%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP168-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 10:09:31 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.48s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 17 RR)
% Number of literals : 20 ( 19 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 : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) != multiply(inverse(c),multiply(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p01b) ).
cnf(c2,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c3,plain,
greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) = greatest_lower_bound(multiply(inverse(c),multiply(b,c)),multiply(inverse(c),multiply(a,c))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,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(c5,plain,
multiply(inverse(c),greatest_lower_bound(multiply(b,c),multiply(a,c))) = greatest_lower_bound(multiply(inverse(c),multiply(b,c)),multiply(inverse(c),multiply(a,c))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
greatest_lower_bound(multiply(inverse(c),multiply(b,c)),multiply(inverse(c),multiply(a,c))) = multiply(inverse(c),greatest_lower_bound(multiply(b,c),multiply(a,c))),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,axiom,
multiply(greatest_lower_bound(Y2,Z2),X2) = greatest_lower_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
cnf(c8,plain,
multiply(greatest_lower_bound(b,a),c) = greatest_lower_bound(multiply(b,c),multiply(a,c)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
greatest_lower_bound(multiply(b,c),multiply(a,c)) = multiply(greatest_lower_bound(b,a),c),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(inverse(c),greatest_lower_bound(multiply(b,c),multiply(a,c))) = multiply(inverse(c),multiply(greatest_lower_bound(b,a),c)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(b,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
greatest_lower_bound(b,a) = greatest_lower_bound(a,b),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,axiom,
greatest_lower_bound(a,b) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c14,plain,
greatest_lower_bound(b,a) = a,
inference(transitivity,[status(thm)],[c12,c13]) ).
cnf(c15,plain,
multiply(greatest_lower_bound(b,a),c) = multiply(a,c),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(inverse(c),multiply(greatest_lower_bound(b,a),c)) = multiply(inverse(c),multiply(a,c)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(inverse(c),greatest_lower_bound(multiply(b,c),multiply(a,c))) = multiply(inverse(c),multiply(a,c)),
inference(transitivity,[status(thm)],[c10,c16]) ).
cnf(c18,plain,
greatest_lower_bound(multiply(inverse(c),multiply(b,c)),multiply(inverse(c),multiply(a,c))) = multiply(inverse(c),multiply(a,c)),
inference(transitivity,[status(thm)],[c6,c17]) ).
cnf(c19,plain,
greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) = multiply(inverse(c),multiply(a,c)),
inference(transitivity,[status(thm)],[c3,c18]) ).
cnf(c20,plain,
$false,
inference(resolution,[status(thm)],[c1,c19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP168-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.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 09:34:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.48 Command-line arguments: --no-flatten-goal
% 0.10/0.48
% 0.10/0.48 % SZS status Unsatisfiable
% 0.10/0.48
% 0.10/0.48 % SZS output start CNFRefutation
% See solution above
% 0.10/0.49
% 0.10/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------