%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP180-2 : 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 10:09:35 AM UTC 2026
% Result : Unsatisfiable 36.15s 5.08s
% Output : CNFRefutation 39.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 17
% Syntax : Number of clauses : 319 ( 319 unt; 0 nHn; 6 RR)
% Number of literals : 319 ( 318 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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 : 674 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != least_upper_bound(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p11) ).
cnf(c2,axiom,
inverse(inverse(X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(X2,multiply(inverse(greatest_lower_bound(X2,X3)),X3)) = multiply(inverse(inverse(X2)),multiply(inverse(greatest_lower_bound(X2,X3)),X3)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
inverse(inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2))) = multiply(inverse(greatest_lower_bound(X3,X2)),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
multiply(inverse(greatest_lower_bound(X3,X2)),X2) = inverse(inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2))),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,hypothesis,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11_3) ).
cnf(c8,plain,
inverse(multiply(inverse(X2),X3)) = multiply(inverse(X3),inverse(inverse(X2))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(inverse(X3),inverse(inverse(X2))) = multiply(inverse(X3),X2),
inference(congruence,[status(thm)],[c2]) ).
cnf(c10,plain,
inverse(multiply(inverse(X2),X3)) = multiply(inverse(X3),X2),
inference(transitivity,[status(thm)],[c8,c9]) ).
cnf(c11,plain,
inverse(multiply(inverse(greatest_lower_bound(X2,X3)),X3)) = multiply(inverse(X3),greatest_lower_bound(X2,X3)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c13,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(inverse(X3),greatest_lower_bound(X2,X3)) = multiply(inverse(X3),greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,axiom,
multiply(X2,greatest_lower_bound(Y2,Z)) = greatest_lower_bound(multiply(X2,Y2),multiply(X2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).
cnf(c17,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c19,plain,
greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = greatest_lower_bound(identity,multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = greatest_lower_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c17,c19]) ).
cnf(c21,plain,
multiply(inverse(X3),greatest_lower_bound(X2,X3)) = greatest_lower_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c15,c20]) ).
cnf(c22,plain,
inverse(multiply(inverse(greatest_lower_bound(X2,X3)),X3)) = greatest_lower_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c11,c21]) ).
cnf(c23,plain,
inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2)) = greatest_lower_bound(identity,multiply(inverse(X2),X3)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c25,plain,
multiply(inverse(X2),X3) = multiply(inverse(X2),inverse(inverse(X3))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
greatest_lower_bound(identity,multiply(inverse(X2),X3)) = greatest_lower_bound(identity,multiply(inverse(X2),inverse(inverse(X3)))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
inverse(multiply(inverse(X3),X2)) = multiply(inverse(X2),inverse(inverse(X3))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c28,plain,
multiply(inverse(X2),inverse(inverse(X3))) = inverse(multiply(inverse(X3),X2)),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
greatest_lower_bound(identity,multiply(inverse(X2),inverse(inverse(X3)))) = greatest_lower_bound(identity,inverse(multiply(inverse(X3),X2))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c31,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
greatest_lower_bound(identity,inverse(multiply(inverse(X3),X2))) = greatest_lower_bound(inverse(identity),inverse(multiply(inverse(X3),X2))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c34,plain,
multiply(inverse(X2),identity) = multiply(inverse(X2),inverse(identity)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
inverse(multiply(identity,X2)) = multiply(inverse(X2),inverse(identity)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c36,plain,
multiply(inverse(X2),inverse(identity)) = inverse(multiply(identity,X2)),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c38,plain,
inverse(multiply(identity,X2)) = inverse(X2),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
multiply(inverse(X2),inverse(identity)) = inverse(X2),
inference(transitivity,[status(thm)],[c36,c38]) ).
cnf(c40,plain,
multiply(inverse(X2),identity) = inverse(X2),
inference(transitivity,[status(thm)],[c34,c39]) ).
cnf(c41,plain,
multiply(inverse(least_upper_bound(X3,X2)),identity) = inverse(least_upper_bound(X3,X2)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
inverse(least_upper_bound(X3,X2)) = multiply(inverse(least_upper_bound(X3,X2)),identity),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
greatest_lower_bound(inverse(X3),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(inverse(X3),multiply(inverse(least_upper_bound(X3,X2)),identity)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
greatest_lower_bound(multiply(X3,X4),X2) = greatest_lower_bound(X2,multiply(X3,X4)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c45,plain,
greatest_lower_bound(X3,multiply(X4,X2)) = greatest_lower_bound(multiply(X4,X2),X3),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(inverse(X4),greatest_lower_bound(X3,multiply(X4,X2))) = multiply(inverse(X4),greatest_lower_bound(multiply(X4,X2),X3)),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(inverse(X4),greatest_lower_bound(multiply(X4,X2),X3)) = greatest_lower_bound(multiply(inverse(X4),multiply(X4,X2)),multiply(inverse(X4),X3)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c48,axiom,
multiply(multiply(X2,Y2),Z2) = multiply(X2,multiply(Y2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c49,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c18]) ).
cnf(c52,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c51,c37]) ).
cnf(c53,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c50,c52]) ).
cnf(c54,plain,
greatest_lower_bound(multiply(inverse(X4),multiply(X4,X2)),multiply(inverse(X4),X3)) = greatest_lower_bound(X2,multiply(inverse(X4),X3)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(inverse(X4),greatest_lower_bound(multiply(X4,X2),X3)) = greatest_lower_bound(X2,multiply(inverse(X4),X3)),
inference(transitivity,[status(thm)],[c47,c54]) ).
cnf(c56,plain,
multiply(inverse(X4),greatest_lower_bound(X3,multiply(X4,X2))) = greatest_lower_bound(X2,multiply(inverse(X4),X3)),
inference(transitivity,[status(thm)],[c46,c55]) ).
