%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP183-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 10:09:36 AM UTC 2026
% Result : Unsatisfiable 5.12s 1.14s
% Output : CNFRefutation 6.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 17
% Syntax : Number of clauses : 332 ( 332 unt; 0 nHn; 5 RR)
% Number of literals : 332 ( 331 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 563 ( 31 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_20x) ).
cnf(c2,axiom,
inverse(inverse(X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(X2,identity) = multiply(inverse(inverse(X2)),identity),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(inverse(X2),identity) = multiply(inverse(X2),inverse(identity)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,hypothesis,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20x_3) ).
cnf(c9,plain,
inverse(multiply(identity,X2)) = multiply(inverse(X2),inverse(identity)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(inverse(X2),inverse(identity)) = inverse(multiply(identity,X2)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c12,plain,
inverse(multiply(identity,X2)) = inverse(X2),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(inverse(X2),inverse(identity)) = inverse(X2),
inference(transitivity,[status(thm)],[c10,c12]) ).
cnf(c14,plain,
multiply(inverse(X2),identity) = inverse(X2),
inference(transitivity,[status(thm)],[c7,c13]) ).
cnf(c15,plain,
multiply(inverse(inverse(X2)),identity) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(inverse(inverse(X2)),identity) = X2,
inference(transitivity,[status(thm)],[c15,c2]) ).
cnf(c17,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c4,c16]) ).
cnf(c18,plain,
multiply(least_upper_bound(inverse(X2),identity),identity) = least_upper_bound(inverse(X2),identity),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
least_upper_bound(inverse(X2),identity) = multiply(least_upper_bound(inverse(X2),identity),identity),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)) = greatest_lower_bound(least_upper_bound(X2,identity),multiply(least_upper_bound(inverse(X2),identity),identity)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c22,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(least_upper_bound(X2,identity),X3) = multiply(least_upper_bound(identity,X2),X3),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,axiom,
multiply(least_upper_bound(Y2,Z),X2) = least_upper_bound(multiply(Y2,X2),multiply(Z,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub2) ).
cnf(c26,plain,
multiply(least_upper_bound(identity,X3),X2) = least_upper_bound(multiply(identity,X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
least_upper_bound(multiply(identity,X2),multiply(X3,X2)) = least_upper_bound(X2,multiply(X3,X2)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c28,plain,
multiply(least_upper_bound(identity,X3),X2) = least_upper_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c26,c27]) ).
cnf(c29,plain,
multiply(least_upper_bound(X3,identity),X2) = least_upper_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c24,c28]) ).
cnf(c30,plain,
multiply(least_upper_bound(inverse(X2),identity),X2) = least_upper_bound(X2,multiply(inverse(X2),X2)),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c32,plain,
least_upper_bound(X2,multiply(inverse(X2),X2)) = least_upper_bound(X2,identity),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(least_upper_bound(inverse(X2),identity),X2) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c30,c32]) ).
cnf(c34,plain,
least_upper_bound(X2,identity) = multiply(least_upper_bound(inverse(X2),identity),X2),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
greatest_lower_bound(least_upper_bound(X3,identity),multiply(least_upper_bound(inverse(X3),identity),X2)) = greatest_lower_bound(multiply(least_upper_bound(inverse(X3),identity),X3),multiply(least_upper_bound(inverse(X3),identity),X2)),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,axiom,
multiply(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb1) ).
cnf(c37,plain,
multiply(least_upper_bound(inverse(X3),identity),greatest_lower_bound(X3,X2)) = greatest_lower_bound(multiply(least_upper_bound(inverse(X3),identity),X3),multiply(least_upper_bound(inverse(X3),identity),X2)),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
greatest_lower_bound(multiply(least_upper_bound(inverse(X3),identity),X3),multiply(least_upper_bound(inverse(X3),identity),X2)) = multiply(least_upper_bound(inverse(X3),identity),greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c40,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(least_upper_bound(inverse(X3),identity),greatest_lower_bound(X3,X2)) = multiply(least_upper_bound(inverse(X3),identity),greatest_lower_bound(X2,X3)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
greatest_lower_bound(multiply(least_upper_bound(inverse(X3),identity),X3),multiply(least_upper_bound(inverse(X3),identity),X2)) = multiply(least_upper_bound(inverse(X3),identity),greatest_lower_bound(X2,X3)),
inference(transitivity,[status(thm)],[c38,c41]) ).
cnf(c43,plain,
greatest_lower_bound(least_upper_bound(X3,identity),multiply(least_upper_bound(inverse(X3),identity),X2)) = multiply(least_upper_bound(inverse(X3),identity),greatest_lower_bound(X2,X3)),
inference(transitivity,[status(thm)],[c35,c42]) ).
cnf(c44,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c45,plain,
multiply(least_upper_bound(inverse(X3),identity),greatest_lower_bound(X2,X3)) = multiply(least_upper_bound(inverse(X3),identity),greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
greatest_lower_bound(least_upper_bound(X3,identity),multiply(least_upper_bound(inverse(X3),identity),X2)) = multiply(least_upper_bound(inverse(X3),identity),greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c43,c45]) ).
cnf(c47,plain,
greatest_lower_bound(least_upper_bound(X2,identity),multiply(least_upper_bound(inverse(X2),identity),identity)) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(X2,identity)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c21]) ).
