%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP167-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 10:09:30 AM UTC 2026
% Result : Unsatisfiable 15.72s 2.55s
% Output : CNFRefutation 17.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 17
% Syntax : Number of clauses : 226 ( 226 unt; 0 nHn; 8 RR)
% Number of literals : 226 ( 225 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 360 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p19) ).
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,multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity))) = greatest_lower_bound(multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
greatest_lower_bound(multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),X2) = greatest_lower_bound(X2,multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
greatest_lower_bound(X2,inverse(identity)) = greatest_lower_bound(inverse(identity),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
greatest_lower_bound(inverse(identity),X2) = greatest_lower_bound(X2,inverse(identity)),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c8,plain,
greatest_lower_bound(X2,inverse(identity)) = greatest_lower_bound(X2,identity),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
greatest_lower_bound(inverse(identity),X2) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c6,c8]) ).
cnf(c10,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(inverse(identity),X2),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(X3,greatest_lower_bound(X2,identity)) = multiply(X3,greatest_lower_bound(inverse(identity),X2)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
greatest_lower_bound(X2,inverse(identity)) = greatest_lower_bound(inverse(identity),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
greatest_lower_bound(inverse(identity),X2) = greatest_lower_bound(X2,inverse(identity)),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(X3,greatest_lower_bound(inverse(identity),X2)) = multiply(X3,greatest_lower_bound(X2,inverse(identity))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
greatest_lower_bound(inverse(identity),X2) = greatest_lower_bound(X2,inverse(identity)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c16,plain,
greatest_lower_bound(X2,inverse(identity)) = greatest_lower_bound(inverse(identity),X2),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(X3,greatest_lower_bound(X2,inverse(identity))) = multiply(X3,greatest_lower_bound(inverse(identity),X2)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,axiom,
multiply(X2,greatest_lower_bound(Y2,Z)) = greatest_lower_bound(multiply(X2,Y2),multiply(X2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb1) ).
cnf(c19,plain,
multiply(X3,greatest_lower_bound(inverse(identity),X2)) = greatest_lower_bound(multiply(X3,inverse(identity)),multiply(X3,X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,axiom,
inverse(inverse(X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c21,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
multiply(X2,inverse(identity)) = multiply(inverse(inverse(X2)),inverse(identity)),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c24,plain,
inverse(identity) = inverse(inverse(identity)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(inverse(X2),inverse(identity)) = multiply(inverse(X2),inverse(inverse(identity))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,axiom,
inverse(multiply(X2,Y2)) = multiply(inverse(Y2),inverse(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19_3) ).
cnf(c27,plain,
inverse(multiply(inverse(identity),X2)) = multiply(inverse(X2),inverse(inverse(identity))),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(inverse(X2),inverse(inverse(identity))) = inverse(multiply(inverse(identity),X2)),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(inverse(identity),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c7]) ).
cnf(c30,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c31,plain,
multiply(inverse(identity),X2) = X2,
inference(transitivity,[status(thm)],[c29,c30]) ).
cnf(c32,plain,
inverse(multiply(inverse(identity),X2)) = inverse(X2),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(inverse(X2),inverse(inverse(identity))) = inverse(X2),
inference(transitivity,[status(thm)],[c28,c32]) ).
cnf(c34,plain,
multiply(inverse(X2),inverse(identity)) = inverse(X2),
inference(transitivity,[status(thm)],[c25,c33]) ).
cnf(c35,plain,
multiply(inverse(inverse(X2)),inverse(identity)) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
multiply(inverse(inverse(X2)),inverse(identity)) = X2,
inference(transitivity,[status(thm)],[c35,c20]) ).
cnf(c37,plain,
multiply(X2,inverse(identity)) = X2,
inference(transitivity,[status(thm)],[c22,c36]) ).
cnf(c38,plain,
greatest_lower_bound(multiply(X3,inverse(identity)),multiply(X3,X2)) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
multiply(X3,greatest_lower_bound(inverse(identity),X2)) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c19,c38]) ).
cnf(c40,plain,
multiply(X3,greatest_lower_bound(X2,inverse(identity))) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c17,c39]) ).
cnf(c41,plain,
multiply(X3,greatest_lower_bound(inverse(identity),X2)) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c14,c40]) ).
