%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP175-4 : 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 10:09:33 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.48s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 10
% Syntax : Number of clauses : 64 ( 64 unt; 0 nHn; 11 RR)
% Number of literals : 64 ( 63 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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 : 84 ( 4 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/sandbox2/benchmark/theBenchmark.p',prove_p06d) ).
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(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,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c6,plain,
greatest_lower_bound(multiply(inverse(X2),multiply(b,X2)),identity) = greatest_lower_bound(identity,multiply(inverse(X2),multiply(b,X2))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
greatest_lower_bound(identity,multiply(inverse(X2),multiply(b,X2))) = greatest_lower_bound(multiply(inverse(X2),multiply(b,X2)),identity),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c9,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
greatest_lower_bound(multiply(inverse(X2),multiply(b,X2)),identity) = greatest_lower_bound(multiply(inverse(X2),multiply(b,X2)),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,axiom,
multiply(X2,greatest_lower_bound(Y2,Z)) = greatest_lower_bound(multiply(X2,Y2),multiply(X2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).
cnf(c12,plain,
multiply(X2,greatest_lower_bound(X4,X3)) = greatest_lower_bound(multiply(X2,X4),multiply(X2,X3)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
greatest_lower_bound(multiply(X4,X3),multiply(X4,X2)) = multiply(X4,greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c15,plain,
multiply(X4,greatest_lower_bound(X3,X2)) = multiply(X4,greatest_lower_bound(X2,X3)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
greatest_lower_bound(multiply(X4,X3),multiply(X4,X2)) = multiply(X4,greatest_lower_bound(X2,X3)),
inference(transitivity,[status(thm)],[c13,c15]) ).
cnf(c17,plain,
greatest_lower_bound(multiply(inverse(X2),multiply(b,X2)),multiply(inverse(X2),X2)) = multiply(inverse(X2),greatest_lower_bound(X2,multiply(b,X2))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
least_upper_bound(multiply(b,X2),X2) = least_upper_bound(X2,multiply(b,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,plain,
least_upper_bound(X2,multiply(b,X2)) = least_upper_bound(multiply(b,X2),X2),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c21,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
least_upper_bound(multiply(b,X2),X2) = least_upper_bound(multiply(b,X2),multiply(identity,X2)),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,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(c24,plain,
multiply(least_upper_bound(X4,X2),X3) = least_upper_bound(multiply(X4,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
least_upper_bound(multiply(X4,X3),multiply(X2,X3)) = multiply(least_upper_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,plain,
multiply(least_upper_bound(X4,X2),X3) = multiply(least_upper_bound(X2,X4),X3),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
least_upper_bound(multiply(X4,X3),multiply(X2,X3)) = multiply(least_upper_bound(X2,X4),X3),
inference(transitivity,[status(thm)],[c25,c27]) ).
cnf(c29,plain,
least_upper_bound(multiply(b,X2),multiply(identity,X2)) = multiply(least_upper_bound(identity,b),X2),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
least_upper_bound(b,identity) = least_upper_bound(identity,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
least_upper_bound(identity,b) = least_upper_bound(b,identity),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,axiom,
greatest_lower_bound(identity,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c33,plain,
identity = greatest_lower_bound(identity,b),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
least_upper_bound(b,identity) = least_upper_bound(b,greatest_lower_bound(identity,b)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c36,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c39,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c37,c39]) ).
cnf(c41,plain,
least_upper_bound(b,greatest_lower_bound(identity,b)) = b,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
least_upper_bound(b,identity) = b,
inference(transitivity,[status(thm)],[c34,c41]) ).
cnf(c43,plain,
least_upper_bound(identity,b) = b,
inference(transitivity,[status(thm)],[c31,c42]) ).
cnf(c44,plain,
multiply(least_upper_bound(identity,b),X2) = multiply(b,X2),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
least_upper_bound(multiply(b,X2),multiply(identity,X2)) = multiply(b,X2),
inference(transitivity,[status(thm)],[c29,c44]) ).
cnf(c46,plain,
least_upper_bound(multiply(b,X2),X2) = multiply(b,X2),
inference(transitivity,[status(thm)],[c22,c45]) ).
cnf(c47,plain,
least_upper_bound(X2,multiply(b,X2)) = multiply(b,X2),
inference(transitivity,[status(thm)],[c19,c46]) ).
cnf(c48,plain,
multiply(b,X2) = least_upper_bound(X2,multiply(b,X2)),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
greatest_lower_bound(X2,multiply(b,X2)) = greatest_lower_bound(X2,least_upper_bound(X2,multiply(b,X2))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c51,plain,
greatest_lower_bound(X2,least_upper_bound(X2,multiply(b,X2))) = X2,
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
greatest_lower_bound(X2,multiply(b,X2)) = X2,
inference(transitivity,[status(thm)],[c49,c51]) ).
cnf(c53,plain,
multiply(inverse(X2),greatest_lower_bound(X2,multiply(b,X2))) = multiply(inverse(X2),X2),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
multiply(inverse(X2),greatest_lower_bound(X2,multiply(b,X2))) = identity,
inference(transitivity,[status(thm)],[c53,c8]) ).
cnf(c55,plain,
greatest_lower_bound(multiply(inverse(X2),multiply(b,X2)),multiply(inverse(X2),X2)) = identity,
inference(transitivity,[status(thm)],[c17,c54]) ).
cnf(c56,plain,
greatest_lower_bound(multiply(inverse(X2),multiply(b,X2)),identity) = identity,
inference(transitivity,[status(thm)],[c10,c55]) ).
cnf(c57,plain,
greatest_lower_bound(identity,multiply(inverse(X2),multiply(b,X2))) = identity,
inference(transitivity,[status(thm)],[c7,c56]) ).
cnf(c58,plain,
identity = greatest_lower_bound(identity,multiply(inverse(X2),multiply(b,X2))),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
least_upper_bound(multiply(inverse(X2),multiply(b,X2)),identity) = least_upper_bound(multiply(inverse(X2),multiply(b,X2)),greatest_lower_bound(identity,multiply(inverse(X2),multiply(b,X2)))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
least_upper_bound(multiply(inverse(X2),multiply(b,X2)),greatest_lower_bound(identity,multiply(inverse(X2),multiply(b,X2)))) = multiply(inverse(X2),multiply(b,X2)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c61,plain,
least_upper_bound(multiply(inverse(X2),multiply(b,X2)),identity) = multiply(inverse(X2),multiply(b,X2)),
inference(transitivity,[status(thm)],[c59,c60]) ).
cnf(c62,plain,
least_upper_bound(identity,multiply(inverse(X2),multiply(b,X2))) = multiply(inverse(X2),multiply(b,X2)),
inference(transitivity,[status(thm)],[c4,c61]) ).
cnf(c63,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),multiply(b,a)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
$false,
inference(resolution,[status(thm)],[c1,c63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP175-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % 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 09:38:59 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.48 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
% 0.14/0.48
% 0.14/0.48 % SZS status Unsatisfiable
% 0.14/0.48
% 0.14/0.48 % SZS output start CNFRefutation
% See solution above
% 0.57/0.51
% 0.57/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------