cnf(c49,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(X3,least_upper_bound(X2,identity)) = multiply(X3,least_upper_bound(identity,X2)),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,axiom,
multiply(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).
cnf(c52,plain,
multiply(X3,least_upper_bound(identity,X2)) = least_upper_bound(multiply(X3,identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
least_upper_bound(multiply(X3,identity),multiply(X3,X2)) = least_upper_bound(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c54,plain,
multiply(X3,least_upper_bound(identity,X2)) = least_upper_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c52,c53]) ).
cnf(c55,plain,
multiply(X3,least_upper_bound(X2,identity)) = least_upper_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c50,c54]) ).
cnf(c56,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(inverse(X2),identity)) = least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(X2))),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)) = greatest_lower_bound(least_upper_bound(inverse(X2),identity),least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c58,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(X2)) = multiply(greatest_lower_bound(least_upper_bound(inverse(X2),identity),least_upper_bound(X2,identity)),inverse(X2)),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
greatest_lower_bound(least_upper_bound(X2,identity),X3) = greatest_lower_bound(X3,least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c60,plain,
greatest_lower_bound(X3,least_upper_bound(X2,identity)) = greatest_lower_bound(least_upper_bound(X2,identity),X3),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
multiply(greatest_lower_bound(X3,least_upper_bound(X2,identity)),inverse(X2)) = multiply(greatest_lower_bound(least_upper_bound(X2,identity),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/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).
cnf(c63,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),X3),inverse(X2)) = greatest_lower_bound(multiply(least_upper_bound(X2,identity),inverse(X2)),multiply(X3,inverse(X2))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(least_upper_bound(X2,identity),inverse(X2)) = least_upper_bound(inverse(X2),multiply(X2,inverse(X2))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c65,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c66,plain,
multiply(X2,inverse(X2)) = multiply(inverse(inverse(X2)),inverse(X2)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = identity,
inference(substitution,[status(thm)],[c31]) ).
cnf(c68,plain,
multiply(X2,inverse(X2)) = identity,
inference(transitivity,[status(thm)],[c66,c67]) ).
cnf(c69,plain,
least_upper_bound(inverse(X2),multiply(X2,inverse(X2))) = least_upper_bound(inverse(X2),identity),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(least_upper_bound(X2,identity),inverse(X2)) = least_upper_bound(inverse(X2),identity),
inference(transitivity,[status(thm)],[c64,c69]) ).
cnf(c71,plain,
greatest_lower_bound(multiply(least_upper_bound(X2,identity),inverse(X2)),multiply(X3,inverse(X2))) = greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(X3,inverse(X2))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),X3),inverse(X2)) = greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(X3,inverse(X2))),
inference(transitivity,[status(thm)],[c63,c71]) ).
cnf(c73,plain,
multiply(greatest_lower_bound(X3,least_upper_bound(X2,identity)),inverse(X2)) = greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(X3,inverse(X2))),
inference(transitivity,[status(thm)],[c61,c72]) ).
cnf(c74,plain,
multiply(greatest_lower_bound(least_upper_bound(inverse(X2),identity),least_upper_bound(X2,identity)),inverse(X2)) = greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(least_upper_bound(inverse(X2),identity),inverse(X2))),
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
multiply(least_upper_bound(X2,identity),X2) = least_upper_bound(X2,multiply(X2,X2)),
inference(substitution,[status(thm)],[c29]) ).
cnf(c76,plain,
multiply(X2,least_upper_bound(X2,identity)) = least_upper_bound(X2,multiply(X2,X2)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c77,plain,
least_upper_bound(X2,multiply(X2,X2)) = multiply(X2,least_upper_bound(X2,identity)),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
multiply(least_upper_bound(X2,identity),X2) = multiply(X2,least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c75,c77]) ).
cnf(c79,plain,
multiply(least_upper_bound(inverse(X2),identity),inverse(X2)) = multiply(inverse(X2),least_upper_bound(inverse(X2),identity)),
inference(substitution,[status(thm)],[c78]) ).
cnf(c80,plain,
greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(least_upper_bound(inverse(X2),identity),inverse(X2))) = greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(inverse(X2),least_upper_bound(inverse(X2),identity))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
inverse(inverse(least_upper_bound(X2,identity))) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c82,plain,
least_upper_bound(X2,identity) = inverse(inverse(least_upper_bound(X2,identity))),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(inverse(X2),identity)) = multiply(inverse(inverse(least_upper_bound(X2,identity))),greatest_lower_bound(inverse(X2),identity)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)) = greatest_lower_bound(least_upper_bound(inverse(X2),identity),least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c85,plain,
multiply(inverse(least_upper_bound(X2,identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = multiply(inverse(least_upper_bound(X2,identity)),greatest_lower_bound(least_upper_bound(inverse(X2),identity),least_upper_bound(X2,identity))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c39]) ).
cnf(c87,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
multiply(inverse(X3),greatest_lower_bound(X2,X3)) = multiply(inverse(X3),greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c36]) ).
cnf(c90,plain,
greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = greatest_lower_bound(identity,multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c91,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = greatest_lower_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c89,c90]) ).
cnf(c92,plain,
multiply(inverse(X3),greatest_lower_bound(X2,X3)) = greatest_lower_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c88,c91]) ).