cnf(c42,plain,
multiply(X3,greatest_lower_bound(X2,identity)) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c11,c41]) ).
cnf(c43,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)) = greatest_lower_bound(least_upper_bound(X2,identity),multiply(least_upper_bound(X2,identity),X2)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
greatest_lower_bound(X2,multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity))) = greatest_lower_bound(X2,greatest_lower_bound(least_upper_bound(X2,identity),multiply(least_upper_bound(X2,identity),X2))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
greatest_lower_bound(multiply(least_upper_bound(X4,identity),X3),X2) = greatest_lower_bound(X2,multiply(least_upper_bound(X4,identity),X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c46,plain,
greatest_lower_bound(X3,multiply(least_upper_bound(X2,identity),X4)) = greatest_lower_bound(multiply(least_upper_bound(X2,identity),X4),X3),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
greatest_lower_bound(X4,greatest_lower_bound(X3,multiply(least_upper_bound(X2,identity),X4))) = greatest_lower_bound(X4,greatest_lower_bound(multiply(least_upper_bound(X2,identity),X4),X3)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,axiom,
greatest_lower_bound(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(greatest_lower_bound(X2,Y2),Z2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_glb) ).
cnf(c49,plain,
greatest_lower_bound(X4,greatest_lower_bound(multiply(least_upper_bound(X2,identity),X4),X3)) = greatest_lower_bound(greatest_lower_bound(X4,multiply(least_upper_bound(X2,identity),X4)),X3),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
greatest_lower_bound(X2,inverse(identity)) = greatest_lower_bound(inverse(identity),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c51,plain,
greatest_lower_bound(inverse(identity),X2) = greatest_lower_bound(X2,inverse(identity)),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(greatest_lower_bound(inverse(identity),X2),X3) = multiply(greatest_lower_bound(X2,inverse(identity)),X3),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
greatest_lower_bound(inverse(identity),X2) = greatest_lower_bound(X2,inverse(identity)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c54,plain,
greatest_lower_bound(X2,inverse(identity)) = greatest_lower_bound(inverse(identity),X2),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(greatest_lower_bound(X3,inverse(identity)),X2) = multiply(greatest_lower_bound(inverse(identity),X3),X2),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,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(c57,plain,
multiply(greatest_lower_bound(inverse(identity),X3),X2) = greatest_lower_bound(multiply(inverse(identity),X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
greatest_lower_bound(multiply(inverse(identity),X2),multiply(X3,X2)) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c59,plain,
multiply(greatest_lower_bound(inverse(identity),X3),X2) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
multiply(greatest_lower_bound(X3,inverse(identity)),X2) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c55,c59]) ).
cnf(c61,plain,
multiply(greatest_lower_bound(X2,inverse(identity)),X3) = greatest_lower_bound(X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
multiply(greatest_lower_bound(inverse(identity),X2),X3) = greatest_lower_bound(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c52,c61]) ).
cnf(c63,plain,
multiply(greatest_lower_bound(inverse(identity),least_upper_bound(X2,identity)),X3) = greatest_lower_bound(X3,multiply(least_upper_bound(X2,identity),X3)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
greatest_lower_bound(X3,multiply(least_upper_bound(X2,identity),X3)) = multiply(greatest_lower_bound(inverse(identity),least_upper_bound(X2,identity)),X3),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c66,plain,
least_upper_bound(X2,inverse(identity)) = least_upper_bound(inverse(identity),X2),
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
least_upper_bound(inverse(identity),X2) = least_upper_bound(X2,inverse(identity)),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
least_upper_bound(X2,inverse(identity)) = least_upper_bound(X2,identity),
inference(congruence,[status(thm)],[c7]) ).
cnf(c69,plain,
least_upper_bound(inverse(identity),X2) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c67,c68]) ).
cnf(c70,plain,
least_upper_bound(X2,identity) = least_upper_bound(inverse(identity),X2),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
greatest_lower_bound(inverse(identity),least_upper_bound(X2,identity)) = greatest_lower_bound(inverse(identity),least_upper_bound(inverse(identity),X2)),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c73,plain,
greatest_lower_bound(inverse(identity),least_upper_bound(inverse(identity),X2)) = inverse(identity),
inference(substitution,[status(thm)],[c72]) ).
