%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO008-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 0.40s 0.34s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 9
% Syntax : Number of clauses : 167 ( 167 unt; 0 nHn; 11 RR)
% Number of literals : 167 ( 166 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 315 ( 25 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
add(a,add(b,c)) != add(add(a,b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity) ).
cnf(c2,axiom,
add(X,Y) = add(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(c3,plain,
add(c,b) = add(b,c),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
add(b,c) = add(c,b),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
add(a,add(b,c)) = add(a,add(c,b)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
multiply(X2,Y2) = multiply(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(c7,plain,
multiply(X2,inverse(X3)) = multiply(inverse(X3),X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(inverse(X3),X2) = multiply(X2,inverse(X3)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
add(X3,multiply(inverse(X3),X2)) = add(X3,multiply(X2,inverse(X3))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
add(X2,multiply(Y2,Z)) = multiply(add(X2,Y2),add(X2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
cnf(c11,plain,
add(X3,multiply(X2,inverse(X3))) = multiply(add(X3,X2),add(X3,inverse(X3))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,axiom,
add(X2,inverse(X2)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c13,plain,
multiply(add(X3,X2),add(X3,inverse(X3))) = multiply(add(X3,X2),multiplicative_identity),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,axiom,
multiply(X2,multiplicative_identity) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id1) ).
cnf(c15,plain,
multiply(add(X3,X2),multiplicative_identity) = add(X3,X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(add(X3,X2),add(X3,inverse(X3))) = add(X3,X2),
inference(transitivity,[status(thm)],[c13,c15]) ).
cnf(c17,plain,
add(X3,multiply(X2,inverse(X3))) = add(X3,X2),
inference(transitivity,[status(thm)],[c11,c16]) ).
cnf(c18,plain,
add(X3,multiply(inverse(X3),X2)) = add(X3,X2),
inference(transitivity,[status(thm)],[c9,c17]) ).
cnf(c19,plain,
add(X2,multiply(inverse(X2),add(X3,X4))) = add(X2,add(X3,X4)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
add(X3,add(X4,X2)) = add(X3,multiply(inverse(X3),add(X4,X2))),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
add(add(X2,inverse(X4)),X3) = add(X3,add(X2,inverse(X4))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
add(X3,add(X2,inverse(X4))) = add(add(X2,inverse(X4)),X3),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(X4,add(X3,add(X2,inverse(X4)))) = multiply(X4,add(add(X2,inverse(X4)),X3)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,axiom,
multiply(X2,add(Y2,Z2)) = add(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
cnf(c25,plain,
multiply(X4,add(add(X2,inverse(X4)),X3)) = add(multiply(X4,add(X2,inverse(X4))),multiply(X4,X3)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(X3,add(X2,inverse(X3))) = add(multiply(X3,X2),multiply(X3,inverse(X3))),
inference(substitution,[status(thm)],[c24]) ).
cnf(c27,axiom,
multiply(X2,inverse(X2)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c28,plain,
add(multiply(X3,X2),multiply(X3,inverse(X3))) = add(multiply(X3,X2),additive_identity),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,axiom,
add(X2,additive_identity) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id1) ).
cnf(c30,plain,
add(multiply(X3,X2),additive_identity) = multiply(X3,X2),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
add(multiply(X3,X2),multiply(X3,inverse(X3))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c28,c30]) ).
cnf(c32,plain,
multiply(X3,add(X2,inverse(X3))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c26,c31]) ).
cnf(c33,plain,
add(multiply(X4,add(X2,inverse(X4))),multiply(X4,X3)) = add(multiply(X4,X2),multiply(X4,X3)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
multiply(X4,add(X2,X3)) = add(multiply(X4,X2),multiply(X4,X3)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c35,plain,
add(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,add(X2,X3)),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c37,plain,
multiply(X4,add(X2,X3)) = multiply(X4,add(X3,X2)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
add(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c35,c37]) ).
cnf(c39,plain,
add(multiply(X4,add(X2,inverse(X4))),multiply(X4,X3)) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c33,c38]) ).