cnf(c93,plain,
multiply(inverse(least_upper_bound(X2,identity)),greatest_lower_bound(least_upper_bound(inverse(X2),identity),least_upper_bound(X2,identity))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X2,identity)),least_upper_bound(inverse(X2),identity))),
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
least_upper_bound(inverse(X2),identity) = multiply(least_upper_bound(X2,identity),inverse(X2)),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c95,plain,
multiply(inverse(least_upper_bound(X2,identity)),least_upper_bound(inverse(X2),identity)) = multiply(inverse(least_upper_bound(X2,identity)),multiply(least_upper_bound(X2,identity),inverse(X2))),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,axiom,
multiply(multiply(X2,Y2),Z2) = multiply(X2,multiply(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
cnf(c97,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c96]) ).
cnf(c98,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c31]) ).
cnf(c100,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c99,c11]) ).
cnf(c101,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c98,c100]) ).
cnf(c102,plain,
multiply(inverse(least_upper_bound(X2,identity)),multiply(least_upper_bound(X2,identity),inverse(X2))) = inverse(X2),
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
multiply(inverse(least_upper_bound(X2,identity)),least_upper_bound(inverse(X2),identity)) = inverse(X2),
inference(transitivity,[status(thm)],[c95,c102]) ).
cnf(c104,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X2,identity)),least_upper_bound(inverse(X2),identity))) = greatest_lower_bound(identity,inverse(X2)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
greatest_lower_bound(identity,inverse(X2)) = greatest_lower_bound(inverse(X2),identity),
inference(substitution,[status(thm)],[c39]) ).
cnf(c106,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X2,identity)),least_upper_bound(inverse(X2),identity))) = greatest_lower_bound(inverse(X2),identity),
inference(transitivity,[status(thm)],[c104,c105]) ).
cnf(c107,plain,
multiply(inverse(least_upper_bound(X2,identity)),greatest_lower_bound(least_upper_bound(inverse(X2),identity),least_upper_bound(X2,identity))) = greatest_lower_bound(inverse(X2),identity),
inference(transitivity,[status(thm)],[c93,c106]) ).
cnf(c108,plain,
multiply(inverse(least_upper_bound(X2,identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = greatest_lower_bound(inverse(X2),identity),
inference(transitivity,[status(thm)],[c85,c107]) ).
cnf(c109,plain,
greatest_lower_bound(inverse(X2),identity) = multiply(inverse(least_upper_bound(X2,identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
multiply(inverse(inverse(least_upper_bound(X2,identity))),greatest_lower_bound(inverse(X2),identity)) = multiply(inverse(inverse(least_upper_bound(X2,identity))),multiply(inverse(least_upper_bound(X2,identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
multiply(inverse(inverse(least_upper_bound(X2,identity))),multiply(inverse(least_upper_bound(X2,identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),
inference(substitution,[status(thm)],[c101]) ).
cnf(c112,plain,
multiply(inverse(inverse(least_upper_bound(X2,identity))),greatest_lower_bound(inverse(X2),identity)) = greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),
inference(transitivity,[status(thm)],[c110,c111]) ).
cnf(c113,plain,
multiply(least_upper_bound(X2,identity),greatest_lower_bound(inverse(X2),identity)) = greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),
inference(transitivity,[status(thm)],[c83,c112]) ).
cnf(c114,plain,
greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)) = multiply(least_upper_bound(X2,identity),greatest_lower_bound(inverse(X2),identity)),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = multiply(inverse(X2),multiply(least_upper_bound(X2,identity),greatest_lower_bound(inverse(X2),identity))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
multiply(multiply(least_upper_bound(inverse(X3),identity),X3),X2) = multiply(least_upper_bound(inverse(X3),identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c96]) ).
cnf(c117,plain,
multiply(least_upper_bound(inverse(X3),identity),multiply(X3,X2)) = multiply(multiply(least_upper_bound(inverse(X3),identity),X3),X2),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
multiply(multiply(least_upper_bound(inverse(X3),identity),X3),X2) = multiply(least_upper_bound(X3,identity),X2),
inference(congruence,[status(thm)],[c33]) ).
cnf(c119,plain,
multiply(least_upper_bound(inverse(X3),identity),multiply(X3,X2)) = multiply(least_upper_bound(X3,identity),X2),
inference(transitivity,[status(thm)],[c117,c118]) ).
cnf(c120,plain,
multiply(least_upper_bound(X3,identity),X2) = multiply(least_upper_bound(inverse(X3),identity),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(inverse(X3),multiply(least_upper_bound(X3,identity),X2)) = multiply(inverse(X3),multiply(least_upper_bound(inverse(X3),identity),multiply(X3,X2))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
multiply(least_upper_bound(X3,identity),multiply(X3,X2)) = least_upper_bound(multiply(X3,X2),multiply(X3,multiply(X3,X2))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c123,plain,
multiply(X3,least_upper_bound(X2,multiply(X3,X2))) = least_upper_bound(multiply(X3,X2),multiply(X3,multiply(X3,X2))),
inference(substitution,[status(thm)],[c51]) ).
