%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP193-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 10:09:40 AM UTC 2026
% Result : Unsatisfiable 0.45s 0.47s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of clauses : 149 ( 149 unt; 0 nHn; 32 RR)
% Number of literals : 149 ( 148 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 225 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p8_9b) ).
cnf(c2,axiom,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
greatest_lower_bound(X2,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(X2,greatest_lower_bound(a,multiply(b,c))),
inference(congruence,[status(thm)],[c2]) ).
cnf(c5,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c6,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(multiply(b,c),a),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
greatest_lower_bound(X2,greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(X2,greatest_lower_bound(multiply(b,c),a)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
greatest_lower_bound(X2,greatest_lower_bound(Y2,Z)) = greatest_lower_bound(greatest_lower_bound(X2,Y2),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_glb) ).
cnf(c9,plain,
greatest_lower_bound(X2,greatest_lower_bound(multiply(b,c),a)) = greatest_lower_bound(greatest_lower_bound(X2,multiply(b,c)),a),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
greatest_lower_bound(a,greatest_lower_bound(X2,multiply(b,c))) = greatest_lower_bound(greatest_lower_bound(X2,multiply(b,c)),a),
inference(substitution,[status(thm)],[c5]) ).
cnf(c11,plain,
greatest_lower_bound(greatest_lower_bound(X2,multiply(b,c)),a) = greatest_lower_bound(a,greatest_lower_bound(X2,multiply(b,c))),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,X4)) = greatest_lower_bound(greatest_lower_bound(X2,X3),X4),
inference(substitution,[status(thm)],[c8]) ).
cnf(c13,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X2,X3)),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c15,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c13,c15]) ).
cnf(c17,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),X2) = greatest_lower_bound(a,greatest_lower_bound(X2,multiply(b,c))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
greatest_lower_bound(a,greatest_lower_bound(X2,multiply(b,c))) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),X2),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
greatest_lower_bound(greatest_lower_bound(X2,multiply(b,c)),a) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),X2),
inference(transitivity,[status(thm)],[c11,c18]) ).
cnf(c20,plain,
greatest_lower_bound(X2,greatest_lower_bound(multiply(b,c),a)) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),X2),
inference(transitivity,[status(thm)],[c9,c19]) ).
cnf(c21,plain,
greatest_lower_bound(X2,greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),X2),
inference(transitivity,[status(thm)],[c7,c20]) ).
cnf(c22,plain,
greatest_lower_bound(X2,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),X2),
inference(transitivity,[status(thm)],[c4,c21]) ).
cnf(c23,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2)),greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2))),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2)),greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2)),greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c26,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2)),greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2))),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X2,X4)),X3) = greatest_lower_bound(X3,multiply(greatest_lower_bound(a,b),greatest_lower_bound(X2,X4))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c28,plain,
greatest_lower_bound(X3,multiply(greatest_lower_bound(a,b),greatest_lower_bound(X2,X4))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X2,X4)),X3),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,axiom,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c30,axiom,
greatest_lower_bound(identity,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c31,plain,
identity = greatest_lower_bound(identity,b),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,axiom,
greatest_lower_bound(identity,a) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c33,plain,
identity = greatest_lower_bound(identity,b),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c34,plain,
greatest_lower_bound(identity,a) = greatest_lower_bound(identity,b),
inference(transitivity,[status(thm)],[c32,c33]) ).
cnf(c35,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(identity,a),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
identity = greatest_lower_bound(identity,a),
inference(transitivity,[status(thm)],[c31,c35]) ).
cnf(c37,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(identity,a),
inference(transitivity,[status(thm)],[c29,c36]) ).
cnf(c38,plain,
multiply(greatest_lower_bound(a,b),X2) = multiply(greatest_lower_bound(identity,a),X2),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
multiply(greatest_lower_bound(identity,a),X2) = multiply(greatest_lower_bound(identity,b),X2),
inference(congruence,[status(thm)],[c34]) ).
cnf(c40,plain,
multiply(greatest_lower_bound(identity,b),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c30]) ).
