%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG008-7 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:34:45 PM UTC 2026
% Result : Unsatisfiable 0.51s 0.49s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 10
% Syntax : Number of clauses : 154 ( 154 unt; 0 nHn; 6 RR)
% Number of literals : 154 ( 153 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 230 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(c2,axiom,
add(X,Y) = add(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_for_addition) ).
cnf(c3,plain,
add(additive_inverse(X3),X2) = add(X2,additive_inverse(X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
add(X2,additive_inverse(X3)) = add(additive_inverse(X3),X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
add(X3,add(X2,additive_inverse(X3))) = add(X3,add(additive_inverse(X3),X2)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
add(X2,add(Y2,Z)) = add(add(X2,Y2),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_for_addition) ).
cnf(c7,plain,
add(X3,add(additive_inverse(X3),X2)) = add(add(X3,additive_inverse(X3)),X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,axiom,
add(X2,additive_inverse(X2)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c9,plain,
add(add(X3,additive_inverse(X3)),X2) = add(additive_identity,X2),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
add(additive_identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c11,plain,
add(add(X3,additive_inverse(X3)),X2) = X2,
inference(transitivity,[status(thm)],[c9,c10]) ).
cnf(c12,plain,
add(X3,add(additive_inverse(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c7,c11]) ).
cnf(c13,plain,
add(X3,add(X2,additive_inverse(X3))) = X2,
inference(transitivity,[status(thm)],[c5,c12]) ).
cnf(c14,plain,
add(X2,add(additive_inverse(X2),additive_inverse(X2))) = additive_inverse(X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
additive_inverse(X2) = add(X2,add(additive_inverse(X2),additive_inverse(X2))),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
add(X2,additive_inverse(X3)) = add(additive_inverse(X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c17,plain,
add(additive_inverse(X3),X2) = add(X2,additive_inverse(X3)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
add(X3,add(additive_inverse(X3),X2)) = add(X3,add(X2,additive_inverse(X3))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
add(X3,add(additive_inverse(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c18,c13]) ).
cnf(c20,plain,
add(X2,add(additive_inverse(X2),additive_inverse(additive_inverse(X2)))) = additive_inverse(additive_inverse(X2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
additive_inverse(additive_inverse(X2)) = add(X2,add(additive_inverse(X2),additive_inverse(additive_inverse(X2)))),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
add(additive_inverse(X2),additive_inverse(additive_inverse(X2))) = additive_identity,
inference(substitution,[status(thm)],[c8]) ).
cnf(c23,plain,
add(X2,add(additive_inverse(X2),additive_inverse(additive_inverse(X2)))) = add(X2,additive_identity),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,axiom,
add(X2,additive_identity) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c25,plain,
add(X2,add(additive_inverse(X2),additive_inverse(additive_inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c23,c24]) ).
cnf(c26,plain,
additive_inverse(additive_inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c21,c25]) ).
cnf(c27,plain,
X2 = additive_inverse(additive_inverse(X2)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(additive_inverse(X2),X2) = multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
add(X2,add(additive_inverse(X2),multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2))))) = multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c30,plain,
multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2))) = add(X2,add(additive_inverse(X2),multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2))))),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,axiom,
multiply(X2,add(Y2,Z2)) = add(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute1) ).
cnf(c32,plain,
multiply(X3,add(X3,X2)) = add(multiply(X3,X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,axiom,
multiply(X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c34,plain,
add(multiply(X3,X3),multiply(X3,X2)) = add(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(X3,add(X3,X2)) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c32,c34]) ).
cnf(c36,plain,
multiply(X2,add(X2,additive_inverse(X2))) = add(X2,multiply(X2,additive_inverse(X2))),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
add(X2,multiply(X2,additive_inverse(X2))) = multiply(X2,add(X2,additive_inverse(X2))),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(X2,add(X2,additive_inverse(X2))) = multiply(X2,additive_identity),
inference(congruence,[status(thm)],[c8]) ).
