%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP186-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 10:09:38 AM UTC 2026
% Result : Unsatisfiable 14.51s 2.37s
% Output : CNFRefutation 14.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 14
% Syntax : Number of clauses : 418 ( 418 unt; 0 nHn; 4 RR)
% Number of literals : 418 ( 417 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 887 ( 46 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
least_upper_bound(multiply(a,b),identity) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p23) ).
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(multiply(X4,X2),multiply(X4,inverse(greatest_lower_bound(X3,inverse(X2))))) = least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X3,inverse(X2)))),multiply(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X3,inverse(X2)))),multiply(X4,X2)) = least_upper_bound(multiply(X4,X2),multiply(X4,inverse(greatest_lower_bound(X3,inverse(X2))))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(X2,least_upper_bound(Y2,Z)) = least_upper_bound(multiply(X2,Y2),multiply(X2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
cnf(c6,plain,
multiply(X4,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X4,X2),multiply(X4,X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
least_upper_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,least_upper_bound(X2,X3)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c9,plain,
multiply(X4,least_upper_bound(X2,X3)) = multiply(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
least_upper_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c7,c9]) ).
cnf(c11,plain,
least_upper_bound(multiply(X4,X2),multiply(X4,inverse(greatest_lower_bound(X3,inverse(X2))))) = multiply(X4,least_upper_bound(inverse(greatest_lower_bound(X3,inverse(X2))),X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
least_upper_bound(X2,inverse(greatest_lower_bound(X3,inverse(X2)))) = least_upper_bound(inverse(greatest_lower_bound(X3,inverse(X2))),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
least_upper_bound(inverse(greatest_lower_bound(X3,inverse(X2))),X2) = least_upper_bound(X2,inverse(greatest_lower_bound(X3,inverse(X2)))),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
multiply(multiply(X2,Y2),Z2) = multiply(X2,multiply(Y2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c15,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c18,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c20,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c18,c19]) ).
cnf(c21,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c16,c20]) ).
cnf(c22,plain,
X2 = multiply(inverse(X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(inverse(inverse(X3)),X2) = multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c21]) ).
cnf(c25,plain,
multiply(inverse(inverse(X3)),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c23,c24]) ).
cnf(c26,plain,
multiply(inverse(inverse(X2)),identity) = multiply(X2,identity),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(X2,identity) = multiply(inverse(inverse(X2)),identity),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c29,plain,
multiply(inverse(inverse(X2)),identity) = multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)) = X2,
inference(substitution,[status(thm)],[c21]) ).
cnf(c31,plain,
multiply(inverse(inverse(X2)),identity) = X2,
inference(transitivity,[status(thm)],[c29,c30]) ).
cnf(c32,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c27,c31]) ).
cnf(c33,plain,
multiply(inverse(inverse(X2)),identity) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
inverse(inverse(X2)) = multiply(inverse(inverse(X2)),identity),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
inverse(inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c34,c31]) ).
cnf(c36,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
least_upper_bound(X2,inverse(greatest_lower_bound(X3,inverse(X2)))) = least_upper_bound(inverse(inverse(X2)),inverse(greatest_lower_bound(X3,inverse(X2)))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c39,plain,
greatest_lower_bound(X3,inverse(X2)) = greatest_lower_bound(inverse(X2),X3),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
inverse(greatest_lower_bound(X3,inverse(X2))) = inverse(greatest_lower_bound(inverse(X2),X3)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
least_upper_bound(inverse(inverse(X2)),inverse(greatest_lower_bound(X3,inverse(X2)))) = least_upper_bound(inverse(inverse(X2)),inverse(greatest_lower_bound(inverse(X2),X3))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
multiply(inverse(X3),multiply(X3,inverse(greatest_lower_bound(X3,X2)))) = inverse(greatest_lower_bound(X3,X2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c43,plain,
inverse(greatest_lower_bound(X3,X2)) = multiply(inverse(X3),multiply(X3,inverse(greatest_lower_bound(X3,X2)))),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
least_upper_bound(inverse(X3),inverse(greatest_lower_bound(X3,X2))) = least_upper_bound(inverse(X3),multiply(inverse(X3),multiply(X3,inverse(greatest_lower_bound(X3,X2))))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c46,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(X3,least_upper_bound(X2,identity)) = multiply(X3,least_upper_bound(identity,X2)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(X3,least_upper_bound(identity,X2)) = least_upper_bound(multiply(X3,identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c49,plain,
least_upper_bound(multiply(X3,identity),multiply(X3,X2)) = least_upper_bound(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c50,plain,
multiply(X3,least_upper_bound(identity,X2)) = least_upper_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c48,c49]) ).
cnf(c51,plain,
multiply(X3,least_upper_bound(X2,identity)) = least_upper_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c47,c50]) ).
cnf(c52,plain,
multiply(inverse(X3),least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),identity)) = least_upper_bound(inverse(X3),multiply(inverse(X3),multiply(X3,inverse(greatest_lower_bound(X3,X2))))),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
least_upper_bound(inverse(X3),multiply(inverse(X3),multiply(X3,inverse(greatest_lower_bound(X3,X2))))) = multiply(inverse(X3),least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),identity)),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c55,plain,
multiply(X2,inverse(X2)) = multiply(inverse(inverse(X2)),inverse(X2)),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = identity,
inference(substitution,[status(thm)],[c17]) ).
cnf(c57,plain,
multiply(X2,inverse(X2)) = identity,
inference(transitivity,[status(thm)],[c55,c56]) ).
cnf(c58,plain,
multiply(greatest_lower_bound(X3,X2),inverse(greatest_lower_bound(X3,X2))) = identity,
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
identity = multiply(greatest_lower_bound(X3,X2),inverse(greatest_lower_bound(X3,X2))),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),identity) = least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),multiply(greatest_lower_bound(X3,X2),inverse(greatest_lower_bound(X3,X2)))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,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(c62,plain,
multiply(least_upper_bound(X3,X4),X2) = least_upper_bound(multiply(X3,X2),multiply(X4,X2)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
least_upper_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(least_upper_bound(X3,X4),X2),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c65,plain,
multiply(least_upper_bound(X3,X4),X2) = multiply(least_upper_bound(X4,X3),X2),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
least_upper_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(least_upper_bound(X4,X3),X2),
inference(transitivity,[status(thm)],[c63,c65]) ).
cnf(c67,plain,
least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),multiply(greatest_lower_bound(X3,X2),inverse(greatest_lower_bound(X3,X2)))) = multiply(least_upper_bound(greatest_lower_bound(X3,X2),X3),inverse(greatest_lower_bound(X3,X2))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = least_upper_bound(greatest_lower_bound(X3,X2),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c69,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X3) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c38]) ).
cnf(c71,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = least_upper_bound(X3,greatest_lower_bound(X2,X3)),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c73,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c75,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c73,c75]) ).
cnf(c77,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c71,c76]) ).
cnf(c78,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X3) = X3,
inference(transitivity,[status(thm)],[c69,c77]) ).
cnf(c79,plain,
multiply(least_upper_bound(greatest_lower_bound(X3,X2),X3),inverse(greatest_lower_bound(X3,X2))) = multiply(X3,inverse(greatest_lower_bound(X3,X2))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),multiply(greatest_lower_bound(X3,X2),inverse(greatest_lower_bound(X3,X2)))) = multiply(X3,inverse(greatest_lower_bound(X3,X2))),
inference(transitivity,[status(thm)],[c67,c79]) ).
cnf(c81,plain,
least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),identity) = multiply(X3,inverse(greatest_lower_bound(X3,X2))),
inference(transitivity,[status(thm)],[c60,c80]) ).
cnf(c82,plain,
multiply(inverse(X3),least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),identity)) = multiply(inverse(X3),multiply(X3,inverse(greatest_lower_bound(X3,X2)))),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(inverse(X3),multiply(X3,inverse(greatest_lower_bound(X3,X2)))) = inverse(greatest_lower_bound(X3,X2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c84,plain,
multiply(inverse(X3),least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),identity)) = inverse(greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c82,c83]) ).
cnf(c85,plain,
least_upper_bound(inverse(X3),multiply(inverse(X3),multiply(X3,inverse(greatest_lower_bound(X3,X2))))) = inverse(greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c53,c84]) ).