cnf(c124,plain,
least_upper_bound(multiply(X3,X2),multiply(X3,multiply(X3,X2))) = multiply(X3,least_upper_bound(X2,multiply(X3,X2))),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
least_upper_bound(X2,multiply(X3,X2)) = multiply(least_upper_bound(X3,identity),X2),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c126,plain,
multiply(X3,least_upper_bound(X2,multiply(X3,X2))) = multiply(X3,multiply(least_upper_bound(X3,identity),X2)),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
least_upper_bound(multiply(X3,X2),multiply(X3,multiply(X3,X2))) = multiply(X3,multiply(least_upper_bound(X3,identity),X2)),
inference(transitivity,[status(thm)],[c124,c126]) ).
cnf(c128,plain,
multiply(least_upper_bound(X3,identity),multiply(X3,X2)) = multiply(X3,multiply(least_upper_bound(X3,identity),X2)),
inference(transitivity,[status(thm)],[c122,c127]) ).
cnf(c129,plain,
multiply(least_upper_bound(inverse(X3),identity),multiply(inverse(X3),multiply(X3,X2))) = multiply(inverse(X3),multiply(least_upper_bound(inverse(X3),identity),multiply(X3,X2))),
inference(substitution,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(inverse(X3),multiply(least_upper_bound(inverse(X3),identity),multiply(X3,X2))) = multiply(least_upper_bound(inverse(X3),identity),multiply(inverse(X3),multiply(X3,X2))),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
multiply(least_upper_bound(inverse(X3),identity),multiply(inverse(X3),multiply(X3,X2))) = multiply(least_upper_bound(inverse(X3),identity),X2),
inference(congruence,[status(thm)],[c101]) ).
cnf(c132,plain,
multiply(inverse(X3),multiply(least_upper_bound(inverse(X3),identity),multiply(X3,X2))) = multiply(least_upper_bound(inverse(X3),identity),X2),
inference(transitivity,[status(thm)],[c130,c131]) ).
cnf(c133,plain,
multiply(inverse(X3),multiply(least_upper_bound(X3,identity),X2)) = multiply(least_upper_bound(inverse(X3),identity),X2),
inference(transitivity,[status(thm)],[c121,c132]) ).
cnf(c134,plain,
multiply(inverse(X2),multiply(least_upper_bound(X2,identity),greatest_lower_bound(inverse(X2),identity))) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(inverse(X2),identity)),
inference(substitution,[status(thm)],[c133]) ).
cnf(c135,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c39]) ).
cnf(c136,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
multiply(X3,greatest_lower_bound(X2,identity)) = multiply(X3,greatest_lower_bound(identity,X2)),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
multiply(X3,greatest_lower_bound(identity,X2)) = greatest_lower_bound(multiply(X3,identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c36]) ).
cnf(c139,plain,
greatest_lower_bound(multiply(X3,identity),multiply(X3,X2)) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c140,plain,
multiply(X3,greatest_lower_bound(identity,X2)) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c138,c139]) ).
cnf(c141,plain,
multiply(X3,greatest_lower_bound(X2,identity)) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c137,c140]) ).
cnf(c142,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(inverse(X2),identity)) = greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(least_upper_bound(inverse(X2),identity),inverse(X2))),
inference(substitution,[status(thm)],[c141]) ).
cnf(c143,plain,
multiply(least_upper_bound(inverse(X2),identity),inverse(X2)) = multiply(inverse(X2),least_upper_bound(inverse(X2),identity)),
inference(substitution,[status(thm)],[c78]) ).
cnf(c144,plain,
greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(least_upper_bound(inverse(X2),identity),inverse(X2))) = greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(inverse(X2),least_upper_bound(inverse(X2),identity))),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(inverse(X2),identity)) = greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(inverse(X2),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c142,c144]) ).
cnf(c146,plain,
multiply(inverse(X2),multiply(least_upper_bound(X2,identity),greatest_lower_bound(inverse(X2),identity))) = greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(inverse(X2),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c134,c145]) ).
cnf(c147,plain,
multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(inverse(X2),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c115,c146]) ).
cnf(c148,plain,
greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(inverse(X2),least_upper_bound(inverse(X2),identity))) = multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(least_upper_bound(inverse(X2),identity),inverse(X2))) = multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c80,c148]) ).
cnf(c150,plain,
multiply(greatest_lower_bound(least_upper_bound(inverse(X2),identity),least_upper_bound(X2,identity)),inverse(X2)) = multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c74,c149]) ).
cnf(c151,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(X2)) = multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c58,c150]) ).
cnf(c152,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(X2))) = least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c154,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(X2))) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c152,c154]) ).
cnf(c156,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(inverse(X2),identity)) = multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(transitivity,[status(thm)],[c56,c155]) ).
cnf(c157,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c158,plain,
least_upper_bound(multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c159,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = least_upper_bound(multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(X2)),
inference(symmetry,[status(thm)],[c151]) ).
cnf(c161,plain,
least_upper_bound(multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = least_upper_bound(multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(X2)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c21]) ).
cnf(c163,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X5,X3)),least_upper_bound(X3,X2)) = least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X5,X3)),least_upper_bound(X2,X3)),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c21]) ).
cnf(c166,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)),least_upper_bound(X2,X4)) = least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)),least_upper_bound(X4,X2)),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,axiom,
least_upper_bound(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(least_upper_bound(X2,Y2),Z2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_lub) ).
