%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP193-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 0.01s 0.47s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of clauses : 132 ( 132 unt; 0 nHn; 87 RR)
% Number of literals : 132 ( 131 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 : 65 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p8_9a) ).
cnf(c2,axiom,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
multiply(greatest_lower_bound(a,b),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c2]) ).
cnf(c4,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c5,plain,
multiply(greatest_lower_bound(a,b),X2) = X2,
inference(transitivity,[status(thm)],[c3,c4]) ).
cnf(c6,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,c),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,axiom,
least_upper_bound(identity,c) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c8,plain,
greatest_lower_bound(least_upper_bound(identity,a),least_upper_bound(identity,c)) = greatest_lower_bound(least_upper_bound(identity,a),c),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
least_upper_bound(identity,a) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c10,plain,
greatest_lower_bound(least_upper_bound(identity,a),c) = greatest_lower_bound(a,c),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
greatest_lower_bound(least_upper_bound(identity,a),least_upper_bound(identity,c)) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(least_upper_bound(identity,a),least_upper_bound(identity,c)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c14,plain,
greatest_lower_bound(least_upper_bound(identity,c),multiply(b,c)) = greatest_lower_bound(multiply(b,c),least_upper_bound(identity,c)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
greatest_lower_bound(multiply(b,c),least_upper_bound(identity,c)) = greatest_lower_bound(least_upper_bound(identity,c),multiply(b,c)),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(greatest_lower_bound(a,b),least_upper_bound(identity,c)) = least_upper_bound(identity,c),
inference(substitution,[status(thm)],[c5]) ).
cnf(c17,plain,
least_upper_bound(identity,c) = multiply(greatest_lower_bound(a,b),least_upper_bound(identity,c)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
least_upper_bound(multiply(b,c),least_upper_bound(identity,c)) = least_upper_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),least_upper_bound(identity,c))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c20,plain,
least_upper_bound(least_upper_bound(identity,b),X2) = least_upper_bound(X2,least_upper_bound(identity,b)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
least_upper_bound(X2,least_upper_bound(identity,b)) = least_upper_bound(least_upper_bound(identity,b),X2),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
multiply(least_upper_bound(X2,least_upper_bound(identity,b)),least_upper_bound(identity,c)) = multiply(least_upper_bound(least_upper_bound(identity,b),X2),least_upper_bound(identity,c)),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,axiom,
multiply(least_upper_bound(Y2,Z),X2) = least_upper_bound(multiply(Y2,X2),multiply(Z,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
cnf(c24,plain,
multiply(least_upper_bound(least_upper_bound(identity,b),X2),least_upper_bound(identity,c)) = least_upper_bound(multiply(least_upper_bound(identity,b),least_upper_bound(identity,c)),multiply(X2,least_upper_bound(identity,c))),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(least_upper_bound(identity,b),least_upper_bound(identity,c)) = multiply(least_upper_bound(identity,b),c),
inference(congruence,[status(thm)],[c7]) ).
cnf(c26,axiom,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c27,plain,
multiply(least_upper_bound(identity,b),c) = multiply(b,c),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(least_upper_bound(identity,b),least_upper_bound(identity,c)) = multiply(b,c),
inference(transitivity,[status(thm)],[c25,c27]) ).
cnf(c29,plain,
least_upper_bound(multiply(least_upper_bound(identity,b),least_upper_bound(identity,c)),multiply(X2,least_upper_bound(identity,c))) = least_upper_bound(multiply(b,c),multiply(X2,least_upper_bound(identity,c))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(least_upper_bound(least_upper_bound(identity,b),X2),least_upper_bound(identity,c)) = least_upper_bound(multiply(b,c),multiply(X2,least_upper_bound(identity,c))),
inference(transitivity,[status(thm)],[c24,c29]) ).
cnf(c31,plain,
multiply(least_upper_bound(X2,least_upper_bound(identity,b)),least_upper_bound(identity,c)) = least_upper_bound(multiply(b,c),multiply(X2,least_upper_bound(identity,c))),
inference(transitivity,[status(thm)],[c22,c30]) ).