cnf(c86,plain,
least_upper_bound(inverse(X3),inverse(greatest_lower_bound(X3,X2))) = inverse(greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c44,c85]) ).
cnf(c87,plain,
least_upper_bound(inverse(inverse(X2)),inverse(greatest_lower_bound(inverse(X2),X3))) = inverse(greatest_lower_bound(inverse(X2),X3)),
inference(substitution,[status(thm)],[c86]) ).
cnf(c88,plain,
greatest_lower_bound(X3,inverse(X2)) = greatest_lower_bound(inverse(X2),X3),
inference(substitution,[status(thm)],[c38]) ).
cnf(c89,plain,
greatest_lower_bound(inverse(X2),X3) = greatest_lower_bound(X3,inverse(X2)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
inverse(greatest_lower_bound(inverse(X2),X3)) = inverse(greatest_lower_bound(X3,inverse(X2))),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
least_upper_bound(inverse(inverse(X2)),inverse(greatest_lower_bound(inverse(X2),X3))) = inverse(greatest_lower_bound(X3,inverse(X2))),
inference(transitivity,[status(thm)],[c87,c90]) ).
cnf(c92,plain,
least_upper_bound(inverse(inverse(X2)),inverse(greatest_lower_bound(X3,inverse(X2)))) = inverse(greatest_lower_bound(X3,inverse(X2))),
inference(transitivity,[status(thm)],[c41,c91]) ).
cnf(c93,plain,
least_upper_bound(X2,inverse(greatest_lower_bound(X3,inverse(X2)))) = inverse(greatest_lower_bound(X3,inverse(X2))),
inference(transitivity,[status(thm)],[c37,c92]) ).
cnf(c94,plain,
least_upper_bound(inverse(greatest_lower_bound(X3,inverse(X2))),X2) = inverse(greatest_lower_bound(X3,inverse(X2))),
inference(transitivity,[status(thm)],[c13,c93]) ).
cnf(c95,plain,
multiply(X4,least_upper_bound(inverse(greatest_lower_bound(X3,inverse(X2))),X2)) = multiply(X4,inverse(greatest_lower_bound(X3,inverse(X2)))),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
least_upper_bound(multiply(X4,X2),multiply(X4,inverse(greatest_lower_bound(X3,inverse(X2))))) = multiply(X4,inverse(greatest_lower_bound(X3,inverse(X2)))),
inference(transitivity,[status(thm)],[c11,c95]) ).
cnf(c97,plain,
least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X3,inverse(X2)))),multiply(X4,X2)) = multiply(X4,inverse(greatest_lower_bound(X3,inverse(X2)))),
inference(transitivity,[status(thm)],[c4,c96]) ).
cnf(c98,plain,
least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),multiply(X3,X2)) = multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),
inference(substitution,[status(thm)],[c97]) ).
cnf(c99,plain,
multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))) = least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X3,least_upper_bound(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c101,plain,
least_upper_bound(X3,least_upper_bound(X4,X2)) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,axiom,
least_upper_bound(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(least_upper_bound(X2,Y2),Z2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).
cnf(c103,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c102]) ).
cnf(c104,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X4,least_upper_bound(X2,X3)),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c106,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c104,c106]) ).
cnf(c108,plain,
least_upper_bound(X3,least_upper_bound(X4,X2)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c101,c107]) ).
cnf(c109,plain,
least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),least_upper_bound(X2,identity)) = least_upper_bound(X2,least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),identity)),
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
least_upper_bound(X2,least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),identity)) = least_upper_bound(X2,multiply(X4,inverse(greatest_lower_bound(X4,X3)))),
inference(congruence,[status(thm)],[c81]) ).
cnf(c111,plain,
least_upper_bound(X2,multiply(X4,inverse(greatest_lower_bound(X4,X3)))) = least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c112,plain,
least_upper_bound(X2,least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),identity)) = least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),X2),
inference(transitivity,[status(thm)],[c110,c111]) ).
cnf(c113,plain,
least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),least_upper_bound(X2,identity)) = least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),X2),
inference(transitivity,[status(thm)],[c109,c112]) ).
cnf(c114,plain,
least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),least_upper_bound(multiply(X3,X2),identity)) = least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),multiply(X3,X2)),
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),multiply(X3,X2)) = least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),least_upper_bound(multiply(X3,X2),identity)),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
inverse(inverse(least_upper_bound(multiply(X3,X2),identity))) = least_upper_bound(multiply(X3,X2),identity),
inference(substitution,[status(thm)],[c35]) ).
cnf(c117,plain,
least_upper_bound(multiply(X3,X2),identity) = inverse(inverse(least_upper_bound(multiply(X3,X2),identity))),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),least_upper_bound(multiply(X3,X2),identity)) = least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),inverse(inverse(least_upper_bound(multiply(X3,X2),identity)))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
inverse(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))) = multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),
inference(substitution,[status(thm)],[c35]) ).
cnf(c120,plain,
multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))) = inverse(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),inverse(inverse(least_upper_bound(multiply(X3,X2),identity)))) = least_upper_bound(inverse(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))),inverse(inverse(least_upper_bound(multiply(X3,X2),identity)))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
greatest_lower_bound(inverse(least_upper_bound(multiply(X3,X2),identity)),inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))) = greatest_lower_bound(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),inverse(least_upper_bound(multiply(X3,X2),identity))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c123,plain,
greatest_lower_bound(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),inverse(least_upper_bound(multiply(X3,X2),identity))) = greatest_lower_bound(inverse(least_upper_bound(multiply(X3,X2),identity)),inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,axiom,
greatest_lower_bound(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(greatest_lower_bound(X2,Y2),Z2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).
cnf(c125,plain,
greatest_lower_bound(multiply(X4,inverse(greatest_lower_bound(X4,inverse(X3)))),greatest_lower_bound(inverse(multiply(X4,X3)),X2)) = greatest_lower_bound(greatest_lower_bound(multiply(X4,inverse(greatest_lower_bound(X4,inverse(X3)))),inverse(multiply(X4,X3))),X2),
inference(substitution,[status(thm)],[c124]) ).
cnf(c126,plain,
greatest_lower_bound(inverse(multiply(X3,X2)),multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))) = greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),inverse(multiply(X3,X2))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c127,plain,
greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),inverse(multiply(X3,X2))) = greatest_lower_bound(inverse(multiply(X3,X2)),multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,plain,
multiply(identity,inverse(multiply(X3,X2))) = inverse(multiply(X3,X2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c129,plain,
inverse(multiply(X3,X2)) = multiply(identity,inverse(multiply(X3,X2))),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
greatest_lower_bound(inverse(multiply(X3,X2)),multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))) = greatest_lower_bound(multiply(identity,inverse(multiply(X3,X2))),multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
greatest_lower_bound(identity,multiply(X3,inverse(greatest_lower_bound(X3,X2)))) = greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),identity),
inference(substitution,[status(thm)],[c38]) ).
cnf(c132,plain,
greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),identity) = greatest_lower_bound(identity,multiply(X3,inverse(greatest_lower_bound(X3,X2)))),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
multiply(X3,inverse(greatest_lower_bound(X3,X2))) = least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),identity),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c134,plain,
greatest_lower_bound(identity,multiply(X3,inverse(greatest_lower_bound(X3,X2)))) = greatest_lower_bound(identity,least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),identity)),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c136,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c139,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c138]) ).
cnf(c140,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c137,c139]) ).
cnf(c141,plain,
greatest_lower_bound(identity,least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),identity)) = identity,
inference(substitution,[status(thm)],[c140]) ).
cnf(c142,plain,
greatest_lower_bound(identity,multiply(X3,inverse(greatest_lower_bound(X3,X2)))) = identity,
inference(transitivity,[status(thm)],[c134,c141]) ).
cnf(c143,plain,
greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),identity) = identity,
inference(transitivity,[status(thm)],[c132,c142]) ).
cnf(c144,plain,
greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),identity) = identity,
inference(substitution,[status(thm)],[c143]) ).
cnf(c145,plain,
identity = greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),identity),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,plain,
multiply(identity,inverse(multiply(X3,X2))) = multiply(greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),identity),inverse(multiply(X3,X2))),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
greatest_lower_bound(multiply(identity,inverse(multiply(X3,X2))),multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))) = greatest_lower_bound(multiply(greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),identity),inverse(multiply(X3,X2))),multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c38]) ).
