(x,z))),add(additive_inverse(multiply(y,multiply(x,multiply(x,z)))),add(additive_inverse(multiply(multiply(x,y),multiply(x,z))),multiply(multiply(x,multiply(x,y)),z)))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_33,c_11468]) ).
cnf(c_11470,plain,
add(multiply(x,multiply(y,multiply(x,z))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(multiply(x,y),multiply(x,z))),multiply(multiply(x,multiply(x,y)),z)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_31,c_11469]) ).
cnf(c_2606,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(y,multiply(x,z))),add(additive_inverse(multiply(multiply(x,y),multiply(x,z))),multiply(multiply(x,multiply(x,y)),z)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_33,c_11470]) ).
cnf(c_11471,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_99,c_54]) ).
cnf(c_11472,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_73,c_11471]) ).
cnf(c_11473,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_73,c_11472]) ).
cnf(c_11474,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_11473]) ).
cnf(c_11475,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_11474]) ).
cnf(c_11476,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_11475]) ).
cnf(c_11477,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_11476]) ).
cnf(c_11478,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_105,c_11477]) ).
cnf(c_11479,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_11478]) ).
cnf(c_3547,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_11479]) ).
cnf(c_4584,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_3547,c_31]) ).
cnf(c_11480,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(y,multiply(x,z))),add(additive_inverse(add(additive_inverse(multiply(multiply(x,multiply(x,z)),y)),add(multiply(x,multiply(y,multiply(x,z))),multiply(x,multiply(multiply(x,z),y))))),multiply(multiply(x,multiply(x,y)),z)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_3547,c_2606]) ).
cnf(c_11481,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(y,multiply(x,z))),add(additive_inverse(add(add(multiply(x,multiply(y,multiply(x,z))),multiply(x,multiply(multiply(x,z),y))),additive_inverse(multiply(multiply(x,multiply(x,z)),y)))),multiply(multiply(x,multiply(x,y)),z)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_10,c_11480]) ).
cnf(c_11482,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(y,multiply(x,z))),add(additive_inverse(add(multiply(x,multiply(y,multiply(x,z))),add(multiply(x,multiply(multiply(x,z),y)),additive_inverse(multiply(multiply(x,multiply(x,z)),y))))),multiply(multiply(x,multiply(x,y)),z)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_12,c_11481]) ).
cnf(c_11483,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(y,multiply(x,z))),add(add(additive_inverse(add(multiply(x,multiply(multiply(x,z),y)),additive_inverse(multiply(multiply(x,multiply(x,z)),y)))),additive_inverse(multiply(x,multiply(y,multiply(x,z))))),multiply(multiply(x,multiply(x,y)),z)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_73,c_11482]) ).
cnf(c_11484,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(y,multiply(x,z))),add(add(add(additive_inverse(additive_inverse(multiply(multiply(x,multiply(x,z)),y))),additive_inverse(multiply(x,multiply(multiply(x,z),y)))),additive_inverse(multiply(x,multiply(y,multiply(x,z))))),multiply(multiply(x,multiply(x,y)),z)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_73,c_11483]) ).
cnf(c_11485,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(y,multiply(x,z))),add(add(add(multiply(multiply(x,multiply(x,z)),y),additive_inverse(multiply(x,multiply(multiply(x,z),y)))),additive_inverse(multiply(x,multiply(y,multiply(x,z))))),multiply(multiply(x,multiply(x,y)),z)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_7,c_11484]) ).
cnf(c_11486,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(y,multiply(x,z))),add(add(add(additive_inverse(multiply(x,multiply(multiply(x,z),y))),multiply(multiply(x,multiply(x,z)),y)),additive_inverse(multiply(x,multiply(y,multiply(x,z))))),multiply(multiply(x,multiply(x,y)),z)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_10,c_11485]) ).
cnf(c_11487,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(y,multiply(x,z))),add(add(additive_inverse(multiply(x,multiply(y,multiply(x,z)))),add(additive_inverse(multiply(x,multiply(multiply(x,z),y))),multiply(multiply(x,multiply(x,z)),y))),multiply(multiply(x,multiply(x,y)),z)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_10,c_11486]) ).
cnf(c_11488,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(y,multiply(x,z))),add(multiply(multiply(x,multiply(x,y)),z),add(additive_inverse(multiply(x,multiply(y,multiply(x,z)))),add(additive_inverse(multiply(x,multiply(multiply(x,z),y))),multiply(multiply(x,multiply(x,z)),y)))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_10,c_11487]) ).