cnf(c169,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)),least_upper_bound(X4,X2)) = least_upper_bound(least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)),X4),X2),
inference(substitution,[status(thm)],[c168]) ).
cnf(c170,plain,
greatest_lower_bound(X3,greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),X3),
inference(substitution,[status(thm)],[c39]) ).
cnf(c171,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),X3) = greatest_lower_bound(X3,greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3))),
inference(symmetry,[status(thm)],[c170]) ).
cnf(c172,plain,
greatest_lower_bound(greatest_lower_bound(X2,X4),X3) = greatest_lower_bound(X3,greatest_lower_bound(X2,X4)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c173,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,X4)) = greatest_lower_bound(greatest_lower_bound(X2,X4),X3),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c174,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c175,plain,
greatest_lower_bound(greatest_lower_bound(X2,X4),X3) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,axiom,
greatest_lower_bound(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(greatest_lower_bound(X2,Y2),Z2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_glb) ).
cnf(c177,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c176]) ).
cnf(c178,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X2,X3)),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c179,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c180,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c178,c180]) ).
cnf(c182,plain,
greatest_lower_bound(greatest_lower_bound(X2,X4),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c175,c181]) ).
cnf(c183,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,X4)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c173,c182]) ).
cnf(c184,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,X4)) = greatest_lower_bound(X4,greatest_lower_bound(X2,X3)),
inference(substitution,[status(thm)],[c183]) ).
cnf(c185,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c186,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,X4)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c184,c186]) ).
cnf(c188,plain,
greatest_lower_bound(X3,greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3))) = greatest_lower_bound(least_upper_bound(X2,X3),greatest_lower_bound(least_upper_bound(X4,X3),X3)),
inference(substitution,[status(thm)],[c187]) ).
cnf(c189,plain,
greatest_lower_bound(X2,least_upper_bound(X3,X2)) = greatest_lower_bound(least_upper_bound(X3,X2),X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c190,plain,
greatest_lower_bound(least_upper_bound(X3,X2),X2) = greatest_lower_bound(X2,least_upper_bound(X3,X2)),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c21]) ).
cnf(c192,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c195,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c194]) ).
cnf(c196,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c193,c195]) ).
cnf(c197,plain,
greatest_lower_bound(X2,least_upper_bound(X3,X2)) = X2,
inference(substitution,[status(thm)],[c196]) ).
cnf(c198,plain,
greatest_lower_bound(least_upper_bound(X3,X2),X2) = X2,
inference(transitivity,[status(thm)],[c190,c197]) ).
cnf(c199,plain,
greatest_lower_bound(least_upper_bound(X2,X3),greatest_lower_bound(least_upper_bound(X4,X3),X3)) = greatest_lower_bound(least_upper_bound(X2,X3),X3),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
greatest_lower_bound(least_upper_bound(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c198]) ).
cnf(c201,plain,
greatest_lower_bound(least_upper_bound(X2,X3),greatest_lower_bound(least_upper_bound(X4,X3),X3)) = X3,
inference(transitivity,[status(thm)],[c199,c200]) ).
cnf(c202,plain,
greatest_lower_bound(X3,greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3))) = X3,
inference(transitivity,[status(thm)],[c188,c201]) ).
cnf(c203,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),X3) = X3,
inference(transitivity,[status(thm)],[c171,c202]) ).
cnf(c204,plain,
X3 = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),X3),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),X3) = least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),X3)),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c207,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),X3)) = greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),
inference(substitution,[status(thm)],[c206]) ).
cnf(c208,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),X3) = greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),
inference(transitivity,[status(thm)],[c205,c207]) ).
cnf(c209,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)),X4),X2) = least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)),X2),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)),X2) = least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c211,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)),X4),X2) = least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4))),
inference(transitivity,[status(thm)],[c209,c210]) ).
cnf(c212,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)),least_upper_bound(X4,X2)) = least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4))),
inference(transitivity,[status(thm)],[c169,c211]) ).
cnf(c213,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)),least_upper_bound(X2,X4)) = least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4))),
inference(transitivity,[status(thm)],[c167,c212]) ).
cnf(c214,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4)),least_upper_bound(X4,X2)) = least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X5,X4),least_upper_bound(X3,X4))),
inference(transitivity,[status(thm)],[c164,c213]) ).
cnf(c215,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(identity,multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(X2)))) = least_upper_bound(multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(X2)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(substitution,[status(thm)],[c214]) ).
cnf(c216,plain,
least_upper_bound(multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(X2)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(identity,multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(X2)))),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c217,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c21]) ).
cnf(c218,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
multiply(least_upper_bound(X3,X2),inverse(X2)) = multiply(least_upper_bound(X2,X3),inverse(X2)),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
multiply(least_upper_bound(X2,X3),inverse(X2)) = least_upper_bound(multiply(X2,inverse(X2)),multiply(X3,inverse(X2))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c221,plain,
least_upper_bound(multiply(X2,inverse(X2)),multiply(X3,inverse(X2))) = least_upper_bound(identity,multiply(X3,inverse(X2))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c222,plain,
multiply(least_upper_bound(X2,X3),inverse(X2)) = least_upper_bound(identity,multiply(X3,inverse(X2))),
inference(transitivity,[status(thm)],[c220,c221]) ).
