%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP170-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 0.12s 0.50s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of clauses : 67 ( 67 unt; 0 nHn; 29 RR)
% Number of literals : 67 ( 66 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; 4 con; 0-2 aty)
% Number of variables : 81 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p03b) ).
cnf(c2,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c3,plain,
least_upper_bound(greatest_lower_bound(multiply(a,c),multiply(b,d)),greatest_lower_bound(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(b,greatest_lower_bound(c,d)))) = greatest_lower_bound(multiply(a,c),multiply(b,d)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
greatest_lower_bound(multiply(a,c),multiply(b,d)) = least_upper_bound(greatest_lower_bound(multiply(a,c),multiply(b,d)),greatest_lower_bound(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(b,greatest_lower_bound(c,d)))),
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(b,greatest_lower_bound(c,d)),greatest_lower_bound(multiply(a,c),multiply(b,d))) = greatest_lower_bound(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(b,greatest_lower_bound(c,d))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
greatest_lower_bound(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(b,greatest_lower_bound(c,d))) = greatest_lower_bound(multiply(b,greatest_lower_bound(c,d)),greatest_lower_bound(multiply(a,c),multiply(b,d))),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X3,greatest_lower_bound(X4,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c9,plain,
greatest_lower_bound(X3,greatest_lower_bound(X4,X2)) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,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(c11,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X2,X3)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c14,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c12,c14]) ).
cnf(c16,plain,
greatest_lower_bound(X3,greatest_lower_bound(X4,X2)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c9,c15]) ).
cnf(c17,plain,
greatest_lower_bound(X2,greatest_lower_bound(X4,X3)) = greatest_lower_bound(X4,greatest_lower_bound(X2,X3)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c19,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
greatest_lower_bound(X2,greatest_lower_bound(X4,X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c17,c19]) ).
cnf(c21,plain,
greatest_lower_bound(multiply(b,greatest_lower_bound(c,d)),greatest_lower_bound(multiply(a,c),multiply(b,d))) = greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(b,d),multiply(b,greatest_lower_bound(c,d)))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,axiom,
multiply(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).
cnf(c23,plain,
multiply(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X4,X2),multiply(X4,X3)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
greatest_lower_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,greatest_lower_bound(X2,X3)),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c26,plain,
multiply(X4,greatest_lower_bound(X2,X3)) = multiply(X4,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
greatest_lower_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c24,c26]) ).
cnf(c28,plain,
greatest_lower_bound(multiply(X3,X2),multiply(X3,greatest_lower_bound(c,d))) = multiply(X3,greatest_lower_bound(greatest_lower_bound(c,d),X2)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,axiom,
greatest_lower_bound(c,d) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c30,plain,
greatest_lower_bound(greatest_lower_bound(c,d),X2) = greatest_lower_bound(c,X2),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(X3,greatest_lower_bound(greatest_lower_bound(c,d),X2)) = multiply(X3,greatest_lower_bound(c,X2)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
greatest_lower_bound(multiply(X3,X2),multiply(X3,greatest_lower_bound(c,d))) = multiply(X3,greatest_lower_bound(c,X2)),
inference(transitivity,[status(thm)],[c28,c31]) ).
cnf(c33,plain,
greatest_lower_bound(multiply(b,d),multiply(b,greatest_lower_bound(c,d))) = multiply(b,greatest_lower_bound(c,d)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(b,d),multiply(b,greatest_lower_bound(c,d)))) = greatest_lower_bound(multiply(a,c),multiply(b,greatest_lower_bound(c,d))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
greatest_lower_bound(X2,greatest_lower_bound(a,b)) = greatest_lower_bound(greatest_lower_bound(a,b),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c36,plain,
greatest_lower_bound(greatest_lower_bound(a,b),X2) = greatest_lower_bound(X2,greatest_lower_bound(a,b)),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
multiply(greatest_lower_bound(greatest_lower_bound(a,b),X2),greatest_lower_bound(c,d)) = multiply(greatest_lower_bound(X2,greatest_lower_bound(a,b)),greatest_lower_bound(c,d)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
greatest_lower_bound(greatest_lower_bound(a,b),X2) = greatest_lower_bound(X2,greatest_lower_bound(a,b)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c39,plain,
greatest_lower_bound(X2,greatest_lower_bound(a,b)) = greatest_lower_bound(greatest_lower_bound(a,b),X2),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
multiply(greatest_lower_bound(X2,greatest_lower_bound(a,b)),greatest_lower_bound(c,d)) = multiply(greatest_lower_bound(greatest_lower_bound(a,b),X2),greatest_lower_bound(c,d)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,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(c42,plain,
multiply(greatest_lower_bound(greatest_lower_bound(a,b),X2),greatest_lower_bound(c,d)) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(c,d)),multiply(X2,greatest_lower_bound(c,d))),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(c,d)) = multiply(greatest_lower_bound(a,b),c),
inference(congruence,[status(thm)],[c29]) ).
