%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP175-1 : 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 10:09:33 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 7 RR)
% Number of literals : 37 ( 36 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p06a) ).
cnf(c2,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c3,plain,
least_upper_bound(multiply(inverse(X2),multiply(b,X2)),identity) = least_upper_bound(identity,multiply(inverse(X2),multiply(b,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
least_upper_bound(identity,multiply(inverse(X2),multiply(b,X2))) = least_upper_bound(multiply(inverse(X2),multiply(b,X2)),identity),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
least_upper_bound(multiply(inverse(X2),multiply(b,X2)),identity) = least_upper_bound(multiply(inverse(X2),multiply(b,X2)),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
multiply(X2,least_upper_bound(Y2,Z)) = least_upper_bound(multiply(X2,Y2),multiply(X2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).
cnf(c9,plain,
multiply(X2,least_upper_bound(X4,X3)) = least_upper_bound(multiply(X2,X4),multiply(X2,X3)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
least_upper_bound(multiply(X4,X3),multiply(X4,X2)) = multiply(X4,least_upper_bound(X3,X2)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
multiply(X4,least_upper_bound(X3,X2)) = multiply(X4,least_upper_bound(X2,X3)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
least_upper_bound(multiply(X4,X3),multiply(X4,X2)) = multiply(X4,least_upper_bound(X2,X3)),
inference(transitivity,[status(thm)],[c10,c12]) ).
cnf(c14,plain,
least_upper_bound(multiply(inverse(X2),multiply(b,X2)),multiply(inverse(X2),X2)) = multiply(inverse(X2),least_upper_bound(X2,multiply(b,X2))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c16,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
least_upper_bound(X3,multiply(X2,X3)) = least_upper_bound(multiply(identity,X3),multiply(X2,X3)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,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(c19,plain,
multiply(least_upper_bound(identity,X2),X3) = least_upper_bound(multiply(identity,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
least_upper_bound(multiply(identity,X3),multiply(X2,X3)) = multiply(least_upper_bound(identity,X2),X3),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
multiply(least_upper_bound(identity,X2),X3) = multiply(least_upper_bound(X2,identity),X3),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
least_upper_bound(multiply(identity,X3),multiply(X2,X3)) = multiply(least_upper_bound(X2,identity),X3),
inference(transitivity,[status(thm)],[c20,c22]) ).
cnf(c24,plain,
least_upper_bound(X3,multiply(X2,X3)) = multiply(least_upper_bound(X2,identity),X3),
inference(transitivity,[status(thm)],[c17,c23]) ).
cnf(c25,plain,
least_upper_bound(X2,multiply(b,X2)) = multiply(least_upper_bound(b,identity),X2),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
least_upper_bound(identity,b) = least_upper_bound(b,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,plain,
least_upper_bound(b,identity) = least_upper_bound(identity,b),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,axiom,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c29,plain,
least_upper_bound(b,identity) = b,
inference(transitivity,[status(thm)],[c27,c28]) ).
cnf(c30,plain,
multiply(least_upper_bound(b,identity),X2) = multiply(b,X2),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
least_upper_bound(X2,multiply(b,X2)) = multiply(b,X2),
inference(transitivity,[status(thm)],[c25,c30]) ).
cnf(c32,plain,
multiply(inverse(X2),least_upper_bound(X2,multiply(b,X2))) = multiply(inverse(X2),multiply(b,X2)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
least_upper_bound(multiply(inverse(X2),multiply(b,X2)),multiply(inverse(X2),X2)) = multiply(inverse(X2),multiply(b,X2)),
inference(transitivity,[status(thm)],[c14,c32]) ).
cnf(c34,plain,
least_upper_bound(multiply(inverse(X2),multiply(b,X2)),identity) = multiply(inverse(X2),multiply(b,X2)),
inference(transitivity,[status(thm)],[c7,c33]) ).
cnf(c35,plain,
least_upper_bound(identity,multiply(inverse(X2),multiply(b,X2))) = multiply(inverse(X2),multiply(b,X2)),
inference(transitivity,[status(thm)],[c4,c34]) ).
cnf(c36,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),multiply(b,a)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
$false,
inference(resolution,[status(thm)],[c1,c36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP175-1 : 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 09:38:44 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.49
% 0.19/0.49 % SZS status Unsatisfiable
% 0.19/0.49
% 0.19/0.49 % SZS output start CNFRefutation
% See solution above
% 0.19/0.50
% 0.19/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------