cnf(c223,plain,
multiply(least_upper_bound(X3,X2),inverse(X2)) = least_upper_bound(identity,multiply(X3,inverse(X2))),
inference(transitivity,[status(thm)],[c219,c222]) ).
cnf(c224,plain,
multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),X3),inverse(X3)) = least_upper_bound(identity,multiply(greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),inverse(X3))),
inference(substitution,[status(thm)],[c223]) ).
cnf(c225,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),inverse(X3))) = multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),X3),inverse(X3)),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3))) = least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),X4),
inference(substitution,[status(thm)],[c21]) ).
cnf(c227,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),X4) = least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3))),
inference(symmetry,[status(thm)],[c226]) ).
cnf(c228,plain,
greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)) = least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),X3),
inference(symmetry,[status(thm)],[c208]) ).
cnf(c229,plain,
least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3))) = least_upper_bound(X4,least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),X3)),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X3,least_upper_bound(X4,X2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c231,plain,
least_upper_bound(X3,least_upper_bound(X4,X2)) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c230]) ).
cnf(c232,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c168]) ).
cnf(c233,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X4,least_upper_bound(X2,X3)),
inference(symmetry,[status(thm)],[c232]) ).
cnf(c234,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c21]) ).
cnf(c235,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c233,c235]) ).
cnf(c237,plain,
least_upper_bound(X3,least_upper_bound(X4,X2)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c231,c236]) ).
cnf(c238,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),least_upper_bound(X4,X3)) = least_upper_bound(X4,least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),X3)),
inference(substitution,[status(thm)],[c237]) ).
cnf(c239,plain,
least_upper_bound(X4,least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),X3)) = least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),least_upper_bound(X4,X3)),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = least_upper_bound(greatest_lower_bound(X3,X2),X3),
inference(substitution,[status(thm)],[c21]) ).
cnf(c241,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X3) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c39]) ).
cnf(c243,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = least_upper_bound(X3,greatest_lower_bound(X2,X3)),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c245,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c206]) ).
cnf(c247,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c245,c246]) ).
cnf(c248,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c243,c247]) ).
cnf(c249,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X3) = X3,
inference(transitivity,[status(thm)],[c241,c248]) ).
cnf(c250,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),least_upper_bound(X4,X3)) = least_upper_bound(X4,X3),
inference(substitution,[status(thm)],[c249]) ).
cnf(c251,plain,
least_upper_bound(X4,least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),X3)) = least_upper_bound(X4,X3),
inference(transitivity,[status(thm)],[c239,c250]) ).
cnf(c252,plain,
least_upper_bound(X4,greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3))) = least_upper_bound(X4,X3),
inference(transitivity,[status(thm)],[c229,c251]) ).
cnf(c253,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X4,X3),least_upper_bound(X2,X3)),X4) = least_upper_bound(X4,X3),
inference(transitivity,[status(thm)],[c227,c252]) ).
cnf(c254,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),X3) = least_upper_bound(X3,identity),
inference(substitution,[status(thm)],[c253]) ).
cnf(c255,plain,
multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),X3),inverse(X3)) = multiply(least_upper_bound(X3,identity),inverse(X3)),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),X3),inverse(X3)) = least_upper_bound(inverse(X3),identity),
inference(transitivity,[status(thm)],[c255,c70]) ).
cnf(c257,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(least_upper_bound(X3,identity),least_upper_bound(X2,identity)),inverse(X3))) = least_upper_bound(inverse(X3),identity),
inference(transitivity,[status(thm)],[c225,c256]) ).
cnf(c258,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(X2))) = least_upper_bound(inverse(X2),identity),
inference(substitution,[status(thm)],[c257]) ).
cnf(c259,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(identity,multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(X2)))) = least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(inverse(X2),identity)),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = least_upper_bound(greatest_lower_bound(X3,X2),X2),
inference(substitution,[status(thm)],[c21]) ).
cnf(c261,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X2) = least_upper_bound(X2,greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c260]) ).
cnf(c262,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c39]) ).
cnf(c263,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = least_upper_bound(X2,greatest_lower_bound(X2,X3)),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
least_upper_bound(X2,greatest_lower_bound(X2,X3)) = X2,
inference(substitution,[status(thm)],[c206]) ).
cnf(c265,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c263,c264]) ).
cnf(c266,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X2) = X2,
inference(transitivity,[status(thm)],[c261,c265]) ).
cnf(c267,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(inverse(X2),identity)) = least_upper_bound(inverse(X2),identity),
inference(substitution,[status(thm)],[c266]) ).
cnf(c268,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(identity,multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(X2)))) = least_upper_bound(inverse(X2),identity),
inference(transitivity,[status(thm)],[c259,c267]) ).
cnf(c269,plain,
least_upper_bound(multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),inverse(X2)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = least_upper_bound(inverse(X2),identity),
inference(transitivity,[status(thm)],[c216,c268]) ).
cnf(c270,plain,
least_upper_bound(multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = least_upper_bound(inverse(X2),identity),
inference(transitivity,[status(thm)],[c161,c269]) ).
cnf(c271,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = least_upper_bound(inverse(X2),identity),
inference(transitivity,[status(thm)],[c159,c270]) ).