cnf(c149,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(symmetry,[status(thm)],[c148]) ).
cnf(c150,plain,
multiply(greatest_lower_bound(X3,identity),X2) = multiply(greatest_lower_bound(identity,X3),X2),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,axiom,
multiply(greatest_lower_bound(Y2,Z2),X2) = greatest_lower_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
cnf(c152,plain,
multiply(greatest_lower_bound(identity,X3),X2) = greatest_lower_bound(multiply(identity,X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c151]) ).
cnf(c153,plain,
greatest_lower_bound(multiply(identity,X2),multiply(X3,X2)) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c154,plain,
multiply(greatest_lower_bound(identity,X3),X2) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c152,c153]) ).
cnf(c155,plain,
multiply(greatest_lower_bound(X3,identity),X2) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c150,c154]) ).
cnf(c156,plain,
multiply(greatest_lower_bound(X2,identity),X3) = greatest_lower_bound(X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c155]) ).
cnf(c157,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X2,identity),X4),X3) = greatest_lower_bound(greatest_lower_bound(X4,multiply(X2,X4)),X3),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
greatest_lower_bound(X4,greatest_lower_bound(multiply(X2,X4),X3)) = greatest_lower_bound(greatest_lower_bound(X4,multiply(X2,X4)),X3),
inference(substitution,[status(thm)],[c124]) ).
cnf(c159,plain,
greatest_lower_bound(greatest_lower_bound(X4,multiply(X2,X4)),X3) = greatest_lower_bound(X4,greatest_lower_bound(multiply(X2,X4),X3)),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
greatest_lower_bound(multiply(X2,X4),X3) = greatest_lower_bound(X3,multiply(X2,X4)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c161,plain,
greatest_lower_bound(X4,greatest_lower_bound(multiply(X2,X4),X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,multiply(X2,X4))),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
greatest_lower_bound(greatest_lower_bound(X4,multiply(X2,X4)),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,multiply(X2,X4))),
inference(transitivity,[status(thm)],[c159,c161]) ).
cnf(c163,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X2,identity),X4),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,multiply(X2,X4))),
inference(transitivity,[status(thm)],[c157,c162]) ).
cnf(c164,plain,
greatest_lower_bound(multiply(greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),identity),inverse(multiply(X3,X2))),multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))) = greatest_lower_bound(inverse(multiply(X3,X2)),greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),multiply(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),inverse(multiply(X3,X2))))),
inference(substitution,[status(thm)],[c163]) ).
cnf(c165,plain,
multiply(inverse(inverse(multiply(X2,inverse(greatest_lower_bound(X2,inverse(X3)))))),inverse(multiply(X2,X3))) = multiply(multiply(X2,inverse(greatest_lower_bound(X2,inverse(X3)))),inverse(multiply(X2,X3))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c166,plain,
multiply(multiply(X2,inverse(greatest_lower_bound(X2,inverse(X3)))),inverse(multiply(X2,X3))) = multiply(inverse(inverse(multiply(X2,inverse(greatest_lower_bound(X2,inverse(X3)))))),inverse(multiply(X2,X3))),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
multiply(inverse(X2),multiply(X2,inverse(multiply(X3,X2)))) = inverse(multiply(X3,X2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c168,plain,
inverse(multiply(X3,X2)) = multiply(inverse(X2),multiply(X2,inverse(multiply(X3,X2)))),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c170,plain,
multiply(inverse(X4),multiply(multiply(X4,X3),X2)) = multiply(inverse(X4),multiply(X4,multiply(X3,X2))),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
multiply(inverse(X4),multiply(X4,multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c21]) ).
cnf(c172,plain,
multiply(inverse(X4),multiply(multiply(X4,X3),X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c170,c171]) ).
cnf(c173,plain,
multiply(inverse(X2),multiply(multiply(X2,X3),inverse(multiply(X2,X3)))) = multiply(X3,inverse(multiply(X2,X3))),
inference(substitution,[status(thm)],[c172]) ).
cnf(c174,plain,
multiply(X3,inverse(multiply(X2,X3))) = multiply(inverse(X2),multiply(multiply(X2,X3),inverse(multiply(X2,X3)))),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,plain,
multiply(multiply(X2,X3),inverse(multiply(X2,X3))) = identity,
inference(substitution,[status(thm)],[c57]) ).
cnf(c176,plain,
multiply(inverse(X2),multiply(multiply(X2,X3),inverse(multiply(X2,X3)))) = multiply(inverse(X2),identity),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
multiply(inverse(X2),identity) = inverse(X2),
inference(substitution,[status(thm)],[c32]) ).
cnf(c178,plain,
multiply(inverse(X2),multiply(multiply(X2,X3),inverse(multiply(X2,X3)))) = inverse(X2),
inference(transitivity,[status(thm)],[c176,c177]) ).
cnf(c179,plain,
multiply(X3,inverse(multiply(X2,X3))) = inverse(X2),
inference(transitivity,[status(thm)],[c174,c178]) ).
cnf(c180,plain,
multiply(X2,inverse(multiply(X3,X2))) = inverse(X3),
inference(substitution,[status(thm)],[c179]) ).
cnf(c181,plain,
multiply(inverse(X2),multiply(X2,inverse(multiply(X3,X2)))) = multiply(inverse(X2),inverse(X3)),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
inverse(multiply(X3,X2)) = multiply(inverse(X2),inverse(X3)),
inference(transitivity,[status(thm)],[c168,c181]) ).
cnf(c183,plain,
inverse(multiply(multiply(X2,X3),inverse(multiply(X2,inverse(greatest_lower_bound(X2,inverse(X3))))))) = multiply(inverse(inverse(multiply(X2,inverse(greatest_lower_bound(X2,inverse(X3)))))),inverse(multiply(X2,X3))),
inference(substitution,[status(thm)],[c182]) ).
cnf(c184,plain,
multiply(inverse(inverse(multiply(X2,inverse(greatest_lower_bound(X2,inverse(X3)))))),inverse(multiply(X2,X3))) = inverse(multiply(multiply(X2,X3),inverse(multiply(X2,inverse(greatest_lower_bound(X2,inverse(X3))))))),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
multiply(inverse(inverse(multiply(X3,X2))),inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))) = multiply(multiply(X3,X2),inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c186,plain,
multiply(multiply(X3,X2),inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))) = multiply(inverse(inverse(multiply(X3,X2))),inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
multiply(X3,inverse(multiply(multiply(X2,inverse(X3)),X3))) = inverse(multiply(X2,inverse(X3))),
inference(substitution,[status(thm)],[c179]) ).
cnf(c188,plain,
inverse(multiply(X2,inverse(X3))) = multiply(X3,inverse(multiply(multiply(X2,inverse(X3)),X3))),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
multiply(multiply(X3,inverse(X2)),X2) = multiply(X3,multiply(inverse(X2),X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c190,plain,
multiply(X3,multiply(inverse(X2),X2)) = multiply(X3,identity),
inference(congruence,[status(thm)],[c17]) ).
cnf(c191,plain,
multiply(multiply(X3,inverse(X2)),X2) = multiply(X3,identity),
inference(transitivity,[status(thm)],[c189,c190]) ).
cnf(c192,plain,
multiply(multiply(X3,inverse(X2)),X2) = X3,
inference(transitivity,[status(thm)],[c191,c32]) ).
cnf(c193,plain,
multiply(multiply(X2,inverse(X3)),X3) = X2,
inference(substitution,[status(thm)],[c192]) ).
cnf(c194,plain,
inverse(multiply(multiply(X2,inverse(X3)),X3)) = inverse(X2),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
multiply(X3,inverse(multiply(multiply(X2,inverse(X3)),X3))) = multiply(X3,inverse(X2)),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
inverse(multiply(X2,inverse(X3))) = multiply(X3,inverse(X2)),
inference(transitivity,[status(thm)],[c188,c195]) ).
cnf(c197,plain,
inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))) = multiply(greatest_lower_bound(X3,inverse(X2)),inverse(X3)),
inference(substitution,[status(thm)],[c196]) ).
cnf(c198,plain,
multiply(X2,inverse(multiply(X3,X2))) = inverse(X3),
inference(substitution,[status(thm)],[c179]) ).