cnf(c74,plain,
greatest_lower_bound(inverse(identity),least_upper_bound(X2,identity)) = inverse(identity),
inference(transitivity,[status(thm)],[c71,c73]) ).
cnf(c75,plain,
multiply(greatest_lower_bound(inverse(identity),least_upper_bound(X2,identity)),X3) = multiply(inverse(identity),X3),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
multiply(greatest_lower_bound(inverse(identity),least_upper_bound(X2,identity)),X3) = X3,
inference(transitivity,[status(thm)],[c75,c31]) ).
cnf(c77,plain,
greatest_lower_bound(X3,multiply(least_upper_bound(X2,identity),X3)) = X3,
inference(transitivity,[status(thm)],[c64,c76]) ).
cnf(c78,plain,
greatest_lower_bound(greatest_lower_bound(X4,multiply(least_upper_bound(X2,identity),X4)),X3) = greatest_lower_bound(X4,X3),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
greatest_lower_bound(X4,greatest_lower_bound(multiply(least_upper_bound(X2,identity),X4),X3)) = greatest_lower_bound(X4,X3),
inference(transitivity,[status(thm)],[c49,c78]) ).
cnf(c80,plain,
greatest_lower_bound(X4,greatest_lower_bound(X3,multiply(least_upper_bound(X2,identity),X4))) = greatest_lower_bound(X4,X3),
inference(transitivity,[status(thm)],[c47,c79]) ).
cnf(c81,plain,
greatest_lower_bound(X2,greatest_lower_bound(least_upper_bound(X2,identity),multiply(least_upper_bound(X2,identity),X2))) = greatest_lower_bound(X2,least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
greatest_lower_bound(X2,least_upper_bound(X2,identity)) = greatest_lower_bound(least_upper_bound(X2,identity),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c83,plain,
greatest_lower_bound(X2,least_upper_bound(X2,identity)) = greatest_lower_bound(least_upper_bound(X2,identity),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c84,plain,
greatest_lower_bound(least_upper_bound(X2,identity),X2) = greatest_lower_bound(X2,least_upper_bound(X2,identity)),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
least_upper_bound(X2,identity) = least_upper_bound(inverse(identity),X2),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c86,plain,
greatest_lower_bound(X2,least_upper_bound(X2,identity)) = greatest_lower_bound(X2,least_upper_bound(inverse(identity),X2)),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c65]) ).
cnf(c88,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c72]) ).
cnf(c91,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c89,c90]) ).
cnf(c92,plain,
greatest_lower_bound(X2,least_upper_bound(inverse(identity),X2)) = X2,
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
greatest_lower_bound(X2,least_upper_bound(X2,identity)) = X2,
inference(transitivity,[status(thm)],[c86,c92]) ).
cnf(c94,plain,
greatest_lower_bound(least_upper_bound(X2,identity),X2) = X2,
inference(transitivity,[status(thm)],[c84,c93]) ).
cnf(c95,plain,
greatest_lower_bound(X2,least_upper_bound(X2,identity)) = X2,
inference(transitivity,[status(thm)],[c82,c94]) ).
cnf(c96,plain,
greatest_lower_bound(X2,greatest_lower_bound(least_upper_bound(X2,identity),multiply(least_upper_bound(X2,identity),X2))) = X2,
inference(transitivity,[status(thm)],[c81,c95]) ).
cnf(c97,plain,
greatest_lower_bound(X2,multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity))) = X2,
inference(transitivity,[status(thm)],[c44,c96]) ).
cnf(c98,plain,
greatest_lower_bound(multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),X2) = X2,
inference(transitivity,[status(thm)],[c4,c97]) ).
cnf(c99,plain,
X2 = greatest_lower_bound(multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),X2),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
least_upper_bound(multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),X2) = least_upper_bound(multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),greatest_lower_bound(multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),X2)),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c102,plain,
least_upper_bound(multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),greatest_lower_bound(multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),X2)) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
least_upper_bound(multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),X2) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),
inference(transitivity,[status(thm)],[c100,c102]) ).