cnf(c41,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c42,plain,
multiply(greatest_lower_bound(identity,b),X2) = X2,
inference(transitivity,[status(thm)],[c40,c41]) ).
cnf(c43,plain,
multiply(greatest_lower_bound(identity,a),X2) = X2,
inference(transitivity,[status(thm)],[c39,c42]) ).
cnf(c44,plain,
multiply(greatest_lower_bound(a,b),X2) = X2,
inference(transitivity,[status(thm)],[c38,c43]) ).
cnf(c45,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X2,X4)),X3) = greatest_lower_bound(greatest_lower_bound(X2,X4),X3),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c48,plain,
greatest_lower_bound(greatest_lower_bound(X2,X4),X3) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c8]) ).
cnf(c50,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X2,X3)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c52,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c50,c52]) ).
cnf(c54,plain,
greatest_lower_bound(greatest_lower_bound(X2,X4),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c48,c53]) ).
cnf(c55,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X2,X4)),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c46,c54]) ).
cnf(c56,plain,
greatest_lower_bound(X3,multiply(greatest_lower_bound(a,b),greatest_lower_bound(X2,X4))) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c28,c55]) ).
cnf(c57,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2))) = greatest_lower_bound(X2,greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),a)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c59,plain,
least_upper_bound(X4,greatest_lower_bound(greatest_lower_bound(X4,X3),X2)) = least_upper_bound(greatest_lower_bound(greatest_lower_bound(X4,X3),X2),X4),
inference(substitution,[status(thm)],[c58]) ).
cnf(c60,plain,
least_upper_bound(greatest_lower_bound(greatest_lower_bound(X4,X3),X2),X4) = least_upper_bound(X4,greatest_lower_bound(greatest_lower_bound(X4,X3),X2)),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
greatest_lower_bound(greatest_lower_bound(X4,X3),X2) = greatest_lower_bound(X4,greatest_lower_bound(X2,X3)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c62,plain,
least_upper_bound(X4,greatest_lower_bound(greatest_lower_bound(X4,X3),X2)) = least_upper_bound(X4,greatest_lower_bound(X4,greatest_lower_bound(X2,X3))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c64,plain,
least_upper_bound(X4,greatest_lower_bound(X4,greatest_lower_bound(X2,X3))) = X4,
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
least_upper_bound(X4,greatest_lower_bound(greatest_lower_bound(X4,X3),X2)) = X4,
inference(transitivity,[status(thm)],[c62,c64]) ).
cnf(c66,plain,
least_upper_bound(greatest_lower_bound(greatest_lower_bound(X4,X3),X2),X4) = X4,
inference(transitivity,[status(thm)],[c60,c65]) ).
cnf(c67,plain,
X4 = least_upper_bound(greatest_lower_bound(greatest_lower_bound(X4,X3),X2),X4),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X4,X3),X2),X4) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X4,X3),X2),least_upper_bound(greatest_lower_bound(greatest_lower_bound(X4,X3),X2),X4)),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c70,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X4,X3),X2),least_upper_bound(greatest_lower_bound(greatest_lower_bound(X4,X3),X2),X4)) = greatest_lower_bound(greatest_lower_bound(X4,X3),X2),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X4,X3),X2),X4) = greatest_lower_bound(greatest_lower_bound(X4,X3),X2),
inference(transitivity,[status(thm)],[c68,c70]) ).
cnf(c72,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),a) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
greatest_lower_bound(X2,greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),a)) = greatest_lower_bound(X2,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
greatest_lower_bound(X2,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c75,plain,
greatest_lower_bound(X2,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c76,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),X2) = greatest_lower_bound(X2,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
greatest_lower_bound(X2,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(X2,greatest_lower_bound(a,multiply(b,c))),
inference(congruence,[status(thm)],[c2]) ).
cnf(c78,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(multiply(b,c),a),
inference(substitution,[status(thm)],[c5]) ).