cnf(c199,plain,
inverse(X3) = multiply(X2,inverse(multiply(X3,X2))),
inference(symmetry,[status(thm)],[c198]) ).
cnf(c200,plain,
multiply(greatest_lower_bound(X3,inverse(X2)),inverse(X3)) = multiply(greatest_lower_bound(X3,inverse(X2)),multiply(X2,inverse(multiply(X3,X2)))),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
greatest_lower_bound(X3,inverse(X2)) = greatest_lower_bound(inverse(X2),X3),
inference(substitution,[status(thm)],[c38]) ).
cnf(c202,plain,
multiply(greatest_lower_bound(X3,inverse(X2)),X2) = multiply(greatest_lower_bound(inverse(X2),X3),X2),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
multiply(greatest_lower_bound(X3,X4),X2) = greatest_lower_bound(multiply(X3,X2),multiply(X4,X2)),
inference(substitution,[status(thm)],[c151]) ).
cnf(c204,plain,
greatest_lower_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(greatest_lower_bound(X3,X4),X2),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c206,plain,
multiply(greatest_lower_bound(X3,X4),X2) = multiply(greatest_lower_bound(X4,X3),X2),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
greatest_lower_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(greatest_lower_bound(X4,X3),X2),
inference(transitivity,[status(thm)],[c204,c206]) ).
cnf(c208,plain,
greatest_lower_bound(multiply(X3,X2),multiply(inverse(X2),X2)) = multiply(greatest_lower_bound(inverse(X2),X3),X2),
inference(substitution,[status(thm)],[c207]) ).
cnf(c209,plain,
multiply(greatest_lower_bound(inverse(X2),X3),X2) = greatest_lower_bound(multiply(X3,X2),multiply(inverse(X2),X2)),
inference(symmetry,[status(thm)],[c208]) ).
cnf(c210,plain,
greatest_lower_bound(multiply(X3,X2),multiply(inverse(X2),X2)) = greatest_lower_bound(multiply(X3,X2),identity),
inference(congruence,[status(thm)],[c17]) ).
cnf(c211,plain,
multiply(greatest_lower_bound(inverse(X2),X3),X2) = greatest_lower_bound(multiply(X3,X2),identity),
inference(transitivity,[status(thm)],[c209,c210]) ).
cnf(c212,plain,
multiply(greatest_lower_bound(X3,inverse(X2)),X2) = greatest_lower_bound(multiply(X3,X2),identity),
inference(transitivity,[status(thm)],[c202,c211]) ).
cnf(c213,plain,
greatest_lower_bound(multiply(X3,X2),identity) = multiply(greatest_lower_bound(X3,inverse(X2)),X2),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
multiply(greatest_lower_bound(multiply(X4,X3),identity),X2) = multiply(multiply(greatest_lower_bound(X4,inverse(X3)),X3),X2),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
multiply(multiply(greatest_lower_bound(X4,inverse(X3)),X3),X2) = multiply(greatest_lower_bound(X4,inverse(X3)),multiply(X3,X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c216,plain,
multiply(greatest_lower_bound(multiply(X4,X3),identity),X2) = multiply(greatest_lower_bound(X4,inverse(X3)),multiply(X3,X2)),
inference(transitivity,[status(thm)],[c214,c215]) ).
cnf(c217,plain,
multiply(greatest_lower_bound(X4,inverse(X3)),multiply(X3,X2)) = multiply(greatest_lower_bound(multiply(X4,X3),identity),X2),
inference(symmetry,[status(thm)],[c216]) ).
cnf(c218,plain,
multiply(greatest_lower_bound(multiply(X4,X3),identity),X2) = greatest_lower_bound(X2,multiply(multiply(X4,X3),X2)),
inference(substitution,[status(thm)],[c155]) ).
cnf(c219,plain,
multiply(greatest_lower_bound(X4,inverse(X3)),multiply(X3,X2)) = greatest_lower_bound(X2,multiply(multiply(X4,X3),X2)),
inference(transitivity,[status(thm)],[c217,c218]) ).
cnf(c220,plain,
multiply(greatest_lower_bound(X3,inverse(X2)),multiply(X2,inverse(multiply(X3,X2)))) = greatest_lower_bound(inverse(multiply(X3,X2)),multiply(multiply(X3,X2),inverse(multiply(X3,X2)))),
inference(substitution,[status(thm)],[c219]) ).
cnf(c221,plain,
multiply(multiply(X3,X2),inverse(multiply(X3,X2))) = identity,
inference(substitution,[status(thm)],[c57]) ).
cnf(c222,plain,
greatest_lower_bound(inverse(multiply(X3,X2)),multiply(multiply(X3,X2),inverse(multiply(X3,X2)))) = greatest_lower_bound(inverse(multiply(X3,X2)),identity),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
greatest_lower_bound(inverse(multiply(X3,X2)),identity) = greatest_lower_bound(identity,inverse(multiply(X3,X2))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c224,plain,
greatest_lower_bound(inverse(multiply(X3,X2)),multiply(multiply(X3,X2),inverse(multiply(X3,X2)))) = greatest_lower_bound(identity,inverse(multiply(X3,X2))),
inference(transitivity,[status(thm)],[c222,c223]) ).
cnf(c225,plain,
multiply(greatest_lower_bound(X3,inverse(X2)),multiply(X2,inverse(multiply(X3,X2)))) = greatest_lower_bound(identity,inverse(multiply(X3,X2))),
inference(transitivity,[status(thm)],[c220,c224]) ).
cnf(c226,plain,
multiply(greatest_lower_bound(X3,inverse(X2)),inverse(X3)) = greatest_lower_bound(identity,inverse(multiply(X3,X2))),
inference(transitivity,[status(thm)],[c200,c225]) ).
cnf(c227,plain,
inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))) = greatest_lower_bound(identity,inverse(multiply(X3,X2))),
inference(transitivity,[status(thm)],[c197,c226]) ).
cnf(c228,plain,
multiply(inverse(inverse(multiply(X3,X2))),inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))) = multiply(inverse(inverse(multiply(X3,X2))),greatest_lower_bound(identity,inverse(multiply(X3,X2)))),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c38]) ).
cnf(c230,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(symmetry,[status(thm)],[c229]) ).
cnf(c231,plain,
multiply(inverse(X3),greatest_lower_bound(X2,X3)) = multiply(inverse(X3),greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,axiom,
multiply(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).
cnf(c233,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c232]) ).
cnf(c234,plain,
greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = greatest_lower_bound(identity,multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c235,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = greatest_lower_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c233,c234]) ).
cnf(c236,plain,
multiply(inverse(X3),greatest_lower_bound(X2,X3)) = greatest_lower_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c231,c235]) ).
cnf(c237,plain,
multiply(inverse(inverse(multiply(X3,X2))),greatest_lower_bound(identity,inverse(multiply(X3,X2)))) = greatest_lower_bound(identity,multiply(inverse(inverse(multiply(X3,X2))),identity)),
inference(substitution,[status(thm)],[c236]) ).
cnf(c238,plain,
multiply(inverse(inverse(multiply(X3,X2))),identity) = multiply(X3,X2),
inference(substitution,[status(thm)],[c31]) ).
cnf(c239,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(multiply(X3,X2))),identity)) = greatest_lower_bound(identity,multiply(X3,X2)),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
greatest_lower_bound(identity,multiply(X3,X2)) = greatest_lower_bound(multiply(X3,X2),identity),
inference(substitution,[status(thm)],[c38]) ).
cnf(c241,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(multiply(X3,X2))),identity)) = greatest_lower_bound(multiply(X3,X2),identity),
inference(transitivity,[status(thm)],[c239,c240]) ).
cnf(c242,plain,
multiply(inverse(inverse(multiply(X3,X2))),greatest_lower_bound(identity,inverse(multiply(X3,X2)))) = greatest_lower_bound(multiply(X3,X2),identity),
inference(transitivity,[status(thm)],[c237,c241]) ).
cnf(c243,plain,
multiply(inverse(inverse(multiply(X3,X2))),inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))) = greatest_lower_bound(multiply(X3,X2),identity),
inference(transitivity,[status(thm)],[c228,c242]) ).
cnf(c244,plain,
multiply(multiply(X3,X2),inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))) = greatest_lower_bound(multiply(X3,X2),identity),
inference(transitivity,[status(thm)],[c186,c243]) ).