cnf(c57,plain,
multiply(inverse(least_upper_bound(X3,X2)),greatest_lower_bound(identity,multiply(least_upper_bound(X3,X2),inverse(X3)))) = greatest_lower_bound(inverse(X3),multiply(inverse(least_upper_bound(X3,X2)),identity)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
greatest_lower_bound(inverse(X3),multiply(inverse(least_upper_bound(X3,X2)),identity)) = multiply(inverse(least_upper_bound(X3,X2)),greatest_lower_bound(identity,multiply(least_upper_bound(X3,X2),inverse(X3)))),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c60,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
multiply(greatest_lower_bound(X3,X2),inverse(X2)) = multiply(greatest_lower_bound(X2,X3),inverse(X2)),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,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(c63,plain,
multiply(greatest_lower_bound(X2,X3),inverse(X2)) = greatest_lower_bound(multiply(X2,inverse(X2)),multiply(X3,inverse(X2))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c65,plain,
multiply(X2,inverse(X2)) = multiply(inverse(inverse(X2)),inverse(X2)),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = identity,
inference(substitution,[status(thm)],[c18]) ).
cnf(c67,plain,
multiply(X2,inverse(X2)) = identity,
inference(transitivity,[status(thm)],[c65,c66]) ).
cnf(c68,plain,
greatest_lower_bound(multiply(X2,inverse(X2)),multiply(X3,inverse(X2))) = greatest_lower_bound(identity,multiply(X3,inverse(X2))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
multiply(greatest_lower_bound(X2,X3),inverse(X2)) = greatest_lower_bound(identity,multiply(X3,inverse(X2))),
inference(transitivity,[status(thm)],[c63,c68]) ).
cnf(c70,plain,
multiply(greatest_lower_bound(X3,X2),inverse(X2)) = greatest_lower_bound(identity,multiply(X3,inverse(X2))),
inference(transitivity,[status(thm)],[c61,c69]) ).
cnf(c71,plain,
multiply(greatest_lower_bound(least_upper_bound(X3,X2),X3),inverse(X3)) = greatest_lower_bound(identity,multiply(least_upper_bound(X3,X2),inverse(X3))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X3,X2),inverse(X3))) = multiply(greatest_lower_bound(least_upper_bound(X3,X2),X3),inverse(X3)),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = greatest_lower_bound(least_upper_bound(X3,X2),X3),
inference(substitution,[status(thm)],[c12]) ).
cnf(c74,plain,
greatest_lower_bound(least_upper_bound(X3,X2),X3) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c76,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
greatest_lower_bound(least_upper_bound(X3,X2),X3) = X3,
inference(transitivity,[status(thm)],[c74,c76]) ).
cnf(c78,plain,
multiply(greatest_lower_bound(least_upper_bound(X3,X2),X3),inverse(X3)) = multiply(X3,inverse(X3)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(greatest_lower_bound(least_upper_bound(X3,X2),X3),inverse(X3)) = identity,
inference(transitivity,[status(thm)],[c78,c67]) ).
cnf(c80,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X3,X2),inverse(X3))) = identity,
inference(transitivity,[status(thm)],[c72,c79]) ).
cnf(c81,plain,
multiply(inverse(least_upper_bound(X3,X2)),greatest_lower_bound(identity,multiply(least_upper_bound(X3,X2),inverse(X3)))) = multiply(inverse(least_upper_bound(X3,X2)),identity),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
multiply(inverse(least_upper_bound(X3,X2)),identity) = inverse(least_upper_bound(X3,X2)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c83,plain,
multiply(inverse(least_upper_bound(X3,X2)),greatest_lower_bound(identity,multiply(least_upper_bound(X3,X2),inverse(X3)))) = inverse(least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c81,c82]) ).
cnf(c84,plain,
greatest_lower_bound(inverse(X3),multiply(inverse(least_upper_bound(X3,X2)),identity)) = inverse(least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c58,c83]) ).
cnf(c85,plain,
greatest_lower_bound(inverse(X3),inverse(least_upper_bound(X3,X2))) = inverse(least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c43,c84]) ).
cnf(c86,plain,
inverse(least_upper_bound(X3,X2)) = greatest_lower_bound(inverse(X3),inverse(least_upper_bound(X3,X2))),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
multiply(inverse(least_upper_bound(X2,X3)),identity) = inverse(least_upper_bound(X2,X3)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c88,plain,
inverse(least_upper_bound(X2,X3)) = multiply(inverse(least_upper_bound(X2,X3)),identity),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
greatest_lower_bound(inverse(X3),inverse(least_upper_bound(X2,X3))) = greatest_lower_bound(inverse(X3),multiply(inverse(least_upper_bound(X2,X3)),identity)),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
multiply(inverse(least_upper_bound(X2,X3)),greatest_lower_bound(identity,multiply(least_upper_bound(X2,X3),inverse(X3)))) = greatest_lower_bound(inverse(X3),multiply(inverse(least_upper_bound(X2,X3)),identity)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c91,plain,
greatest_lower_bound(inverse(X3),multiply(inverse(least_upper_bound(X2,X3)),identity)) = multiply(inverse(least_upper_bound(X2,X3)),greatest_lower_bound(identity,multiply(least_upper_bound(X2,X3),inverse(X3)))),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
multiply(greatest_lower_bound(least_upper_bound(X3,X2),X2),inverse(X2)) = greatest_lower_bound(identity,multiply(least_upper_bound(X3,X2),inverse(X2))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c93,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X3,X2),inverse(X2))) = multiply(greatest_lower_bound(least_upper_bound(X3,X2),X2),inverse(X2)),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
greatest_lower_bound(X2,least_upper_bound(X3,X2)) = greatest_lower_bound(least_upper_bound(X3,X2),X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c95,plain,
greatest_lower_bound(least_upper_bound(X3,X2),X2) = greatest_lower_bound(X2,least_upper_bound(X3,X2)),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c97,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c96]) ).
cnf(c98,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c75]) ).
cnf(c101,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c99,c100]) ).
cnf(c102,plain,
greatest_lower_bound(X2,least_upper_bound(X3,X2)) = X2,
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
greatest_lower_bound(least_upper_bound(X3,X2),X2) = X2,
inference(transitivity,[status(thm)],[c95,c102]) ).
cnf(c104,plain,
multiply(greatest_lower_bound(least_upper_bound(X3,X2),X2),inverse(X2)) = multiply(X2,inverse(X2)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
multiply(greatest_lower_bound(least_upper_bound(X3,X2),X2),inverse(X2)) = identity,
inference(transitivity,[status(thm)],[c104,c67]) ).