cnf(c79,plain,
greatest_lower_bound(X2,greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(X2,greatest_lower_bound(multiply(b,c),a)),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2))) = greatest_lower_bound(X2,greatest_lower_bound(multiply(b,c),a)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c81,plain,
greatest_lower_bound(X2,greatest_lower_bound(multiply(b,c),a)) = greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2))),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2)),multiply(b,c)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c83,plain,
greatest_lower_bound(X2,greatest_lower_bound(multiply(b,c),a)) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2)),multiply(b,c)),
inference(transitivity,[status(thm)],[c81,c82]) ).
cnf(c84,plain,
greatest_lower_bound(X2,greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2)),multiply(b,c)),
inference(transitivity,[status(thm)],[c79,c83]) ).
cnf(c85,plain,
greatest_lower_bound(X2,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2)),multiply(b,c)),
inference(transitivity,[status(thm)],[c77,c84]) ).
cnf(c86,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),X2) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2)),multiply(b,c)),
inference(transitivity,[status(thm)],[c76,c85]) ).
cnf(c87,plain,
greatest_lower_bound(X2,greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2)),multiply(b,c)),
inference(transitivity,[status(thm)],[c74,c86]) ).
cnf(c88,plain,
greatest_lower_bound(X2,greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),a)) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2)),multiply(b,c)),
inference(transitivity,[status(thm)],[c73,c87]) ).
cnf(c89,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2)),multiply(b,c)),
inference(transitivity,[status(thm)],[c57,c88]) ).
cnf(c90,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2)),greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2)),multiply(b,c)),
inference(transitivity,[status(thm)],[c26,c89]) ).
cnf(c91,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,X2)),multiply(b,c)),
inference(transitivity,[status(thm)],[c24,c90]) ).
cnf(c92,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),multiply(b,c)),
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
X2 = multiply(greatest_lower_bound(identity,a),X2),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c94,plain,
least_upper_bound(multiply(b,X2),X2) = least_upper_bound(multiply(b,X2),multiply(greatest_lower_bound(identity,a),X2)),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,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(c96,plain,
multiply(least_upper_bound(X3,X4),X2) = least_upper_bound(multiply(X3,X2),multiply(X4,X2)),
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
least_upper_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(least_upper_bound(X3,X4),X2),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c58]) ).
cnf(c99,plain,
multiply(least_upper_bound(X3,X4),X2) = multiply(least_upper_bound(X4,X3),X2),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
least_upper_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(least_upper_bound(X4,X3),X2),
inference(transitivity,[status(thm)],[c97,c99]) ).
cnf(c101,plain,
least_upper_bound(multiply(b,X2),multiply(greatest_lower_bound(identity,a),X2)) = multiply(least_upper_bound(greatest_lower_bound(identity,a),b),X2),
inference(substitution,[status(thm)],[c100]) ).
cnf(c102,plain,
least_upper_bound(b,greatest_lower_bound(identity,a)) = least_upper_bound(greatest_lower_bound(identity,a),b),
inference(substitution,[status(thm)],[c58]) ).
cnf(c103,plain,
least_upper_bound(greatest_lower_bound(identity,a),b) = least_upper_bound(b,greatest_lower_bound(identity,a)),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
greatest_lower_bound(identity,a) = greatest_lower_bound(a,b),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c105,plain,
least_upper_bound(b,greatest_lower_bound(identity,a)) = least_upper_bound(b,greatest_lower_bound(a,b)),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(b,a),
inference(substitution,[status(thm)],[c5]) ).
cnf(c107,plain,
least_upper_bound(b,greatest_lower_bound(a,b)) = least_upper_bound(b,greatest_lower_bound(b,a)),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
least_upper_bound(b,greatest_lower_bound(b,a)) = b,
inference(substitution,[status(thm)],[c63]) ).
cnf(c109,plain,
least_upper_bound(b,greatest_lower_bound(a,b)) = b,
inference(transitivity,[status(thm)],[c107,c108]) ).
cnf(c110,plain,
least_upper_bound(b,greatest_lower_bound(identity,a)) = b,
inference(transitivity,[status(thm)],[c105,c109]) ).
cnf(c111,plain,
least_upper_bound(greatest_lower_bound(identity,a),b) = b,
inference(transitivity,[status(thm)],[c103,c110]) ).