cnf(c245,plain,
multiply(multiply(X2,X3),inverse(multiply(X2,inverse(greatest_lower_bound(X2,inverse(X3)))))) = greatest_lower_bound(multiply(X2,X3),identity),
inference(substitution,[status(thm)],[c244]) ).
cnf(c246,plain,
inverse(multiply(multiply(X2,X3),inverse(multiply(X2,inverse(greatest_lower_bound(X2,inverse(X3))))))) = inverse(greatest_lower_bound(multiply(X2,X3),identity)),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
greatest_lower_bound(multiply(X3,X2),identity) = multiply(greatest_lower_bound(X3,inverse(X2)),X2),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c248,plain,
inverse(greatest_lower_bound(multiply(X3,X2),identity)) = inverse(multiply(greatest_lower_bound(X3,inverse(X2)),X2)),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
inverse(multiply(greatest_lower_bound(X3,inverse(X2)),X2)) = multiply(inverse(X2),inverse(greatest_lower_bound(X3,inverse(X2)))),
inference(substitution,[status(thm)],[c182]) ).
cnf(c250,plain,
inverse(greatest_lower_bound(multiply(X3,X2),identity)) = multiply(inverse(X2),inverse(greatest_lower_bound(X3,inverse(X2)))),
inference(transitivity,[status(thm)],[c248,c249]) ).
cnf(c251,plain,
inverse(greatest_lower_bound(multiply(X2,X3),identity)) = multiply(inverse(X3),inverse(greatest_lower_bound(X2,inverse(X3)))),
inference(substitution,[status(thm)],[c250]) ).
cnf(c252,plain,
inverse(multiply(multiply(X2,X3),inverse(multiply(X2,inverse(greatest_lower_bound(X2,inverse(X3))))))) = multiply(inverse(X3),inverse(greatest_lower_bound(X2,inverse(X3)))),
inference(transitivity,[status(thm)],[c246,c251]) ).
cnf(c253,plain,
multiply(inverse(inverse(multiply(X2,inverse(greatest_lower_bound(X2,inverse(X3)))))),inverse(multiply(X2,X3))) = multiply(inverse(X3),inverse(greatest_lower_bound(X2,inverse(X3)))),
inference(transitivity,[status(thm)],[c184,c252]) ).
cnf(c254,plain,
multiply(multiply(X2,inverse(greatest_lower_bound(X2,inverse(X3)))),inverse(multiply(X2,X3))) = multiply(inverse(X3),inverse(greatest_lower_bound(X2,inverse(X3)))),
inference(transitivity,[status(thm)],[c166,c253]) ).
cnf(c255,plain,
multiply(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),inverse(multiply(X3,X2))) = multiply(inverse(X2),inverse(greatest_lower_bound(X3,inverse(X2)))),
inference(substitution,[status(thm)],[c254]) ).
cnf(c256,plain,
greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),multiply(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),inverse(multiply(X3,X2)))) = greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),multiply(inverse(X2),inverse(greatest_lower_bound(X3,inverse(X2))))),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),multiply(inverse(X2),inverse(greatest_lower_bound(X3,inverse(X2))))) = multiply(greatest_lower_bound(inverse(X2),X3),inverse(greatest_lower_bound(X3,inverse(X2)))),
inference(substitution,[status(thm)],[c207]) ).
cnf(c258,plain,
greatest_lower_bound(X3,inverse(X2)) = greatest_lower_bound(inverse(X2),X3),
inference(substitution,[status(thm)],[c38]) ).
cnf(c259,plain,
greatest_lower_bound(inverse(X2),X3) = greatest_lower_bound(X3,inverse(X2)),
inference(symmetry,[status(thm)],[c258]) ).
cnf(c260,plain,
multiply(greatest_lower_bound(inverse(X2),X3),inverse(greatest_lower_bound(X3,inverse(X2)))) = multiply(greatest_lower_bound(X3,inverse(X2)),inverse(greatest_lower_bound(X3,inverse(X2)))),
inference(congruence,[status(thm)],[c259]) ).
cnf(c261,plain,
multiply(greatest_lower_bound(X3,inverse(X2)),inverse(greatest_lower_bound(X3,inverse(X2)))) = identity,
inference(substitution,[status(thm)],[c57]) ).
cnf(c262,plain,
multiply(greatest_lower_bound(inverse(X2),X3),inverse(greatest_lower_bound(X3,inverse(X2)))) = identity,
inference(transitivity,[status(thm)],[c260,c261]) ).
cnf(c263,plain,
greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),multiply(inverse(X2),inverse(greatest_lower_bound(X3,inverse(X2))))) = identity,
inference(transitivity,[status(thm)],[c257,c262]) ).
cnf(c264,plain,
greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),multiply(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),inverse(multiply(X3,X2)))) = identity,
inference(transitivity,[status(thm)],[c256,c263]) ).
cnf(c265,plain,
greatest_lower_bound(inverse(multiply(X3,X2)),greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),multiply(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),inverse(multiply(X3,X2))))) = greatest_lower_bound(inverse(multiply(X3,X2)),identity),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
greatest_lower_bound(inverse(multiply(X3,X2)),identity) = greatest_lower_bound(identity,inverse(multiply(X3,X2))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c267,plain,
greatest_lower_bound(identity,inverse(multiply(X3,X2))) = inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),
inference(symmetry,[status(thm)],[c227]) ).
cnf(c268,plain,
greatest_lower_bound(inverse(multiply(X3,X2)),identity) = inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),
inference(transitivity,[status(thm)],[c266,c267]) ).
cnf(c269,plain,
greatest_lower_bound(inverse(multiply(X3,X2)),greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),multiply(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),inverse(multiply(X3,X2))))) = inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),
inference(transitivity,[status(thm)],[c265,c268]) ).
cnf(c270,plain,
greatest_lower_bound(multiply(greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),identity),inverse(multiply(X3,X2))),multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))) = inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),
inference(transitivity,[status(thm)],[c164,c269]) ).
cnf(c271,plain,
greatest_lower_bound(multiply(identity,inverse(multiply(X3,X2))),multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))) = inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),
inference(transitivity,[status(thm)],[c147,c270]) ).
cnf(c272,plain,
greatest_lower_bound(inverse(multiply(X3,X2)),multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))) = inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),
inference(transitivity,[status(thm)],[c130,c271]) ).
cnf(c273,plain,
greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),inverse(multiply(X3,X2))) = inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),
inference(transitivity,[status(thm)],[c127,c272]) ).
cnf(c274,plain,
greatest_lower_bound(greatest_lower_bound(multiply(X4,inverse(greatest_lower_bound(X4,inverse(X3)))),inverse(multiply(X4,X3))),X2) = greatest_lower_bound(inverse(multiply(X4,inverse(greatest_lower_bound(X4,inverse(X3))))),X2),
inference(congruence,[status(thm)],[c273]) ).
cnf(c275,plain,
greatest_lower_bound(inverse(multiply(X4,inverse(greatest_lower_bound(X4,inverse(X3))))),X2) = greatest_lower_bound(X2,inverse(multiply(X4,inverse(greatest_lower_bound(X4,inverse(X3)))))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c276,plain,
greatest_lower_bound(greatest_lower_bound(multiply(X4,inverse(greatest_lower_bound(X4,inverse(X3)))),inverse(multiply(X4,X3))),X2) = greatest_lower_bound(X2,inverse(multiply(X4,inverse(greatest_lower_bound(X4,inverse(X3)))))),
inference(transitivity,[status(thm)],[c274,c275]) ).
cnf(c277,plain,
greatest_lower_bound(multiply(X4,inverse(greatest_lower_bound(X4,inverse(X3)))),greatest_lower_bound(inverse(multiply(X4,X3)),X2)) = greatest_lower_bound(X2,inverse(multiply(X4,inverse(greatest_lower_bound(X4,inverse(X3)))))),
inference(transitivity,[status(thm)],[c125,c276]) ).
cnf(c278,plain,
greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),greatest_lower_bound(inverse(multiply(X3,X2)),inverse(least_upper_bound(multiply(X3,X2),identity)))) = greatest_lower_bound(inverse(least_upper_bound(multiply(X3,X2),identity)),inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))),
inference(substitution,[status(thm)],[c277]) ).