cnf(c39,plain,
add(X2,add(multiply(X2,additive_identity),additive_inverse(X2))) = multiply(X2,additive_identity),
inference(substitution,[status(thm)],[c13]) ).
cnf(c40,plain,
multiply(X2,additive_identity) = add(X2,add(multiply(X2,additive_identity),additive_inverse(X2))),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(X2,add(X2,additive_identity)) = add(X2,multiply(X2,additive_identity)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c42,plain,
add(X2,multiply(X2,additive_identity)) = multiply(X2,add(X2,additive_identity)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(X2,add(X2,additive_identity)) = multiply(X2,X2),
inference(congruence,[status(thm)],[c24]) ).
cnf(c44,plain,
multiply(X2,add(X2,additive_identity)) = X2,
inference(transitivity,[status(thm)],[c43,c33]) ).
cnf(c45,plain,
add(X2,multiply(X2,additive_identity)) = X2,
inference(transitivity,[status(thm)],[c42,c44]) ).
cnf(c46,plain,
X2 = add(X2,multiply(X2,additive_identity)),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
additive_inverse(X2) = additive_inverse(add(X2,multiply(X2,additive_identity))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
add(multiply(X2,additive_identity),additive_inverse(X2)) = add(multiply(X2,additive_identity),additive_inverse(add(X2,multiply(X2,additive_identity)))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
add(X2,add(multiply(X2,additive_identity),additive_inverse(X2))) = add(X2,add(multiply(X2,additive_identity),additive_inverse(add(X2,multiply(X2,additive_identity))))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
add(X3,add(X2,additive_inverse(add(X3,X2)))) = add(add(X3,X2),additive_inverse(add(X3,X2))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c51,plain,
add(add(X3,X2),additive_inverse(add(X3,X2))) = additive_identity,
inference(substitution,[status(thm)],[c8]) ).
cnf(c52,plain,
add(X3,add(X2,additive_inverse(add(X3,X2)))) = additive_identity,
inference(transitivity,[status(thm)],[c50,c51]) ).
cnf(c53,plain,
add(X2,add(multiply(X2,additive_identity),additive_inverse(add(X2,multiply(X2,additive_identity))))) = additive_identity,
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
add(X2,add(multiply(X2,additive_identity),additive_inverse(X2))) = additive_identity,
inference(transitivity,[status(thm)],[c49,c53]) ).
cnf(c55,plain,
multiply(X2,additive_identity) = additive_identity,
inference(transitivity,[status(thm)],[c40,c54]) ).
cnf(c56,plain,
multiply(X2,add(X2,additive_inverse(X2))) = additive_identity,
inference(transitivity,[status(thm)],[c38,c55]) ).
cnf(c57,plain,
add(X2,multiply(X2,additive_inverse(X2))) = additive_identity,
inference(transitivity,[status(thm)],[c37,c56]) ).
cnf(c58,plain,
add(additive_inverse(X2),multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2)))) = additive_identity,
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
add(X2,add(additive_inverse(X2),multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2))))) = add(X2,additive_identity),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
add(X2,add(additive_inverse(X2),multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2))))) = X2,
inference(transitivity,[status(thm)],[c59,c24]) ).
cnf(c61,plain,
multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2))) = X2,
inference(transitivity,[status(thm)],[c30,c60]) ).
cnf(c62,plain,
multiply(additive_inverse(X2),X2) = X2,
inference(transitivity,[status(thm)],[c28,c61]) ).
cnf(c63,plain,
X2 = multiply(additive_inverse(X2),X2),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
add(X2,X2) = add(X2,multiply(additive_inverse(X2),X2)),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,axiom,
multiply(add(X2,Y2),Z2) = add(multiply(X2,Z2),multiply(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute2) ).
