%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP185-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 10:09:37 AM UTC 2026
% Result : Unsatisfiable 1.49s 0.65s
% Output : CNFRefutation 2.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 12
% Syntax : Number of clauses : 165 ( 165 unt; 0 nHn; 5 RR)
% Number of literals : 165 ( 164 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 374 ( 18 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p22a) ).
cnf(c2,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c3,plain,
least_upper_bound(least_upper_bound(X2,X4),X3) = least_upper_bound(X3,least_upper_bound(X2,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
least_upper_bound(X3,least_upper_bound(X2,X4)) = least_upper_bound(least_upper_bound(X2,X4),X3),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
least_upper_bound(least_upper_bound(X2,X4),X3) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
least_upper_bound(X2,least_upper_bound(Y2,Z)) = least_upper_bound(least_upper_bound(X2,Y2),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).
cnf(c9,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X4,least_upper_bound(X2,X3)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c10,c12]) ).
cnf(c14,plain,
least_upper_bound(least_upper_bound(X2,X4),X3) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c7,c13]) ).
cnf(c15,plain,
least_upper_bound(X3,least_upper_bound(X2,X4)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c4,c14]) ).
cnf(c16,plain,
least_upper_bound(X4,least_upper_bound(least_upper_bound(X3,identity),multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity)))) = least_upper_bound(multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity)),least_upper_bound(X4,least_upper_bound(X3,identity))),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
least_upper_bound(least_upper_bound(X3,X2),X4) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
least_upper_bound(X4,least_upper_bound(X3,X2)) = least_upper_bound(least_upper_bound(X3,X2),X4),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
least_upper_bound(X3,least_upper_bound(X2,X4)) = least_upper_bound(least_upper_bound(X3,X2),X4),
inference(substitution,[status(thm)],[c8]) ).
cnf(c20,plain,
least_upper_bound(least_upper_bound(X3,X2),X4) = least_upper_bound(X3,least_upper_bound(X2,X4)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
least_upper_bound(X3,least_upper_bound(X2,X4)) = least_upper_bound(X3,least_upper_bound(X4,X2)),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
least_upper_bound(least_upper_bound(X3,X2),X4) = least_upper_bound(X3,least_upper_bound(X4,X2)),
inference(transitivity,[status(thm)],[c20,c22]) ).
cnf(c24,plain,
least_upper_bound(X4,least_upper_bound(X3,X2)) = least_upper_bound(X3,least_upper_bound(X4,X2)),
inference(transitivity,[status(thm)],[c18,c23]) ).
cnf(c25,plain,
least_upper_bound(X2,least_upper_bound(X3,identity)) = least_upper_bound(X3,least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
least_upper_bound(X3,least_upper_bound(X2,identity)) = least_upper_bound(X2,least_upper_bound(X3,identity)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
least_upper_bound(multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity)),least_upper_bound(X4,least_upper_bound(X3,identity))) = least_upper_bound(multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity)),least_upper_bound(X3,least_upper_bound(X4,identity))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c29,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
least_upper_bound(multiply(least_upper_bound(X4,identity),X3),least_upper_bound(X2,X3)) = least_upper_bound(multiply(least_upper_bound(X4,identity),X3),least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
least_upper_bound(multiply(least_upper_bound(X4,identity),X3),least_upper_bound(X3,X2)) = least_upper_bound(least_upper_bound(multiply(least_upper_bound(X4,identity),X3),X3),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c32,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c33,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
least_upper_bound(multiply(least_upper_bound(X3,identity),X2),X2) = least_upper_bound(multiply(least_upper_bound(X3,identity),X2),multiply(identity,X2)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,axiom,
multiply(least_upper_bound(Y2,Z2),X2) = least_upper_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
cnf(c36,plain,
multiply(least_upper_bound(X4,X2),X3) = least_upper_bound(multiply(X4,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
least_upper_bound(multiply(X4,X3),multiply(X2,X3)) = multiply(least_upper_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
multiply(least_upper_bound(X4,X2),X3) = multiply(least_upper_bound(X2,X4),X3),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
least_upper_bound(multiply(X4,X3),multiply(X2,X3)) = multiply(least_upper_bound(X2,X4),X3),
inference(transitivity,[status(thm)],[c37,c39]) ).
cnf(c41,plain,
least_upper_bound(multiply(least_upper_bound(X3,identity),X2),multiply(identity,X2)) = multiply(least_upper_bound(identity,least_upper_bound(X3,identity)),X2),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
least_upper_bound(least_upper_bound(X2,X3),X3) = least_upper_bound(X3,least_upper_bound(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c43,plain,
least_upper_bound(X3,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X2,X3),X3),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c45,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c47,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c45,c47]) ).