cnf(c44,axiom,
greatest_lower_bound(a,b) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c45,plain,
multiply(greatest_lower_bound(a,b),c) = multiply(a,c),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(c,d)) = multiply(a,c),
inference(transitivity,[status(thm)],[c43,c45]) ).
cnf(c47,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(c,d)),multiply(X2,greatest_lower_bound(c,d))) = greatest_lower_bound(multiply(a,c),multiply(X2,greatest_lower_bound(c,d))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(greatest_lower_bound(greatest_lower_bound(a,b),X2),greatest_lower_bound(c,d)) = greatest_lower_bound(multiply(a,c),multiply(X2,greatest_lower_bound(c,d))),
inference(transitivity,[status(thm)],[c42,c47]) ).
cnf(c49,plain,
multiply(greatest_lower_bound(X2,greatest_lower_bound(a,b)),greatest_lower_bound(c,d)) = greatest_lower_bound(multiply(a,c),multiply(X2,greatest_lower_bound(c,d))),
inference(transitivity,[status(thm)],[c40,c48]) ).
cnf(c50,plain,
multiply(greatest_lower_bound(greatest_lower_bound(a,b),X2),greatest_lower_bound(c,d)) = greatest_lower_bound(multiply(a,c),multiply(X2,greatest_lower_bound(c,d))),
inference(transitivity,[status(thm)],[c37,c49]) ).
cnf(c51,plain,
multiply(greatest_lower_bound(greatest_lower_bound(a,b),b),greatest_lower_bound(c,d)) = greatest_lower_bound(multiply(a,c),multiply(b,greatest_lower_bound(c,d))),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
greatest_lower_bound(multiply(a,c),multiply(b,greatest_lower_bound(c,d))) = multiply(greatest_lower_bound(greatest_lower_bound(a,b),b),greatest_lower_bound(c,d)),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
greatest_lower_bound(greatest_lower_bound(a,b),b) = greatest_lower_bound(a,b),
inference(congruence,[status(thm)],[c44]) ).
cnf(c54,plain,
multiply(greatest_lower_bound(greatest_lower_bound(a,b),b),greatest_lower_bound(c,d)) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(c,d)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(greatest_lower_bound(greatest_lower_bound(a,b),b),greatest_lower_bound(c,d)) = multiply(a,c),
inference(transitivity,[status(thm)],[c54,c46]) ).
cnf(c56,plain,
greatest_lower_bound(multiply(a,c),multiply(b,greatest_lower_bound(c,d))) = multiply(a,c),
inference(transitivity,[status(thm)],[c52,c55]) ).
cnf(c57,plain,
greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(b,d),multiply(b,greatest_lower_bound(c,d)))) = multiply(a,c),
inference(transitivity,[status(thm)],[c34,c56]) ).
cnf(c58,plain,
greatest_lower_bound(multiply(b,greatest_lower_bound(c,d)),greatest_lower_bound(multiply(a,c),multiply(b,d))) = multiply(a,c),
inference(transitivity,[status(thm)],[c21,c57]) ).
cnf(c59,plain,
greatest_lower_bound(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(b,greatest_lower_bound(c,d))) = multiply(a,c),
inference(transitivity,[status(thm)],[c7,c58]) ).
cnf(c60,plain,
least_upper_bound(greatest_lower_bound(multiply(a,c),multiply(b,d)),greatest_lower_bound(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(b,greatest_lower_bound(c,d)))) = least_upper_bound(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c)),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c62,plain,
least_upper_bound(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c)) = least_upper_bound(multiply(a,c),greatest_lower_bound(multiply(a,c),multiply(b,d))),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
least_upper_bound(multiply(a,c),greatest_lower_bound(multiply(a,c),multiply(b,d))) = multiply(a,c),
inference(substitution,[status(thm)],[c2]) ).
cnf(c64,plain,
least_upper_bound(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(a,c)) = multiply(a,c),
inference(transitivity,[status(thm)],[c62,c63]) ).
cnf(c65,plain,
least_upper_bound(greatest_lower_bound(multiply(a,c),multiply(b,d)),greatest_lower_bound(greatest_lower_bound(multiply(a,c),multiply(b,d)),multiply(b,greatest_lower_bound(c,d)))) = multiply(a,c),
inference(transitivity,[status(thm)],[c60,c64]) ).
cnf(c66,plain,
greatest_lower_bound(multiply(a,c),multiply(b,d)) = multiply(a,c),
inference(transitivity,[status(thm)],[c4,c65]) ).
cnf(c67,plain,
$false,
inference(resolution,[status(thm)],[c1,c66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP170-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 09:40:01 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.50 Command-line arguments: --flatten --complete-subsets
% 0.12/0.50
% 0.12/0.50 % SZS status Unsatisfiable
% 0.12/0.50
% 0.12/0.50 % SZS output start CNFRefutation
% See solution above
% 0.60/0.52
% 0.60/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------