cnf(c279,plain,
greatest_lower_bound(inverse(least_upper_bound(multiply(X3,X2),identity)),inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))) = greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),greatest_lower_bound(inverse(multiply(X3,X2)),inverse(least_upper_bound(multiply(X3,X2),identity)))),
inference(symmetry,[status(thm)],[c278]) ).
cnf(c280,plain,
greatest_lower_bound(inverse(least_upper_bound(X3,X2)),inverse(X3)) = greatest_lower_bound(inverse(X3),inverse(least_upper_bound(X3,X2))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c281,plain,
greatest_lower_bound(inverse(X3),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(inverse(least_upper_bound(X3,X2)),inverse(X3)),
inference(symmetry,[status(thm)],[c280]) ).
cnf(c282,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c138]) ).
cnf(c283,plain,
X3 = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(symmetry,[status(thm)],[c282]) ).
cnf(c284,plain,
inverse(X3) = inverse(greatest_lower_bound(X3,least_upper_bound(X3,X2))),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
greatest_lower_bound(inverse(least_upper_bound(X3,X2)),inverse(X3)) = greatest_lower_bound(inverse(least_upper_bound(X3,X2)),inverse(greatest_lower_bound(X3,least_upper_bound(X3,X2)))),
inference(congruence,[status(thm)],[c284]) ).
cnf(c286,plain,
multiply(inverse(greatest_lower_bound(X2,X3)),identity) = inverse(greatest_lower_bound(X2,X3)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c287,plain,
inverse(greatest_lower_bound(X2,X3)) = multiply(inverse(greatest_lower_bound(X2,X3)),identity),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
greatest_lower_bound(inverse(X3),inverse(greatest_lower_bound(X2,X3))) = greatest_lower_bound(inverse(X3),multiply(inverse(greatest_lower_bound(X2,X3)),identity)),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
identity = multiply(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c290,plain,
multiply(inverse(greatest_lower_bound(X2,X3)),identity) = multiply(inverse(greatest_lower_bound(X2,X3)),multiply(X3,inverse(X3))),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
greatest_lower_bound(inverse(X3),multiply(inverse(greatest_lower_bound(X2,X3)),identity)) = greatest_lower_bound(inverse(X3),multiply(inverse(greatest_lower_bound(X2,X3)),multiply(X3,inverse(X3)))),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
multiply(multiply(inverse(greatest_lower_bound(X3,X2)),X2),X4) = multiply(inverse(greatest_lower_bound(X3,X2)),multiply(X2,X4)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c293,plain,
multiply(inverse(greatest_lower_bound(X3,X2)),multiply(X2,X4)) = multiply(multiply(inverse(greatest_lower_bound(X3,X2)),X2),X4),
inference(symmetry,[status(thm)],[c292]) ).
cnf(c294,plain,
greatest_lower_bound(X4,multiply(inverse(greatest_lower_bound(X3,X2)),multiply(X2,X4))) = greatest_lower_bound(X4,multiply(multiply(inverse(greatest_lower_bound(X3,X2)),X2),X4)),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c296,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c295]) ).
cnf(c297,plain,
multiply(inverse(X3),least_upper_bound(X2,X3)) = multiply(inverse(X3),least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c296]) ).
cnf(c298,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c299,plain,
least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = least_upper_bound(identity,multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c300,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = least_upper_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c298,c299]) ).
cnf(c301,plain,
multiply(inverse(X3),least_upper_bound(X2,X3)) = least_upper_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c297,c300]) ).
cnf(c302,plain,
multiply(inverse(greatest_lower_bound(X3,X2)),least_upper_bound(X2,greatest_lower_bound(X3,X2))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),
inference(substitution,[status(thm)],[c301]) ).
cnf(c303,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X3,X2)),X2)) = multiply(inverse(greatest_lower_bound(X3,X2)),least_upper_bound(X2,greatest_lower_bound(X3,X2))),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c304,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = X2,
inference(substitution,[status(thm)],[c76]) ).
cnf(c305,plain,
multiply(inverse(greatest_lower_bound(X3,X2)),least_upper_bound(X2,greatest_lower_bound(X3,X2))) = multiply(inverse(greatest_lower_bound(X3,X2)),X2),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X3,X2)),X2)) = multiply(inverse(greatest_lower_bound(X3,X2)),X2),
inference(transitivity,[status(thm)],[c303,c305]) ).
cnf(c307,plain,
multiply(inverse(greatest_lower_bound(X3,X2)),X2) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),
inference(symmetry,[status(thm)],[c306]) ).
cnf(c308,plain,
multiply(multiply(inverse(greatest_lower_bound(X3,X2)),X2),X4) = multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),X4),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,plain,
greatest_lower_bound(X4,multiply(multiply(inverse(greatest_lower_bound(X3,X2)),X2),X4)) = greatest_lower_bound(X4,multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),X4)),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c311,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(symmetry,[status(thm)],[c310]) ).
cnf(c312,plain,
multiply(least_upper_bound(identity,X2),X3) = multiply(least_upper_bound(X2,identity),X3),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c314,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(symmetry,[status(thm)],[c313]) ).
cnf(c315,plain,
multiply(least_upper_bound(X3,identity),X2) = multiply(least_upper_bound(identity,X3),X2),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
multiply(least_upper_bound(identity,X3),X2) = least_upper_bound(multiply(identity,X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c317,plain,
least_upper_bound(multiply(identity,X2),multiply(X3,X2)) = least_upper_bound(X2,multiply(X3,X2)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c318,plain,
multiply(least_upper_bound(identity,X3),X2) = least_upper_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c316,c317]) ).
cnf(c319,plain,
multiply(least_upper_bound(X3,identity),X2) = least_upper_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c315,c318]) ).
cnf(c320,plain,
multiply(least_upper_bound(X2,identity),X3) = least_upper_bound(X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c319]) ).
cnf(c321,plain,
multiply(least_upper_bound(identity,X2),X3) = least_upper_bound(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c312,c320]) ).
cnf(c322,plain,
greatest_lower_bound(X3,multiply(least_upper_bound(identity,X2),X3)) = greatest_lower_bound(X3,least_upper_bound(X3,multiply(X2,X3))),
inference(congruence,[status(thm)],[c321]) ).
cnf(c323,plain,
greatest_lower_bound(X3,least_upper_bound(X3,multiply(X2,X3))) = X3,
inference(substitution,[status(thm)],[c138]) ).
cnf(c324,plain,
greatest_lower_bound(X3,multiply(least_upper_bound(identity,X2),X3)) = X3,
inference(transitivity,[status(thm)],[c322,c323]) ).
cnf(c325,plain,
greatest_lower_bound(X4,multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),X4)) = X4,
inference(substitution,[status(thm)],[c324]) ).
cnf(c326,plain,
greatest_lower_bound(X4,multiply(multiply(inverse(greatest_lower_bound(X3,X2)),X2),X4)) = X4,
inference(transitivity,[status(thm)],[c309,c325]) ).
cnf(c327,plain,
greatest_lower_bound(X4,multiply(inverse(greatest_lower_bound(X3,X2)),multiply(X2,X4))) = X4,
inference(transitivity,[status(thm)],[c294,c326]) ).
cnf(c328,plain,
greatest_lower_bound(inverse(X3),multiply(inverse(greatest_lower_bound(X2,X3)),multiply(X3,inverse(X3)))) = inverse(X3),
inference(substitution,[status(thm)],[c327]) ).
cnf(c329,plain,
greatest_lower_bound(inverse(X3),multiply(inverse(greatest_lower_bound(X2,X3)),identity)) = inverse(X3),
inference(transitivity,[status(thm)],[c291,c328]) ).
cnf(c330,plain,
greatest_lower_bound(inverse(X3),inverse(greatest_lower_bound(X2,X3))) = inverse(X3),
inference(transitivity,[status(thm)],[c288,c329]) ).
cnf(c331,plain,
greatest_lower_bound(inverse(least_upper_bound(X3,X2)),inverse(greatest_lower_bound(X3,least_upper_bound(X3,X2)))) = inverse(least_upper_bound(X3,X2)),
inference(substitution,[status(thm)],[c330]) ).
cnf(c332,plain,
greatest_lower_bound(inverse(least_upper_bound(X3,X2)),inverse(X3)) = inverse(least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c285,c331]) ).
