%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP178-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 10:09:34 AM UTC 2026
% Result : Unsatisfiable 2.26s 0.72s
% Output : CNFRefutation 3.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 16
% Syntax : Number of clauses : 195 ( 195 unt; 0 nHn; 30 RR)
% Number of literals : 195 ( 194 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 301 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p09a) ).
cnf(c2,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c3,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X3,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
greatest_lower_bound(greatest_lower_bound(X3,X2),X3) = greatest_lower_bound(X3,greatest_lower_bound(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
greatest_lower_bound(X3,greatest_lower_bound(X3,X2)) = greatest_lower_bound(greatest_lower_bound(X3,X2),X3),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c8,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = least_upper_bound(greatest_lower_bound(X3,X2),X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X3) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c11,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X3) = X3,
inference(transitivity,[status(thm)],[c9,c11]) ).
cnf(c13,plain,
X3 = least_upper_bound(greatest_lower_bound(X3,X2),X3),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
greatest_lower_bound(greatest_lower_bound(X3,X2),X3) = greatest_lower_bound(greatest_lower_bound(X3,X2),least_upper_bound(greatest_lower_bound(X3,X2),X3)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c16,plain,
greatest_lower_bound(greatest_lower_bound(X3,X2),least_upper_bound(greatest_lower_bound(X3,X2),X3)) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
greatest_lower_bound(greatest_lower_bound(X3,X2),X3) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c14,c16]) ).
cnf(c18,plain,
greatest_lower_bound(X3,greatest_lower_bound(X3,X2)) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c6,c17]) ).
cnf(c19,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c20,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
greatest_lower_bound(X3,greatest_lower_bound(X3,X2)) = greatest_lower_bound(X2,X3),
inference(transitivity,[status(thm)],[c18,c20]) ).
cnf(c22,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,X3),
inference(transitivity,[status(thm)],[c4,c21]) ).
cnf(c23,plain,
greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,multiply(b,c))),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(b,c)) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,multiply(b,c))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c26,plain,
greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(b,c)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,axiom,
greatest_lower_bound(X2,greatest_lower_bound(Y2,Z)) = greatest_lower_bound(greatest_lower_bound(X2,Y2),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_glb) ).
cnf(c28,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,multiply(X3,c))) = greatest_lower_bound(greatest_lower_bound(X3,X2),multiply(X3,c)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
greatest_lower_bound(multiply(X3,c),greatest_lower_bound(X3,X2)) = greatest_lower_bound(greatest_lower_bound(X3,X2),multiply(X3,c)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c30,plain,
greatest_lower_bound(greatest_lower_bound(X3,X2),multiply(X3,c)) = greatest_lower_bound(multiply(X3,c),greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
greatest_lower_bound(greatest_lower_bound(X4,X3),X2) = greatest_lower_bound(X2,greatest_lower_bound(X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c32,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,X4)) = greatest_lower_bound(greatest_lower_bound(X2,X4),X3),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c34,plain,
greatest_lower_bound(greatest_lower_bound(X2,X4),X3) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c27]) ).
cnf(c36,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X2,X3)),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c38,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c36,c38]) ).
cnf(c40,plain,
greatest_lower_bound(greatest_lower_bound(X2,X4),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c34,c39]) ).
cnf(c41,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,X4)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c32,c40]) ).
cnf(c42,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,X4)) = greatest_lower_bound(X4,greatest_lower_bound(X2,X3)),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c44,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,X4)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c42,c44]) ).
cnf(c46,plain,
greatest_lower_bound(multiply(X3,c),greatest_lower_bound(X3,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X3,multiply(X3,c))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,axiom,
multiply(multiply(X2,Y2),Z2) = multiply(X2,multiply(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
cnf(c48,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c51,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c53,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c51,c52]) ).
cnf(c54,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c49,c53]) ).
cnf(c55,plain,
X2 = multiply(inverse(X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(inverse(inverse(X3)),X2) = multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c54]) ).
cnf(c58,plain,
multiply(inverse(inverse(X3)),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c56,c57]) ).
cnf(c59,plain,
multiply(inverse(inverse(X2)),identity) = multiply(X2,identity),
inference(substitution,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(X2,identity) = multiply(inverse(inverse(X2)),identity),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c62,plain,
multiply(inverse(inverse(X2)),identity) = multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)) = X2,
inference(substitution,[status(thm)],[c54]) ).
cnf(c64,plain,
multiply(inverse(inverse(X2)),identity) = X2,
inference(transitivity,[status(thm)],[c62,c63]) ).
cnf(c65,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c60,c64]) ).
cnf(c66,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
least_upper_bound(multiply(X2,c),X2) = least_upper_bound(multiply(X2,c),multiply(X2,identity)),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,axiom,
multiply(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).
