%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO008-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 09:35:22 AM UTC 2026
% Result : Unsatisfiable 1.08s 0.60s
% Output : CNFRefutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 11
% Syntax : Number of clauses : 257 ( 257 unt; 0 nHn; 11 RR)
% Number of literals : 257 ( 256 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 520 ( 39 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
add(a,add(b,c)) != add(add(a,b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity) ).
cnf(c2,axiom,
add(X,Y) = add(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(c3,plain,
add(add(X3,add(X2,X4)),X4) = add(X4,add(X3,add(X2,X4))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
add(X4,add(X3,add(X2,X4))) = add(add(X3,add(X2,X4)),X4),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
multiply(X3,add(X2,X3)) = multiply(X3,add(X3,X2)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
add(X2,additive_identity) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c8,plain,
X2 = add(X2,additive_identity),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(X3,add(X3,X2)) = multiply(add(X3,additive_identity),add(X3,X2)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
add(X2,multiply(Y2,Z)) = multiply(add(X2,Y2),add(X2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
cnf(c11,plain,
add(X3,multiply(additive_identity,X2)) = multiply(add(X3,additive_identity),add(X3,X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(add(X3,additive_identity),add(X3,X2)) = add(X3,multiply(additive_identity,X2)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,axiom,
multiply(X2,Y2) = multiply(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(c14,plain,
multiply(additive_identity,X2) = multiply(X2,additive_identity),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
add(X3,multiply(additive_identity,X2)) = add(X3,multiply(X2,additive_identity)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(add(X3,additive_identity),add(X3,X2)) = add(X3,multiply(X2,additive_identity)),
inference(transitivity,[status(thm)],[c12,c15]) ).
cnf(c17,plain,
multiply(X3,add(X3,X2)) = add(X3,multiply(X2,additive_identity)),
inference(transitivity,[status(thm)],[c9,c16]) ).
cnf(c18,plain,
add(X3,multiply(X2,additive_identity)) = multiply(X3,add(X3,X2)),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(add(X3,X2),X3) = multiply(X3,add(X3,X2)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c20,plain,
multiply(X3,add(X3,X2)) = multiply(add(X3,X2),X3),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,axiom,
add(additive_identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id2) ).
cnf(c22,plain,
add(additive_identity,multiply(X2,X2)) = multiply(X2,X2),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(X2,X2) = add(additive_identity,multiply(X2,X2)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
add(multiply(X2,X2),X3) = add(X3,multiply(X2,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c25,plain,
add(X3,multiply(X2,X2)) = add(multiply(X2,X2),X3),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,axiom,
add(multiply(X2,Y2),Z2) = multiply(add(X2,Z2),add(Y2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
cnf(c27,plain,
add(multiply(X2,X2),X3) = multiply(add(X2,X3),add(X2,X3)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
add(X2,multiply(X3,X3)) = multiply(add(X2,X3),add(X2,X3)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c29,plain,
multiply(add(X2,X3),add(X2,X3)) = add(X2,multiply(X3,X3)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
add(multiply(X2,X2),X3) = add(X2,multiply(X3,X3)),
inference(transitivity,[status(thm)],[c27,c29]) ).
cnf(c31,plain,
add(X3,multiply(X2,X2)) = add(X2,multiply(X3,X3)),
inference(transitivity,[status(thm)],[c25,c30]) ).
cnf(c32,plain,
add(X2,multiply(additive_identity,additive_identity)) = add(additive_identity,multiply(X2,X2)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
add(additive_identity,multiply(X2,X2)) = add(X2,multiply(additive_identity,additive_identity)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
add(additive_identity,multiply(additive_identity,additive_identity)) = multiply(additive_identity,additive_identity),
inference(substitution,[status(thm)],[c21]) ).