cnf(c_11489,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(y,multiply(x,z))),add(additive_inverse(multiply(x,multiply(y,multiply(x,z)))),add(multiply(multiply(x,multiply(x,y)),z),add(additive_inverse(multiply(x,multiply(multiply(x,z),y))),multiply(multiply(x,multiply(x,z)),y)))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_33,c_11488]) ).
cnf(c_11490,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(y,multiply(x,z))),add(additive_inverse(multiply(x,multiply(y,multiply(x,z)))),add(additive_inverse(multiply(x,multiply(multiply(x,z),y))),add(multiply(multiply(x,multiply(x,y)),z),multiply(multiply(x,multiply(x,z)),y)))))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_33,c_11489]) ).
cnf(c_4822,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(x,multiply(multiply(x,z),y))),add(multiply(multiply(x,multiply(x,y)),z),multiply(multiply(x,multiply(x,z)),y)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,multiply(multiply(x,y),z))),
inference(paramod,[status(thm)],[c_31,c_11490]) ).
cnf(c_11491,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_4584,c_10]) ).
cnf(c_7855,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_11491]) ).
cnf(c_11492,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(x,multiply(multiply(x,z),y))),add(multiply(multiply(x,multiply(x,y)),z),multiply(multiply(x,multiply(x,z)),y)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,add(additive_inverse(multiply(multiply(x,z),y)),add(multiply(x,multiply(y,z)),multiply(x,multiply(z,y)))))),
inference(paramod,[status(thm)],[c_3547,c_4822]) ).
cnf(c_11493,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(x,multiply(multiply(x,z),y))),add(multiply(multiply(x,multiply(x,y)),z),multiply(multiply(x,multiply(x,z)),y)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,add(add(multiply(x,multiply(y,z)),multiply(x,multiply(z,y))),additive_inverse(multiply(multiply(x,z),y))))),
inference(paramod,[status(thm)],[c_10,c_11492]) ).
cnf(c_11494,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(x,multiply(multiply(x,z),y))),add(multiply(multiply(x,multiply(x,y)),z),multiply(multiply(x,multiply(x,z)),y)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),multiply(x,add(multiply(x,multiply(y,z)),add(multiply(x,multiply(z,y)),additive_inverse(multiply(multiply(x,z),y)))))),
inference(paramod,[status(thm)],[c_12,c_11493]) ).
cnf(c_11495,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(x,multiply(multiply(x,z),y))),add(multiply(multiply(x,multiply(x,y)),z),multiply(multiply(x,multiply(x,z)),y)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(x,multiply(y,z))),multiply(x,add(multiply(x,multiply(z,y)),additive_inverse(multiply(multiply(x,z),y)))))),
inference(paramod,[status(thm)],[c_8,c_11494]) ).
cnf(c_11496,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(x,multiply(multiply(x,z),y))),add(multiply(multiply(x,multiply(x,y)),z),multiply(multiply(x,multiply(x,z)),y)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(x,multiply(y,z))),add(multiply(x,multiply(x,multiply(z,y))),multiply(x,additive_inverse(multiply(multiply(x,z),y)))))),
inference(paramod,[status(thm)],[c_8,c_11495]) ).
cnf(c_11497,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(x,multiply(multiply(x,z),y))),add(multiply(multiply(x,multiply(x,y)),z),multiply(multiply(x,multiply(x,z)),y)))) != add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(x,multiply(y,z))),add(multiply(x,multiply(x,multiply(z,y))),additive_inverse(multiply(x,multiply(multiply(x,z),y)))))),
inference(paramod,[status(thm)],[c_20,c_11496]) ).
cnf(c_11498,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(x,multiply(multiply(x,z),y))),add(multiply(multiply(x,multiply(x,y)),z),multiply(multiply(x,multiply(x,z)),y)))) != add(multiply(x,multiply(x,multiply(y,z))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(x,multiply(z,y))),additive_inverse(multiply(x,multiply(multiply(x,z),y)))))),
inference(paramod,[status(thm)],[c_33,c_11497]) ).
cnf(c_10575,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(x,multiply(multiply(x,z),y))),add(multiply(multiply(x,multiply(x,y)),z),multiply(multiply(x,multiply(x,z)),y)))) != add(multiply(x,multiply(x,multiply(z,y))),additive_inverse(multiply(x,multiply(multiply(x,z),y)))),
inference(paramod,[status(thm)],[c_31,c_11498]) ).
