%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP190-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 10:09:39 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.51s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 10
% Syntax : Number of clauses : 87 ( 87 unt; 0 nHn; 32 RR)
% Number of literals : 87 ( 86 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 : 92 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p39c) ).
cnf(c2,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
cnf(c3,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c8,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c4,c8]) ).
cnf(c10,plain,
multiply(inverse(a),multiply(a,greatest_lower_bound(inverse(a),inverse(b)))) = greatest_lower_bound(inverse(a),inverse(b)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
greatest_lower_bound(inverse(a),inverse(b)) = multiply(inverse(a),multiply(a,greatest_lower_bound(inverse(a),inverse(b)))),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(multiply(greatest_lower_bound(inverse(a),inverse(b)),a),X2) = multiply(greatest_lower_bound(inverse(a),inverse(b)),multiply(a,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
multiply(greatest_lower_bound(inverse(a),inverse(b)),multiply(a,X2)) = multiply(multiply(greatest_lower_bound(inverse(a),inverse(b)),a),X2),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c15,plain,
greatest_lower_bound(inverse(b),inverse(a)) = greatest_lower_bound(inverse(a),inverse(b)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
greatest_lower_bound(inverse(a),inverse(b)) = greatest_lower_bound(inverse(b),inverse(a)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(greatest_lower_bound(inverse(a),inverse(b)),a) = multiply(greatest_lower_bound(inverse(b),inverse(a)),a),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c19,plain,
greatest_lower_bound(identity,multiply(X3,X2)) = greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,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(c21,plain,
multiply(greatest_lower_bound(inverse(X2),X3),X2) = greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = multiply(greatest_lower_bound(inverse(X2),X3),X2),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
greatest_lower_bound(inverse(X2),X3) = greatest_lower_bound(X3,inverse(X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c24,plain,
multiply(greatest_lower_bound(inverse(X2),X3),X2) = multiply(greatest_lower_bound(X3,inverse(X2)),X2),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X3,inverse(X2)),X2),
inference(transitivity,[status(thm)],[c22,c24]) ).
cnf(c26,plain,
greatest_lower_bound(identity,multiply(X3,X2)) = multiply(greatest_lower_bound(X3,inverse(X2)),X2),
inference(transitivity,[status(thm)],[c19,c25]) ).
cnf(c27,plain,
greatest_lower_bound(identity,multiply(inverse(b),a)) = multiply(greatest_lower_bound(inverse(b),inverse(a)),a),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(greatest_lower_bound(inverse(b),inverse(a)),a) = greatest_lower_bound(identity,multiply(inverse(b),a)),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c30,plain,
greatest_lower_bound(identity,multiply(inverse(X3),X2)) = greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,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(c32,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = multiply(inverse(X3),greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c35,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = multiply(inverse(X3),greatest_lower_bound(X2,X3)),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = multiply(inverse(X3),greatest_lower_bound(X2,X3)),
inference(transitivity,[status(thm)],[c33,c35]) ).
cnf(c37,plain,
greatest_lower_bound(identity,multiply(inverse(X3),X2)) = multiply(inverse(X3),greatest_lower_bound(X2,X3)),
inference(transitivity,[status(thm)],[c30,c36]) ).
cnf(c38,plain,
greatest_lower_bound(identity,multiply(inverse(b),a)) = multiply(inverse(b),greatest_lower_bound(a,b)),
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
greatest_lower_bound(b,a) = greatest_lower_bound(a,b),
inference(substitution,[status(thm)],[c14]) ).
cnf(c40,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(b,a),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,axiom,
least_upper_bound(a,b) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c42,plain,
a = least_upper_bound(a,b),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
greatest_lower_bound(b,a) = greatest_lower_bound(b,least_upper_bound(a,b)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c45,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c49,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c47,c49]) ).
cnf(c51,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) = b,
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
greatest_lower_bound(b,a) = b,
inference(transitivity,[status(thm)],[c43,c51]) ).
cnf(c53,plain,
greatest_lower_bound(a,b) = b,
inference(transitivity,[status(thm)],[c40,c52]) ).
cnf(c54,plain,
multiply(inverse(b),greatest_lower_bound(a,b)) = multiply(inverse(b),b),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(inverse(b),b) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c56,plain,
multiply(inverse(b),greatest_lower_bound(a,b)) = identity,
inference(transitivity,[status(thm)],[c54,c55]) ).