cnf(c35,plain,
multiply(additive_identity,additive_identity) = add(additive_identity,multiply(additive_identity,additive_identity)),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
add(multiplicative_identity,X2) = add(X2,multiplicative_identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c37,plain,
add(X2,multiplicative_identity) = add(multiplicative_identity,X2),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(X3,add(X2,multiplicative_identity)) = multiply(X3,add(multiplicative_identity,X2)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,axiom,
multiply(X2,add(Y2,Z2)) = add(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
cnf(c40,plain,
multiply(X3,add(multiplicative_identity,X2)) = add(multiply(X3,multiplicative_identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,axiom,
multiply(X2,multiplicative_identity) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c42,plain,
add(multiply(X3,multiplicative_identity),multiply(X3,X2)) = add(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(X3,add(multiplicative_identity,X2)) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c40,c42]) ).
cnf(c44,plain,
multiply(X3,add(X2,multiplicative_identity)) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c38,c43]) ).
cnf(c45,plain,
multiply(X2,add(additive_identity,multiplicative_identity)) = add(X2,multiply(X2,additive_identity)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
add(X2,multiply(X2,additive_identity)) = multiply(X2,add(additive_identity,multiplicative_identity)),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
add(additive_identity,multiplicative_identity) = multiplicative_identity,
inference(substitution,[status(thm)],[c21]) ).
cnf(c48,plain,
multiply(X2,add(additive_identity,multiplicative_identity)) = multiply(X2,multiplicative_identity),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(X2,add(additive_identity,multiplicative_identity)) = X2,
inference(transitivity,[status(thm)],[c48,c41]) ).
cnf(c50,plain,
add(X2,multiply(X2,additive_identity)) = X2,
inference(transitivity,[status(thm)],[c46,c49]) ).
cnf(c51,plain,
add(additive_identity,multiply(additive_identity,additive_identity)) = additive_identity,
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(transitivity,[status(thm)],[c35,c51]) ).
cnf(c53,plain,
add(X2,multiply(additive_identity,additive_identity)) = add(X2,additive_identity),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
add(X2,multiply(additive_identity,additive_identity)) = X2,
inference(transitivity,[status(thm)],[c53,c7]) ).
cnf(c55,plain,
add(additive_identity,multiply(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c33,c54]) ).
cnf(c56,plain,
multiply(X2,X2) = X2,
inference(transitivity,[status(thm)],[c23,c55]) ).
cnf(c57,plain,
X2 = multiply(X2,X2),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
add(X2,X2) = add(X2,multiply(X2,X2)),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(X2,add(X2,multiplicative_identity)) = add(X2,multiply(X2,X2)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c60,plain,
add(X2,multiply(X2,X2)) = multiply(X2,add(X2,multiplicative_identity)),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
multiply(X2,add(X2,multiplicative_identity)) = add(X2,multiply(multiplicative_identity,additive_identity)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c62,axiom,
multiply(multiplicative_identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_id2) ).
cnf(c63,plain,
multiply(multiplicative_identity,additive_identity) = additive_identity,
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
add(X2,multiply(multiplicative_identity,additive_identity)) = add(X2,additive_identity),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
add(X2,multiply(multiplicative_identity,additive_identity)) = X2,
inference(transitivity,[status(thm)],[c64,c7]) ).
cnf(c66,plain,
multiply(X2,add(X2,multiplicative_identity)) = X2,
inference(transitivity,[status(thm)],[c61,c65]) ).
cnf(c67,plain,
add(X2,multiply(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c60,c66]) ).
cnf(c68,plain,
add(X2,X2) = X2,
inference(transitivity,[status(thm)],[c58,c67]) ).
cnf(c69,plain,
X2 = add(X2,X2),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(add(X3,X2),X3) = multiply(add(X3,X2),add(X3,X3)),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
add(X3,multiply(X2,X3)) = multiply(add(X3,X2),add(X3,X3)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c72,plain,
multiply(add(X3,X2),add(X3,X3)) = add(X3,multiply(X2,X3)),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c74,plain,
add(X3,multiply(X2,X3)) = add(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
multiply(add(X3,X2),add(X3,X3)) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c72,c74]) ).
cnf(c76,plain,
multiply(add(X3,X2),X3) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c70,c75]) ).
cnf(c77,plain,
multiply(X3,add(X3,X2)) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c20,c76]) ).