cnf(c106,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X3,X2),inverse(X2))) = identity,
inference(transitivity,[status(thm)],[c93,c105]) ).
cnf(c107,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X2,X3),inverse(X3))) = identity,
inference(substitution,[status(thm)],[c106]) ).
cnf(c108,plain,
multiply(inverse(least_upper_bound(X2,X3)),greatest_lower_bound(identity,multiply(least_upper_bound(X2,X3),inverse(X3)))) = multiply(inverse(least_upper_bound(X2,X3)),identity),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
multiply(inverse(least_upper_bound(X2,X3)),identity) = inverse(least_upper_bound(X2,X3)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c110,plain,
multiply(inverse(least_upper_bound(X2,X3)),greatest_lower_bound(identity,multiply(least_upper_bound(X2,X3),inverse(X3)))) = inverse(least_upper_bound(X2,X3)),
inference(transitivity,[status(thm)],[c108,c109]) ).
cnf(c111,plain,
greatest_lower_bound(inverse(X3),multiply(inverse(least_upper_bound(X2,X3)),identity)) = inverse(least_upper_bound(X2,X3)),
inference(transitivity,[status(thm)],[c91,c110]) ).
cnf(c112,plain,
greatest_lower_bound(inverse(X3),inverse(least_upper_bound(X2,X3))) = inverse(least_upper_bound(X2,X3)),
inference(transitivity,[status(thm)],[c89,c111]) ).
cnf(c113,plain,
greatest_lower_bound(inverse(X2),inverse(least_upper_bound(X3,X2))) = inverse(least_upper_bound(X3,X2)),
inference(substitution,[status(thm)],[c112]) ).
cnf(c114,plain,
inverse(least_upper_bound(X3,X2)) = greatest_lower_bound(inverse(X2),inverse(least_upper_bound(X3,X2))),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
greatest_lower_bound(inverse(X3),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(inverse(X3),greatest_lower_bound(inverse(X2),inverse(least_upper_bound(X3,X2)))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
inverse(X2) = multiply(inverse(X2),identity),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c117,plain,
greatest_lower_bound(inverse(X2),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(multiply(inverse(X2),identity),inverse(least_upper_bound(X3,X2))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
greatest_lower_bound(inverse(X3),greatest_lower_bound(inverse(X2),inverse(least_upper_bound(X3,X2)))) = greatest_lower_bound(inverse(X3),greatest_lower_bound(multiply(inverse(X2),identity),inverse(least_upper_bound(X3,X2)))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,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(c120,plain,
greatest_lower_bound(inverse(X3),greatest_lower_bound(multiply(inverse(X2),identity),inverse(least_upper_bound(X3,X2)))) = greatest_lower_bound(greatest_lower_bound(inverse(X3),multiply(inverse(X2),identity)),inverse(least_upper_bound(X3,X2))),
inference(substitution,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(inverse(X2),greatest_lower_bound(identity,multiply(X2,inverse(X3)))) = greatest_lower_bound(inverse(X3),multiply(inverse(X2),identity)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c122,plain,
greatest_lower_bound(inverse(X3),multiply(inverse(X2),identity)) = multiply(inverse(X2),greatest_lower_bound(identity,multiply(X2,inverse(X3)))),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c123,plain,
greatest_lower_bound(greatest_lower_bound(inverse(X3),multiply(inverse(X2),identity)),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(multiply(inverse(X2),greatest_lower_bound(identity,multiply(X2,inverse(X3)))),inverse(least_upper_bound(X3,X2))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c125,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
multiply(greatest_lower_bound(X3,X2),inverse(X3)) = multiply(greatest_lower_bound(X2,X3),inverse(X3)),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
multiply(greatest_lower_bound(X2,X3),inverse(X3)) = greatest_lower_bound(identity,multiply(X2,inverse(X3))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c128,plain,
multiply(greatest_lower_bound(X3,X2),inverse(X3)) = greatest_lower_bound(identity,multiply(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c126,c127]) ).
cnf(c129,plain,
greatest_lower_bound(identity,multiply(X2,inverse(X3))) = multiply(greatest_lower_bound(X3,X2),inverse(X3)),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(inverse(X2),greatest_lower_bound(identity,multiply(X2,inverse(X3)))) = multiply(inverse(X2),multiply(greatest_lower_bound(X3,X2),inverse(X3))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
greatest_lower_bound(multiply(inverse(X2),greatest_lower_bound(identity,multiply(X2,inverse(X3)))),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(multiply(inverse(X2),multiply(greatest_lower_bound(X3,X2),inverse(X3))),inverse(least_upper_bound(X3,X2))),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
inverse(inverse(greatest_lower_bound(X3,X2))) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c133,plain,
greatest_lower_bound(X3,X2) = inverse(inverse(greatest_lower_bound(X3,X2))),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
multiply(greatest_lower_bound(X3,X2),inverse(X3)) = multiply(inverse(inverse(greatest_lower_bound(X3,X2))),inverse(X3)),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
multiply(inverse(X2),multiply(greatest_lower_bound(X3,X2),inverse(X3))) = multiply(inverse(X2),multiply(inverse(inverse(greatest_lower_bound(X3,X2))),inverse(X3))),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
greatest_lower_bound(multiply(inverse(X2),multiply(greatest_lower_bound(X3,X2),inverse(X3))),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(multiply(inverse(X2),multiply(inverse(inverse(greatest_lower_bound(X3,X2))),inverse(X3))),inverse(least_upper_bound(X3,X2))),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
multiply(multiply(inverse(X2),inverse(inverse(greatest_lower_bound(X3,X2)))),inverse(X3)) = multiply(inverse(X2),multiply(inverse(inverse(greatest_lower_bound(X3,X2))),inverse(X3))),
inference(substitution,[status(thm)],[c48]) ).