cnf(c272,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = least_upper_bound(inverse(X2),identity),
inference(transitivity,[status(thm)],[c157,c271]) ).
cnf(c273,plain,
multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(inverse(X2),identity)) = least_upper_bound(inverse(X2),identity),
inference(transitivity,[status(thm)],[c156,c272]) ).
cnf(c274,plain,
least_upper_bound(inverse(X2),identity) = multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(inverse(X2),identity)),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),least_upper_bound(inverse(X2),identity)) = multiply(inverse(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(inverse(X2),identity))),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),multiply(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),least_upper_bound(inverse(X2),identity))) = least_upper_bound(inverse(X2),identity),
inference(substitution,[status(thm)],[c101]) ).
cnf(c277,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),least_upper_bound(inverse(X2),identity)) = least_upper_bound(inverse(X2),identity),
inference(transitivity,[status(thm)],[c275,c276]) ).
cnf(c278,plain,
least_upper_bound(inverse(X2),identity) = multiply(inverse(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),least_upper_bound(inverse(X2),identity)),
inference(symmetry,[status(thm)],[c277]) ).
cnf(c279,plain,
inverse(least_upper_bound(inverse(X2),identity)) = inverse(multiply(inverse(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),least_upper_bound(inverse(X2),identity))),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,plain,
inverse(multiply(inverse(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),least_upper_bound(inverse(X2),identity))) = multiply(inverse(least_upper_bound(inverse(X2),identity)),inverse(inverse(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c281,plain,
inverse(inverse(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c282,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),inverse(inverse(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))))) = multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
multiply(inverse(inverse(X2)),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)),
inference(substitution,[status(thm)],[c101]) ).
cnf(c284,plain,
greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)) = multiply(inverse(inverse(X2)),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c285,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(inverse(inverse(X2)),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))))),
inference(congruence,[status(thm)],[c284]) ).
cnf(c286,plain,
multiply(multiply(inverse(least_upper_bound(inverse(X2),identity)),inverse(inverse(X2))),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(inverse(inverse(X2)),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))))),
inference(substitution,[status(thm)],[c96]) ).
cnf(c287,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(inverse(inverse(X2)),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))))) = multiply(multiply(inverse(least_upper_bound(inverse(X2),identity)),inverse(inverse(X2))),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
inverse(multiply(inverse(X2),least_upper_bound(inverse(X2),identity))) = multiply(inverse(least_upper_bound(inverse(X2),identity)),inverse(inverse(X2))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c289,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),inverse(inverse(X2))) = inverse(multiply(inverse(X2),least_upper_bound(inverse(X2),identity))),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c290,plain,
multiply(multiply(inverse(least_upper_bound(inverse(X2),identity)),inverse(inverse(X2))),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = multiply(inverse(multiply(inverse(X2),least_upper_bound(inverse(X2),identity))),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
multiply(inverse(multiply(inverse(X2),least_upper_bound(inverse(X2),identity))),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = multiply(inverse(multiply(inverse(X2),least_upper_bound(inverse(X2),identity))),greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(inverse(X2),least_upper_bound(inverse(X2),identity)))),
inference(congruence,[status(thm)],[c147]) ).
cnf(c292,plain,
multiply(inverse(multiply(inverse(X2),least_upper_bound(inverse(X2),identity))),greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(inverse(X2),least_upper_bound(inverse(X2),identity)))) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X2),least_upper_bound(inverse(X2),identity))),least_upper_bound(inverse(X2),identity))),
inference(substitution,[status(thm)],[c92]) ).
cnf(c293,plain,
inverse(multiply(inverse(X2),least_upper_bound(inverse(X2),identity))) = multiply(inverse(least_upper_bound(inverse(X2),identity)),inverse(inverse(X2))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c294,plain,
multiply(inverse(multiply(inverse(X2),least_upper_bound(inverse(X2),identity))),least_upper_bound(inverse(X2),identity)) = multiply(multiply(inverse(least_upper_bound(inverse(X2),identity)),inverse(inverse(X2))),least_upper_bound(inverse(X2),identity)),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X2),least_upper_bound(inverse(X2),identity))),least_upper_bound(inverse(X2),identity))) = greatest_lower_bound(identity,multiply(multiply(inverse(least_upper_bound(inverse(X2),identity)),inverse(inverse(X2))),least_upper_bound(inverse(X2),identity))),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
multiply(multiply(inverse(least_upper_bound(inverse(X2),identity)),inverse(inverse(X2))),least_upper_bound(inverse(X2),identity)) = multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(inverse(inverse(X2)),least_upper_bound(inverse(X2),identity))),
inference(substitution,[status(thm)],[c96]) ).
cnf(c297,plain,
greatest_lower_bound(identity,multiply(multiply(inverse(least_upper_bound(inverse(X2),identity)),inverse(inverse(X2))),least_upper_bound(inverse(X2),identity))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(inverse(inverse(X2)),least_upper_bound(inverse(X2),identity)))),
inference(congruence,[status(thm)],[c296]) ).
cnf(c298,plain,
multiply(inverse(inverse(X2)),least_upper_bound(inverse(X2),identity)) = multiply(X2,least_upper_bound(inverse(X2),identity)),
inference(congruence,[status(thm)],[c2]) ).