cnf(c32,plain,
multiply(least_upper_bound(greatest_lower_bound(a,b),least_upper_bound(identity,b)),least_upper_bound(identity,c)) = least_upper_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),least_upper_bound(identity,c))),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
least_upper_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),least_upper_bound(identity,c))) = multiply(least_upper_bound(greatest_lower_bound(a,b),least_upper_bound(identity,b)),least_upper_bound(identity,c)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
least_upper_bound(least_upper_bound(identity,b),greatest_lower_bound(a,b)) = least_upper_bound(greatest_lower_bound(a,b),least_upper_bound(identity,b)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c35,plain,
least_upper_bound(greatest_lower_bound(a,b),least_upper_bound(identity,b)) = least_upper_bound(least_upper_bound(identity,b),greatest_lower_bound(a,b)),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
least_upper_bound(least_upper_bound(identity,b),greatest_lower_bound(a,b)) = least_upper_bound(least_upper_bound(identity,b),identity),
inference(congruence,[status(thm)],[c2]) ).
cnf(c37,plain,
least_upper_bound(least_upper_bound(identity,b),identity) = least_upper_bound(b,identity),
inference(congruence,[status(thm)],[c26]) ).
cnf(c38,plain,
least_upper_bound(identity,b) = least_upper_bound(b,identity),
inference(substitution,[status(thm)],[c19]) ).
cnf(c39,plain,
least_upper_bound(b,identity) = least_upper_bound(identity,b),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
least_upper_bound(least_upper_bound(identity,b),identity) = least_upper_bound(identity,b),
inference(transitivity,[status(thm)],[c37,c39]) ).
cnf(c41,plain,
least_upper_bound(least_upper_bound(identity,b),greatest_lower_bound(a,b)) = least_upper_bound(identity,b),
inference(transitivity,[status(thm)],[c36,c40]) ).
cnf(c42,plain,
least_upper_bound(greatest_lower_bound(a,b),least_upper_bound(identity,b)) = least_upper_bound(identity,b),
inference(transitivity,[status(thm)],[c35,c41]) ).
cnf(c43,plain,
multiply(least_upper_bound(greatest_lower_bound(a,b),least_upper_bound(identity,b)),least_upper_bound(identity,c)) = multiply(least_upper_bound(identity,b),least_upper_bound(identity,c)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(least_upper_bound(greatest_lower_bound(a,b),least_upper_bound(identity,b)),least_upper_bound(identity,c)) = multiply(b,c),
inference(transitivity,[status(thm)],[c43,c28]) ).
cnf(c45,plain,
least_upper_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),least_upper_bound(identity,c))) = multiply(b,c),
inference(transitivity,[status(thm)],[c33,c44]) ).
cnf(c46,plain,
least_upper_bound(multiply(b,c),least_upper_bound(identity,c)) = multiply(b,c),
inference(transitivity,[status(thm)],[c18,c45]) ).
cnf(c47,plain,
multiply(b,c) = least_upper_bound(multiply(b,c),least_upper_bound(identity,c)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
greatest_lower_bound(least_upper_bound(identity,c),multiply(b,c)) = greatest_lower_bound(least_upper_bound(identity,c),least_upper_bound(multiply(b,c),least_upper_bound(identity,c))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c19]) ).
cnf(c50,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c53,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c51,c53]) ).
cnf(c55,plain,
greatest_lower_bound(least_upper_bound(identity,c),least_upper_bound(multiply(b,c),least_upper_bound(identity,c))) = least_upper_bound(identity,c),
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
greatest_lower_bound(least_upper_bound(identity,c),multiply(b,c)) = least_upper_bound(identity,c),
inference(transitivity,[status(thm)],[c48,c55]) ).
cnf(c57,plain,
greatest_lower_bound(multiply(b,c),least_upper_bound(identity,c)) = least_upper_bound(identity,c),
inference(transitivity,[status(thm)],[c15,c56]) ).
cnf(c58,plain,
least_upper_bound(identity,c) = greatest_lower_bound(multiply(b,c),least_upper_bound(identity,c)),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
greatest_lower_bound(least_upper_bound(identity,a),least_upper_bound(identity,c)) = greatest_lower_bound(least_upper_bound(identity,a),greatest_lower_bound(multiply(b,c),least_upper_bound(identity,c))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
greatest_lower_bound(least_upper_bound(identity,c),X2) = greatest_lower_bound(X2,least_upper_bound(identity,c)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c61,plain,
greatest_lower_bound(X2,least_upper_bound(identity,c)) = greatest_lower_bound(least_upper_bound(identity,c),X2),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
greatest_lower_bound(least_upper_bound(identity,a),greatest_lower_bound(X2,least_upper_bound(identity,c))) = greatest_lower_bound(least_upper_bound(identity,a),greatest_lower_bound(least_upper_bound(identity,c),X2)),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,axiom,
greatest_lower_bound(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(greatest_lower_bound(X2,Y2),Z2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).