cnf(c49,plain,
X3 = greatest_lower_bound(X3,least_upper_bound(X2,X3)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
least_upper_bound(least_upper_bound(X2,X3),X3) = least_upper_bound(least_upper_bound(X2,X3),greatest_lower_bound(X3,least_upper_bound(X2,X3))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c52,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c56,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c54,c56]) ).
cnf(c58,plain,
least_upper_bound(least_upper_bound(X2,X3),greatest_lower_bound(X3,least_upper_bound(X2,X3))) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
least_upper_bound(least_upper_bound(X2,X3),X3) = least_upper_bound(X2,X3),
inference(transitivity,[status(thm)],[c50,c58]) ).
cnf(c60,plain,
least_upper_bound(X3,least_upper_bound(X2,X3)) = least_upper_bound(X2,X3),
inference(transitivity,[status(thm)],[c43,c59]) ).
cnf(c61,plain,
least_upper_bound(identity,least_upper_bound(X2,identity)) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
multiply(least_upper_bound(identity,least_upper_bound(X3,identity)),X2) = multiply(least_upper_bound(X3,identity),X2),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
least_upper_bound(multiply(least_upper_bound(X3,identity),X2),multiply(identity,X2)) = multiply(least_upper_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c41,c62]) ).
cnf(c64,plain,
least_upper_bound(multiply(least_upper_bound(X3,identity),X2),X2) = multiply(least_upper_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c34,c63]) ).
cnf(c65,plain,
least_upper_bound(least_upper_bound(multiply(least_upper_bound(X4,identity),X3),X3),X2) = least_upper_bound(multiply(least_upper_bound(X4,identity),X3),X2),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
least_upper_bound(multiply(least_upper_bound(X4,identity),X3),X2) = least_upper_bound(X2,multiply(least_upper_bound(X4,identity),X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c67,plain,
least_upper_bound(least_upper_bound(multiply(least_upper_bound(X4,identity),X3),X3),X2) = least_upper_bound(X2,multiply(least_upper_bound(X4,identity),X3)),
inference(transitivity,[status(thm)],[c65,c66]) ).
cnf(c68,plain,
least_upper_bound(multiply(least_upper_bound(X4,identity),X3),least_upper_bound(X3,X2)) = least_upper_bound(X2,multiply(least_upper_bound(X4,identity),X3)),
inference(transitivity,[status(thm)],[c31,c67]) ).
cnf(c69,plain,
least_upper_bound(multiply(least_upper_bound(X4,identity),X3),least_upper_bound(X2,X3)) = least_upper_bound(X2,multiply(least_upper_bound(X4,identity),X3)),
inference(transitivity,[status(thm)],[c30,c68]) ).
cnf(c70,plain,
least_upper_bound(multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity)),least_upper_bound(X3,least_upper_bound(X4,identity))) = least_upper_bound(X3,multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity))),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
least_upper_bound(X3,multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity))) = least_upper_bound(multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity)),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c72,plain,
least_upper_bound(X5,least_upper_bound(X3,multiply(least_upper_bound(X4,X3),least_upper_bound(X2,identity)))) = least_upper_bound(least_upper_bound(X5,X3),multiply(least_upper_bound(X4,X3),least_upper_bound(X2,identity))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c73,plain,
least_upper_bound(least_upper_bound(X2,X4),multiply(least_upper_bound(X5,X4),least_upper_bound(X3,identity))) = least_upper_bound(X2,least_upper_bound(X4,multiply(least_upper_bound(X5,X4),least_upper_bound(X3,identity)))),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
least_upper_bound(multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)),X4) = least_upper_bound(X4,multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c75,plain,
least_upper_bound(X4,multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity))) = least_upper_bound(multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)),X4),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,axiom,
inverse(inverse(X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c77,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
multiply(X2,identity) = multiply(inverse(inverse(X2)),identity),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c80,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(inverse(X2),identity) = multiply(inverse(X2),inverse(identity)),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,hypothesis,
inverse(multiply(X2,Y2)) = multiply(inverse(Y2),inverse(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22a_3) ).
cnf(c83,plain,
inverse(multiply(identity,X2)) = multiply(inverse(X2),inverse(identity)),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(inverse(X2),inverse(identity)) = inverse(multiply(identity,X2)),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
inverse(multiply(identity,X2)) = inverse(X2),
inference(congruence,[status(thm)],[c32]) ).