cnf(c333,plain,
greatest_lower_bound(inverse(X3),inverse(least_upper_bound(X3,X2))) = inverse(least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c281,c332]) ).
cnf(c334,plain,
greatest_lower_bound(inverse(multiply(X3,X2)),inverse(least_upper_bound(multiply(X3,X2),identity))) = inverse(least_upper_bound(multiply(X3,X2),identity)),
inference(substitution,[status(thm)],[c333]) ).
cnf(c335,plain,
greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),greatest_lower_bound(inverse(multiply(X3,X2)),inverse(least_upper_bound(multiply(X3,X2),identity)))) = greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),inverse(least_upper_bound(multiply(X3,X2),identity))),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
greatest_lower_bound(inverse(least_upper_bound(X2,identity)),multiply(X4,inverse(greatest_lower_bound(X4,X3)))) = greatest_lower_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),inverse(least_upper_bound(X2,identity))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c337,plain,
greatest_lower_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),inverse(least_upper_bound(X2,identity))) = greatest_lower_bound(inverse(least_upper_bound(X2,identity)),multiply(X4,inverse(greatest_lower_bound(X4,X3)))),
inference(symmetry,[status(thm)],[c336]) ).
cnf(c338,plain,
greatest_lower_bound(inverse(least_upper_bound(X2,identity)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(X2,identity))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c339,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(X2,identity))) = greatest_lower_bound(inverse(least_upper_bound(X2,identity)),identity),
inference(symmetry,[status(thm)],[c338]) ).
cnf(c340,plain,
multiply(least_upper_bound(X2,identity),inverse(least_upper_bound(X2,identity))) = identity,
inference(substitution,[status(thm)],[c57]) ).
cnf(c341,plain,
identity = multiply(least_upper_bound(X2,identity),inverse(least_upper_bound(X2,identity))),
inference(symmetry,[status(thm)],[c340]) ).
cnf(c342,plain,
greatest_lower_bound(inverse(least_upper_bound(X2,identity)),identity) = greatest_lower_bound(inverse(least_upper_bound(X2,identity)),multiply(least_upper_bound(X2,identity),inverse(least_upper_bound(X2,identity)))),
inference(congruence,[status(thm)],[c341]) ).
cnf(c343,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),identity),X3) = greatest_lower_bound(X3,multiply(least_upper_bound(X2,identity),X3)),
inference(substitution,[status(thm)],[c155]) ).
cnf(c344,plain,
greatest_lower_bound(X3,multiply(least_upper_bound(X2,identity),X3)) = multiply(greatest_lower_bound(least_upper_bound(X2,identity),identity),X3),
inference(symmetry,[status(thm)],[c343]) ).
cnf(c345,plain,
greatest_lower_bound(X2,least_upper_bound(X3,X2)) = greatest_lower_bound(least_upper_bound(X3,X2),X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c346,plain,
greatest_lower_bound(least_upper_bound(X3,X2),X2) = greatest_lower_bound(X2,least_upper_bound(X3,X2)),
inference(symmetry,[status(thm)],[c345]) ).
cnf(c347,plain,
greatest_lower_bound(X2,least_upper_bound(X3,X2)) = X2,
inference(substitution,[status(thm)],[c140]) ).
cnf(c348,plain,
greatest_lower_bound(least_upper_bound(X3,X2),X2) = X2,
inference(transitivity,[status(thm)],[c346,c347]) ).
cnf(c349,plain,
greatest_lower_bound(least_upper_bound(X2,identity),identity) = identity,
inference(substitution,[status(thm)],[c348]) ).
cnf(c350,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),identity),X3) = multiply(identity,X3),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),identity),X3) = X3,
inference(transitivity,[status(thm)],[c350,c19]) ).
cnf(c352,plain,
greatest_lower_bound(X3,multiply(least_upper_bound(X2,identity),X3)) = X3,
inference(transitivity,[status(thm)],[c344,c351]) ).
cnf(c353,plain,
greatest_lower_bound(inverse(least_upper_bound(X2,identity)),multiply(least_upper_bound(X2,identity),inverse(least_upper_bound(X2,identity)))) = inverse(least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c352]) ).
cnf(c354,plain,
greatest_lower_bound(inverse(least_upper_bound(X2,identity)),identity) = inverse(least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c342,c353]) ).
cnf(c355,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(X2,identity))) = inverse(least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c339,c354]) ).
cnf(c356,plain,
inverse(least_upper_bound(X2,identity)) = greatest_lower_bound(identity,inverse(least_upper_bound(X2,identity))),
inference(symmetry,[status(thm)],[c355]) ).
cnf(c357,plain,
least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),inverse(least_upper_bound(X2,identity))) = least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),greatest_lower_bound(identity,inverse(least_upper_bound(X2,identity)))),
inference(congruence,[status(thm)],[c356]) ).
cnf(c358,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c359,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(symmetry,[status(thm)],[c358]) ).
cnf(c360,plain,
least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),greatest_lower_bound(identity,X2)) = least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c359]) ).
cnf(c361,plain,
greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),multiply(X2,inverse(greatest_lower_bound(X3,X2)))) = multiply(greatest_lower_bound(X2,X3),inverse(greatest_lower_bound(X3,X2))),
inference(substitution,[status(thm)],[c207]) ).
cnf(c362,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c38]) ).
cnf(c363,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(symmetry,[status(thm)],[c362]) ).
cnf(c364,plain,
multiply(greatest_lower_bound(X2,X3),inverse(greatest_lower_bound(X3,X2))) = multiply(greatest_lower_bound(X3,X2),inverse(greatest_lower_bound(X3,X2))),
inference(congruence,[status(thm)],[c363]) ).
cnf(c365,plain,
multiply(greatest_lower_bound(X3,X2),inverse(greatest_lower_bound(X3,X2))) = identity,
inference(substitution,[status(thm)],[c57]) ).
cnf(c366,plain,
multiply(greatest_lower_bound(X2,X3),inverse(greatest_lower_bound(X3,X2))) = identity,
inference(transitivity,[status(thm)],[c364,c365]) ).
cnf(c367,plain,
greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),multiply(X2,inverse(greatest_lower_bound(X3,X2)))) = identity,
inference(transitivity,[status(thm)],[c361,c366]) ).
cnf(c368,plain,
identity = greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,X2))),multiply(X2,inverse(greatest_lower_bound(X3,X2)))),
inference(symmetry,[status(thm)],[c367]) ).
cnf(c369,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(X2,greatest_lower_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),multiply(X3,inverse(greatest_lower_bound(X4,X3))))),
inference(congruence,[status(thm)],[c368]) ).
cnf(c370,plain,
least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),greatest_lower_bound(X2,identity)) = least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),greatest_lower_bound(X2,greatest_lower_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),multiply(X3,inverse(greatest_lower_bound(X4,X3)))))),
inference(congruence,[status(thm)],[c369]) ).
cnf(c371,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c38]) ).
cnf(c372,plain,
greatest_lower_bound(X3,greatest_lower_bound(X4,X2)) = greatest_lower_bound(X3,greatest_lower_bound(X2,X4)),
inference(congruence,[status(thm)],[c371]) ).
cnf(c373,plain,
least_upper_bound(X4,greatest_lower_bound(X3,greatest_lower_bound(X4,X2))) = least_upper_bound(X4,greatest_lower_bound(X3,greatest_lower_bound(X2,X4))),
inference(congruence,[status(thm)],[c372]) ).
cnf(c374,plain,
greatest_lower_bound(greatest_lower_bound(X2,X4),X3) = greatest_lower_bound(X3,greatest_lower_bound(X2,X4)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c375,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,X4)) = greatest_lower_bound(greatest_lower_bound(X2,X4),X3),
inference(symmetry,[status(thm)],[c374]) ).
cnf(c376,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c377,plain,
greatest_lower_bound(greatest_lower_bound(X2,X4),X3) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(congruence,[status(thm)],[c376]) ).
cnf(c378,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c124]) ).
cnf(c379,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X2,X3)),
inference(symmetry,[status(thm)],[c378]) ).
cnf(c380,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c381,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c380]) ).
cnf(c382,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c379,c381]) ).
cnf(c383,plain,
greatest_lower_bound(greatest_lower_bound(X2,X4),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c377,c382]) ).
cnf(c384,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,X4)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c375,c383]) ).