cnf(c138,plain,
multiply(inverse(X2),multiply(inverse(inverse(greatest_lower_bound(X3,X2))),inverse(X3))) = multiply(multiply(inverse(X2),inverse(inverse(greatest_lower_bound(X3,X2)))),inverse(X3)),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
greatest_lower_bound(multiply(inverse(X2),multiply(inverse(inverse(greatest_lower_bound(X3,X2))),inverse(X3))),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(multiply(multiply(inverse(X2),inverse(inverse(greatest_lower_bound(X3,X2)))),inverse(X3)),inverse(least_upper_bound(X3,X2))),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2)) = multiply(inverse(X2),inverse(inverse(greatest_lower_bound(X3,X2)))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c141,plain,
multiply(inverse(X2),inverse(inverse(greatest_lower_bound(X3,X2)))) = inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2)),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
multiply(multiply(inverse(X2),inverse(inverse(greatest_lower_bound(X3,X2)))),inverse(X3)) = multiply(inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2)),inverse(X3)),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
greatest_lower_bound(multiply(multiply(inverse(X2),inverse(inverse(greatest_lower_bound(X3,X2)))),inverse(X3)),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(multiply(inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2)),inverse(X3)),inverse(least_upper_bound(X3,X2))),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
inverse(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2))) = multiply(inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2)),inverse(X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c145,plain,
multiply(inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2)),inverse(X3)) = inverse(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2))),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,plain,
greatest_lower_bound(multiply(inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2)),inverse(X3)),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(inverse(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2))),inverse(least_upper_bound(X3,X2))),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
greatest_lower_bound(inverse(least_upper_bound(X3,X2)),inverse(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)))) = greatest_lower_bound(inverse(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2))),inverse(least_upper_bound(X3,X2))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c148,plain,
greatest_lower_bound(inverse(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2))),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(inverse(least_upper_bound(X3,X2)),inverse(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)))),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X3,least_upper_bound(X4,X2)),
inference(substitution,[status(thm)],[c96]) ).
cnf(c150,plain,
least_upper_bound(X3,least_upper_bound(X4,X2)) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,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(c152,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c151]) ).
cnf(c153,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X4,least_upper_bound(X2,X3)),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c154,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c96]) ).
cnf(c155,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c153,c155]) ).
cnf(c157,plain,
least_upper_bound(X3,least_upper_bound(X4,X2)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c150,c156]) ).
cnf(c158,plain,
least_upper_bound(multiply(X4,multiply(inverse(greatest_lower_bound(X4,X3)),X2)),least_upper_bound(X5,X2)) = least_upper_bound(X5,least_upper_bound(multiply(X4,multiply(inverse(greatest_lower_bound(X4,X3)),X2)),X2)),
inference(substitution,[status(thm)],[c157]) ).
cnf(c159,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c160,plain,
multiply(X3,multiply(inverse(X3),X2)) = multiply(inverse(inverse(X3)),multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),X2)) = X2,
inference(substitution,[status(thm)],[c53]) ).
cnf(c162,plain,
multiply(X3,multiply(inverse(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c160,c161]) ).
cnf(c163,plain,
multiply(greatest_lower_bound(X4,X3),multiply(inverse(greatest_lower_bound(X4,X3)),X2)) = X2,
inference(substitution,[status(thm)],[c162]) ).
cnf(c164,plain,
X2 = multiply(greatest_lower_bound(X4,X3),multiply(inverse(greatest_lower_bound(X4,X3)),X2)),
inference(symmetry,[status(thm)],[c163]) ).
cnf(c165,plain,
least_upper_bound(multiply(X4,multiply(inverse(greatest_lower_bound(X4,X3)),X2)),X2) = least_upper_bound(multiply(X4,multiply(inverse(greatest_lower_bound(X4,X3)),X2)),multiply(greatest_lower_bound(X4,X3),multiply(inverse(greatest_lower_bound(X4,X3)),X2))),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,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(c167,plain,
multiply(least_upper_bound(X3,X4),X2) = least_upper_bound(multiply(X3,X2),multiply(X4,X2)),
inference(substitution,[status(thm)],[c166]) ).
cnf(c168,plain,
least_upper_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(least_upper_bound(X3,X4),X2),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c96]) ).
cnf(c170,plain,
multiply(least_upper_bound(X3,X4),X2) = multiply(least_upper_bound(X4,X3),X2),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
least_upper_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(least_upper_bound(X4,X3),X2),
inference(transitivity,[status(thm)],[c168,c170]) ).
cnf(c172,plain,
least_upper_bound(multiply(X4,multiply(inverse(greatest_lower_bound(X4,X3)),X2)),multiply(greatest_lower_bound(X4,X3),multiply(inverse(greatest_lower_bound(X4,X3)),X2))) = multiply(least_upper_bound(greatest_lower_bound(X4,X3),X4),multiply(inverse(greatest_lower_bound(X4,X3)),X2)),
inference(substitution,[status(thm)],[c171]) ).
cnf(c173,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = least_upper_bound(greatest_lower_bound(X3,X2),X3),
inference(substitution,[status(thm)],[c96]) ).
cnf(c174,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X3) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c176,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c175]) ).
cnf(c177,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X3) = X3,
inference(transitivity,[status(thm)],[c174,c176]) ).
cnf(c178,plain,
multiply(least_upper_bound(greatest_lower_bound(X4,X3),X4),multiply(inverse(greatest_lower_bound(X4,X3)),X2)) = multiply(X4,multiply(inverse(greatest_lower_bound(X4,X3)),X2)),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
least_upper_bound(multiply(X4,multiply(inverse(greatest_lower_bound(X4,X3)),X2)),multiply(greatest_lower_bound(X4,X3),multiply(inverse(greatest_lower_bound(X4,X3)),X2))) = multiply(X4,multiply(inverse(greatest_lower_bound(X4,X3)),X2)),
inference(transitivity,[status(thm)],[c172,c178]) ).
cnf(c180,plain,
least_upper_bound(multiply(X4,multiply(inverse(greatest_lower_bound(X4,X3)),X2)),X2) = multiply(X4,multiply(inverse(greatest_lower_bound(X4,X3)),X2)),
inference(transitivity,[status(thm)],[c165,c179]) ).
cnf(c181,plain,
least_upper_bound(X2,least_upper_bound(multiply(X5,multiply(inverse(greatest_lower_bound(X5,X4)),X3)),X3)) = least_upper_bound(X2,multiply(X5,multiply(inverse(greatest_lower_bound(X5,X4)),X3))),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
least_upper_bound(X2,multiply(X5,multiply(inverse(greatest_lower_bound(X5,X4)),X3))) = least_upper_bound(multiply(X5,multiply(inverse(greatest_lower_bound(X5,X4)),X3)),X2),
inference(substitution,[status(thm)],[c96]) ).