cnf(c86,plain,
multiply(inverse(X2),inverse(identity)) = inverse(X2),
inference(transitivity,[status(thm)],[c84,c85]) ).
cnf(c87,plain,
multiply(inverse(X2),identity) = inverse(X2),
inference(transitivity,[status(thm)],[c81,c86]) ).
cnf(c88,plain,
multiply(inverse(inverse(X2)),identity) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c89,plain,
multiply(inverse(inverse(X2)),identity) = X2,
inference(transitivity,[status(thm)],[c88,c76]) ).
cnf(c90,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c78,c89]) ).
cnf(c91,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
least_upper_bound(multiply(X3,least_upper_bound(X2,identity)),X3) = least_upper_bound(multiply(X3,least_upper_bound(X2,identity)),multiply(X3,identity)),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,axiom,
multiply(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
cnf(c94,plain,
multiply(X4,least_upper_bound(X3,X2)) = least_upper_bound(multiply(X4,X3),multiply(X4,X2)),
inference(substitution,[status(thm)],[c93]) ).
cnf(c95,plain,
least_upper_bound(multiply(X4,X3),multiply(X4,X2)) = multiply(X4,least_upper_bound(X3,X2)),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c97,plain,
multiply(X4,least_upper_bound(X3,X2)) = multiply(X4,least_upper_bound(X2,X3)),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
least_upper_bound(multiply(X4,X3),multiply(X4,X2)) = multiply(X4,least_upper_bound(X2,X3)),
inference(transitivity,[status(thm)],[c95,c97]) ).
cnf(c99,plain,
least_upper_bound(multiply(X3,least_upper_bound(X2,identity)),multiply(X3,identity)) = multiply(X3,least_upper_bound(identity,least_upper_bound(X2,identity))),
inference(substitution,[status(thm)],[c98]) ).
cnf(c100,plain,
least_upper_bound(identity,least_upper_bound(X2,identity)) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c60]) ).
cnf(c101,plain,
multiply(X3,least_upper_bound(identity,least_upper_bound(X2,identity))) = multiply(X3,least_upper_bound(X2,identity)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
least_upper_bound(multiply(X3,least_upper_bound(X2,identity)),multiply(X3,identity)) = multiply(X3,least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c99,c101]) ).
cnf(c103,plain,
least_upper_bound(multiply(X3,least_upper_bound(X2,identity)),X3) = multiply(X3,least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c92,c102]) ).
cnf(c104,plain,
least_upper_bound(multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)),least_upper_bound(X3,X4)) = multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)) = least_upper_bound(multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)),least_upper_bound(X3,X4)),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
greatest_lower_bound(X4,multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity))) = greatest_lower_bound(X4,least_upper_bound(multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)),least_upper_bound(X3,X4))),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
greatest_lower_bound(X4,least_upper_bound(X3,least_upper_bound(X2,X4))) = greatest_lower_bound(X4,least_upper_bound(X4,least_upper_bound(X3,X2))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c108,plain,
greatest_lower_bound(X4,least_upper_bound(X4,least_upper_bound(X3,X2))) = X4,
inference(substitution,[status(thm)],[c46]) ).
cnf(c109,plain,
greatest_lower_bound(X4,least_upper_bound(X3,least_upper_bound(X2,X4))) = X4,
inference(transitivity,[status(thm)],[c107,c108]) ).
cnf(c110,plain,
greatest_lower_bound(X4,least_upper_bound(multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)),least_upper_bound(X3,X4))) = X4,
inference(substitution,[status(thm)],[c109]) ).
cnf(c111,plain,
greatest_lower_bound(X4,multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity))) = X4,
inference(transitivity,[status(thm)],[c106,c110]) ).
cnf(c112,plain,
X4 = greatest_lower_bound(X4,multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity))),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
least_upper_bound(multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)),X4) = least_upper_bound(multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)),greatest_lower_bound(X4,multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)))),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
least_upper_bound(multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)),greatest_lower_bound(X4,multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)))) = multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c57]) ).
cnf(c115,plain,
least_upper_bound(multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)),X4) = multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c113,c114]) ).
cnf(c116,plain,
least_upper_bound(X4,multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity))) = multiply(least_upper_bound(X3,X4),least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c75,c115]) ).