cnf(c385,plain,
least_upper_bound(X4,greatest_lower_bound(X3,greatest_lower_bound(X2,X4))) = least_upper_bound(X4,greatest_lower_bound(X4,greatest_lower_bound(X3,X2))),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
least_upper_bound(X4,greatest_lower_bound(X4,greatest_lower_bound(X3,X2))) = X4,
inference(substitution,[status(thm)],[c74]) ).
cnf(c387,plain,
least_upper_bound(X4,greatest_lower_bound(X3,greatest_lower_bound(X2,X4))) = X4,
inference(transitivity,[status(thm)],[c385,c386]) ).
cnf(c388,plain,
least_upper_bound(X4,greatest_lower_bound(X3,greatest_lower_bound(X4,X2))) = X4,
inference(transitivity,[status(thm)],[c373,c387]) ).
cnf(c389,plain,
least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),greatest_lower_bound(X2,greatest_lower_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),multiply(X3,inverse(greatest_lower_bound(X4,X3)))))) = multiply(X4,inverse(greatest_lower_bound(X4,X3))),
inference(substitution,[status(thm)],[c388]) ).
cnf(c390,plain,
least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),greatest_lower_bound(X2,identity)) = multiply(X4,inverse(greatest_lower_bound(X4,X3))),
inference(transitivity,[status(thm)],[c370,c389]) ).
cnf(c391,plain,
least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),greatest_lower_bound(identity,X2)) = multiply(X4,inverse(greatest_lower_bound(X4,X3))),
inference(transitivity,[status(thm)],[c360,c390]) ).
cnf(c392,plain,
least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),greatest_lower_bound(identity,inverse(least_upper_bound(X2,identity)))) = multiply(X4,inverse(greatest_lower_bound(X4,X3))),
inference(substitution,[status(thm)],[c391]) ).
cnf(c393,plain,
least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),inverse(least_upper_bound(X2,identity))) = multiply(X4,inverse(greatest_lower_bound(X4,X3))),
inference(transitivity,[status(thm)],[c357,c392]) ).
cnf(c394,plain,
multiply(X4,inverse(greatest_lower_bound(X4,X3))) = least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),inverse(least_upper_bound(X2,identity))),
inference(symmetry,[status(thm)],[c393]) ).
cnf(c395,plain,
greatest_lower_bound(inverse(least_upper_bound(X2,identity)),multiply(X4,inverse(greatest_lower_bound(X4,X3)))) = greatest_lower_bound(inverse(least_upper_bound(X2,identity)),least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),inverse(least_upper_bound(X2,identity)))),
inference(congruence,[status(thm)],[c394]) ).
cnf(c396,plain,
greatest_lower_bound(inverse(least_upper_bound(X2,identity)),least_upper_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),inverse(least_upper_bound(X2,identity)))) = inverse(least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c140]) ).
cnf(c397,plain,
greatest_lower_bound(inverse(least_upper_bound(X2,identity)),multiply(X4,inverse(greatest_lower_bound(X4,X3)))) = inverse(least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c395,c396]) ).
cnf(c398,plain,
greatest_lower_bound(multiply(X4,inverse(greatest_lower_bound(X4,X3))),inverse(least_upper_bound(X2,identity))) = inverse(least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c337,c397]) ).
cnf(c399,plain,
greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),inverse(least_upper_bound(multiply(X3,X2),identity))) = inverse(least_upper_bound(multiply(X3,X2),identity)),
inference(substitution,[status(thm)],[c398]) ).
cnf(c400,plain,
greatest_lower_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),greatest_lower_bound(inverse(multiply(X3,X2)),inverse(least_upper_bound(multiply(X3,X2),identity)))) = inverse(least_upper_bound(multiply(X3,X2),identity)),
inference(transitivity,[status(thm)],[c335,c399]) ).
cnf(c401,plain,
greatest_lower_bound(inverse(least_upper_bound(multiply(X3,X2),identity)),inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))) = inverse(least_upper_bound(multiply(X3,X2),identity)),
inference(transitivity,[status(thm)],[c279,c400]) ).
cnf(c402,plain,
greatest_lower_bound(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),inverse(least_upper_bound(multiply(X3,X2),identity))) = inverse(least_upper_bound(multiply(X3,X2),identity)),
inference(transitivity,[status(thm)],[c123,c401]) ).
cnf(c403,plain,
inverse(least_upper_bound(multiply(X3,X2),identity)) = greatest_lower_bound(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),inverse(least_upper_bound(multiply(X3,X2),identity))),
inference(symmetry,[status(thm)],[c402]) ).
cnf(c404,plain,
inverse(inverse(least_upper_bound(multiply(X3,X2),identity))) = inverse(greatest_lower_bound(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),inverse(least_upper_bound(multiply(X3,X2),identity)))),
inference(congruence,[status(thm)],[c403]) ).
cnf(c405,plain,
least_upper_bound(inverse(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))),inverse(inverse(least_upper_bound(multiply(X3,X2),identity)))) = least_upper_bound(inverse(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))),inverse(greatest_lower_bound(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),inverse(least_upper_bound(multiply(X3,X2),identity))))),
inference(congruence,[status(thm)],[c404]) ).
cnf(c406,plain,
least_upper_bound(inverse(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))),inverse(greatest_lower_bound(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),inverse(least_upper_bound(multiply(X3,X2),identity))))) = inverse(greatest_lower_bound(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),inverse(least_upper_bound(multiply(X3,X2),identity)))),
inference(substitution,[status(thm)],[c86]) ).
cnf(c407,plain,
inverse(greatest_lower_bound(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),inverse(least_upper_bound(multiply(X3,X2),identity)))) = inverse(inverse(least_upper_bound(multiply(X3,X2),identity))),
inference(congruence,[status(thm)],[c402]) ).
cnf(c408,plain,
inverse(inverse(least_upper_bound(multiply(X3,X2),identity))) = least_upper_bound(multiply(X3,X2),identity),
inference(substitution,[status(thm)],[c35]) ).
cnf(c409,plain,
inverse(greatest_lower_bound(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),inverse(least_upper_bound(multiply(X3,X2),identity)))) = least_upper_bound(multiply(X3,X2),identity),
inference(transitivity,[status(thm)],[c407,c408]) ).
cnf(c410,plain,
least_upper_bound(inverse(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))),inverse(greatest_lower_bound(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2))))),inverse(least_upper_bound(multiply(X3,X2),identity))))) = least_upper_bound(multiply(X3,X2),identity),
inference(transitivity,[status(thm)],[c406,c409]) ).
cnf(c411,plain,
least_upper_bound(inverse(inverse(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))))),inverse(inverse(least_upper_bound(multiply(X3,X2),identity)))) = least_upper_bound(multiply(X3,X2),identity),
inference(transitivity,[status(thm)],[c405,c410]) ).
cnf(c412,plain,
least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),inverse(inverse(least_upper_bound(multiply(X3,X2),identity)))) = least_upper_bound(multiply(X3,X2),identity),
inference(transitivity,[status(thm)],[c121,c411]) ).
cnf(c413,plain,
least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),least_upper_bound(multiply(X3,X2),identity)) = least_upper_bound(multiply(X3,X2),identity),
inference(transitivity,[status(thm)],[c118,c412]) ).
cnf(c414,plain,
least_upper_bound(multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))),multiply(X3,X2)) = least_upper_bound(multiply(X3,X2),identity),
inference(transitivity,[status(thm)],[c115,c413]) ).
cnf(c415,plain,
multiply(X3,inverse(greatest_lower_bound(X3,inverse(X2)))) = least_upper_bound(multiply(X3,X2),identity),
inference(transitivity,[status(thm)],[c99,c414]) ).
cnf(c416,plain,
multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) = least_upper_bound(multiply(a,b),identity),
inference(substitution,[status(thm)],[c415]) ).
cnf(c417,plain,
least_upper_bound(multiply(a,b),identity) = multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(symmetry,[status(thm)],[c416]) ).
cnf(c418,plain,
$false,
inference(resolution,[status(thm)],[c1,c417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP186-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % 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 09:41:46 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.51/2.37 Command-line arguments: --flatten-regeneralise
% 14.51/2.37
% 14.51/2.37 % SZS status Unsatisfiable
% 14.51/2.37
% 14.51/2.40 % SZS output start CNFRefutation
% See solution above
% 14.62/2.60
% 14.62/2.60 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------