%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP170-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 0.31s 0.55s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of clauses : 79 ( 79 unt; 0 nHn; 23 RR)
% Number of literals : 79 ( 78 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 : 127 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p03d) ).
cnf(c2,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c3,plain,
least_upper_bound(multiply(b,d),multiply(a,c)) = least_upper_bound(multiply(a,c),multiply(b,d)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
least_upper_bound(multiply(a,c),multiply(b,d)) = least_upper_bound(multiply(b,d),multiply(a,c)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(X2,least_upper_bound(Y2,Z)) = least_upper_bound(multiply(X2,Y2),multiply(X2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).
cnf(c6,plain,
multiply(X4,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X4,X2),multiply(X4,X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
least_upper_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,least_upper_bound(X2,X3)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c9,plain,
multiply(X4,least_upper_bound(X2,X3)) = multiply(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
least_upper_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c7,c9]) ).
cnf(c11,plain,
least_upper_bound(multiply(X2,d),multiply(X2,c)) = multiply(X2,least_upper_bound(c,d)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
least_upper_bound(d,c) = least_upper_bound(c,d),
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
least_upper_bound(c,d) = least_upper_bound(d,c),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
greatest_lower_bound(c,d) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c15,plain,
c = greatest_lower_bound(c,d),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
least_upper_bound(d,c) = least_upper_bound(d,greatest_lower_bound(c,d)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c18,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c22,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c20,c22]) ).
cnf(c24,plain,
least_upper_bound(d,greatest_lower_bound(c,d)) = d,
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
least_upper_bound(d,c) = d,
inference(transitivity,[status(thm)],[c16,c24]) ).
cnf(c26,plain,
least_upper_bound(c,d) = d,
inference(transitivity,[status(thm)],[c13,c25]) ).
cnf(c27,plain,
multiply(X2,least_upper_bound(c,d)) = multiply(X2,d),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
least_upper_bound(multiply(X2,d),multiply(X2,c)) = multiply(X2,d),
inference(transitivity,[status(thm)],[c11,c27]) ).
cnf(c29,plain,
least_upper_bound(multiply(b,d),multiply(b,c)) = multiply(b,d),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(b,d) = least_upper_bound(multiply(b,d),multiply(b,c)),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
greatest_lower_bound(multiply(a,c),multiply(b,d)) = greatest_lower_bound(multiply(a,c),least_upper_bound(multiply(b,d),multiply(b,c))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
least_upper_bound(multiply(a,X2),least_upper_bound(X3,multiply(b,X2))) = least_upper_bound(least_upper_bound(X3,multiply(b,X2)),multiply(a,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c33,plain,
least_upper_bound(least_upper_bound(X3,multiply(b,X2)),multiply(a,X2)) = least_upper_bound(multiply(a,X2),least_upper_bound(X3,multiply(b,X2))),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X3,least_upper_bound(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c35,plain,
least_upper_bound(X3,least_upper_bound(X4,X2)) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,axiom,
least_upper_bound(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(least_upper_bound(X2,Y2),Z2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_lub) ).
cnf(c37,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X4,least_upper_bound(X2,X3)),
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,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c38,c40]) ).
cnf(c42,plain,
least_upper_bound(X3,least_upper_bound(X4,X2)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c35,c41]) ).
cnf(c43,plain,
least_upper_bound(X2,least_upper_bound(X4,X3)) = least_upper_bound(X4,least_upper_bound(X2,X3)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c45,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
least_upper_bound(X2,least_upper_bound(X4,X3)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c43,c45]) ).
cnf(c47,plain,
least_upper_bound(multiply(a,X2),least_upper_bound(X3,multiply(b,X2))) = least_upper_bound(X3,least_upper_bound(multiply(b,X2),multiply(a,X2))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,axiom,
multiply(least_upper_bound(Y2,Z2),X2) = least_upper_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub2) ).
