%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP191-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 10:09:40 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.38s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of clauses : 86 ( 86 unt; 0 nHn; 31 RR)
% Number of literals : 86 ( 85 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,
least_upper_bound(inverse(a),inverse(b)) != inverse(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p39d) ).
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(b),multiply(b,least_upper_bound(inverse(a),inverse(b)))) = least_upper_bound(inverse(a),inverse(b)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
least_upper_bound(inverse(a),inverse(b)) = multiply(inverse(b),multiply(b,least_upper_bound(inverse(a),inverse(b)))),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(multiply(least_upper_bound(inverse(a),inverse(b)),b),X2) = multiply(least_upper_bound(inverse(a),inverse(b)),multiply(b,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
multiply(least_upper_bound(inverse(a),inverse(b)),multiply(b,X2)) = multiply(multiply(least_upper_bound(inverse(a),inverse(b)),b),X2),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c15,plain,
least_upper_bound(identity,multiply(X3,X2)) = least_upper_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,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(c17,plain,
multiply(least_upper_bound(inverse(X2),X3),X2) = least_upper_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
least_upper_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = multiply(least_upper_bound(inverse(X2),X3),X2),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c20,plain,
least_upper_bound(inverse(X2),X3) = least_upper_bound(X3,inverse(X2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(least_upper_bound(inverse(X2),X3),X2) = multiply(least_upper_bound(X3,inverse(X2)),X2),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
least_upper_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = multiply(least_upper_bound(X3,inverse(X2)),X2),
inference(transitivity,[status(thm)],[c18,c21]) ).
cnf(c23,plain,
least_upper_bound(identity,multiply(X3,X2)) = multiply(least_upper_bound(X3,inverse(X2)),X2),
inference(transitivity,[status(thm)],[c15,c22]) ).
cnf(c24,plain,
least_upper_bound(identity,multiply(inverse(a),b)) = multiply(least_upper_bound(inverse(a),inverse(b)),b),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(least_upper_bound(inverse(a),inverse(b)),b) = least_upper_bound(identity,multiply(inverse(a),b)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c27,plain,
least_upper_bound(identity,multiply(inverse(X3),X2)) = least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,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(c29,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = multiply(inverse(X3),least_upper_bound(X3,X2)),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c19]) ).
cnf(c32,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = multiply(inverse(X3),least_upper_bound(X2,X3)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = multiply(inverse(X3),least_upper_bound(X2,X3)),
inference(transitivity,[status(thm)],[c30,c32]) ).
cnf(c34,plain,
least_upper_bound(identity,multiply(inverse(X3),X2)) = multiply(inverse(X3),least_upper_bound(X2,X3)),
inference(transitivity,[status(thm)],[c27,c33]) ).
cnf(c35,plain,
least_upper_bound(identity,multiply(inverse(a),b)) = multiply(inverse(a),least_upper_bound(b,a)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
least_upper_bound(a,b) = least_upper_bound(b,a),
inference(substitution,[status(thm)],[c19]) ).
cnf(c37,plain,
least_upper_bound(b,a) = least_upper_bound(a,b),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c39,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(b,a),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
greatest_lower_bound(b,a) = greatest_lower_bound(a,b),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,axiom,
greatest_lower_bound(a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c42,plain,
greatest_lower_bound(b,a) = b,
inference(transitivity,[status(thm)],[c40,c41]) ).
cnf(c43,plain,
b = greatest_lower_bound(b,a),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
least_upper_bound(a,b) = least_upper_bound(a,greatest_lower_bound(b,a)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c38]) ).
cnf(c46,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c49,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c47,c49]) ).
cnf(c51,plain,
least_upper_bound(a,greatest_lower_bound(b,a)) = a,
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
least_upper_bound(a,b) = a,
inference(transitivity,[status(thm)],[c44,c51]) ).
cnf(c53,plain,
least_upper_bound(b,a) = a,
inference(transitivity,[status(thm)],[c37,c52]) ).