cnf(c78,plain,
add(X3,multiply(X2,additive_identity)) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c18,c77]) ).
cnf(c79,plain,
multiply(X3,add(X3,X2)) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c17,c78]) ).
cnf(c80,plain,
multiply(X3,add(X2,X3)) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c6,c79]) ).
cnf(c81,plain,
add(X3,multiply(X3,X2)) = add(X3,multiply(X2,additive_identity)),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c82,plain,
add(inverse(X3),X2) = add(X2,inverse(X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c83,plain,
add(X2,inverse(X3)) = add(inverse(X3),X2),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(X3,add(X2,inverse(X3))) = multiply(X3,add(inverse(X3),X2)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
multiply(X3,add(inverse(X3),X2)) = add(multiply(X3,inverse(X3)),multiply(X3,X2)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c86,axiom,
multiply(X2,inverse(X2)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c87,plain,
add(multiply(X3,inverse(X3)),multiply(X3,X2)) = add(additive_identity,multiply(X3,X2)),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
add(additive_identity,multiply(X3,X2)) = multiply(X3,X2),
inference(substitution,[status(thm)],[c21]) ).
cnf(c89,plain,
add(multiply(X3,inverse(X3)),multiply(X3,X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c87,c88]) ).
cnf(c90,plain,
multiply(X3,add(inverse(X3),X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c85,c89]) ).
cnf(c91,plain,
multiply(X3,add(X2,inverse(X3))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c84,c90]) ).
cnf(c92,plain,
multiply(X2,add(additive_identity,inverse(X2))) = multiply(X2,additive_identity),
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
multiply(X2,additive_identity) = multiply(X2,add(additive_identity,inverse(X2))),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
add(additive_identity,inverse(X2)) = inverse(X2),
inference(substitution,[status(thm)],[c21]) ).
cnf(c95,plain,
multiply(X2,add(additive_identity,inverse(X2))) = multiply(X2,inverse(X2)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
multiply(X2,add(additive_identity,inverse(X2))) = additive_identity,
inference(transitivity,[status(thm)],[c95,c86]) ).
cnf(c97,plain,
multiply(X2,additive_identity) = additive_identity,
inference(transitivity,[status(thm)],[c93,c96]) ).
cnf(c98,plain,
add(X3,multiply(X2,additive_identity)) = add(X3,additive_identity),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
add(X3,multiply(X2,additive_identity)) = X3,
inference(transitivity,[status(thm)],[c98,c7]) ).
cnf(c100,plain,
add(X3,multiply(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c81,c99]) ).
cnf(c101,plain,
multiply(X3,add(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c80,c100]) ).
cnf(c102,plain,
X3 = multiply(X3,add(X2,X3)),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
add(add(X3,add(X2,X4)),X4) = add(add(X3,add(X2,X4)),multiply(X4,add(X2,X4))),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c105,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
add(add(X4,X3),multiply(X2,X3)) = add(add(X4,X3),multiply(X3,X2)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
add(add(X4,X3),multiply(X3,X2)) = multiply(add(add(X4,X3),X3),add(add(X4,X3),X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c108,plain,
X2 = add(additive_identity,X2),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c109,plain,
multiply(add(X2,X3),X3) = multiply(add(X2,X3),add(additive_identity,X3)),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c111,plain,
add(X2,X3) = add(X3,X2),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
multiply(add(X4,X3),add(X2,X3)) = multiply(add(X4,X3),add(X3,X2)),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c114,plain,
multiply(add(X4,X3),add(X3,X2)) = multiply(add(X3,X4),add(X3,X2)),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
add(X3,multiply(X4,X2)) = multiply(add(X3,X4),add(X3,X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c116,plain,
multiply(add(X3,X4),add(X3,X2)) = add(X3,multiply(X4,X2)),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c118,plain,
add(X3,multiply(X4,X2)) = add(X3,multiply(X2,X4)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
multiply(add(X3,X4),add(X3,X2)) = add(X3,multiply(X2,X4)),
inference(transitivity,[status(thm)],[c116,c118]) ).