cnf(c104,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)) = least_upper_bound(multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),X2),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
least_upper_bound(X2,multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity))) = least_upper_bound(multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),X2),
inference(substitution,[status(thm)],[c65]) ).
cnf(c106,plain,
least_upper_bound(multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),X2) = least_upper_bound(X2,multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity))),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,axiom,
multiply(multiply(X2,Y2),Z2) = multiply(X2,multiply(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
cnf(c108,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c107]) ).
cnf(c109,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c111,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c112,plain,
multiply(inverse(X2),X2) = inverse(identity),
inference(transitivity,[status(thm)],[c110,c111]) ).
cnf(c113,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(identity),X2),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c113,c31]) ).
cnf(c115,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c109,c114]) ).
cnf(c116,plain,
multiply(inverse(X2),multiply(X2,multiply(least_upper_bound(X3,identity),greatest_lower_bound(X3,identity)))) = multiply(least_upper_bound(X3,identity),greatest_lower_bound(X3,identity)),
inference(substitution,[status(thm)],[c115]) ).
cnf(c117,plain,
multiply(least_upper_bound(X3,identity),greatest_lower_bound(X3,identity)) = multiply(inverse(X2),multiply(X2,multiply(least_upper_bound(X3,identity),greatest_lower_bound(X3,identity)))),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
least_upper_bound(X2,identity) = least_upper_bound(inverse(identity),X2),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c119,plain,
multiply(X3,least_upper_bound(X2,identity)) = multiply(X3,least_upper_bound(inverse(identity),X2)),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
least_upper_bound(X2,inverse(identity)) = least_upper_bound(inverse(identity),X2),
inference(substitution,[status(thm)],[c65]) ).
cnf(c121,plain,
least_upper_bound(inverse(identity),X2) = least_upper_bound(X2,inverse(identity)),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
multiply(X3,least_upper_bound(inverse(identity),X2)) = multiply(X3,least_upper_bound(X2,inverse(identity))),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
least_upper_bound(inverse(identity),X2) = least_upper_bound(X2,inverse(identity)),
inference(substitution,[status(thm)],[c65]) ).
cnf(c124,plain,
least_upper_bound(X2,inverse(identity)) = least_upper_bound(inverse(identity),X2),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
multiply(X3,least_upper_bound(X2,inverse(identity))) = multiply(X3,least_upper_bound(inverse(identity),X2)),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,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(c127,plain,
multiply(X3,least_upper_bound(inverse(identity),X2)) = least_upper_bound(multiply(X3,inverse(identity)),multiply(X3,X2)),
inference(substitution,[status(thm)],[c126]) ).
cnf(c128,plain,
least_upper_bound(multiply(X3,inverse(identity)),multiply(X3,X2)) = least_upper_bound(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c129,plain,
multiply(X3,least_upper_bound(inverse(identity),X2)) = least_upper_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c127,c128]) ).
cnf(c130,plain,
multiply(X3,least_upper_bound(X2,inverse(identity))) = least_upper_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c125,c129]) ).
cnf(c131,plain,
multiply(X3,least_upper_bound(inverse(identity),X2)) = least_upper_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c122,c130]) ).
cnf(c132,plain,
multiply(X3,least_upper_bound(X2,identity)) = least_upper_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c119,c131]) ).
cnf(c133,plain,
multiply(multiply(X3,greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)) = least_upper_bound(multiply(X3,greatest_lower_bound(X2,identity)),multiply(multiply(X3,greatest_lower_bound(X2,identity)),X2)),
inference(substitution,[status(thm)],[c132]) ).
cnf(c134,plain,
multiply(multiply(X3,greatest_lower_bound(X2,identity)),X2) = multiply(X3,multiply(greatest_lower_bound(X2,identity),X2)),
inference(substitution,[status(thm)],[c107]) ).
cnf(c135,plain,
least_upper_bound(multiply(X3,greatest_lower_bound(X2,identity)),multiply(multiply(X3,greatest_lower_bound(X2,identity)),X2)) = least_upper_bound(multiply(X3,greatest_lower_bound(X2,identity)),multiply(X3,multiply(greatest_lower_bound(X2,identity),X2))),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(inverse(identity),X2),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c137,plain,
multiply(greatest_lower_bound(X2,identity),X3) = multiply(greatest_lower_bound(inverse(identity),X2),X3),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
multiply(greatest_lower_bound(X2,identity),X3) = greatest_lower_bound(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c137,c62]) ).
