%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP172-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 10:09:32 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of clauses : 77 ( 77 unt; 0 nHn; 23 RR)
% Number of literals : 77 ( 76 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 : 83 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p04d) ).
cnf(c2,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c3,plain,
least_upper_bound(greatest_lower_bound(identity,a),X2) = least_upper_bound(X2,greatest_lower_bound(identity,a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
least_upper_bound(X2,greatest_lower_bound(identity,a)) = least_upper_bound(greatest_lower_bound(identity,a),X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
greatest_lower_bound(identity,a) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
least_upper_bound(greatest_lower_bound(identity,a),X2) = least_upper_bound(identity,X2),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
least_upper_bound(X2,greatest_lower_bound(identity,a)) = least_upper_bound(identity,X2),
inference(transitivity,[status(thm)],[c4,c6]) ).
cnf(c8,plain,
least_upper_bound(multiply(a,b),greatest_lower_bound(identity,a)) = least_upper_bound(identity,multiply(a,b)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
least_upper_bound(identity,multiply(a,b)) = least_upper_bound(multiply(a,b),greatest_lower_bound(identity,a)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c11,plain,
greatest_lower_bound(b,X2) = greatest_lower_bound(X2,b),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
greatest_lower_bound(X2,b) = greatest_lower_bound(b,X2),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
greatest_lower_bound(greatest_lower_bound(identity,a),greatest_lower_bound(X2,b)) = greatest_lower_bound(greatest_lower_bound(identity,a),greatest_lower_bound(b,X2)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,axiom,
greatest_lower_bound(X2,greatest_lower_bound(Y2,Z)) = greatest_lower_bound(greatest_lower_bound(X2,Y2),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).
cnf(c15,plain,
greatest_lower_bound(greatest_lower_bound(identity,a),greatest_lower_bound(b,X2)) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(identity,a),b),X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
greatest_lower_bound(greatest_lower_bound(identity,a),b) = greatest_lower_bound(identity,b),
inference(congruence,[status(thm)],[c5]) ).
cnf(c17,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(identity,a),b),X2) = greatest_lower_bound(greatest_lower_bound(identity,b),X2),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,axiom,
greatest_lower_bound(identity,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c19,plain,
identity = greatest_lower_bound(identity,a),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c20,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(identity,a),
inference(transitivity,[status(thm)],[c18,c19]) ).
cnf(c21,plain,
greatest_lower_bound(greatest_lower_bound(identity,b),X2) = greatest_lower_bound(greatest_lower_bound(identity,a),X2),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
greatest_lower_bound(greatest_lower_bound(identity,a),X2) = greatest_lower_bound(X2,greatest_lower_bound(identity,a)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c23,plain,
greatest_lower_bound(greatest_lower_bound(identity,b),X2) = greatest_lower_bound(X2,greatest_lower_bound(identity,a)),
inference(transitivity,[status(thm)],[c21,c22]) ).
cnf(c24,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(identity,a),b),X2) = greatest_lower_bound(X2,greatest_lower_bound(identity,a)),
inference(transitivity,[status(thm)],[c17,c23]) ).
cnf(c25,plain,
greatest_lower_bound(greatest_lower_bound(identity,a),greatest_lower_bound(b,X2)) = greatest_lower_bound(X2,greatest_lower_bound(identity,a)),
inference(transitivity,[status(thm)],[c15,c24]) ).
cnf(c26,plain,
greatest_lower_bound(greatest_lower_bound(identity,a),greatest_lower_bound(X2,b)) = greatest_lower_bound(X2,greatest_lower_bound(identity,a)),
inference(transitivity,[status(thm)],[c13,c25]) ).
cnf(c27,plain,
greatest_lower_bound(greatest_lower_bound(identity,a),greatest_lower_bound(multiply(a,b),b)) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,a)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,a)) = greatest_lower_bound(greatest_lower_bound(identity,a),greatest_lower_bound(multiply(a,b),b)),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
greatest_lower_bound(X2,multiply(a,X2)) = greatest_lower_bound(multiply(a,X2),X2),
inference(substitution,[status(thm)],[c10]) ).
cnf(c30,plain,
greatest_lower_bound(multiply(a,X2),X2) = greatest_lower_bound(X2,multiply(a,X2)),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(greatest_lower_bound(identity,a),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c5]) ).
cnf(c32,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c33,plain,
multiply(greatest_lower_bound(identity,a),X2) = X2,
inference(transitivity,[status(thm)],[c31,c32]) ).
