%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG001-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 : Tue Sep 29 12:34:42 PM UTC 2026
% Result : Unsatisfiable 137.05s 17.80s
% Output : CNFRefutation 138.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 11
% Syntax : Number of clauses : 129 ( 129 unt; 0 nHn; 3 RR)
% Number of literals : 129 ( 128 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 336 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
product(a,additive_identity,additive_identity) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_additive_id_is_additive_id) ).
cnf(c2,axiom,
ifeq2(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c3,plain,
ifeq2(true,true,additive_identity,X2) = additive_identity,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
additive_identity = ifeq2(true,true,additive_identity,X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
ifeq2(sum(X3,X2,X3),true,additive_identity,X2) = ifeq2(sum(X3,X2,X3),true,ifeq2(true,true,additive_identity,X2),X2),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
sum(X2,additive_identity,X2) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c7,plain,
true = sum(X2,additive_identity,X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
ifeq2(true,true,additive_identity,X2) = ifeq2(sum(X3,additive_identity,X3),true,additive_identity,X2),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
ifeq2(sum(X3,X2,X3),true,ifeq2(true,true,additive_identity,X2),X2) = ifeq2(sum(X3,X2,X3),true,ifeq2(sum(X3,additive_identity,X3),true,additive_identity,X2),X2),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
ifeq2(sum(X,W,Z),true,ifeq2(sum(X,Y,Z),true,Y,W),W) = W,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation1) ).
cnf(c11,plain,
ifeq2(sum(X3,X2,X3),true,ifeq2(sum(X3,additive_identity,X3),true,additive_identity,X2),X2) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
ifeq2(sum(X3,X2,X3),true,ifeq2(true,true,additive_identity,X2),X2) = X2,
inference(transitivity,[status(thm)],[c9,c11]) ).
cnf(c13,plain,
ifeq2(sum(X3,X2,X3),true,additive_identity,X2) = X2,
inference(transitivity,[status(thm)],[c5,c12]) ).
cnf(c14,plain,
ifeq2(sum(multiply(X3,X2),multiply(X3,additive_identity),multiply(X3,X2)),true,additive_identity,multiply(X3,additive_identity)) = multiply(X3,additive_identity),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(X3,additive_identity) = ifeq2(sum(multiply(X3,X2),multiply(X3,additive_identity),multiply(X3,X2)),true,additive_identity,multiply(X3,additive_identity)),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
ifeq2(true,true,multiply(X3,X2),X4) = multiply(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c17,plain,
multiply(X4,X3) = ifeq2(true,true,multiply(X4,X3),X2),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
ifeq2(product(X4,X3,X2),true,multiply(X4,X3),X2) = ifeq2(product(X4,X3,X2),true,ifeq2(true,true,multiply(X4,X3),X2),X2),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,axiom,
product(X2,Y2,multiply(X2,Y2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(c20,plain,
product(X3,X2,multiply(X3,X2)) = true,
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
true = product(X3,X2,multiply(X3,X2)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
ifeq2(true,true,multiply(X4,X3),X2) = ifeq2(product(X4,X3,multiply(X4,X3)),true,multiply(X4,X3),X2),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
ifeq2(product(X4,X3,X2),true,ifeq2(true,true,multiply(X4,X3),X2),X2) = ifeq2(product(X4,X3,X2),true,ifeq2(product(X4,X3,multiply(X4,X3)),true,multiply(X4,X3),X2),X2),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,axiom,
ifeq2(product(X2,Y2,V),true,ifeq2(product(X2,Y2,U),true,U,V),V) = V,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
cnf(c25,plain,
ifeq2(product(X4,X3,X2),true,ifeq2(product(X4,X3,multiply(X4,X3)),true,multiply(X4,X3),X2),X2) = X2,
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
ifeq2(product(X4,X3,X2),true,ifeq2(true,true,multiply(X4,X3),X2),X2) = X2,
inference(transitivity,[status(thm)],[c23,c25]) ).
cnf(c27,plain,
ifeq2(product(X4,X3,X2),true,multiply(X4,X3),X2) = X2,
inference(transitivity,[status(thm)],[c18,c26]) ).