cnf(c120,plain,
multiply(add(X4,X3),add(X3,X2)) = add(X3,multiply(X2,X4)),
inference(transitivity,[status(thm)],[c114,c119]) ).
cnf(c121,plain,
multiply(add(X4,X3),add(X2,X3)) = add(X3,multiply(X2,X4)),
inference(transitivity,[status(thm)],[c112,c120]) ).
cnf(c122,plain,
multiply(add(X2,X3),add(additive_identity,X3)) = add(X3,multiply(additive_identity,X2)),
inference(substitution,[status(thm)],[c121]) ).
cnf(c123,plain,
multiply(additive_identity,X2) = multiply(X2,additive_identity),
inference(substitution,[status(thm)],[c13]) ).
cnf(c124,plain,
add(X3,multiply(additive_identity,X2)) = add(X3,multiply(X2,additive_identity)),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
multiply(add(X2,X3),add(additive_identity,X3)) = add(X3,multiply(X2,additive_identity)),
inference(transitivity,[status(thm)],[c122,c124]) ).
cnf(c126,plain,
multiply(add(X2,X3),X3) = add(X3,multiply(X2,additive_identity)),
inference(transitivity,[status(thm)],[c109,c125]) ).
cnf(c127,plain,
multiply(add(X3,X2),X2) = add(X2,multiply(X3,additive_identity)),
inference(substitution,[status(thm)],[c126]) ).
cnf(c128,plain,
add(X2,multiply(X3,additive_identity)) = add(X2,additive_identity),
inference(congruence,[status(thm)],[c97]) ).
cnf(c129,plain,
add(X2,multiply(X3,additive_identity)) = X2,
inference(transitivity,[status(thm)],[c128,c7]) ).
cnf(c130,plain,
multiply(add(X3,X2),X2) = X2,
inference(transitivity,[status(thm)],[c127,c129]) ).
cnf(c131,plain,
X2 = multiply(add(X3,X2),X2),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
add(add(X3,X2),X2) = add(add(X3,X2),multiply(add(X3,X2),X2)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
multiply(X3,add(X2,multiplicative_identity)) = multiply(add(X2,multiplicative_identity),X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c134,plain,
multiply(add(X2,multiplicative_identity),X3) = multiply(X3,add(X2,multiplicative_identity)),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c135,plain,
multiply(add(X2,multiplicative_identity),X3) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c134,c44]) ).
cnf(c136,plain,
multiply(add(X2,multiplicative_identity),add(X3,X2)) = add(add(X3,X2),multiply(add(X3,X2),X2)),
inference(substitution,[status(thm)],[c135]) ).
cnf(c137,plain,
add(add(X3,X2),multiply(add(X3,X2),X2)) = multiply(add(X2,multiplicative_identity),add(X3,X2)),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
multiply(multiplicative_identity,add(multiplicative_identity,X2)) = add(multiplicative_identity,multiply(X2,additive_identity)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c139,plain,
add(multiplicative_identity,multiply(X2,additive_identity)) = multiply(multiplicative_identity,add(multiplicative_identity,X2)),
inference(symmetry,[status(thm)],[c138]) ).
cnf(c140,plain,
multiply(multiplicative_identity,add(multiplicative_identity,X2)) = add(multiplicative_identity,X2),
inference(substitution,[status(thm)],[c62]) ).
cnf(c141,plain,
add(multiplicative_identity,X2) = add(X2,multiplicative_identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c142,plain,
multiply(multiplicative_identity,add(multiplicative_identity,X2)) = add(X2,multiplicative_identity),
inference(transitivity,[status(thm)],[c140,c141]) ).
cnf(c143,plain,
add(multiplicative_identity,multiply(X2,additive_identity)) = add(X2,multiplicative_identity),
inference(transitivity,[status(thm)],[c139,c142]) ).
cnf(c144,plain,
add(X2,multiplicative_identity) = add(multiplicative_identity,multiply(X2,additive_identity)),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
add(multiplicative_identity,multiply(X2,additive_identity)) = add(multiplicative_identity,additive_identity),
inference(congruence,[status(thm)],[c97]) ).