cnf(c117,plain,
least_upper_bound(X3,multiply(least_upper_bound(X4,X3),least_upper_bound(X2,identity))) = multiply(least_upper_bound(X4,X3),least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c116]) ).
cnf(c118,plain,
least_upper_bound(X2,least_upper_bound(X4,multiply(least_upper_bound(X5,X4),least_upper_bound(X3,identity)))) = least_upper_bound(X2,multiply(least_upper_bound(X5,X4),least_upper_bound(X3,identity))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
least_upper_bound(X2,multiply(least_upper_bound(X5,X4),least_upper_bound(X3,identity))) = least_upper_bound(multiply(least_upper_bound(X5,X4),least_upper_bound(X3,identity)),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c120,plain,
least_upper_bound(X2,least_upper_bound(X4,multiply(least_upper_bound(X5,X4),least_upper_bound(X3,identity)))) = least_upper_bound(multiply(least_upper_bound(X5,X4),least_upper_bound(X3,identity)),X2),
inference(transitivity,[status(thm)],[c118,c119]) ).
cnf(c121,plain,
least_upper_bound(least_upper_bound(X2,X4),multiply(least_upper_bound(X5,X4),least_upper_bound(X3,identity))) = least_upper_bound(multiply(least_upper_bound(X5,X4),least_upper_bound(X3,identity)),X2),
inference(transitivity,[status(thm)],[c73,c120]) ).
cnf(c122,plain,
least_upper_bound(least_upper_bound(X3,identity),multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity))) = least_upper_bound(multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity)),X3),
inference(substitution,[status(thm)],[c121]) ).
cnf(c123,plain,
least_upper_bound(multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity)),X3) = least_upper_bound(least_upper_bound(X3,identity),multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity))),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
least_upper_bound(X3,multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity))) = least_upper_bound(least_upper_bound(X3,identity),multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity))),
inference(transitivity,[status(thm)],[c71,c123]) ).
cnf(c125,plain,
least_upper_bound(multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity)),least_upper_bound(X3,least_upper_bound(X4,identity))) = least_upper_bound(least_upper_bound(X3,identity),multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity))),
inference(transitivity,[status(thm)],[c70,c124]) ).
cnf(c126,plain,
least_upper_bound(multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity)),least_upper_bound(X4,least_upper_bound(X3,identity))) = least_upper_bound(least_upper_bound(X3,identity),multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity))),
inference(transitivity,[status(thm)],[c27,c125]) ).
cnf(c127,plain,
least_upper_bound(X4,least_upper_bound(least_upper_bound(X3,identity),multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity)))) = least_upper_bound(least_upper_bound(X3,identity),multiply(least_upper_bound(X2,identity),least_upper_bound(X4,identity))),
inference(transitivity,[status(thm)],[c16,c126]) ).
cnf(c128,plain,
least_upper_bound(X2,least_upper_bound(least_upper_bound(multiply(X3,X2),identity),multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)))) = least_upper_bound(least_upper_bound(multiply(X3,X2),identity),multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity))),
inference(substitution,[status(thm)],[c127]) ).
cnf(c129,plain,
least_upper_bound(least_upper_bound(multiply(X3,X2),identity),multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity))) = least_upper_bound(X2,least_upper_bound(least_upper_bound(multiply(X3,X2),identity),multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)))),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
least_upper_bound(least_upper_bound(multiply(X3,X2),identity),multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity))) = least_upper_bound(multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),multiply(X3,X2)),
inference(substitution,[status(thm)],[c121]) ).
cnf(c131,plain,
least_upper_bound(X2,least_upper_bound(least_upper_bound(multiply(X3,X2),identity),multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)))) = least_upper_bound(X2,least_upper_bound(multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),multiply(X3,X2))),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
least_upper_bound(multiply(X2,X3),X3) = least_upper_bound(X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c133,plain,
least_upper_bound(X3,multiply(X2,X3)) = least_upper_bound(multiply(X2,X3),X3),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c135,plain,
least_upper_bound(multiply(X2,X3),X3) = least_upper_bound(multiply(X2,X3),multiply(identity,X3)),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
least_upper_bound(multiply(X2,X3),multiply(identity,X3)) = multiply(least_upper_bound(identity,X2),X3),
inference(substitution,[status(thm)],[c40]) ).
cnf(c137,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c138,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
multiply(least_upper_bound(identity,X2),X3) = multiply(least_upper_bound(X2,identity),X3),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
least_upper_bound(multiply(X2,X3),multiply(identity,X3)) = multiply(least_upper_bound(X2,identity),X3),
inference(transitivity,[status(thm)],[c136,c139]) ).
