%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG025-4 : 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 : 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 08:26:23 AM UTC 2026
% Result : Unsatisfiable 56.35s 7.77s
% Output : CNFRefutation 56.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 10
% Syntax : Number of formulae : 84 ( 84 unt; 0 def)
% Number of atoms : 84 ( 83 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 22 ( 22 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 9 ( 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 : 159 ( 0 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_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(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(prove_equation,axiom,
add(associator(x,y,z),associator(x,z,y)) != additive_identity,
file('theBenchmark.p',prove_equation) ).
cnf(c_18,plain,
add(associator(x,y,z),associator(x,z,y)) != additive_identity,
inference(clausify,[status(thm)],[prove_equation]) ).
cnf(c_4577,plain,
add(add(additive_inverse(multiply(x,multiply(y,z))),multiply(multiply(x,y),z)),associator(x,z,y)) != additive_identity,
inference(paramod,[status(thm)],[c_16,c_18]) ).
cnf(c_4578,plain,
add(add(additive_inverse(multiply(x,multiply(y,z))),multiply(multiply(x,y),z)),add(additive_inverse(multiply(x,multiply(z,y))),multiply(multiply(x,z),y))) != additive_identity,
inference(paramod,[status(thm)],[c_16,c_4577]) ).
cnf(c_19,plain,
add(additive_inverse(multiply(x,multiply(y,z))),add(multiply(multiply(x,y),z),add(additive_inverse(multiply(x,multiply(z,y))),multiply(multiply(x,z),y)))) != additive_identity,
inference(paramod,[status(thm)],[c_12,c_4578]) ).
cnf(c_4579,plain,
add(additive_identity,A) = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_6,c_12]) ).
cnf(c_4580,plain,
A = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_4579]) ).
cnf(c_25,plain,
add(A,add(additive_inverse(A),B)) = B,
inference(copy,[status(thm)],[c_4580]) ).
cnf(c_4581,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_4581]) ).
cnf(c_28,plain,
add(additive_inverse(multiply(x,multiply(y,z))),add(additive_inverse(multiply(x,multiply(z,y))),add(multiply(multiply(x,y),z),multiply(multiply(x,z),y)))) != additive_identity,
inference(paramod,[status(thm)],[c_27,c_19]) ).
cnf(c_4582,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_4583,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_4582]) ).
cnf(c_4584,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_4583]) ).
cnf(c_4585,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_4584]) ).
cnf(c_4586,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_4585]) ).
cnf(c_4587,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_4586]) ).
cnf(c_4588,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_4587]) ).
cnf(c_4589,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_4588]) ).
cnf(c_4590,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_4589]) ).
cnf(c_4591,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_4590]) ).
cnf(c_4592,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_4591]) ).
cnf(c_4593,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_4592]) ).
cnf(c_4594,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_4593]) ).
cnf(c_4595,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_4594]) ).
cnf(c_4596,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_4595]) ).
cnf(c_29,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_4596]) ).
cnf(c_37,plain,
add(A,add(B,additive_inverse(A))) = B,
inference(paramod,[status(thm)],[c_10,c_25]) ).
cnf(c_39,plain,
add(additive_inverse(A),add(B,A)) = B,
inference(paramod,[status(thm)],[c_7,c_37]) ).
cnf(c_48,plain,
add(additive_inverse(A),add(B,add(C,A))) = add(B,C),
inference(paramod,[status(thm)],[c_12,c_39]) ).
cnf(c_4597,plain,
add(additive_inverse(add(A,B)),A) = additive_inverse(B),
inference(paramod,[status(thm)],[c_39,c_39]) ).
cnf(c_51,plain,
add(A,additive_inverse(add(A,B))) = additive_inverse(B),
inference(paramod,[status(thm)],[c_10,c_4597]) ).
cnf(c_4598,plain,
add(additive_inverse(A),additive_inverse(B)) = additive_inverse(add(B,A)),
inference(paramod,[status(thm)],[c_39,c_51]) ).
cnf(c_72,plain,
additive_inverse(add(A,B)) = add(additive_inverse(B),additive_inverse(A)),
inference(copy,[status(thm)],[c_4598]) ).