cnf(c139,plain,
multiply(greatest_lower_bound(X2,identity),X2) = greatest_lower_bound(X2,multiply(X2,X2)),
inference(substitution,[status(thm)],[c138]) ).
cnf(c140,plain,
multiply(X2,greatest_lower_bound(inverse(identity),X2)) = greatest_lower_bound(X2,multiply(X2,X2)),
inference(substitution,[status(thm)],[c41]) ).
cnf(c141,plain,
greatest_lower_bound(X2,multiply(X2,X2)) = multiply(X2,greatest_lower_bound(inverse(identity),X2)),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
multiply(X2,greatest_lower_bound(inverse(identity),X2)) = multiply(X2,greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c143,plain,
greatest_lower_bound(X2,multiply(X2,X2)) = multiply(X2,greatest_lower_bound(X2,identity)),
inference(transitivity,[status(thm)],[c141,c142]) ).
cnf(c144,plain,
multiply(greatest_lower_bound(X2,identity),X2) = multiply(X2,greatest_lower_bound(X2,identity)),
inference(transitivity,[status(thm)],[c139,c143]) ).
cnf(c145,plain,
multiply(X3,multiply(greatest_lower_bound(X2,identity),X2)) = multiply(X3,multiply(X2,greatest_lower_bound(X2,identity))),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
least_upper_bound(multiply(X3,greatest_lower_bound(X2,identity)),multiply(X3,multiply(greatest_lower_bound(X2,identity),X2))) = least_upper_bound(multiply(X3,greatest_lower_bound(X2,identity)),multiply(X3,multiply(X2,greatest_lower_bound(X2,identity)))),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
multiply(multiply(X3,X2),greatest_lower_bound(X2,identity)) = multiply(X3,multiply(X2,greatest_lower_bound(X2,identity))),
inference(substitution,[status(thm)],[c107]) ).
cnf(c148,plain,
multiply(X3,multiply(X2,greatest_lower_bound(X2,identity))) = multiply(multiply(X3,X2),greatest_lower_bound(X2,identity)),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
least_upper_bound(multiply(X3,greatest_lower_bound(X2,identity)),multiply(X3,multiply(X2,greatest_lower_bound(X2,identity)))) = least_upper_bound(multiply(X3,greatest_lower_bound(X2,identity)),multiply(multiply(X3,X2),greatest_lower_bound(X2,identity))),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,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(c151,plain,
multiply(least_upper_bound(X3,multiply(X3,X2)),greatest_lower_bound(X2,identity)) = least_upper_bound(multiply(X3,greatest_lower_bound(X2,identity)),multiply(multiply(X3,X2),greatest_lower_bound(X2,identity))),
inference(substitution,[status(thm)],[c150]) ).
cnf(c152,plain,
least_upper_bound(multiply(X3,greatest_lower_bound(X2,identity)),multiply(multiply(X3,X2),greatest_lower_bound(X2,identity))) = multiply(least_upper_bound(X3,multiply(X3,X2)),greatest_lower_bound(X2,identity)),
inference(symmetry,[status(thm)],[c151]) ).
cnf(c153,plain,
least_upper_bound(X3,multiply(X3,X2)) = multiply(X3,least_upper_bound(X2,identity)),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c154,plain,
multiply(least_upper_bound(X3,multiply(X3,X2)),greatest_lower_bound(X2,identity)) = multiply(multiply(X3,least_upper_bound(X2,identity)),greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
multiply(multiply(X3,least_upper_bound(X2,identity)),greatest_lower_bound(X2,identity)) = multiply(X3,multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity))),
inference(substitution,[status(thm)],[c107]) ).
cnf(c156,plain,
multiply(least_upper_bound(X3,multiply(X3,X2)),greatest_lower_bound(X2,identity)) = multiply(X3,multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity))),
inference(transitivity,[status(thm)],[c154,c155]) ).