cnf(c69,plain,
multiply(X4,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X4,X2),multiply(X4,X3)),
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
least_upper_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,least_upper_bound(X2,X3)),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c72,plain,
multiply(X4,least_upper_bound(X2,X3)) = multiply(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
least_upper_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c70,c72]) ).
cnf(c74,plain,
least_upper_bound(multiply(X2,c),multiply(X2,identity)) = multiply(X2,least_upper_bound(identity,c)),
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,axiom,
least_upper_bound(identity,c) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c76,plain,
multiply(X2,least_upper_bound(identity,c)) = multiply(X2,c),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
least_upper_bound(multiply(X2,c),multiply(X2,identity)) = multiply(X2,c),
inference(transitivity,[status(thm)],[c74,c76]) ).
cnf(c78,plain,
least_upper_bound(multiply(X2,c),X2) = multiply(X2,c),
inference(transitivity,[status(thm)],[c67,c77]) ).
cnf(c79,plain,
multiply(X2,c) = least_upper_bound(multiply(X2,c),X2),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
greatest_lower_bound(X2,multiply(X2,c)) = greatest_lower_bound(X2,least_upper_bound(multiply(X2,c),X2)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c82,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c15]) ).
cnf(c85,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c83,c84]) ).
cnf(c86,plain,
greatest_lower_bound(X2,least_upper_bound(multiply(X2,c),X2)) = X2,
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
greatest_lower_bound(X2,multiply(X2,c)) = X2,
inference(transitivity,[status(thm)],[c80,c86]) ).
cnf(c88,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,multiply(X3,c))) = greatest_lower_bound(X2,X3),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c90,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,multiply(X3,c))) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c88,c90]) ).
cnf(c92,plain,
greatest_lower_bound(multiply(X3,c),greatest_lower_bound(X3,X2)) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c46,c91]) ).
cnf(c93,plain,
greatest_lower_bound(greatest_lower_bound(X3,X2),multiply(X3,c)) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c30,c92]) ).
cnf(c94,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,multiply(X3,c))) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c28,c93]) ).
cnf(c95,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,multiply(b,c)),c))) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(b,c)),
inference(substitution,[status(thm)],[c94]) ).
cnf(c96,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(b,c)) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,multiply(b,c)),c))),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,axiom,
multiply(greatest_lower_bound(Y2,Z2),X2) = greatest_lower_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).
cnf(c98,plain,
multiply(greatest_lower_bound(X3,X4),X2) = greatest_lower_bound(multiply(X3,X2),multiply(X4,X2)),
inference(substitution,[status(thm)],[c97]) ).
cnf(c99,plain,
greatest_lower_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(greatest_lower_bound(X3,X4),X2),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c101,plain,
multiply(greatest_lower_bound(X3,X4),X2) = multiply(greatest_lower_bound(X4,X3),X2),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
greatest_lower_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(greatest_lower_bound(X4,X3),X2),
inference(transitivity,[status(thm)],[c99,c101]) ).
cnf(c103,plain,
greatest_lower_bound(multiply(b,X2),multiply(greatest_lower_bound(a,multiply(b,c)),X2)) = multiply(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),b),X2),
inference(substitution,[status(thm)],[c102]) ).
cnf(c104,plain,
greatest_lower_bound(b,greatest_lower_bound(a,X2)) = greatest_lower_bound(greatest_lower_bound(a,X2),b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c105,plain,
greatest_lower_bound(greatest_lower_bound(a,X2),b) = greatest_lower_bound(b,greatest_lower_bound(a,X2)),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
greatest_lower_bound(a,X2) = greatest_lower_bound(X2,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c107,plain,
greatest_lower_bound(b,greatest_lower_bound(a,X2)) = greatest_lower_bound(b,greatest_lower_bound(X2,a)),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
greatest_lower_bound(a,X2) = greatest_lower_bound(X2,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c109,plain,
greatest_lower_bound(X2,a) = greatest_lower_bound(a,X2),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
greatest_lower_bound(b,greatest_lower_bound(X2,a)) = greatest_lower_bound(b,greatest_lower_bound(a,X2)),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
greatest_lower_bound(b,greatest_lower_bound(a,X2)) = greatest_lower_bound(greatest_lower_bound(b,a),X2),
inference(substitution,[status(thm)],[c27]) ).
cnf(c112,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(b,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c113,plain,
greatest_lower_bound(b,a) = greatest_lower_bound(a,b),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,axiom,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c115,plain,
greatest_lower_bound(b,a) = identity,
inference(transitivity,[status(thm)],[c113,c114]) ).
cnf(c116,plain,
greatest_lower_bound(greatest_lower_bound(b,a),X2) = greatest_lower_bound(identity,X2),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c118,plain,
greatest_lower_bound(greatest_lower_bound(b,a),X2) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c116,c117]) ).
cnf(c119,plain,
greatest_lower_bound(b,greatest_lower_bound(a,X2)) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c111,c118]) ).