cnf(c28,plain,
ifeq2(product(X3,X2,add(multiply(X3,X2),multiply(X3,additive_identity))),true,multiply(X3,X2),add(multiply(X3,X2),multiply(X3,additive_identity))) = add(multiply(X3,X2),multiply(X3,additive_identity)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
add(multiply(X3,X2),multiply(X3,additive_identity)) = ifeq2(product(X3,X2,add(multiply(X3,X2),multiply(X3,additive_identity))),true,multiply(X3,X2),add(multiply(X3,X2),multiply(X3,additive_identity))),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,axiom,
ifeq(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(c31,plain,
ifeq(true,true,product(X3,X2,add(multiply(X3,X2),multiply(X3,additive_identity))),true) = product(X3,X2,add(multiply(X3,X2),multiply(X3,additive_identity))),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
product(X3,X2,add(multiply(X3,X2),multiply(X3,additive_identity))) = ifeq(true,true,product(X3,X2,add(multiply(X3,X2),multiply(X3,additive_identity))),true),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
product(X3,X2,multiply(X3,X2)) = true,
inference(substitution,[status(thm)],[c19]) ).
cnf(c34,plain,
true = product(X3,X2,multiply(X3,X2)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
ifeq(true,true,product(X3,X2,add(multiply(X3,X2),multiply(X3,additive_identity))),true) = ifeq(product(X3,X2,multiply(X3,X2)),true,product(X3,X2,add(multiply(X3,X2),multiply(X3,additive_identity))),true),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
ifeq2(true,true,add(X4,X3),X2) = add(X4,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c37,plain,
add(X4,X3) = ifeq2(true,true,add(X4,X3),X2),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
ifeq2(sum(X4,X3,X2),true,add(X4,X3),X2) = ifeq2(sum(X4,X3,X2),true,ifeq2(true,true,add(X4,X3),X2),X2),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,axiom,
sum(X2,Y2,add(X2,Y2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
cnf(c40,plain,
sum(X3,X2,add(X3,X2)) = true,
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
true = sum(X3,X2,add(X3,X2)),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
ifeq2(true,true,add(X4,X3),X2) = ifeq2(sum(X4,X3,add(X4,X3)),true,add(X4,X3),X2),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
ifeq2(sum(X4,X3,X2),true,ifeq2(true,true,add(X4,X3),X2),X2) = ifeq2(sum(X4,X3,X2),true,ifeq2(sum(X4,X3,add(X4,X3)),true,add(X4,X3),X2),X2),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,axiom,
ifeq2(sum(X2,Y2,V5),true,ifeq2(sum(X2,Y2,U2),true,U2,V5),V5) = V5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(c45,plain,
ifeq2(sum(X4,X3,X2),true,ifeq2(sum(X4,X3,add(X4,X3)),true,add(X4,X3),X2),X2) = X2,
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
ifeq2(sum(X4,X3,X2),true,ifeq2(true,true,add(X4,X3),X2),X2) = X2,
inference(transitivity,[status(thm)],[c43,c45]) ).
cnf(c47,plain,
ifeq2(sum(X4,X3,X2),true,add(X4,X3),X2) = X2,
inference(transitivity,[status(thm)],[c38,c46]) ).
cnf(c48,plain,
ifeq2(sum(X2,X3,add(X3,X2)),true,add(X2,X3),add(X3,X2)) = add(X3,X2),
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
add(X3,X2) = ifeq2(sum(X2,X3,add(X3,X2)),true,add(X2,X3),add(X3,X2)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
ifeq(true,true,sum(X3,X2,add(X2,X3)),true) = sum(X3,X2,add(X2,X3)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c51,plain,
sum(X3,X2,add(X2,X3)) = ifeq(true,true,sum(X3,X2,add(X2,X3)),true),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
sum(X2,X3,add(X2,X3)) = true,
inference(substitution,[status(thm)],[c39]) ).
cnf(c53,plain,
true = sum(X2,X3,add(X2,X3)),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
ifeq(true,true,sum(X3,X2,add(X2,X3)),true) = ifeq(sum(X2,X3,add(X2,X3)),true,sum(X3,X2,add(X2,X3)),true),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,axiom,
ifeq(sum(X2,Y2,Z2),true,sum(Y2,X2,Z2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
cnf(c56,plain,
ifeq(sum(X2,X3,add(X2,X3)),true,sum(X3,X2,add(X2,X3)),true) = true,
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
ifeq(true,true,sum(X3,X2,add(X2,X3)),true) = true,
inference(transitivity,[status(thm)],[c54,c56]) ).
cnf(c58,plain,
sum(X3,X2,add(X2,X3)) = true,
inference(transitivity,[status(thm)],[c51,c57]) ).
cnf(c59,plain,
sum(X2,X3,add(X3,X2)) = true,
inference(substitution,[status(thm)],[c58]) ).