cnf(c183,plain,
least_upper_bound(X2,least_upper_bound(multiply(X5,multiply(inverse(greatest_lower_bound(X5,X4)),X3)),X3)) = least_upper_bound(multiply(X5,multiply(inverse(greatest_lower_bound(X5,X4)),X3)),X2),
inference(transitivity,[status(thm)],[c181,c182]) ).
cnf(c184,plain,
least_upper_bound(multiply(X5,multiply(inverse(greatest_lower_bound(X5,X4)),X3)),least_upper_bound(X2,X3)) = least_upper_bound(multiply(X5,multiply(inverse(greatest_lower_bound(X5,X4)),X3)),X2),
inference(transitivity,[status(thm)],[c158,c183]) ).
cnf(c185,plain,
least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),least_upper_bound(X3,X2)) = least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),X3),
inference(substitution,[status(thm)],[c184]) ).
cnf(c186,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c187,plain,
multiply(X2,identity) = multiply(inverse(inverse(X2)),identity),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
multiply(inverse(inverse(X2)),identity) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c189,plain,
multiply(inverse(inverse(X2)),identity) = X2,
inference(transitivity,[status(thm)],[c188,c2]) ).
cnf(c190,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c187,c189]) ).
cnf(c191,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),X3) = least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),multiply(X3,identity)),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,axiom,
multiply(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
cnf(c194,plain,
multiply(X3,least_upper_bound(multiply(inverse(greatest_lower_bound(X3,X2)),X2),identity)) = least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),multiply(X3,identity)),
inference(substitution,[status(thm)],[c193]) ).
cnf(c195,plain,
least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),multiply(X3,identity)) = multiply(X3,least_upper_bound(multiply(inverse(greatest_lower_bound(X3,X2)),X2),identity)),
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,plain,
multiply(inverse(greatest_lower_bound(X3,X2)),greatest_lower_bound(X3,X2)) = identity,
inference(substitution,[status(thm)],[c18]) ).
cnf(c197,plain,
identity = multiply(inverse(greatest_lower_bound(X3,X2)),greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c198,plain,
least_upper_bound(multiply(inverse(greatest_lower_bound(X3,X2)),X2),identity) = least_upper_bound(multiply(inverse(greatest_lower_bound(X3,X2)),X2),multiply(inverse(greatest_lower_bound(X3,X2)),greatest_lower_bound(X3,X2))),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
multiply(X4,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X4,X2),multiply(X4,X3)),
inference(substitution,[status(thm)],[c193]) ).
cnf(c200,plain,
least_upper_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,least_upper_bound(X2,X3)),
inference(symmetry,[status(thm)],[c199]) ).
cnf(c201,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c96]) ).
cnf(c202,plain,
multiply(X4,least_upper_bound(X2,X3)) = multiply(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
least_upper_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c200,c202]) ).
cnf(c204,plain,
least_upper_bound(multiply(inverse(greatest_lower_bound(X3,X2)),X2),multiply(inverse(greatest_lower_bound(X3,X2)),greatest_lower_bound(X3,X2))) = multiply(inverse(greatest_lower_bound(X3,X2)),least_upper_bound(greatest_lower_bound(X3,X2),X2)),
inference(substitution,[status(thm)],[c203]) ).
cnf(c205,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = least_upper_bound(greatest_lower_bound(X3,X2),X2),
inference(substitution,[status(thm)],[c96]) ).
cnf(c206,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X2) = least_upper_bound(X2,greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c205]) ).
cnf(c207,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c12]) ).
cnf(c208,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c175]) ).
cnf(c211,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c209,c210]) ).
cnf(c212,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = X2,
inference(substitution,[status(thm)],[c211]) ).
cnf(c213,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X2) = X2,
inference(transitivity,[status(thm)],[c206,c212]) ).
cnf(c214,plain,
multiply(inverse(greatest_lower_bound(X3,X2)),least_upper_bound(greatest_lower_bound(X3,X2),X2)) = multiply(inverse(greatest_lower_bound(X3,X2)),X2),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
least_upper_bound(multiply(inverse(greatest_lower_bound(X3,X2)),X2),multiply(inverse(greatest_lower_bound(X3,X2)),greatest_lower_bound(X3,X2))) = multiply(inverse(greatest_lower_bound(X3,X2)),X2),
inference(transitivity,[status(thm)],[c204,c214]) ).
cnf(c216,plain,
least_upper_bound(multiply(inverse(greatest_lower_bound(X3,X2)),X2),identity) = multiply(inverse(greatest_lower_bound(X3,X2)),X2),
inference(transitivity,[status(thm)],[c198,c215]) ).
cnf(c217,plain,
multiply(X3,least_upper_bound(multiply(inverse(greatest_lower_bound(X3,X2)),X2),identity)) = multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),multiply(X3,identity)) = multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),
inference(transitivity,[status(thm)],[c195,c217]) ).
cnf(c219,plain,
least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),X3) = multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),
inference(transitivity,[status(thm)],[c192,c218]) ).
cnf(c220,plain,
least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),least_upper_bound(X3,X2)) = multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),
inference(transitivity,[status(thm)],[c185,c219]) ).
cnf(c221,plain,
multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)) = least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),least_upper_bound(X3,X2)),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c222,plain,
inverse(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2))) = inverse(least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),least_upper_bound(X3,X2))),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
greatest_lower_bound(inverse(least_upper_bound(X3,X2)),inverse(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)))) = greatest_lower_bound(inverse(least_upper_bound(X3,X2)),inverse(least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),least_upper_bound(X3,X2)))),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
greatest_lower_bound(inverse(least_upper_bound(X3,X2)),inverse(least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),least_upper_bound(X3,X2)))) = inverse(least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),least_upper_bound(X3,X2))),
inference(substitution,[status(thm)],[c112]) ).
cnf(c225,plain,
inverse(least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),least_upper_bound(X3,X2))) = inverse(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2))),
inference(congruence,[status(thm)],[c220]) ).