cnf(c66,plain,
multiply(add(X3,X2),X3) = add(multiply(X3,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
add(multiply(X3,X3),multiply(X2,X3)) = add(X3,multiply(X2,X3)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c68,plain,
multiply(add(X3,X2),X3) = add(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c66,c67]) ).
cnf(c69,plain,
multiply(add(X2,additive_inverse(X2)),X2) = add(X2,multiply(additive_inverse(X2),X2)),
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
add(X2,multiply(additive_inverse(X2),X2)) = multiply(add(X2,additive_inverse(X2)),X2),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
multiply(add(X2,additive_inverse(X2)),X2) = multiply(additive_identity,X2),
inference(congruence,[status(thm)],[c8]) ).
cnf(c72,plain,
add(X2,add(multiply(additive_identity,X2),additive_inverse(X2))) = multiply(additive_identity,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c73,plain,
multiply(additive_identity,X2) = add(X2,add(multiply(additive_identity,X2),additive_inverse(X2))),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
multiply(add(X2,additive_identity),X2) = add(X2,multiply(additive_identity,X2)),
inference(substitution,[status(thm)],[c68]) ).
cnf(c75,plain,
add(X2,multiply(additive_identity,X2)) = multiply(add(X2,additive_identity),X2),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
multiply(add(X2,additive_identity),X2) = multiply(X2,X2),
inference(congruence,[status(thm)],[c24]) ).
cnf(c77,plain,
multiply(add(X2,additive_identity),X2) = X2,
inference(transitivity,[status(thm)],[c76,c33]) ).
cnf(c78,plain,
add(X2,multiply(additive_identity,X2)) = X2,
inference(transitivity,[status(thm)],[c75,c77]) ).
cnf(c79,plain,
X2 = add(X2,multiply(additive_identity,X2)),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
additive_inverse(X2) = additive_inverse(add(X2,multiply(additive_identity,X2))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
add(multiply(additive_identity,X2),additive_inverse(X2)) = add(multiply(additive_identity,X2),additive_inverse(add(X2,multiply(additive_identity,X2)))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
add(X2,add(multiply(additive_identity,X2),additive_inverse(X2))) = add(X2,add(multiply(additive_identity,X2),additive_inverse(add(X2,multiply(additive_identity,X2))))),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
add(X2,add(multiply(additive_identity,X2),additive_inverse(add(X2,multiply(additive_identity,X2))))) = additive_identity,
inference(substitution,[status(thm)],[c52]) ).
cnf(c84,plain,
add(X2,add(multiply(additive_identity,X2),additive_inverse(X2))) = additive_identity,
inference(transitivity,[status(thm)],[c82,c83]) ).
cnf(c85,plain,
multiply(additive_identity,X2) = additive_identity,
inference(transitivity,[status(thm)],[c73,c84]) ).
cnf(c86,plain,
multiply(add(X2,additive_inverse(X2)),X2) = additive_identity,
inference(transitivity,[status(thm)],[c71,c85]) ).
cnf(c87,plain,
add(X2,multiply(additive_inverse(X2),X2)) = additive_identity,
inference(transitivity,[status(thm)],[c70,c86]) ).
cnf(c88,plain,
add(X2,X2) = additive_identity,
inference(transitivity,[status(thm)],[c64,c87]) ).
cnf(c89,plain,
add(additive_inverse(X2),additive_inverse(X2)) = additive_identity,
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
add(X2,add(additive_inverse(X2),additive_inverse(X2))) = add(X2,additive_identity),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
add(X2,add(additive_inverse(X2),additive_inverse(X2))) = X2,
inference(transitivity,[status(thm)],[c90,c24]) ).
cnf(c92,plain,
additive_inverse(X2) = X2,
inference(transitivity,[status(thm)],[c15,c91]) ).