cnf(c299,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(inverse(inverse(X2)),least_upper_bound(inverse(X2),identity))) = multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(X2,least_upper_bound(inverse(X2),identity))),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(inverse(inverse(X2)),least_upper_bound(inverse(X2),identity)))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(X2,least_upper_bound(inverse(X2),identity)))),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
multiply(X2,least_upper_bound(inverse(X2),identity)) = least_upper_bound(X2,multiply(X2,inverse(X2))),
inference(substitution,[status(thm)],[c55]) ).
cnf(c302,plain,
least_upper_bound(X2,multiply(X2,inverse(X2))) = least_upper_bound(X2,identity),
inference(congruence,[status(thm)],[c68]) ).
cnf(c303,plain,
multiply(X2,least_upper_bound(inverse(X2),identity)) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c301,c302]) ).
cnf(c304,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(X2,least_upper_bound(inverse(X2),identity))) = multiply(inverse(least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity)),
inference(congruence,[status(thm)],[c303]) ).
cnf(c305,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(X2,least_upper_bound(inverse(X2),identity)))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity))),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
least_upper_bound(X2,identity) = multiply(least_upper_bound(inverse(X2),identity),X2),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c307,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity)) = multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(least_upper_bound(inverse(X2),identity),X2)),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(least_upper_bound(inverse(X2),identity),X2)) = X2,
inference(substitution,[status(thm)],[c101]) ).
cnf(c309,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity)) = X2,
inference(transitivity,[status(thm)],[c307,c308]) ).
cnf(c310,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity))) = greatest_lower_bound(identity,X2),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c39]) ).
cnf(c312,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X2),identity)),least_upper_bound(X2,identity))) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c310,c311]) ).
cnf(c313,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(X2,least_upper_bound(inverse(X2),identity)))) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c305,c312]) ).
cnf(c314,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(inverse(inverse(X2)),least_upper_bound(inverse(X2),identity)))) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c300,c313]) ).
cnf(c315,plain,
greatest_lower_bound(identity,multiply(multiply(inverse(least_upper_bound(inverse(X2),identity)),inverse(inverse(X2))),least_upper_bound(inverse(X2),identity))) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c297,c314]) ).
cnf(c316,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X2),least_upper_bound(inverse(X2),identity))),least_upper_bound(inverse(X2),identity))) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c295,c315]) ).
cnf(c317,plain,
multiply(inverse(multiply(inverse(X2),least_upper_bound(inverse(X2),identity))),greatest_lower_bound(least_upper_bound(inverse(X2),identity),multiply(inverse(X2),least_upper_bound(inverse(X2),identity)))) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c292,c316]) ).
cnf(c318,plain,
multiply(inverse(multiply(inverse(X2),least_upper_bound(inverse(X2),identity))),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c291,c317]) ).
cnf(c319,plain,
multiply(multiply(inverse(least_upper_bound(inverse(X2),identity)),inverse(inverse(X2))),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)))) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c290,c318]) ).
cnf(c320,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),multiply(inverse(inverse(X2)),multiply(inverse(X2),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))))) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c287,c319]) ).
cnf(c321,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c285,c320]) ).
cnf(c322,plain,
multiply(inverse(least_upper_bound(inverse(X2),identity)),inverse(inverse(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))))) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c282,c321]) ).
cnf(c323,plain,
inverse(multiply(inverse(greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity))),least_upper_bound(inverse(X2),identity))) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c280,c322]) ).
cnf(c324,plain,
inverse(least_upper_bound(inverse(X2),identity)) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c279,c323]) ).
cnf(c325,plain,
greatest_lower_bound(X2,identity) = inverse(least_upper_bound(inverse(X2),identity)),
inference(symmetry,[status(thm)],[c324]) ).
cnf(c326,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(X2,identity)) = multiply(least_upper_bound(inverse(X2),identity),inverse(least_upper_bound(inverse(X2),identity))),
inference(congruence,[status(thm)],[c325]) ).
cnf(c327,plain,
multiply(least_upper_bound(inverse(X2),identity),inverse(least_upper_bound(inverse(X2),identity))) = identity,
inference(substitution,[status(thm)],[c68]) ).
cnf(c328,plain,
multiply(least_upper_bound(inverse(X2),identity),greatest_lower_bound(X2,identity)) = identity,
inference(transitivity,[status(thm)],[c326,c327]) ).
cnf(c329,plain,
greatest_lower_bound(least_upper_bound(X2,identity),multiply(least_upper_bound(inverse(X2),identity),identity)) = identity,
inference(transitivity,[status(thm)],[c47,c328]) ).
cnf(c330,plain,
greatest_lower_bound(least_upper_bound(X2,identity),least_upper_bound(inverse(X2),identity)) = identity,
inference(transitivity,[status(thm)],[c20,c329]) ).
cnf(c331,plain,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) = identity,
inference(substitution,[status(thm)],[c330]) ).
cnf(c332,plain,
$false,
inference(resolution,[status(thm)],[c1,c331]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP183-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:36:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.12/1.14 Command-line arguments: --flatten-regeneralise
% 5.12/1.14
% 5.12/1.14 % SZS status Unsatisfiable
% 5.12/1.14
% 5.12/1.16 % SZS output start CNFRefutation
% See solution above
% 6.10/1.26
% 6.10/1.26 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------