cnf(c40,plain,
multiply(X4,add(add(X2,inverse(X4)),X3)) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c25,c39]) ).
cnf(c41,plain,
multiply(X4,add(X3,add(X2,inverse(X4)))) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c23,c40]) ).
cnf(c42,plain,
multiply(inverse(X3),add(X4,add(X2,inverse(inverse(X3))))) = multiply(inverse(X3),add(X4,X2)),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(inverse(X3),add(X4,X2)) = multiply(inverse(X3),add(X4,add(X2,inverse(inverse(X3))))),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
add(X3,multiply(inverse(X3),add(X4,X2))) = add(X3,multiply(inverse(X3),add(X4,add(X2,inverse(inverse(X3)))))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
add(X3,multiply(inverse(X3),add(X4,add(X2,inverse(inverse(X3)))))) = add(X3,add(X4,add(X2,inverse(inverse(X3))))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c46,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c47,plain,
add(X2,X3) = add(X3,X2),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(X3,add(X2,X3)) = multiply(X3,add(X3,X2)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(additive_identity,X2) = multiply(X2,additive_identity),
inference(substitution,[status(thm)],[c6]) ).
cnf(c50,plain,
multiply(X2,additive_identity) = multiply(additive_identity,X2),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
add(X3,multiply(X2,additive_identity)) = add(X3,multiply(additive_identity,X2)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
add(X3,multiply(additive_identity,X2)) = multiply(add(X3,additive_identity),add(X3,X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c53,plain,
multiply(add(X3,additive_identity),add(X3,X2)) = multiply(X3,add(X3,X2)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c54,plain,
add(X3,multiply(additive_identity,X2)) = multiply(X3,add(X3,X2)),
inference(transitivity,[status(thm)],[c52,c53]) ).
cnf(c55,plain,
add(X3,multiply(X2,additive_identity)) = multiply(X3,add(X3,X2)),
inference(transitivity,[status(thm)],[c51,c54]) ).
cnf(c56,plain,
multiply(X3,add(X3,X2)) = add(X3,multiply(X2,additive_identity)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
X2 = multiply(X2,multiplicative_identity),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c58,plain,
add(X3,multiply(X3,X2)) = add(multiply(X3,multiplicative_identity),multiply(X3,X2)),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(X3,add(multiplicative_identity,X2)) = add(multiply(X3,multiplicative_identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c60,plain,
add(multiply(X3,multiplicative_identity),multiply(X3,X2)) = multiply(X3,add(multiplicative_identity,X2)),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
add(multiplicative_identity,X2) = add(X2,multiplicative_identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c62,plain,
multiply(X3,add(multiplicative_identity,X2)) = multiply(X3,add(X2,multiplicative_identity)),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
add(multiply(X3,multiplicative_identity),multiply(X3,X2)) = multiply(X3,add(X2,multiplicative_identity)),
inference(transitivity,[status(thm)],[c60,c62]) ).
cnf(c64,plain,
add(X3,multiply(X3,X2)) = multiply(X3,add(X2,multiplicative_identity)),
inference(transitivity,[status(thm)],[c58,c63]) ).
cnf(c65,plain,
add(additive_identity,multiply(additive_identity,X2)) = multiply(additive_identity,add(X2,multiplicative_identity)),
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(additive_identity,add(X2,multiplicative_identity)) = add(additive_identity,multiply(additive_identity,X2)),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
add(X2,additive_identity) = add(additive_identity,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c68,plain,
add(additive_identity,X2) = add(X2,additive_identity),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
add(additive_identity,X2) = X2,
inference(transitivity,[status(thm)],[c68,c29]) ).
cnf(c70,plain,
add(additive_identity,multiply(additive_identity,X2)) = multiply(additive_identity,X2),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
multiply(additive_identity,X2) = multiply(X2,additive_identity),
inference(substitution,[status(thm)],[c6]) ).