cnf(c60,plain,
ifeq2(sum(X2,X3,add(X3,X2)),true,add(X2,X3),add(X3,X2)) = ifeq2(true,true,add(X2,X3),add(X3,X2)),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
ifeq2(true,true,add(X2,X3),add(X3,X2)) = add(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c62,plain,
ifeq2(sum(X2,X3,add(X3,X2)),true,add(X2,X3),add(X3,X2)) = add(X2,X3),
inference(transitivity,[status(thm)],[c60,c61]) ).
cnf(c63,plain,
add(X3,X2) = add(X2,X3),
inference(transitivity,[status(thm)],[c49,c62]) ).
cnf(c64,plain,
add(multiply(X3,additive_identity),X2) = add(X2,multiply(X3,additive_identity)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
add(X2,multiply(X3,additive_identity)) = add(multiply(X3,additive_identity),X2),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
product(X4,X3,add(X2,multiply(X4,additive_identity))) = product(X4,X3,add(multiply(X4,additive_identity),X2)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
ifeq(product(X4,X3,X2),true,product(X4,X3,add(X2,multiply(X4,additive_identity))),true) = ifeq(product(X4,X3,X2),true,product(X4,X3,add(multiply(X4,additive_identity),X2)),true),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
ifeq(true,true,ifeq(product(X4,X3,X2),true,product(X4,X3,add(multiply(X4,additive_identity),X2)),true),true) = ifeq(product(X4,X3,X2),true,product(X4,X3,add(multiply(X4,additive_identity),X2)),true),
inference(substitution,[status(thm)],[c30]) ).
cnf(c69,plain,
ifeq(product(X4,X3,X2),true,product(X4,X3,add(multiply(X4,additive_identity),X2)),true) = ifeq(true,true,ifeq(product(X4,X3,X2),true,product(X4,X3,add(multiply(X4,additive_identity),X2)),true),true),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
product(X2,additive_identity,multiply(X2,additive_identity)) = true,
inference(substitution,[status(thm)],[c19]) ).
cnf(c71,plain,
true = product(X2,additive_identity,multiply(X2,additive_identity)),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
ifeq(true,true,ifeq(product(X4,X3,X2),true,product(X4,X3,add(multiply(X4,additive_identity),X2)),true),true) = ifeq(product(X4,additive_identity,multiply(X4,additive_identity)),true,ifeq(product(X4,X3,X2),true,product(X4,X3,add(multiply(X4,additive_identity),X2)),true),true),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c63]) ).
cnf(c74,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
product(X5,X3,add(X4,X2)) = product(X5,X3,add(X2,X4)),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
ifeq(product(X5,X3,X2),true,product(X5,X3,add(X4,X2)),true) = ifeq(product(X5,X3,X2),true,product(X5,X3,add(X2,X4)),true),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
ifeq(product(X5,additive_identity,X4),true,ifeq(product(X5,X3,X2),true,product(X5,X3,add(X4,X2)),true),true) = ifeq(product(X5,additive_identity,X4),true,ifeq(product(X5,X3,X2),true,product(X5,X3,add(X2,X4)),true),true),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
ifeq(true,true,product(X5,X3,add(X2,X4)),true) = product(X5,X3,add(X2,X4)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c79,plain,
product(X5,X3,add(X2,X4)) = ifeq(true,true,product(X5,X3,add(X2,X4)),true),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
ifeq(product(X5,X3,X2),true,product(X5,X3,add(X2,X4)),true) = ifeq(product(X5,X3,X2),true,ifeq(true,true,product(X5,X3,add(X2,X4)),true),true),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
ifeq(product(X5,additive_identity,X4),true,ifeq(product(X5,X3,X2),true,product(X5,X3,add(X2,X4)),true),true) = ifeq(product(X5,additive_identity,X4),true,ifeq(product(X5,X3,X2),true,ifeq(true,true,product(X5,X3,add(X2,X4)),true),true),true),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
sum(X2,X3,add(X2,X3)) = true,
inference(substitution,[status(thm)],[c39]) ).
cnf(c83,plain,
true = sum(X2,X3,add(X2,X3)),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
ifeq(true,true,product(X5,X3,add(X2,X4)),true) = ifeq(sum(X2,X4,add(X2,X4)),true,product(X5,X3,add(X2,X4)),true),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
ifeq(product(X5,X3,X2),true,ifeq(true,true,product(X5,X3,add(X2,X4)),true),true) = ifeq(product(X5,X3,X2),true,ifeq(sum(X2,X4,add(X2,X4)),true,product(X5,X3,add(X2,X4)),true),true),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
ifeq(product(X5,additive_identity,X4),true,ifeq(product(X5,X3,X2),true,ifeq(true,true,product(X5,X3,add(X2,X4)),true),true),true) = ifeq(product(X5,additive_identity,X4),true,ifeq(product(X5,X3,X2),true,ifeq(sum(X2,X4,add(X2,X4)),true,product(X5,X3,add(X2,X4)),true),true),true),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
ifeq(true,true,product(X3,X2,X4),true) = product(X3,X2,X4),
inference(substitution,[status(thm)],[c30]) ).