cnf(c226,plain,
inverse(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2))) = multiply(inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2)),inverse(X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c227,plain,
inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2)) = multiply(inverse(X2),inverse(inverse(greatest_lower_bound(X3,X2)))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c228,plain,
multiply(inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2)),inverse(X3)) = multiply(multiply(inverse(X2),inverse(inverse(greatest_lower_bound(X3,X2)))),inverse(X3)),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
multiply(multiply(inverse(X2),inverse(inverse(greatest_lower_bound(X3,X2)))),inverse(X3)) = multiply(inverse(X2),multiply(inverse(inverse(greatest_lower_bound(X3,X2))),inverse(X3))),
inference(substitution,[status(thm)],[c48]) ).
cnf(c230,plain,
inverse(inverse(greatest_lower_bound(X3,X2))) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c231,plain,
multiply(inverse(inverse(greatest_lower_bound(X3,X2))),inverse(X3)) = multiply(greatest_lower_bound(X3,X2),inverse(X3)),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
multiply(inverse(X2),multiply(inverse(inverse(greatest_lower_bound(X3,X2))),inverse(X3))) = multiply(inverse(X2),multiply(greatest_lower_bound(X3,X2),inverse(X3))),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
multiply(inverse(X2),multiply(greatest_lower_bound(X3,X2),inverse(X3))) = multiply(inverse(X2),greatest_lower_bound(identity,multiply(X2,inverse(X3)))),
inference(congruence,[status(thm)],[c128]) ).
cnf(c234,plain,
multiply(inverse(X2),greatest_lower_bound(identity,multiply(X2,inverse(X3)))) = greatest_lower_bound(inverse(X3),multiply(inverse(X2),identity)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c235,plain,
greatest_lower_bound(inverse(X3),multiply(inverse(X2),identity)) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c236,plain,
multiply(inverse(X2),greatest_lower_bound(identity,multiply(X2,inverse(X3)))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c234,c235]) ).
cnf(c237,plain,
multiply(inverse(X2),multiply(greatest_lower_bound(X3,X2),inverse(X3))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c233,c236]) ).
cnf(c238,plain,
multiply(inverse(X2),multiply(inverse(inverse(greatest_lower_bound(X3,X2))),inverse(X3))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c232,c237]) ).
cnf(c239,plain,
multiply(multiply(inverse(X2),inverse(inverse(greatest_lower_bound(X3,X2)))),inverse(X3)) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c229,c238]) ).
cnf(c240,plain,
multiply(inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2)),inverse(X3)) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c228,c239]) ).
cnf(c241,plain,
inverse(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c226,c240]) ).
cnf(c242,plain,
inverse(least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),least_upper_bound(X3,X2))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c225,c241]) ).
cnf(c243,plain,
greatest_lower_bound(inverse(least_upper_bound(X3,X2)),inverse(least_upper_bound(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)),least_upper_bound(X3,X2)))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c224,c242]) ).
cnf(c244,plain,
greatest_lower_bound(inverse(least_upper_bound(X3,X2)),inverse(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c223,c243]) ).
cnf(c245,plain,
greatest_lower_bound(inverse(multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2))),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c148,c244]) ).
cnf(c246,plain,
greatest_lower_bound(multiply(inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2)),inverse(X3)),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c146,c245]) ).
cnf(c247,plain,
greatest_lower_bound(multiply(multiply(inverse(X2),inverse(inverse(greatest_lower_bound(X3,X2)))),inverse(X3)),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c143,c246]) ).
cnf(c248,plain,
greatest_lower_bound(multiply(inverse(X2),multiply(inverse(inverse(greatest_lower_bound(X3,X2))),inverse(X3))),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c139,c247]) ).
cnf(c249,plain,
greatest_lower_bound(multiply(inverse(X2),multiply(greatest_lower_bound(X3,X2),inverse(X3))),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c136,c248]) ).
cnf(c250,plain,
greatest_lower_bound(multiply(inverse(X2),greatest_lower_bound(identity,multiply(X2,inverse(X3)))),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c131,c249]) ).
cnf(c251,plain,
greatest_lower_bound(greatest_lower_bound(inverse(X3),multiply(inverse(X2),identity)),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c123,c250]) ).
cnf(c252,plain,
greatest_lower_bound(inverse(X3),greatest_lower_bound(multiply(inverse(X2),identity),inverse(least_upper_bound(X3,X2)))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c120,c251]) ).
cnf(c253,plain,
greatest_lower_bound(inverse(X3),greatest_lower_bound(inverse(X2),inverse(least_upper_bound(X3,X2)))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c118,c252]) ).
cnf(c254,plain,
greatest_lower_bound(inverse(X3),inverse(least_upper_bound(X3,X2))) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c115,c253]) ).
cnf(c255,plain,
inverse(least_upper_bound(X3,X2)) = greatest_lower_bound(inverse(X3),inverse(X2)),
inference(transitivity,[status(thm)],[c86,c254]) ).
cnf(c256,plain,
inverse(least_upper_bound(identity,multiply(inverse(X3),X2))) = greatest_lower_bound(inverse(identity),inverse(multiply(inverse(X3),X2))),
inference(substitution,[status(thm)],[c255]) ).
cnf(c257,plain,
greatest_lower_bound(inverse(identity),inverse(multiply(inverse(X3),X2))) = inverse(least_upper_bound(identity,multiply(inverse(X3),X2))),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c258,plain,
multiply(inverse(inverse(X2)),multiply(inverse(X2),least_upper_bound(X4,X3))) = least_upper_bound(X4,X3),
inference(substitution,[status(thm)],[c53]) ).
cnf(c259,plain,
least_upper_bound(X4,X3) = multiply(inverse(inverse(X2)),multiply(inverse(X2),least_upper_bound(X4,X3))),
inference(symmetry,[status(thm)],[c258]) ).
cnf(c260,plain,
multiply(inverse(X4),least_upper_bound(X4,X3)) = multiply(inverse(X4),multiply(inverse(inverse(X2)),multiply(inverse(X2),least_upper_bound(X4,X3)))),
inference(congruence,[status(thm)],[c259]) ).