cnf(c72,plain,
add(additive_identity,multiply(additive_identity,X2)) = multiply(X2,additive_identity),
inference(transitivity,[status(thm)],[c70,c71]) ).
cnf(c73,plain,
multiply(additive_identity,add(X2,multiplicative_identity)) = multiply(X2,additive_identity),
inference(transitivity,[status(thm)],[c66,c72]) ).
cnf(c74,plain,
multiply(X2,additive_identity) = multiply(additive_identity,add(X2,multiplicative_identity)),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
add(X2,multiply(multiplicative_identity,inverse(X2))) = add(X2,multiplicative_identity),
inference(substitution,[status(thm)],[c17]) ).
cnf(c76,plain,
add(X2,multiplicative_identity) = add(X2,multiply(multiplicative_identity,inverse(X2))),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
multiply(X2,multiplicative_identity) = multiply(multiplicative_identity,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c78,plain,
multiply(multiplicative_identity,X2) = multiply(X2,multiplicative_identity),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(multiplicative_identity,X2) = X2,
inference(transitivity,[status(thm)],[c78,c14]) ).
cnf(c80,plain,
multiply(multiplicative_identity,inverse(X2)) = inverse(X2),
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
add(X2,multiply(multiplicative_identity,inverse(X2))) = add(X2,inverse(X2)),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
add(X2,multiply(multiplicative_identity,inverse(X2))) = multiplicative_identity,
inference(transitivity,[status(thm)],[c81,c12]) ).
cnf(c83,plain,
add(X2,multiplicative_identity) = multiplicative_identity,
inference(transitivity,[status(thm)],[c76,c82]) ).
cnf(c84,plain,
multiply(additive_identity,add(X2,multiplicative_identity)) = multiply(additive_identity,multiplicative_identity),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
multiply(additive_identity,multiplicative_identity) = additive_identity,
inference(substitution,[status(thm)],[c14]) ).
cnf(c86,plain,
multiply(additive_identity,add(X2,multiplicative_identity)) = additive_identity,
inference(transitivity,[status(thm)],[c84,c85]) ).
cnf(c87,plain,
multiply(X2,additive_identity) = additive_identity,
inference(transitivity,[status(thm)],[c74,c86]) ).
cnf(c88,plain,
add(X3,multiply(X2,additive_identity)) = add(X3,additive_identity),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
add(X3,multiply(X2,additive_identity)) = X3,
inference(transitivity,[status(thm)],[c88,c29]) ).
cnf(c90,plain,
multiply(X3,add(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c56,c89]) ).
cnf(c91,plain,
multiply(X3,add(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c48,c90]) ).
cnf(c92,plain,
multiply(inverse(inverse(X2)),add(X2,inverse(inverse(X2)))) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
inverse(inverse(X2)) = multiply(inverse(inverse(X2)),add(X2,inverse(inverse(X2)))),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
add(X2,multiply(inverse(X2),inverse(inverse(X2)))) = add(X2,inverse(inverse(X2))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c95,plain,
add(X2,inverse(inverse(X2))) = add(X2,multiply(inverse(X2),inverse(inverse(X2)))),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
multiply(inverse(X2),inverse(inverse(X2))) = additive_identity,
inference(substitution,[status(thm)],[c27]) ).
cnf(c97,plain,
add(X2,multiply(inverse(X2),inverse(inverse(X2)))) = add(X2,additive_identity),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
add(X2,multiply(inverse(X2),inverse(inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c97,c29]) ).
cnf(c99,plain,
add(X2,inverse(inverse(X2))) = X2,
inference(transitivity,[status(thm)],[c95,c98]) ).
cnf(c100,plain,
multiply(inverse(inverse(X2)),add(X2,inverse(inverse(X2)))) = multiply(inverse(inverse(X2)),X2),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
multiply(inverse(inverse(X2)),X2) = multiply(X2,inverse(inverse(X2))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c102,plain,
add(X2,inverse(X3)) = add(inverse(X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c103,plain,
add(inverse(X3),X2) = add(X2,inverse(X3)),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
multiply(X3,add(inverse(X3),X2)) = multiply(X3,add(X2,inverse(X3))),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
multiply(X3,add(inverse(X3),X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c104,c32]) ).