cnf(c34,plain,
X2 = multiply(greatest_lower_bound(identity,a),X2),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
least_upper_bound(multiply(a,X2),X2) = least_upper_bound(multiply(a,X2),multiply(greatest_lower_bound(identity,a),X2)),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,axiom,
multiply(least_upper_bound(Y2,Z2),X2) = least_upper_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
cnf(c37,plain,
multiply(least_upper_bound(X4,X2),X3) = least_upper_bound(multiply(X4,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
least_upper_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(least_upper_bound(X3,X4),X2),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c40,plain,
multiply(least_upper_bound(X3,X4),X2) = multiply(least_upper_bound(X4,X3),X2),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
least_upper_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(least_upper_bound(X4,X3),X2),
inference(transitivity,[status(thm)],[c38,c40]) ).
cnf(c42,plain,
least_upper_bound(multiply(a,X2),multiply(greatest_lower_bound(identity,a),X2)) = multiply(least_upper_bound(greatest_lower_bound(identity,a),a),X2),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = least_upper_bound(greatest_lower_bound(X3,X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c44,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X2) = least_upper_bound(X2,greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c46,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = least_upper_bound(X2,greatest_lower_bound(X2,X3)),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c48,plain,
least_upper_bound(X2,greatest_lower_bound(X2,X3)) = X2,
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c46,c48]) ).
cnf(c50,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X2) = X2,
inference(transitivity,[status(thm)],[c44,c49]) ).
cnf(c51,plain,
least_upper_bound(greatest_lower_bound(identity,a),a) = a,
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(least_upper_bound(greatest_lower_bound(identity,a),a),X2) = multiply(a,X2),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
least_upper_bound(multiply(a,X2),multiply(greatest_lower_bound(identity,a),X2)) = multiply(a,X2),
inference(transitivity,[status(thm)],[c42,c52]) ).
cnf(c54,plain,
least_upper_bound(multiply(a,X2),X2) = multiply(a,X2),
inference(transitivity,[status(thm)],[c35,c53]) ).
cnf(c55,plain,
multiply(a,X2) = least_upper_bound(multiply(a,X2),X2),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
greatest_lower_bound(X2,multiply(a,X2)) = greatest_lower_bound(X2,least_upper_bound(multiply(a,X2),X2)),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c58,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c61,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c59,c61]) ).
cnf(c63,plain,
greatest_lower_bound(X2,least_upper_bound(multiply(a,X2),X2)) = X2,
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
greatest_lower_bound(X2,multiply(a,X2)) = X2,
inference(transitivity,[status(thm)],[c56,c63]) ).
cnf(c65,plain,
greatest_lower_bound(multiply(a,X2),X2) = X2,
inference(transitivity,[status(thm)],[c30,c64]) ).
cnf(c66,plain,
greatest_lower_bound(multiply(a,b),b) = b,
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
greatest_lower_bound(greatest_lower_bound(identity,a),greatest_lower_bound(multiply(a,b),b)) = greatest_lower_bound(greatest_lower_bound(identity,a),b),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
greatest_lower_bound(greatest_lower_bound(identity,a),b) = greatest_lower_bound(identity,b),
inference(congruence,[status(thm)],[c5]) ).
cnf(c69,plain,
greatest_lower_bound(greatest_lower_bound(identity,a),b) = greatest_lower_bound(identity,a),
inference(transitivity,[status(thm)],[c68,c20]) ).
cnf(c70,plain,
greatest_lower_bound(greatest_lower_bound(identity,a),greatest_lower_bound(multiply(a,b),b)) = greatest_lower_bound(identity,a),
inference(transitivity,[status(thm)],[c67,c69]) ).
cnf(c71,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,a)) = greatest_lower_bound(identity,a),
inference(transitivity,[status(thm)],[c28,c70]) ).
cnf(c72,plain,
greatest_lower_bound(identity,a) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,a)),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
least_upper_bound(multiply(a,b),greatest_lower_bound(identity,a)) = least_upper_bound(multiply(a,b),greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,a))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
least_upper_bound(multiply(a,b),greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,a))) = multiply(a,b),
inference(substitution,[status(thm)],[c47]) ).
cnf(c75,plain,
least_upper_bound(multiply(a,b),greatest_lower_bound(identity,a)) = multiply(a,b),
inference(transitivity,[status(thm)],[c73,c74]) ).
cnf(c76,plain,
least_upper_bound(identity,multiply(a,b)) = multiply(a,b),
inference(transitivity,[status(thm)],[c9,c75]) ).
cnf(c77,plain,
$false,
inference(resolution,[status(thm)],[c1,c76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP172-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n015.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 09:38:45 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.45 Command-line arguments: --flatten --complete-subsets
% 0.14/0.45
% 0.14/0.45 % SZS status Unsatisfiable
% 0.14/0.45
% 0.14/0.45 % SZS output start CNFRefutation
% See solution above
% 0.14/0.48
% 0.14/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------