cnf(c_4599,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_29,c_27]) ).
cnf(c_108,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_4599]) ).
cnf(c_116,plain,
add(additive_inverse(A),add(B,add(C,add(D,A)))) = add(B,add(C,D)),
inference(paramod,[status(thm)],[c_12,c_48]) ).
cnf(c_4600,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_108,c_39]) ).
cnf(c_4601,plain,
add(add(additive_inverse(add(multiply(multiply(A,B),C),multiply(A,multiply(C,C)))),additive_inverse(multiply(A,multiply(B,B)))),add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C)))))) = multiply(multiply(A,C),B),
inference(paramod,[status(thm)],[c_72,c_4600]) ).
cnf(c_4602,plain,
add(add(add(additive_inverse(multiply(A,multiply(C,C))),additive_inverse(multiply(multiply(A,B),C))),additive_inverse(multiply(A,multiply(B,B)))),add(multiply(A,multiply(B,B)),add(multiply(A,multiply(C,B)),add(multiply(A,multiply(B,C)),multiply(A,multiply(C,C)))))) = multiply(multiply(A,C),B),
inference(paramod,[status(thm)],[c_72,c_4601]) ).
cnf(c_4603,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_4602]) ).
cnf(c_4604,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_4603]) ).
cnf(c_4605,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_4604]) ).
cnf(c_4606,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_4605]) ).
cnf(c_4607,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_116,c_4606]) ).
cnf(c_4608,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_4607]) ).
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_4608]) ).
cnf(c_4609,plain,
add(additive_inverse(multiply(x,multiply(y,z))),add(additive_inverse(multiply(x,multiply(z,y))),add(add(additive_inverse(multiply(multiply(x,z),y)),add(multiply(x,multiply(y,z)),multiply(x,multiply(z,y)))),multiply(multiply(x,z),y)))) != additive_identity,
inference(paramod,[status(thm)],[c_3098,c_28]) ).
cnf(c_4610,plain,
add(additive_inverse(multiply(x,multiply(y,z))),add(additive_inverse(multiply(x,multiply(z,y))),add(add(add(multiply(x,multiply(y,z)),multiply(x,multiply(z,y))),additive_inverse(multiply(multiply(x,z),y))),multiply(multiply(x,z),y)))) != additive_identity,
inference(paramod,[status(thm)],[c_10,c_4609]) ).
cnf(c_4611,plain,
add(additive_inverse(multiply(x,multiply(y,z))),add(additive_inverse(multiply(x,multiply(z,y))),add(add(multiply(x,multiply(y,z)),add(multiply(x,multiply(z,y)),additive_inverse(multiply(multiply(x,z),y)))),multiply(multiply(x,z),y)))) != additive_identity,
inference(paramod,[status(thm)],[c_12,c_4610]) ).
cnf(c_4612,plain,
add(additive_inverse(multiply(x,multiply(y,z))),add(additive_inverse(multiply(x,multiply(z,y))),add(multiply(multiply(x,z),y),add(multiply(x,multiply(y,z)),add(multiply(x,multiply(z,y)),additive_inverse(multiply(multiply(x,z),y))))))) != additive_identity,
inference(paramod,[status(thm)],[c_10,c_4611]) ).
cnf(c_4613,plain,
add(additive_inverse(multiply(x,multiply(y,z))),add(additive_inverse(multiply(x,multiply(z,y))),add(multiply(x,multiply(y,z)),add(multiply(multiply(x,z),y),add(multiply(x,multiply(z,y)),additive_inverse(multiply(multiply(x,z),y))))))) != additive_identity,
inference(paramod,[status(thm)],[c_27,c_4612]) ).
cnf(c_4614,plain,
add(additive_inverse(multiply(x,multiply(y,z))),add(additive_inverse(multiply(x,multiply(z,y))),add(multiply(x,multiply(y,z)),add(multiply(x,multiply(z,y)),add(multiply(multiply(x,z),y),additive_inverse(multiply(multiply(x,z),y))))))) != additive_identity,
inference(paramod,[status(thm)],[c_27,c_4613]) ).
