%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP166-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 10:09:29 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of clauses : 64 ( 64 unt; 0 nHn; 16 RR)
% Number of literals : 64 ( 63 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
greatest_lower_bound(a,multiply(a,b)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lat2b) ).
cnf(c2,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c6,axiom,
greatest_lower_bound(b,identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c7,plain,
identity = greatest_lower_bound(b,identity),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
greatest_lower_bound(a,identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c9,plain,
identity = greatest_lower_bound(b,identity),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c10,plain,
greatest_lower_bound(a,identity) = greatest_lower_bound(b,identity),
inference(transitivity,[status(thm)],[c8,c9]) ).
cnf(c11,plain,
greatest_lower_bound(b,identity) = greatest_lower_bound(a,identity),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
identity = greatest_lower_bound(a,identity),
inference(transitivity,[status(thm)],[c7,c11]) ).
cnf(c13,plain,
multiply(inverse(X2),X2) = greatest_lower_bound(a,identity),
inference(transitivity,[status(thm)],[c5,c12]) ).
cnf(c14,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(greatest_lower_bound(a,identity),X2),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(greatest_lower_bound(a,identity),X2) = multiply(greatest_lower_bound(b,identity),X2),
inference(congruence,[status(thm)],[c10]) ).
cnf(c16,plain,
multiply(greatest_lower_bound(b,identity),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c6]) ).
cnf(c17,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c18,plain,
multiply(greatest_lower_bound(b,identity),X2) = X2,
inference(transitivity,[status(thm)],[c16,c17]) ).
cnf(c19,plain,
multiply(greatest_lower_bound(a,identity),X2) = X2,
inference(transitivity,[status(thm)],[c15,c18]) ).
cnf(c20,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c14,c19]) ).
cnf(c21,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c4,c20]) ).
cnf(c22,plain,
X2 = multiply(inverse(X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(inverse(inverse(X3)),X2) = multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c21]) ).
cnf(c25,plain,
multiply(inverse(inverse(X3)),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c23,c24]) ).
cnf(c26,plain,
multiply(inverse(inverse(X2)),greatest_lower_bound(a,identity)) = multiply(X2,greatest_lower_bound(a,identity)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(X2,greatest_lower_bound(a,identity)) = multiply(inverse(inverse(X2)),greatest_lower_bound(a,identity)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
greatest_lower_bound(a,identity) = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c29,plain,
multiply(inverse(inverse(X2)),greatest_lower_bound(a,identity)) = multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)) = X2,
inference(substitution,[status(thm)],[c21]) ).
cnf(c31,plain,
multiply(inverse(inverse(X2)),greatest_lower_bound(a,identity)) = X2,
inference(transitivity,[status(thm)],[c29,c30]) ).
cnf(c32,plain,
multiply(X2,greatest_lower_bound(a,identity)) = X2,
inference(transitivity,[status(thm)],[c27,c31]) ).
cnf(c33,plain,
X2 = multiply(X2,greatest_lower_bound(a,identity)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
least_upper_bound(multiply(X2,b),X2) = least_upper_bound(multiply(X2,b),multiply(X2,greatest_lower_bound(a,identity))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,axiom,
multiply(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
cnf(c36,plain,
multiply(X3,least_upper_bound(X4,X2)) = least_upper_bound(multiply(X3,X4),multiply(X3,X2)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
least_upper_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,least_upper_bound(X2,X3)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c39,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
multiply(X4,least_upper_bound(X2,X3)) = multiply(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
least_upper_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c37,c40]) ).
cnf(c42,plain,
least_upper_bound(multiply(X2,b),multiply(X2,greatest_lower_bound(a,identity))) = multiply(X2,least_upper_bound(greatest_lower_bound(a,identity),b)),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
least_upper_bound(b,greatest_lower_bound(a,identity)) = least_upper_bound(greatest_lower_bound(a,identity),b),
inference(substitution,[status(thm)],[c38]) ).
cnf(c44,plain,
least_upper_bound(greatest_lower_bound(a,identity),b) = least_upper_bound(b,greatest_lower_bound(a,identity)),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
least_upper_bound(b,greatest_lower_bound(a,identity)) = least_upper_bound(b,greatest_lower_bound(b,identity)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c46,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c47,plain,
least_upper_bound(b,greatest_lower_bound(b,identity)) = b,
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
least_upper_bound(b,greatest_lower_bound(a,identity)) = b,
inference(transitivity,[status(thm)],[c45,c47]) ).
cnf(c49,plain,
least_upper_bound(greatest_lower_bound(a,identity),b) = b,
inference(transitivity,[status(thm)],[c44,c48]) ).
cnf(c50,plain,
multiply(X2,least_upper_bound(greatest_lower_bound(a,identity),b)) = multiply(X2,b),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
least_upper_bound(multiply(X2,b),multiply(X2,greatest_lower_bound(a,identity))) = multiply(X2,b),
inference(transitivity,[status(thm)],[c42,c50]) ).
cnf(c52,plain,
least_upper_bound(multiply(X2,b),X2) = multiply(X2,b),
inference(transitivity,[status(thm)],[c34,c51]) ).
cnf(c53,plain,
multiply(X2,b) = least_upper_bound(multiply(X2,b),X2),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
greatest_lower_bound(X2,multiply(X2,b)) = greatest_lower_bound(X2,least_upper_bound(multiply(X2,b),X2)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c38]) ).
cnf(c56,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c59,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c58]) ).
cnf(c60,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c57,c59]) ).
cnf(c61,plain,
greatest_lower_bound(X2,least_upper_bound(multiply(X2,b),X2)) = X2,
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
greatest_lower_bound(X2,multiply(X2,b)) = X2,
inference(transitivity,[status(thm)],[c54,c61]) ).
cnf(c63,plain,
greatest_lower_bound(a,multiply(a,b)) = a,
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
$false,
inference(resolution,[status(thm)],[c1,c63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP166-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:34:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.44 Command-line arguments: --flatten --complete-subsets
% 0.13/0.44
% 0.13/0.44 % SZS status Unsatisfiable
% 0.13/0.44
% 0.13/0.44 % SZS output start CNFRefutation
% See solution above
% 0.13/0.46
% 0.13/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------