cnf(c106,plain,
multiply(X2,add(inverse(X2),inverse(inverse(X2)))) = multiply(X2,inverse(inverse(X2))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c107,plain,
multiply(X2,inverse(inverse(X2))) = multiply(X2,add(inverse(X2),inverse(inverse(X2)))),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
add(inverse(X2),inverse(inverse(X2))) = multiplicative_identity,
inference(substitution,[status(thm)],[c12]) ).
cnf(c109,plain,
multiply(X2,add(inverse(X2),inverse(inverse(X2)))) = multiply(X2,multiplicative_identity),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
multiply(X2,add(inverse(X2),inverse(inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c109,c14]) ).
cnf(c111,plain,
multiply(X2,inverse(inverse(X2))) = X2,
inference(transitivity,[status(thm)],[c107,c110]) ).
cnf(c112,plain,
multiply(inverse(inverse(X2)),X2) = X2,
inference(transitivity,[status(thm)],[c101,c111]) ).
cnf(c113,plain,
multiply(inverse(inverse(X2)),add(X2,inverse(inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c100,c112]) ).
cnf(c114,plain,
inverse(inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c93,c113]) ).
cnf(c115,plain,
add(X2,inverse(inverse(X3))) = add(X2,X3),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
add(X4,add(X2,inverse(inverse(X3)))) = add(X4,add(X2,X3)),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
add(X3,add(X4,add(X2,inverse(inverse(X3))))) = add(X3,add(X4,add(X2,X3))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c119,plain,
add(X4,add(X2,X3)) = add(X4,add(X3,X2)),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
add(X3,add(X4,add(X2,X3))) = add(X3,add(X4,add(X3,X2))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
add(add(X3,add(X4,X2)),X4) = add(X4,add(X3,add(X4,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c122,plain,
add(X4,add(X3,add(X4,X2))) = add(add(X3,add(X4,X2)),X4),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c123,plain,
add(add(X4,X2),X3) = add(X3,add(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c124,plain,
add(X3,add(X4,X2)) = add(add(X4,X2),X3),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
multiply(X4,add(X3,add(X4,X2))) = multiply(X4,add(add(X4,X2),X3)),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c127,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,plain,
add(multiply(X4,X3),multiply(X2,X4)) = add(multiply(X4,X3),multiply(X4,X2)),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
multiply(X4,add(X3,X2)) = add(multiply(X4,X3),multiply(X4,X2)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c130,plain,
add(multiply(X4,X3),multiply(X4,X2)) = multiply(X4,add(X3,X2)),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
add(multiply(X4,X3),multiply(X2,X4)) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c128,c130]) ).
cnf(c132,plain,
add(multiply(X4,add(X4,X2)),multiply(X3,X4)) = multiply(X4,add(add(X4,X2),X3)),
inference(substitution,[status(thm)],[c131]) ).
cnf(c133,plain,
multiply(X4,add(add(X4,X2),X3)) = add(multiply(X4,add(X4,X2)),multiply(X3,X4)),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
multiply(X3,add(X3,X2)) = add(X3,multiply(X2,additive_identity)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c135,plain,
add(multiply(X4,add(X4,X2)),multiply(X3,X4)) = add(add(X4,multiply(X2,additive_identity)),multiply(X3,X4)),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
add(X3,multiply(X2,additive_identity)) = add(X3,additive_identity),
inference(congruence,[status(thm)],[c87]) ).
cnf(c137,plain,
add(add(X4,multiply(X2,additive_identity)),multiply(X3,X4)) = add(add(X4,additive_identity),multiply(X3,X4)),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
add(add(X3,additive_identity),multiply(X2,X3)) = add(X3,multiply(X2,X3)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c139,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c140,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
add(X3,multiply(X2,X3)) = add(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
multiply(X3,add(X2,multiplicative_identity)) = multiply(X3,multiplicative_identity),
inference(congruence,[status(thm)],[c83]) ).