cnf(c112,plain,
multiply(least_upper_bound(greatest_lower_bound(identity,a),b),X2) = multiply(b,X2),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
least_upper_bound(multiply(b,X2),multiply(greatest_lower_bound(identity,a),X2)) = multiply(b,X2),
inference(transitivity,[status(thm)],[c101,c112]) ).
cnf(c114,plain,
least_upper_bound(multiply(b,X2),X2) = multiply(b,X2),
inference(transitivity,[status(thm)],[c94,c113]) ).
cnf(c115,plain,
multiply(b,X2) = least_upper_bound(multiply(b,X2),X2),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),multiply(b,X2)) = least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),least_upper_bound(multiply(b,X2),X2)),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c58]) ).
cnf(c118,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X4,X3)),least_upper_bound(X2,X3)) = least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X4,X3)),least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,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(c121,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X4,X3)),least_upper_bound(X3,X2)) = least_upper_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X4,X3)),X3),X2),
inference(substitution,[status(thm)],[c120]) ).
cnf(c122,plain,
least_upper_bound(X2,multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2))) = least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),X2),
inference(substitution,[status(thm)],[c58]) ).
cnf(c123,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),X2) = least_upper_bound(X2,multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2))),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c44]) ).
cnf(c125,plain,
least_upper_bound(X2,multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2))) = least_upper_bound(X2,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c127,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = least_upper_bound(X2,greatest_lower_bound(X2,X3)),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
least_upper_bound(X2,greatest_lower_bound(X2,X3)) = X2,
inference(substitution,[status(thm)],[c63]) ).
cnf(c129,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c127,c128]) ).
cnf(c130,plain,
least_upper_bound(X2,multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2))) = X2,
inference(transitivity,[status(thm)],[c125,c129]) ).
cnf(c131,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),X2) = X2,
inference(transitivity,[status(thm)],[c123,c130]) ).
cnf(c132,plain,
least_upper_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X4,X3)),X3),X2) = least_upper_bound(X3,X2),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c58]) ).
cnf(c134,plain,
least_upper_bound(least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X4,X3)),X3),X2) = least_upper_bound(X2,X3),
inference(transitivity,[status(thm)],[c132,c133]) ).
cnf(c135,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X4,X3)),least_upper_bound(X3,X2)) = least_upper_bound(X2,X3),
inference(transitivity,[status(thm)],[c121,c134]) ).
cnf(c136,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X4,X3)),least_upper_bound(X2,X3)) = least_upper_bound(X2,X3),
inference(transitivity,[status(thm)],[c119,c135]) ).
cnf(c137,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),least_upper_bound(multiply(b,X2),X2)) = least_upper_bound(multiply(b,X2),X2),
inference(substitution,[status(thm)],[c136]) ).
cnf(c138,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),least_upper_bound(multiply(b,X2),X2)) = multiply(b,X2),
inference(transitivity,[status(thm)],[c137,c114]) ).
cnf(c139,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),multiply(b,X2)) = multiply(b,X2),
inference(transitivity,[status(thm)],[c116,c138]) ).
cnf(c140,plain,
multiply(b,X2) = least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),multiply(b,X2)),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),multiply(b,X2)) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),multiply(b,X2))),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),multiply(b,X2))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c143,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),multiply(b,X2)) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c141,c142]) ).
cnf(c144,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),multiply(b,c)) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(substitution,[status(thm)],[c143]) ).
cnf(c145,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(transitivity,[status(thm)],[c92,c144]) ).
cnf(c146,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,c),
inference(substitution,[status(thm)],[c44]) ).
cnf(c147,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[c145,c146]) ).
cnf(c148,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[c3,c147]) ).
cnf(c149,plain,
$false,
inference(resolution,[status(thm)],[c1,c148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP193-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.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 09:37:15 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.47 Command-line arguments: --flatten --complete-subsets
% 0.45/0.47
% 0.45/0.47 % SZS status Unsatisfiable
% 0.45/0.47
% 0.45/0.48 % SZS output start CNFRefutation
% See solution above
% 0.45/0.52
% 0.45/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------