cnf(c146,plain,
add(multiplicative_identity,additive_identity) = multiplicative_identity,
inference(substitution,[status(thm)],[c7]) ).
cnf(c147,plain,
add(multiplicative_identity,multiply(X2,additive_identity)) = multiplicative_identity,
inference(transitivity,[status(thm)],[c145,c146]) ).
cnf(c148,plain,
add(X2,multiplicative_identity) = multiplicative_identity,
inference(transitivity,[status(thm)],[c144,c147]) ).
cnf(c149,plain,
multiply(add(X2,multiplicative_identity),add(X3,X2)) = multiply(multiplicative_identity,add(X3,X2)),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
multiply(multiplicative_identity,add(X3,X2)) = add(X3,X2),
inference(substitution,[status(thm)],[c62]) ).
cnf(c151,plain,
multiply(add(X2,multiplicative_identity),add(X3,X2)) = add(X3,X2),
inference(transitivity,[status(thm)],[c149,c150]) ).
cnf(c152,plain,
add(add(X3,X2),multiply(add(X3,X2),X2)) = add(X3,X2),
inference(transitivity,[status(thm)],[c137,c151]) ).
cnf(c153,plain,
add(add(X3,X2),X2) = add(X3,X2),
inference(transitivity,[status(thm)],[c132,c152]) ).
cnf(c154,plain,
multiply(add(add(X4,X3),X3),add(add(X4,X3),X2)) = multiply(add(X4,X3),add(add(X4,X3),X2)),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
multiply(add(X4,X3),add(add(X4,X3),X2)) = add(add(X4,X3),multiply(X2,additive_identity)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c156,plain,
add(add(X4,X3),multiply(X2,additive_identity)) = add(add(X4,X3),additive_identity),
inference(congruence,[status(thm)],[c97]) ).
cnf(c157,plain,
add(add(X3,X2),additive_identity) = add(X3,X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c158,plain,
add(add(X4,X3),multiply(X2,additive_identity)) = add(X4,X3),
inference(transitivity,[status(thm)],[c156,c157]) ).
cnf(c159,plain,
multiply(add(X4,X3),add(add(X4,X3),X2)) = add(X4,X3),
inference(transitivity,[status(thm)],[c155,c158]) ).
cnf(c160,plain,
multiply(add(add(X4,X3),X3),add(add(X4,X3),X2)) = add(X4,X3),
inference(transitivity,[status(thm)],[c154,c159]) ).
cnf(c161,plain,
add(add(X4,X3),multiply(X3,X2)) = add(X4,X3),
inference(transitivity,[status(thm)],[c107,c160]) ).
cnf(c162,plain,
add(add(X4,X3),multiply(X2,X3)) = add(X4,X3),
inference(transitivity,[status(thm)],[c106,c161]) ).
cnf(c163,plain,
add(add(X3,add(X2,X4)),multiply(X4,add(X2,X4))) = add(X3,add(X2,X4)),
inference(substitution,[status(thm)],[c162]) ).
cnf(c164,plain,
add(add(X3,add(X2,X4)),X4) = add(X3,add(X2,X4)),
inference(transitivity,[status(thm)],[c103,c163]) ).
cnf(c165,plain,
add(X4,add(X3,add(X2,X4))) = add(X3,add(X2,X4)),
inference(transitivity,[status(thm)],[c4,c164]) ).
cnf(c166,plain,
add(X2,add(X4,add(X3,X2))) = add(X4,add(X3,X2)),
inference(substitution,[status(thm)],[c165]) ).
cnf(c167,plain,
add(X4,add(X3,X2)) = add(X2,add(X4,add(X3,X2))),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c168,plain,
multiply(add(add(X4,X3),X2),add(X4,add(X3,X2))) = multiply(add(add(X4,X3),X2),add(X2,add(X4,add(X3,X2)))),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c170,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
multiply(add(X4,X3),add(X3,X2)) = multiply(add(X4,X3),add(X2,X3)),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
multiply(add(X4,X3),add(X3,X2)) = add(X3,multiply(X2,X4)),
inference(transitivity,[status(thm)],[c171,c121]) ).