cnf(c157,plain,
least_upper_bound(multiply(X3,greatest_lower_bound(X2,identity)),multiply(multiply(X3,X2),greatest_lower_bound(X2,identity))) = multiply(X3,multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity))),
inference(transitivity,[status(thm)],[c152,c156]) ).
cnf(c158,plain,
least_upper_bound(multiply(X3,greatest_lower_bound(X2,identity)),multiply(X3,multiply(X2,greatest_lower_bound(X2,identity)))) = multiply(X3,multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity))),
inference(transitivity,[status(thm)],[c149,c157]) ).
cnf(c159,plain,
least_upper_bound(multiply(X3,greatest_lower_bound(X2,identity)),multiply(X3,multiply(greatest_lower_bound(X2,identity),X2))) = multiply(X3,multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity))),
inference(transitivity,[status(thm)],[c146,c158]) ).
cnf(c160,plain,
least_upper_bound(multiply(X3,greatest_lower_bound(X2,identity)),multiply(multiply(X3,greatest_lower_bound(X2,identity)),X2)) = multiply(X3,multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity))),
inference(transitivity,[status(thm)],[c135,c159]) ).
cnf(c161,plain,
multiply(multiply(X3,greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)) = multiply(X3,multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity))),
inference(transitivity,[status(thm)],[c133,c160]) ).
cnf(c162,plain,
multiply(multiply(X2,greatest_lower_bound(X3,identity)),least_upper_bound(X3,identity)) = multiply(X2,multiply(least_upper_bound(X3,identity),greatest_lower_bound(X3,identity))),
inference(substitution,[status(thm)],[c161]) ).
cnf(c163,plain,
multiply(X2,multiply(least_upper_bound(X3,identity),greatest_lower_bound(X3,identity))) = multiply(multiply(X2,greatest_lower_bound(X3,identity)),least_upper_bound(X3,identity)),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
multiply(inverse(X2),multiply(X2,multiply(least_upper_bound(X3,identity),greatest_lower_bound(X3,identity)))) = multiply(inverse(X2),multiply(multiply(X2,greatest_lower_bound(X3,identity)),least_upper_bound(X3,identity))),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c107]) ).
cnf(c166,plain,
multiply(inverse(X4),multiply(multiply(X4,X3),X2)) = multiply(inverse(X4),multiply(X4,multiply(X3,X2))),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
multiply(inverse(X4),multiply(X4,multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c115]) ).
cnf(c168,plain,
multiply(inverse(X4),multiply(multiply(X4,X3),X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c166,c167]) ).
cnf(c169,plain,
multiply(inverse(X2),multiply(multiply(X2,greatest_lower_bound(X3,identity)),least_upper_bound(X3,identity))) = multiply(greatest_lower_bound(X3,identity),least_upper_bound(X3,identity)),
inference(substitution,[status(thm)],[c168]) ).
cnf(c170,plain,
multiply(inverse(X2),multiply(X2,multiply(least_upper_bound(X3,identity),greatest_lower_bound(X3,identity)))) = multiply(greatest_lower_bound(X3,identity),least_upper_bound(X3,identity)),
inference(transitivity,[status(thm)],[c164,c169]) ).
cnf(c171,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c117,c170]) ).
cnf(c172,plain,
least_upper_bound(X2,multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity))) = least_upper_bound(X2,multiply(greatest_lower_bound(X2,identity),least_upper_bound(X2,identity))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
multiply(greatest_lower_bound(X2,identity),least_upper_bound(X2,identity)) = least_upper_bound(greatest_lower_bound(X2,identity),multiply(greatest_lower_bound(X2,identity),X2)),
inference(substitution,[status(thm)],[c132]) ).
cnf(c174,plain,
least_upper_bound(X2,multiply(greatest_lower_bound(X2,identity),least_upper_bound(X2,identity))) = least_upper_bound(X2,least_upper_bound(greatest_lower_bound(X2,identity),multiply(greatest_lower_bound(X2,identity),X2))),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
least_upper_bound(multiply(greatest_lower_bound(X2,identity),X4),X3) = least_upper_bound(X3,multiply(greatest_lower_bound(X2,identity),X4)),
inference(substitution,[status(thm)],[c65]) ).