cnf(c_11499,plain,
add(multiply(multiply(A,multiply(A,B)),C),multiply(multiply(multiply(A,A),C),B)) = add(multiply(multiply(A,A),multiply(B,C)),multiply(multiply(A,A),multiply(C,B))),
inference(paramod,[status(thm)],[c_14,c_7855]) ).
cnf(c_11500,plain,
add(multiply(multiply(A,multiply(A,B)),C),multiply(multiply(A,multiply(A,C)),B)) = add(multiply(multiply(A,A),multiply(B,C)),multiply(multiply(A,A),multiply(C,B))),
inference(paramod,[status(thm)],[c_14,c_11499]) ).
cnf(c_11501,plain,
add(multiply(multiply(A,multiply(A,B)),C),multiply(multiply(A,multiply(A,C)),B)) = add(multiply(A,multiply(A,multiply(B,C))),multiply(multiply(A,A),multiply(C,B))),
inference(paramod,[status(thm)],[c_14,c_11500]) ).
cnf(c_11352,plain,
add(multiply(multiply(A,multiply(A,B)),C),multiply(multiply(A,multiply(A,C)),B)) = add(multiply(A,multiply(A,multiply(B,C))),multiply(A,multiply(A,multiply(C,B)))),
inference(paramod,[status(thm)],[c_14,c_11501]) ).
cnf(c_11502,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(additive_inverse(multiply(x,multiply(multiply(x,z),y))),add(multiply(x,multiply(x,multiply(y,z))),multiply(x,multiply(x,multiply(z,y)))))) != add(multiply(x,multiply(x,multiply(z,y))),additive_inverse(multiply(x,multiply(multiply(x,z),y)))),
inference(paramod,[status(thm)],[c_11352,c_10575]) ).
cnf(c_11503,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(add(multiply(x,multiply(x,multiply(y,z))),multiply(x,multiply(x,multiply(z,y)))),additive_inverse(multiply(x,multiply(multiply(x,z),y))))) != add(multiply(x,multiply(x,multiply(z,y))),additive_inverse(multiply(x,multiply(multiply(x,z),y)))),
inference(paramod,[status(thm)],[c_10,c_11502]) ).
cnf(c_11504,plain,
add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(x,multiply(y,z))),add(multiply(x,multiply(x,multiply(z,y))),additive_inverse(multiply(x,multiply(multiply(x,z),y)))))) != add(multiply(x,multiply(x,multiply(z,y))),additive_inverse(multiply(x,multiply(multiply(x,z),y)))),
inference(paramod,[status(thm)],[c_12,c_11503]) ).
cnf(c_11505,plain,
add(multiply(x,multiply(x,multiply(y,z))),add(additive_inverse(multiply(x,multiply(x,multiply(y,z)))),add(multiply(x,multiply(x,multiply(z,y))),additive_inverse(multiply(x,multiply(multiply(x,z),y)))))) != add(multiply(x,multiply(x,multiply(z,y))),additive_inverse(multiply(x,multiply(multiply(x,z),y)))),
inference(paramod,[status(thm)],[c_33,c_11504]) ).
cnf(c_11506,plain,
add(multiply(x,multiply(x,multiply(z,y))),additive_inverse(multiply(x,multiply(multiply(x,z),y)))) != add(multiply(x,multiply(x,multiply(z,y))),additive_inverse(multiply(x,multiply(multiply(x,z),y)))),
inference(paramod,[status(thm)],[c_31,c_11505]) ).
cnf(c_11402,plain,
$false,
inference(copy,[status(thm)],[c_11506]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG028-9 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 05:49:29 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2913903 was started by sandbox on n008,
% 0.08/0.35 % Sat Sep 26 05:49:29 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 160.46/21.71
% 160.46/21.71 % SZS status Unsatisfiable for theBenchmark
% 160.46/21.71
% 160.46/21.71 % Proof 1 at 20.24 (+ 0.92) seconds.
% 160.46/21.71 % Length of proof is 40.
% 160.46/21.71 % Level of proof is 15.
% 160.46/21.71 % Maximum clause weight is 50.000.
% 160.46/21.71 % Given clauses 244.
% 160.46/21.71
% 160.46/21.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------