cnf(c141,plain,
least_upper_bound(multiply(X2,X3),X3) = multiply(least_upper_bound(X2,identity),X3),
inference(transitivity,[status(thm)],[c135,c140]) ).
cnf(c142,plain,
least_upper_bound(X3,multiply(X2,X3)) = multiply(least_upper_bound(X2,identity),X3),
inference(transitivity,[status(thm)],[c133,c141]) ).
cnf(c143,plain,
multiply(least_upper_bound(X2,identity),X3) = least_upper_bound(X3,multiply(X2,X3)),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
least_upper_bound(X3,multiply(least_upper_bound(X2,identity),X4)) = least_upper_bound(X3,least_upper_bound(X4,multiply(X2,X4))),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
least_upper_bound(X3,least_upper_bound(X4,multiply(X2,X4))) = least_upper_bound(X4,least_upper_bound(X3,multiply(X2,X4))),
inference(substitution,[status(thm)],[c24]) ).
cnf(c146,plain,
least_upper_bound(X3,multiply(least_upper_bound(X2,identity),X4)) = least_upper_bound(X4,least_upper_bound(X3,multiply(X2,X4))),
inference(transitivity,[status(thm)],[c144,c145]) ).
cnf(c147,plain,
least_upper_bound(multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),multiply(least_upper_bound(X3,identity),X2)) = least_upper_bound(X2,least_upper_bound(multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),multiply(X3,X2))),
inference(substitution,[status(thm)],[c146]) ).
cnf(c148,plain,
least_upper_bound(X2,least_upper_bound(multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),multiply(X3,X2))) = least_upper_bound(multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),multiply(least_upper_bound(X3,identity),X2)),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
least_upper_bound(multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),multiply(least_upper_bound(X3,identity),X2)) = multiply(least_upper_bound(X3,identity),least_upper_bound(X2,least_upper_bound(X2,identity))),
inference(substitution,[status(thm)],[c98]) ).
cnf(c150,plain,
least_upper_bound(least_upper_bound(X3,X2),X3) = least_upper_bound(X3,least_upper_bound(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c151,plain,
least_upper_bound(X3,least_upper_bound(X3,X2)) = least_upper_bound(least_upper_bound(X3,X2),X3),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c46]) ).
cnf(c153,plain,
X3 = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c154,plain,
least_upper_bound(least_upper_bound(X3,X2),X3) = least_upper_bound(least_upper_bound(X3,X2),greatest_lower_bound(X3,least_upper_bound(X3,X2))),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
least_upper_bound(least_upper_bound(X3,X2),greatest_lower_bound(X3,least_upper_bound(X3,X2))) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c57]) ).
cnf(c156,plain,
least_upper_bound(least_upper_bound(X3,X2),X3) = least_upper_bound(X3,X2),
inference(transitivity,[status(thm)],[c154,c155]) ).
cnf(c157,plain,
least_upper_bound(X3,least_upper_bound(X3,X2)) = least_upper_bound(X3,X2),
inference(transitivity,[status(thm)],[c151,c156]) ).
cnf(c158,plain,
least_upper_bound(X2,least_upper_bound(X2,identity)) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c157]) ).
cnf(c159,plain,
multiply(least_upper_bound(X3,identity),least_upper_bound(X2,least_upper_bound(X2,identity))) = multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
least_upper_bound(multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),multiply(least_upper_bound(X3,identity),X2)) = multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c149,c159]) ).
cnf(c161,plain,
least_upper_bound(X2,least_upper_bound(multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),multiply(X3,X2))) = multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c148,c160]) ).
cnf(c162,plain,
least_upper_bound(X2,least_upper_bound(least_upper_bound(multiply(X3,X2),identity),multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)))) = multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c131,c161]) ).
cnf(c163,plain,
least_upper_bound(least_upper_bound(multiply(X3,X2),identity),multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity))) = multiply(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c129,c162]) ).
cnf(c164,plain,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(substitution,[status(thm)],[c163]) ).
cnf(c165,plain,
$false,
inference(resolution,[status(thm)],[c1,c164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP185-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 09:31:50 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.49/0.65 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 1.49/0.65
% 1.49/0.65 % SZS status Unsatisfiable
% 1.49/0.65
% 1.78/0.68 % SZS output start CNFRefutation
% See solution above
% 2.49/0.81
% 2.49/0.81 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------