cnf(c57,plain,
greatest_lower_bound(identity,multiply(inverse(b),a)) = identity,
inference(transitivity,[status(thm)],[c38,c56]) ).
cnf(c58,plain,
multiply(greatest_lower_bound(inverse(b),inverse(a)),a) = identity,
inference(transitivity,[status(thm)],[c28,c57]) ).
cnf(c59,plain,
multiply(greatest_lower_bound(inverse(a),inverse(b)),a) = identity,
inference(transitivity,[status(thm)],[c17,c58]) ).
cnf(c60,plain,
multiply(multiply(greatest_lower_bound(inverse(a),inverse(b)),a),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
multiply(multiply(greatest_lower_bound(inverse(a),inverse(b)),a),X2) = X2,
inference(transitivity,[status(thm)],[c60,c7]) ).
cnf(c62,plain,
multiply(greatest_lower_bound(inverse(a),inverse(b)),multiply(a,X2)) = X2,
inference(transitivity,[status(thm)],[c13,c61]) ).
cnf(c63,plain,
X2 = multiply(greatest_lower_bound(inverse(a),inverse(b)),multiply(a,X2)),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(inverse(greatest_lower_bound(inverse(a),inverse(b))),X2) = multiply(inverse(greatest_lower_bound(inverse(a),inverse(b))),multiply(greatest_lower_bound(inverse(a),inverse(b)),multiply(a,X2))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(inverse(greatest_lower_bound(inverse(a),inverse(b))),multiply(greatest_lower_bound(inverse(a),inverse(b)),multiply(a,X2))) = multiply(a,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c66,plain,
multiply(inverse(greatest_lower_bound(inverse(a),inverse(b))),X2) = multiply(a,X2),
inference(transitivity,[status(thm)],[c64,c65]) ).
cnf(c67,plain,
multiply(inverse(greatest_lower_bound(inverse(a),inverse(b))),greatest_lower_bound(inverse(a),inverse(b))) = multiply(a,greatest_lower_bound(inverse(a),inverse(b))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(a,greatest_lower_bound(inverse(a),inverse(b))) = multiply(inverse(greatest_lower_bound(inverse(a),inverse(b))),greatest_lower_bound(inverse(a),inverse(b))),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
multiply(inverse(greatest_lower_bound(inverse(a),inverse(b))),greatest_lower_bound(inverse(a),inverse(b))) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c70,plain,
multiply(a,greatest_lower_bound(inverse(a),inverse(b))) = identity,
inference(transitivity,[status(thm)],[c68,c69]) ).
cnf(c71,plain,
multiply(inverse(a),multiply(a,greatest_lower_bound(inverse(a),inverse(b)))) = multiply(inverse(a),identity),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
X2 = multiply(inverse(X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c73,plain,
multiply(inverse(inverse(X3)),X2) = multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c75,plain,
multiply(inverse(inverse(X3)),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c73,c74]) ).
cnf(c76,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
multiply(X2,inverse(X2)) = multiply(inverse(inverse(X2)),inverse(X2)),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c79,plain,
multiply(X2,inverse(X2)) = identity,
inference(transitivity,[status(thm)],[c77,c78]) ).
cnf(c80,plain,
identity = multiply(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(inverse(X2),identity) = multiply(inverse(X2),multiply(X2,inverse(X2))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
multiply(inverse(X2),multiply(X2,inverse(X2))) = inverse(X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c83,plain,
multiply(inverse(X2),identity) = inverse(X2),
inference(transitivity,[status(thm)],[c81,c82]) ).
cnf(c84,plain,
multiply(inverse(a),identity) = inverse(a),
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
multiply(inverse(a),multiply(a,greatest_lower_bound(inverse(a),inverse(b)))) = inverse(a),
inference(transitivity,[status(thm)],[c71,c84]) ).
cnf(c86,plain,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
inference(transitivity,[status(thm)],[c11,c85]) ).
cnf(c87,plain,
$false,
inference(resolution,[status(thm)],[c1,c86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP190-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:40:14 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.51 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.17/0.51
% 0.17/0.51 % SZS status Unsatisfiable
% 0.17/0.51
% 0.17/0.51 % SZS output start CNFRefutation
% See solution above
% 0.17/0.55
% 0.17/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------