cnf(c88,plain,
product(X4,X3,X2) = ifeq(true,true,product(X4,X3,X2),true),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
ifeq(sum(X3,X5,X2),true,product(X6,X4,X2),true) = ifeq(sum(X3,X5,X2),true,ifeq(true,true,product(X6,X4,X2),true),true),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,product(X6,X4,X2),true),true) = ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,ifeq(true,true,product(X6,X4,X2),true),true),true),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
ifeq(product(X6,additive_identity,X5),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,product(X6,X4,X2),true),true),true) = ifeq(product(X6,additive_identity,X5),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,ifeq(true,true,product(X6,X4,X2),true),true),true),true),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
true = sum(X2,additive_identity,X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c93,plain,
ifeq(true,true,product(X4,X3,X2),true) = ifeq(sum(X3,additive_identity,X3),true,product(X4,X3,X2),true),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
ifeq(sum(X3,X5,X2),true,ifeq(true,true,product(X6,X4,X2),true),true) = ifeq(sum(X3,X5,X2),true,ifeq(sum(X4,additive_identity,X4),true,product(X6,X4,X2),true),true),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,ifeq(true,true,product(X6,X4,X2),true),true),true) = ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,ifeq(sum(X4,additive_identity,X4),true,product(X6,X4,X2),true),true),true),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
ifeq(product(X6,additive_identity,X5),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,ifeq(true,true,product(X6,X4,X2),true),true),true),true) = ifeq(product(X6,additive_identity,X5),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,ifeq(sum(X4,additive_identity,X4),true,product(X6,X4,X2),true),true),true),true),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,axiom,
ifeq(product(X2,Z2,V2),true,ifeq(product(X2,Y2,V1),true,ifeq(sum(V1,V2,V4),true,ifeq(sum(Y2,Z2,V3),true,product(X2,V3,V4),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
cnf(c98,plain,
ifeq(product(X6,additive_identity,X5),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,ifeq(sum(X4,additive_identity,X4),true,product(X6,X4,X2),true),true),true),true) = true,
inference(substitution,[status(thm)],[c97]) ).
cnf(c99,plain,
ifeq(product(X6,additive_identity,X5),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,ifeq(true,true,product(X6,X4,X2),true),true),true),true) = true,
inference(transitivity,[status(thm)],[c96,c98]) ).
cnf(c100,plain,
ifeq(product(X6,additive_identity,X5),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,product(X6,X4,X2),true),true),true) = true,
inference(transitivity,[status(thm)],[c91,c99]) ).
cnf(c101,plain,
ifeq(product(X5,additive_identity,X4),true,ifeq(product(X5,X3,X2),true,ifeq(sum(X2,X4,add(X2,X4)),true,product(X5,X3,add(X2,X4)),true),true),true) = true,
inference(substitution,[status(thm)],[c100]) ).
cnf(c102,plain,
ifeq(product(X5,additive_identity,X4),true,ifeq(product(X5,X3,X2),true,ifeq(true,true,product(X5,X3,add(X2,X4)),true),true),true) = true,
inference(transitivity,[status(thm)],[c86,c101]) ).
cnf(c103,plain,
ifeq(product(X5,additive_identity,X4),true,ifeq(product(X5,X3,X2),true,product(X5,X3,add(X2,X4)),true),true) = true,
inference(transitivity,[status(thm)],[c81,c102]) ).
cnf(c104,plain,
ifeq(product(X5,additive_identity,X4),true,ifeq(product(X5,X3,X2),true,product(X5,X3,add(X4,X2)),true),true) = true,
inference(transitivity,[status(thm)],[c77,c103]) ).
cnf(c105,plain,
ifeq(product(X4,additive_identity,multiply(X4,additive_identity)),true,ifeq(product(X4,X3,X2),true,product(X4,X3,add(multiply(X4,additive_identity),X2)),true),true) = true,
inference(substitution,[status(thm)],[c104]) ).
cnf(c106,plain,
ifeq(true,true,ifeq(product(X4,X3,X2),true,product(X4,X3,add(multiply(X4,additive_identity),X2)),true),true) = true,
inference(transitivity,[status(thm)],[c72,c105]) ).