cnf(c120,plain,
greatest_lower_bound(b,greatest_lower_bound(X2,a)) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c110,c119]) ).
cnf(c121,plain,
greatest_lower_bound(b,greatest_lower_bound(a,X2)) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c107,c120]) ).
cnf(c122,plain,
greatest_lower_bound(greatest_lower_bound(a,X2),b) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c105,c121]) ).
cnf(c123,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),b) = greatest_lower_bound(multiply(b,c),identity),
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
multiply(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),b),X2) = multiply(greatest_lower_bound(multiply(b,c),identity),X2),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
greatest_lower_bound(identity,multiply(b,c)) = greatest_lower_bound(multiply(b,c),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c126,plain,
greatest_lower_bound(multiply(b,c),identity) = greatest_lower_bound(identity,multiply(b,c)),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
least_upper_bound(multiply(b,c),b) = multiply(b,c),
inference(substitution,[status(thm)],[c78]) ).
cnf(c128,plain,
multiply(b,c) = least_upper_bound(multiply(b,c),b),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
greatest_lower_bound(identity,multiply(b,c)) = greatest_lower_bound(identity,least_upper_bound(multiply(b,c),b)),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
least_upper_bound(b,X2) = least_upper_bound(X2,b),
inference(substitution,[status(thm)],[c7]) ).
cnf(c131,plain,
least_upper_bound(X2,b) = least_upper_bound(b,X2),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
least_upper_bound(identity,least_upper_bound(X2,b)) = least_upper_bound(identity,least_upper_bound(b,X2)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,axiom,
least_upper_bound(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(least_upper_bound(X2,Y2),Z2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_lub) ).
cnf(c134,plain,
least_upper_bound(identity,least_upper_bound(b,X2)) = least_upper_bound(least_upper_bound(identity,b),X2),
inference(substitution,[status(thm)],[c133]) ).
cnf(c135,axiom,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c136,plain,
least_upper_bound(least_upper_bound(identity,b),X2) = least_upper_bound(b,X2),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
least_upper_bound(b,X2) = least_upper_bound(X2,b),
inference(substitution,[status(thm)],[c7]) ).
cnf(c138,plain,
least_upper_bound(least_upper_bound(identity,b),X2) = least_upper_bound(X2,b),
inference(transitivity,[status(thm)],[c136,c137]) ).
cnf(c139,plain,
least_upper_bound(identity,least_upper_bound(b,X2)) = least_upper_bound(X2,b),
inference(transitivity,[status(thm)],[c134,c138]) ).
cnf(c140,plain,
least_upper_bound(identity,least_upper_bound(X2,b)) = least_upper_bound(X2,b),
inference(transitivity,[status(thm)],[c132,c139]) ).
cnf(c141,plain,
least_upper_bound(X2,b) = least_upper_bound(identity,least_upper_bound(X2,b)),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
greatest_lower_bound(identity,least_upper_bound(X2,b)) = greatest_lower_bound(identity,least_upper_bound(identity,least_upper_bound(X2,b))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
greatest_lower_bound(identity,least_upper_bound(identity,least_upper_bound(X2,b))) = identity,
inference(substitution,[status(thm)],[c15]) ).
cnf(c144,plain,
greatest_lower_bound(identity,least_upper_bound(X2,b)) = identity,
inference(transitivity,[status(thm)],[c142,c143]) ).
cnf(c145,plain,
greatest_lower_bound(identity,least_upper_bound(multiply(b,c),b)) = identity,
inference(substitution,[status(thm)],[c144]) ).
cnf(c146,plain,
greatest_lower_bound(identity,multiply(b,c)) = identity,
inference(transitivity,[status(thm)],[c129,c145]) ).
cnf(c147,plain,
greatest_lower_bound(multiply(b,c),identity) = identity,
inference(transitivity,[status(thm)],[c126,c146]) ).
cnf(c148,plain,
multiply(greatest_lower_bound(multiply(b,c),identity),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
multiply(greatest_lower_bound(multiply(b,c),identity),X2) = X2,
inference(transitivity,[status(thm)],[c148,c52]) ).
cnf(c150,plain,
multiply(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),b),X2) = X2,
inference(transitivity,[status(thm)],[c124,c149]) ).
cnf(c151,plain,
greatest_lower_bound(multiply(b,X2),multiply(greatest_lower_bound(a,multiply(b,c)),X2)) = X2,
inference(transitivity,[status(thm)],[c103,c150]) ).
cnf(c152,plain,
greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,multiply(b,c)),c)) = c,
inference(substitution,[status(thm)],[c151]) ).