cnf(c_4615,plain,
add(additive_inverse(multiply(x,multiply(y,z))),add(additive_inverse(multiply(x,multiply(z,y))),add(multiply(x,multiply(y,z)),add(multiply(x,multiply(z,y)),additive_identity)))) != additive_identity,
inference(paramod,[status(thm)],[c_6,c_4614]) ).
cnf(c_4616,plain,
add(additive_inverse(multiply(x,multiply(y,z))),add(additive_inverse(multiply(x,multiply(z,y))),add(multiply(x,multiply(y,z)),add(additive_identity,multiply(x,multiply(z,y)))))) != additive_identity,
inference(paramod,[status(thm)],[c_10,c_4615]) ).
cnf(c_4617,plain,
add(additive_inverse(multiply(x,multiply(y,z))),add(additive_inverse(multiply(x,multiply(z,y))),add(multiply(x,multiply(y,z)),multiply(x,multiply(z,y))))) != additive_identity,
inference(paramod,[status(thm)],[c_1,c_4616]) ).
cnf(c_4618,plain,
add(additive_inverse(multiply(x,multiply(y,z))),add(add(multiply(x,multiply(y,z)),multiply(x,multiply(z,y))),additive_inverse(multiply(x,multiply(z,y))))) != additive_identity,
inference(paramod,[status(thm)],[c_10,c_4617]) ).
cnf(c_4619,plain,
add(additive_inverse(multiply(x,multiply(y,z))),add(multiply(x,multiply(y,z)),add(multiply(x,multiply(z,y)),additive_inverse(multiply(x,multiply(z,y)))))) != additive_identity,
inference(paramod,[status(thm)],[c_12,c_4618]) ).
cnf(c_4620,plain,
add(additive_inverse(multiply(x,multiply(y,z))),add(multiply(x,multiply(y,z)),additive_identity)) != additive_identity,
inference(paramod,[status(thm)],[c_6,c_4619]) ).
cnf(c_4621,plain,
add(additive_inverse(multiply(x,multiply(y,z))),add(additive_identity,multiply(x,multiply(y,z)))) != additive_identity,
inference(paramod,[status(thm)],[c_10,c_4620]) ).
cnf(c_4622,plain,
add(additive_inverse(multiply(x,multiply(y,z))),multiply(x,multiply(y,z))) != additive_identity,
inference(paramod,[status(thm)],[c_1,c_4621]) ).
cnf(c_4623,plain,
add(multiply(x,multiply(y,z)),additive_inverse(multiply(x,multiply(y,z)))) != additive_identity,
inference(paramod,[status(thm)],[c_10,c_4622]) ).
cnf(c_4624,plain,
additive_identity != additive_identity,
inference(paramod,[status(thm)],[c_6,c_4623]) ).
cnf(c_4576,plain,
$false,
inference(copy,[status(thm)],[c_4624]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG025-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.55 % Computer : n007.cluster.edu
% 0.08/0.55 % Model : x86_64 x86_64
% 0.08/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.55 % Memory : 8046.5625MB
% 0.08/0.55 % OS : Linux 6.8.0-71-generic
% 0.08/0.55 % CPULimit : 300
% 0.08/0.55 % WCLimit : 300
% 0.08/0.55 % DateTime : Sat Sep 26 05:45:09 UTC 2026
% 0.08/0.55 % CPUTime :
% 0.08/0.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.56 % Process 2924624 was started by sandbox on n007,
% 0.08/0.56 % Sat Sep 26 05:45:09 2026
% 0.08/0.56 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.56
% 0.08/0.56 % From the command line: assign(max_seconds, 300).
% 56.35/7.77
% 56.35/7.77 % SZS status Unsatisfiable for theBenchmark
% 56.35/7.77
% 56.35/7.77 % Proof 1 at 6.76 (+ 0.38) seconds.
% 56.35/7.77 % Length of proof is 26.
% 56.35/7.77 % Level of proof is 8.
% 56.35/7.77 % Maximum clause weight is 47.000.
% 56.35/7.77 % Given clauses 130.
% 56.35/7.77
% 56.35/7.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------