%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP178-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n014.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 1.06s 1.22s
% Output : CNFRefutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 8 RR)
% Number of literals : 31 ( 30 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 : 46 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('theBenchmark.p',prove_p09b) ).
cnf(c3,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c6,axiom,
greatest_lower_bound(identity,c) = identity,
file('theBenchmark.p',p09b_3) ).
cnf(c7,axiom,
greatest_lower_bound(a,b) = identity,
file('theBenchmark.p',p09b_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(c10,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
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(c13,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(c14,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c16,plain,
least_upper_bound(X,greatest_lower_bound(Y,X)) = X,
inference(equational,[status(thm)],[c9,c13]) ).
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(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(c28,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c12,c17,c18]) ).
cnf(c30,plain,
least_upper_bound(c,greatest_lower_bound(b,a)) = c,
inference(equational,[status(thm)],[c6,c8,c9,c16]) ).
cnf(c32,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c28]) ).
cnf(c35,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c28,c32]) ).
cnf(c36,plain,
multiply(X,greatest_lower_bound(b,a)) = X,
inference(equational,[status(thm)],[c12,c35]) ).
cnf(c38,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c39,plain,
least_upper_bound(X,multiply(X,c)) = multiply(X,c),
inference(equational,[status(thm)],[c10,c30,c36,c38]) ).
cnf(c41,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c47,plain,
greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X,Y),Z)) = greatest_lower_bound(X,Z),
inference(equational,[status(thm)],[c14,c22]) ).
cnf(c54,plain,
greatest_lower_bound(multiply(b,X),multiply(a,X)) = X,
inference(equational,[status(thm)],[c17,c41]) ).
cnf(c63,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(X,Z))) = greatest_lower_bound(X,Y),
inference(equational,[status(thm)],[c9,c47]) ).
cnf(c148,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,multiply(X,c))) = greatest_lower_bound(X,Y),
inference(equational,[status(thm)],[c39,c63]) ).
cnf(c149,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(c,a),
inference(equational,[status(thm)],[c9,c54,c148]) ).
cnf(g1,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c),
inference(equational,[status(thm)],[c9,c149]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP178-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n014.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 08:14:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.06/1.22 % SZS status Unsatisfiable
% 1.06/1.22 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------