cnf(c93,plain,
X2 = additive_inverse(X2),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
multiply(X2,X3) = multiply(additive_inverse(X2),X3),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
add(X2,add(additive_inverse(X2),multiply(additive_inverse(X2),X3))) = multiply(additive_inverse(X2),X3),
inference(substitution,[status(thm)],[c19]) ).
cnf(c96,plain,
multiply(additive_inverse(X2),X3) = add(X2,add(additive_inverse(X2),multiply(additive_inverse(X2),X3))),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
add(X3,add(X3,X2)) = add(add(X3,X3),X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c98,plain,
add(add(X3,X3),X2) = add(additive_identity,X2),
inference(congruence,[status(thm)],[c88]) ).
cnf(c99,plain,
add(add(X3,X3),X2) = X2,
inference(transitivity,[status(thm)],[c98,c10]) ).
cnf(c100,plain,
add(X3,add(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c97,c99]) ).
cnf(c101,plain,
add(X2,add(X2,multiply(X2,X3))) = multiply(X2,X3),
inference(substitution,[status(thm)],[c100]) ).
cnf(c102,plain,
multiply(X2,X3) = add(X2,add(X2,multiply(X2,X3))),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
add(X3,multiply(X2,X3)) = add(X3,add(X2,add(X2,multiply(X2,X3)))),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c105,plain,
add(X2,X3) = add(X3,X2),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
multiply(X3,add(X2,X3)) = multiply(X3,add(X3,X2)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
multiply(X3,add(X2,X3)) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c106,c35]) ).
cnf(c108,plain,
multiply(X2,add(X3,X2)) = add(X2,multiply(X2,X3)),
inference(substitution,[status(thm)],[c107]) ).
cnf(c109,plain,
add(X2,multiply(X2,X3)) = multiply(X2,add(X3,X2)),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
add(X2,add(X2,multiply(X2,X3))) = add(X2,multiply(X2,add(X3,X2))),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
add(X3,add(X2,add(X2,multiply(X2,X3)))) = add(X3,add(X2,multiply(X2,add(X3,X2)))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
X2 = additive_inverse(X2),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c113,plain,
add(X2,multiply(X2,add(X3,X2))) = add(additive_inverse(X2),multiply(X2,add(X3,X2))),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
add(X3,add(X2,multiply(X2,add(X3,X2)))) = add(X3,add(additive_inverse(X2),multiply(X2,add(X3,X2)))),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
X2 = additive_inverse(X2),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c116,plain,
add(X3,X2) = add(X3,additive_inverse(X2)),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
multiply(X2,add(X3,X2)) = multiply(X2,add(X3,additive_inverse(X2))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
add(additive_inverse(X2),multiply(X2,add(X3,X2))) = add(additive_inverse(X2),multiply(X2,add(X3,additive_inverse(X2)))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
add(X3,add(additive_inverse(X2),multiply(X2,add(X3,X2)))) = add(X3,add(additive_inverse(X2),multiply(X2,add(X3,additive_inverse(X2))))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
add(X3,add(additive_inverse(X2),multiply(X2,add(X3,additive_inverse(X2))))) = add(add(X3,additive_inverse(X2)),multiply(X2,add(X3,additive_inverse(X2)))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c121,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c122,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c123,plain,
multiply(add(X3,X2),X2) = multiply(add(X2,X3),X2),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
multiply(add(X2,X3),X2) = add(X2,multiply(X3,X2)),
inference(substitution,[status(thm)],[c68]) ).
cnf(c125,plain,
multiply(add(X3,X2),X2) = add(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c123,c124]) ).
cnf(c126,plain,
multiply(add(X2,add(X3,additive_inverse(X2))),add(X3,additive_inverse(X2))) = add(add(X3,additive_inverse(X2)),multiply(X2,add(X3,additive_inverse(X2)))),
inference(substitution,[status(thm)],[c125]) ).