cnf(c261,plain,
multiply(multiply(inverse(X4),inverse(inverse(X2))),multiply(inverse(X2),least_upper_bound(X4,X3))) = multiply(inverse(X4),multiply(inverse(inverse(X2)),multiply(inverse(X2),least_upper_bound(X4,X3)))),
inference(substitution,[status(thm)],[c48]) ).
cnf(c262,plain,
multiply(inverse(X4),multiply(inverse(inverse(X2)),multiply(inverse(X2),least_upper_bound(X4,X3)))) = multiply(multiply(inverse(X4),inverse(inverse(X2))),multiply(inverse(X2),least_upper_bound(X4,X3))),
inference(symmetry,[status(thm)],[c261]) ).
cnf(c263,plain,
inverse(multiply(inverse(X2),X3)) = multiply(inverse(X3),inverse(inverse(X2))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c264,plain,
multiply(inverse(X3),inverse(inverse(X2))) = inverse(multiply(inverse(X2),X3)),
inference(symmetry,[status(thm)],[c263]) ).
cnf(c265,plain,
multiply(multiply(inverse(X4),inverse(inverse(X2))),multiply(inverse(X2),least_upper_bound(X4,X3))) = multiply(inverse(multiply(inverse(X2),X4)),multiply(inverse(X2),least_upper_bound(X4,X3))),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
least_upper_bound(multiply(inverse(X2),X3),multiply(inverse(X2),X4)) = multiply(inverse(X2),least_upper_bound(X4,X3)),
inference(substitution,[status(thm)],[c203]) ).
cnf(c267,plain,
multiply(inverse(X2),least_upper_bound(X4,X3)) = least_upper_bound(multiply(inverse(X2),X3),multiply(inverse(X2),X4)),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c268,plain,
multiply(inverse(multiply(inverse(X2),X4)),multiply(inverse(X2),least_upper_bound(X4,X3))) = multiply(inverse(multiply(inverse(X2),X4)),least_upper_bound(multiply(inverse(X2),X3),multiply(inverse(X2),X4))),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c96]) ).
cnf(c270,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c269]) ).
cnf(c271,plain,
multiply(inverse(X3),least_upper_bound(X2,X3)) = multiply(inverse(X3),least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c193]) ).
cnf(c273,plain,
least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = least_upper_bound(identity,multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c274,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = least_upper_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c272,c273]) ).
cnf(c275,plain,
multiply(inverse(X3),least_upper_bound(X2,X3)) = least_upper_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c271,c274]) ).
cnf(c276,plain,
multiply(inverse(multiply(inverse(X2),X4)),least_upper_bound(multiply(inverse(X2),X3),multiply(inverse(X2),X4))) = least_upper_bound(identity,multiply(inverse(multiply(inverse(X2),X4)),multiply(inverse(X2),X3))),
inference(substitution,[status(thm)],[c275]) ).
cnf(c277,plain,
inverse(multiply(inverse(X2),X3)) = multiply(inverse(X3),inverse(inverse(X2))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c278,plain,
multiply(inverse(multiply(inverse(X2),X4)),multiply(inverse(X2),X3)) = multiply(multiply(inverse(X4),inverse(inverse(X2))),multiply(inverse(X2),X3)),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
least_upper_bound(identity,multiply(inverse(multiply(inverse(X2),X4)),multiply(inverse(X2),X3))) = least_upper_bound(identity,multiply(multiply(inverse(X4),inverse(inverse(X2))),multiply(inverse(X2),X3))),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,plain,
multiply(multiply(inverse(X4),inverse(inverse(X2))),multiply(inverse(X2),X3)) = multiply(inverse(X4),multiply(inverse(inverse(X2)),multiply(inverse(X2),X3))),
inference(substitution,[status(thm)],[c48]) ).
cnf(c281,plain,
least_upper_bound(identity,multiply(multiply(inverse(X4),inverse(inverse(X2))),multiply(inverse(X2),X3))) = least_upper_bound(identity,multiply(inverse(X4),multiply(inverse(inverse(X2)),multiply(inverse(X2),X3)))),
inference(congruence,[status(thm)],[c280]) ).
cnf(c282,plain,
multiply(inverse(inverse(X2)),multiply(inverse(X2),X3)) = multiply(X2,multiply(inverse(X2),X3)),
inference(congruence,[status(thm)],[c2]) ).
cnf(c283,plain,
multiply(inverse(X4),multiply(inverse(inverse(X2)),multiply(inverse(X2),X3))) = multiply(inverse(X4),multiply(X2,multiply(inverse(X2),X3))),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
least_upper_bound(identity,multiply(inverse(X4),multiply(inverse(inverse(X2)),multiply(inverse(X2),X3)))) = least_upper_bound(identity,multiply(inverse(X4),multiply(X2,multiply(inverse(X2),X3)))),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
multiply(X2,multiply(inverse(X2),X3)) = X3,
inference(substitution,[status(thm)],[c162]) ).
cnf(c286,plain,
multiply(inverse(X4),multiply(X2,multiply(inverse(X2),X3))) = multiply(inverse(X4),X3),
inference(congruence,[status(thm)],[c285]) ).
cnf(c287,plain,
least_upper_bound(identity,multiply(inverse(X4),multiply(X2,multiply(inverse(X2),X3)))) = least_upper_bound(identity,multiply(inverse(X4),X3)),
inference(congruence,[status(thm)],[c286]) ).
cnf(c288,plain,
least_upper_bound(identity,multiply(inverse(X4),multiply(inverse(inverse(X2)),multiply(inverse(X2),X3)))) = least_upper_bound(identity,multiply(inverse(X4),X3)),
inference(transitivity,[status(thm)],[c284,c287]) ).
cnf(c289,plain,
least_upper_bound(identity,multiply(multiply(inverse(X4),inverse(inverse(X2))),multiply(inverse(X2),X3))) = least_upper_bound(identity,multiply(inverse(X4),X3)),
inference(transitivity,[status(thm)],[c281,c288]) ).
cnf(c290,plain,
least_upper_bound(identity,multiply(inverse(multiply(inverse(X2),X4)),multiply(inverse(X2),X3))) = least_upper_bound(identity,multiply(inverse(X4),X3)),
inference(transitivity,[status(thm)],[c279,c289]) ).