cnf(c173,plain,
multiply(add(add(X4,X3),X2),add(X2,add(X4,add(X3,X2)))) = add(X2,multiply(add(X4,add(X3,X2)),add(X4,X3))),
inference(substitution,[status(thm)],[c172]) ).
cnf(c174,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c175,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c174]) ).
cnf(c176,plain,
multiply(add(X4,X3),add(X4,X2)) = multiply(add(X4,X3),add(X2,X4)),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c178,plain,
add(X2,X3) = add(X3,X2),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c179,plain,
multiply(add(X4,X3),add(X2,X4)) = multiply(add(X4,X3),add(X4,X2)),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
add(X4,multiply(X3,X2)) = multiply(add(X4,X3),add(X4,X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c181,plain,
multiply(add(X4,X3),add(X4,X2)) = add(X4,multiply(X3,X2)),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c183,plain,
add(X4,multiply(X3,X2)) = add(X4,multiply(X2,X3)),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
multiply(add(X4,X3),add(X4,X2)) = add(X4,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c181,c183]) ).
cnf(c185,plain,
multiply(add(X4,X3),add(X2,X4)) = add(X4,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c179,c184]) ).
cnf(c186,plain,
multiply(add(X4,X3),add(X4,X2)) = add(X4,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c176,c185]) ).
cnf(c187,plain,
multiply(add(X4,add(X3,X2)),add(X4,X3)) = add(X4,multiply(X3,add(X3,X2))),
inference(substitution,[status(thm)],[c186]) ).
cnf(c188,plain,
add(X3,multiply(X2,additive_identity)) = add(X3,additive_identity),
inference(congruence,[status(thm)],[c97]) ).
cnf(c189,plain,
add(X3,multiply(X2,additive_identity)) = X3,
inference(transitivity,[status(thm)],[c188,c7]) ).
cnf(c190,plain,
multiply(X3,add(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c17,c189]) ).
cnf(c191,plain,
add(X4,multiply(X3,add(X3,X2))) = add(X4,X3),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
multiply(add(X4,add(X3,X2)),add(X4,X3)) = add(X4,X3),
inference(transitivity,[status(thm)],[c187,c191]) ).
cnf(c193,plain,
add(X2,multiply(add(X4,add(X3,X2)),add(X4,X3))) = add(X2,add(X4,X3)),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
add(add(X4,X3),X2) = add(X2,add(X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c195,plain,
add(X2,add(X4,X3)) = add(add(X4,X3),X2),
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,plain,
add(X2,multiply(add(X4,add(X3,X2)),add(X4,X3))) = add(add(X4,X3),X2),
inference(transitivity,[status(thm)],[c193,c195]) ).
cnf(c197,plain,
multiply(add(add(X4,X3),X2),add(X2,add(X4,add(X3,X2)))) = add(add(X4,X3),X2),
inference(transitivity,[status(thm)],[c173,c196]) ).
cnf(c198,plain,
multiply(add(add(X4,X3),X2),add(X4,add(X3,X2))) = add(add(X4,X3),X2),
inference(transitivity,[status(thm)],[c168,c197]) ).
cnf(c199,plain,
add(add(X4,X3),X2) = multiply(add(add(X4,X3),X2),add(X4,add(X3,X2))),
inference(symmetry,[status(thm)],[c198]) ).
cnf(c200,plain,
multiply(add(X4,add(X3,X2)),add(add(X4,X3),X2)) = multiply(add(add(X4,X3),X2),add(X4,add(X3,X2))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c201,plain,
multiply(add(add(X4,X3),X2),add(X4,add(X3,X2))) = multiply(add(X4,add(X3,X2)),add(add(X4,X3),X2)),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
add(add(add(X4,X3),X2),X4) = add(X4,add(add(X4,X3),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c203,plain,
add(X4,add(add(X4,X3),X2)) = add(add(add(X4,X3),X2),X4),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c204,plain,
X3 = multiply(X3,add(X3,X2)),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c205,plain,
add(add(add(X4,X3),X2),X4) = add(add(add(X4,X3),X2),multiply(X4,add(X4,X3))),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c207,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c206]) ).