cnf(c127,plain,
add(add(X3,additive_inverse(X2)),multiply(X2,add(X3,additive_inverse(X2)))) = multiply(add(X2,add(X3,additive_inverse(X2))),add(X3,additive_inverse(X2))),
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,plain,
add(X2,add(X3,additive_inverse(X2))) = X3,
inference(substitution,[status(thm)],[c13]) ).
cnf(c129,plain,
multiply(add(X2,add(X3,additive_inverse(X2))),add(X3,additive_inverse(X2))) = multiply(X3,add(X3,additive_inverse(X2))),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(X3,add(X3,additive_inverse(X2))) = add(X3,multiply(X3,additive_inverse(X2))),
inference(substitution,[status(thm)],[c35]) ).
cnf(c131,plain,
multiply(X3,additive_inverse(X2)) = multiply(X3,X2),
inference(congruence,[status(thm)],[c92]) ).
cnf(c132,plain,
add(X3,multiply(X3,additive_inverse(X2))) = add(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
multiply(X3,add(X3,additive_inverse(X2))) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c130,c132]) ).
cnf(c134,plain,
multiply(add(X2,add(X3,additive_inverse(X2))),add(X3,additive_inverse(X2))) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c129,c133]) ).
cnf(c135,plain,
add(add(X3,additive_inverse(X2)),multiply(X2,add(X3,additive_inverse(X2)))) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c127,c134]) ).
cnf(c136,plain,
add(X3,add(additive_inverse(X2),multiply(X2,add(X3,additive_inverse(X2))))) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c120,c135]) ).
cnf(c137,plain,
add(X3,add(additive_inverse(X2),multiply(X2,add(X3,X2)))) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c119,c136]) ).
cnf(c138,plain,
add(X3,add(X2,multiply(X2,add(X3,X2)))) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c114,c137]) ).
cnf(c139,plain,
add(X3,add(X2,add(X2,multiply(X2,X3)))) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c111,c138]) ).
cnf(c140,plain,
add(X3,multiply(X2,X3)) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c103,c139]) ).
cnf(c141,plain,
add(additive_inverse(X2),multiply(X3,additive_inverse(X2))) = add(additive_inverse(X2),multiply(additive_inverse(X2),X3)),
inference(substitution,[status(thm)],[c140]) ).
cnf(c142,plain,
add(additive_inverse(X2),multiply(additive_inverse(X2),X3)) = add(additive_inverse(X2),multiply(X3,additive_inverse(X2))),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
add(X2,add(additive_inverse(X2),multiply(additive_inverse(X2),X3))) = add(X2,add(additive_inverse(X2),multiply(X3,additive_inverse(X2)))),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
add(X2,add(additive_inverse(X2),multiply(X3,additive_inverse(X2)))) = multiply(X3,additive_inverse(X2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c145,plain,
multiply(X3,additive_inverse(X2)) = multiply(X3,X2),
inference(congruence,[status(thm)],[c92]) ).
cnf(c146,plain,
add(X2,add(additive_inverse(X2),multiply(X3,additive_inverse(X2)))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c144,c145]) ).
cnf(c147,plain,
add(X2,add(additive_inverse(X2),multiply(additive_inverse(X2),X3))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c143,c146]) ).
cnf(c148,plain,
multiply(additive_inverse(X2),X3) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c96,c147]) ).
cnf(c149,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c94,c148]) ).
cnf(c150,plain,
multiply(a,b) = multiply(b,a),
inference(substitution,[status(thm)],[c149]) ).
cnf(c151,plain,
multiply(b,a) = multiply(a,b),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,axiom,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c153,plain,
multiply(b,a) = c,
inference(transitivity,[status(thm)],[c151,c152]) ).
cnf(c154,plain,
$false,
inference(resolution,[status(thm)],[c1,c153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 23:00:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.51/0.49 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
% 0.51/0.49
% 0.51/0.49 % SZS status Unsatisfiable
% 0.51/0.49
% 0.51/0.50 % SZS output start CNFRefutation
% See solution above
% 0.51/0.57
% 0.51/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------