cnf(c291,plain,
multiply(inverse(multiply(inverse(X2),X4)),least_upper_bound(multiply(inverse(X2),X3),multiply(inverse(X2),X4))) = least_upper_bound(identity,multiply(inverse(X4),X3)),
inference(transitivity,[status(thm)],[c276,c290]) ).
cnf(c292,plain,
multiply(inverse(multiply(inverse(X2),X4)),multiply(inverse(X2),least_upper_bound(X4,X3))) = least_upper_bound(identity,multiply(inverse(X4),X3)),
inference(transitivity,[status(thm)],[c268,c291]) ).
cnf(c293,plain,
multiply(multiply(inverse(X4),inverse(inverse(X2))),multiply(inverse(X2),least_upper_bound(X4,X3))) = least_upper_bound(identity,multiply(inverse(X4),X3)),
inference(transitivity,[status(thm)],[c265,c292]) ).
cnf(c294,plain,
multiply(inverse(X4),multiply(inverse(inverse(X2)),multiply(inverse(X2),least_upper_bound(X4,X3)))) = least_upper_bound(identity,multiply(inverse(X4),X3)),
inference(transitivity,[status(thm)],[c262,c293]) ).
cnf(c295,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = least_upper_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c260,c294]) ).
cnf(c296,plain,
least_upper_bound(identity,multiply(inverse(X3),X2)) = multiply(inverse(X3),least_upper_bound(X3,X2)),
inference(symmetry,[status(thm)],[c295]) ).
cnf(c297,plain,
inverse(least_upper_bound(identity,multiply(inverse(X3),X2))) = inverse(multiply(inverse(X3),least_upper_bound(X3,X2))),
inference(congruence,[status(thm)],[c296]) ).
cnf(c298,plain,
inverse(multiply(inverse(X3),least_upper_bound(X3,X2))) = multiply(inverse(least_upper_bound(X3,X2)),inverse(inverse(X3))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c299,plain,
multiply(inverse(least_upper_bound(X3,X2)),inverse(inverse(X3))) = multiply(inverse(least_upper_bound(X3,X2)),X3),
inference(congruence,[status(thm)],[c2]) ).
cnf(c300,plain,
inverse(multiply(inverse(X3),least_upper_bound(X3,X2))) = multiply(inverse(least_upper_bound(X3,X2)),X3),
inference(transitivity,[status(thm)],[c298,c299]) ).
cnf(c301,plain,
inverse(least_upper_bound(identity,multiply(inverse(X3),X2))) = multiply(inverse(least_upper_bound(X3,X2)),X3),
inference(transitivity,[status(thm)],[c297,c300]) ).
cnf(c302,plain,
greatest_lower_bound(inverse(identity),inverse(multiply(inverse(X3),X2))) = multiply(inverse(least_upper_bound(X3,X2)),X3),
inference(transitivity,[status(thm)],[c257,c301]) ).
cnf(c303,plain,
greatest_lower_bound(identity,inverse(multiply(inverse(X3),X2))) = multiply(inverse(least_upper_bound(X3,X2)),X3),
inference(transitivity,[status(thm)],[c32,c302]) ).
cnf(c304,plain,
greatest_lower_bound(identity,multiply(inverse(X2),inverse(inverse(X3)))) = multiply(inverse(least_upper_bound(X3,X2)),X3),
inference(transitivity,[status(thm)],[c29,c303]) ).
cnf(c305,plain,
greatest_lower_bound(identity,multiply(inverse(X2),X3)) = multiply(inverse(least_upper_bound(X3,X2)),X3),
inference(transitivity,[status(thm)],[c26,c304]) ).
cnf(c306,plain,
inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2)) = multiply(inverse(least_upper_bound(X3,X2)),X3),
inference(transitivity,[status(thm)],[c23,c305]) ).
cnf(c307,plain,
inverse(inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2))) = inverse(multiply(inverse(least_upper_bound(X3,X2)),X3)),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
inverse(multiply(inverse(least_upper_bound(X3,X2)),X3)) = multiply(inverse(X3),inverse(inverse(least_upper_bound(X3,X2)))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c309,plain,
inverse(inverse(least_upper_bound(X3,X2))) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c310,plain,
multiply(inverse(X3),inverse(inverse(least_upper_bound(X3,X2)))) = multiply(inverse(X3),least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
inverse(multiply(inverse(least_upper_bound(X3,X2)),X3)) = multiply(inverse(X3),least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c308,c310]) ).
cnf(c312,plain,
inverse(inverse(multiply(inverse(greatest_lower_bound(X3,X2)),X2))) = multiply(inverse(X3),least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c307,c311]) ).
cnf(c313,plain,
multiply(inverse(greatest_lower_bound(X3,X2)),X2) = multiply(inverse(X3),least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c6,c312]) ).
cnf(c314,plain,
multiply(inverse(inverse(X3)),multiply(inverse(greatest_lower_bound(X3,X2)),X2)) = multiply(inverse(inverse(X3)),multiply(inverse(X3),least_upper_bound(X3,X2))),
inference(congruence,[status(thm)],[c313]) ).
cnf(c315,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),least_upper_bound(X3,X2))) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c53]) ).
cnf(c316,plain,
multiply(inverse(inverse(X3)),multiply(inverse(greatest_lower_bound(X3,X2)),X2)) = least_upper_bound(X3,X2),
inference(transitivity,[status(thm)],[c314,c315]) ).
cnf(c317,plain,
multiply(X3,multiply(inverse(greatest_lower_bound(X3,X2)),X2)) = least_upper_bound(X3,X2),
inference(transitivity,[status(thm)],[c4,c316]) ).
cnf(c318,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) = least_upper_bound(a,b),
inference(substitution,[status(thm)],[c317]) ).
cnf(c319,plain,
$false,
inference(resolution,[status(thm)],[c1,c318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP180-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 09:41:01 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.15/5.08 Command-line arguments: --flatten-regeneralise
% 36.15/5.08
% 36.15/5.08 % SZS status Unsatisfiable
% 36.15/5.08
% 36.99/5.13 % SZS output start CNFRefutation
% See solution above
% 39.38/5.43
% 39.38/5.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------