%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP166-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 10:09:30 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 7 RR)
% Number of literals : 26 ( 25 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
least_upper_bound(a,multiply(b,a)) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lat3a) ).
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(X2,identity) = least_upper_bound(identity,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(least_upper_bound(identity,X2),X3) = multiply(least_upper_bound(X2,identity),X3),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(least_upper_bound(X3,identity),X2) = multiply(least_upper_bound(identity,X3),X2),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,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(c10,plain,
multiply(least_upper_bound(identity,X3),X2) = least_upper_bound(multiply(identity,X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c12,plain,
least_upper_bound(multiply(identity,X2),multiply(X3,X2)) = least_upper_bound(X2,multiply(X3,X2)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(least_upper_bound(identity,X3),X2) = least_upper_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c10,c12]) ).
cnf(c14,plain,
multiply(least_upper_bound(X3,identity),X2) = least_upper_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c8,c13]) ).
cnf(c15,plain,
multiply(least_upper_bound(X2,identity),X3) = least_upper_bound(X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(least_upper_bound(identity,X2),X3) = least_upper_bound(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c5,c15]) ).
cnf(c17,plain,
multiply(least_upper_bound(identity,b),X2) = least_upper_bound(X2,multiply(b,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
least_upper_bound(X2,multiply(b,X2)) = multiply(least_upper_bound(identity,b),X2),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
least_upper_bound(b,identity) = least_upper_bound(identity,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c20,plain,
least_upper_bound(identity,b) = least_upper_bound(b,identity),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,axiom,
least_upper_bound(b,identity) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c22,plain,
least_upper_bound(identity,b) = b,
inference(transitivity,[status(thm)],[c20,c21]) ).
cnf(c23,plain,
multiply(least_upper_bound(identity,b),X2) = multiply(b,X2),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
least_upper_bound(X2,multiply(b,X2)) = multiply(b,X2),
inference(transitivity,[status(thm)],[c18,c23]) ).
cnf(c25,plain,
least_upper_bound(a,multiply(b,a)) = multiply(b,a),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
$false,
inference(resolution,[status(thm)],[c1,c25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP166-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 09:34:31 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47 Command-line arguments: --no-flatten-goal
% 0.17/0.47
% 0.17/0.47 % SZS status Unsatisfiable
% 0.17/0.47
% 0.17/0.47 % SZS output start CNFRefutation
% See solution above
% 0.17/0.47
% 0.17/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------