cnf(c153,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,multiply(b,c)),c))) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,multiply(b,X2))) = greatest_lower_bound(greatest_lower_bound(X3,multiply(b,X2)),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c155,plain,
greatest_lower_bound(greatest_lower_bound(X3,multiply(b,X2)),X2) = greatest_lower_bound(X2,greatest_lower_bound(X3,multiply(b,X2))),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,multiply(b,X2))) = greatest_lower_bound(multiply(b,X2),greatest_lower_bound(X3,X2)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c157,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X3,greatest_lower_bound(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c158,plain,
greatest_lower_bound(X3,greatest_lower_bound(X4,X2)) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c27]) ).
cnf(c160,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X2,X3)),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c162,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c160,c162]) ).
cnf(c164,plain,
greatest_lower_bound(X3,greatest_lower_bound(X4,X2)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c158,c163]) ).
cnf(c165,plain,
greatest_lower_bound(multiply(b,X3),greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(multiply(b,X3),X3)),
inference(substitution,[status(thm)],[c164]) ).
cnf(c166,plain,
greatest_lower_bound(X2,multiply(b,X2)) = greatest_lower_bound(multiply(b,X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c167,plain,
greatest_lower_bound(multiply(b,X2),X2) = greatest_lower_bound(X2,multiply(b,X2)),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c168,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c169,plain,
least_upper_bound(multiply(b,X2),X2) = least_upper_bound(multiply(b,X2),multiply(identity,X2)),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,axiom,
multiply(least_upper_bound(Y2,Z2),X2) = least_upper_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub2) ).
cnf(c171,plain,
multiply(least_upper_bound(X3,X4),X2) = least_upper_bound(multiply(X3,X2),multiply(X4,X2)),
inference(substitution,[status(thm)],[c170]) ).
cnf(c172,plain,
least_upper_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(least_upper_bound(X3,X4),X2),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c174,plain,
multiply(least_upper_bound(X3,X4),X2) = multiply(least_upper_bound(X4,X3),X2),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
least_upper_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(least_upper_bound(X4,X3),X2),
inference(transitivity,[status(thm)],[c172,c174]) ).
cnf(c176,plain,
least_upper_bound(multiply(b,X2),multiply(identity,X2)) = multiply(least_upper_bound(identity,b),X2),
inference(substitution,[status(thm)],[c175]) ).
cnf(c177,plain,
multiply(least_upper_bound(identity,b),X2) = multiply(b,X2),
inference(congruence,[status(thm)],[c135]) ).
cnf(c178,plain,
least_upper_bound(multiply(b,X2),multiply(identity,X2)) = multiply(b,X2),
inference(transitivity,[status(thm)],[c176,c177]) ).
cnf(c179,plain,
least_upper_bound(multiply(b,X2),X2) = multiply(b,X2),
inference(transitivity,[status(thm)],[c169,c178]) ).
cnf(c180,plain,
multiply(b,X2) = least_upper_bound(multiply(b,X2),X2),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
greatest_lower_bound(X2,multiply(b,X2)) = greatest_lower_bound(X2,least_upper_bound(multiply(b,X2),X2)),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
greatest_lower_bound(X2,least_upper_bound(multiply(b,X2),X2)) = X2,
inference(substitution,[status(thm)],[c85]) ).
cnf(c183,plain,
greatest_lower_bound(X2,multiply(b,X2)) = X2,
inference(transitivity,[status(thm)],[c181,c182]) ).
cnf(c184,plain,
greatest_lower_bound(multiply(b,X2),X2) = X2,
inference(transitivity,[status(thm)],[c167,c183]) ).
cnf(c185,plain,
greatest_lower_bound(X2,greatest_lower_bound(multiply(b,X3),X3)) = greatest_lower_bound(X2,X3),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
greatest_lower_bound(multiply(b,X3),greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,X3),
inference(transitivity,[status(thm)],[c165,c185]) ).
cnf(c187,plain,
greatest_lower_bound(multiply(b,X2),greatest_lower_bound(X3,X2)) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c186]) ).
cnf(c188,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,multiply(b,X2))) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c156,c187]) ).
cnf(c189,plain,
greatest_lower_bound(greatest_lower_bound(X3,multiply(b,X2)),X2) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c155,c188]) ).
cnf(c190,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c) = greatest_lower_bound(a,c),
inference(substitution,[status(thm)],[c189]) ).
cnf(c191,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,multiply(b,c)),c))) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[c153,c190]) ).
cnf(c192,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(b,c)) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[c96,c191]) ).
cnf(c193,plain,
greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[c26,c192]) ).
cnf(c194,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[c24,c193]) ).
cnf(c195,plain,
$false,
inference(resolution,[status(thm)],[c1,c194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP178-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 09:36:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.26/0.72 Command-line arguments: --flatten-regeneralise
% 2.26/0.72
% 2.26/0.72 % SZS status Unsatisfiable
% 2.26/0.72
% 2.26/0.73 % SZS output start CNFRefutation
% See solution above
% 3.04/0.82
% 3.04/0.82 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------