cnf(c176,plain,
least_upper_bound(X3,multiply(greatest_lower_bound(X2,identity),X4)) = least_upper_bound(multiply(greatest_lower_bound(X2,identity),X4),X3),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
least_upper_bound(X4,least_upper_bound(X3,multiply(greatest_lower_bound(X2,identity),X4))) = least_upper_bound(X4,least_upper_bound(multiply(greatest_lower_bound(X2,identity),X4),X3)),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,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(c179,plain,
least_upper_bound(X4,least_upper_bound(multiply(greatest_lower_bound(X2,identity),X4),X3)) = least_upper_bound(least_upper_bound(X4,multiply(greatest_lower_bound(X2,identity),X4)),X3),
inference(substitution,[status(thm)],[c178]) ).
cnf(c180,plain,
least_upper_bound(X2,inverse(identity)) = least_upper_bound(inverse(identity),X2),
inference(substitution,[status(thm)],[c65]) ).
cnf(c181,plain,
least_upper_bound(inverse(identity),X2) = least_upper_bound(X2,inverse(identity)),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
multiply(least_upper_bound(inverse(identity),X2),X3) = multiply(least_upper_bound(X2,inverse(identity)),X3),
inference(congruence,[status(thm)],[c181]) ).
cnf(c183,plain,
least_upper_bound(inverse(identity),X2) = least_upper_bound(X2,inverse(identity)),
inference(substitution,[status(thm)],[c65]) ).
cnf(c184,plain,
least_upper_bound(X2,inverse(identity)) = least_upper_bound(inverse(identity),X2),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
multiply(least_upper_bound(X3,inverse(identity)),X2) = multiply(least_upper_bound(inverse(identity),X3),X2),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
multiply(least_upper_bound(inverse(identity),X3),X2) = least_upper_bound(multiply(inverse(identity),X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c150]) ).
cnf(c187,plain,
least_upper_bound(multiply(inverse(identity),X2),multiply(X3,X2)) = least_upper_bound(X2,multiply(X3,X2)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c188,plain,
multiply(least_upper_bound(inverse(identity),X3),X2) = least_upper_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c186,c187]) ).
cnf(c189,plain,
multiply(least_upper_bound(X3,inverse(identity)),X2) = least_upper_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c185,c188]) ).
cnf(c190,plain,
multiply(least_upper_bound(X2,inverse(identity)),X3) = least_upper_bound(X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c189]) ).
cnf(c191,plain,
multiply(least_upper_bound(inverse(identity),X2),X3) = least_upper_bound(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c182,c190]) ).
cnf(c192,plain,
multiply(least_upper_bound(inverse(identity),greatest_lower_bound(X2,identity)),X3) = least_upper_bound(X3,multiply(greatest_lower_bound(X2,identity),X3)),
inference(substitution,[status(thm)],[c191]) ).
cnf(c193,plain,
least_upper_bound(X3,multiply(greatest_lower_bound(X2,identity),X3)) = multiply(least_upper_bound(inverse(identity),greatest_lower_bound(X2,identity)),X3),
inference(symmetry,[status(thm)],[c192]) ).
cnf(c194,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(inverse(identity),X2),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c195,plain,
least_upper_bound(inverse(identity),greatest_lower_bound(X2,identity)) = least_upper_bound(inverse(identity),greatest_lower_bound(inverse(identity),X2)),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
least_upper_bound(inverse(identity),greatest_lower_bound(inverse(identity),X2)) = inverse(identity),
inference(substitution,[status(thm)],[c101]) ).
cnf(c197,plain,
least_upper_bound(inverse(identity),greatest_lower_bound(X2,identity)) = inverse(identity),
inference(transitivity,[status(thm)],[c195,c196]) ).
cnf(c198,plain,
multiply(least_upper_bound(inverse(identity),greatest_lower_bound(X2,identity)),X3) = multiply(inverse(identity),X3),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
multiply(least_upper_bound(inverse(identity),greatest_lower_bound(X2,identity)),X3) = X3,
inference(transitivity,[status(thm)],[c198,c31]) ).
cnf(c200,plain,
least_upper_bound(X3,multiply(greatest_lower_bound(X2,identity),X3)) = X3,
inference(transitivity,[status(thm)],[c193,c199]) ).