cnf(c143,plain,
multiply(X3,add(X2,multiplicative_identity)) = X3,
inference(transitivity,[status(thm)],[c142,c14]) ).
cnf(c144,plain,
add(X3,multiply(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c64,c143]) ).
cnf(c145,plain,
add(X3,multiply(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c141,c144]) ).
cnf(c146,plain,
add(add(X3,additive_identity),multiply(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c138,c145]) ).
cnf(c147,plain,
add(add(X4,multiply(X2,additive_identity)),multiply(X3,X4)) = X4,
inference(transitivity,[status(thm)],[c137,c146]) ).
cnf(c148,plain,
add(multiply(X4,add(X4,X2)),multiply(X3,X4)) = X4,
inference(transitivity,[status(thm)],[c135,c147]) ).
cnf(c149,plain,
multiply(X4,add(add(X4,X2),X3)) = X4,
inference(transitivity,[status(thm)],[c133,c148]) ).
cnf(c150,plain,
multiply(X4,add(X3,add(X4,X2))) = X4,
inference(transitivity,[status(thm)],[c125,c149]) ).
cnf(c151,plain,
X4 = multiply(X4,add(X3,add(X4,X2))),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
add(add(X3,add(X4,X2)),X4) = add(add(X3,add(X4,X2)),multiply(X4,add(X3,add(X4,X2)))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
add(add(X3,add(X4,X2)),multiply(X4,add(X3,add(X4,X2)))) = add(X3,add(X4,X2)),
inference(substitution,[status(thm)],[c145]) ).
cnf(c154,plain,
add(add(X3,add(X4,X2)),X4) = add(X3,add(X4,X2)),
inference(transitivity,[status(thm)],[c152,c153]) ).
cnf(c155,plain,
add(X4,add(X3,add(X4,X2))) = add(X3,add(X4,X2)),
inference(transitivity,[status(thm)],[c122,c154]) ).
cnf(c156,plain,
add(X3,add(X4,add(X3,X2))) = add(X4,add(X3,X2)),
inference(substitution,[status(thm)],[c155]) ).
cnf(c157,plain,
add(X3,add(X4,add(X2,X3))) = add(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c120,c156]) ).
cnf(c158,plain,
add(X3,add(X4,add(X2,inverse(inverse(X3))))) = add(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c117,c157]) ).
cnf(c159,plain,
add(X3,multiply(inverse(X3),add(X4,add(X2,inverse(inverse(X3)))))) = add(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c45,c158]) ).
cnf(c160,plain,
add(X3,multiply(inverse(X3),add(X4,X2))) = add(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c44,c159]) ).
cnf(c161,plain,
add(X3,add(X4,X2)) = add(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c20,c160]) ).
cnf(c162,plain,
add(a,add(c,b)) = add(c,add(a,b)),
inference(substitution,[status(thm)],[c161]) ).
cnf(c163,plain,
add(add(a,b),c) = add(c,add(a,b)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c164,plain,
add(c,add(a,b)) = add(add(a,b),c),
inference(symmetry,[status(thm)],[c163]) ).
cnf(c165,plain,
add(a,add(c,b)) = add(add(a,b),c),
inference(transitivity,[status(thm)],[c162,c164]) ).
cnf(c166,plain,
add(a,add(b,c)) = add(add(a,b),c),
inference(transitivity,[status(thm)],[c5,c165]) ).
cnf(c167,plain,
$false,
inference(resolution,[status(thm)],[c1,c166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO008-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n015.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 21:07:01 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/0.34 Command-line arguments: --no-flatten-goal
% 0.40/0.34
% 0.40/0.34 % SZS status Unsatisfiable
% 0.40/0.34
% 0.40/0.34 % SZS output start CNFRefutation
% See solution above
% 0.40/0.39
% 0.40/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------