cnf(c54,plain,
multiply(inverse(a),least_upper_bound(b,a)) = multiply(inverse(a),a),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(inverse(a),a) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c56,plain,
multiply(inverse(a),least_upper_bound(b,a)) = identity,
inference(transitivity,[status(thm)],[c54,c55]) ).
cnf(c57,plain,
least_upper_bound(identity,multiply(inverse(a),b)) = identity,
inference(transitivity,[status(thm)],[c35,c56]) ).
cnf(c58,plain,
multiply(least_upper_bound(inverse(a),inverse(b)),b) = identity,
inference(transitivity,[status(thm)],[c25,c57]) ).
cnf(c59,plain,
multiply(multiply(least_upper_bound(inverse(a),inverse(b)),b),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(multiply(least_upper_bound(inverse(a),inverse(b)),b),X2) = X2,
inference(transitivity,[status(thm)],[c59,c7]) ).
cnf(c61,plain,
multiply(least_upper_bound(inverse(a),inverse(b)),multiply(b,X2)) = X2,
inference(transitivity,[status(thm)],[c13,c60]) ).
cnf(c62,plain,
X2 = multiply(least_upper_bound(inverse(a),inverse(b)),multiply(b,X2)),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(inverse(least_upper_bound(inverse(a),inverse(b))),X2) = multiply(inverse(least_upper_bound(inverse(a),inverse(b))),multiply(least_upper_bound(inverse(a),inverse(b)),multiply(b,X2))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(inverse(least_upper_bound(inverse(a),inverse(b))),multiply(least_upper_bound(inverse(a),inverse(b)),multiply(b,X2))) = multiply(b,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c65,plain,
multiply(inverse(least_upper_bound(inverse(a),inverse(b))),X2) = multiply(b,X2),
inference(transitivity,[status(thm)],[c63,c64]) ).
cnf(c66,plain,
multiply(inverse(least_upper_bound(inverse(a),inverse(b))),least_upper_bound(inverse(a),inverse(b))) = multiply(b,least_upper_bound(inverse(a),inverse(b))),
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
multiply(b,least_upper_bound(inverse(a),inverse(b))) = multiply(inverse(least_upper_bound(inverse(a),inverse(b))),least_upper_bound(inverse(a),inverse(b))),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(inverse(least_upper_bound(inverse(a),inverse(b))),least_upper_bound(inverse(a),inverse(b))) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c69,plain,
multiply(b,least_upper_bound(inverse(a),inverse(b))) = identity,
inference(transitivity,[status(thm)],[c67,c68]) ).
cnf(c70,plain,
multiply(inverse(b),multiply(b,least_upper_bound(inverse(a),inverse(b)))) = multiply(inverse(b),identity),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
X2 = multiply(inverse(X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c72,plain,
multiply(inverse(inverse(X3)),X2) = multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c74,plain,
multiply(inverse(inverse(X3)),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c72,c73]) ).
cnf(c75,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
multiply(X2,inverse(X2)) = multiply(inverse(inverse(X2)),inverse(X2)),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c78,plain,
multiply(X2,inverse(X2)) = identity,
inference(transitivity,[status(thm)],[c76,c77]) ).
cnf(c79,plain,
identity = multiply(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
multiply(inverse(X2),identity) = multiply(inverse(X2),multiply(X2,inverse(X2))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(inverse(X2),multiply(X2,inverse(X2))) = inverse(X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c82,plain,
multiply(inverse(X2),identity) = inverse(X2),
inference(transitivity,[status(thm)],[c80,c81]) ).
cnf(c83,plain,
multiply(inverse(b),identity) = inverse(b),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(inverse(b),multiply(b,least_upper_bound(inverse(a),inverse(b)))) = inverse(b),
inference(transitivity,[status(thm)],[c70,c83]) ).
cnf(c85,plain,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
inference(transitivity,[status(thm)],[c11,c84]) ).
cnf(c86,plain,
$false,
inference(resolution,[status(thm)],[c1,c85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP191-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 09:36:50 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.38 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.07/0.38
% 0.07/0.38 % SZS status Unsatisfiable
% 0.07/0.38
% 0.07/0.39 % SZS output start CNFRefutation
% See solution above
% 0.07/0.41
% 0.07/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------