cnf(c107,plain,
ifeq(product(X4,X3,X2),true,product(X4,X3,add(multiply(X4,additive_identity),X2)),true) = true,
inference(transitivity,[status(thm)],[c69,c106]) ).
cnf(c108,plain,
ifeq(product(X4,X3,X2),true,product(X4,X3,add(X2,multiply(X4,additive_identity))),true) = true,
inference(transitivity,[status(thm)],[c67,c107]) ).
cnf(c109,plain,
ifeq(product(X3,X2,multiply(X3,X2)),true,product(X3,X2,add(multiply(X3,X2),multiply(X3,additive_identity))),true) = true,
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
ifeq(true,true,product(X3,X2,add(multiply(X3,X2),multiply(X3,additive_identity))),true) = true,
inference(transitivity,[status(thm)],[c35,c109]) ).
cnf(c111,plain,
product(X3,X2,add(multiply(X3,X2),multiply(X3,additive_identity))) = true,
inference(transitivity,[status(thm)],[c32,c110]) ).
cnf(c112,plain,
ifeq2(product(X3,X2,add(multiply(X3,X2),multiply(X3,additive_identity))),true,multiply(X3,X2),add(multiply(X3,X2),multiply(X3,additive_identity))) = ifeq2(true,true,multiply(X3,X2),add(multiply(X3,X2),multiply(X3,additive_identity))),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
ifeq2(true,true,multiply(X3,X2),add(multiply(X3,X2),multiply(X3,additive_identity))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c114,plain,
ifeq2(product(X3,X2,add(multiply(X3,X2),multiply(X3,additive_identity))),true,multiply(X3,X2),add(multiply(X3,X2),multiply(X3,additive_identity))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c112,c113]) ).
cnf(c115,plain,
add(multiply(X3,X2),multiply(X3,additive_identity)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c29,c114]) ).
cnf(c116,plain,
multiply(X3,X2) = add(multiply(X3,X2),multiply(X3,additive_identity)),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
sum(multiply(X3,X2),multiply(X3,additive_identity),multiply(X3,X2)) = sum(multiply(X3,X2),multiply(X3,additive_identity),add(multiply(X3,X2),multiply(X3,additive_identity))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
sum(multiply(X3,X2),multiply(X3,additive_identity),add(multiply(X3,X2),multiply(X3,additive_identity))) = true,
inference(substitution,[status(thm)],[c39]) ).
cnf(c119,plain,
sum(multiply(X3,X2),multiply(X3,additive_identity),multiply(X3,X2)) = true,
inference(transitivity,[status(thm)],[c117,c118]) ).
cnf(c120,plain,
ifeq2(sum(multiply(X3,X2),multiply(X3,additive_identity),multiply(X3,X2)),true,additive_identity,multiply(X3,additive_identity)) = ifeq2(true,true,additive_identity,multiply(X3,additive_identity)),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
ifeq2(true,true,additive_identity,multiply(X2,additive_identity)) = additive_identity,
inference(substitution,[status(thm)],[c2]) ).
cnf(c122,plain,
ifeq2(sum(multiply(X3,X2),multiply(X3,additive_identity),multiply(X3,X2)),true,additive_identity,multiply(X3,additive_identity)) = additive_identity,
inference(transitivity,[status(thm)],[c120,c121]) ).
cnf(c123,plain,
multiply(X2,additive_identity) = additive_identity,
inference(transitivity,[status(thm)],[c15,c122]) ).
cnf(c124,plain,
additive_identity = multiply(X2,additive_identity),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
product(X2,additive_identity,additive_identity) = product(X2,additive_identity,multiply(X2,additive_identity)),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
product(X2,additive_identity,multiply(X2,additive_identity)) = true,
inference(substitution,[status(thm)],[c19]) ).
cnf(c127,plain,
product(X2,additive_identity,additive_identity) = true,
inference(transitivity,[status(thm)],[c125,c126]) ).
cnf(c128,plain,
product(a,additive_identity,additive_identity) = true,
inference(substitution,[status(thm)],[c127]) ).
cnf(c129,plain,
$false,
inference(resolution,[status(thm)],[c1,c128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG001-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n010.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 22:58:01 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 137.05/17.80 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 137.05/17.80
% 137.05/17.80 % SZS status Unsatisfiable
% 137.05/17.80
% 137.86/17.81 % SZS output start CNFRefutation
% See solution above
% 138.70/17.92
% 138.70/17.92 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------