cnf(c201,plain,
least_upper_bound(least_upper_bound(X4,multiply(greatest_lower_bound(X2,identity),X4)),X3) = least_upper_bound(X4,X3),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
least_upper_bound(X4,least_upper_bound(multiply(greatest_lower_bound(X2,identity),X4),X3)) = least_upper_bound(X4,X3),
inference(transitivity,[status(thm)],[c179,c201]) ).
cnf(c203,plain,
least_upper_bound(X4,least_upper_bound(X3,multiply(greatest_lower_bound(X2,identity),X4))) = least_upper_bound(X4,X3),
inference(transitivity,[status(thm)],[c177,c202]) ).
cnf(c204,plain,
least_upper_bound(X2,least_upper_bound(greatest_lower_bound(X2,identity),multiply(greatest_lower_bound(X2,identity),X2))) = least_upper_bound(X2,greatest_lower_bound(X2,identity)),
inference(substitution,[status(thm)],[c203]) ).
cnf(c205,plain,
least_upper_bound(X2,greatest_lower_bound(X2,identity)) = least_upper_bound(greatest_lower_bound(X2,identity),X2),
inference(substitution,[status(thm)],[c65]) ).
cnf(c206,plain,
least_upper_bound(X2,greatest_lower_bound(X2,identity)) = least_upper_bound(greatest_lower_bound(X2,identity),X2),
inference(substitution,[status(thm)],[c65]) ).
cnf(c207,plain,
least_upper_bound(greatest_lower_bound(X2,identity),X2) = least_upper_bound(X2,greatest_lower_bound(X2,identity)),
inference(symmetry,[status(thm)],[c206]) ).
cnf(c208,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(inverse(identity),X2),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c209,plain,
least_upper_bound(X2,greatest_lower_bound(X2,identity)) = least_upper_bound(X2,greatest_lower_bound(inverse(identity),X2)),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c211,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c212,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c101]) ).
cnf(c214,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c212,c213]) ).
cnf(c215,plain,
least_upper_bound(X2,greatest_lower_bound(inverse(identity),X2)) = X2,
inference(substitution,[status(thm)],[c214]) ).
cnf(c216,plain,
least_upper_bound(X2,greatest_lower_bound(X2,identity)) = X2,
inference(transitivity,[status(thm)],[c209,c215]) ).
cnf(c217,plain,
least_upper_bound(greatest_lower_bound(X2,identity),X2) = X2,
inference(transitivity,[status(thm)],[c207,c216]) ).
cnf(c218,plain,
least_upper_bound(X2,greatest_lower_bound(X2,identity)) = X2,
inference(transitivity,[status(thm)],[c205,c217]) ).
cnf(c219,plain,
least_upper_bound(X2,least_upper_bound(greatest_lower_bound(X2,identity),multiply(greatest_lower_bound(X2,identity),X2))) = X2,
inference(transitivity,[status(thm)],[c204,c218]) ).
cnf(c220,plain,
least_upper_bound(X2,multiply(greatest_lower_bound(X2,identity),least_upper_bound(X2,identity))) = X2,
inference(transitivity,[status(thm)],[c174,c219]) ).
cnf(c221,plain,
least_upper_bound(X2,multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity))) = X2,
inference(transitivity,[status(thm)],[c172,c220]) ).
cnf(c222,plain,
least_upper_bound(multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)),X2) = X2,
inference(transitivity,[status(thm)],[c106,c221]) ).
cnf(c223,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(X2,identity)) = X2,
inference(transitivity,[status(thm)],[c104,c222]) ).
cnf(c224,plain,
multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) = a,
inference(substitution,[status(thm)],[c223]) ).
cnf(c225,plain,
a = multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
$false,
inference(resolution,[status(thm)],[c1,c225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP167-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n011.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sun Sep 27 09:34:59 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.72/2.55 Command-line arguments: --flatten --complete-subsets
% 15.72/2.55
% 15.72/2.55 % SZS status Unsatisfiable
% 15.72/2.55
% 15.72/2.57 % SZS output start CNFRefutation
% See solution above
% 17.20/2.76
% 17.20/2.76 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------