cnf(c64,plain,
greatest_lower_bound(least_upper_bound(identity,a),greatest_lower_bound(least_upper_bound(identity,c),X2)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(identity,a),least_upper_bound(identity,c)),X2),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(identity,a),least_upper_bound(identity,c)),X2) = greatest_lower_bound(greatest_lower_bound(a,c),X2),
inference(congruence,[status(thm)],[c11]) ).
cnf(c66,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,c),
inference(substitution,[status(thm)],[c5]) ).
cnf(c67,plain,
greatest_lower_bound(a,c) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
greatest_lower_bound(greatest_lower_bound(a,c),X2) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),X2),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),X2) = greatest_lower_bound(X2,multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c70,plain,
greatest_lower_bound(greatest_lower_bound(a,c),X2) = greatest_lower_bound(X2,multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(transitivity,[status(thm)],[c68,c69]) ).
cnf(c71,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(identity,a),least_upper_bound(identity,c)),X2) = greatest_lower_bound(X2,multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(transitivity,[status(thm)],[c65,c70]) ).
cnf(c72,plain,
greatest_lower_bound(least_upper_bound(identity,a),greatest_lower_bound(least_upper_bound(identity,c),X2)) = greatest_lower_bound(X2,multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(transitivity,[status(thm)],[c64,c71]) ).
cnf(c73,plain,
greatest_lower_bound(least_upper_bound(identity,a),greatest_lower_bound(X2,least_upper_bound(identity,c))) = greatest_lower_bound(X2,multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(transitivity,[status(thm)],[c62,c72]) ).
cnf(c74,plain,
greatest_lower_bound(least_upper_bound(identity,a),greatest_lower_bound(multiply(b,c),least_upper_bound(identity,c))) = greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
greatest_lower_bound(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)],[c13]) ).
cnf(c76,plain,
greatest_lower_bound(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)],[c13]) ).
cnf(c77,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),multiply(b,c)) = greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
least_upper_bound(least_upper_bound(identity,a),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),least_upper_bound(identity,a)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c79,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),least_upper_bound(identity,a)) = least_upper_bound(least_upper_bound(identity,a),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,c),
inference(substitution,[status(thm)],[c5]) ).
cnf(c81,plain,
least_upper_bound(least_upper_bound(identity,a),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = least_upper_bound(least_upper_bound(identity,a),greatest_lower_bound(a,c)),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(least_upper_bound(identity,a),least_upper_bound(identity,c)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c83,plain,
least_upper_bound(least_upper_bound(identity,a),greatest_lower_bound(a,c)) = least_upper_bound(least_upper_bound(identity,a),greatest_lower_bound(least_upper_bound(identity,a),least_upper_bound(identity,c))),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c85,plain,
least_upper_bound(least_upper_bound(identity,a),greatest_lower_bound(least_upper_bound(identity,a),least_upper_bound(identity,c))) = least_upper_bound(identity,a),
inference(substitution,[status(thm)],[c84]) ).
cnf(c86,plain,
least_upper_bound(least_upper_bound(identity,a),greatest_lower_bound(a,c)) = least_upper_bound(identity,a),
inference(transitivity,[status(thm)],[c83,c85]) ).
cnf(c87,plain,
least_upper_bound(least_upper_bound(identity,a),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = least_upper_bound(identity,a),
inference(transitivity,[status(thm)],[c81,c86]) ).
cnf(c88,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),least_upper_bound(identity,a)) = least_upper_bound(identity,a),
inference(transitivity,[status(thm)],[c79,c87]) ).
cnf(c89,plain,
least_upper_bound(identity,a) = least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),least_upper_bound(identity,a)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),least_upper_bound(identity,a)) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),least_upper_bound(identity,a))),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),least_upper_bound(identity,a))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c92,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),least_upper_bound(identity,a)) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(transitivity,[status(thm)],[c90,c91]) ).
cnf(c93,plain,
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)),least_upper_bound(identity,a)),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),least_upper_bound(identity,a))),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
greatest_lower_bound(least_upper_bound(identity,a),X2) = greatest_lower_bound(X2,least_upper_bound(identity,a)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c96,plain,
greatest_lower_bound(X2,least_upper_bound(identity,a)) = greatest_lower_bound(least_upper_bound(identity,a),X2),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,least_upper_bound(identity,a))) = greatest_lower_bound(X3,greatest_lower_bound(least_upper_bound(identity,a),X2)),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
greatest_lower_bound(X3,greatest_lower_bound(least_upper_bound(identity,a),X2)) = greatest_lower_bound(greatest_lower_bound(X3,least_upper_bound(identity,a)),X2),
inference(substitution,[status(thm)],[c63]) ).