cnf(c208,plain,
add(add(X4,X3),multiply(X2,X4)) = add(add(X4,X3),multiply(X4,X2)),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
add(add(X4,X3),multiply(X4,X2)) = multiply(add(add(X4,X3),X4),add(add(X4,X3),X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c210,plain,
X2 = add(additive_identity,X2),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c211,plain,
multiply(add(X3,X2),X3) = multiply(add(X3,X2),add(additive_identity,X3)),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
multiply(add(X3,X2),add(additive_identity,X3)) = add(X3,multiply(additive_identity,X2)),
inference(substitution,[status(thm)],[c185]) ).
cnf(c213,plain,
multiply(additive_identity,X2) = multiply(X2,additive_identity),
inference(substitution,[status(thm)],[c13]) ).
cnf(c214,plain,
add(X3,multiply(additive_identity,X2)) = add(X3,multiply(X2,additive_identity)),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
multiply(add(X3,X2),add(additive_identity,X3)) = add(X3,multiply(X2,additive_identity)),
inference(transitivity,[status(thm)],[c212,c214]) ).
cnf(c216,plain,
multiply(add(X3,X2),X3) = add(X3,multiply(X2,additive_identity)),
inference(transitivity,[status(thm)],[c211,c215]) ).
cnf(c217,plain,
add(X3,multiply(X2,additive_identity)) = add(X3,additive_identity),
inference(congruence,[status(thm)],[c97]) ).
cnf(c218,plain,
add(X3,multiply(X2,additive_identity)) = X3,
inference(transitivity,[status(thm)],[c217,c7]) ).
cnf(c219,plain,
multiply(add(X3,X2),X3) = X3,
inference(transitivity,[status(thm)],[c216,c218]) ).
cnf(c220,plain,
X3 = multiply(add(X3,X2),X3),
inference(symmetry,[status(thm)],[c219]) ).
cnf(c221,plain,
add(add(X3,X2),X3) = add(add(X3,X2),multiply(add(X3,X2),X3)),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
multiply(add(X3,multiplicative_identity),add(X3,X2)) = add(add(X3,X2),multiply(add(X3,X2),X3)),
inference(substitution,[status(thm)],[c135]) ).
cnf(c223,plain,
add(add(X3,X2),multiply(add(X3,X2),X3)) = multiply(add(X3,multiplicative_identity),add(X3,X2)),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
multiply(add(X3,multiplicative_identity),add(X3,X2)) = multiply(multiplicative_identity,add(X3,X2)),
inference(congruence,[status(thm)],[c148]) ).
cnf(c225,plain,
multiply(multiplicative_identity,add(X3,X2)) = add(X3,X2),
inference(substitution,[status(thm)],[c62]) ).
cnf(c226,plain,
multiply(add(X3,multiplicative_identity),add(X3,X2)) = add(X3,X2),
inference(transitivity,[status(thm)],[c224,c225]) ).
cnf(c227,plain,
add(add(X3,X2),multiply(add(X3,X2),X3)) = add(X3,X2),
inference(transitivity,[status(thm)],[c223,c226]) ).
cnf(c228,plain,
add(add(X3,X2),X3) = add(X3,X2),
inference(transitivity,[status(thm)],[c221,c227]) ).
cnf(c229,plain,
multiply(add(add(X4,X3),X4),add(add(X4,X3),X2)) = multiply(add(X4,X3),add(add(X4,X3),X2)),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
multiply(add(X4,X3),add(add(X4,X3),X2)) = add(add(X4,X3),multiply(X2,additive_identity)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c231,plain,
add(add(X4,X3),multiply(X2,additive_identity)) = add(add(X4,X3),additive_identity),
inference(congruence,[status(thm)],[c97]) ).
