%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP169-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 10:09:31 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.49s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 11
% Syntax : Number of clauses : 92 ( 92 unt; 0 nHn; 42 RR)
% Number of literals : 92 ( 91 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 89 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
least_upper_bound(a,b) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p02a) ).
cnf(c2,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(inverse(inverse(X2)),identity) = multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
cnf(c6,plain,
multiply(multiply(inverse(X2),X2),X3) = multiply(inverse(X2),multiply(X2,X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c2]) ).
cnf(c9,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c10,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c8,c9]) ).
cnf(c11,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c7,c10]) ).
cnf(c12,plain,
multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)) = X2,
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(inverse(inverse(X2)),identity) = X2,
inference(transitivity,[status(thm)],[c4,c12]) ).
cnf(c14,plain,
multiply(inverse(inverse(least_upper_bound(a,b))),identity) = least_upper_bound(a,b),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
least_upper_bound(a,b) = multiply(inverse(inverse(least_upper_bound(a,b))),identity),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
X2 = multiply(inverse(X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c17,plain,
multiply(inverse(inverse(X3)),X2) = multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c19,plain,
multiply(inverse(inverse(X3)),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c17,c18]) ).
cnf(c20,plain,
multiply(inverse(inverse(X2)),identity) = multiply(X2,identity),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(X2,identity) = multiply(inverse(inverse(X2)),identity),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c21,c13]) ).
cnf(c23,plain,
multiply(inverse(least_upper_bound(a,b)),identity) = inverse(least_upper_bound(a,b)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
inverse(least_upper_bound(a,b)) = multiply(inverse(least_upper_bound(a,b)),identity),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c26,plain,
least_upper_bound(b,a) = least_upper_bound(a,b),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
least_upper_bound(a,b) = least_upper_bound(b,a),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(least_upper_bound(a,b),inverse(a)) = multiply(least_upper_bound(b,a),inverse(a)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(inverse(inverse(X2)),identity) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c30,plain,
inverse(inverse(X2)) = multiply(inverse(inverse(X2)),identity),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
inverse(inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c30,c13]) ).
cnf(c32,plain,
inverse(inverse(a)) = a,
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
a = inverse(inverse(a)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
least_upper_bound(b,a) = least_upper_bound(b,inverse(inverse(a))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(least_upper_bound(b,a),inverse(a)) = multiply(least_upper_bound(b,inverse(inverse(a))),inverse(a)),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c37,plain,
least_upper_bound(identity,multiply(X3,X2)) = least_upper_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,axiom,
multiply(least_upper_bound(Y2,Z2),X2) = least_upper_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub2) ).
cnf(c39,plain,
multiply(least_upper_bound(inverse(X2),X3),X2) = least_upper_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
least_upper_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = multiply(least_upper_bound(inverse(X2),X3),X2),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
least_upper_bound(inverse(X2),X3) = least_upper_bound(X3,inverse(X2)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c42,plain,
multiply(least_upper_bound(inverse(X2),X3),X2) = multiply(least_upper_bound(X3,inverse(X2)),X2),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
least_upper_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = multiply(least_upper_bound(X3,inverse(X2)),X2),
inference(transitivity,[status(thm)],[c40,c42]) ).
cnf(c44,plain,
least_upper_bound(identity,multiply(X3,X2)) = multiply(least_upper_bound(X3,inverse(X2)),X2),
inference(transitivity,[status(thm)],[c37,c43]) ).
cnf(c45,plain,
least_upper_bound(identity,multiply(b,inverse(a))) = multiply(least_upper_bound(b,inverse(inverse(a))),inverse(a)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(least_upper_bound(b,inverse(inverse(a))),inverse(a)) = least_upper_bound(identity,multiply(b,inverse(a))),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(inverse(inverse(b)),inverse(a)) = multiply(b,inverse(a)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c48,plain,
multiply(b,inverse(a)) = multiply(inverse(inverse(b)),inverse(a)),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
least_upper_bound(identity,multiply(b,inverse(a))) = least_upper_bound(identity,multiply(inverse(inverse(b)),inverse(a))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,axiom,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c51,plain,
inverse(b) = least_upper_bound(inverse(a),inverse(b)),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
greatest_lower_bound(inverse(a),inverse(b)) = greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c54,plain,
greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))) = inverse(a),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
inference(transitivity,[status(thm)],[c52,c54]) ).