cnf(c99,plain,
greatest_lower_bound(least_upper_bound(identity,a),X2) = greatest_lower_bound(X2,least_upper_bound(identity,a)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c100,plain,
greatest_lower_bound(X2,least_upper_bound(identity,a)) = greatest_lower_bound(least_upper_bound(identity,a),X2),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
greatest_lower_bound(least_upper_bound(identity,a),X2) = greatest_lower_bound(a,X2),
inference(congruence,[status(thm)],[c9]) ).
cnf(c102,plain,
greatest_lower_bound(X2,least_upper_bound(identity,a)) = greatest_lower_bound(a,X2),
inference(transitivity,[status(thm)],[c100,c101]) ).
cnf(c103,plain,
greatest_lower_bound(greatest_lower_bound(X3,least_upper_bound(identity,a)),X2) = greatest_lower_bound(greatest_lower_bound(a,X3),X2),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
greatest_lower_bound(greatest_lower_bound(a,X3),X2) = greatest_lower_bound(X2,greatest_lower_bound(a,X3)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c105,plain,
greatest_lower_bound(greatest_lower_bound(X3,least_upper_bound(identity,a)),X2) = greatest_lower_bound(X2,greatest_lower_bound(a,X3)),
inference(transitivity,[status(thm)],[c103,c104]) ).
cnf(c106,plain,
greatest_lower_bound(X3,greatest_lower_bound(least_upper_bound(identity,a),X2)) = greatest_lower_bound(X2,greatest_lower_bound(a,X3)),
inference(transitivity,[status(thm)],[c98,c105]) ).
cnf(c107,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,least_upper_bound(identity,a))) = greatest_lower_bound(X2,greatest_lower_bound(a,X3)),
inference(transitivity,[status(thm)],[c97,c106]) ).
cnf(c108,plain,
greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),least_upper_bound(identity,a))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))),
inference(substitution,[status(thm)],[c107]) ).
cnf(c109,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)),greatest_lower_bound(a,multiply(b,c))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c110,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),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)],[c109]) ).
cnf(c111,axiom,
least_upper_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)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c112,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,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(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))) = least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c115,plain,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_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)),least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c)))),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)),
inference(substitution,[status(thm)],[c54]) ).
cnf(c118,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),least_upper_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)),
inference(transitivity,[status(thm)],[c116,c117]) ).
cnf(c119,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,multiply(b,c)),
inference(transitivity,[status(thm)],[c113,c118]) ).
cnf(c120,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(transitivity,[status(thm)],[c110,c119]) ).
cnf(c121,plain,
greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),least_upper_bound(identity,a))) = greatest_lower_bound(a,multiply(b,c)),
inference(transitivity,[status(thm)],[c108,c120]) ).
cnf(c122,plain,
greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(transitivity,[status(thm)],[c94,c121]) ).
cnf(c123,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),multiply(b,c)) = greatest_lower_bound(a,multiply(b,c)),
inference(transitivity,[status(thm)],[c77,c122]) ).
cnf(c124,plain,
greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(transitivity,[status(thm)],[c75,c123]) ).
cnf(c125,plain,
greatest_lower_bound(least_upper_bound(identity,a),greatest_lower_bound(multiply(b,c),least_upper_bound(identity,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(transitivity,[status(thm)],[c74,c124]) ).
cnf(c126,plain,
greatest_lower_bound(least_upper_bound(identity,a),least_upper_bound(identity,c)) = greatest_lower_bound(a,multiply(b,c)),
inference(transitivity,[status(thm)],[c59,c125]) ).
cnf(c127,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(a,multiply(b,c)),
inference(transitivity,[status(thm)],[c12,c126]) ).
cnf(c128,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,multiply(b,c)),
inference(transitivity,[status(thm)],[c6,c127]) ).
cnf(c129,plain,
greatest_lower_bound(a,multiply(b,c)) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,c),
inference(substitution,[status(thm)],[c5]) ).
cnf(c131,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[c129,c130]) ).
cnf(c132,plain,
$false,
inference(resolution,[status(thm)],[c1,c131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP193-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n002.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sun Sep 27 09:39:52 UTC 2026
% 0.01/0.36 % CPUTime :
% 0.01/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.01/0.47 Command-line arguments: --flatten --complete-subsets
% 0.01/0.47
% 0.01/0.47 % SZS status Unsatisfiable
% 0.01/0.47
% 0.01/0.48 % SZS output start CNFRefutation
% See solution above
% 0.49/0.51
% 0.49/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------