%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP171-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 10:09:32 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.46s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of clauses : 56 ( 56 unt; 0 nHn; 14 RR)
% Number of literals : 56 ( 55 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p04a) ).
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(least_upper_bound(X4,X2),X3) = least_upper_bound(X3,least_upper_bound(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
least_upper_bound(X3,least_upper_bound(X4,X2)) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
least_upper_bound(X2,least_upper_bound(Y2,Z)) = least_upper_bound(least_upper_bound(X2,Y2),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_lub) ).
cnf(c6,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X4,least_upper_bound(X2,X3)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c9,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c7,c9]) ).
cnf(c11,plain,
least_upper_bound(X3,least_upper_bound(X4,X2)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c4,c10]) ).
cnf(c12,plain,
least_upper_bound(X3,least_upper_bound(X2,multiply(a,X3))) = least_upper_bound(X2,least_upper_bound(X3,multiply(a,X3))),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
least_upper_bound(multiply(a,X2),X2) = least_upper_bound(X2,multiply(a,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
least_upper_bound(X2,multiply(a,X2)) = least_upper_bound(multiply(a,X2),X2),
inference(symmetry,[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(multiply(a,X2),X2) = least_upper_bound(multiply(a,X2),multiply(identity,X2)),
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(X4,X2),X3) = least_upper_bound(multiply(X4,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
least_upper_bound(multiply(X4,X3),multiply(X2,X3)) = multiply(least_upper_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
multiply(least_upper_bound(X4,X2),X3) = multiply(least_upper_bound(X2,X4),X3),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
least_upper_bound(multiply(X4,X3),multiply(X2,X3)) = multiply(least_upper_bound(X2,X4),X3),
inference(transitivity,[status(thm)],[c20,c22]) ).
cnf(c24,plain,
least_upper_bound(multiply(a,X2),multiply(identity,X2)) = multiply(least_upper_bound(identity,a),X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,axiom,
least_upper_bound(identity,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c26,plain,
multiply(least_upper_bound(identity,a),X2) = multiply(a,X2),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
least_upper_bound(multiply(a,X2),multiply(identity,X2)) = multiply(a,X2),
inference(transitivity,[status(thm)],[c24,c26]) ).
cnf(c28,plain,
least_upper_bound(multiply(a,X2),X2) = multiply(a,X2),
inference(transitivity,[status(thm)],[c17,c27]) ).
cnf(c29,plain,
least_upper_bound(X2,multiply(a,X2)) = multiply(a,X2),
inference(transitivity,[status(thm)],[c14,c28]) ).
cnf(c30,plain,
least_upper_bound(X2,least_upper_bound(X3,multiply(a,X3))) = least_upper_bound(X2,multiply(a,X3)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
least_upper_bound(X3,least_upper_bound(X2,multiply(a,X3))) = least_upper_bound(X2,multiply(a,X3)),
inference(transitivity,[status(thm)],[c12,c30]) ).
cnf(c32,plain,
least_upper_bound(b,least_upper_bound(identity,multiply(a,b))) = least_upper_bound(identity,multiply(a,b)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
least_upper_bound(identity,multiply(a,b)) = least_upper_bound(b,least_upper_bound(identity,multiply(a,b))),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
least_upper_bound(b,least_upper_bound(identity,multiply(a,b))) = least_upper_bound(identity,least_upper_bound(b,multiply(a,b))),
inference(substitution,[status(thm)],[c11]) ).
cnf(c35,plain,
least_upper_bound(X2,b) = least_upper_bound(b,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c36,plain,
least_upper_bound(b,X2) = least_upper_bound(X2,b),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
least_upper_bound(identity,least_upper_bound(b,X2)) = least_upper_bound(identity,least_upper_bound(X2,b)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
least_upper_bound(b,X2) = least_upper_bound(X2,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
least_upper_bound(X2,b) = least_upper_bound(b,X2),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
least_upper_bound(identity,least_upper_bound(X2,b)) = least_upper_bound(identity,least_upper_bound(b,X2)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
least_upper_bound(identity,least_upper_bound(b,X2)) = least_upper_bound(least_upper_bound(identity,b),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c42,axiom,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c43,plain,
least_upper_bound(least_upper_bound(identity,b),X2) = least_upper_bound(b,X2),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
least_upper_bound(b,X2) = least_upper_bound(X2,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c45,plain,
least_upper_bound(least_upper_bound(identity,b),X2) = least_upper_bound(X2,b),
inference(transitivity,[status(thm)],[c43,c44]) ).
cnf(c46,plain,
least_upper_bound(identity,least_upper_bound(b,X2)) = least_upper_bound(X2,b),
inference(transitivity,[status(thm)],[c41,c45]) ).
cnf(c47,plain,
least_upper_bound(identity,least_upper_bound(X2,b)) = least_upper_bound(X2,b),
inference(transitivity,[status(thm)],[c40,c46]) ).
cnf(c48,plain,
least_upper_bound(identity,least_upper_bound(b,X2)) = least_upper_bound(X2,b),
inference(transitivity,[status(thm)],[c37,c47]) ).
cnf(c49,plain,
least_upper_bound(identity,least_upper_bound(b,multiply(a,b))) = least_upper_bound(multiply(a,b),b),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
least_upper_bound(multiply(a,b),b) = least_upper_bound(b,multiply(a,b)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c51,plain,
least_upper_bound(b,multiply(a,b)) = multiply(a,b),
inference(substitution,[status(thm)],[c29]) ).
cnf(c52,plain,
least_upper_bound(multiply(a,b),b) = multiply(a,b),
inference(transitivity,[status(thm)],[c50,c51]) ).
cnf(c53,plain,
least_upper_bound(identity,least_upper_bound(b,multiply(a,b))) = multiply(a,b),
inference(transitivity,[status(thm)],[c49,c52]) ).
cnf(c54,plain,
least_upper_bound(b,least_upper_bound(identity,multiply(a,b))) = multiply(a,b),
inference(transitivity,[status(thm)],[c34,c53]) ).
cnf(c55,plain,
least_upper_bound(identity,multiply(a,b)) = multiply(a,b),
inference(transitivity,[status(thm)],[c33,c54]) ).
cnf(c56,plain,
$false,
inference(resolution,[status(thm)],[c1,c55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP171-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:37:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.46 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
% 0.18/0.46
% 0.18/0.46 % SZS status Unsatisfiable
% 0.18/0.46
% 0.18/0.47 % SZS output start CNFRefutation
% See solution above
% 0.18/0.48
% 0.18/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------