cnf(c56,plain,
inverse(a) = greatest_lower_bound(inverse(a),inverse(b)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(inverse(inverse(b)),inverse(a)) = multiply(inverse(inverse(b)),greatest_lower_bound(inverse(a),inverse(b))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
least_upper_bound(identity,multiply(inverse(inverse(b)),inverse(a))) = least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(inverse(a),inverse(b)))),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c60,plain,
least_upper_bound(identity,multiply(inverse(X3),X2)) = least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,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(c62,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = multiply(inverse(X3),least_upper_bound(X3,X2)),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
least_upper_bound(identity,multiply(inverse(X3),X2)) = multiply(inverse(X3),least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c60,c63]) ).
cnf(c65,plain,
least_upper_bound(identity,multiply(inverse(X3),greatest_lower_bound(X2,X3))) = multiply(inverse(X3),least_upper_bound(X3,greatest_lower_bound(X2,X3))),
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c67,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c71,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c69,c71]) ).
cnf(c73,plain,
multiply(inverse(X3),least_upper_bound(X3,greatest_lower_bound(X2,X3))) = multiply(inverse(X3),X3),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
multiply(inverse(X3),least_upper_bound(X3,greatest_lower_bound(X2,X3))) = identity,
inference(transitivity,[status(thm)],[c73,c2]) ).
cnf(c75,plain,
least_upper_bound(identity,multiply(inverse(X3),greatest_lower_bound(X2,X3))) = identity,
inference(transitivity,[status(thm)],[c65,c74]) ).
cnf(c76,plain,
least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(inverse(a),inverse(b)))) = identity,
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
least_upper_bound(identity,multiply(inverse(inverse(b)),inverse(a))) = identity,
inference(transitivity,[status(thm)],[c58,c76]) ).
cnf(c78,plain,
least_upper_bound(identity,multiply(b,inverse(a))) = identity,
inference(transitivity,[status(thm)],[c49,c77]) ).
cnf(c79,plain,
multiply(least_upper_bound(b,inverse(inverse(a))),inverse(a)) = identity,
inference(transitivity,[status(thm)],[c46,c78]) ).
cnf(c80,plain,
multiply(least_upper_bound(b,a),inverse(a)) = identity,
inference(transitivity,[status(thm)],[c35,c79]) ).
cnf(c81,plain,
multiply(least_upper_bound(a,b),inverse(a)) = identity,
inference(transitivity,[status(thm)],[c28,c80]) ).
cnf(c82,plain,
identity = multiply(least_upper_bound(a,b),inverse(a)),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(inverse(least_upper_bound(a,b)),identity) = multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,b),inverse(a))),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,b),inverse(a))) = inverse(a),
inference(substitution,[status(thm)],[c11]) ).
cnf(c85,plain,
multiply(inverse(least_upper_bound(a,b)),identity) = inverse(a),
inference(transitivity,[status(thm)],[c83,c84]) ).
cnf(c86,plain,
inverse(least_upper_bound(a,b)) = inverse(a),
inference(transitivity,[status(thm)],[c24,c85]) ).
cnf(c87,plain,
inverse(inverse(least_upper_bound(a,b))) = inverse(inverse(a)),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
multiply(inverse(inverse(least_upper_bound(a,b))),identity) = multiply(inverse(inverse(a)),identity),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
multiply(inverse(inverse(a)),identity) = a,
inference(substitution,[status(thm)],[c13]) ).
cnf(c90,plain,
multiply(inverse(inverse(least_upper_bound(a,b))),identity) = a,
inference(transitivity,[status(thm)],[c88,c89]) ).
cnf(c91,plain,
least_upper_bound(a,b) = a,
inference(transitivity,[status(thm)],[c15,c90]) ).
cnf(c92,plain,
$false,
inference(resolution,[status(thm)],[c1,c91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP169-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:37:23 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.49 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.09/0.49
% 0.09/0.49 % SZS status Unsatisfiable
% 0.09/0.49
% 0.09/0.49 % SZS output start CNFRefutation
% See solution above
% 0.57/0.50
% 0.57/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------