cnf(c49,plain,
multiply(least_upper_bound(X3,X4),X2) = least_upper_bound(multiply(X3,X2),multiply(X4,X2)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
least_upper_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(least_upper_bound(X3,X4),X2),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c52,plain,
multiply(least_upper_bound(X3,X4),X2) = multiply(least_upper_bound(X4,X3),X2),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
least_upper_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(least_upper_bound(X4,X3),X2),
inference(transitivity,[status(thm)],[c50,c52]) ).
cnf(c54,plain,
least_upper_bound(multiply(b,X2),multiply(a,X2)) = multiply(least_upper_bound(a,b),X2),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,axiom,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c56,plain,
multiply(least_upper_bound(a,b),X2) = multiply(b,X2),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
least_upper_bound(multiply(b,X2),multiply(a,X2)) = multiply(b,X2),
inference(transitivity,[status(thm)],[c54,c56]) ).
cnf(c58,plain,
least_upper_bound(X3,least_upper_bound(multiply(b,X2),multiply(a,X2))) = least_upper_bound(X3,multiply(b,X2)),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
least_upper_bound(multiply(a,X2),least_upper_bound(X3,multiply(b,X2))) = least_upper_bound(X3,multiply(b,X2)),
inference(transitivity,[status(thm)],[c47,c58]) ).
cnf(c60,plain,
least_upper_bound(least_upper_bound(X3,multiply(b,X2)),multiply(a,X2)) = least_upper_bound(X3,multiply(b,X2)),
inference(transitivity,[status(thm)],[c33,c59]) ).
cnf(c61,plain,
least_upper_bound(least_upper_bound(X2,multiply(b,X3)),multiply(a,X3)) = least_upper_bound(X2,multiply(b,X3)),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
least_upper_bound(X2,multiply(b,X3)) = least_upper_bound(least_upper_bound(X2,multiply(b,X3)),multiply(a,X3)),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
greatest_lower_bound(multiply(a,X3),least_upper_bound(X2,multiply(b,X3))) = greatest_lower_bound(multiply(a,X3),least_upper_bound(least_upper_bound(X2,multiply(b,X3)),multiply(a,X3))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c65,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c68,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c66,c68]) ).
cnf(c70,plain,
greatest_lower_bound(multiply(a,X3),least_upper_bound(least_upper_bound(X2,multiply(b,X3)),multiply(a,X3))) = multiply(a,X3),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
greatest_lower_bound(multiply(a,X3),least_upper_bound(X2,multiply(b,X3))) = multiply(a,X3),
inference(transitivity,[status(thm)],[c63,c70]) ).
cnf(c72,plain,
greatest_lower_bound(multiply(a,c),least_upper_bound(multiply(b,d),multiply(b,c))) = multiply(a,c),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
greatest_lower_bound(multiply(a,c),multiply(b,d)) = multiply(a,c),
inference(transitivity,[status(thm)],[c31,c72]) ).
cnf(c74,plain,
multiply(a,c) = greatest_lower_bound(multiply(a,c),multiply(b,d)),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
least_upper_bound(multiply(b,d),multiply(a,c)) = least_upper_bound(multiply(b,d),greatest_lower_bound(multiply(a,c),multiply(b,d))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
least_upper_bound(multiply(b,d),greatest_lower_bound(multiply(a,c),multiply(b,d))) = multiply(b,d),
inference(substitution,[status(thm)],[c23]) ).
cnf(c77,plain,
least_upper_bound(multiply(b,d),multiply(a,c)) = multiply(b,d),
inference(transitivity,[status(thm)],[c75,c76]) ).
cnf(c78,plain,
least_upper_bound(multiply(a,c),multiply(b,d)) = multiply(b,d),
inference(transitivity,[status(thm)],[c4,c77]) ).
cnf(c79,plain,
$false,
inference(resolution,[status(thm)],[c1,c78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP170-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.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 09:36:09 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.31/0.55 Command-line arguments: --flatten-regeneralise
% 0.31/0.55
% 0.31/0.55 % SZS status Unsatisfiable
% 0.31/0.55
% 0.31/0.55 % SZS output start CNFRefutation
% See solution above
% 0.31/0.57
% 0.31/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------