cnf(c232,plain,
add(add(X3,X2),additive_identity) = add(X3,X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c233,plain,
add(add(X4,X3),multiply(X2,additive_identity)) = add(X4,X3),
inference(transitivity,[status(thm)],[c231,c232]) ).
cnf(c234,plain,
multiply(add(X4,X3),add(add(X4,X3),X2)) = add(X4,X3),
inference(transitivity,[status(thm)],[c230,c233]) ).
cnf(c235,plain,
multiply(add(add(X4,X3),X4),add(add(X4,X3),X2)) = add(X4,X3),
inference(transitivity,[status(thm)],[c229,c234]) ).
cnf(c236,plain,
add(add(X4,X3),multiply(X4,X2)) = add(X4,X3),
inference(transitivity,[status(thm)],[c209,c235]) ).
cnf(c237,plain,
add(add(X4,X3),multiply(X2,X4)) = add(X4,X3),
inference(transitivity,[status(thm)],[c208,c236]) ).
cnf(c238,plain,
add(add(add(X4,X3),X2),multiply(X4,add(X4,X3))) = add(add(X4,X3),X2),
inference(substitution,[status(thm)],[c237]) ).
cnf(c239,plain,
add(add(add(X4,X3),X2),X4) = add(add(X4,X3),X2),
inference(transitivity,[status(thm)],[c205,c238]) ).
cnf(c240,plain,
add(X4,add(add(X4,X3),X2)) = add(add(X4,X3),X2),
inference(transitivity,[status(thm)],[c203,c239]) ).
cnf(c241,plain,
add(add(X4,X3),X2) = add(X4,add(add(X4,X3),X2)),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
multiply(add(X4,add(X3,X2)),add(add(X4,X3),X2)) = multiply(add(X4,add(X3,X2)),add(X4,add(add(X4,X3),X2))),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
multiply(add(X4,add(X3,X2)),add(X4,add(add(X4,X3),X2))) = add(X4,multiply(add(add(X4,X3),X2),add(X3,X2))),
inference(substitution,[status(thm)],[c186]) ).
cnf(c244,plain,
multiply(add(add(X4,X3),X2),add(X3,X2)) = add(X2,multiply(X3,add(X4,X3))),
inference(substitution,[status(thm)],[c121]) ).
cnf(c245,plain,
multiply(X2,add(X3,X2)) = X2,
inference(substitution,[status(thm)],[c101]) ).
cnf(c246,plain,
add(X2,multiply(X3,add(X4,X3))) = add(X2,X3),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c248,plain,
add(X2,multiply(X3,add(X4,X3))) = add(X3,X2),
inference(transitivity,[status(thm)],[c246,c247]) ).
cnf(c249,plain,
multiply(add(add(X4,X3),X2),add(X3,X2)) = add(X3,X2),
inference(transitivity,[status(thm)],[c244,c248]) ).
cnf(c250,plain,
add(X4,multiply(add(add(X4,X3),X2),add(X3,X2))) = add(X4,add(X3,X2)),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
multiply(add(X4,add(X3,X2)),add(X4,add(add(X4,X3),X2))) = add(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c243,c250]) ).
cnf(c252,plain,
multiply(add(X4,add(X3,X2)),add(add(X4,X3),X2)) = add(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c242,c251]) ).
cnf(c253,plain,
multiply(add(add(X4,X3),X2),add(X4,add(X3,X2))) = add(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c201,c252]) ).
cnf(c254,plain,
add(add(X4,X3),X2) = add(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c199,c253]) ).
cnf(c255,plain,
add(add(a,b),c) = add(a,add(b,c)),
inference(substitution,[status(thm)],[c254]) ).
cnf(c256,plain,
add(a,add(b,c)) = add(add(a,b),c),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c257,plain,
$false,
inference(resolution,[status(thm)],[c1,c256]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO008-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.22 % Computer : n020.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Mon Sep 28 21:04:34 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.08/0.60 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 1.08/0.60
% 1.08/0.60 % SZS status Unsatisfiable
% 1.08/0.60
% 2.34/0.64 % SZS output start CNFRefutation
% See solution above
% 3.26/0.83
% 3.26/0.83 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------