%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP178-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 06:43:40 AM UTC 2025
% Result : Unsatisfiable 5.69s 5.91s
% Output : CNFRefutation 5.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 7 RR)
% Number of literals : 36 ( 35 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('theBenchmark.p',prove_p09a) ).
cnf(c1,axiom,
least_upper_bound(X,X) = X,
file('GRP004-2.ax',idempotence_of_lub) ).
cnf(c3,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c6,axiom,
least_upper_bound(identity,c) = c,
file('theBenchmark.p',p09a_3) ).
cnf(c7,axiom,
greatest_lower_bound(a,b) = identity,
file('theBenchmark.p',p09a_4) ).
cnf(c8,plain,
identity = greatest_lower_bound(a,b),
inference(equational,[status(thm)],[c7]) ).
cnf(c9,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(c11,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c12,plain,
multiply(inverse(X),X) = greatest_lower_bound(b,a),
inference(equational,[status(thm)],[c8,c9,c11]) ).
cnf(c14,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c17,plain,
multiply(greatest_lower_bound(b,a),X) = X,
inference(equational,[status(thm)],[c3,c8,c9]) ).
cnf(c18,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c19,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z),
file('GRP004-2.ax',associativity_of_lub) ).
cnf(c20,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c19]) ).
cnf(c21,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z),
file('GRP004-2.ax',associativity_of_glb) ).
cnf(c22,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c21]) ).
cnf(c26,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(Y,greatest_lower_bound(X,Z)),
inference(equational,[status(thm)],[c9,c22]) ).
cnf(c29,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c12,c17,c18]) ).
cnf(c32,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c29]) ).
cnf(c33,plain,
multiply(X,inverse(X)) = greatest_lower_bound(b,a),
inference(equational,[status(thm)],[c12,c32]) ).
cnf(c35,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c29,c32]) ).
cnf(c36,plain,
multiply(X,greatest_lower_bound(b,a)) = X,
inference(equational,[status(thm)],[c12,c35]) ).
cnf(c37,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c32,c36]) ).
cnf(c38,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c39,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c43,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c50,plain,
greatest_lower_bound(multiply(X,b),multiply(X,a)) = X,
inference(equational,[status(thm)],[c33,c35,c37,c38]) ).
cnf(c53,plain,
greatest_lower_bound(multiply(b,X),multiply(a,X)) = X,
inference(equational,[status(thm)],[c17,c39]) ).
cnf(c59,plain,
least_upper_bound(greatest_lower_bound(b,a),least_upper_bound(c,X)) = least_upper_bound(c,X),
inference(equational,[status(thm)],[c6,c8,c9,c20]) ).
cnf(c508,plain,
greatest_lower_bound(multiply(b,X),greatest_lower_bound(Y,multiply(a,X))) = greatest_lower_bound(Y,X),
inference(equational,[status(thm)],[c26,c53]) ).
cnf(c588,plain,
least_upper_bound(X,least_upper_bound(multiply(X,c),multiply(X,Y))) = least_upper_bound(multiply(X,c),multiply(X,Y)),
inference(equational,[status(thm)],[c38,c43,c50,c59]) ).
cnf(c589,plain,
least_upper_bound(X,multiply(X,c)) = multiply(X,c),
inference(equational,[status(thm)],[c1,c588]) ).
cnf(c590,plain,
greatest_lower_bound(X,multiply(X,c)) = X,
inference(equational,[status(thm)],[c14,c589]) ).
cnf(c591,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c),
inference(equational,[status(thm)],[c9,c508,c590]) ).
cnf(g1,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c),
inference(equational,[status(thm)],[c591]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP178-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.00/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 08:14:04 EDT 2025
% 0.11/0.34 % CPUTime :
% 5.69/5.91 % SZS status Unsatisfiable
% 5.69/5.91 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------